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Three-dimensional invariant-based failure criteria for transversely isotropic fibre-reinforced composites
Abstract
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.
... The methodology introduced in this work consists of a composite material model proposed in the literature [34], representing the quasi-brittle behavior of composite structures. To account for the effect of complex 3D stress states during the onset and broadening of longitudinal compressive failure mechanisms, a 3D invariant-based failure theory [35,36] was implemented not only for damage initiation [34], but also for damage propagation by finding the longitudinal component of the stress tensor at the intersection with the failure surface, and including it in the damage dissipation function. The formulation of the constitutive model implemented for this work is described in the next section, followed by the verification and validation of the model to predict scaling effects in UNT composite laminates. ...
... To account for the effect of complex 3D stress states, 3D invariant-based failure criteria [35,36] are implemented as damage activation functions. This set of criteria is coupled with a smeared crack model (SCM) for transverse cracking and continuum damage mechanics (CDM) models for fiber-dominated damage, which together account for the kinematics of matrix cracking and fiber tensile or compressive fracture during damage propagation. ...
... The onset of transverse failure was predicted using the 3D invariant-based failure criterion for matrix-dominated failure [35,36]. To ensure that transverse cracking initiates at the intersection with the failure surface, i.e., when the condition f M (σ) = 1 is met, an iterative scheme based on the Newton-Raphson method was employed, following Refs. ...
This paper presents a mesoscale damage model for composite materials and its validation at the coupon level by predicting scaling effects in un-notched carbon-fiber reinforced polymer (CFRP) laminates. The proposed material model presents a revised longitudinal damage law that accounts for the effect of complex 3D stress states in the prediction of onset and broadening of longitudinal compressive failure mechanisms. To predict transverse failure mechanisms of unidirectional CFRPs, this model was then combined with a 3D frictional smeared crack model. The complete mesoscale damage model was implemented in ABAQUS®/Explicit. Intralaminar damage onset and propagation were predicted using solid elements, and in-situ properties were included using different material cards according to the position and effective thickness of the plies. Delamination was captured using cohesive elements. To validate the implemented damage model, the analysis of size effects in quasi-isotropic un-notched coupons under tensile and compressive loading was compared with the test data available in the literature. Two types of scaling were addressed: sublaminate-level scaling, obtained by the repetition of the sublaminate stacking sequence, and ply-level scaling, realized by changing the effective thickness of each ply block. Validation was successfully completed as the obtained results were in agreement with the experimental findings, having an acceptable deviation from the mean experimental values.
... However, state-of-art approaches to ply failure onset have achieved a high degree of accuracy, being able to represent several relevant aspects of the failure process of laminated composites, e.g. the increase on apparent shear strength when applying moderate values of transverse compression, or the detrimental effect of the inplane shear stresses in failure by fibre kinking. The most advanced set of phenomenological failure criteria account for the effect of ply thickness, fibre misalignment in compression, the effect of hydrostatic stresses and the effect of shear nonlinearity on fibre kinking, and the in-situ strengths [62][63][64][65]. ...
... By exploiting the fully 3D description of failure provided by the invariant-based theory proposed in [65], omni strain failure envelopes can be extended to omni strain failure surfaces by finding the controlling plies in the 3D principal strain space. Indeed, with this extension, the resulting design space can predict failure under complex 3D stress states of any laminate, independently of lay-up or stacking sequence, and address, for instance, the design of bolted joints or thick composite laminates, where through-thickness stress states cannot be neglected. ...
... As part of the OptiMACS project, the 3D invariant-based failure theory [65] is used for the prediction of FPF of laminated composite structures. With this aim, the formulation of this set of criteria was implemented in a post-processing Python script, compatible with Abaqus/Standard and Abaqus/Explicit, to generate new element output fields, by using the full stress tensor of each element and computing the failure index for each of the failure modes tackled by the criteria. ...
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.
... Several experimental studies in the literature show that the transverse tensile strength (Y T is ) and the in-plane shear strength (S L is ) of an embedded ply depend on the ply thickness [19][20][21][22]74,24,67], on the orientation (or stiffness) of the adjacent plies [22,74] (see Fig. 4), and on the ply location in the laminate [76,40] (see Fig. 5). Indirect observations also show that the transverse shear strength (S T is ) [77][78][79]16,80] and the transverse compressive strength (Y C is ) [77,78,81] are in situ properties too. ...
... Several experimental studies in the literature show that the transverse tensile strength (Y T is ) and the in-plane shear strength (S L is ) of an embedded ply depend on the ply thickness [19][20][21][22]74,24,67], on the orientation (or stiffness) of the adjacent plies [22,74] (see Fig. 4), and on the ply location in the laminate [76,40] (see Fig. 5). Indirect observations also show that the transverse shear strength (S T is ) [77][78][79]16,80] and the transverse compressive strength (Y C is ) [77,78,81] are in situ properties too. ...
... The application of three-dimensional (3D) phenomenological failure criteria has been proposed to estimate and take into account the in situ effect on the transverse shear and transverse compressive strengths of embedded plies [77,78]. According to these models, not only Y T is and S L is are assumed in situ properties (calculated using e.g. the models proposed by Camanho et al. [69]), but also Y C is and S T is (Fig. 9). ...
