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An extended invariant approach to laminate failure of fibre-reinforced polymer structures
Abstract
This paper presents the extension and validation of omni-failure envelopes for first-ply failure (FPF) and last-ply failure (LPF) analysis of advanced composite materials under general three-dimensional (3D) stress states. Phenomenological failure criteria based on invariant structural tensors are implemented to address failure events in multidirectional laminates using the “omni strain failure envelope” concept. This concept enables the generation of safe predictions of FPF and LPF of composite laminates, providing reliable and fast laminate failure indications that can be particularly useful as a design tool for conceptual and preliminary design of composite structures. The proposed extended omni strain failure envelopes allow not only identification of the controlling plies for FPF and LPF, but also of the controlling failure modes. FPF/LPF surfaces for general 3D stress states can be obtained using only the material properties extracted from the unidirectional (UD) material, and can predict membrane FPF or LPF of any laminate independently of lay-up, while considering the effect of out-of-plane stresses. The predictions of the LPF envelopes and surfaces are compared with experimental data on multidirectional laminates from the first and second World-Wide Failure Exercise (WWFE), showing a satisfactory agreement and validating the conservative character of omni-failure envelopes also in the presence of high levels of triaxiality.
... The challenge of this research work was to develop a laminate strength analysis method using an advanced phenomenological failure theory. To tackle this challenge, an extended failure prediction approach, based on a recently introduced concept called omni strain failure envelope [90,93], was developed in order to address laminate failure under general 3D stress states and to identify critical failure modes [94]. A omni strain envelope is an envelope obtained by superposing failure envelopes for all possible ply orientation in strain space and extracting the inner design space. ...
... Furthermore, in this case, the envelopes allow the identification of the critical failure modes for each controlling ply, which cannot be investigated with the Tsai-Wu based omni strain envelopes. An illustration of this extension of omni failure criteria is provided in Fig. 7, while a detailed presentation of this work is provided in [94]. ...
... However, the unique feature of the omni strain failure concept (for both theories) is that laminate failure predictions require only the material properties extracted from the UD material. Despite the two omni strain failure envelopes provide similar failure prediction for biaxial test cases, the added value brought by the proposed envelopes can be still highlighted when analysing glass-fibre composites, whose LPF is governed by different failure modes (as shown in [94]); LPF of CFRP laminates, on the other hand, is always governed by fibre failure, as confirmed by this analysis. ...
Designing an airframe is a complex process as it requires knowledge from multiple disciplines such as aerodynamics, structural mechanics, manufacturing, flight dynamics, which individually lead to very different optimal designs. Furthermore, the growing use of Carbon Fibre Reinforced Plastics (CFRP), while allowing for more design freedom, has at the same time increased the complexity of the structural designers job. This has sparked the development of Multidisciplinary Design Optimization (MDO), a framework aimed at integrating intelligence from multiple disciplines in one optimal design. Initially employed as a tool to coordinate the work of several design teams over months, MDO is now becoming an integrated software procedure which has evolved over the decades and has become a prominent tool in modern design of aerostructures.
A modern challenge in airframe design is the early use of MDO, motivated by a pressing industrial need for an increased level of detail at the beginning of the design process, to minimize late setbacks in product development. Originally employed only during preliminary design, MDO has recently being pushed into early evaluation of conceptual designs with the outlook of becoming established in the conceptual stage. Using MDO during conceptual design is a promising way to address the paradox of design. By improving each concept, evaluating whether it is capable of meeting the design requirements and computing the sensitivities of various performance measures with respect to a design change, MDO enables designers to gain valuable knowledge in a design phase, in which most of the design freedom is still available.
We hereby exhibit the contemporary trends of MDO with specific focus on composite aircraft and aerial vehicles. We present the recent developments and current state-of-the-art, describing the contemporary challenges and requirements for innovation that are in the development process by academic and industrial researchers, as well as the challenges designers face in further improving the MDO workflow. Within the European OptiMACS project, we devised a novel holistic MDO approach to integrate a number of solutions to challenges identified as industrial technological gaps. These include two-stage optimization for layers of composites, addressing the presence of process-induced distortions and consideration of advanced failure criteria, including refined local models in early design stages, and seamlessly integrating software tools in the design process. The proposed methods are integrated and tested for structural case studies and the obtained results show the potential benefits of their integration into MDO tools.
