Behavior of graphite/epoxy plates with holes under biaxial loading

An experimental investigation was conducted to study the behavior under biaxial tensile loading of quasiisotropic graphite/epoxy plates with circular holes and to determine the influence of hole diameter on failure. The specimens were 40 cm×40 cm (16 in.×16 in.) laminates of [0/±45/90] _s layup. Four hole diameters, 2.54 cm (1.00 in.), 1.91 cm (0.75 in.), 1.27 cm (0.50 in.) and 0.64 cm (0.25 in.), were investigated. Deformations and strains were measured using strain gages and birefringent coatings. Equal biaxial loading was introduced by means fo four whiffle-tree grip linkages and controlled with a servohyraulic system. Initially, the circumferential strain is uniform around the boundary of the hole. Subsequently, with increasing load, regions of high strain concentration with nonlinear response develop at eight characteristic locations 22.5 deg off the fiber axes. Failure in the form of cracking and delamination initiates at these points. Maximum strains at failure on the hole boundary reach values up to twice the ultimate strain of the unnotched laminate. The effect of hole diameter on strength was described satisfactorily using an average biaxial-stress criterion. Good correlation was also obtained with theoretical predictions based on a tensor-polynomial failure criterion for the lamina and a progressive degradation model.     

The fracture behavior of graphite/epoxy laminates

The results of uniaxial tensile tests conducted on a variety of graphite/epoxy laminates containing narrow rectangular slits and square or circular holes with various aspect ratios are discussed. The techniques used to study stable-crack or damage-zone growth—namely, birefringence coatings, COD gages, and microscopic observations are discussed. Initial and final-fracture modes are discussed as well as the effect of notch size and shape and laminate type on the fracture process. Characteristic lengths are calculated using the point, average and inherent flaw theories and comparisons with observations are discussed. Further, the effect of flaw geometry on stress states and deformations is assessed.Y. T. Yeow is associated with Allied Chemical Corporation, Morristown, NJ 07960; was formerly Research Associate, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061Paper was presented at 1977 SESA Spring Meeting held in Dallas, TX on May 15–20.     

Closure effects in delaminated graphite epoxy laminate under compression

Flaws in composite laminates may result in a severe loss of static and dynamic strength. Such flaws may be inherent or gained by misadventure. The extent of this loss can be influenced by several factors including loading, laminate stacking sequence, lamina properties, flaw size and damage type.In this study, the free-edge delamination of a laminated composite under compression loading is investigated. Computational, analytical and experimental tests are performed on a graphite/epoxy laminate AS4/3501-6 containing near surface edge defects and the crack opening behaviour is investigated.The computational analysis consists of a three dimensional finite element model where the plies can be catered for individually and interply delamination modelled. In the experimental investigations, a delamination is simulated by inserting teflon film at appropriate locations during the lay-up process.     

Stability of graphite/epoxy structures with arbitrary symmetrical laminates

This paper is concerned with compression testing of thin-walled graphite/epoxy structures and the development of empirical stability methods of analysis. The laminates of the structures tested were T-300/5208 graphite/epoxy with arbitrary, symmetrical stacking sequences. Crippling tests were performed on flat plates to generate no-edge-free and one-edge-free empirical crippling curves for use in buckling analysis of thin-walled graphite/epoxy short columns. Crippling tests of square tubes confirmed correlation with flat plates. Short-column tests of similar square tubes and tests of lsection members substantiated use of the Johnson short-column method. Ultimate compression tests were performed for most laminates, and nonlinear stress-strain curves were recorded in all cases.     

Thermal residual stresses in thick graphite/epoxy composite laminates—Uniaxial approach

Thermal residual stresses have been known to be very large in laminates of continuous-fiber-reinforced polymer composites. When the thickness of the laminate is large, however, the measurement of the residual stresses raises questions on the accuracy of the conventional methods. A novel concept of layer separation is developed to measure quantitatively and precisely the tensile residual stresses in thick plates with layered distribution of residual stresses. It is applied to thick [O₂/9O₄]_13s, AS/3501-6 graphite/epoxy laminates. The test specimens were mechanically modeled into the thin strips for the application of the new concept of layer separation. The tensile residual stresses measured in the 90-deg layers of these laminates are nonuniform throughout the specimen, and vary from 55.6 MPa to 71.4 MPa. It is very interesting to compare these values with the transverse strengthF ₂ ^tu of AS/3501-6 unidirectional composites, which is 65.4 MPa.     

