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Mixed Mode Fracture Toughness of Stitched Laminated Composites

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MIXED MODE FRACTURE TOUGHNESS OF STITCHED LAMINATED COMPOSITES By TOMEK RYS A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2004

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Copyright 2004 By Tomek Rys

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ACKNOWLEDGMENTS First and foremost I would like to thank my advisor and sponsor, Dr. Bhavani V. Sankar. Without his direct guidance and support the work presented in this thesis would not have been possible. Additionally, I would like to thank my colleagues at the Center for Advanced Composites located on the University of Florida campus. Their support and assistance were invaluable throughout my research. iii

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TABLE OF CONTENTS page ACKNOWLEDGMENTS .................................................................................................iii LIST OF TABLES .............................................................................................................vi LIST OF FIGURES ..........................................................................................................vii ABSTRACT .......................................................................................................................ix CHAPTER 1 INTRODUCTION........................................................................................................1 Background Information...............................................................................................1 Literature Survey..........................................................................................................4 Scope of the Thesis.......................................................................................................5 2 BACKGROUND..........................................................................................................7 Theory...........................................................................................................................7 Testing of Stitched Composites....................................................................................9 3 EXPERIMENTAL SETUP........................................................................................11 Testing Fixture............................................................................................................11 Specimen Preparation.................................................................................................14 Experimental Method.................................................................................................16 4 FRACTURE TESTS...................................................................................................20 Introduction.................................................................................................................20 Testing and Discussion...............................................................................................20 5 FINITE ELEMENT ANALYSIS...............................................................................30 Introduction.................................................................................................................30 Procedure of Modeling...............................................................................................31 Modeling Results........................................................................................................33 Crack Propagation Model...........................................................................................35 iv

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6 CONCLUSIONS........................................................................................................38 Summary.....................................................................................................................38 Conclusions.................................................................................................................38 LIST OF REFERENCES...................................................................................................40 BIOGRAPHICAL SKETCH.............................................................................................42 v

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LIST OF TABLES Table page 3-1 Material properties for AS4/3501-6 graphite/epoxy................................................15 3-2 Variation in thickness of each layer in the stacking sequence.................................15 4-1 Average apparent fracture toughness of low-density stitched specimens................21 4-2 Average apparent fracture toughness of high-density stitched specimens...............21 5-1 FE parent and effective fracture toughness..............................................................33 5-2 Stress intensity factors at crack tip...........................................................................35 5-3 Global versus local mode-mixity ratios...................................................................35 5-4 Data needed to simulate crack propagation..............................................................36 vi

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LIST OF FIGURES Figure page 1-1 Stitching and Z-pinning of a laminate........................................................................3 1-2 Stitching Types: (a) Lock stitch, (b) Modified Lock stitch, (c) Chain stitch............4 2-1 DCB specimen geometry...........................................................................................8 2-2 Modes of Fracture. From left to right: Mode I, Mode II, Mode III..........................9 2-3 Stitched specimen showing failure due to bending moment....................................10 3-1 Mixed Mode testing fixture......................................................................................11 3-2 Free body diagram (FBD) of specimen showing horizontal and vertical force components...............................................................................................................12 3-3 Grip and specimen ends showing machined arcs used for attachment....................13 3-4 Mixed Mode fixture showing counterbalance weight for balancing of mechanism prior to testing..........................................................................................................14 3-5 Specimens showing stitch densities and pre-crack lengths......................................16 3-6 Load versus crosshead displacement plot for a stitched specimen..........................17 3-7 Stitched DCB specimen undergoing testing.............................................................18 3-8 Schematic of forces for strength of material calculations........................................19 4-1 Fracture toughness versus mode-mixity over entire Mode I to Mode II range........22 4-2 Mode I loading: low density specimens, load vs. crosshead displacement..............23 4-3 Mixed Mode 1 loading: low density specimens, load vs. crosshead displacement.24 4-4 Mixed Mode 2 loading: low density specimens, load vs. crosshead displacement.25 4-5 Mixed Mode 3 loading: low density specimens, load vs. crosshead displacement.26 4-6 Mode I loading: high density specimens, load vs. crosshead displacement............27 vii

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4-7 Mixed Mode 1 loading: high density specimens, load vs. crosshead displacement28 4-8 Mixed Mode 2 loading: high density specimens, load vs. crosshead displacement28 4-9 Mixed Mode 3 loading: high density specimens, load vs. crosshead displacement29 5-1 2D FE model of fixture and laminate.......................................................................32 5-2 FE model showing crack tip and stitches including the stitch bridging distance.....32 5-3 Strain energy release rate versus J-Integral contour number...................................34 5-4 Crack propagation model showing first stitch failure..............................................37 viii

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Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science MIXED MODE FRACTURE TOUGHNESS OF LAMINATED STITCHED COMPOSITES By Tomek Rys August 2004 Chair: Bhavani V. Sankar Cochair: Peter G. Ifju Major Department: Mechanical and Aerospace Engineering The research presented in this thesis is an effort to better understand the failure phenomenon in laminated composites that are reinforced through their thickness with stitches. Through-the-thickness stitching is a method that increases translaminar strength while at the same time preventing crack propagation. A novel test fixture was developed to measure mixed mode fracture toughness under combined Mode I and Mode II loadings. In addition, a finite element (FEM) model has been created which allows for the prediction of the apparent fracture toughness of various stitched laminates under mixed mode loadings. In the FEM model, the material properties of the laminate, including the stitch material, stitching density, and stitch diameter, can be varied in order to quickly evaluate the sensitivity of fracture toughness with respect to these parameters. ix

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CHAPTER 1 INTRODUCTION Background Information Composite materials have many advantages over conventional materials in aerospace and other applications where the strength to weight ratio is a critical factor. Graphite/epoxy laminated composites have high stiffness-to-weight and strength-to-weight ratios that make them suitable for structural applications. Additionally, composite materials can be tailored to obtain specific properties in various directions and the overall thickness and lay-up of the composite can be optimized for given loading conditions. Composites offer many other advantages over conventional materials including but not limited to: high corrosion resistance, high energy absorption, low thermal expansion, good thermal insulation and electrical resistivity. Despite all these advantages, graphite/epoxy composite production volumes have not increased drastically in recent years. This stems from two major deficiencies of composite materials. The first being the high material cost and slow manufacturing time of graphite/epoxy composites compared to conventional structural materials. The second major deficiency is the poor inter-laminar strength, fracture toughness and low impact resistance and damage tolerance that composites typically possess. The properties of these composite laminates depend highly on the fiber orientation and the fiber volume ratio. The strength in the translaminar (through-thickness) direction tends to be significantly smaller than in the fiber direction. For example, the tensile strength of graphite/epoxy laminates is approximately 72 to 116 ksi (500 to 800 MPa) in 1

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2 the fiber direction while in the translaminar direction the strength is around 2.9 to 4.3 ksi (20 to 30 MPa). This is due to the fact that the load is being predominately carried by the resin matrix, making the composite susceptible to delamination. This delamination is typically an interface crack or a debonded zone between two adjacent layers. This delamination can be initiated by imperfect manufacture or during the impact of a foreign body during service. Typically this delamination is located within the composite and cannot be detected through visual inspection. This initial delamination (crack) can grow rapidly under subsequent application of external load. This can lead to either catastrophic failure of the structure and/or a significant decrease in the load carrying capability. The poor translaminar strength of graphite/epoxy laminates has limited the number of aerospace applications. Many methods have been developed to improve the translaminar strength and decrease the occurrence of delamination. These methods include the introduction of translaminar reinforcements (TLR) into the composite. TLR can either be of the continuous or discontinuous form. Continuous weaving, knitting, braiding, threads, yarns and tows can be inserted into the laminated using industrial sewing/stitching technology. Discontinuous reinforcements such as short fibers, whiskers and pins can also be inserted into a composite to increase the translaminar strength. Refer to Figure 1-1. 3D weaving, braiding and knitting improve the translaminar strength due to the increased number of fibers in the out of plane direction. The major downfall of these TLR are the large resin pockets that are introduced during manufacture and the reduced number of fibers in the in plane direction. This can lead to reduced in-plane properties. The stitching process differentiates itself by having the stitch as a non-integral part of the

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3 laminate. The stitch is inserted into a 2D preform as a secondary process after lay-up but before the introduction of the resin and subsequent curing. By using stitches as a TLR, the onset of large resin pockets is reduced, especially when compared to 3D weaving. Stitching is one of the most common techniques used to suppress delamination. Figure 1-1: Stitching and Z-pinning of a laminate Composites can be stitched either as prepregs (resin impregnated fabrics) or preforms (resin free fabrics). Unfortunately considerable fiber damage occurs when stitching prepreg laminates. This reduces the in plane fiber properties of the composite. Alternatively, stitching of the preform can be done without causing as much fiber damage due to the ability to pull a needle through the resin free fabric. One of the most critical factors in stitching a laminated composite is the type of stitch used. One of the most common types of stitches is known as the lock stitch. It consists of a two thread loop between the needle and the bobbin threads. The lock stitch requires access to both top and bottom of the laminate. This stitch is used in the apparel industry due to its aesthetic appeal. The intersection of the bobbin and needle threads is concealed in the fabric. This is not favorable for stitching composites because the thread intersection in the middle of the laminate would cause a stress concentration. Therefore,

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4 when stitching composites a modified lock stitch is typically used that allows the needle thread to travel along the surface of the composite rather then in the middle of it. Additionally, a chain stitch can be used that has a similar mechanism to that of the lock stitch. Figure 1-2 shows all three stitch types discussed above. Figure 1-2: Stitching Types: (a) Lock stitch, (b) Modified Lock stitch, (c) Chain stitch Literature Survey Mignery et al. [1] investigated the use of stitching using Kevlar yarn to suppress delamination in graphite/epoxy laminates. Results showed that stitching was an effective suppressant of delamination. In addition, Dexter and Funk [2] investigated the Mode I

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5 fracture toughness of laminates reinforced with Kevlar stitches. Results showed that the fracture toughness increased 30 fold when compared to the unstitched laminate. Currently, the double cantilever beam (DCB) test is used to determine the Mode I fracture toughness of unstitched composite laminates. In practical applications it is rare to encounter pure Mode I or Mode II loadings. Typical loads are comprised of a combination of both Mode I and Mode II loads referred to as a mixed mode loading condition. Richards and Korjakin [3] used the traditional mixed mode setup to test the fracture toughness of unstitched laminated composites. In their experiments the ratio of Mode I to Mode II was fixed at 1.33 according to linear beam analysis. Reeder and Crews [4-5] developed a new mixed mode experimental setup that simultaneously created a Mode I and Mode II bending load on the specimen from a single applied load. This setup allowed for numerous mixed mode ratios to be tested. Although many researchers have used different approaches to investigate the delamination fracture toughness of composites including mixed mode fracture properties of composites, none have successfully tested the mixed mode fracture toughness of composites with dense translaminar reinforcement. The standard DCB test is not suitable for testing stitched laminates. Typically during the standard DCB test the specimen fails due to high compressive stresses caused by the large bending moment at the crack tip. Due to these problems with the standard DCB test a novel test fixture has been developed by Chen et al. [6] for stitched composites. Scope of the Thesis Due to the lack of transverse strength, composite materials are vulnerable to delamination which is either an interface crack or a debond between two adjacent layers. This delamination is typically not detectable by visual inspection of a composites outer

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6 surfaces. This delamination can be initiated during imperfect manufacture or simply caused by impact of a foreign body during service. Methods to improve this translaminar strength include stitching. The stitching process improves the apparent fracture toughness of the laminated composite. The aim of the current study is to accurately measure the increase in the fracture toughness incurred by the addition of stitches, and to investigate the effect of various ratios of fracture modes on the composites fracture toughness.

