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Fracture plane based failure criteria for fibre-reinforced composite materials under three-dimensional stress state are presented. The failure function is taken as a polynomial expansion in terms of the stress components on fracture plane, which provides a general mathematical technique for constructing Mohr’s fracture hypothesis-based criteria. The polynomial expansion is then truncated at the quadratic terms to approximately describe the failure function. Besides the basic strengths of UD laminates, the fracture plane angles under transverse tension/compression and pure shear are introduced to calibrate the failure criteria, since Mohr’s concept can be described completely and exactly only by both the basic strengths and the fracture plane angles. According to experimental evidences, the interaction between matrix-dominated and fibre-dominated failure modes is also considered in the present study. No empirical or artificially defined parameters are included in the criteria. Experimental verification for different kinds of unidirectional composites under various stress states demonstrates that the proposed failure criteria have a good predictive ability.

Puck's action plane failure criteria have already proven their capability in the first and second world-wide failure exercises (WWFE-I and WWFE-II). However, Puck and his co-workers have only recommended inclination parameters for GFRP/Epoxy and CFRP/Epoxy. These UD composites generally have high transverse compressive-to-tensile strength ratios YC/YT, and are regarded by them as intrinsically brittle materials. Therefore, Puck's inter fibre fracture (IFF) criteria might not be directly applied to other types of UD composites with low YC/YT ratios. In particular, Puck's original IFF criteria will result in unrealistic predictions if YC/YT is extremely low. In the present study, Puck's original IFF criteria are extended to all types of UD composite materials to solve the problem. Composites are divided into three categories, namely semi-brittle materials, brittle materials, and intrinsically brittle materials. Depending on the material category, three different algorithms are proposed for determination of the two parameters in Puck's IFF criteria, namely the resistance of the action plane against transverse tensile stressing, R ⊥ A t , as well as the inclination parameter of contour lines of the fracture body, p ⊥ ⊥ . The present criteria are theoretically evaluated for composites with low YC/YT ratios, while the predictions of the present criteria are compared with the test results of composites with high YC/YT ratios such as thermoset GFRP and CFRP. Theoretical and experimental assessment demonstrates the reasonableness of the extension of Puck's IFF criteria.

A physically based failure criterion distinguishing the different effects of hydrostatic tensile and compressive stress is developed for homogeneous and isotropic materials. It is reasonably assumed that failure is related to the shape and volume change of isotropic materials at the macroscopic scale. Shape distortion and volume dilation (i.e., hydrostatic tension) are capable of producing material failure, while volume contraction (i.e., hydrostatic compression) has an impeding effect upon failure initiation. The different roles of hydrostatic tension and compression may lead to differences of the applied failure functions. In the present study, two failure formulas are proposed, considering the different effects of hydrostatic stress upon yielding/fracture of homogeneous and isotropic materials separately. The good agreement of the present theory with a large number of experimental data is observed, and the present theory shows a wide range of applicability.

This paper presents a numerical investigation into the effects of missing fasteners on the mechanical characteristics of double-lap, multi-row composite bolted joints. A highly efficient explicit finite element model, which was validated effective and accurate by experiments, was developed and employed to conduct the virtual tests. Single-column and multi-column joints with various positions of missing fastener were considered. It is shown that the removal of fasteners can reduce the joint stiffness significantly, especially in joints with fewer columns or missing fasteners in the outside rows. The removal of fasteners can also cause considerable reductions in both the initial significant failure loads and ultimate loads of multi-column joints, while in single-column joints only the initial significant failure loads are influenced. Considering the load distribution, it is suggested that bolts in the same column as or in the adjacent column to the missing fastener experience a notable growth in load. Meanwhile, if a bolt bears more loads in the pristine joint, the larger changes in stiffness, ultimate strength, and load distribution may be obtained when it is lost.

A failure criterion for isotropic materials is developed in the present study. The fundamental hypotheses of the Mohr-Coulomb criterion are re-examined and re-evaluated. The failure function of Mohr’s envelope is firstly expanded into a polynomial in terms of the stress components (σn, τn) on the failure plane, then truncated at the second order due to the fine curve-fitting results of quadratic functions with experimental data. The parameters of the nonlinear failure functions are calibrated by the three basic mechanical properties—the uniaxial tensile and compressive strengths, T and C, as well as the pure shear strength, S. Theoretical and experimental evaluation for various isotropic materials demonstrates that the present failure criterion provides no worse results for ductile materials and far better results for brittle materials compared with the linear Mohr-Coulomb criterion. The strength theory shows good agreement with physical reality and has a wide range of applicability.

