A.S. Kaddour

A comparison of the predictive capabilities of current failure theories for composite laminates, judged against experimental evidence

Abstract This paper draws together the results from a co-ordinated study, known as the World-Wide Failure Exercise, whereby 12 of the leading theories for predicting failure in composite laminates have been tested against experimental evidence. The comparison has been effected through 14 carefully selected test cases, which include biaxial strength envelopes for a range of unidirectional and multi-directional laminates, and stress–strain curves for a range of multi-directional laminates, loaded under uniaxial or biaxial conditions. The predictions were provided by the originators of the theories, not by third parties, and were made without access to the experimental results beforehand. The predictions and experimental data have been compared in a systematic and detailed manner, to identify the strengths and weaknesses of each theory, together with a ranking of the overall effectiveness of each theory. Careful reading of this analysis and study of the figures provided will inform the reader when selecting an appropriate failure theory for use in a given design situation. It will also provide a qualitative assessment of the likely accuracy and reliability of the prediction in a given circumstance.

Recommendations for designers and researchers resulting from the world-wide failure exercise

The World-Wide Failure Exercise (WWFE) contained a detailed assessment of 19 theoretical approaches for predicting the deformation and failure response of polymer composite laminates when subjected to complex states of stress. The leading five theories are explored in greater detail to demonstrate their strengths and weaknesses in predicting various types of structural failure. Recommendations are then derived, as to how the theories can be best utilised to provide safe and economic predictions in a wide range of engineering design applications. Further guidance is provided for designers on the level of confidence and bounds of applicability of the current theories. The need for careful interpretation of initial failure predictions is emphasised, as is the need to allow for multiple sources of non-linearity (including progressive damage) where accuracy is sought for certain classes of large deformation and final failure strength predictions. Aspects requiring further experimental and theoretical investigation are identified. Direction is also provided to the research community by highlighting specific, tightly focussed, experimental and theoretical studies that, if carried out in the very near future, would pay great dividends from the designers perspective, by increasing their confidence in the theoretical foundations.

Biaxial test results for strength and deformation of a range of E-glass and carbon fibre reinforced composite laminates: Failure exercise benchmark data

Abstract In Part A of the World Wide Failure Exercise (published in Composite Science and Technology , Vol 58, No 7, 1998), all contributors were given exactly the same set of material properties and were asked to predict the strength and deformation of the same set of laminates under a range of specified loading conditions. In this part (Part B) of the exercise, available experimental results are superimposed on the theoretical predictions and returned to the contributors for comment. The test data were for (a) 0° unidirectional laminae under biaxial direct and shear loads (b) (90°/±30°) s , (0°/±45°/90°) s , (±55°) s multi-directional laminates under biaxial loads and (c) stress strain curves for (0°/±45°/90°) s , (±55°) s , (±45°) s and (0°/90°) s laminates under uniaxial and biaxial loads. This paper briefly describes the experimental results issued in Part B of the Exercise and their origin and limitations. Comments are made on the material properties given for the unidirectional fibre reinforced layers and constituents used in Part A of the Exercise and on approximations in the laminate models specified in Part A.

A further assessment of the predictive capabilities of current failure theories for composite laminates: comparison with experimental evidence

Abstract This paper presents supplementary conclusions from an international exercise to establish the current status of failure prediction theories for polymer composite laminates. In previous stages of the exercise leading theoreticians in the field used 15 different approaches to predict a range of biaxial failure envelopes and stress–strain curves for composite laminates. The theoretical predictions were compared with experimental results and their performance was assessed using a process designed by the organisers Hinton, Soden and Kaddour [Compos Sci Technol 62 (2002) 1725]. During the course of the exercise four additional theories have emerged that add to the overall picture. The performance of the new theories is assessed here and compared with that of the other fifteen theories, using an identical methodology. The theories are ranked according to their abilities to predict the experimental results for failure of a unidirectional fibre reinforced lamina, initial and final failure of multi-directional laminates and large deformation of laminates under biaxial loads. An attempt is made to identify the most accurate approaches for use in a wide range of applications. The predictions of the four most highly ranked theories, which included two of the new approaches, were within ±50% (i.e. a factor of 2) of the experimental results in more than 75% of the test cases.

A comparison of the predictive capabilities of current failure theories for composite laminates: additional contributions

Abstract Following the publication of an article by Soden, Hinton and Kaddour (Compos Sci Technol, V58, pp. 1225–54, 1998), which compared the predictions of 14 internationally recognised failure theories for fibre reinforced polymer composite laminates, the present paper extends that comparative study to include five more theories, supplied by their originators. Evaluation of the predictive capabilities of the additional theories was carried out in an identical manner to the original study. The same test cases were utilised, covering a wide range of lay-ups, materials and in-plane loading conditions. The results (initial and final failure envelopes and representative stress–strain curves) have been superimposed to show similarities and differences between the predictions of the 19 theories. Final failure predictions for the additional theories fall within the existing range obtained from the original 14 theories but the initial failure predictions for the additional theories have widened the previously observed range. Comments are provided on the possible reasons for the increased spread.