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CHAPTER 2 BACKGROUND Theory There are two main approaches to analyzing the fracture toughness of a given material: the energy approach and the stress intensity factor approach. Both are commonly used. The energy approach was used during this research due to its ease of adaptability to experimental work. The energy approach states that a crack will only propagate when the energy provided for crack growth is sufficient to overcome the resistance of the material [7]. The material resistance includes but is not limited to the surface energy, plastic work, or any other type of energy dissipation associated with crack propagation [7]. The energy release rate (G) is defined as the rate of change in potential energy with crack area. At the onset of crack propagation, the energy release rate is defined as the critical energy release rate, which provides a measure of fracture toughness [7]. For a double cantilever beam (DCB) specimen (Figure 2-1), the Mode I fracture toughness can be found as 22CICFaGbEI (2-1) where F C is the load at which the crack propagation occurs, a is the current crack length, b is the width of the specimen and EI is the equivalent flexural rigidity of the specimen. 7

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8 Figure 2-1: DCB specimen geometry The fracture toughness of stitched laminated composites can be broken into two subcategories. G parent is the fracture toughness of the parent material and is constant throughout a structure for a given loading mode. Modes of loading are discussed below. The parent material can be defined as the material which contains the stitches. Alternatively, G eff is the fracture toughness related to the parent material but also dependent on the properties of the stitches. In basic fracture mechanics there are three loading modes: Mode I, Mode II and Mode III. Figure 2-2 shows examples of how each mode is loaded. Mode I is dominated by an opening load, Mode II is dominated by an in plane shearing load, and Mode III is dominated by an out of plane shear.

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9 Figure 2-2: Modes of Fracture. From left to right: Mode I, Mode II, Mode III Typically in real world applications a crack propagates under a combination of these loading conditions. Mixed-mode loading in this research is defined as some combination of Mode I and Mode II loading conditions. Mixed-mode conditions are quantified by a mode-mixity phase angle ( ) (Equation 2-2), which is 0 for pure mode I and 90 for pure mode II. Understanding the mode-mixity of a loading condition is important because of its effects on crack propagation. 1tanIIIGG (2-2) A crack in pure mode II loading commonly requires several times as much energy to initiate crack propagation as compared to a crack propagated under pure mode I loading [7]. Therefore, it becomes necessary to identify the mode-mixity of an experimental setup in order to thoroughly understand results. Testing of Stitched Composites Currently the DCB test as described above is used to measure the Mode I fracture toughness of laminated composites. This method works well for specimens that do not contain translaminar reinforcements. The standard DCB test is not suitable for laminated composites that contain stitches as through the thickness reinforcements. The main reason for this is that the strength of the stitches is very high and a large amount of force

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10 is required to either break them or cause pullout. As the load is increased in the standard DCB test the specimen arms are subjected to large bending moments Figure 2-3. This moment causes the specimen arms to fail due to buckling on the compression side of the arm before crack propagation can be initiated Figure 2-3: Stitched specimen showing failure due to bending moment Much research has been conducted in investigating new fixtures for testing the fracture toughness of stitched composites. The main focus has been on reducing the aforementioned compressive failure. To effectively eliminate this failure the maximum compressive stress must be reduced. A novel testing fixture has been developed at the University of Florida that incorporates an additional tensile force to neutralize the maximum compressive stress. This fixture is further discussed in Chapter 3.

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CHAPTER 3 EXPERIMENTAL SETUP Testing Fixture The standard DCB is not suitable for testing stitched composites due to high compressive stresses that cause the specimen to fail before the crack propagation can be initiated. A novel test fixture has been developed to allow for the testing of the fracture toughness of stitched composites. The novel fixture incorporates a horizontal bar that has a series of holes corresponding to numerous mixed mode ratios (Figure 3-1). Figure 3-1: Mixed Mode testing fixture 11

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12 Figure 3-2: Free body diagram (FBD) of specimen showing horizontal and vertical force components At the right end of the bar, a bearing reacts to create a horizontal force which helps balance the fixture as well as reduce compressive bending stresses that might otherwise lead to premature failure of the specimen (before stitch failure). This fixture applies tension to both arms of the DCB specimen, which also reduces the compressive bending stresses. This tensile force effectively neutralizes the compressive bending stresses in the specimen arms. By changing the loading position, various mixed mode ratios are obtained. Mode I is achieved by loading the fixture at a hole directly inline with the specimen. By offsetting the load from the longitudinal axis of the specimen, various mixed mode ratios are achieved as the ratio of forces in each loading bar is changed. In addition, the fixture can be self balanced by adding weights to the left side of the

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13 horizontal bar to account for errors caused by the unbalanced weight of the fixture (Fig. 3-4). This fixture relies on specimen grips that can transmit both axial and transverse forces (Fig. 3-3). Figure 3-3: Grip and specimen ends showing machined arcs used for attachment The transverse component of the force is for crack opening and the axial component is used to provide the tensile stresses as mentioned earlier. The conventional method of bonding tabs to the specimen does not work as the large tensile and shear stresses caused by the load required to propagate the crack simply debond the tabs. A notch in the form of a circular arc was machined in the specimen ends (Fig. 3-3). A pair of grips that match the notch profile in the specimen were machined out of steel.

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14 Figure 3-4: Mixed Mode fixture showing counterbalance weight for balancing of mechanism prior to testing Specimen Preparation The stitched specimens were made of 28 plies of AS4 uniweave graphite fabric and 3501-6 epoxy resin using the RTM process by NASA Langley Research Center. The specimens were stitched with 1600 denier Kevlar 29 where there are two Kevlar yarns in each stitch. In addition, each specimen consisted of three rows of stitches. The specimens were approximately 190.5 mm (7.5 inches) long and 19.05 mm (0.75 inches) wide. Two different stitch densities were used to evaluate the effects of stitch density on fracture toughness. Linear stitch densities evaluated were 5 stitches per inch (referred to as low density) and 9 stitches per inch (high density). The spacing between adjacent

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15 rows of stitches was 5 mm (0.2 inch). Typically stitch density is defined as the number of stitches per square inch. This is represented by the stitching pattern, which is: (number of stitches per inch) (spacing between two adjacent stitch lines). Therefore the stitch densities evaluated were 5/5 and 91/5. Refer to Figure 3-5. Additionally, the top and bottom plies of the specimen were covered with 1 layer of plane weave fiberglass cloth to act as a retainer for the stitches. The specimens also included a Teflon insert either 65 mm (2.55 in.) or 90 mm (3.55 in.) in length that created the pre-crack needed for crack propagation (Figs.3-3 and 3-5). The pre-crack started at the machined end of the specimen and continued up to the first row of stitches. The specimen was made up of 4 stacks where each stack consisted of 7 plies, which were oriented at [45/-45/0/90/0/-45/45]. The materials used in each stack have slightly different properties (Tables 3-1 and 3-2). Table 3-1: Material properties for AS4/3501-6 graphite/epoxy MATERIAL E1 psi (GPa) E2 psi (GPa) 12 G12 psi (GPa) G13 psi (GPa) G23 psi (GPa) AS4-3501-00 15.3 e6 (105) 1.6 e6 (11) 0.34 0.8 e6 (6) 0.8 e6 (6) 0.52 e6 (3.6) AS4-3501-45 15.04 e6 (103) 1.6 e6 (11) 0.34 0.8 e6 (6) 0.8 e6 (6) 0.52 e6 (3.6) AS4-3501-90 14.88 e6 (102) 1.6 e6 (11) 0.34 0.8 e6 (6) 0.8 e6 (6) 0.52 e6 (3.6) Table 3-2: Variation in thickness of each layer in the stacking sequence PLY NUMBER THICKNESS in. (mm) ORIENTATION (DEGREE) MATERIAL NAME 1 0.00633 (0.16) 45 AS4-3501-45 2 0.00633 (0.16) 45 AS4-3501-45 3 0.01285 (0.32) 0 AS4-3501-00 4 0.007018 (0.18) 90 AS4-3501-90 5 0.01285 (0.32) 0 AS4-3501-00 6 0.00633 (0.16) 45 AS4-3501-45 7 0.00633 (0.16) 45 AS4-3501-45

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16 Figure 3-5: Specimens showing stitch densities and pre-crack lengths Experimental Method Many experimental techniques are available for determining the fracture toughness of laminates. The double cantilever beam (DCB) test was chosen to accurately determine the fracture toughness of the stitched composites due to its simplicity. The DCB test consists of a specimen prepared with an initial crack length at the interface of which the fracture toughness is of interest. Tests were conducted in a screw driven universal testing machine (MTI). The crack propagation was observed using a CCD camera. A computer monitored and recorded both force and crosshead displacement. The crack propagation length was measured using a micrometer. Once the data was taken, a plot of force versus crosshead displacement was created. The area under the load deflection plot represents the work done (W) in propagating the crack. Calculation of the fracture toughness was accomplished by dividing the work done to propagate the crack by the crack propagation length (a) multiplied by the specimen width (b).

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17 abGIC W (3-1) For pure Mode I loading, the fixture is setup with the universal testing machine attached directly in line with the specimen. The load increases until the first row of stitches break, at which time the load suddenly drops (Figs. 3-6, 3-7). Subsequent rows of stitches are loaded until failure. The cycle continues in this saw tooth pattern until the specimen is unloaded. When testing stitched specimens, unloading can never be complete as the broken stitches protrude out of the newly created delamination surface and prevent the specimen from closing fully. In this case we assume that the unloading would have been elastic, and hence connect the current point on the load-deflection plot to the origin. As seen in Figure 3-6 each peak and valley corresponds to a stitch breaking. By having a peak and valley for every row of stitches in the specimen shows that the crack propagation is stable. Figure 3-6: Load versus crosshead displacement plot for a stitched specimen

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18 Figure 3-7: Stitched DCB specimen undergoing testing The same procedure described for Mode I was used for mixed mode loading. To achieve various mixed mode ratios the MTI machine was attached to the horizontal bar offset from the specimen. The larger the offset the greater the mixed mode ratio becomes. The average fracture toughness values for both the low-density and high-density stitched composites are listed under Tables 4-1 and 4-2 in Chapter 4. The Mode Mixity parameter () defined as follows is used to describe the mixed mode ratio: 1tanIIIKK (3-2) where K I and K II are the Mode I and Mode II stress intensity factors, respectively. One can note that =0 for pure Mode I and = /2 for pure Mode II. For mixed mode conditions 0< < /2. The stress intensity factor approach to calculate mode-mixity is further explained in Chapter 5. In the present work we use a simple mechanics of materials approach to estimate the mode-mixity which is based on the ratio between the forces transmitted to the

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19 specimen in each bar of the fixture. We calculate both G I and G II (energy release rates) based on strength of material calculations (Fig. 3-8 and Eq. 3-3) and use the superposition of the symmetric and anti-symmetric loads to calculate The energy release rates are proportional to the square of the stress intensity factors. Therefore, the energy release rates are calculated and then converted to stress intensity factors values, which are then used in Equation 3-2 to calculate Figure 3-8: Schematic of forces for strength of material calculations 221211341IIIFGFFGF (3-3)