The introduction of the spread-tow thin-ply technology enabled the development of composite plies as thin as 0.020 mm. The availability of composite plies with a broader thickness range makes the understanding of the effects of ply thickness more pertinent than ever, therefore, a comprehensive literature review is presented in this paper. The micro-structural effects of ply thickness and ply uniformity on the mechanical response of unidirectional laminae is described. Then, the effect of ply thickness scaling on several aspects of the mechanical response of composite laminates is reviewed. Finally, the current state-of-art and recent developments in manufacturing, design and application of thin plies on novel engineered composite laminates are presented. This review demonstrates that thin plies not only bring improvements to the plain strengths and design flexibility of composite laminates, but can also enhance the performance of primary structural applications, namely those driven by residual strength and damage tolerance requirements. This can be achieved by either combining thin plies with existing material technologies, or through novel design principles. Moreover, it is shown that thin plies provide increased flexibility for multifunctional optimisation and for adoption of more efficient manufacturing technologies, with great potential gains in terms of weight savings and cost reduction during conceptual and detailed design and operation.
... Important aspects that failure criteria for FRPs should be able to capture include the increase on apparent shear strength when applying moderate values of transverse compression, the effect of ply thickness on the strengths of each ply (in-situ effect), the detrimental effect of the inplane shear stresses due to fibre misalignment under longitudinal compressive failure by fibre kinking, or the ability to predict failure under hydrostatic pressure. Until very recently [38,39], many of the available failure criteria used to predict the onset of matrix cracking and fibre fracture [47,64,87,91,138,153] did not address all these issues. ...
... The accurate determination of the in-situ effect is crucial for the implementation of any physically-based failure criteria for transverse damage initiation [37,38,47,50,64,71,111,117,138]. It has been shown that using as ply properties those measured directly from UD plies to predict the strength of multidirectional laminates results in very conservative predictions that could differ substantially from the experimental results [49,59,78,140]. ...
... In laminate analysis, the in-situ effect is typically taken into account by using analytical Fracture Mechanics models [33,67] and through application of 3D phenomenological failure criteria [38,47]. Figure 30 shows the in-situ transverse tensile strength as a function of the embedded 90 ply thickness determined using computational micro-mechanics, and a comparison with the predictions of the Fracture Mechanics model proposed by Camanho et al. [33]: A. Arteiro et al. ...
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.
... and shear fracture and fiber kinking, can also be attributed to the in situ effect. This has been addressed in the past through application of 3D phenomenological failure criteria [71,72]. According to these models, when embedded in a multidirectional laminate, not only the transverse tensile and in-plane shear strengths (calculated using e.g. the models proposed by Camanho et al. [56]), but also the transverse compressive and transverse shear strengths are in situ properties. ...
... According to these models, when embedded in a multidirectional laminate, not only the transverse tensile and in-plane shear strengths (calculated using e.g. the models proposed by Camanho et al. [56]), but also the transverse compressive and transverse shear strengths are in situ properties. In addition, assuming that kink bands are triggered by localized matrix failure in the vicinity of misaligned fibers [71,72], the in situ effect has also a direct, positive influence on the resistance of embedded plies to fiber kinking. ...
... As the ply thickness decreases, damage progression becomes more and more gradual, and through-the-thickness transverse fracture is delayed, indicating that an in situ effect exists in transverse compression. Figure 19 shows the in situ transverse compressive strength as a function of the ply thickness determined from the micro-mechanical models presented in this work, and the predictions from the analytical models for the in situ effect based on phenomenological 3D failure criteria [71,72]. Several RVEs have been analyzed, and the respective data has been plotted in Fig. 19. ...
This chapter presents the analysis models, developed at different length scales, for the prediction of inelastic deformation and fracture of polymer composite materials reinforced by unidirectional fibers. Three different length scales are covered. Micro-mechanical models are used to understand in detail the effects of the constituents on the response of the composite material, and to support the development of analysis models based on homogenized representations of composite materials. Meso-mechanical models are used to predict the strength of composite structural components under general loading conditions. Finally, macro-mechanical models based on Finite Fracture Mechanics, which enable fast strength predictions of simple structural details, are discussed.
... If transverse microcracking is delayed, the strengths associated with other matrixdominated failure mechanisms, such as wedge compressive fracture, may also increase due to the constraining effect imposed by adjacent plies. This can be addressed through the application of three-dimensional (3D) phenomenological failure criteria [36,37]. According to these models, when embedded in a multidirectional laminate, not only the transverse tensile and in-plane shear strengths (Y T and S L , respectively), calculated using e.g. the models proposed by Camanho et al. [33], but also the transverse compressive and transverse shear strengths (Y C and S T , respectively) are in situ properties. ...
... According to these models, when embedded in a multidirectional laminate, not only the transverse tensile and in-plane shear strengths (Y T and S L , respectively), calculated using e.g. the models proposed by Camanho et al. [33], but also the transverse compressive and transverse shear strengths (Y C and S T , respectively) are in situ properties. In addition, assuming that kink bands 1 are triggered by localised matrix failure in the vicinity of misaligned fibres [36,37], the in situ effect will also result in an increased longitudinal compressive strength in multidirectional laminated composites. ...
... The objective of this paper is to investigate whether there is an in situ effect for transverse compressive loads as predicted by some failure criteria [36,37]. In the absence of experimental information, a micro-mechanical model is used to study the in situ effect observed on constrained plies subjected to transverse compressive loading. ...
