Influence of the Matrix Type on the Mode I Fracture of Carbon-Epoxy Composites Under Dynamic Delamination

The delamination energy and fracture behaviour under static and dynamic mode I loading of two composites, made of the same unidirectional carbon reinforcement embedded in two different matrices, one tough and the other brittle, was investigated with the aim of analyzing the influence of the employed resin on the fatigue delamination behaviour of both composites. In the case of dynamic loading, the number of cycles necessary for the onset of delamination was determined for a given elastic energy release rate and crack growth rate for different critical energy rates. The double cantilever beam (DCB) test was found to be suitable for promoting the initial delamination. The experimental results confirm the enhanced performance of the tough resin both in terms of crack initiation and growth rate.     

Crack-tip damage and fracture toughness of borsic/titanium composite

The fracture behavior of center-notched unidirectional borsic/titanium composites under uniaxial tensile loading has been investigated. Load-crack-opening displacement (COD) curves were obtained for crack length-to-width ratios ranging from 0.05 to 0.5. The COD was measured across the crack surfaces by means of laser interferometric displacement gage (gage length of 500 μm). As expected, the interferometric displacement gage (IDG) was very sensitive to the appearance of damage at the crack tip, yielding nonlinear load-COD curves. The crack-tip damage in borsic/titanium was found to grow coplanarly with the original crack and consist of fiber breaks and matrix plastic deformation, the former preceding the latter. The failure mode and the crack-tip-damage growth were found to be different from those observed in unidirectional boron/aluminum and these differences are discussed. The examination techniques include radiography, SEM, photomicrographs, interference microscope and optical-interferometry technique. It was found that the fracture strengths and crack-tip-damage growth can be analyzed by the analytical models proposed in the literature. The resistance-curve method was also tried and found to be applicable. A correlation has been established among the fracture strength, crack-opening displacement and failure mode.     

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.     

Intrinsic coupling of near-tip matrix crack formation to mode III delamination advance in laminated polymeric matrix composites

Laminated carbon/epoxy specimens are loaded in anti-plane shear to investigate the relationship between near-tip matrix crack formation and the apparent mode III delamination toughness. Specimens are tested with different insert lengths to various load levels and examined fractographically. Near-tip matrix cracks are found to initiate and propagate intralaminarly before the onset of planar growth. These cracks are inclined at approximately 45° to the delamination plane and are perpendicular to the direction of maximum near-tip tensile stress. It is found that this represents an intrinsically coupled sequence of events for anti-plane shear loading of continuous fiber laminated polymeric composites when a preexisting delamination is bounded by plies that have their fiber direction aligned with the direction of macroscopic advance. This sequence of events violates the assumptions used in the reduction of data from common mode III tests. It therefore invalidates the associated toughness measurements, and may account for or strongly contribute to the common observation that laminated polymeric composites exhibit an apparent mode III delamination toughness that is dependent on test geometry.     

Moving interfacial crack between piezoelectric ceramic and elastic layers

An analysis is performed for the problem of a finite Griffith crack moving with constant velocity along the interface of a two-layered strip composed of a piezoelectric ceramic and an elastic layers. The combined out-of-plane mechanical and in-plane electrical loads are applied to the strip. Fourier transforms are used to reduce the problem to a pair of dual integral equations, which is then expressed in terms of a Fredholm integral equation of the second kind. The dynamic stress intensity factor(DSIF) is determined, and numerical results show that DSIF depends on the crack length, the ratio of stiffness and thickness, and the magnitude and direction of electrical loads as well as the crack speed. In case that the crack moves along the interface of piezoelectric and elastic half planes, DSIF is independent of the crack speed.     

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.     

An experimental method for determining dynamic fracture toughness

The boundary and loading conditions in many dynamic fracture test methods are frequently not well defined and, therefore, introduce a degree of uncertainty in the modeling of the experiment to extract the dynamic fracture resistance for a rapidly propagating crack. A new dynamic fracture test method is presented that overcomes many of these difficulties. In this test, a precracked, three-point bend specimen is loaded by a transmitter bar that is impacted by a striker bar fired from a gas gun. Different levels of energy can be imparted to the specimen by varying the speed and length of the striker to induce different crack growth rates in the material. The specimen is instrumented with a crack ladder gage, crack-opening displacement gage and strain gages to develop requisite data to determine toughness. Typical data for AISI 4340 steel specimen are presented. A simple quasi-dynamic analysis model for deducing the fracture toughness for a running crack from these data is presented, and the results are compared with independent measurements.     

