Maria Kashtalyan

Stiffness degradation in cross-ply laminates damaged by transverse cracking and splitting

Abstract In contrast to the few existing theoretical models (Highsmith and Reifsnider, ASTM STP 1986;907:233–251; Hashin, Trans ASME J Appl Mech 1987;54:872–879; Daniel and Tsai, Comp Eng 1991;1(6):355–362; Tsai and Daniel, Int J Solid Structures 1992;29(24)3251–3267; Henaff-Gardin et al., Comp Structures 1996;36:113–130; 1996;36:131–140), based on the consideration of a repeated laminate element defined by the intersecting pairs of transverse cracks and splits, the new approach for evaluating the stiffness degradation in [0 m /90 n ] s laminates due to matrix cracking both in the 90° (transverse cracking) and 0° (splitting) plies employs the Equivalent Constraint Model (Fan and Zhang, Composites Science and Technology 1993;47:291–298). It also uses an improved 2-D shear lag analysis (Zhang et al., Composites 1992;23(5):291–298; 1992;23(5):299–304) for determination of stress field in the cracked or split lamina and In-situ Damage Effective Functions for description of stiffness degradation. Reduced stiffness properties of the damaged lamina are found to depend explicitly upon the crack density of that lamina and implicitly upon the crack density of the neighbouring lamina. Theoretical predictions for carbon and glass fibre reinforced plastic cross-ply laminates with matrix cracking in the 90° ply revealed significant reduction in the Poissons ratio and shear modulus due to additional damage (splitting) in the 0° ply.

The effect of delaminations induced by transverse cracks and splits on stiffness properties of composite laminates

In an effort to evaluate stiffness degradation due to delaminations growing at the 0 8/908 interface from the tips of transverse cracks in the 908 plies and splits in the 08 plies of cross-plyâ0m=90nas laminates, a new theoretical approach was developed. It employs the Equivalent Constraint Model of the damaged lamina [Fan J, Zhang J. In-situ damage evolution and micro/macro transition for laminated composites. Composites Science and Technology 1993;47:107‐118], which allows one to avoid cumbersome consideration of the repeated laminate element defined by the intersecting pairs of transverse cracks and splits. It also uses an improved 2D shear-lag analysis [Zhang J, Soutis C, Fan J. Strain energy release rate associated with local delamination in cracked composite laminates. Composites 1994;25(9):851‐862] to determine the stress fields in the explicitly damaged lamina and the In situ Damage Effective Functions to describe its reduced stiffness properties. Reduced stiffness properties of the damaged lamina are found to depend explicitly upon the crack density and relative delamination area associated with that lamina and implicitly upon two damage parameters associated with the neighbouring lamina. Theoretical predictions reveal that transverse crack tip delaminations cause significant reduction in the shear modulus and Poisson’s ratio of cross-ply and symmetric balancedâ^um=90nas laminates. Dependence of the laminate reduced elastic properties on the orientation angle of the constraining ply is examined. Contribution of each damage mode (transverse cracking, transverse crack tip delaminations, splitting and split tip delaminations) into stiffness loss is established. q 2000 Elsevier Science Ltd. All rights reserved.

Predicting residual stiffness of cracked composite laminates subjected to multi-axial inplane loading

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 / 90 8 / 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.

Three-dimensional analysis of a functionally graded coating/substrate system of finite thickness

The concept of functionally graded material (FGM) is currently actively explored in coating design for the purpose of eliminating the mismatch of thermomechanical properties at the interfaces and thus increasing the resistance of coatings to functional failure. In the present paper, three-dimensional elastic deformation of a functionally graded coating/substrate system of finite thickness subjected to mechanical loading is investigated. A comparative study of FGM versus homogeneous coating is conducted to examine the effect of the coating type on stress and displacement fields in the system.

Strain energy release rate for off-axis ply cracking in laminated composites

Strain energy release rate associated with matrix cracking in the θ- layer of unbalanced symmetric [0/θ], composite laminate is predicted analytically using a 2-D shear lag stress analysis and the Equivalent Constraint Model (ECM). Its dependence on the crack density and ply orientation angle is examined for glass/epoxy and carbon/epoxy laminates. Suitability of a mixed mode fracture criterion to predict the cracking onset strain is discussed.

Delamination Growth and Residual Properties of Cracked Orthotropic Laminates Under Tensile Loading

The expressions for the strain-energy release rate associated with local delaminations growing from the tips of angle-ply matrix cracks in orthotropic composite laminates loaded in tension are presented. The strain energy release rate and the laminate residual stiffness properties are predicted as functions of matrix-crack density and delamination length.

Use of a Functionally Graded Interlayer to Improve Bonding in Coated Plates

Coatings play an important role in a variety of engineering applications, protecting metallic or ceramic substrates against oxidation, heat penetration, wear and corrosion. Conventional coatings, which usually consist of one or two homogeneous layers deposited on a substrate, are susceptible to cracking and debonding due to the mismatch of thermomechanical properties between the coating and the substrate. To increase resistance of coatings to functional failure, the concept of a functionally graded material is being actively explored in coating design. One of the possible ways to eliminate the mismatch of material parameters between the coating and the substrate is to introduce a functionally graded interlayer between the substrate and the top coat. This paper investigates elastic deformation of coated plates with and without a functionally graded interlayer in the context of three-dimensional elasticity, assuming the Youngs modulus of the interlayer varies exponentially through the thickness. It is shown that the use of the functionally graded interlayer in plates subjected to transverse loading eliminates discontinuity of the in-plane normal stress across interfaces without increasing the stress magnitude at the top surface of the coating.

Modelling of stiffness degradation due to cracking in laminates subjected to multi-axial loading

The paper presents an analytical approach to predicting the effect of intra- and interlaminar cracking on 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 laminate with multiple damaged plies. The application of the approach to predicting degraded stiffness properties of multidirectional laminates under multi-axial loading is demonstrated on cross-ply glass/epoxy and carbon/epoxy laminates with transverse and longitudinal matrix cracks and crack-induced transverse and longitudinal delaminations. This article is part of the themed issue ‘Multiscale modelling of the structural integrity of composite materials’.

Influence of the Crack Widening on the Transverse Cracking in Lamellar Metal-Ceramic Composites

Stress field in the ceramic layer containing multiple transverse cracks is determined using a modified 2-D shear lag approach and a finite element method.

Stress analysis of cracked MMCs with Lamellar microstructure

Stress fields in a single-domain sample of MMC containing multiple cracks in the ceramic layer are investigated using a direct analytical method and finite element modeling.