Cracking In Cross-ply Laminates Research Articles

Equivalent stress concept to account for the effect of local cyclic stress ratio on transverse cracking in tension–tension fatigue

Presented test results on transverse cracking in cross-ply laminates upon tension–tension cyclic loading show that the increase of crack density depends not only on the maximum transverse stress in the cycle but also on the local cyclic stress ratio RTloc in the analyzed layer. To include the effect of the RTloc in the model with statistical failure stress distribution for crack initiation (based on Weibull distribution) adapted for fatigue, an equivalent stress is introduced in a similar manner as the equivalent strain energy release rate has been used for delamination crack propagation. The equivalent stress in the layer is defined as a power function of the maximum stress and the stress ratio in the layer. It was found, testing laminates with two different fiber contents that higher the local stress ratio in 90-layer, higher the transverse cracking resistance. Transverse crack density simulation using the developed equivalent stress model has been validated against test results.

Phase-Field Modeling of Damage and Fracture in Laminated Unidirectional Fiber Reinforced Polymers

The damage and fracture behavior of Fiber Reinforced Polymers (FRPs) is quite complex and is different than the failure behavior of the traditionally employed metals. There are various types of failure mechanisms that can develop during the service life of composite structures. Each of these mechanisms can initiate and propagate independently. However, in practice, they act synergistically and appear simultaneously. The difficulties that engineers face to understand and predict how these different failure mechanisms result in a structural failure enforce them to use high design safety factors and also increases the number of certification tests needed. Considering that the experimental investigations of composites can be limited, very expensive, and time-consuming, in this contribution the newly developed multi Phase-Field (PF) fracture model [1] is employed to numerically study the failure in different Unidirectional Fiber Reinforced Polymers (UFRPs) laminates, namely, fracture in single-edge notched laminated specimens, matrix cracking in cross-ply laminates, and delamination migration in multi-layered UFRPs. The formulation of the PF model incorporates two independent PF variables and length scales to differentiate between fiber and inter-fiber (matrix-dominated) failure mechanisms. The physically motivated failure criterion of Puck is integrated into the model to control the activation and evolution of the PF parameters. The corresponding governing equations in terms of variational formulation is implemented into the Finite Element (FE) code ABAQUS utilizing the user-defined subroutines UMAT and UEL.

Analytical study of transverse cracking in cross-ply laminates under combined loading based on a new coupled micro-meso approach

In this study, an analytical solution based on plane strain model in classical linear elasticity theory is presented for damage analyses of general cross-ply laminates under combined thermo mechanical loading. Equally spaced transverse cracks are considered in any of the 90° plies allows to apply a unit cell based coupled micro-meso model. Thereby, a unit cell includes transverse cracking in the composite ply level is considered to predict the stress and displacement fields that satisfy the equilibrium equations and continuity conditions. Then, a set of fourth order ordinary differential equations is derived and solved by an analytical method. The exact solutions of the differential equations are presented to determine the stress distributions at any point in the laminate subjected to the thermo mechanical in-plane and out-of-plane loadings. It is shown that the predicted stress distributions in the unit-cell are in good agreement with the results of finite element method and the available analytical methods. This method explicitly provides the stress and displacement functions for any point considering transverse cracking, which is an important inquiry for the continuum damage analyses of composite laminates.

The effect of voids on matrix cracking in composite laminates as revealed by combined computations at the micro- and meso-scales

Voids are an important type of manufacturing defects in fiber-reinforced composites. Matrix cracking is sensitive to the presence of voids. Although this cracking occurs at the ply scale, its dynamics is strongly affected by ply’s microstructure, in particular, fiber distribution, fiber content, and the presence of voids. In the current study, a computational approach to simulate the influence of intra-laminar voids on cracking in composite laminates is developed. The approach combines finite element models of two scales: a micro-scale model, where the fibers and voids are modeled explicitly, and a meso-scale model, where the cracking phenomenon is captured on the ply scale. The micro-scale model, incorporating plasticity and damage in the matrix, provides input for the meso-scale model, which simulates the progressive cracking by means of the extended finite element method. The methodology is applied to investigate the effect of voids on the density of transverse cracks in cross-ply laminates in function of the quasi-static tensile load. Different sizes and contents of voids, which are chosen based on experimental micro-computed tomography data, are simulated. The numerical experiments show that the presence of voids leads to earlier start of the cracking, with the crack density evolution less sensitive to voids.