A multidimensional-crack-growth prediction methodology for flaws originating at fastener holes

A multidimensional-crack-growth prediction methodology for flawed fastener holes is described. The methodology uses a slice-synthesis model of the flawed hole for predicting the crack-driving force around the periphery after each increment of advance. Analytic predictions of the crack-growth rate are compared with test results for various examples. It is shown that residual stresses due to yielding at the hole edge and the cycle-by-cycle shape changes are a major cause of apparent crack-growth retardation or acceleration, and that the assumption of a constant shape, as is a common practice, can lead to highly misleading estimates of service life.     

An experimental investigation on the tensile moduli and strengths of graphite/epoxy laminates

The results of a series of tensile tests on graphite/epoxy [0°]_8S and [0°/±30°/0°]_2S laminates at rates varying from 0.002 in/min to 2 in./min are reported. The loads are applied at various angles to the fiber directions in each case. The rate-dependent behavior of the stress-strain response is assessed. Evidence is presented to indicate that failure first occurs on inner plies. Also, evidence is presented to indicate that, in some cases, moduli increase with increased stress or strain level. Lamination theory is used to predict moduli and comparisons with experiment are given. This theory is also used in conjunction with three failure theories to predict ultimate strengths with varying degrees of success. Further, two approaches to ply unloading after first-ply failure are used and discussed. One is a standard method found in the literature while the other is a proposed ‘strength-of-materials’ type of technique which is computationally much simpler.     

On the use of crack-tip-opening displacement to predict the fracture strength of notched graphite/epoxy laminates

The fracture strength and crack-opening displacement of notched graphite/epoxy laminates were measured experimentally using the center-cracked tension-specimen geometry. Four replicate tests were conducted for a variety of laminate stacking sequences, thicknesses, and notch lengths. Most laminates exhibited extensive notch-tip damage prior to fracture. Values of crack-tip-opening displacement (CTOD) at fracture were estimated from values of crack-opening displacement measured at the crack center line. CTOD was independent of specimen crack length for the [0/±45/90] _s , [0/±45/90]_15s , [0/±45] _s , [0/±45/]_15s , and [0/90]_24s laminates. In addition, notched laminate strength was accurately predicted using a Dugdale-type model along with the estimated CTOD.Paper was presented at V International Congress on Experimental Mechanics held in Montreal, Quebec, Canada on June 10–15, 1984.     

Biaxial testing of [O2/±45] s graphite/epoxy plates with holes

An experimental investigation was conducted to study the behavior under biaxial-tensile loading of [O₂/±45] _s graphite/epoxy plates with circular holes and to determine the influence of hole diameter on failure. The specimens were 40-cm×40-cm (16-in.×16-in.) graphite/epoxy plates of [O₂/±45] _s layup. Four hole diameters, 2.54 cm (1.00 in.), 1.91 cm (0.75 in.), 1.27 cm (0.50 in.) and 0.64 cm (0.25 in.), were investigated. Deformations and strains were measured using strain gages and birefringent coatings. Biaxial tension in a 2∶1 ratio was applied by means of four whiffle-tree grip linkages and controlled with a servohydraulic system. Stress and strain redistributions occur around the hole at a stress level corresponding to localized failure around the 67.5-deg location and nonlinear strain response at the 0-deg location. Maximum measured strains at failure on the hole boundary are higher (approximately 0.016) than the highest ultimate strain of the unnotched laminate (0.010). Two basic patterns of failure were observed: (a) horizontal cracking initiating at points off the horizontal axis and accompanied by extensive delamination of the subsurface ±45 deg plies, and (b) vertical cracking along vertical tangents to the hole and accompanied by delamination of the outer 0-deg plies. The strength reduction ratios are lower than corresponding values for uniaxial loading by approximately 16 percent, although the stress-concentration factor under biaxial loading is lower.     