Bending effect of through-thickness reinforcement rods on mode I delamination toughness of DCB specimen. I. Linearly elastic and rigid-perfectly plastic models

The use of through-thickness reinforcement in the form of short rods has been proposed to improve the interlaminar properties of laminated composites in the recent years. Compared to a fibrous short rod, which is often referred to as z-fiber, a metallic rod, referred to as z-rod in this paper, has reasonably high capability to carry transverse loading, i.e., a z-rod can provide both axial and transverse bridging tractions to the delamination crack. Therefore, a new analytical model is proposed to study the bending effect of the z-rods on mode I delamination toughness of laminated composites. In this new model, both the axial pull-out and the transverse bending are considered simultaneously. New bending moment and displacement relationships for a single z-rod are established by modeling the z-rod embedded in a linearly elastic and rigid-perfectly plastic matrix using the classical beam theory. By using an approximate expression for mode I fracture toughness of double-cantilever-beam (DCB) specimen, a parametric analysis of DCB specimen reinforced by the z-rods is conducted. The present numerical results show that the bending effect should not be ignored when stiffer z-rods are employed to reinforce the laminated composites.     

Application of carbon-powder-polymer composite as a continuous crack-length sensor

This paper explores the application of carbon-powder-impregnated polymeric composites for measuring crack extensions. The strain sensitivity of the gage material is shown to be very small. In the first series of tests, the gage material is characterized by measuring the change in electrical resistance due to machined slits for various gage lengths. The measured response is compared with the response predicted from a very simple electrical model. On the basis of good correlation and repeatability, the usefulness of such gages to measure crack extensions is assessed by a second series of tests. Further work to improve the gage response by optimizing the shape of the gage and making the gage and the adhesive layer thinner is proposed. The presented concept, with improvements, can result in a reliable, inexpensive crack gage requiring inexpensive instrumentation. Paper was presented at the 1990 SEM Spring Conference on Experimental Mechanics held in Albuquerque, NM on June 3–6.     

Monitoring short fatigue cracks with miniature strain gages

An experimental technique to monitor the length and the opening level of a short fatigue crack is presented. It is based on the progressive decrease with crack length of the response of miniature strain gages installed on the surface near the crack plane. A first gage installed close to the crack plane can monitor cracks from 10 μm in depth to half a millimeter where the response saturates. Other gages at larger distances from the crack plane are less sensitive but can monitor longer cracks. The response is measured so that it is independent of strain-gage calibration, Young's modulus and Poisson's ratio. The paper first presents the basic principles and possibilities of the technique as well as a finite-element analysis performed on automatic welded joints with straight-fronted cracks for which the technique has been developed. The results give a correlation between gage response, crack length and gage location and the conditions of replacement of a gage reaching saturation. The practical exploitation of the technique has required further work to derive a continuous calibration of the gage response that includes corrections to account for the gage finite dimensions and the crack-plane inclination. This calibration is shown to give crack lengths that compare well with fractographic marks and typical results that have been obtained on short crack growth at the weld toe are presented. In particular, the resolution of the technique is put into evidence with results on the initial growth of a 0.1 mm nonpropagating crack. The paper finally points out the distinctive features that appear in current works to adapt the technique to the growth of semi-elliptical cracks of low and high aspect ratio.     