... The trace can be used to scale the stiffness. The concept of invariants has been known for a long time [33], and it has been found to be useful in the design of laminates [28,[34][35][36]. All the material coefficients U i are a linear combination of on-axis stiffness moduli, normalized by the trace and Q * ij = Q ij Tr given by: ...
There is a growing trend toward the use of natural fibers as reinforcing materials, with flax being a significant part of this market. The mechanical properties of these polymer composites, like those of synthetic fibers, are governed by parameters and material invariants. The challenge is to minimize these parameters, and to reveal these invariants to make stiffness and strength easily comparable with each other and with other composites, while avoiding excessive complexity. To this end, a simple methodology has been developed using the following parameters: Tsai’s modulus or the trace of the stiffness tensor and the area of the Omni Failure Envelope in stress space. Based on the analysis of significant published experimental data on flax composites, new insights were found. The trace-normalized longitudinal Young modulus is a material property that were found to be 0.77 for tension and 0.67 compression with a coefficient of variation of 5.6% and 15%, respectively. The area of the Omni Failure Envelopes and the strength are linearly related. The use of the proposed parameters and some invariants has been discussed and they are used to compare and rank them with each other and with other composites, including carbon, aramid, and glass fiber-reinforced polymer composites.
... The world-wide failure exercises generated a considerable amount of experimental data regarding the characterisation of failure in fibrereinforced polymers, which allowed the definition and assessment of failure criteria (Hinton et al., 2004;Kaddour et al., 2013;Tsai and Melo, 2016;Corrado et al., 2022). As a matter of fact, the support of reliable numerical models and simulations is essential to reduce costs and hasten the development and certification stages. ...
This paper focuses on the analytical formulation of laminate-level failure criteria which are expressed (under a unified matrix formulation) in the framework of the first-order shear deformation theory (FSDT) in order to take into account the influence of the transverse shear stresses on the failure mechanisms. The proposed unified formulation relies on the utilisation of the polar formalism generalised to the FSDT framework: in this background all the considered criteria are stated in terms of tensor invariants. Furthermore an important theoretical result is proven: the existence of a set of analytical relationships between the laminate strength and stiffness invariants.
A novel invariant-based approach to describe elastic properties and failure of composite plies and laminates has been recently proposed in the literature. An omni strain failure envelope has been defined as the minimum inner failure envelope in strain space, which describes the failure of a given composite material for all ply orientations. In this work, a unit circle is proposed as a strain normalized failure envelope for any carbon fiber reinforced polymer laminate. Based on this unit circle, a failure envelope can be generated from the longitudinal tensile and compressive strains-to-failure of a unidirectional ply. The calculated failure envelope was found in good agreement with experimental data published in the well-known World Wide Failure Exercise.
Fiber reinforced polymer composites are an extremely broad and versatile class of material. Their high strength coupled with lightweight leads to their use wherever structural efficiency is at a premium. Applications can be found in aircraft, process plants, sporting goods and military equipment. However they are heterogeneous in construction and antisotropic, which makes making strength prediction extremely difficult especially compared to that of a metal. This book brings together the results of a 12year worldwide failure exercise encompassing 19 theories in a single volume. Each contributor describes their own theory and employs it to solve 14 challenging problems. The accuracy of predictions and the performance of the theories are assessed and recommendations made on the uses of the theories in engineering design. All the necessary information is provided for the methodology to be readily employed for validating and benchmarking new theories as they emerge. Brings together 19 failure theories, with many application examples. Compares the leading failure theories with one another and with experimental data Failure to apply these theories could result in potentially unsafe designs or over design.
A novel invariant-based approach to describe elastic properties and failure of composite plies and laminates is proposed. The approach is based on the trace of the plane stress stiffness matrix as a material property, which can be used to reduce the number of tests and simplify the design of laminates. Omni strain failure envelopes are proposed as the minimum inner failure envelope in strain space, which defines the failure of a given composite material for all ply orientations. The proposed approach is demonstrated using various carbon/epoxy composites and offers radically new scaling to improve design and manufacturing.