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CHAPTER 4 FRACTURE TESTS Introduction As explained previously the fracture toughness (G c ) of a material can be described or defined as the energy needed to initiate crack propagation. Fracture toughness is a material property and therefore should remain constant under a given loading condition. Typical G c values for a graphite/epoxy laminate are on the order of 300 J/m 2 (1.7 lbin/in 2 ) for Mode I delamination crack propagation. Previous research has shown that the addition of stitches increases the fracture toughness significantly especially under Mode I loading conditions. This is most likely due to the fact that stitches are primarily effective in tension rather than shear. Testing and Discussion As previously discussed the specimens were tested using an MTI machine configured with the test fixture described in the previous chapter. Both low stitch-density and high stitch-density specimens were tested. For the high-density specimens, the fixture was adjusted by moving the arms inward toward the loading attachment point. This increases the tension force in each arm, effectively reducing the compressive bending stresses, which cause specimen breakage. Average apparent fracture toughness for both low-density and high-density specimens can be found in Tables 4-1 and 4-2 respectively. 20

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21 Table 4-1: Average apparent fracture toughness of low-density stitched specimens MODE RATIO = tan -1 (K II /K I ) AVERAGE G lb-in/in 2 (J/m 2 ) 0 40.45 (7083) 8.2 36.27 (6351) 16.0 43.16 (7557) 29.9 46.60 (8160) Table 4-2: Average apparent fracture toughness of high-density stitched specimens MODE RATIO = tan -1 (K II /K I ) AVERAGE G lb-in/in 2 (J/m 2 ) 0 81.80 (14323) 12.1 96.80 (16950) 23.3 100.74 (17640) 29.9 As the mixed mode ratio increases from Mode I to Mode II the apparent fracture toughness value increases significantly over that of an unstitched specimen and remains fairly constant over the mixed mode range with a decrease most likely appearing near the pure Mode II loading condition. One may notice that no fracture toughness value can be found for high-density specimens above the mixed mode ratio of 23.3. This is due to the fact that at mixed mode ratios higher than this, the specimen would break either from compressive breakage in one of the arms or in shear at one of the end grips. Figure 4-1 shows a plot of the fracture toughness versus the mode-mixity angle for low-density stitched specimens. A linear trend line has been fitted to the experimental data to show the trend of the fracture toughness with respect to the mode-mixity angle. As the mode-mixity angle increases there is a slight increase in the fracture toughness value over a 30 mode-mixity range. The Mode II (90) fracture toughness value was found for a stitched specimen using an End-Notch-Flexure test by Chen et al. [6]. The

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22 dotted trend line is shown as an illustration that the fracture toughness will eventually decrease to the Mode II value. The exact shape of this trend line between 30 and 90 (dashed line in Fig. 4-1) at the present moment is unknown. Fracture Toughness vs. Mode Mixity01020304050600102030405060708090Mode Mixity (degree)Fracture Toughness (lb-in/in^2) Figure 4-1: Fracture toughness versus mode-mixity over entire Mode I to Mode II range The force versus crosshead displacement data collected from the MTI machine is shown in Figures 4-2 thru 4-9. Shown in Figure 4-2 is the load versus crosshead displacement for a Mode I loading done on three low density specimens. As one can observe, there is some non-linearity to both the loading and unloading of the specimen. Additionally, one of the specimens has a different loading slope curve. This is due to stitches starting further down on that specimen compared to the other two specimens (Refer to chapter 3).

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23 Specimens with a pre-crack length of both 65 mm (2.55 in.) and 90 mm (3.55 in.) were tested. Due to this fact the loading curves will have slightly different shapes. Mode I: Low Density05010015020025030035000.10.20.30.40.50.60.70.80.91Crosshead Displacement (in.)Force (lbs.) Figure 4-2: Mode I loading: low density specimens, load vs. crosshead displacement Figure 4-3 shows the load versus crosshead displacement curve for a mixed mode loading of 8.2 on two low density specimens. There is slightly more non-linearity under the mixed mode loading compared to that of the Mode I loading. Very good repeatability between the two specimens can be observed. Notice that each peak and valley corresponds to a row of stitches breaking, meaning the crack propagated in a stable manner. By the crack propagating in a stable manner the analysis of the fracture toughness can more easily be performed. Meaning that for each stitch breaking there is crack length that corresponds to the breakage.

PAGE 33

24 Mixed Mode I: Low Density05010015020025030035000.10.20.30.40.50.60.70.80.91Crosshead Displacement (in.)Force (lbs.) Figure 4-3: Mixed Mode 1 loading: low density specimens, load vs. crosshead displacement Figure 4-4 shows the load versus displacement curve for a mixed mode loading of 16.0 for low density specimens. The non-linearity of the initial load buildup grows even greater when compared to the previous two loading conditions. The average force for stitch breakage and crack propagation has increased from approximately 200 lb. (890 N) to 250 lb. (1100 N). Additionally, it can be observed that the force needed for stitch breakage has quite a large (up to 45% difference) variation between specimens. Figure 4-5 shows the load versus displacement curve for a mixed mode loading of 29.9 for low density specimens. These specimens have a very non-linear initial loading curve. Also, it is important to point out that on one of the specimens, crack propagation was unstable as there was a large peak load which broke a number of rows of stitches at once. This can easily be seen as one specimen does not have nearly as many peaks and

PAGE 34

25 valleys as the other. Notice the drastic increase in average stitch breaking force when compared to the previous three loading conditions. This shows that as the mixed mode ratio increases the force needed to break stitches and propagate the crack increases. This is very important because specimen breakage can occur if this force gets too large. Mixed Mode 2: Low Density05010015020025030035040000.10.20.30.40.50.60.70.80.91Crosshead Displacement (in.)Force (lbs.) Figure 4-4: Mixed Mode 2 loading: low density specimens, load vs. crosshead displacement Figure 4-6 shows the load versus displacement curve for a mode I loading on high density specimens. When compared to the low density specimens, it can be observed that the average force for crack propagation has increased significantly to an average force of approximately 550 lb. (2400 N). Because these specimens are stitched more densely, the number of peaks and valleys has increased.

PAGE 35

26 Mixed Mode 3: Low Density05010015020025030035040045050000.10.20.30.40.50.60.70.80.91Crosshead Displacement (in.)Force (lbs.) Figure 4-5: Mixed Mode 3 loading: low density specimens, load vs. crosshead displacement Figure 4-7 shows the load versus displacement curve for a mixed mode loading of 12.1 for a high density specimen. Notice the increase in non-linearity on the loading curve and the large increase in stitch propagation force. This non-linearity may be due to the complex mechanism used in the fixture. Average force is approximately 900 lb. (4000 N). Figure 4-8 shows the load versus displacement curve for a mixed mode loading of 23.3 for high-density specimens. Notice that one specimen is loaded and fails due to compressive bending in the arm. After the specimen broke, the fixture was adjusted by moving the loading arms inward to increase the tensile force in each arm to aid in reducing bending stresses. The next specimen does not fail, but the crack propagates unstably as there are three peaks and valleys which correspond to approximately 15 rows

PAGE 36

27 of stitches breaking. Also, the average crack propagation force has increased once again to approximately 2000 lb. (8900 N), which is an increase of almost 1100 lb. (5000 N) from the previous loading condition. Mode I: High Density0100200300400500600700800900100000.10.20.30.40.50.60.7Crosshead Displacement (in.)Force (lbs.) Figure 4-6: Mode I loading: high density specimens, load vs. crosshead displacement Figure 4-9 shows the load versus displacement curve for a mixed mode loading of 29.9 for a high density specimen. Notice that the specimen is unable to open and breaks due to shearing at the grip attachment point. Testing highly stitched specimens is an intricate process and refinement to the testing fixture or a new fixture must be developed in order to test specimens such as these.

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28 Mixed Mode 1: High Density020040060080010001200140000.10.20.30.40.50.60.7Crosshead Displacement (in.)Force (lbs.) Figure 4-7: Mixed Mode 1 loading: high density specimens, load vs. crosshead displacement Mixed Mode 2: High Density0500100015002000250000.10.20.30.40.50.6Crosshead Displacement (in.)Force (lbs.) Figure 4-8: Mixed Mode 2 loading: high density specimens, load vs. crosshead displacement

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29 Mixed Mode 3: High Density0500100015002000250000.10.20.30.40.50.6Crosshead Displacement (in.)Force (lbs.) Figure 4-9: Mixed Mode 3 loading: high density specimens, load vs. crosshead displacement

PAGE 39

CHAPTER 5 FINITE ELEMENT ANALYSIS Introduction To better investigate and understand the mechanics of the loading fixture and the stitched laminate, a finite element (FE) model was created. This model would allow for the investigation of the stitch interactions with the parent laminate and investigation of stitch failure mechanisms. Additionally, in the FE model the material properties of the laminate, including the stitch material, stitching density, and stitch diameter, could be varied in order to quickly evaluate the sensitivity of fracture toughness with respect to these parameters. By modeling the entire loading fixture instead of just the stitched laminate, the mode-mixity could be evaluated at the crack tip under a given loading arrangement as described in the previous sections. This would allow verification of the experimental setup. The FE simulation was performed using a two dimensional (2D) model to exploit mechanical symmetry, and also to minimize required computation time. Data gathered from experimentation was directly incorporated into the model. Specifically, the entire specimen geometry and ultimate failure loads were incorporated in the model to ensure its representation of the physical test setup. The FE model was created with a goal of extracting stresses in the laminate and forces transmitted through the loading fixture. In particular, the strain energy release rate, stresses at the crack tip and the strain in the stitches were of interest. The J-integral was used to calculate G parent (strain energy release rate of the parent material) by using a contour which did not include the stitches. G eff 30

PAGE 40

31 (effective strain energy release rate) was also evaluated by using a contour that circumvented the stitches in the laminate. G parent is a material property of the parent laminate while G eff depends on both the properties of the laminate and the properties of the stitches. Procedure of Modeling The first step in the modeling process was to create the DCB specimen. This was done by creating each individual half of the specimen and then attaching the halves in such a way that a pre-crack was created down the centerline of the model, mimicking the Teflon insert on the physical model. Appropriate orientation-dependent material properties were assigned to individual layers. The elements used for the laminate were planar (plane stress) 2D elements. After the model was assembled, the next step was to add the stitches to the specimen. The stitches were modeled as truss elements, which were attached by sharing nodes at the very top and bottom of the laminate. This does not completely characterize how the stitches are truly attached within the physical model but can be assumed a close approximation. The stitches were assigned isotropic material properties of Kevlar 29. The stitches were estimated as having a circular cross-section with the diameter being calculated by knowing that Dupont Kevlar 29 yarns have a denier of 1600. Next, the grips were modeled and attached to the laminate, making sure that all dimensions are representative of the physical setup. Finally, beam elements were used to model both the top and side bars of the fixture. The beams were assigned the material properties of steel and the dimensions of the physical model. Careful attention during the assembly was needed to ensure that no degrees of freedom were constrained unintentionally. The FE model can be seen in Figures 5-1 and 5-2.

