A. Arteiro

Three-dimensional invariant-based failure criteria for transversely isotropic fibre-reinforced composites

Abstract This chapter describes failure criteria for polymer composites reinforced by unidirectional fibres. The failure criteria are based on an invariant quadratic formulation based on structural tensors that accounts for the preferred directions of the transversely isotropic material. Failure in a single UD ply is predicted, requiring the analysis of strains and stresses ply-by-ply when analysing multidirectional laminates. Because the proposed failure criteria does not use geometrical information to predict failure (due to its invariant-based formulation), we propose a pragmatic approach to estimate the orientation of the fracture plane. To account for the effect of ply thickness when the laminae are embedded in a multidirectional laminate, the in situ properties are defined in the framework of the failure criterion for transverse damage mechanisms. When compared against experimental data available in the literature, good agreement for transverse failure modes, for failure under off-axis loading and for the effect of superposed hydrostatic pressure on failure behaviour of different fibre-reinforced composites is obtained. For more complex three-dimensional stress states, where the test data available shows large scatter or is not available at all, a computational micro-mechanics framework is used to validate the failure criteria. We obtain a good correlation between the predictions of the two modelling strategies.

A Finite Fracture Mechanics Model for the Prediction of the Notched Response and Large Damage Capability of Composite Laminates

A new model based on Finite Fracture Mechanics (FFMs) has been proposed to predict the open-hole tensile strength of composite laminates [1]. Failure is predicted when bothstress-based and energy-based criteria are satisfied. This model is based on an analytical solution, and no empirical adjusting parameters are required, but only two material properties: the unnotched strength and the fracture toughness. In the present work, an extension of the proposed FFMs model to predict the notched response of composite laminates with notch geometries other than a circular opening [2] is presented and applied to the prediction of size effects on the tensile and compressive notched strength of composite laminates. The present model is also used to assess the notch sensitivity and brittleness of composite laminates by means of versatile design charts and by the identification of a dimensionless parameter designated as notch sensitivity factor. A further extension of the FFMs model is proposed, which takes into account the crack resistance curve of the laminate in the models formulation, and it is used to predict the large damage capability of a non-crimp fabric thin-ply laminate [3].

A trace-based approach to design for manufacturing of composite laminates

A novel invariant-based approach to describe stiffness and strength of carbon-fiber-reinforced plastic composites has been recently proposed in the literature. In this work, a direct sizing method based on trace of the plane stress stiffness matrix and unit circle failure criterion is proposed. Strength-based profile of a panel is first determined for a baseline material based on the upper-bound value of the calculated failure index k-field from a boundary-value problem. The structural component can then be scaled linearly to meet the stiffness requirements that include deformation, deflection, natural frequency, and buckling. Material selection by scaling is the last step in this sizing method. The proposed approach is conceptually simple to implement, not material specific, and immediately applicable for automated tape laying. Although this is a 2D formulation of an orthotropic homogenized laminate, the 3D stiffness can be separated into two uncoupled in- and out-of-plane submatrices. Thus, the in-plane results of this method are independent of the out-of-plane behavior.

Analysis Models for Polymer Composites Across Different Length Scales

This chapter presents the analysis models, developed at different length scales, for the prediction of inelastic deformation and fracture of polymer composite materials reinforced by unidirectional fibers. Three different length scales are covered. Micro-mechanical models are used to understand in detail the effects of the constituents on the response of the composite material, and to support the development of analysis models based on homogenized representations of composite materials. Meso-mechanical models are used to predict the strength of composite structural components under general loading conditions. Finally, macro-mechanical models based on Finite Fracture Mechanics, which enable fast strength predictions of simple structural details, are discussed.