Applied Composite Materials (v.18, #1)

Two main damage mechanisms of laminates—matrix cracking and inter-ply delaminationare closely linked together (Joshi and Sun 1). This paper is focussed on interaction between matrix cracking and delamination failure mechanisms in CFRP cross-ply laminates under quasi-static tensile loading. In the first part of the work, a transverse crack is introduced in 90o layers of the cross-ply laminate [01/904/01], and the stresses and strains that arise due to tensile loading are analyzed. In the second part, the cohesive zone modelling approach where the constitutive behaviour of the cohesive elements is governed by traction-displacement relationship is employed to deal with the problem of delamination initiation from the matrix crack introduced in the 90o layers of the laminate specimen. Additionally, the effect of microstructural randomness, exhibited by CFRP laminates on the damage behaviour of these laminates is also accounted for in simulations. This effect is studied in numerical finite-element simulations by introducing stochastic cohesive zone elements. The proposed damage modelling effectively simulated the interaction between the matrix crack and delamination and the variations in the stresses, damage and crack lengths of the laminate specimen due to the microstructural randomness.
Keywords: Cross-ply laminates; CFRP; Matrix cracking; Delamination; Microstructural randomness; Cohesive zone modelling

2D Elastodynamics of Interface Microcracks: The Effect of Cracks Interaction by Igor A. Guz; Maryna V. Menshykova; Oleksandr V. Menshykov (17-29).
The study is devoted to a 2D problem for interface cracks under harmonic external loading. The system of boundary integral equations for displacements and tractions is derived from the dynamic Somigliana identity. The distributions of the displacements and tractions at the bonding interface and the surface of the cracks are analysed for the normally incident tension-compression wave. The dynamic stress intensity factors are also computed for different values of the frequency of the incident wave and the distance between cracks. The effect of distance between cracks on the solution of the problem is studied.
Keywords: Interface cracks; Cracks interaction; Harmonic loading; Stress intensity factor

In this paper, the Equivalent Constraint Model (ECM) together with a 2-D shear lag stress analysis approach is applied to predict residual stiffness properties of polymer and ceramic matrix [0/90 n /0] cross-ply laminates subjected to in-plane biaxial loading and damaged by transverse and longitudinal matrix cracks. It is found that the longitudinal Young’s modulus, shear modulus and major Poisson’s ratio undergo large degradation as the matrix crack density increases, with Poisson’s ratio appearing to be the most affected by transverse cracking. In cross-ply laminates with thick 90° layer strip-shaped delaminations begin to initiate and grow from the tips of matrix cracks at the 0°/90° interface. These delaminations contribute to further stiffness degradation of such laminates, and hence have to be taken into account in failure analysis models. The thickness of the 90° layer plays an important role; the thicker the 90° layer, the bigger stiffness reduction suggesting a size (volume) effect at ply level. In SiC/CAS cross-ply laminates reduction in the longitudinal modulus occurs mainly due to transverse cracks, while the shear modulus appears to be the most affected by the presence of longitudinal cracks. The shear modulus reduction ratio predicted previously by a semi-empirical formula is, in the most of cases, within 10% of the current ECM/2-D shear lag approach value. In some cases, though, the error of the semi-empirical finite element expression can be as big as 20% since it fails to capture damage mode interaction.
Keywords: Composite laminate; Cross-ply laminate; Matrix cracking; Delamination; Stiffness; Stiffness degradation; Residual stiffness; Equivalent Constraint Model; Shear lag analysis

A modeling method aimed at eliminating the need of explicit crack representation in bi-dimensional structures is presented for the simulation of the initiation and subsequent propagation within composite materials. This is achieved by combining a meshless method with a physical stress–displacement based criterion known as Cohesive Model. This model consents to apply a penalty-based approach to delamination modeling where a variable penalty factor along the crack segment allows to loosen or tight the two parts according to their relative displacements. Results are showed for classical single mode loading benchmark cases and compared to experimental results taken from the literature.
Keywords: Penalty; Meshless; Cohesive zone model; Delamination

The in-plane shear and compressive properties of unidirectional (UD) HTS40/977-2 carbon fibre-toughened resin (CF/TR) laminates are investigated. Scanning Electron microscopy (SEM) and optical microscopy are used to reveal the failure mechanisms developed during compression. It is found that damage initiates by fibre microbuckling (a fibre instability failure mode) which then is followed by yielding of the matrix to form a fibre kink band zone that leads to final fracture. Analytical models are briefly reviewed and a graphical method, based on the shear response of the composite system, is described in order to estimate the UD compressive strength. Predictions for the HTS40/977-2 system are compared to experimental measurements and to data of five other unidirectional carbon fibre reinforced polymer (CFRP) composites that are currently used in aerospace and other structural applications. It is shown that the estimated values are in a good agreement with the measured results.
Keywords: Polymer-matrix composites; Analytical modelling; Compressive strength; Fibre microbuckling; Toughened resins

Analysis and Compression Testing of Laminates Optimised for Damage Tolerance by Andrew T. Rhead; Richard Butler; Neil Baker (85-100).
Barely Visible Impact Damage (BVID) can occur when laminated composite material is subject to out-of-plane impact loads and can result in a significant reduction in compressive strength. This paper reports on three compression tests of laminates optimised to maximise damage tolerance. Results from these tests were analysed using a semi-analytical, fracture mechanics based method that predicts the strain below which laminated coupons containing BVID subject to axial compression will not fail. A further experiment was conducted on an artificially delaminated coupon in order to validate the modelling methodology. Results from one of the two optimised stacking sequences considered show an increase of over 40% in Compression After Impact (CAI) strength compared with a baseline configuration. Analysis of results has indicated that CAI strength is dependent to a great extent on damage morphology and stability of damage growth, both of which are functions of laminate stacking sequence.
Keywords: Static strength; Delamination; Compression; Impact; Damage tolerance