The use of a characteristic damage variable in the study of transverse cracking development under fatigue loading in cross-ply laminates

A two dimensional shear lag analysis of a cracked cross-ply composite laminate subjected to uniaxial loading, taking into account residual thermal stresses, has been developed. This analysis has led us to introduce a characteristic non-dimensional damage variable η, which is a function of the crack density, material properties, and lamina stacking sequence. This analysis has been applied to a CFRP composite material (T300/914). The use of the characteristic damage variable has led to phenomenological laws that allow accurate prediction of the number of fatigue cycles necessary for the initiation of the first matrix cracks, and the kinetics of this damage, up to the “saturation” stage, in any cross-ply laminate subjected to a uniaxial fatigue loading.     

A probabilistic static fatigue model for transverse cracking in CFRP cross-ply laminates

This paper presents a delayed-fracture model for transverse cracking in CFRP cross-ply laminates under static fatigue loading. First, a delayed-fracture model for a crack in a brittle material was established on the basis of the slow crack growth (SCG) concept in conjunction with a probabilistic fracture model using the three-parameter Weibull distribution. Second, the above probabilistic SCG model was applied to transverse cracking in cross-ply laminates under static fatigue loading. The stress and the length of the unit element in the transverse layers were calculated with the aid of a shear-lag analysis, taking the residual stress into account. The transverse crack density was expressed as a function of applied stress and time with the parameters in the Paris law and the Weibull distribution function specified, in addition to the mechanical and geometrical properties. Unknown parameters were determined from experiment data gathered in static tensile and static fatigue tests. The reproduced transverse crack density at various applied loads agreed well with the experiment results.     

A simplified analysis of transverse ply cracking in cross-ply laminates

This paper presents a method of analyzing transverse crack initiation and multiplication in symmetric cross-ply laminates. The method is based on the concept of a through-the-thickness inherent flaw and the energy balance principle. With a second-order polynomial assumed for the crack opening displacement, the perturbed stress field due to the presence of ply cracks is determined from the equilibrium conditions. The energy released as a result of ply cracking is then calculated and used to predict the increase in crack density. Based on an experimental correlation of the analytical result, a resistance curve is proposed to be used as a measure of the resistance to crack multiplication. The resistance to crack multiplication is shown to increase with the increasing crack density.     

Analysis of the transverse cracking in hybrid cross-ply composite laminates

A modified shear-lag analysis, taking into account the concept of interlaminar shear stress, is employed to evaluate the effect of transverse cracks on the stiffness reductions in different glass/epoxy and graphite/epoxy hybrid cross-ply laminates. The modified shear-lag model is proposed that assumes interlaminar adhesive layer between two neighbouring layers transferring not only interlaminar shear stress but also normal stress. The stress distribution is solved by the used model which rigorously satisfies the stress equilibrium equations, boundary conditions and the traction continuity at interfaces between layers.     

On multiple transverse cracking in glass fibre epoxy cross-ply laminates

An investigation has been made of multiple transverse cracking in glass fibre epoxy cross-ply laminates. Four laminates of differing transverse ply thicknesses were investigated. Transverse crack spacing was found to decrease with increasing applied stress and decreasing transverse ply thickness. Very close agreement has been found between the experimental results and a multiple cracking theory based on shear lag analysis in which the plies remain essentially elastically bonded. In these composites a small modulus change is observed at a strain lower than that at which cracking initiated. This phenomenon is associated with a visual, under some circumstances reversible, whitening effect.     

Effect of transverse cracking on stiffness reduction of cross-ply laminates

An analytical model based on the principle of minimum potential energy is developed and applied to study the effect of multiple cracks in cross-plies on the stiffness of a laminated composite. The transverse cracks are assumed to span the thickness of the cross-ply group only partially unlike in the previous studies in which they were assumed to span the entire thickness of the cross-ply group. This arrangement facilitates the study of competition between the self-similar extension of an inherent flaw within the cross-plies and the multiple parallel cracking. The numerical results for the axial stiffness as a function of both the crack density and the crack length are presented for three different composite material systems (glass/epoxy, graphite/epoxy and ceramic/ceramic) or which experimental results are available so as to validate the model.     

On transverse matrix cracking in cross-ply laminates loaded in simple bending

A one-dimensional analysis of a cross-ply laminate, containing cracked transverse plies, loaded in flexure is presented. Simple bending theory is used in conjunction with a shear-lag analysis, to calculate the degraded longitudinal modulus of a cracked transverse ply, enabling the flexural modulus of the laminate to be determined. The solution is shown to agree well with a more sophisticated stress transfer model in the literature. The analysis is then extended to calculate the applied bending moment at transverse crack onset under flexural loading using a fracture mechanics approach. The results suggest that the in situ transverse ply stress at which matrix cracking commences for the beam loaded in flexure is very close to the stress level at which the same ply would crack if the laminate were loaded in tension.     