A new set of six phenomenological failure criteria for fiber-reinforced polymer laminates denoted LaRC03 is described. These criteria can predict matrix and fiber failure accurately, without the curve-fitting parameters. For matrix failure under transverse compression, the angle of the fracture plane is solved by maximizing the Mohr-Coulomb effective stresses. A criterion for fiber kinking is obtained by calculating the fiber misalignment under load and applying the matrix failure criterion in the coordinate frame of the misalignment. Fracture mechanics models of matrix cracks are used to develop a criterion for matrix failure in tension and to calculate the associated in situ strengths. The LaRC03 criteria are applied to a few examples to predict failure load envelopes and to predict the failure mode for each region of the envelope. The analysis results are compared to the predictions using other available failure criteria and with experimental results.
Composites design has always been perceived to be complicated, time-consuming and therefore not affordable. With a paradigm shift, it is possible to make composites are as straightforward as metals. Each metal is characterized by two key material properties: its Young’s modulus and strength. The adoption of the Tsai’s modulus as the only stiffness constant characterising any CFRP, and failure strain as the only measure of strength, we can make composite design as straightforward as metals design. Actually, with these two material characteristics, for any CFRP, material, laminate, and strain allowable can all be scaled, just like metals. Another break-through is the replacement of the traditional quad laminates of 0, ±45, 90 by double-double (DD) in [±Φ/±ψ]. This replacement allows to substuture a discrete collection by a continuous field of orientations. A few dozen choices, replaced by hundreds. Indeed, double-double can make structures lighter that quad cannot do, thanks to the Lam-search optimizer, which is able, in combination with Fem tools, to sort, instantaneously, the best DD angles allowing laminates stiffness and strength tailored on specific loading conditions. The bottom line: Tsai’s modulus and double-double are new but are simple conceptually, and Lam-search makes their use practical. In the end, lower weight and lower cost are derived by DD to deliver aggressive taper and 1-axis layup that will be stiff, strong, easy to layup, not prone to error, wrinkle, warpage and delaminatnion.
This paper provides an overview of the current approaches to predict damage and failure of composite laminates at the micro-(constituent), meso-(ply), and macro-(structural) levels, and their application to understand the underlying physical phenomena that govern the mechanical response of thin-ply composites. In this context, computational micro-mechanics is used in the analysis of ply thickness effects, with focus on the prediction of in-situ strengths. At the mesoscale, to account for ply thickness effects, theoretical results are presented related with the implementation of failure criteria that account for the in-situ strengths. Finally, at the structural level, analytical and computational fracture approaches are proposed to predict the strength of composite structures made of thin plies. While computational mechanics models at the lower (micro- and meso-) length-scales already show a sufficient level of maturity, the strength prediction of thin-ply composite structures subjected to complex loading scenarios is still a challenge. The former (micro- and meso-models) provide already interesting bases for in-silico material design and virtual testing procedures, with most of current and future research focused on reducing the computational cost of such strategies. In the latter (structural level), analytical Finite Fracture Mechanics models—when closed-form solutions can be used, or the phase field approach to brittle fracture seem to be the most promising techniques to predict structural failure of thin-ply composite structures.
In this article, a constitutive formulation of a transversely-isotropic material and failure model for fiber-reinforced polymers is presented comprising pre-failure material nonlinearities, a novel invariant based quadratic failure criterion (IQC) as well as post failure material softening. The failure surface of the IQ criterion is assumed to take the influence of triaxiality on fracture into account. Further, a distinction between fiber failure and inter-fiber failure is conducted. Material softening is governed by a fracture energy formulation and the introduction of an internal length. The constitutive model is implemented into a programming user interface of the commercial finite element program Abaqus. As results, different laminate lay-ups are modelled and exposed to different stress states in an FE analysis. The obtained failure surfaces and stress strain curves for each laminate lay-up are compared to experimental data. As further applications of the material model presented, a curved composite beam, showing delamination, and a 0̊/90̊/0̊-rod, showing the characteristic damage state in the 90̊layer, are simulated and compared to tests.