Nonlinear progressive damage model for composite laminates used for low-velocity impact

In order to effectively describe the progressively intralaminar and interlam- inar damage for composite laminates, a three dimensional progressive damage model for composite laminates to be used for low-velocity impact is presented. Being applied to three-dimensional （3D） solid elements and cohesive elements, the nonlinear damage model can be used to analyze the dynamic performance of composite structure and its failure be- havior. For the intralaminar damage, as a function of the energy release rate, the damage model in an exponential function can describe progressive development of the damage. For the interlaminar damage, the damage evolution is described by the framework of the continuum mechanics through cohesive elements. Coding the user subroutine VUMAT of the finite element software ABAQUS/Explicit, the model is applied to an example, i.e., carbon fiber reinforced epoxy composite laminates under low-velocity impact. It is shown that the prediction of damage and deformation agrees well with the experimental results.     

Post-buckling behaviour of graphite/epoxy stiffened panels with initial imperfections subjected to eccentric biaxial compression loading

The post-buckling behaviour of anisotropic stiffened panels with initial imperfections is investigated. Since buckling of the skin between the stiffeners often occurs first, a non-linear analysis is developed for symmetric panels under biaxial compression in order to obtain the out-of-plane panel deflection in the post-buckling range. The non-linear differential equations are expressed in terms of the out-of-plane displacement and the Airy function. They are solved with the Galerkin method for various boundary conditions by imposing an edge displacement control. The theoretical and experimental results obtained by the present analysis show that the transverse load can greatly influence the buckling loads and halfwave number. Since no experimental results have been found in the literature, several tests have been carried out on graphite/epoxy blade stiffened panels 900 mm long and 620 mm wide applying simultaneously biaxial compression loads with several combined ratios. An eccentricity results between longitudinal and transverse load, because the longitudinal compression is applied along the centroidal axes of the stiffened section while the transverse compression is applied to the skin panel. The correlation between the experimental and analytical results has been quite good; the experimental results demonstrate the influence of eccentricity of the transverse load on panel deflection in the pre- and post-buckling range.     

Interlaminar fracture toughness of graphite/epoxy composite under mixed-mode deformations

An antisymmetric test fixture is employed to investigate interlaminar fracture behavior in graphite/epoxy composite material under mixed-mode deformations. Finite correction factors for the graphite/epoxy fracture specimen with various crack lengths are used to determine the interlaminar fracture toughness by finite-element stress analysis. Interlaminar fracture characteristics of graphite/epoxy composite material under mode-I, mode-II and mixed-mode deformations are evaluated experimentally. A mixed-mode fracture criterion is also investigated to obtain information on mixedmode interlaminar fracture behavior of graphite/epoxy composite material.Paper was presented at the 1988 SEM Spring Conference on Experimental Mechanics held in Portland, OR on June 5–10.     

Residual stresses and warpage in woven-glass/epoxy laminates

Residual stresses are introduced in composite laminates during curing as a result of differential thermal expansion of the various plies. Residual stresses coupled with asymmetries in the laminate produce warpage. To study these phenomena, symmetric and asymmetric glass-fabric-reinforced laminates were fabricated. The laminate material was fully characterized by determining its physical and mechanical properties at room and elevated temperatures. Thermal strains during curing and subsequent thermal cycling were measured by means of embedded strain gages. Residual stresses were then calculated using the mechanical properties determined before. Warpage for known types of asymmetry was calculated by means of lamination theory and compared with experimental measurements using a projection moire technique. The residual stresses in the studied laminates were very low, owing to the balancing effect of the woven-fabric reinforcement. A crossplied antisymmetric laminate showed saddle-shaped warpage in agreement with the analytical prediction. Unexpected warpage found in symmetric laminates may be due to imperfections in fiber orientations and/or temperature nonuniformities during laminations. Paper was presented at the 1985 SEM Fall Conference on Experimental Mechanics held in Grenelefe, FL on Nov. 17–20.     

Laser-generated rayleigh waves in graphite/epoxy composites

This study explores the potential for application of laser-induced surface or Rayleigh waves on graphite/epoxy composites. Rayleigh waves were generated by a Q-switched ruby laser in the ablation regime and detected by a pinducer which permitted accurate phase-velocity measurements. The Rayleigh wave velocity was measured in various directions relative to the fiber direction. Experimental results agreed closely with numerical predictions in the thick plate, but showed some increase of phase velocity in the thin plate. Laser-generated Rayleigh waves, particularly along the fiber direction, showed good potential for applications in NDT.     

