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This paper presents an experimental study of tensile properties, using a carbon–polypropylene uni-directional sheet with a thickness of 0.15 mm, which shows that highly non-linear stress–strain curves can be achieved with cross-angle-ply laminates. Generally, these properties are studied from the scanning electronic microscope and X-ray computed tomography. Cross-ply laminates with fiber orientation angles from 15 to 60° are investigated and it is found that there are the pseudo-ductile behavior with the fiber rotation, especially at fiber orientation angles from 30° to 60°.The Pseudo-ductile behavior is a phenomenon in which the apparent strain increases after yielding with strain hardening. It is greatly affected by the fiber reorientation in the loading direction. The fiber reorientation is allowed the plasticity of the polypropylene and thickness of each layer. [ABSTRACT FROM AUTHOR]

The concept of the "effective stiffness" for plies in laminates containing intralaminar cracks is revisited presenting rather accurate fitting expressions for the effective stiffness dependence on crack density in the ply. In this article, the effective stiffness at certain crack density is back-calculated from the stiffness difference between the undamaged and damaged laminate. Earlier finite element method analysis of laminates with cracked 90-plies showed that the effective longitudinal modulus and Poisson's ratio of the ply do not change during cracking, whereas the transverse modulus reduction can be described by a simple crack density dependent function. In this article, focus is on the remaining effective constant: in-plane shear modulus. Finite element method parametric analysis shows that the dependence on crack density is exponential and the fitting function is almost independent of geometrical and elastic parameters of the surrounding plies. The above independence justifies using the effective ply stiffness in expressions of the classical laminate theory to predict the intralaminar cracking caused stiffness reduction in laminates with off-axis plies. Results are in a very good agreement with (a) finite element method calculations; (b) experimental data, and (c) with the GLOB-LOC model, which gives a very accurate solution in cases where the crack face opening and sliding displacements are accurately described. [ABSTRACT FROM AUTHOR]

This paper presents a numerical study evaluating the influence of nonlinear material behavior on the stiffness reduction due to inter-fiber cracks. It is shown that the relation between crack density and damage variables changes as the load level increases. A three-dimensional nonlinear material model is used in a representative volume element study to accurately calculate the local stress distribution around cracks. The studies show that as the load increases the stress recovers to the far-field level within a shorter distance, and consequently the plastic deformation causes a decrease in the crack-induced stiffness reduction. To provide damage variables for a coupled elastoplastic-damage material approach at the homogenized ply level, the results of a systematic representative volume element study are used for interpolation. For verification, the response curves of several laminates influenced by inter-fiber cracks are simulated and compared to experimental results. The presented procedure enables the constitutive laminate response under large deformations to be accurately predicted. [ABSTRACT FROM AUTHOR]

The old concept of the effective stiffness of a 90-layer with intralaminar cracks is revisited performing 3-D FEM parametric analysis of symmetric and balanced laminates. It is shown, focusing on the effective transverse modulus, that the expected dependence of this property on composite elastic properties and laminate lay-up is very weak and follows very simple rules. Calculations show that the effective longitudinal modulus and Poisson’s ratio of the layer are not affected at all by intralaminar cracking. Simple fitting curve for effective transverse modulus change with normalized crack density is obtained from analysis of GF/EP cross-ply laminate. It is shown, comparing with FEM results and experimental data, that this expression can be used as a ‘master curve’ in laminate theory to predict macroscopic elastic property change with crack density in laminates with very different lay-ups and made of different unidirectional composites. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This is a contribution to the exercise that aims to benchmark and validate the current continuum damage and fracture mechanics methodologies used for predicting the mechanical behaviour of fibre-reinforced plastic composites under complex loadings. The paper describes an analytical approach to predict the effect of intra- (matrix cracking and splitting) and inter-laminar (delamination) damage on the residual stiffness properties of the laminate, which can be used in the post-initial failure analysis, taking full account of damage mode interaction. The approach is based on a two-dimensional shear lag stress analysis and the equivalent constraint model of the damaged laminate with multiple damaged plies. The application of the approach to predicting degraded stiffness properties of a multidirectional laminate with multilayer intra- and inter-laminar damage is demonstrated for [0/90/0] and [0/908/0] cross-ply laminates made from a specific glass/epoxy system under in-plane uniaxial and biaxial loading damaged by transverse and longitudinal matrix cracks and crack-induced transverse and longitudinal delamination. [ABSTRACT FROM AUTHOR]