Influence of specimen gage length and loading method on the axial compressive strength of a unidirectional composite material

Various compression test methods for composite materials have been developed during the past few years incorporating specimens of different gage lengths and modes of load introduction. Most of these test methods are not recognized as standards at the present time. Thus the question arises as to whether these various test methods produce similar results.Two commonly used test fixtures are compared in detail here, viz., the ASTM Standard D 3410 IITRI compression test fixture, and another often referred to as the Boeing-Modified D 695 compression test fixture. The IITRI fixture loads a specimen of 12.7-mm gage length via shear through end tabs and wedge grips. The Boeing-Modified D 695 fixture also uses a tabbed specimen, but with only a 4.8-mm gage length and loaded directly on its ends.Hercules S2/3501-6 glass/epoxy and AS4/3501-6 carbon/epoxy unidirectional composites were used as the primary material configurations in the present comparison. Highstrength, highly orthotropic materials such as these are among the most difficult composites to test successfully in compression. However, a carbon/epoxy quasi-isotropic laminate was tested as well.The results obtained are compared with similar data available in the literature. It is concluded that there is relatively little influence of specimen gage length as long as it is sufficiently small so that gross buckling does not occur. Also, the differences between shear loading and end loading of the specimen are small, as long as the ends of the end-loaded specimen do not crush, and that in either case the tabs do not debond.     

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.     

石墨改性碳布复合材料湿式摩擦磨损性能研究

采用树脂浸渍工艺制备了石墨质量分数0%～20%的5种碳布复合材料.借助扫描电镜和湿式摩擦试验机,研究了石墨含量对其表面形貌和摩擦磨损性能的影响.实验结果表明:石墨的固体润滑作用,主要造成了制动过程中动摩擦力矩的下降,而对锁止静摩擦力矩的影响却很小;石墨可以明显降低复合材料的动摩擦系数,并有助于提高动摩擦系数的稳定性;石墨的加入有效降低了碳布复合材料和对偶的磨损率,当石墨含量为15%时复合材料的磨损率最低.引入稳定系数对动摩擦系数的稳定性进行了定量分析,当石墨含量为10%时复合材料的动摩擦系数稳定性最好.     

Strain and failure analysis of graphite/epoxy plates with cracks

The objective of this investigation was to study the deformation and failure of uniaxially loaded graphite/epoxy plates with cracks and to determine the influence of notch size on failure. The specimens were quasi-isotropic laminates with cracks of various lengths. They were instrumented with strain gages, photoelastic coatings and moiré grids. Strains near the crack tip show two distinct points of rate change at strain levels of 0.002 and 0.006, the latter corresponding to the ultimate strain of the 90-deg plies. Failure near the crack tip takes the form of a damage zone consisting of ply subcracking along fibers, local delamination and fiber breakage. Failure occurs when this damage zone reaches some critical value. Measured maximum strains at failure exceeded twice the ultimate strain of the unnotched laminate. The average stress over a characteristic distance (5 mm) from the crack tip was used as a criterion to describe the influence of crack length on failure. Comparison of results with those from similar specimens with circular holes showed that strength was nearly independent of notch geometry in this case, i.e., specimens with holes and cracks of the same size had nearly the same strength.     

Influence on fiber inclination and interfacial conditions on fracture in composite materials

Dynamic photoelasticity has been used to study the effect of the fiber-matrix interface and fiber orientation on dynamic crack growth in fiber composites. Two types of fiber-matrix interfaces are considered: well bonded and partly debonded. The fiber-matrix interface is characterized by conducting fiber pullout tests. Partly debonded fibers aligned with the loading direction, result in higher fiber debonded lengths, lower dynamic stress-intensity factorK _ID and lower fracture surface roughness compared to well bonded fibers. Orientation of brittle fibers, with respect to the loading direction, impairs their ability to lowerK _ID , while oriented ductile fibers produce no significant change inK _ID . Misalignment of fibers from the loading direction reduces the fiber debonded length due to kinding of the fiber at the crack face.     