A micro-mechanical model is used to study the effect of ply thickness on constrained 90° plies subjected to transverse compressive loading (in situ effect). For cross-ply sublaminates with conventional, standard-thickness 90° plies, failure is dominated by fibre-matrix interface cracking and large localised plastic deformation of the matrix, forming a localised band in a plane that is not aligned with the loading direction. Ultra-thin plies show a dispersed damage mechanism, combining wedge cracking with ply fragmentation/separation. Moreover, a transverse crack suppression effect is clearly observed. To the authors’ knowledge, it is the first time an in situ effect in transverse compression has been identified. When comparing the results of the micro-mechanical model with the predictions from analytical models for the in situ effect, the same trends are obtained. These results also show that, for realistic ply thicknesses, these analytical models can be considered fairly accurate.
... The three-dimensional invariant-based transverse failure criterion proposed by Camanho et al. (2015b) is employed to evaluate the onset of matrix cracking. The orientation of the crack plane in the reference configuration is estimated according to the procedure presented in Camanho et al. (2015a), Zhuang et al. (2019). ...
... The smeared crack model requires the definition of the crack plane orientation. The pragmatic approach introduced by Camanho et al. (2015a) to estimate the angle of the transverse crack plane from the stress state at the fracture onset is employed here. This approach is summarised in Zhuang et al. (2019). ...
... It is important to emphasise that this set of invariant-based failure criteria is completely formulated in a 3D setting, unlike other phenomenological failure criteria that were initially formulated in a 2D setting and then extended to the 3D case. Additional details, such as a pragmatic approach for the determination of the fracture plane and the definition of the in situ properties, can be found in Ref. [15]. ...
... An example of omni FPF envelope, obtained using the invariant-based failure model for IM7/8552, is shown in Fig. 8. On the left-hand side, several ply failure envelopes are represented with different colours, from which the omni strain FPF envelope (outlined with a black dotted line) can be obtained. Figure 8(b) provides a detailed view of the omni FPF envelope only, where the failure loci are represented using different markers in order to identify the critical failure modes for each controlling ply ([0], [15], [75] and [90]). In this way, it is possible to identify fibre failure as the most prominent FPF mode shaping the omni FPF envelope of IM7/8552. ...
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 formulations are summarized below. For further details, the reader is referred to Refs [17,[24][25][26]. ...
This paper presents the development and validation of a mesoscale numerical model to predict the bearing failure of composite laminates reinforced by unidirectional continuous fibers, focusing on specimens that show a significant non-linear response prior to failure. Half-hole pin bearing tests were carried out with multiple instrumentation for the comprehensive characterization of the failure process. Three-dimensional finite element models were used for the simulation of plastic deformation and damage of the cross- and angle-ply specimens using fiber-aligned mesh for the composite plies. To consider the non-linear material behavior prior to crack propagation, the constitutive model proposed includes a bi-linear elastoplastic model to represent the non-linear response under longitudinal shear. For the prediction of the peak and post-peak behavior, 3D invariant-based failure criteria and mechanism-based continuum damage models were used for intralaminar damage, together with a discrete cohesive zone model for delamination. Thorough analyses and comparisons of the experimental and numerical results show a good correlation of the bearing strengths and overall deformation, as well as good agreement in terms of damage size and damage shape. Relevant limitations include difficulties in predicting the post-peak plateau stresses and the loading displacements in some configurations, setting the stage for additional future research.
... The critical stress of the laminate ðr c Þ for which matrix cracking is first observed is presented in Table 7. r c is calculated using Classical Lamination Theory (CLT) [18] together with a recent failure criteria formulated by Camanho et al. [29,32] that Table 2 Material properties for T800S/M21 [28]. a Calculated base on equations in [17]. ...
Delaminations at the free-edges of a laminated composite under tension can be triggered by transverse cracks or by high interlaminar stresses. The capability for predicting these phenomena when the ply thickness is reduced (thin-ply laminates) is particularly challenging because damage mechanisms are delayed or even suppressed. In this work, an existing energy-based failure criterion and a simplified finite element model with cohesive elements are combined to develop a computationally inexpensive predictive tool. Its comparison with experimental data demonstrates that this approach captures the trends of the critical strain for delamination with respect to ply thickness and ply location and the quantitative agreement with the predictions is satisfactory.
The fibre–matrix interface represents a vital element in the development and characterisation of fibre-reinforced polymers (FRPs). Extensive ranges of interfacial properties exist for different composite systems, measured with various interface characterisation techniques. However, the discrepancies in interfacial properties of similar fibre–matrix systems have not been fully addressed or explained. In this review, first, the interface-forming mechanisms of FRPs are established. Following a discourse on three primary factors that affect the fibre–matrix interface, the four main interface characterisation methods (single-fibre fragmentation, single-fibre pull-out, microbond and fibre push-in/-out tests) are described and critically reviewed. These sections review various detailed data reduction schemes, numerical approaches, accompanying challenges and sources of reported scatter. Finally, following the assessment of several infrequent test methods, comprehensive conclusions, prospective directions and intriguing extensions to the field are provided.