Failure criteria for unidirectional composite materials based on Hashin’s theory are developed. Although Hashin’s criteria are very popular in composite structural applications due to their simplicity of concept and ease of use, they do not always fit experimental results well. In the present study, the fundamental hypotheses proposed by Hashin are re-examined and re-evaluated. Hashin’s criteria for the tensile fiber mode and tensile matrix mode are modified based on physical considerations. The interaction between the fiber and matrix failure modes is also taken into account. Experimental verification for different kinds of unidirectional composites under various stress states demonstrates that the proposed failure criteria have good improvements over Hashin’s criteria, especially in the tensile fiber and matrix mode region. The present theory is in good agreement with physical reality and has a wide range of applicability.

A method was developed to predict numerically the damage of composite laminates with multiple plies under low-velocity impact loading. The Puck criterion for 3D stress states was adopted to model the intralaminar damage including matrix cracking and fibre breakage, and to obtain the orientation of the fracture plane due to matrix failure. According to interlaminar delamination mechanism, a new delamination criterion was proposed. The influence of transverse and through-thickness normal stress, interlaminar shear stress and damage conditions of adjacent plies on delamination was considered. In order to predict the impact-induced damage of composite laminates with more plies quickly and efficiently, an approach, which can predict the specific damage of several plies in a single solid element, was proposed by interpolation on the strains of element integration points. Moreover, the proposed model can predict specific failure modes. A good agreement between the predicted delamination shapes and sizes and the experimental results shows correctness of the developed numerical method for predicting low-velocity impact damage on composite laminates.

Low-velocity impact on the free edge of composite stiffener is considered as a critical factor on the loss of compression strength. This paper proposes a phenomenologically-based mechanical finite element model for the Compression-After-Edge-Impact (CAEI) failure prediction of the composite panel stiffened with T-shaped stiffeners, of which the web is subjected to edge impact damage. Based on the specific failure mechanisms during an edge impact, localized crushing failure, which is insignificant during a classic skin impact, however is considered as a key point of the proposed model for the simplification of impact-induced damage. With the help of a composite damage model comprising both continuum damage mechanics model and surface-based cohesive contact model, a good correlation between the experimental and numerical results is obtained, and therefore validates correctness and effectiveness of the proposed mechanical model. Furthermore, the results reveal that the propagation of fiber compressive failure plays a major role in the compressive failure of the impacted web, of which complete fracture determines the ultimate failure load of the T-stiffened composite panel.

A phenomenological-based mechanical finite element model is developed for the prediction of ultimate compression loads and failure modes of wing relevant composite panels stiffened with I-shaped stiffeners, of which the edge is subjected to impact loading. The initiation of intralaminar failure including fiber and inter-fiber fracture is evaluated by Puck criteria, and its evolution is assumed to be controlled by equivalent strains. The interlaminar failure, namely delamination, is simulated by employing a surface-based cohesive contact model. For R-sections of the impacted stiffener, interfacial delamination, which may cause premature failure and to some extent reduce the load carrying capacity, is efficiently considered. A good correlation between the experimental and numerical results shows correctness and effectiveness of the proposed mechanical method for predicting CAEI response. Furthermore, numerical results reveal that not only failure propagation of the impacted site but that of the other undamaged side dominate the compressive mechanism of the edge impacted stiffener, of which complete fracture determines the ultimate failure load of the I-stiffened composite panel.

Experiments along with the finite element model were used to analyze the influences of thickness ratio of flange and skin (hereinafter referred to as thickness ratio) of T-joint on the reinforcing effect of Z-pin. Results showed that the thickness ratio significantly influences the reinforcement effect of Z-pin. Whether or not Z-pin should be applied to a specific T-joint can be decided by the thickness ratio. For T-joints with large thickness ratios (larger than 0.32 for the studied T-joint), the application of Z-pin is an effective way to increase the carrying capacities of the T-joints, while for T-joints with small thickness ratios (smaller than 0.32 for the studied T-joint), the reinforcing effect of Z-pin is not obvious. Besides, the corresponding load value under large displacement in the load-displacement curves of T-joints with different thickness ratios are similar.

A phenomenological-based micro–macro mechanical method, comprising the coupling of a 3D continuum damage mechanics (CDM) model with an original micromechanical FE model, is presented to predict low velocity impact response of composite laminates. The key point of the proposed method is the definition and computation of saturation crack density, which is used to scale impact-induced delamination instead of via expensive cohesive zone model based FEM. In order to gain the specific value of the saturation crack density, a micromechanical FE model is established based on the RVE technique. Additionally, the initiation of intralaminar failure including fiber fracture (FF) and inter-fiber fracture (IFF) is evaluated by Puck criteria, and its evolution, with considering effects of the fracture plane angle, is assumed to be controlled by equivalent strains on the fracture plane rather than the classic material principal axis plane. A good agreement between the experimental and simulated results shows correctness and effectiveness of the developed micro–macro mechanical method for predicting impact response and damage using a relatively coarse mesh. Furthermore, significant reduction of computational cost, compared with existing techniques, can be achieved with the novel mesh-independent method.