This chapter describes failure criteria for polymer composites reinforced by unidirectional fibres. The failure criteria are based on an invariant quadratic formulation based on structural tensors that accounts for the preferred directions of the transversely isotropic material. Failure in a single UD ply is predicted, requiring the analysis of strains and stresses ply-by-ply when analysing multidirectional laminates. Because the proposed failure criteria does not use geometrical information to predict failure (due to its invariant-based formulation), we propose a pragmatic approach to estimate the orientation of the fracture plane. To account for the effect of ply thickness when the laminae are embedded in a multidirectional laminate, the in situ properties are defined in the framework of the failure criterion for transverse damage mechanisms. When compared against experimental data available in the literature, good agreement for transverse failure modes, for failure under off-axis loading and for the effect of superposed hydrostatic pressure on failure behaviour of different fibre-reinforced composites is obtained. For more complex three-dimensional stress states, where the test data available shows large scatter or is not available at all, a computational micro-mechanics framework is used to validate the failure criteria. We obtain a good correlation between the predictions of the two modelling strategies.
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.
A new three-dimensional failure criteria for fibre-reinforced composite materials based on structural tensors is presented. The transverse and the longitudinal failure mechanisms are formulated considering different criteria: for the transverse failure mechanisms, the proposed three-dimensional invariant-based criterion is formulated directly from invariant theory. Regarding the criteria for longitudinal failure, tensile fracture in the fibre direction is predicted using a noninteracting maximum allowable strain criterion. Longitudinal compressive failure is predicted using a three-dimensional kinking model based on the invariant failure criteria formulated for transverse fracture. The proposed kinking model is able to account for the nonlinear shear response typically observed in fibre-reinforced polymers. For validation, the failure envelopes for several fibre-reinforced polymers under different stress states are generated and compared with the test data available in the literature. For more complex three-dimensional stress states, where the test data available shows large scatter or is not available at all, a computational micro-mechanics framework is used to validate the failure criteria. It is observed that, in the case of the IM7/8552 carbon fibre-reinforced polymer, the effect of the nonlinear shear behaviour in the failure loci is negligible. In general, the failure predictions were in good agreement with previous three-dimensional failure criteria and experimental data. The computational micro-mechanics framework is shown to be a very useful tool to validate failure criteria under complex three-dimensional stress states.
This article draws to a conclusion the results from the co-ordinated study known as the Second World-Wide Failure Exercise (WWFE-II). It contains an objective assessment of the performance of 12 leading failure criteria for predicting the response of fibre-reinforced polymer composites when subjected to 3D states of stress. Twelve challenging test problems (Test Cases) were defined by the organisers of WWFE-II, encompassing a range of materials (polymer, glass/epoxy, carbon/epoxy), lay-ups (unidirectional, angle ply, cross ply and quasi-isotropic laminates) and various 3D stress states (various triaxial strength envelopes, through-thickness and shear loading, and stress-strain curves). A systematic comparison has then been conducted between 'blind' predictions (i.e. without access to the experimental results beforehand) made for each Test Case by the originators of each theory and previously obtained experimental results for each Test Case. In-depth quantitative and qualitative ranking procedures have been employed to identify the strengths and weaknesses of each theory, and the overall effectiveness of each theory as a potential design tool. The theories are grouped according to their degree of maturity and ability to predict accurately the 3D behaviour of composites. The results from this study provide unique information to the community, the intent being that it will form a guide for the selection of the most appropriate failure theory for use in a given design situation. © The Author(s), 2013 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav.
This article describes a unique set of experimental results employed in benchmarking leading three-dimensional failure criteria, as a part of the SecondWorld Wide Failure Exercise (WWFE-II). In Part A of WWFE-II, the originators of those criteria (or their representative) made blind theoretical predictions of the triaxial strength, stress-strain curves and deformation of 12 Test Cases, selected by the organisers to challenge the contributors' models. The cases covered various materials and laminates subjected to a wide range of triaxial and through-thickness loading conditions. The Test Cases were for (a) an isotropic material made of an epoxy polymer, (b) various 0 degrees unidirectional laminae and (c) (0 degrees/90 degrees) s, (0 degrees /+/- 45 degrees/90 degrees) s and (+/- 35 degrees) s multi-directional laminates. In Part B of WWFE-II, a comparison is made by the contributors between available experimental results, described here, and their theoretical predictions, made in Part A. Discussion is also made on the accuracy of these results.