PAGE 41

32 Figure 5-1: 2D FE model of fixture and laminate Figure 5-2: FE model showing crack tip and stitches including the stitch bridging distance

PAGE 42

33 Modeling Results The J-Integral approach was used to gather both the G parent and G eff from the FE models. Each model was loaded with the ultimate failure load of the stitches as measured from experimental testing. Then the G values were recorded at the crack tip. The J-Integral approach in the ABAQUS FE software returns a plot of contour number versus strain energy release rate. An example of this chart is shown in Figure 5-3. One can observe that near the crack tip the strain energy release rate is approximately 2 lb-in/in 2 (350 J/m 2 ) which is very representative of the actual fracture toughness value of a graphite/epoxy laminate. Also, it can be seen that once the contour grows large enough to include the stitch the strain energy release rate increases to a value of about 53 lb-in/in 2 which is similar to the experimental fracture toughness values. The G values are found in Table 5-1. The importance here more then the actual number values is the trend of both G parent and G eff G parent increases as the mode-mixity increases, which agrees with conventional theory. On the other hand G eff remains fairly constant over the mixed mode loading range. This matches the trend observed during experimental testing. Table 5-1: FE parent and effective fracture toughness Specimen ID (Low Density) FEM Parent G lb-in/in 2 (J/m 2 ) FEM Effective G lb-in/in 2 (J/m 2 ) Mode I 2.3 (403) 53 (9275) Mixed Mode 1 6.5 (1138) 76 (13300) Mixed Mode 2 15 (2625) 81 (14175) Mixed Mode 3 22 (3850) 74 (12950)

PAGE 43

34 Mode I: Strain Energy Release Rate vs. Contour Number0510152025303540455055600102030405060708090100110Contour NumberStrain Energy Release Rate (lbin/in^2) Figure 5-3: Strain energy release rate versus J-Integral contour number Additionally, given the stresses incurred at the crack tip the stress intensity factors were calculated at the crack tip (Table 5-2). From the intensity factors the mixed mode ratio at the crack tip was calculated. 1tanIIIKK (5-1) This local mixed mode ratio () is significantly different from the global mixed mode ratio () of which the fixture was loaded. This may be due to the fact that the stitches act as a shield, which effectively modifies the loading at the crack tip, such that the local-stress state defining local mode-mixity is different from the global mode-mixity defined by the fixture loads. The stitch acts like a cable which carries the Mode I loading, while allowing the shear stress from the Mode II loading to transfer to the crack tip. Table 5-3 shows a comparison of the global mixed mode ratio to the local mixed

PAGE 44

35 mode ratio. Further research in this area should be conducted. Experimental work needs to be done to further characterize the movement of the stitches through the parent laminate. From this research further refinement of the FE model could be done which could verify the possibility of the two different mixed mode ratios occurring in stitched composites. Table 5-2: Stress intensity factors at crack tip Specimen ID (Low Density) K I psi-in (MPa-m) K II psi-in (MPa-m) Mode I 2472.9 (2.7) 136.7 (0.15) Mixed Mode 1 2686.9 (2.95) 2274.2 (2.5) Mixed Mode 2 2545.0 (2.8) 4702.4 (5.2) Mixed Mode 3 2066.9 (2.3) 6773.2 (7.4) Table 5-3: Global versus local mode-mixity ratios Specimen ID (Low Density) Global Mode Mixity () Local Mode Mixity () Mode I 0 3 Mixed Mode 1 8.2 40 Mixed Mode 2 16.0 61 Mixed Mode 3 29.9 74 Crack Propagation Model To simulate the experimental testing that was performed, a crack propagation model was created. Initially a given crack length and bridging length is chosen. The model is loaded and both the strain in the stitches and the energy release rate of the parent material is monitored. If the strain in the stitches exceeds the failure strain (4%) then the stitch is considered broken and removed from the model. Additionally, if the strain energy release rate of the parent material exceeds the critical fracture toughness value the crack is allowed to propagate. Then this procedure repeats itself. The modeling process is an iterative one in which the strain and energy release rate are continuously being measured and compared to the critical values. A linear assumption was used in creating this model. Therefore the model will not mimic the experimental results perfectly. The

PAGE 45

36 data collected in simulating the loading and failure of one stitch is shown in Table 5-4. Additionally, Figure 5-4 shows the plot created from this model showing the first stitch failure. There is a close agreement between this crack propagation model and the experimental results which were gathered for a Mode I low density specimen. Failure occurs at approximately a load of 225 lb. (1000 N) in both cases. The displacement in the crack propagation model is greater then the experimental case, but this is due to the fact that the crack propagation model used a linear assumption which did not incorporate any non-linear effects. Additionally, the load drop after stitch failure is very similar to that of the experimental case. Table 5-4: Data needed to simulate crack propagation Crack Length from specimen edge in. (mm) Crack Length from leading stitch in. (mm) Displacement in. (mm) Load lb. (N) G lb-in/in 2 (J/m 2 ) Stitch Strain 2.55 (64.8) 0 0.318 (8.1) 225 (1000) 45.5 (7963) 0.006 2.634 (66.9) 0.084 (2.1) 0.345 (8.8) 225 27 (4725) 0.0229 2.717 (69.0) 0.167 (4.2) 0.357 (9.1) 225 8.5 (1488) 0.037 2.8 (71.1) 0.25 (6.4) 0.361 (9.2) 225 1.1 (193) 0.0423 2.884 (73.3) 0.334 (8.5) 0.3655 (9.3) 225 0.02 (3.5) 0.0466 2.967 (75.4) 0.417 (10.6) 0.3644 (9.25) 225 1.17 (204) 0.0462 3.05 (77.5) 0.5 (12.7) 0.3635 (9.23) 225 2.5 (438) 0.0407 3.05 (77.5) 0.5 (12.7) 0.438 (11.1) 225 54 (9450) 0.0067 3.133 (79.6) 0.583 (14.8) 0.472 (12.0) 225 34 (5950) 0.026 3.217 (81.7) 0.667 (16.9) 0.4875 (12.4) 225 12 (2100) 0.043 3.3 (83.8) 0.75 (19.1) 0.49 (12.45) 225 2.25 (394) 0.051 Note: Denotes leading stitch was removed from FE model to simulate stitch failure

PAGE 46

37 FEM Load vs. Displacement Crack Propagation Model05010015020025000.050.10.150.20.250.30.350.40.45Displacement (in.)Force (lbs.) Figure 5-4: Crack propagation model showing first stitch failure

PAGE 47

CHAPTER 6 CONCLUSIONS Summary The research presented in this thesis is an effort to better understand the failure phenomenon in laminated composites that are reinforced through their thickness with stitches. Through-the-thickness stitching is a method that increases translaminar strength while at the same time preventing crack propagation. The fracture toughness of stitched composites was evaluated under combined Mode I and Mode II loadings (known as mixed-mode loading). Additionally, a finite element (FE) model was created to be able to rapidly study the effects of stitching on a laminate under numerous loading conditions. Conclusions As a result of this study, the following conclusions were reached. 1. Stitching effectively increases the apparent fracture toughness of stitched composites. The increase is on the order of 20 fold for low-density stitched specimens and 40 fold for high-density stitched specimens. 2. For the limited global mode-mixity (range observed (0<<30), the apparent fracture toughness G c seems to increase slightly with increasing his agrees with theory as stitches are most effective in tension and keep the fracture toughness value fairly constant. 3. FE models can be used to accurately simulate the crack propagation in stitched composites. From these models, the material properties and physical dimensions of both the parent laminate and stitch can be varied to see what effect these changes have on apparent fracture toughness. 4. The J-Integral approach can be effectively implemented to evaluate stitched composites. Care should be taken to make sure that the contour either includes or excludes the stitches depending if one is interested in the value of G parent or G eff respectively. 38

PAGE 48

39 5. Local and global mode-mixity ratios are not the same for stitched composites. The stitches effectively modify the loading condition by carrying the tensile forces while allowing the shearing forces to transfer to the crack tip. Thus, resulting in higher mixed mode ratios at the crack tip.

PAGE 49

LIST OF REFERENCES 1. Mignery LA, Tan TM and Sun CT. The Use of Stitching to Suppress Delamination in Laminated Composites, ASTM STP 876, American Society for Testing and Materials, 1985, pp 371-385. 2. Dexter HB and Funk JG. Impact Resistance and Interlaminar Fracture Toughness of Through-the-Thickness Reinforced Graphite/Epoxy, AIAA paper 86-1020-CP, 1986 pp 700-709. 3. Ridards R and Korjakin A. Interlaminar Fracture Toughness of GFRP Influenced by Fiber Surface Treatment, Journal of Composite Materials, Vol. 32, No. 17, 1998, pp 1528-1559. 4. Reeder JR and Crews JH Jr. Mixed Mode Bending Method for Delamination Testing, AIAA paper Vol. 28, No. 7, Jul. 1990, pp 1270-1276. 5. Reeder JR and Crews JH Jr. Redesign of the Mixed Mode Bending Delamination Test to Reduce Nonlinear Effects, Journal Composites Technology and Research 1992 pp 12-18. 6. Chen L, Sankar BV and Ifju PG. Mixed Mode Fracture Toughness Tests for Stitched Composite Laminates, AIAA paper 2003-1874, 2003 CD Rom. 7. Anderson TL. Fracture Mechanics: Fundamentals and Applications, Second Edition, CRC Press, Boca Raton, FL 1995. 8. Sharma SK and Sankar BV. Effects of Through The Thickness Stitching on Impact and Interlaminar Fracture Properties of Textile Graphite/Epoxy Laminates, NASA Contractor Report 195042, Feb. 1995. 9. Sankar BV and Sharma SK. Mode II Delamination Toughness of Stitched Graphite/Epoxy Textile Composites, Journal of Composites Science and Technology, Vol. 57, 1997 pp 729-737. 10. Jain LK, Dransfield KA, and Mai YW. On the Effects of Stitching in CFRPs-II. Mode II Delamination Toughness, Journal of Composites Science and Technology, Vol. 58, 1998 pp 829-837. 11. Gui L and Li Z. Delamination Buckling of Stitched Laminates, Journal of Composite Science and Technology, Vol. 61, 2001 pp 629-636. 40

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41 12. Yeh HY, Lee JJ and Yang DYT. Study of Stitched and Unstitched Composite Panels Under Shear Loadings, Journal of Aircraft Vol. 41, No.2, March-April 2004 pp 386-392.

PAGE 51

BIOGRAPHICAL SKETCH Tomek P. Rys was born in Jelenia Gora, Poland, on August 30 th 1980. He attended public schools in Manhattan, KS, for the first 18 years of his life. After graduating Manhattan High School in August 1998 he enrolled at Kansas State University (KSU). Mr. Rys studied mechanical engineering at KSU. He was actively involved in many activities while attending KSU including Pi Tau Sigma, Tau Beta Pi and Steel Ring honor societies. He also participated in societies such as S.M.E. and A.S.M.E. and was also involved in intramural sports. After graduating from KSU in December of 2002, Mr. Rys decided to attend graduate school at the University of Florida (UF). Mr. Rys had an interest in composite materials and therefore chose solid mechanics as his area of specialization for his graduate studies. His research and focus has been presented in this thesis. Mr. Rys graduated from UF in August 2004. Upon graduating Mr. Rys accepted a position as a composites engineer at one of the nations largest defense contractors working on missile systems. 42


Permanent Link: http://ufdc.ufl.edu/UFE0006994/00001

Material Information

Title: Mixed Mode Fracture Toughness of Stitched Laminated Composites
Physical Description: Mixed Material
Copyright Date: 2008

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Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
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Permanent Link: http://ufdc.ufl.edu/UFE0006994/00001

Material Information

Title: Mixed Mode Fracture Toughness of Stitched Laminated Composites
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0006994:00001


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MIXED MODE FRACTURE TOUGHNESS OF STITCHED LAMINATED
COMPOSITES
















By

TOMEK RYS


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA


2004
































Copyright 2004

By

Tomek Rys

















ACKNOWLEDGMENTS

First and foremost I would like to thank my advisor and sponsor, Dr. Bhavani V.

Sankar. Without his direct guidance and support the work presented in this thesis would

not have been possible. Additionally, I would like to thank my colleagues at the Center

for Advanced Composites located on the University of Florida campus. Their support

and assistance were invaluable throughout my research.





















TABLE OF CONTENTS


page


ACKNOWLEDGMENT S .........__.. ..... .__. .............._ iii..


LIST OF TABLES ........._.___..... .__. ..............vi....