含分层损伤的变角度纤维层合板后屈曲力学行为研究

变角度（Variable angle tow,简称VAT）纤维复合材料层合板的纤维方向能够连续变化．相较于传统的直线纤维层合板,此类层合板通过刚度变化,整体的屈曲性能可以得到很大的提升．本文利用ABAQUS 自带的粘结单元(Cohesive Element)对预制圆形分层的变角度纤维复合材料层合板进行了后屈曲力学行为研究,得出载荷位移曲线,以及分层裂纹萌生和扩展的情况．然后本文分析了预制分层尺寸对板的刚度、前后屈曲阶段和裂纹萌生及扩展的影响．最后通过变角度纤维层合板和直线纤维层合板的后屈曲力学行为进行对比,深入探索了变角度复合材料层合板在抵抗分层裂纹萌生和扩展方面的优势．     

Mode I crack growth rate for yield strip model of a narrow piezoelectric ceramic body

A crack growth rate equation is found for a finite crack in a narrow transversely isotropic piezoelectric ceramic body under tensile loading. Use is made of the yield strip model. The crack is situated in the mid-plane and is parallel to the edges of the body. Integral transforms are applied to reduce the problem to a Fredholm integral equation of the second kind. The accumulated plastic displacement criterion is applied to crack growth at low stress levels. This results in a small crack growth rate equation with fourth-power stress intensity factor dependence. Numerical examples are given for piezoelectric ceramics and the crack growth rates are plotted as a function of body height to crack length ratio for various values of the electrical loads.     

Effects of voids on postbuckling delamination growth in unidirectional composites

This work examines the effects of manufacturing induced voids on the postbuckling behavior of delaminated unidirectional composites. In the finite element model developed, a through-width delamination is introduced close to one surface of a flat panel, and a void is placed in the delamination plane ahead of each delamination front. The panel is subjected to compression in the fiber direction. The postbuckling delamination growth is studied by calculating the strain energy release rate (SERR) using the virtual crack closure technique. Local stress analyses of the region near the delamination front are also performed to further investigate the void effects. It is found that although the presence of void does not significantly alter the postbuckling transverse displacement of the delaminated panel, the induced stress perturbation by the void affects the SERR. The Mode II SERR as well as the total SERR increase depending on the size of the void and its distance from the delamination front. Since the Mode I SERR shows non-monotonic behavior with the applied load, the effects of voids are studied on its maximum value.     

The effects of bridging in a 3D composite on buckling, postbuckling and growth of delamination

Summary Buckling and postbuckling solutions to circular delamination constrained by transversal restoring forces, which occur extensively in stitched or woven composites with three-dimensional (3D) reinforcement, are obtained by using von Karman's geometrically nonlinear thin plate theory by means of Taylor's series expansion. The through-thickness tows are assumed to provide continuous and linear restoring tractions, opposing the deflection of the annular delaminated region adjacent to a penny-shaped crack. When the end of the delaminated layer is clamped, and the deflection is permitted in the positive direction of the z-axis only, there exists a characteristic delamination radius a _* for initial buckling. In the case that the initial delamination radius a ₀ exceeds a _*, it will consist of waves whose sizes decrease gradually, as they are apart from the delamination center with larger distances, and will usually not span the whole crack region. Therefore, buckling profiles can be divided into two types: (1) lacking contact phenomena between the delaminated layer and the base plate; (2) having contact surfaces inside the delamination region. In this paper, growth laws of buckling, postbuckling and growth of delamination at lacking contact surface are discussed. The corresponding stability of the delamination growth under fixed boundary load is studied, and the dependence of stable scope upon the fracture toughness of the composite and the elastic constant of bridging fiber is summarized. It follows from the analysis that bridging can increase the load-bearing capacity of composite structure, improve its mechanical performances and restrain the growth of delamination. Received 23 November 1998; accepted for publication on 13 January 1999     

Relative orientation constraints in the nonlinear large displacement analysis: application to soft materials

This study dealt with the dynamic stability and geometrical nonlinear problems of carbon nanotube/fiber/polymer composite (CNTFPC) cylindrical panels without or with delamination around a central cutout. A multiscale analysis using the Hewitt and Malherbe model was performed to determine the carbon nanotube (CNT) weight ratios, thickness–radius ratios, thickness–length ratios, and delamination area ratios around a cutout. A delamination around a central cutout was modeled in two dimensions by introducing continuity conditions of displacements at the delamination boundaries. The proposed approach in this study has been verified by previous studies. Parametric results showed the significance of a proper CNT ratio and curvature for better structural performance on the dynamic instability and nonlinearity of delaminated CNTFPC cylindrical panels.