Numerical and experimental research programs have been carried out to investigate the effect of scaling on the tensile strength of notched composites. This paper presents a computational study of scaled open-hole tensile tests using the Discrete Ply Model (DPM) method. This finite element model is discrete, and only a small number of parameters are required from experimental characterization tests. Experimental and numerical strength values are compared here, and reveal that DPM simulations tend to slightly overestimate strength values, with an average discrepancy of 9.7%. However, DPM Results show that such modeling simulates both the reduction in strength when specimen size is increased for sublaminate level scaled specimens, where failure is fiber dominated, and the increase in strength when specimen size is increased for ply level scaled specimens, where failure is delamination dominated. In all cases, increasing the total thickness of the specimen leads to a decrease in strength and this effect is dominant over the effect of increasing hole diameter. As well as the variation in strength, three distinct failure mechanisms are observed: fiber failure with extensive matrix damage (pull-out failure), fiber failure with little or no matrix damage (brittle failure) and delamination failure. Comparisons with experiments demonstrate that tensile strengths, damage propagation scenarios and failure patterns are predicted with acceptable accuracy.
Stiffened composite panels have been extensively used thanks to their ability to withstand high load and large deflection. However, their nonlinear behavior and complex damage modes during the post-buckling regime remain challenging and still require research work to improve understanding. In the current study, the buckling and post-buckling responses of a hat-stiffened panel made with carbon fiber reinforced polymer composite material are investigated experimentally and numerically with identifying the damage process and its effect on the panel stiffness. The experimental analysis is achieved by performing quasi-static multi-step compressive loading up to failure with full displacement assessment. A Structural Health Monitoring strategy is also deployed for registering and localizing the Acoustic Emission (AE) activities during each run. Matrix data extracted from the AE waveforms are processed and classified with respect to damage mechanism. Additionally, this research proposes predictive Finite Element Model based on Progressive Failure Analysis. Modified Chang-Chang failure criteria is adopted and implemented using Ansys Usermat subroutine. Numerical and experimental data have been compared and good agreement is demonstrated.
Curved laminates in aero-structures, such as the L-angle sections where webs and flanges meet, are prone to delamination due to high interlaminar stresses in these regions. Some efforts to investigate delamination in these structures can be found in the literature but commonly structures are limited to unidirectional layups or modelling approaches are constrained to the cohesive element based methods. In this work, multi-directional L-angle laminates were manufactured using unidirectional prepregs and tested under four-point bending load conditions to examine the interface damage. Acoustic emission technique was used to assist the capture of damage initiation and propagation. Three interface modelling strategies for predicting delamination, namely cohesive element, cohesive surface and perfectly bonded interface were used in the numerical study. The interface damage behaviour was successfully predicted by the simulation methods and differences among the strategies were compared.
The effectiveness of studying inter-laminar delamination in laminated composites with the help of thickness-stretch shell elements which utilize a 3-D material model sub-routine as compared to the traditional plane-stress shell elements has been investigated using a non-linear finite element solver (LS-DYNA®). A strain-rate-dependent micro-mechanical material model using ply-level progressive failure criteria has been used to simulate the initiation and propagation of delamination. A methodology of assigning physical significance to the choice of damage parameters has been presented. The numerical delamination growth has been qualitatively analyzed against the experimental C-scan images for multiple impact events on different composite plates.
Considerable effort has been put into the development of models describing damage and failure of fiber composites. This paper aims at providing an overview of models for intralaminate fracture of continuous fiber-reinforced polymer composites under quasi-static load. The models are grouped into homogeneous ones, those with some effect of inhomogeneity between fibers and the matrix, and fully inhomogeneous ones. Even a world-wide competition was not able to decide for the one and only homogeneous model. Accounting for the inhomogeneity between fibers and the matrix allows being more close to the real behavior on the account of higher computational effort. They suffer, however, from the difficulty to gather reliable material data. In summary, it must be concluded that a fully satisfying solution is not yet available. Consequently, for the time being, a real test remains the authentic way to secure structural strength.
In order to examine the effect of ply thickness on the crack initiation and propagation in the 90° layer in [0°/90°n/0°] laminates, we conducted numerical simulations using two-dimensional mesoscopic numerical models. We found that the stress increase in the thin layer with 40 µm thickness was restricted in the vicinity of the adjacent layers, leading to restriction of crack penetration through the 90° layer. In addition, we confirmed the effect of stiffness of adjacent layers. In the case where the 90° layer was sandwiched between 45° layers, which had lower stiffness than the 0° layers, crack propagation in the 90° layer was faster than that observed with the 0° adjacent layers. Thus, the crack propagation behavior in the 90° layer was significantly influenced by the change in the stiffness caused by the orientation angle of the adjacent layers.
In Part A of the World Wide Failure Exercise, presented in Chapters 3 and 4, 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 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.
This work is concerned with physical testing and numerical simulations of flat and round nose drop-weight impact of carbon fibre-reinforced laminate composite panels to predict ply level failure. Majority of the existing studies on impact of composites by spherical nose impactors are experimental, computational models are simplified, and based on classical laminated plate theories where contributions of through-thickness stresses are neglected. Present work considers flat nose impact and contributions from through-thickness stresses and is mainly simulation based. A computational model was developed in ABAQUS™ software using adaptive meshing techniques. Simulation produced (2D model) stresses were numerically integrated using MATALB™ code to predict through-thickness (3D) stresses. Through-the-thickness stresses were then utilised in advanced failure criteria coded in MATLAB™ software to predict ply level failures. Simulation produced results demonstrate that the computational model can efficiently and effectively predict ply-by-ply failure status of relatively thick laminates.