LI ST OF FIGURE S .............. .................... vii


AB STRAC T ................ .............. ix


CHAPTER


1 INTRODUCTION ................. ...............1.......... ......


Back ground Information............... ...............
Literature Survey .............. ...............4.....
S cope of the Thesis............... ...............5.


2 BACKGROUND .............. ...............7.....


Theory ............... ... .. ......... ...............7.......
Testing of Stitched Composites ................. ...............9................


3 EXPERIMENTAL SETUP ................. ...............11................


Testing Fixture ................. ...............11.................
Specimen Preparation ................ ...............14.................
Experimental Method .............. ...............16....


4 FRACTURE TESTS............... ...............20.


Introducti on ................. ...............20.................
Testing and Discussion ................. ...............20........... ....


5 FINITE ELEMENT ANALYSIS .............. ...............30....


Introducti on ................. ...............30.................
Procedure of Modeling ................. ...............3.. 1......... ...
Modeling Results ................. ...............33.................
Crack Propagation Model .............. ...............35....













6 CONCLUSIONS .............. ...............38....


Sum m ary ................. ...............3.. 8..............
Conclusions............... ..............3


LIST OF REFERENCES ................. ...............40........... ....


BIOGRAPHICAL SKETCH .............. ...............42....

















LIST OF TABLES


Table pg

3-1 Material properties for AS4/3 501-6 graphite/epoxy ................. .......................15

3-2 Variation in thickness of each layer in the stacking sequence ................. ...............15

4-1 Average apparent fracture toughness of low-density stitched specimens ...............21

4-2 Average apparent fracture toughness of high-density stitched specimens ...............21

5-1 FE parent and effective fracture toughness ....._._._ .... ... .__ ........_.........3

5-2 Stress intensity factors at crack tip ...._. ......_._._ .......__. ...........3

5-3 Global versus local mode-mixity ratios .............. ...............35....

5-4 Data needed to simulate crack propagation............... ..............3

















LIST OF FIGURES


Figure pg

1-1 Stitching and Z-pinning of a laminate ......___ ... ......___...... ...........

1-2 Stitching Types: (a) Lock stitch, (b) Modified Lock stitch, (c) Chain stitch............4

2-1 DCB specimen geometry .............. ...............8.....

2-2 Modes of Fracture. From left to right: Mode I, Mode II, Mode III..........................9

2-3 Stitched specimen showing failure due to bending moment ........._...... ................10

3-1 Mixed Mode testing fixture ........... _............ ...............11....

3-2 Free body diagram (FBD) of specimen showing horizontal and vertical force
components ................. ...............12.................

3-3 Grip and specimen ends showing machined arcs used for attachment ................... .13

3-4 Mixed Mode fixture showing counterbalance weight for balancing of mechanism
prior to testing .............. ...............14....

3-5 Specimens showing stitch densities and pre-crack lengths ................. ................. 16

3-6 Load versus crosshead displacement plot for a stitched specimen ..........................17

3-7 Stitched DCB specimen undergoing testing ................. ............... ......... ...18

3-8 Schematic of forces for strength of material calculations ................. ................. 19

4-1 Fracture toughness versus mode-mixity over entire Mode I to Mode II range........22

4-2 Mode I loading: low density specimens, load vs. crosshead displacement. .............23

4-3 Mixed Mode 1 loading: low density specimens, load vs. crosshead displacement .24

4-4 Mixed Mode 2 loading: low density specimens, load vs. crosshead displacement .25

4-5 Mixed Mode 3 loading: low density specimens, load vs. crosshead displacement .26

4-6 Mode I loading: high density specimens, load vs. crosshead displacement ............27










4-7 Mixed Mode 1 loading: high density specimens, load vs. crosshead displacement 28

4-8 Mixed Mode 2 loading: high density specimens, load vs. crosshead displacement 28

4-9 Mixed Mode 3 loading: high density specimens, load vs. crosshead displacement 29

5-1 2D FE model of fixture and laminate ................. ...............32..............

5-2 FE model showing crack tip and stitches including the stitch bridging distance.....32

5-3 Strain energy release rate versus J-Integral contour number .............. ..................34

5-4 Crack propagation model showing first stitch failure .............. ....................3
















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

MIXED MODE FRACTURE TOUGHNESS OF LAMINATED STITCHED
COMPOSITES

By

Tomek Rys

August 2004

Chair: Bhavani V. Sankar
Cochair: Peter G. Ifju
Major Department: Mechanical and Aerospace Engineering

The research presented in this thesis is an effort to better understand the failure

phenomenon in laminated composites that are reinforced through their thickness with

stitches. Through-the-thickness stitching is a method that increases translaminar strength

while at the same time preventing crack propagation. A novel test Eixture was developed

to measure mixed mode fracture toughness under combined Mode I and Mode II

loadings.

In addition, a Einite element (FEM) model has been created which allows for the

prediction of the apparent fracture toughness of various stitched laminates under mixed

mode loadings. In the FEM model, the material properties of the laminate, including the

stitch material, stitching density, and stitch diameter, can be varied in order to quickly

evaluate the sensitivity of fracture toughness with respect to these parameters.















CHAPTER 1
INTTRODUCTION

Background Information

Composite materials have many advantages over conventional materials in

aerospace and other applications where the strength to weight ratio is a critical factor.

Graphite/epoxy laminated composites have high stiffness-to-weight and strength-to-

weight ratios that make them suitable for structural applications. Additionally, composite

materials can be tailored to obtain specific properties in various directions and the overall

thickness and lay-up of the composite can be optimized for given loading conditions.

Composites offer many other advantages over conventional materials including but not

limited to: high corrosion resistance, high energy absorption, low thermal expansion,

good thermal insulation and electrical resistivity.

Despite all these advantages, graphite/epoxy composite production volumes have

not increased drastically in recent years. This stems from two major deficiencies of

composite materials. The first being the high material cost and slow manufacturing time

of graphite/epoxy composites compared to conventional structural materials. The second

maj or deficiency is the poor inter-laminar strength, fracture toughness and low impact

resistance and damage tolerance that composites typically possess.

The properties of these composite laminates depend highly on the fiber orientation

and the fiber volume ratio. The strength in the translaminar (through-thickness) direction

tends to be significantly smaller than in the fiber direction. For example, the tensile

strength of graphite/epoxy laminates is approximately 72 to 1 16 ksi (500 to 800 MPa) in









the fiber direction while in the translaminar direction the strength is around 2.9 to 4.3 ksi

(20 to 30 MPa). This is due to the fact that the load is being predominately carried by the

resin matrix, making the composite susceptible to delamination. This delamination is

typically an interface crack or a debonded zone between two adj acent layers. This

delamination can be initiated by imperfect manufacture or during the impact of a foreign

body during service. Typically this delamination is located within the composite and

cannot be detected through visual inspection. This initial delamination (crack) can grow

rapidly under subsequent application of external load. This can lead to either catastrophic

failure of the structure and/or a significant decrease in the load carrying capability. The

poor translaminar strength of graphite/epoxy laminates has limited the number of

aerospace applications.

Many methods have been developed to improve the translaminar strength and

decrease the occurrence of delamination. These methods include the introduction of

translaminar reinforcements (TLR) into the composite. TLR can either be of the

continuous or discontinuous form. Continuous weaving, knitting, braiding, threads, yarns

and tows can be inserted into the laminated using industrial sewing/stitching technology.

Discontinuous reinforcements such as short fibers, whiskers and pins can also be inserted

into a composite to increase the translaminar strength. Refer to Figure 1-1.

3D weaving, braiding and knitting improve the translaminar strength due to the

increased number of fibers in the out of plane direction. The maj or downfall of these

TLR are the large resin pockets that are introduced during manufacture and the reduced

number of fibers in the in plane direction. This can lead to reduced in-plane properties.

The stitching process differentiates itself by having the stitch as a non-integral part of the









laminate. The stitch is inserted into a 2D preform as a secondary process after lay-up but

before the introduction of the resin and subsequent curing. By using stitches as a TLR,

the onset of large resin pockets is reduced, especially when compared to 3D weaving.

Stitching is one of the most common techniques used to suppress delamination.













Sltfchlng Z-pinning


Figure 1-1: Stitching and Z-pinning of a laminate

Composites can be stitched either as prepregs (resin impregnated fabrics) or

reforms (resin free fabrics). Unfortunately considerable fiber damage occurs when

stitching prepreg laminates. This reduces the in plane fiber properties of the composite.

Alternatively, stitching of the preform can be done without causing as much fiber damage

due to the ability to pull a needle through the resin free fabric.

One of the most critical factors in stitching a laminated composite is the type of

stitch used. One of the most common types of stitches is known as the lock stitch. It

consists of a two thread loop between the needle and the bobbin threads. The lock stitch

requires access to both top and bottom of the laminate. This stitch is used in the apparel

industry due to its aesthetic appeal. The intersection of the bobbin and needle threads is

concealed in the fabric. This is not favorable for stitching composites because the thread

intersection in the middle of the laminate would cause a stress concentration. Therefore,









when stitching composites a modified lock stitch is typically used that allows the needle

thread to travel along the surface of the composite rather then in the middle of it.

Additionally, a chain stitch can be used that has a similar mechanism to that of the lock

stitch. Figure 1-2 shows all three stitch types discussed above.







(A)


(c)s


Figure 1-2: Stitching Types: (a) Lock stitch, (b) Modified Lock stitch, (c) Chain stitch

Literature Survey

Mignery et al. [1] investigated the use of stitching using Kevlar yarn to suppress

delamination in graphite/epoxy laminates. Results showed that stitching was an effective

suppressant of delamination. In addition, Dexter and Funk [2] investigated the Mode I









fracture toughness of laminates reinforced with Kevlar stitches. Results showed that the

fracture toughness increased 30 fold when compared to the unstitched laminate.

Currently, the double cantilever beam (DCB) test is used to determine the Mode I

fracture toughness of unstitched composite laminates. In practical applications it is rare

to encounter pure Mode I or Mode II loadings. Typical loads are comprised of a

combination of both Mode I and Mode II loads referred to as a mixed mode loading

condition. Richards and Korj akin [3] used the traditional mixed mode setup to test the

fracture toughness of unstitched laminated composites. In their experiments the ratio of

Mode I to Mode II was fixed at 1.33 according to linear beam analysis. Reeder and

Crews [4-5] developed a new mixed mode experimental setup that simultaneously

created a Mode I and Mode II bending load on the specimen from a single applied load.

This setup allowed for numerous mixed mode ratios to be tested. Although many

researchers have used different approaches to investigate the delamination fracture

toughness of composites including mixed mode fracture properties of composites, none

have successfully tested the mixed mode fracture toughness of composites with dense

translaminar reinforcement. The standard DCB test is not suitable for testing stitched

laminates. Typically during the standard DCB test the specimen fails due to high

compressive stresses caused by the large bending moment at the crack tip. Due to these

problems with the standard DCB test a novel test fixture has been developed by Chen et

al. [6] for stitched composites.

Scope of the Thesis

Due to the lack of transverse strength, composite materials are vulnerable to

delamination which is either an interface crack or a debond between two adj acent layers.

This delamination is typically not detectable by visual inspection of a composite's outer









surfaces. This delamination can be initiated during imperfect manufacture or simply

caused by impact of a foreign body during service.

Methods to improve this translaminar strength include stitching. The stitching

process improves the apparent fracture toughness of the laminated composite. The aim of

the current study is to accurately measure the increase in the fracture toughness incurred

by the addition of stitches, and to investigate the effect of various ratios of fracture modes

on the composite's fracture toughness.