Experimental study of the size effect on transverse cracking in cross-ply laminates and comparison with the main theoretical models

Transverse cracking of off-axis plies is typically the first step of some failure mechanisms in long fiber reinforced laminated composites. It is well known that the off-axis ply thickness affects strongly the strain level which this ply is able to withstand without cracking. Experimental evidences show that this critical strain level increases strongly with decreasing ply thickness for the thinnest plies, confirming a clear size effect. This fact could be used to inhibit transverse cracking with the use of the recently developed ultra-thin plies. However the classical failure criteria for composites are not able to predict this size effect. From the first tests in the 1970s, several models with very different hypotheses were proposed to predict this size effect. Surprisingly there is still not a clear consensus in the scientific community about which is the adequate model, though their fundamentals are radically different. In this work an extensive test campaign is carried out on self-similar [0/90]s cross-ply laminates of AS4/8552 carbon/epoxy. The size effect is evaluated spanning a broader spectrum of thicknesses than in the tests presented in the literature until now, in order to explore the range of thicknesses where the differences between predictions of the main theoretical models are larger. In spite of the inherent dispersion in the experimental results, the comparison shows that the purely stress-based criteria underestimates the apparent strength of the off-axis ply. The other models predict very similar results, particularly for the thinnest laminates, with slight underestimations or overestimations, depending on the model.

Modelling Cracked Cross-Ply Laminates with Delamination Buckling

The mechanical behavior of cross-ply laminates loaded under in-plane compression containing matrix cracks and delaminations is investigated in order to study their influence on the structural stability behavior. This is done by employing a semi-analytical modelling approach which comprises an analytical framework for a structural stability analysis of damageable structures and the Equivalent Constrained Model for deriving reduced stiffness properties of the cracked layers. Cross-ply laminates with varying delamination depths as well as varying matrix crack densities are studied.

The effect of residual thermal stresses on transverse cracking in cross-ply laminates: an application of the coupled criterion of the finite fracture mechanics

A model to predict transverse cracking in cross-ply laminates in the presence of residual thermal stresses is developed here. This model is based on the coupled criterion of the finite fracture mechanics. This criterion has been successfully used for different materials, structures and scales to predict crack initiation. It is based on two main hypotheses: (i) crack initiation occurs as a finite-length crack onset and (ii) the crack onset requires that both stress and energy criteria are fulfilled simultaneously. The present model is developed under the generalized-plane-strain hypotheses combining the results obtained using the laminate theory and a boundary element code. The present analysis shows that the residual thermal stresses affect both the stress and the energy criteria in the form of adding a residual elastic-strain to the strain imposed by external mechanical loads. An explicit expression for this residual elastic-strain is provided. For certain composite materials as carbon/epoxy the value of this residual elastic-strain is shown to be relatively large in comparison with the nominal critical transverse strain of the material. The comparison with experiments shows that considering the residual thermal stresses using the strategy proposed here improves drastically the accuracy of the model predictions.

A numerical study of transverse cracking in cross-ply laminates by 3D finite fracture mechanics

Abstract Transverse cracking in cross-ply laminates is a key failure mechanism which needs to be understood in order to predict the failure initiation in these laminates. A new 2D model has recently been presented (Garcia et al., Int J Solids Struct 51, pp. 3844–3856, 2014) for predicting the first crack onsets in cross-ply laminates under tensile loading, which is based on the coupled criterion of the Finite Fracture Mechanics (FFM). This 2D model is able to predict a strong size effect on the critical strain leading to the first crack onsets, which agrees with some experiments found in the literature. However, some earlier studies have shown that the 3D effects can be relevant in determining the origin of the size effect found in these experiments. Therefore, a 3D application of the coupled criterion, which formulates this criterion as an optimization problem, is proposed here. The objective function to be minimized, under the stress and energy criteria described previously, is the critical strain leading to the first crack onset. The finite number of variables of the optimization define the crack geometry after its onset. Since the crack geometry is parametrized, the variables in the optimization are the parameters defining the crack geometry. The objective function is evaluated by combining FRANC3D and Abaqus. As occurs in the 2D model, the results predict the strong influence of the transverse-ply thickness on the process of transverse cracking. In particular, a slightly larger critical strain is predicted for thinner laminates. In addition, the optimal crack position also varies with the thickness: a free-edge crack onset is predicted for thick laminates, whereas for thin ones, the inside and free-edge crack positions are essentially equivalent.

