Effect of transverse cracks on the elastic properties of high temperature angle-ply laminated composites

The development of transverse cracks can be detrimental to the stiffness and dimensional stability of composite laminates. In this investigation, a modified shear lag analysis, taking into account the concept of stress perturbation function, is employed to evaluate the effect of transverse cracks on the stiffness reduction in high temperature angle-ply laminated composites. The results present well the effect of high temperature and the fibre orientation of the outer layers on the degradation of mechanical properties of the angle-ply polymer composite laminates.     

Micromechanical characterization of local deformation in interlaminar-toughened CFRP laminates

The in situ SEM micro-line/grid methods were applied for quantitative evaluation of microscopic deformation in interlaminar-toughened CFRP cross-ply laminates with transverse cracks. Both the local deformation in the interlaminar region around the transverse crack tip and the crack opening displacement (COD) were observed at different temperatures to evaluate the effect of thermal residual stress. A two-dimensional approximate elastic analysis of stress and displacement fields in interlaminar-toughened cross-ply laminates with transverse cracks was conducted and compared with the experimental results. A reasonable agreement was obtained which implied the applicability of the analysis. The analysis will be a basis for the optimal design of interlaminar-toughened composite laminates.     

Three-dimensional stress analysis of cracked satin woven carbon fiber reinforced/polymer composites under tension at cryogenic temperatures

We present a thermo-mechanical stress analysis for five harness satin (5HS) woven carbon fiber reinforced polymer (CFRP) composite laminates with cracks under tension at cryogenic temperatures. The three-dimensional finite element model assumes the cracks to be located in the transverse fiber bundles and to span the thickness of the fiber bundles. Numerical calculations are carried out, and the Young’s modulus and stress distributions near the crack fronts for two-layer and infinite-layer woven composite laminates are obtained and shown in graphical form. Results of this analysis demonstrate the effects of the residual thermal stresses and cracks on the mechanical behavior.     

Simulation of fatigue performance of cross-ply composite laminates

The fatigue life of cross-ply composite laminates was evaluated using a statistical model. A modified shear-lag analysis was applied to describe the cycle-number-dependent stiffness reduction and consequent stress redistribution processes in the laminates resulted from both progressive transverse matrix cracking in transverse plies and local delamination at tips of transverse cracks. From the strength degradation behaviour and the static strength distribution of 0° plies as well as the fatigue behaviour of 90° plies, the fatigue life of cross-ply laminates with various types of lay-up can be simulated from the model. Predictions of fatigue performance are compared with experimental data for [0/90₂] _s , [02/90₂] _s and [0₂/90₄] _s graphite/epoxy cross-ply laminates: good agreements are obtained.     

Residual Stiffness of Cracked Cross-Ply Composite Laminates Under Multi-Axial In-plane Loading

In this paper, the Equivalent Constraint Model (ECM) together with a 2-D shear lag stress analysis approach is applied to predict residual stiffness properties of polymer and ceramic matrix [0/90 _n /0] cross-ply laminates subjected to in-plane biaxial loading and damaged by transverse and longitudinal matrix cracks. It is found that the longitudinal Young’s modulus, shear modulus and major Poisson’s ratio undergo large degradation as the matrix crack density increases, with Poisson’s ratio appearing to be the most affected by transverse cracking. In cross-ply laminates with thick 90° layer strip-shaped delaminations begin to initiate and grow from the tips of matrix cracks at the 0°/90° interface. These delaminations contribute to further stiffness degradation of such laminates, and hence have to be taken into account in failure analysis models. The thickness of the 90° layer plays an important role; the thicker the 90° layer, the bigger stiffness reduction suggesting a size (volume) effect at ply level. In SiC/CAS cross-ply laminates reduction in the longitudinal modulus occurs mainly due to transverse cracks, while the shear modulus appears to be the most affected by the presence of longitudinal cracks. The shear modulus reduction ratio predicted previously by a semi-empirical formula is, in the most of cases, within 10% of the current ECM/2-D shear lag approach value. In some cases, though, the error of the semi-empirical finite element expression can be as big as 20% since it fails to capture damage mode interaction.     

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.     

Effect of embedded optical fiber sensors on transverse crack spacing of smart composite structures

In this study the effect of the presence of embedded optical fiber sensors on the transverse cracking of cross-ply laminates was investigated. The transverse crack spacing of cross-ply laminates with embedded optical fiber sensors was predicted using modified shear-lag analysis considering the presence of optical fibers and compared with experimental results. The effect of the orientation and quantity of optical fibers was evaluated and the effect of the coating of optical fiber was also investigated. Specimens were made with transparent glass/epoxy prepreg because the transverse crack and other damages such as delamination, splitting and bleeding of laser can be examined directly and visually. It has been found that the transverse crack spacing was not affected significantly by the embedding of optical fibers at low volume fraction of optical fibers. However, the cracks of specimens with embedded optical fibers which were initiated at a slightly lower stress level showed smaller spacing at the same stress level than those of specimens without embedded optical fibers. The theoretical crack spacing evaluated from the shear lag analysis showed good agreements with experimental results.     