CHAPTER 2
BACKGROUND

Theory

There are two main approaches to analyzing the fracture toughness of a given

material: the energy approach and the stress intensity factor approach. Both are

commonly used. The energy approach was used during this research due to its ease of

adaptability to experimental work. The energy approach states that a crack will only

propagate when the energy provided for crack growth is sufficient to overcome the

resistance of the material [7]. The material resistance includes but is not limited to the

surface energy, plastic work, or any other type of energy dissipation associated with

crack propagation [7]. The energy release rate (G) is defined as the rate of change in

potential energy with crack area. At the onset of crack propagation, the energy release

rate is defined as the critical energy release rate, which provides a measure of fracture

toughness [7].

For a double cantilever beam (DCB) specimen (Figure 2-1), the Mode I fracture

toughness can be found as


G (2-1)
bEl

where Fc is the load at which the crack propagation occurs, a is the current crack length,

b is the width of the specimen and El is the equivalent flexural rigidity of the specimen.
















nInitia crack




F aa












Figure 2-1: DCB specimen geometry

The fracture toughness of stitched laminated composites can be broken into two

subcategories. Gparent is the fracture toughness of the parent material and is constant

throughout a structure for a given loading mode. Modes of loading are discussed below.

The parent material can be defined as the material which contains the stitches.

Alternatively, Gerr is the fracture toughness related to the parent material but also

dependent on the properties of the stitches.

In basic fracture mechanics there are three loading modes: Mode I, Mode II and

Mode III. Figure 2-2 shows examples of how each mode is loaded. Mode I is dominated

by an opening load, Mode II is dominated by an in plane shearing load, and Mode III is

dominated by an out of plane shear.





















Figure 2-2: Modes of Fracture. From left to right: Mode I, Mode II, Mode III

Typically in real world applications a crack propagates under a combination of

these loading conditions. Mixed-mode loading in this research is defined as some

combination of Mode I and Mode II loading conditions. Mixed-mode conditions are

quantified by a mode-mixity phase angle (7y) (Equation 2-2), which is 00 for pure mode I

and 900 for pure mode II. Understanding the mode-mixity of a loading condition is

important because of its effects on crack propagation.


7 = tanC (2-2)


A crack in pure mode II loading commonly requires several times as much energy

to initiate crack propagation as compared to a crack propagated under pure mode I

loading [7]. Therefore, it becomes necessary to identify the mode-mixity of an

experimental setup in order to thoroughly understand results.

Testing of Stitched Composites

Currently the DCB test as described above is used to measure the Mode I fracture

toughness of laminated composites. This method works well for specimens that do not

contain translaminar reinforcements. The standard DCB test is not suitable for laminated

composites that contain stitches as through the thickness reinforcements. The main

reason for this is that the strength of the stitches is very high and a large amount of force








is required to either break them or cause pullout. As the load is increased in the standard

DCB test the specimen arms are subj ected to large bending moments Figure 2-3. This

moment causes the specimen arms to fail due to buckling on the compression side of the

arm before crack propagation can be initiated









stitChes


F1

failure due t cormpressive~
/ instability






Figure 2-3: Stitched specimen showing failure due to bending moment
Much research has been conducted in investigating new Eixtures for testing the

fracture toughness of stitched composites. The main focus has been on reducing the

aforementioned compressive failure. To effectively eliminate this failure the maximum

compressive stress must be reduced. A novel testing Eixture has been developed at the

University of Florida that incorporates an additional tensile force to neutralize the

maximum compressive stress. This Eixture is further discussed in Chapter 3.















CHAPTER 3
EXPERIMENTAL SETUP

Testing Fixture

The standard DCB is not suitable for testing stitched composites due to high

compressive stresses that cause the specimen to fail before the crack propagation can be

initiated. A novel test fixture has been developed to allow for the testing of the fracture

toughness of stitched composites. The novel fixture incorporates a horizontal bar that has

a series of holes corresponding to numerous mixed mode ratios (Figure 3-1).



Bearing



















< 0~00000000000

F, F,
F, + F,

Figure 3-1: Mixed Mode testing fixture














FLL) 1 BO -





















Figure 3-2: Free body diagram (FBD) of specimen showing horizontal and vertical force
components

At the right end of the bar, a bearing reacts to create a horizontal force which helps

balance the Eixture as well as reduce compressive bending stresses that might otherwise

lead to premature failure of the specimen (before stitch failure). This Eixture applies

tension to both arms of the DCB specimen, which also reduces the compressive bending

stresses. This tensile force effectively neutralizes the compressive bending stresses in the

specimen arms. By changing the loading position, various mixed mode ratios are

obtained. Mode I is achieved by loading the fixture at a hole directly inline with the

specimen. By offsetting the load from the longitudinal axis of the specimen, various

mixed mode ratios are achieved as the ratio of forces in each loading bar is changed. In

addition, the Eixture can be self balanced by adding weights to the left side of the










horizontal bar to account for errors caused by the unbalanced weight of the Eixture (Fig.

3 -4). This Eixture relies on specimen grips that can transmit both axial and transverse

forces (Fig. 3-3).


Gripping area
of a specimen


Telfloriprecrack


Figure 3-3: Grip and specimen ends showing machined arcs used for attachment

The transverse component of the force is for crack opening and the axial

component is used to provide the tensile stresses as mentioned earlier. The conventional

method of bonding tabs to the specimen does not work as the large tensile and shear

stresses caused by the load required to propagate the crack simply debond the tabs. A

notch in the form of a circular arc was machined in the specimen ends (Fig. 3-3). A pair

of grips that match the notch profie in the specimen were machined out of steel.








































Figure 3-4: Mixed Mode fixture showing counterbalance weight for balancing of
mechanism prior to testing

Specimen Preparation

The stitched specimens were made of 28 plies of AS4 uniweave graphite fabric and

3501-6 epoxy resin using the RTM process by NASA Langley Research Center. The

specimens were stitched with 1600 denier Kevlar 29 where there are two Kevlar yarns in

each stitch. In addition, each specimen consisted of three rows of stitches. The

specimens were approximately 190.5 mm (7.5 inches) long and 19.05 mm (0.75 inches)

wide. Two different stitch densities were used to evaluate the effects of stitch density on

fracture toughness. Linear stitch densities evaluated were 5 stitches per inch (referred to

as low density) and 9 stitches per inch (high density). The spacing between adjacent









rows of stitches was 5 mm (0.2 inch). Typically stitch density is defined as the number

of stitches per square inch. This is represented by the stitching pattern, which is:

(number of stitches per inch) x (spacing between two adjacent stitch lines). Therefore the

stitch densities evaluated were 5 x1/5 and 9x 1/5. Refer to Figure 3-5. Additionally, the

top and bottom plies of the specimen were covered with 1 layer of plane weave fiberglass

cloth to act as a retainer for the stitches. The specimens also included a Teflon insert

either 65 mm (2.55 in.) or 90 mm (3.55 in.) in length that created the pre-crack needed

for crack propagation (Figs.3-3 and 3-5). The pre-crack started at the machined end of

the specimen and continued up to the first row of stitches. The specimen was made up of

4 stacks where each stack consisted of 7 plies, which were oriented at

[450/-450/00/900/00/-450/450]. The materials used in each stack have slightly different

properties (Tables 3-1 and 3-2).

Table 3-1: Material properties for AS4/3501-6 graphite/epx
El psi E2 psi Gl2 psi Gl3 psi G23 psi
MATERIAL u12
(GPa) (GPa) (GPa) (GPa) (GPa)
AS4-3 501- 15.3 e6 1.6 e6 0.52 e6
0.34 0.8 e6 (6) 0.8 e6 (6)
00 (105) (11) (3.6)
AS4-3 501- 15.04 e6 1.6 e6 0.52 e6
0.34 0.8 e6 (6) 0.8 e6 (6)
45 (103) (11) (3.6)
AS4-3 501- 14.88 e6 1.6 e6 0.52 e6
0.34 0.8 e6 (6) 0.8 e6 (6)
90 (102) (11) (3.6)

Table 3-2: Variation in thickness of each layer in the stacking sequence
PLY THICKNESS ORIENTATION
MATERIAL NAME
NUMBER in. (mm) (DEGREE)
1 0.00633 (0.16) 45 AS4-3 501-45
2 0.00633 (0.16) 45 AS4-3 501-45
3 0.01285 (0.32) 0 AS4-3 501-00
4 0.007018 (0.18) 90 AS4-3 501-90
5 0.01285 (0.32) 0 AS4-3 501-00
6 0.00633 (0.16) 45 AS4-3 501-45
7 0.00633 (0.16) 45 AS4-3 501-45
































Figure 3-5: Specimens showing stitch densities and pre-crack lengths

Experimental Method

Many experimental techniques are available for determining the fracture toughness

of laminates. The double cantilever beam (DCB) test was chosen to accurately determine

the fracture toughness of the stitched composites due to its simplicity. The DCB test

consists of a specimen prepared with an initial crack length at the interface of which the

fracture toughness is of interest. Tests were conducted in a screw driven universal testing

machine (MTI). The crack propagation was observed using a CCD camera. A computer

monitored and recorded both force and crosshead displacement. The crack propagation

length was measured using a micrometer. Once the data was taken, a plot of force versus

crosshead displacement was created. The area under the load deflection plot represents

the work done (AW) in propagating the crack. Calculation of the fracture toughness was

accomplished by dividing the work done to propagate the crack by the crack propagation

length (Aa) multiplied by the specimen width (b).










AW
G;, =(3-1)
b~a


For pure Mode I loading, the fixture is setup with the universal testing machine

attached directly in line with the specimen. The load increases until the first row of

stitches break, at which time the load suddenly drops (Figs. 3-6, 3-7). Subsequent rows

of stitches are loaded until failure. The cycle continues in this saw tooth pattern until the

specimen is unloaded. When testing stitched specimens, unloading can never be

complete as the broken stitches protrude out of the newly created delamination surface

and prevent the specimen from closing fully. In this case we assume that the unloading

would have been elastic, and hence connect the current point on the load-deflection plot

to the origin. As seen in Figure 3-6 each peak and valley corresponds to a stitch

breaking. By having a peak and valley for every row of stitches in the specimen shows

that the crack propagation is stable.

Mode 1: Load vs. Displacement

300


250


200


,150


100


50



0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
crosshead Displacement (in.)

Figure 3-6: Load versus crosshead displacement plot for a stitched specimen































Figure 3-7: Stitched DCB specimen undergoing testing

The same procedure described for Mode I was used for mixed mode loading. To

achieve various mixed mode ratios the MTI machine was attached to the horizontal bar

offset from the specimen. The larger the offset the greater the mixed mode ratio

becomes. The average fracture toughness values for both the low-density and high-

density stitched composites are listed under Tables 4-1 and 4-2 in Chapter 4. The Mode

Mixity parameter (F) defined as follows is used to describe the mixed mode ratio:


ry= tan "(3 -2)
K,

where KI and KII are the Mode I and Mode II stress intensity factors, respectively. One

can note that F=0 for pure Mode I and 7= n/2 for pure Mode II. For mixed mode

conditions 0< 7< /2. The stress intensity factor approach to calculate mode-mixity is

further explained in Chapter 5.