FBG-based real-time evaluation of transverse cracking in cross-ply laminates

Transverse cracking is one of the most common initial failure modes of composites and has detrimental effects on the structural integrity. In this paper a novel real-time non-destructive testing method is proposed to evaluate the transverse cracking in cross-ply laminates. The FBG sensors were embedded in the cross-ply specimens [02/90n]s and [90n/02]s, n=2,3,4, at the interface along the fiber direction. The Digital Image Correlation measurement was applied in the tensile testing to determine the density of the transverse cracks. The FBG spectrum was distorted as the crack density increased and its width at a quarter of the peak w1/4 showed a high correlation with the crack density. A numerical method based on spectrum reconstruction using the Transfer Matrix Method was then introduced to investigate the relations between spectrum distortion and transverse cracking. The reconstructed spectrum has an accurate reproduction of the reflective spectrum of FBG. The results demonstrate that the spectrum distortion attributes to the non-uniform distributions of the longitudinal strain due to the transverse cracks and w1/4 can be applied as an effective indicator to evaluate the transverse crack density. The demodulation method using the FBG spectrum can be used to real-time detect the internal transverse cracks of composites.

XFEM simulation of delamination in composite laminates

In this paper, the extended finite element method (XFEM) is extended to simulate delamination problems in composite laminates. A crack-leading model is proposed and implemented in the ABAQUS® to discriminate different delamination morphologies, i.e., the 0°/0° interface in unidirectional laminates and the 0°/90° interface in multidirectional laminates, which accounts for both interlaminar and intralaminar crack propagation. Three typical delamination problems were simulated and verified. The results of single delamination in unidirectional laminates under pure mode I, mode II, and mixed mode I/II correspond well with the analytical solutions. The results of multiple delaminations in unidirectional laminates are in good agreement with experimental data. Finally, using a recently proposed test that characterizes the interaction of delamination and matrix cracks in cross-ply laminates, the present numerical results of the delamination migration caused by the coupled failure mechanisms are consistent with experimental observations.

Experimental and numerical study of oblique transverse cracking in cross-ply laminates under tension

The first damage mode in cross-ply laminates under tension is broadly accepted as transverse cracks normal to the loading direction in the 90° layers, but there is not the same agreement about the second damage mode. While most of the analytical and experimental results are based on delamination induced by transverse cracking, another type of damage, oblique cracks within the 90° layers, has also been observed as the second damage mode in [0/904]s laminates. To understand the cause of this phenomenon, FE analyses considering damage development at the interfaces were performed. The obtained results indicate that the main reason for the oblique cracking damage mode is the higher toughness of the material in mode-II compared with mode-I: when the value of shear toughness is close to the opening toughness, the second damage mode in cross-ply laminates under tensile loading is delamination induced by transverse cracks, however, if the difference between the two values is large, oblique cracks in the 90° layers are likely to appear. In the specific tested and analysed laminate, if the mode II toughness is double the mode I toughness, oblique cracking occurs but if the values of mode I and mode II toughness are close, delamination is the second damage mode.

Statistical methodology for assessing manufacturing quality related to transverse cracking in cross ply laminates

Abstract We present a statistical analysis based methodology for making assessment of the manufacturing quality of cross ply composite laminates as it relates to its effect on transverse cracking evolution. Assuming a two-parameter Weibull distribution of tensile strength of the transverse plies to represent randomly distributed manufacturing defects, multiple crack formation in the plies is simulated in the non-interactive and interactive regimes of cracking using the local stress fields calculated by a variational analysis. The statistical methodology is demonstrated on crack density evolution in cross ply laminates manufactured by four different processing routes and loaded in monotonic tension in the axial direction. The differences in the crack density evolution, supposedly due to different defect population induced by the four manufacturing conditions, could be described by the proposed statistical simulation method.

Statistical analysis of oblique crack evolution in composite laminates

A previously developed statistical model for transverse cracking in cross ply laminates is extended to oblique cracking in multidirectional laminates. The oblique cracks are assumed to form in a ply when the local in-plane tensile stress normal to fibers exceeds the transverse strength of the ply. This strength is assumed to have a statistical distribution given by a two-parameter Weibull function. The model is applied to a glass–epoxy [0/602/0/−602]s laminate in which cracking evolution of the four −60° plies in the middle of the laminate is examined. The local stress field in the cracked −60° plies is calculated by a three-dimensional finite element method based on a unit cell construction developed by Li et al. [1]. The measured crack density is found to agree well with that calculated by the statistical model.

Cohesive modeling of transverse cracking in laminates under in-plane loading with a single layer of elements per ply

This study aims to bridge the gap between classical understanding of transverse cracking in cross-ply laminates and recent computational methods for the modeling of progressive laminate failure. Specifically, the study investigates under what conditions a finite element model with cohesive X-FEM cracks can reproduce the in situ effect for the ply strength. It is shown that it is possible to do so with a single element across the thickness of the ply, provided that the interface stiffness is properly selected. The optimal value for this interface stiffness is derived with an analytical shear lag model. It is also shown that, when the appropriate statistical variation of properties has been applied, models with a single element through the thickness of a ply can predict the density of transverse matrix cracks.

