Journal of Composite Materials

The authors have recently completed two world-wide failure exercises, which dealt with benchmarking recognised failure criteria under two-dimensional and three-dimensional loadings, respectively. A new phase, called the ‘third world-wide failure exercise’ is currently underway to fill some of the major gaps identified in the previous activities. The third world-wide failure exercise is concerned with highlighting the degree of maturity of the current capabilities of 12 internationally recognised methods for modelling various aspects of damage in composite materials. Such problems include matrix cracks due to thermal and mechanical loads; delamination; ply constraint and stacking sequence effects; loading and unloading phenomena; failure due to stress gradients (in particular the hole size effect). The topics addressed within the third world-wide failure exercise represent an extremely important and crucial area for advanced modelling and virtual testing of composites. The third world-wide failure exercise runs in two stages (1) Part A which is devoted to providing full details and a comparison between the 12 theories together with their ‘blind’ predictions, made by their originators, for a challenging set of test problems and (2) Part B which is concerned with comparing the theoretical predictions with experimental results and assessing the accuracy and maturity of the methods. This paper provides details of the background to third world-wide failure exercise, the process of completing Part A and a summary of key conclusions.

This paper gives details of the input data and a full description of a set of 13 test cases provided to the participants of the third world-wide failure exercise for use in their theoretical models. World-wide failure exercise is aimed at benchmarking leading methods, capable of predicting initiation and progression matrix cracking and damage and failure in composites. The originators of leading theories were requested to use the exact input data provided here in their blind predictions of the test cases. The input data include all of the elastic constants, ultimate strains and strengths and the nonlinear stress–strain curves for the unidirectional laminae and their constituents. Various types of laminates, chosen for the analysis, are described together with the lay-up, layer thicknesses, stacking sequences and the loading conditions. Detailed instructions, issued to the contributors, are also presented at the end of this paper.

This article is the author’s contribution to the third World-Wide Failure Exercise which aims at benchmarking current damage models for composites. Reduction of thermo-elastic constants of laminates and their nonlinear behaviour due to intralaminar cracking and nonlinear shear response of the composite are analysed using global–local approach. The macroscopic properties of damaged laminates are expressed in simple forms containing density of intralaminar cracks and their surface displacement features obtained from local solutions. The initiation and evolution of the intralaminar damage is analysed using strength-based approach for laminates with thick layers and fracture mechanics approach for thin layers. Due to a lack of information, certain characteristics, such as statistical failure properties distribution parameters and transition point (thickness) from strength to fracture mechanics applicability, were assumed. All calculations are based on analytical expressions, some of which were developed previously through numerical analysis. The present method was applied to solve 9 out of the 13 test cases of the third World-Wide Failure Exercise and that was sufficient to illustrate the capability of the damage model.

We treat selected test cases in the third world wide failure exercise by the approach described as synergistic damage mechanics. This approach utilizes micromechanics and continuum damage mechanics to predict the overall mechanical response of composite laminates with ply cracking in multiple orientations. The material constants needed in the continuum damage mechanic formulation are calculated from stiffness property changes incurred in a reference laminate. For other laminate configurations, the stiffness changes are derived using a relative constraint parameter which is calculated from the constraint on the opening displacement of ply cracks within the given cracked laminate evaluated numerically by a finite element analysis of appropriately constructed representative unit cell. The number density of ply cracks (cracks per unit length normal to the crack planes) under quasi-static loading is calculated by an energy-based approach. Finally, the stress–strain response of a laminate is determined by combining stiffness property changes and evolution of crack number density.

This paper examines the application of a cohesive zone model to predict the open hole compressive strength of an IM7/8552 carbon fibre/epoxy quasi-isotropic multidirectional laminate and investigates the level-ply scaling or ply blocking effect on notch sensitivity. Cohesive zone models have been successfully applied to predict the damage from notches in engineering materials loaded in tension. They have also been used to determine the growth of fibre microbuckling from a hole in composite laminates under compression. The usual strategy is to replace the inelastic deformation associated with plasticity or microbuckling with a line-crack and to assume some form of stress-displacement (σ − δ) bridging law across the crack faces. Here a plastic fibre kinking analysis and a linear reduced (softening) σ − δ relationship are used for the prediction of the unnotched and open hole compressive strength; the theoretical results will be compared with experimental data in Part B of the 3rd World-Wide Failure Exercise.

