Journal of Composite Materials

In 2004, the authors completed the First World-Wide Failure Exercise dealing with benchmarking recognised failure criteria under two-dimensional, in-plane loadings. Based on the success and the lessons learnt, and using the same strategy, the authors have organised the ‘Second World-Wide Failure Exercise’. It aims at filling key gaps identified and establishing the status of 12 theoretical methods for predicting failure in fibre-reinforced composite materials subjected to three-dimensional or (triaxial) states of stress. This paper gives an account of the background to the Second World-Wide Failure Exercise, the process of completing the first part (Part A) and a summary of key conclusions.

This article gives details of the input data provided for use in the Second World-Wide Failure Exercise (WWFE-II) for benchmarking triaxial failure criteria. It includes (a) three-dimensional elastic constants, ultimate strains and strengths and the nonlinear stress–strain curves for five unidirectional laminae and their constituents and (b) a description of 12 challenging test cases of 5 composite laminates, the lay-ups, layer thicknesses, stacking sequences and the loading conditions. The originators of 3D failure theories were requested to use the exact data provided here in their blind predictions of the test cases. The instructions issued to the contributors are also presented at the end of this article.

This paper presents a pressure-dependent three-dimensional constitutive law to predict failure for laminated composites. The nonlinear constitutive response in shear and in the transverse and through-the-thickness directions, which is measured experimentally, is incorporated directly into the model. In addition, secant stiffnesses are dependent on the state of hydrostatic pressure and on the general state of strain. 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. A detailed discussion is undertaken of the mismatch between the available experimental data and the physical properties required to characterise the constitutive response up to final failure. The model is employed to make blind predictions of the triaxial failure envelopes and stress–strain curves of all 12 test cases provided by the organisers of the second World-Wide Failure Exercise.

A pseudo three-dimensional laminate theory is incorporated with the three-dimensional bridging model, based on micromechanics formulae, to predict failure under triaxial loads. A lamina failure is considered to occur as long as any of its constituents has failed. A laminate ultimate failure is assumed to take place when the fibres have failed or when the resin has failed in compression. In order to account for the effect of a three-dimensional compression on increasing the load-carrying ability of a resin material, a modified maximum compressive stress failure criterion is introduced. The methodology was used successfully to solve all the 12 challenging test cases of the Second World-Wide Failure Exercise.

The present article describes the application of Rotem failure criterion to solve 12 test cases employed in the Second World-Wide Failure Exercise (WWFE-II). The criterion distinguishes between fiber failure and matrix failures (transverse-isotropic strength and the square of the deviatory and shear strengths). Effect of hydrostatic pressure is taken into account for the matrix dominated failure. The nonlinear progressive model is used to predict three-dimensional failure envelopes and stress strain curves for all 12 test cases, which involved isotropic, unidirectional lamina and multi-directional laminates loaded both through-thickness and in-plane directions. The calculation technique and the final results are given in the article.

A new micromechanical-based hybrid mesoscopic 3D approach has presented for the prediction of failure under triaxial loadings. The failure criterion is based on physical principles and introduces micromechanical aspects (such as the effect of the local debonding) at the mesoscopic scale. It is capable of distinguishing between various modes of failure (e.g. fibre tension, fibre compression, in-plane and through-thickness interfibre (matrix or fibre/matrix failure modes). The model was successfully implemented to provide predictions of failure envelopes and non-linear stress–strain curves of isotropic, unidirectional and mutli-directional laminates made of glass/epoxy and carbon/epoxy materials and subjected to 3D loadings, including through-thickness stresses.

This article presents a methodology for predicting the stress–strain response and failure behavior of fiber composite laminates. First, a stress transfer method is proposed by using the concept of the state space equation. The generalized plane strain deformation is assumed in the model. The state space equation was derived by using Fourier series expansions in the width direction and the layer refinement technique through the thickness. Secondly, Christensen’s stress-based failure criteria are adopted to predict failure of individual plies. Finally, the applications of the methodology are shown by predicting the failure envelopes and stress–strain curves of the test cases provided by the organizers of the Second World-Wide Failure Exercise (WWFE-II).

A three-dimensional micromechanics of failure model was developed and applied in order to predict triaxial failure envelopes and stress–strain curves for 12 test cases in the Second World-Wide Failure Exercise (WWFE-II), which involves five continuous fiber–matrix laminates and multi-axial loadings, including those in through-thickness direction. The micromechanics of failure is based on micromechanical unit cell models, which characterize the microstructure of composites, and consists of independent constituent failure criteria and a progressive damage model for the matrix. Nonlinear ply behavior in the matrix-dominant directions was successfully simulated. Thermal stresses were also considered. Results of prediction were presented together with an explanation of the phenomena.