Use of full-field measurements to evaluate analytical models for laminates with intralaminar cracks

Full-field displacement measurements between intralaminar cracks in cross-ply laminates were performed to evaluate the accuracy of shear lag models and Hashin’s model. The dependence of the average crack opening displacement on the crack density was measured and compared with model predictions. It was found that Hashin’s model overestimates the average COD by at least 25%. The value of the shear lag parameter was back-calculated by fitting. With the same goal the strain in the middle between two cracks was measured rendering shear lag parameter which was only 1% different. The found value does not agree with any of the used shear lag models. Measurement shows nonzero intralaminar shear zones in both layers covering a part of the ply thickness.

Evaluation of Edge Cracks in Cross-Ply Laminates Using Image Correlation and Thermoelastic Stress Analysis

The paper describes initial work on using 2D digital image correlation (DIC) and thermoelastic stress analysis (TSA) to obtain data from edge cracks in cross-ply laminates. It is demonstrated that detailed data related to the crack tip stresses can be obtained using TSA. The work reveals some of the limitations experienced when using DIC in applications where high spatial resolution is required. A detailed discussion is provided along with an outline for future work.

A Probabilistic SCG Model for Transverse Cracking in CFRP Cross-ply Laminates under Cyclic Loading

This paper presents a probabilistic fatigue model for transverse cracking in CFRP cross-ply laminates. First, a delayed fracture model for a crack in a brittle material subjected to cyclic loading was established on the basis of the slow crack growth (SCG) concept in conjunction with the Weibull's probabilistic failure model. Second, the above probabilistic delayed fracture model was applied to transverse cracking in cross-ply laminates during cyclic loading. The stress distribution and the length of the unit element were calculated with the aid of a shear lag analysis. The transverse crack density was expressed as a function of maximum stress, stress ratio and number of cycles using the parameters associated with the Paris equation and the Weibull distribution in addition to the mechanical properties. Unknown parameters were determined from experiment data for three kinds of cross-ply laminates to reproduce the transverse crack density against the number of cycles. The parametric studies using the obtained parameters revealed the effects of the Weibull modulus, crack propagation exponent and stress ratio on evolution of transverse cracking under 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.

Statistical model of the transverse ply cracking in cross-ply laminates by strength and fracture toughness based failure criteria

Cross-ply laminate subjected to tensile loading provides a relatively well understood and widely used model system for studying progressive cracking of the transverse ply. This test allows to identify material strength and/or toughness characteristics as well as to establish relation between damage level and the composite stiffness reduction. The transverse ply cracking is an inherently stochastic process due to the random variability of local material properties of the plies. The variability affects both crack initiation (governed by the local strength) and propagation (governed by the local fracture toughness). The primary aim of the present study is elucidation of the relative importance of these phenomena in the fragmentation process at different transverse and longitudinal ply thickness ratios. The effect of the random crack distribution on the mechanical properties reduction of the laminate is also considered. Transverse ply cracking in glass fiber/epoxy cross-ply laminates of the lay-ups [0 2/90 2] s, [0/90 2] s, and [0/90 4] s is studied. Several specimens of each lay-up were subjected to uniaxial quasistatic tension to obtain crack density as a function of applied strain. Crack spacing distributions at the edge of the specimen also were determined at a predefined applied strain. Statistical model of the cracking process is derived, calibrated using crack density vs. strain data, and verified against the measured crack spacing distributions.

Effects of nonlinear viscoelastic behaviour and loading rate on transverse cracking in CFRP laminates

The progressive multiplication of matrix transverse cracks in cross-ply laminates made of long carbon fibre reinforced polymer (CFRP) is addressed in this study. Monotonic tensile tests performed on [03/903]S laminates at 120°C have shown a marked dependence of cracking development on loading rate. This paper aims to assess the impact of the material nonlinearity on the loading rate sensitivity of the damaging process. A “shear-lag” damage analysis, using the nonlinear correspondence principle and appropriate failure criteria, is carried out to numerically predict the cracking evolution. This work shows that, though important, the material nonlinearity of the undamaged material does not significantly enhance the loading rate sensitivity of the cracking process and it cannot explain alone the phenomenon. On the other hand, taking into account the loading rate dependence of the critical strength, together with the R-curve effect, which gives good predicted cracking curves, suggests that the observed rate effect pertains to the viscoelastic character of the damaged material in the process zone close to crack fronts.