In the present work we use a simple mechanics of materials approach to estimate

the mode-mixity 7, which is based on the ratio between the forces transmitted to the









specimen in each bar of the fixture. We calculate both GI and GII (energy release rates)

based on strength of material calculations (Fig. 3-8 and Eq. 3-3) and use the superposition

of the symmetric and anti-symmetric loads to calculate 7. The energy release rates are

proportional to the square of the stress intensity factors. Therefore, the energy release

rates are calculated and then converted to stress intensity factors values, which are then

used in Equation 3-2 to calculate E'

F, (F + F,)12 (F F,)12



F, (F + F,)/2! (F F,)/2

Figure 3-8: Schematic of forces for strength of material calculations






cG, 4 1 F2FF,1 (3 -3)















CHAPTER 4
FRACTURE TESTS

Introduction

As explained previously the fracture toughness (G,) of a material can be described

or defined as the energy needed to initiate crack propagation. Fracture toughness is a

material property and therefore should remain constant under a given loading condition.

Typical Go values for a graphite/epoxy laminate are on the order of 300 J/m2 (1.7 lbin/in2)

for Mode I delamination crack propagation. Previous research has shown that the

addition of stitches increases the fracture toughness significantly especially under Mode I

loading conditions. This is most likely due to the fact that stitches are primarily effective

in tension rather than shear.

Testing and Discussion

As previously discussed the specimens were tested using an MTI machine

configured with the test Eixture described in the previous chapter. Both low stitch-density

and high stitch-density specimens were tested. For the high-density specimens, the

Eixture was adjusted by moving the arms inward toward the loading attachment point.

This increases the tension force in each arm, effectively reducing the compressive

bending stresses, which cause specimen breakage.

Average apparent fracture toughness for both low-density and high-density

specimens can be found in Tables 4-1 and 4-2 respectively.









Table 4-1: Average apparent fracture toughness of low-density stitched specimens
MODE RATIO AVERAGE G
y' = tan' (II/KI) lb-in/in2 (/m2
00 40.45 (7083)
8.20 36.27 (6351)
16.00 43.16 (7557)
29.90 46.60 (8160)


Table 4-2: Average parent fracture toughness of high-densit stitched spcmens
MODE RATIO AVERAGE G
y' = tan' (II/KI) lb-in/in2 (/m2
00 81.80 (14323)
12.10 96.80 (16950)
23.30 100.74 (17640)
29.90


As the mixed mode ratio increases from Mode I to Mode II the apparent fracture

toughness value increases significantly over that of an unstitched specimen and remains

fairly constant over the mixed mode range with a decrease most likely appearing near the

pure Mode II loading condition.

One may notice that no fracture toughness value can be found for high-density

specimens above the mixed mode ratio of 23.30. This is due to the fact that at mixed

mode ratios higher than this, the specimen would break either from compressive breakage

in one of the arms or in shear at one of the end grips.

Figure 4-1 shows a plot of the fracture toughness versus the mode-mixity angle for

low-density stitched specimens. A linear trend line has been fitted to the experimental

data to show the trend of the fracture toughness with respect to the mode-mixity angle.

As the mode-mixity angle increases there is a slight increase in the fracture toughness

value over a 300 mode-mixity range. The Mode II (900) fracture toughness value was

found for a stitched specimen using an End-Notch-Flexure test by Chen et al. [6]. The










dotted trend line is shown as an illustration that the fracture toughness will eventually

decrease to the Mode II value. The exact shape of this trend line between 300 and 900

(dashed line in Fig. 4-1) at the present moment is unknown.


Fracture Toughness vs. Mode Mixity


60


i3 50












20



0 10 20 30 40 50 60 70 80 90
Mode Mixity (degree)

Figure 4-1: Fracture toughness versus mode-mixity over entire Mode I to Mode II range

The force versus crosshead displacement data collected from the MTI machine is

shown in Figures 4-2 thru 4-9.

Shown in Figure 4-2 is the load versus crosshead displacement for a Mode I

loading done on three low density specimens. As one can observe, there is some non-

linearity to both the loading and unloading of the specimen. Additionally, one of the

specimens has a different loading slope curve. This is due to stitches starting further

down on that specimen compared to the other two specimens (Refer to chapter 3).











Specimens with a pre-crack length of both 65 mm (2.55 in.) and 90 mm (3.55 in.) were

tested. Due to this fact the loading curves will have slightly different shapes.


Mode 1: Low Density

350


300


250-


,200-


8 150-


100-


50-



0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Cross head Dis placement (in.)


Figure 4-2: Mode I loading: low density specimens, load vs. crosshead displacement

Figure 4-3 shows the load versus crosshead displacement curve for a mixed mode

loading of 8.20 on two low density specimens. There is slightly more non-linearity under

the mixed mode loading compared to that of the Mode I loading. Very good repeatability

between the two specimens can be observed. Notice that each peak and valley

corresponds to a row of stitches breaking, meaning the crack propagated in a stable

manner. By the crack propagating in a stable manner the analysis of the fracture


toughness can more easily be performed. Meaning that for each stitch breaking there is

crack length that corresponds to the breakage.






















01
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Crosshead Displacement (in.)

Figure 4-3: Mixed Mode 1 loading: low density specimens, load vs. crosshead
displacement
Figure 4-4 shows the load versus displacement curve for a mixed mode loading of
16.00 for low density specimens. The non-linearity of the initial load buildup grows
even greater when compared to the previous two loading conditions. The average force
for stitch breakage and crack propagation has increased from approximately 200 lb.
(890 N) to 250 lb. (1100 N). Additionally, it can be observed that the force needed for
stitch breakage has quite a large (up to 45% difference) variation between specimens.
Figure 4-5 shows the load versus displacement curve for a mixed mode loading of
29.90 for low density specimens. These specimens have a very non-linear initial loading
curve. Also, it is important to point out that on one of the specimens, crack propagation
was unstable as there was a large peak load which broke a number of rows of stitches at
once. This can easily be seen as one specimen does not have nearly as many peaks and


~"kki~~


Mixed Mode 1: Low Density


300


52U 0


m 200


100

50n











valleys as the other. Notice the drastic increase in average stitch breaking force when


compared to the previous three loading conditions. This shows that as the mixed mode

ratio increases the force needed to break stitches and propagate the crack increases. This

is very important because specimen breakage can occur if this force gets too large.


Mixed Mode 2: Low Density

100

350

300-

250-

200-

150-

100-

50-


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Crosshead Displacement (in.)


Figure 4-4: Mixed Mode 2 loading: low density specimens, load vs. crosshead
displacement

Figure 4-6 shows the load versus displacement curve for a mode I loading on high

density specimens. When compared to the low density specimens, it can be observed that

the average force for crack propagation has increased significantly to an average force of


approximately 550 lb. (2400 N). Because these specimens are stitched more densely, the

number of peaks and valleys has increased.






















4f~


Mixed Mode 3: Low Density


500
450
400
350-
S300-
250-
o
u.. 200-
150-
100-
50-
0 1


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Crosshead Displacement (in.)
Figure 4-5: Mixed Mode 3 loading: low density specimens, load vs. crosshead
displacement
Figure 4-7 shows the load versus displacement curve for a mixed mode loading of
12.10 for a high density specimen. Notice the increase in non-linearity on the loading
curve and the large increase in stitch propagation force. This non-linearity may be due to
the complex mechanism used in the fixture. Average force is approximately 900 lb.
(4000 N).
Figure 4-8 shows the load versus displacement curve for a mixed mode loading of
23.30 for high-density specimens. Notice that one specimen is loaded and fails due to
compressive bending in the arm. After the specimen broke, the fixture was adjusted by
moving the loading arms inward to increase the tensile force in each arm to aid in
reducing bending stresses. The next specimen does not fail, but the crack propagates
unstably as there are three peaks and valleys which correspond to approximately 15 rows
























~""s~4~


of stitches breaking. Also, the average crack propagation force has increased once again
to approximately 2000 lb. (8900 N), which is an increase of almost 1 100 lb. (5000 N)
from the previous loading condition.

Mode 1: High Density


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Crosshead Displacement (in.)
Figure 4-6: Mode I loading: high density specimens, load vs. crosshead displacement
Figure 4-9 shows the load versus displacement curve for a mixed mode loading of
29.90 for a high density specimen. Notice that the specimen is unable to open and breaks
due to shearing at the grip attachment point. Testing highly stitched specimens is an
intricate process and refinement to the testing fixture or a new fixture must be developed
in order to test specimens such as these.


1000
9000
800-
700-
600-
S500-
u. 400-
300
200
100-





Mixed Mlode 1: High Density


0 0.1 0.2 0.3 0.4 0.5 0.6
Crosshead Displacement (in.)


Figure 4-7: Mixed Mode 1 loading: high density specimens, load vs. crosshead
displacement


Mixed Mlode 2: High Density


2000



1500


o
u.. 1 00 0



500



0


0 0.1 0.2 0.3 0.4 0.5
Crosshead Displacement (in.)


Figure 4-8: Mixed Mode 2 loading: high density specimens, load vs. crosshead
displacement













Mixed Mode 3: High Density


2500



2000



S1500

o

u.. 1 00 0



500





0 0.1 0.2 0.3 0.4 0.5
Crosshead Displacement (in.)


Figure 4-9: Mixed Mode 3 loading: high density specimens, load vs. crosshead
displacement















CHAPTER 5
FINITE ELEMENT ANALYSIS

Introduction

To better investigate and understand the mechanics of the loading fixture and the

stitched laminate, a finite element (FE) model was created. This model would allow for

the investigation of the stitch interactions with the parent laminate and investigation of

stitch failure mechanisms. Additionally, in the FE model the material properties of the

laminate, including the stitch material, stitching density, and stitch diameter, could be

varied in order to quickly evaluate the sensitivity of fracture toughness with respect to

these parameters. By modeling the entire loading fixture instead of just the stitched

laminate, the mode-mixity could be evaluated at the crack tip under a given loading

arrangement as described in the previous sections. This would allow verification of the

experimental setup.

The FE simulation was performed using a two dimensional (2D) model to exploit

mechanical symmetry, and also to minimize required computation time. Data gathered

from experimentation was directly incorporated into the model. Specifically, the entire

specimen geometry and ultimate failure loads were incorporated in the model to ensure

its representation of the physical test setup. The FE model was created with a goal of

extracting stresses in the laminate and forces transmitted through the loading fixture. In

particular, the strain energy release rate, stresses at the crack tip and the strain in the

stitches were of interest. The J-integral was used to calculate Gparent (strain energy release

rate of the parent material) by using a contour which did not include the stitches. Gerr










(effective strain energy release rate) was also evaluated by using a contour that

circumvented the stitches in the laminate. Gparent is a material property of the parent

laminate while Gerr depends on both the properties of the laminate and the properties of

the stitches.

Procedure of Modeling

The first step in the modeling process was to create the DCB specimen. This was

done by creating each individual half of the specimen and then attaching the halves in

such a way that a pre-crack was created down the centerline of the model, mimicking the

Teflon insert on the physical model. Appropriate orientation-dependent material

properties were assigned to individual layers. The elements used for the laminate were

planar (plane stress) 2D elements. After the model was assembled, the next step was to

add the stitches to the specimen. The stitches were modeled as truss elements, which

were attached by sharing nodes at the very top and bottom of the laminate. This does not

completely characterize how the stitches are truly attached within the physical model but

can be assumed a close approximation. The stitches were assigned isotropic material

properties of Kevlar 29. The stitches were estimated as having a circular cross-section

with the diameter being calculated by knowing that DupontTM Kevlar 29 yarns have a

denier of 1600. Next, the grips were modeled and attached to the laminate, making sure

that all dimensions are representative of the physical setup. Finally, beam elements were

used to model both the top and side bars of the fixture. The beams were assigned the

material properties of steel and the dimensions of the physical model. Careful attention

during the assembly was needed to ensure that no degrees of freedom were constrained

unintentionally. The FE model can be seen in Figures 5-1 and 5-2.



