On cross-ply cracking in glass and carbon fibre-reinforced epoxy laminates

The transverse tensile strength (or fracture strain) of unidirectional fibre-reinforced materials is an important mechanical property. The transverse fracture strain of a single ply in an angle-ply laminate, however, is not an independent mechanical property as it is influenced by its thickness and neighbouring plies. The present investigation describes the phenomenon of multiple fracture of glass and carbon fibre-reinforced epoxy 90° plies. Based on the model that a 90° ply consists of elements all of which can break, the applicability of Weibull statistics in describing the fracture strain is investigated.     

Prediction of initiation of transverse cracks in cross-ply CFRP laminates under fatigue loading by fatigue properties of unidirectional CFRP in 90° direction

A fatigue life to the initiation of transverse cracks in cross-ply carbon fiber-reinforced plastic (CFRP) laminates has been predicted using properties of the fatigue strength of unidirectional CFRP in the 90° direction. In the experiments, unidirectional [90]₁₂ laminates were used to obtain a plot of maximum stress versus number of cycles to breaking, and two types of cross-ply laminates of [0/90₄]_S and [0/90₆]_S were used to evaluate the initiation and multiplication of transverse cracks under fatigue loading. Transverse cracks were studied by optical microscopy and soft X-ray photography. Analytical and experimental results showed good agreement, and the fatigue life for transverse crack initiation in cross-ply laminates was predicted successfully from the fatigue strength properties of the unidirectional CFRP in the 90° direction. The prediction results showed a conservative fatigue life than the experimental results.     

Analysis of transverse cracking and stiffness loss in cross-ply laminates with hygrothermal conditions

The change in longitudinal modulus as a result of transverse ply cracking in simple cross-ply laminate is examined theoretically with the taking into consideration the decrease of the mechanical properties of material by the variation of temperature and moisture. The results show that the hygrothermal environment has a significant effect on the relative reduction of longitudinal Young’s modulus at the higher crack density, in contrast with the complete reduction of longitudinal Young’s modulus in which the sensitivity of the hygrothermal effects become weaker but significant at the lower crack density.     

Time-temperature behavior of carbon/epoxy laminates under creep loading

Mechanics of Time-Dependent Materials - The time-temperature creep behavior of advanced composite laminates is herein determined through a comprehensive set of experiments and analytical modeling....     

Experimental and numerical studies of initial cracking in CFRP cross-ply laminates

This work is concerned with the conditions for formation of the first (initial) cracks in composite laminates with cutouts or ply drop-offs subjected to in-plane loading. We study here the crack formation on the free edge of CFRP cross-ply laminates experimentally and by numerical stress and failure analysis. The free-edge surface strains are measured by the digital image correlation (DIC) technique. The numerical analysis consists of a two-scale approach, where the macro-level analysis is performed with a three-dimensional finite-element method (3D FEM) and the micro-level analysis uses a periodic unit-cell (PUC) in the transverse plies. The constitutive assumption made for the macro-level analysis is an orthotropic linear thermo-elastic solid for the unidirectional plies with a thin isotropic viscoplastic layer between the longitudinal and transverse plies. In the PUC, the fibers are assumed linear elastic, while the matrix is modeled as an elastic–viscoplastic solid. Crack formation is assumed to occur in the matrix by the dilatation induced brittle failure mechanism for which the dilatation energy density criterion is used.     

Ply cracking and stiffness degradation in cross-ply laminates under biaxial extension, bending and thermal loading

Transverse ply cracking often leads to the loss of stiffness and reduction in thermal expansion coefficients. This paper presents the thermoelastic degradation of general cross-ply laminates, containing transverse ply cracks, subjected to biaxial extension, bending and thermal loading. The stress and displacement fields are calculated by using the state space equation method [Zhang D, Ye JQ, Sheng HY. Free-edge and ply cracking effect in cross-ply laminated composites under uniform extension and thermal loading. Compos Struct [in press].]. By this approach, a laminated plate may be composed of an arbitrary number of orthotropic layers, each of which may have different material properties and thickness. The method takes into account all independent material constants and guarantees continuous fields of all interlaminar stresses across interfaces between material layers. After introducing the concept of the effective thermoelastic properties of a laminate, the degradations of axial elastic moduli, Poisson’s ratios, thermal expansion coefficients and flexural moduli are predicted and compared with numerical results from other methods or available test results. It is found that the theory provides good predictions of the stiffness degradation in both symmetric and antisymmetric cross-ply laminates. The predictions of stiffness reduction in nonsymmetric cross-ply laminates can be used as benchmark test for other methods.     