A new end tab fabricated using a fiberglass knit in a silicon rubber matrix was used for off-axis tension tests on unidirectional composites. It was shown experimentally that this new tab allowed shear deformation of the specimen to occur in the hydraulic grips and, thus, produce a uniform state of strain in the specimen. Consequently, the shear modulus could be determined accurately using this new tab. Furthermore, due to the absence of stress concentrations, this procedure could also be used to determine shear strength.
An experimental and analytical investigation was performed to study the in situ ply shear strength in fiber-reinforced laminated composites. The effects of ply orientation and laminate thickness on the ply shear strength in laminates were the major concerns of the study. T300/1034-C Graphite/Epoxy cross-ply laminates were selected for the tests, and a rail shear fixture was used for measuring ply shear strengths. A three-dimensional finite element program was also developed to analyze the interlaminar stress distributions in the specimens. The results of test data strongly indicate that the ply orientation and laminate thickness significantly influence the in-plane shear strengths of the laminates. This effect could be attributed to the inherent flaws introduced during manufacturing processes and to interlaminar stresses in laminates. As a consequence, ply shear strength should not be regarded as an intrinsic property of fiber-reinforced laminates. Due to the free edge effect, the results of shear strength distributions measured from the rail shear fixture were conser vative.
An investigation was conducted to study tensile failure of laminated composites containing an open hole. This investigation was especially concerned with determining the response, type and extent of damage in composites as a function of applied load. Both an analysis and experiments were performed for graphite/epoxy composites during the study. A progressive damage analysis was developed to study the problem. The analysis was verified by an extensive comparison between the numerical calculations based on the analysis and the experimental data obtained during the investigation as well as from published literature. Different graphite/epoxy composite materials were considered in the study. Overall, good agreements were found between the calculations and the data. Based on the study, it was found that the types and extent of internal damage in the notched composites strongly depend on the ply orientation of the laminates. The types and the size of damage directly affect the strength and failure mode of the composites.
A three-dimensional finite element model is developed to predict damage progression and strength of mechanically fastened joints in carbon fibre-reinforced plastics that fail in the bearing, tension and shear-out modes. The model is based on a three-dimensional finite element model, on a three-dimensional failure criterion and on a constitutive equation that takes into account the effects of damage on the material elastic properties. This is accomplished using internal state variables that are functions of the type of damage. This formulation is used together with a global failure criterion to predict the ultimate strength of the joint. Experimental results concerning damage progression, joint stiffness and strength are obtained and compared with the predictions. A good agreement between experimental results and numerical predictions is obtained.
It is well known that matrix failure in carbon/epoxy composites is influenced by multiaxial states of stress. However most of the experimental work to measure this inter action has not focused exclusively on matrix failure, and a general multiaxial stress criterion for matrix failure has not been established. To examine this question experimen tally we have carried out a series of tests involving torsional shear combined with axial tension or compression of unidirectional hoop wound cylinders, using AS4/55A carbon/ epoxy lamina. The matrix failure stresses are seen to be well correlated with the Tsai-Wu quadratic polynomial. There is also a strong interaction between the strains at failure, with small amounts of transverse tension giving a significant reduction in the shear strain at fail ure. The effect of σ2 on the nonlinear shear stress-strain curves is also presented.
The mechanics of transverse cracking in an elastic fibrous composite ply is explored for the case of low crack density. Cracks are assumed to initiate from a nucleus created by localized fiber debonding and matrix cracking. Conditions for onset of unstable cracking from such nuclei are evaluated with regard to interaction of cracks with adjacent plies of different elastic properties. It is found that cracks may propagate in two directions on planes which are parallel to the fiber axis and perpendicular to the midplane of the ply. In general, crack propagation in the direction of the fiber axis controls the strength of thin plies, while cracking in the direction perpendicular to the fiber axis determines the strength of thick plies. The theory relates ply thickness, crack geometry, and ply tough ness to ply strength. It predicts a significant increase in strength with decreasing ply thick ness in constrained thin plies. The strength of thick plies is found to be constant, but it may be reduced by preexisting damage. Strength of plies of intermediate thickness, and of unconstrained thick plies is evaluated as well. Results are illustrated by comparison with experimental data.
A conceptually simple mixed mode fracture analysis method is presented for the prediction of tensile matrix failure in composite laminates. The analysis technique, which makes use of a mixed mode strain energy release rate fracture criteria in con junction with an approximate two-dimensional shear-lag model, is cast in terms of a tensile matrix strength criterion. In contrast to presently available point stress tech niques, surprisingly accurate predctions of mode I matrix failure in the 90° lamina of (±θ/90 n ) s and mixed mode matrix failure in the θ° lamina of (02/θ) s T300/934 com posite laminates are observed.
A progressive damage model was developed for bolted joints in laminated composites which may fail in either tension mode or shear-out mode. The model is capable of assess ing damage accumulated in laminates with arbitrary ply orientations during mechanical loading and of predicting the ultimate strength of the joints which failed in tension or shear-out mode. The model consists of two parts, namely, the stress analysis and the failure analysis. Stresses and strains in laminates were analyzed on the basis of the theory of finite elasticity with the consideration of material and geometric nonlinearities. Damage accumulation in laminates was evaluated by the proposed failure criteria combined with a proposed property degradation model. Based on the model, a nonlinear finite element code was developed. Numerical results were compared with available experimental data. An excellent agreement was found between the analytical predictions and the experimental data.