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.     

Matrix cracking and delamination in laminated composites. Part II: Evolution of crack density and delamination

This paper presents a model to predict the propagation of transverse cracks in polymer matrix composite laminates. Different possibilities for the crack pattern are analyzed and the different stress-strain response are compared. Taking into account that matrix cracking promotes delamination between the plies, the propagation of delamination is also simulated. The model predictions are compared with experimental data obtained in composite laminates that accumulate transverse cracks and delaminations before failing catastrophically. The possibility and limitations of a general constitutive law applied at ply level, as a mesomodel, is analyzed and the bounds of applicability of the model are explained.     

Transverse matrix cracks in cross-ply laminates: Stress transfer, stiffness reduction and crack opening profiles

Summary Cross-ply laminates with transverse plies containing through-width matrix cracks across the thickness of the transverse plies are studied using an energy-based approach,complementary to that of Hashin. An upper bound on the effective axial stiffness of the cracked laminates with a uniform distribution of transverse cracks is derived. The equations governing the field variables in a typical RVE are derived using thelayerwise laminate theory of Reddy and are solved using the finite element method. The predicted reduction in the effective axial modulus is in good agreement with experimental results, and it approaches a fixed value with increase in crack density for laminates with bothstaggered andnon-staggered cracking. Laminates with staggered cracks showed a greater reduction in effective modulus at lower crack densities. The stress distribution and mechanics of load transfer is examined in detail, at two crack densities including the characteristic damage state. The crack opening profile has been normalized in a special way in terms of the crack density, layup parameters and material properties.     

High-cycle fatigue characteristics of quasi-isotropic CFRP laminates over 10 cycles (Initiation and propagation of delamination considering interaction with transverse cracks)

High-cycle fatigue features of over 10⁸ cycles, particularly the initiation and propagation of edge delamination considering the effects of transverse cracks, were investigated using quasi-isotropic carbon-fiber-reinforced plastic (CFRP) laminates with a stacking sequence of [45/0/−45/90]_s in this study. In the relationship between a transverse crack density and initiation and growth of edge delamination, it was found that fatigue damage growth behavior varied depending on applied stress. It was observed that edge delamination initiated and grew at parts where transverse cracks were dense at ordinary applied stress, whereas it was observed that edge delamination grew before or simultaneously with transverse crack propagation at a low applied stress and high-cycle loading. In addition, the critical transverse crack density where delamination begins growing was calculated to evaluate the interaction between transverse crack and edge delamination growth.     

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.     

Microscopic observation of voids and transverse crack initiation in CFRP laminates

In situ three-point bending tests under observation using scanning electron microscopy were performed for specimens including voids to investigate the effect of voids on transverse crack initiation in carbon fiber-reinforced plastic (CFRP) laminates. First, initial failure load (i.e. applied load at the first transverse crack initiation) was investigated. Microscopic strain distributions were then measured by digital image correlation analysis using SEM pictures taken before and during loading in the in situ tests. In addition, specimens including voids and transverse cracks after the in situ tests were observed using X-ray computed tomography to clarify transverse crack onset locations with respect to void shapes and distributions. These experiment results suggested that voids actually caused strain concentration and corresponding local plastic deformation, and finally resulted in reduction of macroscopic initial failure strains in CFRP laminates.     

Analysis of composite laminates with transverse cracks

The analysis of the behaviour of composite laminates with general balanced lay-up sequences and containing distributed transverse cracks is discussed and demonstrated in this paper. It is shown that a constitutive model of damage for composites, which has been successfully used to analyse the effects of uniformly distributed transverse cracks in cross-ply laminates, can be readily extended to the analysis of uniformly distributed transverse cracks in more general symmetric laminates. The further extension of the theory to non-uniformly distributed damage can be achieved by finite element analysis. It is shown that the finite element implementation of the theory is particularly simple since the contribution of the damage to the overall behaviour can be incorporated into the force vectors.     

Fracture behavior in CFRP cross-ply laminates with initially cut fibers

This study qualitatively investigates the effects of initially cut fibers (slits) on fracture behavior in carbon fiber reinforced plastic (CFRP) cross-ply laminates, which had alternate or identical slit angle ±θ in the 0° plies. Damage progress during tensile tests was observed for several geometries of cutting. We also numerically evaluated fracture behavior in laminates with slits by a layer-wise finite-element model with cohesive elements. The simulated damage patterns included matrix cracks along the slits, splits in the 0° layer from the slit tips, and transverse cracks in the 90° layer. Delamination was also generated at the crossing point of ply cracks due to the large shear stress, and then extended to form the triangular region bounded by the slits and splits. The predicted damage extension to the final failure agreed with the observations. A numerical study demonstrated that the damage near the slits produced a stress field similar to that of a penetrating notch.     