This is a contribution to the exercise that aims to benchmark and validate the current continuum damage and fracture mechanics methodologies used for predicting the mechanical behaviour of fibre-reinforced plastic composites under complex loadings. The paper describes an analytical approach to predict the effect of intra- (matrix cracking and splitting) and inter-laminar (delamination) damage on the residual stiffness properties of the laminate, which can be used in the post-initial failure analysis, taking full account of damage mode interaction. The approach is based on a two-dimensional shear lag stress analysis and the equivalent constraint model of the damaged laminate with multiple damaged plies. The application of the approach to predicting degraded stiffness properties of a multidirectional laminate with multilayer intra- and inter-laminar damage is demonstrated for [ 0 / 90 / 0 ] and [ 0 / 90 8 / 0 ] cross-ply laminates made from a specific glass/epoxy system under in-plane uniaxial and biaxial loading damaged by transverse and longitudinal matrix cracks and crack-induced transverse and longitudinal delamination.

This article presents a model, known as generalized Daniels’ model, describing the process of micro-damage accumulation, deformation and failure of multilayered fibre reinforced composite structures under complex internal states of stress responding to external plane-stress loading. The model considers three independent kinds of ply micro-damage: longitudinal, transverse and shear. Non-linear analysis, taking into account scissoring effects, is used to make theoretical predictions for all the 13 test cases involved in the third world-wide failure exercise. The cases cover the biaxial failure behaviour of a unidirectional and multi-directional laminates, failure of thick and thin cross ply and quasi-isotropic laminates under tension, damage due to thermal loading, bending of a general laminate, loading and re-loading and the predictions of the tensile and compressive strength values of test specimens with an open hole. For the prediction of notched strength of laminates with hole, the model is used with a non-local approach based on the specific size of ply microstructure and Neuber’s hyperbola of specific deformation energy. The results are presented for all the 13 test cases.

This article presents the latest developments of a constitutive modelling framework, CODAM (COmposite DAmage Model), for predicting the non-linear in-plane response of composite laminates using continuum damage mechanics. The methodology is best suited for non-linear structural analysis of large-scale laminated composites whose boundaries do not interfere/interact with the damage zone that develops and grows within the structure. The new development presented here, CODAM2, addresses the deficiencies in both the numerical and material objectivity of the original version of CODAM. While the previous CODAM formulation was essentially a local smeared crack model that was augmented with crack band scaling to overcome one aspect of the numerical objectivity, namely the mesh-sensitivity, CODAM2 introduces a non-local regularisation scheme to alleviate both the spurious mesh dependency and mesh orientation problems that plague all local strain-softening models. Two of the 13 test cases, provided in the third-world wide failure exercise, which were related to the in-plane tensile and compressive loading of open hole specimens, were used in order to demonstrate the effectiveness of CODAM2 in predicting the damage development and the corresponding overall response in such structural loading configurations.

This paper represents the authors' contribution to Part A of the third World Wide Failure Exercise where a constitutive model is proposed which considers stiffness degradation and plastic strain accumulation for the prediction of stress–strain curves and failure envelopes of 13 test cases, involving various continuous fiber-reinforced laminates with polymeric matrix materials. The model calibration by means of the provided material data is described and the limits of applicability of the proposed constitutive model are discussed. Finally, the predictions are presented as being obtained without any experimental results available. The test cases consider unidirectional and multidirectional laminates under biaxial loads, laminates under various loading conditions (uniaxial, bending, thermal, loading and unloading) and laminates with open hole under tension or compression. Most of the predictions are documented in terms of stress–strain curves and curves presenting the evolution of brittle damage and of plastic strains.

This paper showcases the authors’ predictions for the 13 challenging test cases of the third World Wide Failure Exercise. The cases involve the prediction of lamina biaxial stress–strain curves, matrix cracking and delamination in various cross-ply and quasi-isotropic laminates under uniaxial loading, variation of thermal expansion coefficient of a laminate with matrix cracking, bending of a general laminate, loading-unloading behaviour and the strength of various thin and thick laminates containing an open hole. The laminates were made of various glass and carbon fibre/epoxy materials. The constitutive model is based on plasticity theory, includes hydrostatic pressure effects and accounts for multiaxial load combination effects. The failure criteria distinguish between matrix failure, fibre kinking and fibre tensile failure. In-situ strengths are used for matrix failure. Propagation of failure takes into consideration the fracture energy associated with each failure mode and, for matrix failure, the accumulation of cracks in the plies. The model is used to make blind predictions of all test cases from the third World-Wide Failure Exercise.

The paper represents the author’s contribution to the Third World-Wide Failure Exercise, which is aimed at benchmarking current models of damage, matrix cracking, initiation of delamination and their interaction with fibre failure. The approach used for the development of damage in laminates is based on an energy methodology that requires knowledge of the dependence of thermo-elastic constants on damage. The various models, developed by the author, are applied to the majority of the Third World-Wide Failure Exercise Test Cases, which included thin and thick cross ply and quasi-isotropic laminates, loading and unloading of an angle ply laminate, bending of a general laminate, and cracking under thermal loadings. Methods used to predict ply properties from those of the fibres and matrix are also described. Crack density in the 90 degree plies was modelled using a ply refinement technique. Detailed discussion is made on a number of relevant issues (initiating defect size and shape, fibre strength, ply saturation, off-axis ply cracking, delamination, mixed mode ply cracking) and their likely effects on design.