This contribution is a post-runner to the ‘failure exercise’. It focuses on two aspects of the theoretical prediction of failure in composites [1–3]: the first is the derivation of failure conditions for a unidirectional (UD) lamina with the prediction of initial failure of the embedded lamina, and the second the treatment of non-linear, progressive failure of 3-dimensionally stressed laminates until final failure. The failure conditions are based on the so-called Failure Mode Concept (FMC) which takes into account the material-symmetries (by the application of invariants) of the UD-lamina homogenized to a ‘material’, and on a strict failure mode thinking. The results of the investigation are stress–strain curves for the various given GFRP-/CFRP-UD-laminae, biaxial failure stress envelopes for the UD-laminae, and initial as well as final biaxial failure envelopes for the laminates. In addition a brief comparison between Puck's and Cuntze's failure theory is presented by the authors themselves.
An operationally simple strength criterion for anisotropic materials is developed from a scalar function of two strength tensors. Differing from existing quadratic approximations of failure surfaces, the present theory satisfies the invariant requirements of coordinate transforma tion, treats interaction terms as independent components, takes into account the difference in strengths due to positive and negative stresses, and can be specialized to account for different material symmetries, multi-dimensional space, and multi-axial stresses. The measured off-axis uniaxial and pure shear data are shown to be in good agreement with the predicted values based on the present theory.
Complementary elastic energy density is used to derive a stress-strain relation, which is linear in uniaxial loadings in the longitudinal and trans verse directions, but nonlinear in shear. In the case of composite laminae under plane stress, one additional fourth-order constant is introduced. Comparison is shown between the present theory and experimental data on off-axis tests.
Three-dimensional fatigue failure criteria for unidirectional fiber composites under states of cyclic stress are established in terms of quadratic stress polynomials which are expressed in terms of the transversely isotropic invariants of the cyclic stress. Two distinct fatigue failure modes, fiber mode, and matrix mode, are modeled separately. Material information needed for the failure criteria are the S-N curves for single stress components. A preliminary approach to incorporate scatter into the failure criteria is presented.
It is common in many branches of continuum mechanics to treat material as though it is incompressible. Although no material is truly incompressible, there are many materials in which the ability to resist volume changes greatly exceeds the ability to resist shearing deformations; examples are liquids with low viscosity, like water, and some natural and artificial rubbers. For such materials, the assumption of incompressibility is a good approximation in many circumstances, and often greatly simplifies the solution of specific problems. It should be noted, though, that there are occasions when even a small degree of compressibility may produce a major effect; an example is the propagation of sound waves in water.
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.
A suitable framework allowing to describe yielding and failure of anisotropic materials with the required generality and pertinence is furnished by the theory of representations for tensor functions. In this Chapter, invariant formulations of the plastic behavior and failure of transversely isotropic solids are developed. For other material symmetries, the corresponding constitutive relations can be derived in a similar manner.
This paper gives 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 described together with the lay-up, layer thicknesses, stacking sequences and the loading conditions. Consideration is given as to why these six laminates were selected and of the challenges imposed by the selected problems. The detailed instructions issued to the contributors are also presented.
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.
Hydrostatic pressure can cause significant changes in the mechanical properties of composite materials. A thorough understanding of these effects is essential for the effective design of composite structures for high-pressure applications. In this report, the literature on the effects of hydrostatic pressure on the mechanical behavior of composite materials is reviewed. This includes a general description of the effects of hydrostatic pressure on unreinforced polymers and a detailed critique of the experimental work that has been done on composite materials. The section on composites is divided into three sections: compressive, tensile, and shear testing. For each type of testing, the test materials and techniques and the physical and quantitative results are discussed.
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.
The impact is particularly damaging in the case of composites where the fibers are elastic and brittle as well as the matrix when compared with conventional ductile metals. This paper deals with the prediction of the delamination damage induced by low velocity impact in a laminated composite performed using the progressive damage model MAT162 implemented in the transient non-linear finite element code LS-DYNA. Good agreement with the experimental result was observed, especially for shape and orientation of the delaminations.
A new transversely-isotropic elastic–plastic constitutive model for unidirectional fiber reinforced polymers (FRP) is presented. The model is able to represent the fully nonlinear mechanical behavior under multi-axial loading conditions and under triaxial stress states prior to the onset of cracking. Since associated flow rules often give a wrong prediction of plastic Poisson coefficients, a non-associated flow rule is introduced to provide realistic predictions of the volumetric plastic strains. This paper focusses on the simulation of triaxiality dependent plasticity based nonlinearities of FRP until failure occurs. The onset and propagation of failure is predicted by a new smeared crack model presented in an accompanying paper (Camanho et al., 2012). In order to demonstrate the capabilities of the new material model, a yield surface parameter identification for IM7-8552 carbon epoxy is presented and simulations of quasi-static transverse and off-axis compression tests and of uniaxial compression tests superimposed with various values of hydrostatic pressure are shown as a model verification.