The accurate prediction of damage and failure in laminated composites is still a major issue in many structural applications. The paper provides a detailed description of a new damage mesomodel and examines its application to solve material and structural problems for the Test Cases proposed in the Third World-Wide Failure Exercise (WWFE-III). The cases cover various materials (glass/epoxy and carbon/epoxy), lay-ups (unidirectional, cross ply, quasi-isotropic, angle ply and general multi-directional laminates), loadings (uniaxial, biaxial, bending, thermal and loading-unloading) and features (ply sequence, size effects and open hole). The model deals with various damage scenarios and mechanisms of degradation, including diffuse intralaminar damage, diffuse interface damage, localized delamination, fibre breakage and plasticity, and can predict the evolution of a laminate’s response until final failure. Some issues concerning the limited information available in the exercise for the identification of the parameters of the mesomodel are also discussed. [ABSTRACT FROM AUTHOR]

Stiffness reduction simulation in laminates with intralaminar cracks is usually performed assuming that cracks are equidistant and crack density is the only parameter needed. However, the crack distribution in the damaged layer is very non-uniform, especially in the initial stage of multiple cracking. In this article, the earlier developed model for general symmetric laminates is generalized to account for non-uniform crack distribution. This model, in which the normalized average crack-opening and crack-sliding displacements are the main characteristics of the crack, is used to calculate the axial modulus of cross-ply laminates with cracks in internal and surface layers. In parametric analysis, the crack-opening displacement and crack-sliding displacement are calculated using finite element method, considering the smallest versus the average crack spacing ratio as non-uniformity parameter. It is shown that assuming uniform distribution, we obtain lower bond to elastic modulus. A ‘double-periodic’ approach presented to calculate the crack-opening displacement of a crack in a non-uniform case as the average of two solutions for periodic crack systems is very accurate for cracks in internal layers of cross-ply laminates, whereas for high crack density in surface layers, it underestimates the modulus reduction. [ABSTRACT FROM AUTHOR]

A theoretical model is proposed to evaluate effective stiffness in general symmetric composite laminates due to transverse cracking. In the model, the crack shape is assumed to be a function of crack density. The original contribution of this article is that crack geometries are not constrained to the forms of assumed shape functions. Instead, the natural forms of the crack shape functions are shown to have forms containing hyperbolic sine and hyperbolic cosines based on elastic analysis. Displacement fields and stress components satisfy the boundary and continuity conditions. The change in stillness reduction is examined theoretically. Predicted results are compared with experimental data for [θm/90n]s glass/epoxy laminates and [θm/90n]s AS4/epoxy laminates. [ABSTRACT FROM AUTHOR]

A variational model is presented to analyze the effect of transverse cracking in [90n/±θm]s composite laminates under uniaxial tensile loading. Crack geometry in the model is an unknown function which is determined by the derived governing equation rather than assumed shape functions. Analysis shows that the crack shape varies with crack density. Predicted results for stiffness reduction in [90n/±θm]s and [±θm/90n]s laminates indicate that the stacking sequence of laminates is important to the stiffness degradation with damage of composite materials. [ABSTRACT FROM AUTHOR]

Transverse cracking detection in a uniaxially loaded symmetric cross-ply hybrid composite laminate is studied using modal-based acoustic emission (MAE) method. Transverse cracking in the hybrid laminate is identified in conjunction with the finite element analysis and acoustic emission (AE) testing on unidirectional carbon/epoxy specimens. Higher wave modes are involved in various damage events in both types of specimens. Wave attenuation in the hybrid laminate is observed to be much stronger than in the unidirectional carbon/epoxy specimen, resulting in fewer AE events detected. A material failure kinetics-based characterization of the transverse cracking process is proposed. Results of dynamic response analysis of the hybrid laminate show good agreement with the AE experiment data. [ABSTRACT FROM AUTHOR]

A generalized approach has been developed to evaluate the two-dimensional stress distribution in cracked cross-ply laminates. Comparisons between finite element analysis and analytical models show that a complete parabolic analysis extended to 0° and 90° layers yields a fairly good approximation of the strain and stress distributions in the case of [0°/90°]s, with equal thicknesses of 0° and 90° layers. However a deviation is observed in the case of thick 0° layers. The analysis presented in this paper keeps a parabolic variation of the longitudinal displacement across the thickness of 90° layer, and generalizes the longitudinal displacement distribution across the thickness of 0° layers by taking an indeterminate distribution. The development of this analysis allows us to obtain the general form of the stress distributions in 0° and 90° layers. Finally, it is proposed a particular form of the variation of the longitudinal displacement across the thickness of 0° plies which yields a good agreement of the stress distributions with finite element analysis for the different stacking sequences investigated. [ABSTRACT FROM PUBLISHER]

A two-dimensional shear-lag analysis predicting the effect of interlayers on transverse cracking is developed. The orthotropic nature of the material, as well as crack interactions are incorporated, and a Griffith's type fracture criterion is used to predict the transverse crack failure. The obtained stress solution satisfies the traction-free crack surface boundary conditions. The analysis results are compared to experimental data of a well characterized model material, and parametric studies identifying key parameters in mechanical behavior of interlayered composites are presented. [ABSTRACT FROM PUBLISHER]