Free vibration analysis of thick laminated plates using a mixed finite element

Abstract

A mixed finite element scheme based on assumed local high‐order displacements is proposed for the free vibration of thick laminated plates. The effects of transverse shear deformation, transverse normal stress and rotary inertia are considered in the formulation. Cross‐ply laminates with simple supports and angle‐ply laminates with clamped edges are presented as examples. The three dimensional elasticity solutions of cross‐ply laminates with simple supports are used to assess the accuracy of the present scheme. The effects of the span‐to‐thickness, aspect and material anisotropy ratio on the fundamental natural frequency are investigated. The present results are compared with the results in the published literature, and agree closely with the 3‐D elasticity solutions.     

Fatigue damage mechanisms and residual properties of graphite/epoxy laminates

Damage mechanisms and accumulation, and associated stiffness and residual strength reductions were studied in cross-ply graphite/epoxy laminates under cyclic tensile loading. Stress-life data were fitted by a two-parameter wearout model and by a second-degree polynomial on a log-log scale. The fatigue sensitivity is highest for the unidirectional laminates and it decreases for the crossply laminates with increasing number of contiguous 90° plies. Five different damage mechanisms were observed: transverse matrix cracking, dispersed longitudinal cracking, localized longitudinal cracking, delaminations along transverse cracks, and local delaminations at the intersection of longitudinal and transverse cracks. Failure patterns vary with cyclic stress level and number of cycles to failure. Under monotonie loading, failure is brittle-like and concentrated. At high stress amplitudes and short fatigue lives failure results from few localized flaws, whereas at lower stress amplitudes and longer fatigue lives failure results from more dispersed flaws. The residual modulus shows a sharp reduction initially, followed by a more gradual decrease up to failure. The residual strength showed a sharp reduction initially, followed by a plateau or even some increase in the middle part of the fatigue life, and a rapid decrease in the last part of the fatigue life. A tentative cumulative damage model is proposed based on residual strength and the concept of equal damage curves.     

Thermoelastic analysis of cracked woven GFRP laminates at cryogenic temperatures

We deal with the thermal-mechanical response of multi-layered G-11 woven glass/epoxy laminates with cracks and temperature-dependent properties under tension at liquid helium temperature (4 K). The composite material is assumed to be in generalized plane strain. Cracks are located in the fill fiber bundles and are assumed to span the width of the fill fiber bundles. Finite element model is used to study the influence of residual thermal stresses on the mechanical behavior of multi-layered woven laminates with cracks. Numerical calculations are carried out, and the Young's modulus and stress distributions near the crack tip are shown graphically.     

Interaction between transverse cracks and delamination during damage progress in CFRP cross-ply laminates

In previous papers the microscopic failure process of (0/90_n/0) (n = 4,8,12) cross-ply laminates was investigated. Progressive damage parameters, such as the transverse crack density and the delamination ratio, were measured. A simple modified shear-lag analysis including the thermal residual strains was conducted to predict the transverse crack density and the delamination length. The analysis did not consider the interaction between the transverse cracks and the delamination. In the present paper, a prediction is presented for the transverse crack density including the effect of delamination growth. The prediction shows better agreement with the experimental results, especially for laminates with thicker 90 ° plies in which extensive delamination occurs.

Loading/unloading tests have also been performed to obtain the Young's modulus reduction and the permanent strain as functions of the damage state. The shear-lag predictions of the Young's modulus reduction and the permanent strain are compared with the experimental data. Better agreement is obtained when the interaction between transverse cracks and delamination is considered.     

Temperature changes in polymer composites during tensile loading

Temperature changes in polymeric composite laminates subjected to uniaxial monotonic tensile loading were studied. The laminates were transverse and longitudinal unidirectional glass fibre-epoxy and carbon fibre-epoxy laminates, and hybrid crossply laminates with longitudinal glass fibre-epoxy and transverse carbon fibre-epoxy layers. The temperature decreased linearly with increased tensile stress in the elastic region, except for longitudinal carbon fibre specimens (where the fibres have a small but negative coefficient of thermal expansion), which exhibited a small temperature increase. The occurrence of non-linear stress-strain behaviour in transverse carbon fibre specimens altered the rate of temperature change. When cracks appeared in laminates, the temperature immediately started to rise. The temperature changes in crossply laminates were interpreted from measurements on unidirectional specimens and knowledge of the damage mechanisms. This revised version was published online in November 2006 with corrections to the Cover Date.