This paper describes and validates a new fully three-dimensional smeared crack model to predict the onset and propagation of ply failure mechanisms in polymer composites reinforced by unidirectional fibers. The failure criteria are used to predict not only the onset of the failure mechanisms but also the orientation of the fracture plane. This information is used in a smeared crack model for transverse cracking that imposes a linear softening relation between the traction acting on the fracture planes and the crack opening displacements. The longitudinal failure mechanisms are represented using bi-linear softening relations. The model is validated using off-axis compression tests performed in unidirectional specimens as well as using tensile tests in notched multidirectional laminates. A good correlation between experimental observations and numerical predictions is obtained.
Micromechanical analyses of unidirectional continuous-fibre reinforced composite materials were performed to study the mechanisms of deformation and fracture of the constituents, and their influence on the mechanical properties of the composite. Special focus was given to the matrix material behaviour as well as to the interface between constituents. The matrix was modelled using a pressure dependent, elasto-plastic thermodynamically consistent damage model. Cohesive elements were used to model the interface between matrix and fibres. Part I of this paper details the continuum model developed for a typical epoxy matrix. Part II will focus on micromechanical analyses of composite materials and the estimation of its elastic and strength properties.
This paper presents the application of a new constitutive damage model for an epoxy matrix on micromechanical analyses of polymer composite materials. Different representative volume elements (RVEs) are developed with a random distribution of fibres. Upon application of periodic boundary conditions (PBCs) on the RVEs, different loading scenarios are applied and the mechanical response of the composite studied. Focus is given to the influence of the interface between fibre and matrix, as well as to the influence of the epoxy matrix, on the strength properties of the composite, damage initiation and propagation under different loading conditions.
In this paper, a systematic and detailed observation was made of the crack extension behavior of thin 90° layers of cross-ply carbon fiber reinforced plastics (CFRP) laminates. The effect of ply thickness on the crack propagation mechanism was discussed with respect to the energy release rate of the intralaminar transverse crack, calculated using finite element analysis. In a laminate with a 40 μm-thick-ply, the crack gradually extended with increasing strain. Conversely, extreme crack extension was found at around 1.0% strain in a laminate with a standard thick ply. Based on the numerical analysis, the crack suppression effect is verified using a thin ply; the effect is apparently caused by a decrease in the energy release rate at the crack tip in the thin layer.
The objective of this study was to characterize the quasi-static and dynamic behavior of composite materials and develop/expand failure theories to describe static and dynamic failure under multi-axial states of stress. A unidirectional carbon/epoxy material was investigated. Multi-axial experiments were conducted at three strain rates, quasi-static, intermediate and high, 10−4, 1 and 180–400s−1, respectively, using off-axis specimens to produce stress states combining transverse normal and in-plane shear stresses. A Hopkinson bar apparatus and off-axis specimens loaded in this system were used for multi-axial characterization of the material at high strain rates. Stress–strain curves were obtained at the three strain rates mentioned. The measured strengths were evaluated based on classical failure criteria, (maximum stress, maximum strain, Tsai–Hill, Tsai–Wu, and failure mode based and partially interactive criteria (Hashin–Rotem, Sun, and Daniel). The latter (NU theory) is primarily applicable to interfiber/interlaminar failure for stress states including transverse normal and in-plane shear stresses. The NU theory was expressed in terms of three subcriteria and presented as a single normalized (master) failure envelope including strain rate effects. The NU theory was shown to be in excellent agreement with experimental results.
A 3D matrix failure algorithm based upon Puck’s failure theory has been developed. The problem of calculating the orientation of a potential fracture plane, which is necessary to assess the onset of matrix failure, has been addressed. Consequently, a fracture angle search algorithm is proposed. The developed algorithm incorporates a numerical search of function extremes which minimises the required computational time for finding the accurate orientation of a potential fracture plane. For illustration, the algorithm together with the three-dimensional Puck failure model has been implemented in LS-DYNA explicit FE code. The fracture angle search algorithm is verified using a virtual uniaxial compression test.
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.
Two theoretical models were used by Sun and Tao [Comp. Sci. Technol. 58 (1998) 1125] in Part A of the exercise to predict the strength and stress/strain curves for a number of test problems. The strength model was based on linear elasticity in conjunction with a ply-discount method using parallel spring stiffness reduction, and the stress/strain curves were predicted by the linear model and a non-linear model incorporating simplified shear-lag analysis and an ABAQUS finite-element package. This paper provides a description of the correlation between experimental results provided by the organizers of the ‘failure exercise’ and the theoretical predictions, published in Part A for (a) biaxial failure envelopes of [0°] unidirectional and [0°/±45°/90°]s, [±30°/90°]s and [±55°]s multi-layered composite laminates, and (b) stress/strain curves for [0°/±45°/90°]s, [±55°]s, [0°/90°]s and [±45°]s under uniaxial and biaxial loadings.
The individual plies of fiber composites are typically used under conditions of multiaxial stress. However, relatively little is known about the response of fiber composites to multiaxial stress, and this is particularly true with respect to strength properties. This paper presents the results of an investigation into the multiaxial strength and stiffness properties of Toray T800/3900-2, which is a high-strain-capability carbon fiber with a high-toughness epoxy-matrix system. Tests were carried out on tubular specimens loaded under combinations of internal pressure, axial tension or compression, and torsion. The tests involved both unidirectional lamina specimens, to determine matrix-dominated properties, and laminate specimens involving three different types of layup. The laminate test results showed that ultimate failure could be satisfactorily correlated by using a maximum-fiber-direction-strain failure criterion.