This paper proposes a new fully three-dimensional failure criteria for polymer composites reinforced by unidirectional fibers. Existing failure criteria based on three-dimensional stress states are revisited and their limitations and pitfalls are identified. A new set of failure criteria for both longitudinal and transverse failure mechanisms where the effect of ply thickness on the material strength is accounted for is proposed. The accuracy of the failure criteria is assessed by comparing the analytical predictions with existing experimental data obtained under multiaxial stress states. A good agreement between the predictions and experimental data is generally observed.
Several strength criteria for laminae and laminates are presented and compared numerically. It is concluded that the von Mises hypothesis is not suitable for composites, instead strength criteria should be derived from Mohr's hypothesis. In industry mostly laminates are used. It would be desirable if the strength properties could be determined for any arbitrary laminate from those of the laminae included. Since this is spoiled by interaction between the layers, some of these interaction effects are described. In order to become established, a strength criterion has to be verified experimentally. Thus, different techniques for biaxial testing with their characteristic problems are shown.
Composite materials exhibit various and complex failure behavior. Different formalisms have been used to predict failure. Improvement of old theories and new ones continue to be published. In this paper, the most recent and widely used models are presented. Failure criteria such as Tsai-Wu, parametric formulations, maximal stress and strain, Hashin criterion, Hart-Smith criterion, and the method based on kriging are presented. These failure theories may be classified in two categories, depending whether they integrate failure modes or not. The formalism of each theory is briefly described and their application to model failure of composite laminates is discussed by comparing the advantages and limitations of each method. The diversity of experimental failure envelopes, as reported in the literature on composites, is outlined and it is shown that most criteria permit modeling only particular failure properties of composite laminates.
The successive failure of different laminates subjected to a variety of loading conditions has been treated by a layer-by-layer failure analysis. Three sources of non-linearity are considered, namely material non-linearity due to microdamage, matrix cracking, and changes in fibre angle with increasing strains. In general there is good agreement between predictions and experimental results. Some disagreement is due to imperfections in certain tests, therefore, these tests should be repeated. Three categories of laminate configuration/loading condition can be distinguished: (I) laminates with 3 or more fibre directions with arbitrary loading conditions; (II) balanced angle ply laminates with stress ratios in accordance with netting analysis; (III) laminates with 2 fibre directions and loadings which are not in accordance with netting analysis. The analysis of category (I) is straight forward. Category (II) is sensitive to the stiffness degradation after the onset of matrix cracking. Category (III) fails at low stresses and large strains of the laminate due to a rapid deterioration. An intensive discussion is necessary to define a failure limit for category (III).For the detection of the different modes (A, B, C) of interfibre fracture (IFF), refined action plane related IFF-criteria developed by Puck on the basis of Mohr's and Hashin's considerations on brittle fracture are used. They provide much more information than has been reported from the experiments. Their unique ability to predict the inclination of the fibre parallel fracture plane is the key for assessing of the risk of delamination and local buckling due to a wedge effect which occurs when oblique fracture planes are exposed to high transverse compression.
Failure models and criteria for FRP under in-plane or three-dimensional stress states including shear non-linearity
- S T Pinho
- C G Dávila
- P P Camanho
- L Iannucci
- P Robinson
Pinho, S.T., Dávila, C.G., Camanho, P.P., Iannucci, L. and Robinson, P. Failure models and criteria for FRP under in-plane
or three-dimensional stress states including shear non-linearity, Nasa/Tm-2005-213530, (February), 68, 2005.
A study of failure criteria of fibrous composite materials, NASA Scientific and Technical Information (STI) Program Office
- F Paris
- K E Jackson
Paris, F. and Jackson, K.E. A study of failure criteria of fibrous composite materials, NASA Scientific and Technical
Information (STI) Program Office, (March), 76, 2001.