As a part of the Second World-Wide Failure Exercise, a three-dimensional nonlinear maximum progressive strain model, based on laminate analysis, is employed to make blind predictions for 12 test cases representing failure envelopes and stress strain curves for isotropic, unidirectional, and multidirectional composite laminates. This approach allows for redistribution of ply stresses and differentiation of the various potential modes of failure. These cases include initial and final ply failure envelopes under tri-axial loading, as well as 3 cases, requiring nonlinear stress–strain analysis. Comparison of predictions with actual experimental data will be made in Part B of the Second World-Wide Failure Exercise.

Triaxial failure analysis using multicontinuum decomposition has been employed at the constituent level to predict nonlinear damage behavior and failure envelopes, all involving through-thickness stresses. In addition, a structural analysis algorithm is presented and is found to be numerically highly efficient in that the relationships between composite properties and damaged or failed constituent properties are completely determined prior to structural analysis. As a part of the Second World-Wide Failure Exercise, three-dimensional failure envelopes and stress–strain curves involving isotropic materials as well various unidirectional and multi-directional materials are presented for 12 test cases requested by the organizers. The present paper provides new developments in the multicontinuum methodology including: (a) modification of the constituent failure criteria, (b) incorporation of pressure effects, (c) new damage analyses, and (d) implementation into a commercial finite element package. Correlation with experimental results is provided in a second article addressing Part B of the Second World-Wide Failure Exercise.

The objectives of this article are to apply Puck’s failure criteria to predict the failure of 12 test problems, proposed in Part A of the second World-Wide Failure Exercise. These problems include a polymer material, various unidirectional laminae and three multi-directional laminates under a variety of 3D stress loadings. The implementation was carried out through a commercial finite element code where material nonlinearities, due to material behaviour under shear and transverse and through-thickness loadings and due to post failure damage, were taken into account. This is the first time where the critertion has been stretched to its limits. Some of the challenges found include the need to determine the fracture angle of action plane under 3D stresses and the treatment of the strengthening effects on the nonlinear stress strain curves when a lamina is subjected to combined compressive stresses in both the transverse and through-thickness directions. The successful methodology developed here will be used to analyse the effects of boundary conditions in Part B of the second World-Wide Failure Exercise to improve correlation with experimental results for the test problems.

A new strain energy based failure model is developed for fibrous composite laminates under multi-axial loadings, taking into account the effect of hydrostatic stress. A failure mode dependent exponential stiffness reduction model is used to predict material response beyond the initial failure. Predicted mechanical responses and failure envelopes are presented for the 12 benchmark test cases of Part A of the Second World Wide Failure Exercise. The cases cover a wide variety of isotropic, unidirectional and multidirectional laminates under combined in-plane, out-of-plane and triaxial loadings. Both stress–strain curves and the complete failure envelopes were successfully predicted. In some instances, the failure envelopes were open. The predictions together with suitable adjustment of certain parameters are compared with test data in Part B of the Second World Wide Failure Exercise, to be published in Journal of Composite Materials.

The second world-wide failure exercise is an international activity, organised by Kaddour and Hinton, aiming at a better understanding of the limitations of existing failure criteria to predict failure under triaxial stressing. The present work is a response to an invitation to take part and employ Hashin's failure criteria to the 12 test cases defined by the organizers of the second world-wide failure exercise. Methods, based on nonlinear analysis, used to perform the required simulations are explained and the predictions are presented. Observed problems are discussed.

This paper represents the author’s contribution to the second world-wide failure exercise using his failure mode concept modelling capability. The second world-wide failure exercise deals with the behaviour of isotropic material and unidirectional as well as multidirectional unidirectional laminae-composed laminates subjected to three-dimensional (triaxial) states of stress. Twelve challenging test cases were provided by the organisers and those covered stress–strain curves and failure envelopes under three-dimensional stress states. The application of the new failure mode concept model has extended the three-dimensional modelling by taking into account the effects of hydrostatic pressure and second glass temperature shift factor on the stress–strain curves and failure envelopes. The failure mode concept model was capable of successfully solving the majority of all the problems and a comparison between the predictions and test data is planned to be published in Part B of the second world-wide failure exercise.

As a part of the Second World-Wide Failure Exercise, the originators (or their collaborators) of three-dimensional failure theories applied their methods to 12 carefully selected challenging problems (test cases). In this article, the ‘blind’ theoretical predictions from 12 failure theories, making the backbone of Part (A) of the Second World-Wide Failure Exercise, are compiled in a structured manner. Key features in each theory are identified including: types of failure models employed, whether linear or nonlinear analysis was carried out, reliance on software and numerical methods, allowance for thermal stresses and identification of modes of failure. The results (failure envelopes and stress–strain curves) have been superimposed to show similarities and differences between the predictions of the various theories. In addition, bar charts have been constructed to demonstrate the levels of agreement between the predicted failure stresses and strains. Sources of differences between the predictions of the various three-dimensional failure theories are discussed. Further publications are planned in Part B in which comparison will be made between the predictions described here and the experimental results.