Recently, as a part of the third World-Wide Failure Exercise (WWFE-III), the author provided a modelling capability, entitled ‘Energy methods for modelling damage in laminates’, published in this special issue (2013, Vol 20–21, pages 2613–2640). This paper describes full details and the mathematical basis of the author’s methods used to predict the properties of undamaged laminates and the development of damage in laminates, based on an energy balance methodology.

The accurate prediction of damage and failure in laminated composites is still a major issue in many structural applications. The paper provides a detailed description of a new damage mesomodel and examines its application to solve material and structural problems for the Test Cases proposed in the Third World-Wide Failure Exercise (WWFE-III). The cases cover various materials (glass/epoxy and carbon/epoxy), lay-ups (unidirectional, cross ply, quasi-isotropic, angle ply and general multi-directional laminates), loadings (uniaxial, biaxial, bending, thermal and loading-unloading) and features (ply sequence, size effects and open hole). The model deals with various damage scenarios and mechanisms of degradation, including diffuse intralaminar damage, diffuse interface damage, localized delamination, fibre breakage and plasticity, and can predict the evolution of a laminate’s response until final failure. Some issues concerning the limited information available in the exercise for the identification of the parameters of the mesomodel are also discussed.

As a part of a world-wide study, a commercial code (General Optimization Analyzer), based on multi-scale (micro–macro) progressive failure analysis (PFA), is used to provide theoretical predictions for damage development for a set of challenging 13 test cases proposed in the Third World-Wide Failure Exercise (WWFE-III). Multiple failure criteria were utilized aimed at tackling issues related to a wide range of damage modes, being addressed by the WWFE-III. The critical damage events/indexes predictions tracked translaminar and interlaminar composite failures, namely matrix cracking/crack density, damage initiation/propagation, delamination initiation/growth, and their interaction with fiber failure. The composite laminates analysed were both with and without a central hole and the predictions were made using constituent fiber properties and matrix properties based on materials data or identification from ply stress–strain curve inputs. Loadings included uniaxial tension or compression, biaxial, bending, thermal, and loading–unloading.

This paper presents a multiscale hybrid approach for predicting damage and failure of laminated composite structures based on the thermo-mechanical properties (stress/strain behaviour and strength) of the unidirectional plies. This kind of approach is thus predictive for different stacking sequences. The approach introduces viscosity of the matrix in order to obtain an accurate description of the mesoscopic behaviour, especially the non-linearity under shear loading. The failure criterion used is based on physical principles and introduces micromechanical aspects (such as the effect of the local debonding on the non-linear failure behaviour) at the mesoscopic scale. The main improvements, over those proposed in the second world-wide failure exercise, are related to (1) the evolution and effects of the mesoscopic cracks and (2) the coupling between those cracks and delamination (inter-ply damage). This approach has been implemented in an implicit finite element code in order to predict the strength of composite structures, exhibiting different levels of complexity (unnotched plates, open-hole plates) and subjected to complex loadings (membrane or bending loadings). All the 13 Test Cases of the third world-wide failure exercise have been solved.

This paper provides a set of concluding remarks on Part A of the third world-wide failure exercise where a comparison has been made between the capabilities of 12 different mathematical models for predicting the evolution of matrix cracking, damage and failure in continuous fibre-reinforced polymer composites when subjected to multi-axial loading. The originators (or their collaborators) of those theories have employed their methods to 13 carefully selected challenging problems (test cases) addressing the cracking and damage evolution arising from ply thickness, lay-up sequence, size effects and a variety of loading conditions (biaxial, bending, thermal loading and loading-unloading) of a number of unidirectional and multi-directional glass and carbon epoxy laminates. These covered eight different lay-ups consisting of 0°, [0°/90°/0°], [0°/90°₈/0°], [0°/90°]_s, [±45°]_s, [±50°]_s, [30°/90°/−30°/90°]_s and a family of [0°_m/45°_m/90°_m/−45°_m]_s, [45°/0°/90°/−45°]_s and [0°/45°/−45°/90°]_s quasi-isotropic laminates. Key features in each theory are identified including: types of damage models employed, whether linear or nonlinear analysis was carried out, reliance on software and numerical methods and identification of modes of damage. The results of stress–strain curves, crack density and damage curves have been superimposed and bar charts were constructed to show similarities and differences between the predictions of the various theories.