Figure 5-1: 2D FE model of fixture and laminate


Figure 5-2: FE model showing crack tip and stitches including the stitch bndging
distance









Modeling Results

The J-Integral approach was used to gather both the Gparent and Geef from the FE

models. Each model was loaded with the ultimate failure load of the stitches as measured

from experimental testing. Then the G values were recorded at the crack tip. The J-

Integral approach in the ABAQUS FE software returns a plot of contour number versus

strain energy release rate. An example of this chart is shown in Figure 5-3. One can

observe that near the crack tip the strain energy release rate is approximately 2 lb-in/in2

(3 50 J/m2) which is very representative of the actual fracture toughness value of a

graphite/epoxy laminate. Also, it can be seen that once the contour grows large enough

to include the stitch the strain energy release rate increases to a value of about

53 lb-in/in2, which is similar to the experimental fracture toughness values. The G values

are found in Table 5-1. The importance here more then the actual number values is the

trend of both Gparent and Gerf. Gparent increases as the mode-mixity increases, which agrees

with conventional theory. On the other hand Gegf remains fairly constant over the mixed

mode loading range. This matches the trend observed during experimental testing.

Table 5-1: FE parent and effective fracture toughness
Specimen ID (Low Density) FEM Parent G lb-in/in2 FEM Effective G lb-in/in2
(J/m2) /m2
Mode I 2.3 (403) 53 (9275)
Mixed Mode 1 6.5 (1138) 76 (13300)
Mixed Mode 2 15 (2625) 81 (14175)
Mixed Mode 3 22 (3850) 74 (12950)











Mode 1: Strain Energy Release Rate vs. contour Number

60
55


.c 45
40


S30


S20
15
S10



0 10 20 30 40 50 60 70 80 90 100 110
Contour Number


Figure 5-3: Strain energy release rate versus J-Integral contour number

Additionally, given the stresses incurred at the crack tip the stress intensity factors

were calculated at the crack tip (Table 5-2). From the intensity factors the mixed mode

ratio at the crack tip was calculated.


T =tan K" (5-1)
K,


This local mixed mode ratio (T) is significantly different from the global mixed

mode ratio (W) of which the Eixture was loaded. This may be due to the fact that the

stitches act as a shield, which effectively modifies the loading at the crack tip, such that

the local-stress state defining local mode-mixity is different from the global mode-mixity

defined by the fixture loads. The stitch acts like a cable which carries the Mode I

loading, while allowing the shear stress from the Mode II loading to transfer to the crack

tip. Table 5-3 shows a comparison of the global mixed mode ratio to the local mixed










mode ratio. Further research in this area should be conducted. Experimental work needs

to be done to further characterize the movement of the stitches through the parent

laminate. From this research further refinement of the FE model could be done which

could verify the possibility of the two different mixed mode ratios occurring in stitched

composites.

Table 5-2: Stress intensity factors at crack tip
Specmen ID (Low Density KI ps-iMPa--9m) KII ps-iMPa-lm)
Mode I 2472.9 (2.7) 136.7 (0.15)
Mixed Mode 1 2686.9 (2.95) 2274.2 (2.5)
Mixed Mode 2 2545.0 (2.8) 4702.4 (5.2)
Mixed Mode 3 2066.9 (.3) 6773.2 (.4)


Table 5-3: Global versus local mode-mixity ratios
Speien ID (LwDensity Global Mode Miiy() Local Mode Mxt T
Model 00 30
Mixed Mode 1 8.20 400
Mixed Mode 2 16.00 610
Mixed Mode 3 29.90 740

Crack Propagation Model

To simulate the experimental testing that was performed, a crack propagation

model was created. Initially a given crack length and bridging length is chosen. The

model is loaded and both the strain in the stitches and the energy release rate of the parent

material is monitored. If the strain in the stitches exceeds the failure strain (4%) then the

stitch is considered broken and removed from the model. Additionally, if the strain

energy release rate of the parent material exceeds the critical fracture toughness value the

crack is allowed to propagate. Then this procedure repeats itself. The modeling process

is an iterative one in which the strain and energy release rate are continuously being

measured and compared to the critical values. A linear assumption was used in creating

this model. Therefore the model will not mimic the experimental results perfectly. The









data collected in simulating the loading and failure of one stitch is shown in Table 5-4.

Additionally, Figure 5-4 shows the plot created from this model showing the first stitch

failure .

There is a close agreement between this crack propagation model and the

experimental results which were gathered for a Mode I low density specimen. Failure

occurs at approximately a load of 225 lb. (1000 N) in both cases. The displacement in

the crack propagation model is greater then the experimental case, but this is due to the

fact that the crack propagation model used a linear assumption which did not incorporate

any non-linear effects. Additionally, the load drop after stitch failure is very similar to

that of the experimental case.

Table 5-4: Data needed to simulate crack propagation
Crack Crack Length Displacement Load lb. G lb-in/in2 Stitch
Length from from leading in. (mm) (N) (J/m2) Strain
specimen stitch in.
edge in. (mm)
(mm)
2.55 (64.8) 0 0.318 (8.1) 225 (1000) 45.5 (7963) 0.006
2.634 (66.9) 0.084 (2.1) 0.345 (8.8) 225 27 (4725) 0.0229
2.717 (69.0) 0. 167 (4.2) 0.3 57 (9. 1) 225 8.5 (1488) 0.037
2.8 (71.1) 0.25 (6.4) 0.361 (9.2) 225 1.1 (193) 0.0423
2.884 (73.3) 0.334 (8.5) 0.3655 (9.3) 225 0.02 (3.5) 0.0466
2.967 (75.4) 0.417 (10.6) 0.3644 (9.25) 225 1.17 (204) 0.0462
3.05 (77.5) 0.5 (12.7) 0.3635 (9.23) 225 2.5 (438) 0.0407
3.05* (77.5) 0.5 (12.7) 0.438 (11.1) 225 54 (9450) 0.0067
3.133* (79.6) 0.583 (14.8) 0.472 (12.0) 225 34 (5950) 0.026
3.217* (81.7) 0.667 (16.9) 0.4875 (12.4) 225 12 (2100) 0.043
3.3* (83.8) 0.75 (19. 1) 0.49 (12.45) 225 2.25 (394) 0.051
Note: Denotes leading stitch was removed from FE model to simulate stitch failure













FEMI Load vs. Displacement Crack Propagation Mlodel


250



200



150



oL 100



50


OY
0 0.05 0.1 0.15 0.2 0.25 0.3

Displacement (in.)


Figure 5-4: Crack propagation model showing first stitch failure


0.35 0.4 0.45















CHAPTER 6
CONCLUSIONS

Summary

The research presented in this thesis is an effort to better understand the failure

phenomenon in laminated composites that are reinforced through their thickness with

stitches. Through-the-thickness stitching is a method that increases translaminar strength

while at the same time preventing crack propagation. The fracture toughness of stitched

composites was evaluated under combined Mode I and Mode II loadings (known as

mixed-mode loading). Additionally, a finite element (FE) model was created to be able

to rapidly study the effects of stitching on a laminate under numerous loading conditions.

Conclusions

As a result of this study, the following conclusions were reached.

1. Stitching effectively increases the apparent fracture toughness of stitched
composites. The increase is on the order of 20 fold for low-density stitched
specimens and 40 fold for high-density stitched specimens.

2. For the limited global mode-mixity (7j) range observed (00< r<300), the apparent
fracture toughness Go seems to increase slightly with increasing ry This agrees
with theory as stitches are most effective in tension and keep the fracture
toughness value fairly constant.

3. FE models can be used to accurately simulate the crack propagation in stitched
composites. From these models, the material properties and physical dimensions
of both the parent laminate and stitch can be varied to see what effect these
changes have on apparent fracture toughness.

4. The J-Integral approach can be effectively implemented to evaluate stitched
composites. Care should be taken to make sure that the contour either includes or
excludes the stitches depending if one is interested in the value of Gparent or Gerr
respectively.






39


5. Local and global mode-mixity ratios are not the same for stitched composites.
The stitches effectively modify the loading condition by carrying the tensile
forces while allowing the shearing forces to transfer to the crack tip. Thus,
resulting in higher mixed mode ratios at the crack tip.
















LIST OF REFERENCES


1. Mignery LA, Tan TM and Sun CT. "The Use of Stitching to Suppress
Delamination in Laminated Composites", ASTM STP 876, American Society for
Testing and Materials, 1985, pp 371-385.

2. Dexter HB and Funk JG. "Impact Resistance and Interlaminar Fracture Toughness
of Through-the-Thickness Reinforced Graphite/Epoxy," AIAA paper 86-1020-CP,
1986 pp 700-709.

3. Ridards R and Korj akin A. "Interlaminar Fracture Toughness of GFRP Influenced
by Fiber Surface Treatment," Joumnal of Composite Materials, Vol. 32, No. 17,
1998, pp 1528-1559.

4. Reeder JR and Crews JH Jr. "Mixed Mode Bending Method for Delamination
Testing," AIAA paper Vol. 28, No. 7, Jul. 1990, pp 1270-1276.

5. Reeder JR and Crews JH Jr. "Redesign of the Mixed Mode Bending Delamination
Test to Reduce Nonlinear Effects," Journal Composites Technology and Research
1992 pp 12-18.

6. Chen L, Sankar BV and Ifju PG. "Mixed Mode Fracture Toughness Tests for
Stitched Composite Laminates," AIAA paper 2003-1874, 2003 CD Rom.

7. Anderson TL. Fracture Mechanics: Fundamentals and Applications, Second
Edition, CRC Press, Boca Raton, FL 1995.

8. Sharma SK and Sankar BV. "Effects of Through The Thickness Stitching on
Impact and Interlaminar Fracture Properties of Textile Graphite/Epoxy Laminates,"
NASA Contractor Report 195042, Feb. 1995.

9. Sankar BV and Sharma SK. "Mode II Delamination Toughness of Stitched
Graphite/Epoxy Textile Composites," Joumnal of Composites Science and
Technology, Vol. 57, 1997 pp 729-737.

10. Jain LK, Dransfield KA, and Mai YW. "On the Effects of Stitching in CFRPs-II.
Mode II Delamination Toughness," Journal of Composites Science and
Technology, Vol. 58, 1998 pp 829-837.

11. Gui L and Li Z. "Delamination Buckling of Stitched Laminates," Joumnal of
Composite Science and Technology, Vol. 61, 2001 pp 629-636.









12. Yeh HY, Lee JJ and Yang DYT. "Study of Stitched and Unstitched Composite
Panels Under Shear Loadings," Journal of Aircraft Vol. 41, No.2, March-April
2004 pp 386-392.
















BIOGRAPHICAL SKETCH

Tomek P. Rys was born in Jelenia Gora, Poland, on August 30th, 1980. He

attended public schools in Manhattan, KS, for the first 18 years of his life. After

graduating Manhattan High School in August 1998 he enrolled at Kansas State

University (KSU). Mr. Rys studied mechanical engineering at KSU. He was actively

involved in many activities while attending KSU including Pi Tau Sigma, Tau Beta Pi

and Steel Ring honor societies. He also participated in societies such as S.M.E. and

A.S.M.E. and was also involved in intramural sports.

After graduating from KSU in December of 2002, Mr. Rys decided to attend

graduate school at the University of Florida (UF). Mr. Rys had an interest in composite

materials and therefore chose solid mechanics as his area of specialization for his

graduate studies. His research and focus has been presented in this thesis.

Mr. Rys graduated from UF in August 2004. Upon graduating Mr. Rys accepted a

position as a composites engineer at one of the nation' s largest defense contractors

working on missile systems.