Evaluation of failure prediction in composite laminates: background to ‘part B’ of the exercise

Abstract Over the past 10 years, an international study has been underway to determine the accuracy of current theories for predicting failure in polymer composite laminates. The study, known as the World-Wide Failure Exercise (WWFE), has been carried out in three distinct stages (referred to as Part A, Part B and Part C). Two previous special editions of the Composites Science and Technology journal were dedicated to the first two stages. Part A (Vol. 58, No. 7, 1998) contained detailed descriptions of 14 leading failure theories and predictions by each for a set of test cases defined by the organisers of the exercise (the authors of this paper). Part B (Vol. 62, Nos. 12–13, 2002) provided a detailed comparison between the theoretical predictions and the experimental results, in order to assess the level of maturity of the theories. Part C is aimed at serving a number of purposes. It extends the breadth of the study by including four additional theories that have emerged since the WWFE was first initiated. It provides a comprehensive view on the perceived strengths and weaknesses of all of the leading failure theories considered. It provides direction to designers on choice of theory and likely confidence in the prediction. It provides recommendations to the composites research community as to where efforts should be focussed to develop improved failure prediction tools. This introductory paper to the third special edition contains a detailed description of the process adopted for carrying out ‘Part C’, so that the composites community can draw appropriate conclusions on the overall probity (and hence reliability) of the study.

Behaviour of ±45° glass/epoxy filament wound composite tubes under quasi-static equal biaxial tension–compression loading: experimental results

Abstract The primary aim of this paper is to present results describing in detail the behaviour of ±45° E-glass/MY750 (GRP) tubes, of various wall thicknesses, subjected to equal biaxial tension–compression loading, generated under combined internal pressure and axial compression. The role played by the non-linear lamina shear has also been assessed by comparing various shear stress–strain curves for embedded laminae (extracted from tests on ±45° tubes subjected to circumferential: axial stress ratios SR=1:0, 1:−1 and 2.3:−1) with that of an ‘isolated’ lamina (measured from torsion of 90° tubes). Extracted shear failure strains, for embedded laminae, were more than four fold larger than those measured at ultimate failure for an ‘isolated’ lamina. Soft characteristics were observed in the embedded lamina and these were believed to be due to interaction between early matrix damage initiation (and propagation) and shear. Factors affecting the behaviour of the tubes, such as bulging, scissoring, thermal stresses and stress variation through the thickness are discussed.

Lamina properties, lay-up configurations and loading conditions for a range of fibre reinforced composite laminates

Publisher Summary This chapter provides the details of the input data and a description of the laminates provided to all participants in an exercise to predict the strength of composite laminates. The input data include the elastic constants and the stress strain curves for four unidirectional laminae and their constituents. Six types of laminates, chosen for the analysis are selected and described to represent a wide range of parameters. These parameters include the type of composite material (fiber and matrix), the type of laminate lay-up (unidirectional, angle ply, cross ply, and quasi-isotropic), and the loading conditions. The chapter explains the schematic diagrams showing the loading directions, layer and laminate dimensions, and stacking sequence of the laminates. The six laminates chosen for analysis by the participants are considered to be the representative of a wide range of composite laminates encountered in practical use in a variety of industries. The materials selected have been widely used in practical applications and their properties are well characterized. The chapter presents nonlinear stress–strain data and elastic constants for linear elastic analysis and discusses a wide range of practical biaxial loading conditions, which produce a variety of modes of failure. In some cases, a succession of failures may occur before the laminate can no longer carry load. In some cases, the stress–strain behavior of the laminates is expected to be linear and in some other cases, highly nonlinear.

Chapter 2.2 – Biaxial test results for strength and deformation of a range of E-glass and carbon fibre reinforced composite laminates: Failure exercise benchmark data

Publisher Summary This chapter presents a wide range of experimental data, results, and comments on the experiments, which determine the accuracy of current theories for predicting failure in composite laminates. It outlines the source of data and the methods used in deriving the material properties for the unidirectional laminae and constituents. In some cases where laminates of similar materials are tested in different laboratories, the same set of material properties is employed to minimize the number of data sets issued. It also compares the predictions of 12 different failure theories with experimental data. The experimental data covered 14 test cases involving 0° unidirectional laminae under biaxial direct and shear loads. Other test cases include (a) (90°/ ± 30°)s, (0°/ ± 45°/90°)s, and ( ± 55°)s multidirectional laminates under biaxial loads and (b) stress strain curves for (0°/ ± 45°/90°)s, ( ± 55°)s, ( ± 45°)s, and (0°/90°)s laminates under uniaxial and biaxial loads. It discusses the differences between the symmetric laminated plate models used in the theoretical analysis and the tubular test specimens. Almost all of the experimental results chosen for use in the World Wide Failure Exercise (WWFE) are derived from tests on tubular specimens. Testing of tubes avoids problems associated with free edge effects that are encountered with coupon and other specimens and a wide range of biaxial and triaxial stresses that can be applied by subjecting tubular specimens to combinations of internal or external pressure, torsion and axial load.

The world-wide failure exercise: Its origin, concept and content

Publisher Summary This chapter presents an investigation into the status of polymer composite failure theories. It provides a historical context for the origin of the study and also provides a detailed account of the methodology employed by the organizers to attain an impartial, independent, and broad ranging assessment of the leading failure theories. The study is known within the composites community as the “World-Wide Failure Exercise” (WWFE) and in some circles, the “Failure Olympics”. The origin of the WWFE can be traced to an “experts meeting” held at St Albans (UK) in 1991, on the subject of “Failure of Polymeric Composites and Structures: Mechanisms and Criteria for the Prediction of Performance”. The chapter includes a comprehensive description of the process by which the failure theories are selected, a brief description of the failure theories, the data and instructions supplied to the contributors, and the chronology of the key milestones. It evaluates the current level of maturity of theories for predicting the failure response of fiber reinforced plastic (FRP) laminates, minimizing the knowledge gap between theoreticians and design practitioners in this field, and stimulating the composites community into providing design engineers with more robust and accurate failure prediction methods and the confidence to use them. The chapter compares the 19 theories featured within the study and the overall performance of the theories.