The purpose of this paper was to investigate the effect of low velocity edge impact damage on the damage tolerance of wing relevant composite panels stiffened with both T-shaped and I-shaped stiffeners under uniaxial compression load. Six stiffened composite panel configurations, including four specimens for each configuration, were manufactured and tested. Before Compression-After-Impact (CAI) tests, the key dimensions of specimens were measured and a vertical drop-weight testing device was used to impact on critical locations such as the skin and the free edge of a stiffener. Different damage types and shapes were discovered from different locations of impact after careful inspection by visual and ultrasonic C-scan. The experimental results reveal the compression failure mechanism that local buckling, subsequent damage propagation and final fracture of the edge impacted stiffener are triggers of the final failure of a stiffened composite panel, which as well determine the ultimate load carrying capacity. In addition, under identical edge impact levels, the damage tolerance behavior of T-stiffened composite panel is distinctly superior to that of I-stiffened composite panel, which results in more cautious design regarding edge impact damage tolerance of the panel stiffened with I-stiffeners.

Composite laminates have been extensively used in the aerospace and automotive industries due to their excellent stiffness and strength. Fiber bridging is a unique phenomenon of layered composite materials that increases the fracture toughness of the composites several times. This characteristic enables fiber bridging to be an important crack shielding mechanism during delamination and arouses wide attention from researchers. Most research is focused on studying the mechanism of fiber bridging and establishing the traction separation relation of bridging for delamination simulation, while for a given composite material, a simple and direct approach to identify whether fiber bridging could occur during the delamination is still lacking. This paper provides an efficient method to deal with this problem. It is based on the weak fiber/matrix interface assumption so that fibers can be pulled out easier to bridge the cracked faces. Eleven groups of DCB tests, both with and without fiber bridging, are used to validate the feasibility of this approach. Besides, this approach can also be extended to Mode II or mixed Mode I/II test.

Different failure modes are not explicitly accounted for in the Tsai–Wu failure criterion for composite materials, and the factor F12 in the expression cannot be determined by the basic strength values of the materials. In view of these two shortcomings of the Tsai–Wu criterion, an improved criterion was proposed based on the reasonable assumption that composites exhibit infinite strength under pure hydrostatic pressure. Some coefficients in the quadratic tensor expression of the Tsai–Wu failure criterion are redetermined using the basic strength value of the material, including the coefficient F12, under four different stress states (fiber tension and compression, matrix tension and compression). The reconstructed Tsai–Wu failure criterion can distinguish the failure modes based on different coefficient values under different stress states. In the progressive damage analysis of composite materials, the stiffness can be reduced in different manners based on each failure mode. Experimental verification for different kinds of unidirectional composites under various stress states was conducted, demonstrating that the improved Tsai–Wu failure criterion has a better prediction ability and accuracy than the original criterion.

Through-thickness compressive stress of composite laminates can inhibit the interlaminar shear failure which has been proved by experiments. However, common delamination damage initiation criterion cannot well describe this mechanism. For this issue, in this article, based on the insight of the failure mechanism, an interlaminar failure function is constructed at first. Then, a delamination failure criterion considering the effect of through-thickness compression on interlaminar shear failure is established based on logical deductions from a polynomial expansion of the failure function. In the criterion, a constant coefficient with physical meaning is used to describe the effect of through-thickness compression on the interlaminar shear failure, and the estimation method of the coefficient is also given in this study. Here, this failure criterion can be considered as a general form to describe the delamination between laminae, by defining different coefficient, it can be converted to other criteria such as the conventional secondary stress failure criterion or the Christensen failure criterion. Finally, by comparing the numerical calculation and experimental results, the delamination failure criterion proposed in this study exhibited a good prediction ability for the interlaminar damage under different loading conditions.