Prediction for progression of transverse cracking in CFRP cross-ply laminates using Monte Carlo method

This study predicted transverse cracking progression in laminates including 90° plies. The refined stress field (RSF) model, which takes into account thermal residual strain for plies including transverse cracks is formulated, and the energy release rate associated with transverse cracking is calculated using this model. For comparison, the energy release rate based on the continuum damage mechanics (CDM) model is formulated. Next, transverse cracking progression in CFRP cross-ply laminates including 90° plies is predicted based on both stress and energy criteria using the Monte Carlo method. The results indicated that the RSF model and the CDM model proposed in this study can predict the experiment results for the relationship between transverse crack density and ply strain in 90° ply. The models presented in this paper can be applied to an arbitrary laminate including 90° plies.     

动态载荷下C/C复合材料的压缩破坏行为

利用电子万能试验机以及Split Hopkinson Compressive Bar(SHPB)测试了2DC/C复合材料在准静态、动态载荷下的压缩性能,结合光学显微镜分析了其在不同应变率下的破坏形貌、讨论了应变率对压缩破坏形貌的影响。结果表明:与准静态(10-4/s)相比,动态载荷下(5×102/s)复合材料的压缩强度提高了55%,压缩刚度提高了66%,具有较强的应变率效应;在准静态载荷下,C/C复合材料沿40°角剪切破坏,断口上炭纤维破坏具有溃散及剪切破坏特征,而在动态载荷下,C/C复合材料破坏成大小不一的碎片,其炭纤维破坏具有劈裂特征。C/C复合材料破坏模式的不同可归结为基体及界面强度的应变率效应。     

Damage mechanics characterization of transverse cracking behavior in quasi-isotropic CFRP laminates with interlaminar-toughened layers

Microscopic damage behavior in quasi-isotropic CFRP laminates with interlaminar-toughened layers under tensile fatigue loading is investigated. Damage observation is conducted using an optical microscope and soft X-ray radiography. The material used is CFRP with interlaminar-toughened layers, T800H/3900-2. The laminate configurations are quasi-isotropic [45/0/−45/90]_s, [0/45/−45/90]_s and [45/−45/0/90]_s to discuss the effect of stacking sequence on microscopic fatigue damages. A damage mechanics analysis is used to obtain the energy release rate for transverse cracking which is correlated to the transverse crack density growth rate. The modified Paris-law analysis proves to be valid for characterization of transverse crack multiplication when the effect of other damage is small.     

Matrix cracking behavior of K3B/IM7 composite laminates subject to static and fatigue loading

The matrix cracking behavior of a new high-performance thermoplastic composite material, K3B/IM7, was systematically investigated. Laminates in various grouped thickness and ply stacking sequences, [0₂/90₂/0₂], [0₂/90₄/0₂], and a quasi-isotropic laminate [+45/0/−45/90]_s were tested under static and tension–tension fatigue loading. Depending on the stacking sequence of the laminates and the type of loading, various matrix cracking behavior were found. Under static loading, the matrix cracks were mainly close to the specimen edges. A few cracks were found to penetrate the specimen width, even when the load was large enough to break the specimen. However, under fatigue cyclic load, the edge initiated cracks propagated fully across the specimen width. Combined with the fatigue Paris Rule and considering the ply thickness and stacking sequence, the energy release rate method was applied to predict the relations between the loading strain amplitude and fatigue cycles for matrix cracking failure.     

Fracture behavior of cross-ply graphite/ epoxy laminates

Fracture behavior of cross-ply (0/90)_4s, (0/90)_10s, (0₂/90₂)_2s and (0₄/90₈/0₄)_T laminates of T300/934 graphite/epoxy material was studied using compact tension specimens of several widths and thicknesses, center notched tension and three point bend specimens. The process of damage initiation and propagation was studied and is discussed in detail. The critical stress intensity factor was evaluated and its variation with specimen size and type is shown. On the basis of these investigations, a suitable specimen for the evaluation of meaningful fracture toughness is suggested.     

Alumina carbon/epoxy laminates under cyclic loading

The behaviour of alumina carbon/epoxy laminate under cyclic loading was investigated. The laminate was constructed by alternating dense alumina thin plates with unidirectional carbon/epoxy (C/E) prepreg tapes. Several cyclic load amplitudes were applied in unidirectional tension, corresponding to the stresses at onset of cracks in the alumina layers. The experimental results revealed high threshold stresses before damage occurred. These threshold stresses are matched with the stresses at onset of cracks in the alumina layers at static tensile tests. When the maximum stresses exceed this threshold, a very rapid stiffness reduction follows. The rate of loss of stiffness was examined. The short range rate was varied as a function of the maximum stress amplitude, but the long-term rate of loss of stiffness was found to be independent of the maximum stresses. A plastic shakedown mechanism was evident for cracked system undergoing high number of cycles, and is attributed to the nearly elastic plastic feature of the epoxy, the bonding agent between the alumina and the C/E layers. This revised version was published online in November 2006 with corrections to the Cover Date.