A new oblique-shaped end-tab was investigated for use in testing off-axis coupon specimens. This tab is able to ensure the axial displacement that is necessary in off-axis specimens under uniaxial loading. The explicit expression of the oblique angle was obtained as a function of the off-axis angle and composite properties. Finite element analysis and experiments were performed to evaluate the effectiveness of the oblique tab. Both results indicated that the oblique tab is more suitable than the conventional rectangular tab for uniaxial off-axis testing.
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.
An experimental study was carried out to characterise the constitutive response of carbon fibre-reinforced epoxy laminates. While maintaining essentially linear behaviour in the fibre and transverse directions, this material displays significant non-linear shear stress–strain behaviour to rupture. It is shown that the well known Hahn-Tsai non-linear shear model does not provide an acceptable fit for the strain range examined and so a novel approach was derived where a cubic spline interpolation method was used to capture the non-linear shear behaviour. The well known ply discount model, based on Hashin’s failure criteria, was also used to predict fibre and transverse matrix damage in the laminates. The spline approach is coupled with maximum strain failure criteria to predict the response in the in-plane and out-of-plane shear directions. The material Jacobian matrix is fully defined, thus allowing a full implicit material model to be implemented. Hence, the model is suitable for both implicit and explicit finite element codes. It is shown that the model accurately predicts the response of the material for load cases in which shear stresses dominate. The performance of the model is demonstrated by considering a number of laminate configurations and failure of an open-hole tension specimen.
The aim of this work is to develop a unified and rational formulation of isotropic and anisotropic hardening with;_n the framework of the tensor functions representation theory. We consider the evolution of the yield criteria during plastic deformations and we assume that this evolution depends on the strain history only through the present value of the plastic strain. For more complicated situations, the proposed concepts can be developed in a straightforward manner.
Three-dimensional fatigue failure criteria for unidirectional fibre composites under states of cyclic stress are established in terms of quadratic stress polynominals which are expressed in terms of the transversely isotropic invariants of the cyclic stress. Two distinct fatigue failure modes, fibre mode, and matrix mode, are modelled separately. Material information needed for the failure criteria are the S-N curves for single stress components. A preliminary approach to incorporate scatter into the failure criteria is presented. (A)
Unidirectional and textile carbon/epoxy composites were characterized under multi-axial states of stress. In-plane and through-thickness tensile, compressive, and shear tests were conducted at various orientations with the principal material axes. The stress–strain behavior, failure modes, and strengths were recorded. Results were compared with three types of failure criteria in three dimensions, limit criteria (maximum stress), fully interactive criteria (Tsai-Hill, Tsai-Wu), and failure mode based and partially interactive criteria (Hashin–Rotem, Sun, NU). The latter, a new interfiber/interlaminar failure theory developed by the authors, was found to be in excellent agreement with experimental results, especially in cases involving interfiber/interlaminar shear and compression. Of special note was the failure mode in transverse compression, where the failure plane was not predictable by conventional composite failure theories. The orientation of the failure plane was more in line with predictions by a Mohr–Coulomb failure model.
An analytical model based on the analysis of a cracked unit cell of a composite laminate subjected to multiaxial loads is proposed to predict the onset and accumulation of transverse matrix cracks in the 90n plies of uniformly stressed {±θ/90n} s laminates. The model predicts the effect of matrix cracks on the stiffness of the laminate, as well as the ultimate failure of the laminate, and it accounts for the effect of the ply thickness on the ply strength. Several examples describing the predictions of laminate response, from damage onset up to final failure under both uniaxial and multiaxial loads, are presented.
The predictions for UD and laminated composites from Part A of this exercise [Compos. Sci. Technol. (1998) 1023] are compared with test data [Compos. Sci. Technol. (in press)]. Questions concerning the accuracy and flexibility of our progressive criterion are answered herein. In general, the intact and degraded models provide good agreement. So do several stress/strain curves. The selective damage scheme was found to be the source of some problems at certain loading conditions. By eliminating this selective degradation, agreement between the prediction and the test data were improved. Empirical factors are easily adjusted to close the gap between theory and data. Those factors are within the bounds set by the theory in Part A. Discrepancies do happen and some can be attributed to bad data while some have no simple explanation. All in all, the exercise has been worthwhile and may have impact on the growth of composites in the years to come. An easy to learn Excel-based program for plotting failure envelopes can be downloaded free of charge for interested parties.
Using a recently developed failure theory for transversely isotropic fiber composites, it is shown how the orientation of the failure surface can be determined for transverse tension and compression. It is also shown that failure surface orientations decompose into those of ductile type versus those of brittle type. Experimental data on failure surface orientations have been obtained for carbon fiber composite systems based on both thermoplastic and thermosetting matrix materials. Average compression failure planes for the different composite materials were measured to range from 31° to 38° from the load axis. Reasonable agreement was obtained between these measured angles and those predicted from application of the new failure theory.
An experimental procedure has been developed in order to determine a failure envelope for unidirectional fiber-reinforced materials (FRM). This method provides failure data for a wide range,
- 0.47 < s22 /s12 < 0.47 - 0.47< \sigma _{22} /\sigma _{12}< 0.47
. These results provided a way to build a failure envelope for investigated material as well as to verify failure criteria. The proposed method of inducing bidimensional state of stress may be used for a wide range of other materials as well as FRM.