This paper presents the development and validation of a mesoscale numerical model for predicting damage and failure of bolted joints in laminated composites with different configurations and geometries. Double-shear and single-shear composite bolted joints with different widths and end distances were analyzed. The composite material model combined smeared crack models for all types of intralaminar failure mechanisms, and an interface discrete cohesive-zone model for interlaminar failure. Three dimensional (3D) phenomenological invariant-based failure criteria using in-situ ply strengths were used for the prediction of intralaminar damage onset, together with mechanism-based continuum damage models (longitudinal bi-linear damage model and transverse 3D smeared crack model) for intralaminar damage propagation. An interface cohesive-zone model with consistent initiation and evolution criteria based on the Benzeggagh-Kenane (B-K) law was used to simulate delamination. Particularly, for the first time, the model considered the inherent cohesive-frictional behavior in the intralaminar transverse failure and delamination, namely the frictional sliding in diffuse micro-cracks during damage propagation and in localized meso-cracks after complete fracture. In the 3D explicit finite element models, a fiber-aligned mesh was used for the discretization of composite plies. A multi-zone modelling strategy was used to make the computational cost acceptable for engineering applications. Detailed comparisons between the numerical results and the experimental data previously obtained were performed, with focus on the macroscopic mechanical behavior and mesoscale failure mechanisms. A good correlation between tests and analyses was found. Additionally, several complex failure mechanisms were revealed by the numerical simulations, which could not be clearly identified in previous experimental studies.

A new cohesive damage model was proposed to analyze the Mode I, Mode II, and mixed-mode bridging micromechanisms of a single Z-pin in the quasi-isotropic laminate. One zero-thickness cohesive element was embedded into each pair of adjacent elements in the damage zone to model the multi-directional Z-pin failure including splitting and rupture, snubbing damage in the resin-rich region, and interfacial debonding during bridging. The FE predicted bridging laws and damage modes of the Z-pin under Mode I, 30° and 60° mixed-mode, Mode II loading all agreed well with the experimental results. Besides, it was found that the splitting damage of the Z-pin and the snubbing damage in the resin-rich region were non-negligible.

Although the linear Mohr&ndash, Coulomb criterion is frequently applied to predict the failure of brittle materials such as cast iron, it can be used for ductile metals too. However, the criterion has some significant deficiencies which limit its predictive ability. In the present study, the underlying failure hypotheses of the linear Mohr&ndash, Coulomb criterion were thoroughly discussed. Based on Mohr&rsquo, s physically meaningful concept of fracture plane, a macroscopic strength criterion was developed to explain the failure mechanism of isotropic metals. The failure function was expressed as a polynomial expansion in terms of the stresses acting on the fracture plane, and the quadratic approximation was employed to describe the non-linear behavior of the failure envelope. With an in-depth understanding of Mohr&rsquo, s fracture plane concept, the failure angle was regarded as a generalized strength parameter in addition to the failure stress (i.e., the conventional basic strength). The undetermined coefficients of the non-linear failure function were calibrated by the strength parameters obtained from the common uniaxial tension and compression tests. Theoretical and experimental assessment for different types of isotropic metals validated the effectiveness of the proposed criterion in predicting material failure.

An approach based on a displacement compatibility model is presented for both riveted and bonded stiffened composite panels containing impact damage. This represents the first application of the displacement compatibility model to the failure analysis of impacted stiffened composite panels, and some newresults are obtained for the impact damage tolerance properties of stiffened composite panels. In the present analysis, the previous displacement compatibility model for a stringer/orthotropic skin panel is improved for a stringer/unbalanced skin panel. The impact damage is simplified as an elliptic hole based on the compressive failure mechanisms of impacted composite laminates and stiffened panels. Predictions for failure loads and damage arrest capability agree well with experimental results for several composite panel configurations. The important results obtained in this study are: (1) damage arrest capability is dominated by the strength of the skin/stringer attachment; (2) distinct two-stage failure shows that the riveted panels have significant damage arrest capability due to the high shear strength of the rivets; and (3) since the very low shear strength of the skin/stringer attachment, the co-cured panels have no damage arrest capability.

An approach based on a displacement compatibility model is developed for stiffened composite panels with a crack. Some important improvements on the damage tolerance analysis of the stiffened composite panels have been made in comparison with previous work. Some new results are obtained regarding the effects of adhesive nonlinearity, stringer stiffness and bending, and stringer spacing on strengths and crack growth behaviours of bonded skin/stringer panels. The study indicates that the adhesive nonlinearity benefits the load bearing capacity of the panels. When the stringer is quite thick in comparison to the skin thickness, its out-of-plane bending will lower panel failure strains. Increasing stringer stiffness can not often guarantee the high failure strains of bonded skin/stringer composite panels. As the stringer stiffness exceeds some value, its increase has a negative effect on the load bearing capacity of the panels. For a given ratio of stringer stiffness to panel stiffness, the failure strains of the panels increase as stringer spacing, Wa, decreases. Predictions for failure strains and crack arrest capability agree well with experimental results for several composite panel configurations.