Delamination-crack propagation in ballistically impacted glass/epoxy composite laminates

For ballistically impacted glass/epoxy cross-ply laminated plates with three five-layer unidirectional laminas, high-speed photos were taken from the back of plates, illuminated from the front side. The semitransparency of the plates enabled a Nova high-speed camera to record delamination-crack propagations at speeds of up to 40,000 frames/s. The delamination crack in the fiber direction of the first (second) lamina at the first (second) interface, propagated initially at 300–400 (400–500) m/s which decreased to 200–300 (270–400) m/s during the period of observation, and decelerated to a stop within 100 (300) μs. This last velocity range (270–400 m/s) agreed well with the largest-amplitude flexural-wave velocity measured by strain gages. This is a documentation that delamination is associated with the flexural wave. A velocity gage consisting of a silver conductive paint was modified to measure propagation velocities of the generator strip which was cut from the first lamina by two through-the-thickness cracks and which initiated a sequential delamination. This generator-strip-formation velocity was higher than the measured delamination-crack-propagation velocity. This fact is consistent with the assumption that the generator strip initiates delamination cracks.     

编织Kevlar/Epoxy复合材料层合板在冲击荷载下的动态响应

通过编织Kevlar/Epoxy复合材料层合板的平头弹冲击实验,分析了结构在不同冲量下的变形失效模式以及结构的抗冲击性能。实验表明复合板的变形失效模式主要表现为:(1)弹性变形;(2)复合板表面嵌入失效及整体塑性大变形;(3)背面纤维拉伸断裂及分层失效。基于实验研究,运用LS-DYNA 971有限元程序对铺层数不同的复合板在冲击载荷作用下的动态响应过程进行了数值模拟,模拟结果与实验吻合较好,子弹作用区域边缘处首先发生近似圆形的嵌入失效,而在板背面发生近似正方形的破坏区域;计算中重点分析了铺层数对结构动力响应的影响,在一定冲量范围内,通过对铺层数的优化,能够有效地减小后面板挠度,提高结构的能量吸收效率,增强结构的抗冲击性能。     

Environmental and fatigue behavior of Kevlar/epoxy composites with prior impact damage

Experimental Techniques -     

Fatigue damage in centrally notched GR/EP laminates

The fatigue properties of graphite/epoxy (Gr/Ep) T300/5208 composite laminates of 16 plies with a central circular hole subjected to tension-tension (T-T) constant-stress amplitudes at room temperature and low humidity have been fully investigated. Studied are four types of notched laminates which are classified as unidirectional, off-axis, orthotropic shear and quasi-isotropic. Some of them were precracked to initiate and guide the crack growth transversely. Our work is experimental and the analysis is based on a semiempirical approach. We have experimentally measured S-N curves, failure surfaces, crack lengths and their corresponding growth directions, delamination areas and transverse delamination lengths for the above series of composites. The fatigue failure mechanism was observed and expressed schematically. To analyze the experimental results, we have categorized the S-N curves by three common equations. The effective transverse crack length of quasi-isotropic laminates was found to be independent of the applied stress. For simplicity, it was modeled by a power law of applied cycles. It was also found that the delamination area could be expressed by a power law of applied cycles. Hence, the so-called modified Paris law, i.e., the power law of cycles, proposed here has been verified as satisfactorily acceptable.     

Imminent fracture detection in graphite/epoxy using acoustic emission

An experiment designed to detect incipient failure in graphite/epoxy tensile specimens is described. Tests using eighteen samples of six different graphite/epoxy compositions in six-ply balanced [0/+45/?45], laminates indicate that a failure precursor does exist. This precursor takes the form of a sudden reduction in the acoustic-emission output at 99 percent of the ultimate tensile load, and evidence indicates that the reduction is the result of a change in the fundamental failure mechanism. The shape of the acoustic-emission countrate curve is analyzed and found to correlate well with micro-mechanical fracture activity.