Strain distributions for tensile and shear loading around multiple holes in a thermoplastic composite introduced by thermally assisted piercing

Analysis of stiffness loss in cross-ply composite laminates

6 - Multi-scale modelling of cracking in cross-ply laminates

The development of damage in cross-ply Hercules AS4/3502 graphite/epoxy laminates has been investigated. Specific endeavors were to identify the mechanisms for initiation and growth of matrix cracks and to determine the effect of matrix cracking on the stiffness loss in cross-ply laminates. Two types of matrix cracks were identified. These include both straight and curved cracks. The experimental study of matrix crack damage revealed that the curved cracks formed after the straight cracks and followed a repeatable pattern of location and orientation relative to the straight cracks. Therefore, it was postulated that the growth mechanism for curved cracks is driven by the stress state resulting from the formation of the straight cracks. This phenomenon was analytically investigated by a finite-element model of straight cracks in a cross-ply laminate. The finite-element results provide supporting evidence for the postulated growth mechanism. The experimental study also revealed that the number of curved cracks increased with the number of consecutive 90-deg plies. Finally, experimental results show as much as 10-percent degradation in axial stiffness due to matrix cracking in cross-ply graphite/epoxy laminates.

A modified variational analysis based on the principle of minimum com plementary energy, is used to describe the stress state around a through-the-thickness transverse crack in [0 m/90n]s cross-ply laminates. The analysis takes into account nonlinear stress distribution in the thickness direction of the 0°-plies and contains a thermoelastic consideration. A failure criterion based on linear elastic fracture mechanics is used to pre dict the onset of transverse matrix cracking in cross-ply laminates. The predictions are compared with experimental data and with previous analyses developed in the framework of the shear lag theory or the variational approach suggested by Hashin.

Time-dependent matrix cracking in cross-ply laminates

A fuzzy set analysis for a fracture and fatigue damage response of composite materials

On the behaviour of the residual strain produced by matrix cracking in cross-ply laminates

On transverse matrix cracking in cross-ply laminates loaded in simple bending

The damage and fracture behavior of Fiber Reinforced Polymers (FRPs) is quite complex and is different than the failure behavior of the traditionally employed metals. There are various types of failure mechanisms that can develop during the service life of composite structures. Each of these mechanisms can initiate and propagate independently. However, in practice, they act synergistically and appear simultaneously. The difficulties that engineers face to understand and predict how these different failure mechanisms result in a structural failure enforce them to use high design safety factors and also increases the number of certification tests needed. Considering that the experimental investigations of composites can be limited, very expensive, and time-consuming, in this contribution the newly developed multi Phase-Field (PF) fracture model [1] is employed to numerically study the failure in different Unidirectional Fiber Reinforced Polymers (UFRPs) laminates, namely, fracture in single-edge notched laminated specimens, matrix cracking in cross-ply laminates, and delamination migration in multi-layered UFRPs. The formulation of the PF model incorporates two independent PF variables and length scales to differentiate between fiber and inter-fiber (matrix-dominated) failure mechanisms. The physically motivated failure criterion of Puck is integrated into the model to control the activation and evolution of the PF parameters. The corresponding governing equations in terms of variational formulation is implemented into the Finite Element (FE) code ABAQUS utilizing the user-defined subroutines UMAT and UEL.

Matrix cracking in cross-ply laminates: effect of randomness

This paper presents a probabilistic fatigue model for transverse cracking in CFRP cross-ply laminates. First, a delayed fracture model for a crack in a brittle material subjected to cyclic loading was established on the basis of the slow crack growth (SCG) concept in conjunction with the Weibull's probabilistic failure model. Second, the above probabilistic delayed fracture model was applied to transverse cracking in cross-ply laminates during cyclic loading. The stress distribution and the length of the unit element were calculated with the aid of a shear lag analysis. The transverse crack density was expressed as a function of maximum stress, stress ratio and number of cycles using the parameters associated with the Paris equation and the Weibull distribution in addition to the mechanical properties. Unknown parameters were determined from experiment data for three kinds of cross-ply laminates to reproduce the transverse crack density against the number of cycles. The parametric studies using the obtained parameters revealed the effects of the Weibull modulus, crack propagation exponent and stress ratio on evolution of transverse cracking under fatigue loading.

A numerical study of transverse cracking in cross-ply laminates by 3D finite fracture mechanics

Austenite stability in TRIP steels studied by synchrotron radiation

The stiffness reduction as a result of multiple transverse cracking in cross-ply laminates and the crack density dependence on the applied tensile stress are analyzed by linear elastic fracture mechanics. The stress field distribution is obtained by the principle of minimum complementary energy. Two models are suggested which describe the non-uniform stress distribution in the thickness direction of the 0° layer. They contain the variational approach presented by Hashin as a particular case. Elastic ply properties and the Mode I critical strain energy release rate GIc for transverse cracking are the experimental data needed. Model predictions are compared with experimental data for glass fiber/epoxy, AS4/3502, and AS/3501-06 carbon fiber/epoxy cross-ply laminates. The predictions from the suggested models describe both the constraint effect and the crack saturation phenomenon.

Transverse cracks in cross-ply laminates are investigated experimentally to reveal the essential characteristics of their opening displacement under tensile loads. The average crack opening displacement is studied as a function of the longitudinal overall strain and the effects of matrix toughness and transverse ply thickness on this parameter are examined. The interactive effects between closely spaced transverse cracks are also ex amined and found to be significant. Implications of the experimentally observed features on the micromechanics and continuum damage type models are discussed.