P. Maimí

A Three-dimensional Damage Model for Transversely Isotropic Composite Laminates

This article proposes a fully three-dimensional continuum damage model, developed at the sub-ply level, to predict in an integrated way both the intralaminar and the interlaminar failure mechanisms that occur in laminated fiber-reinforced polymer composites. The constitutive model is based on the assumption that the composite material is transversely isotropic, and accounts for the effects of crack closure under load reversal cycles. The damage model is implemented in an implicit finite element code taking into account the requirement to ensure a mesh-independent computation of the dissipated energy. The comparison between the model predictions and published experimental data indicates that the model can accurately predict the effects of transverse matrix cracks on the residual stiffness of quasi-isotropic laminates, the interaction between transverse matrix cracks and delamination, and final failure of the laminate.

Size Effect Law and Critical Distance Theories to Predict the Nominal Strength of Quasibrittle Structures

The design of structures with a nonuniform stress field is of great industrial interest. The ability of the size effect law and critical distance theories to predict the nominal strength of notched and open hole specimens is analyzed in the present paper. The results obtained with these methods are compared with the solution of the problem computed, taking into account the material cohesive law. A conclusion of this paper is that the role of the critical fracture energy in determining the structural strength is negligible, except in large cracked structures. For unnotched structures of any size and for small cracked structures, the key parameter is the initial part of the softening cohesive law. This allows us to define design charts that relate the structural strength to a specimen size normalized with respect to a material characteristic length.

Analytical and Numerical Investigation of the Length of the Cohesive Zone in Delaminated Composite Materials

An accurate prediction of the length of the cohesive zone ahead of a crack tip is fundamental for the correct simulation of delamination in composite materials under both quasi-static and fatigue loading. To ensure a correct dissipation of energy during delamination propagation, several cohesive finite elements have to span the cohesive zone. The length of the cohesive zone depends on the material properties, the geometry/size of the structure, and on the loading mode. This chapter presents new expressions to estimate the length of the cohesive zone under general mixed-mode loading conditions and for finite-sized geometries. The analytical model is validated by comparing its predictions with numerical results based on cohesive-zone models. The relevance of the proposed analytical solutions to the effective simulation of delamination is demonstrated by simulating delamination growth under mixed-mode loading using meshes with the length of the elements greater than the cohesive zone length.

Comment to the paper ‘Analysis of Progressive Matrix Cracking in Composite Laminates II. First Ply Failure’ by George J Dvorak and Norman Laws:

Dvorak and Laws published in Ref. 1 a paper that addresses transverse cracking of composite laminates for small crack densities. An accurate cracking criterion is obtained by means of linear elastic fracture mechanics. The equations developed in the paper are used by many researchers – this is shown by the 75 citations in the last 25 years. More significantly, the 44% of the citations occurred in the last decade. Furthermore, to the authors’ knowledge, the expressions developed are implemented in design codes used by the aerospace and aeronautical companies. The determination of the elastic energy stored in the ply requires the computation of its compliance, denoted as ij in Ref. 1. Equation 3 in the commented paper is written as:

Specimen geometry and specimen size dependence of the \({\mathcal {R}}\)-curve and the size effect law from a cohesive model point of view

An analytic model has been developed for a Compact Tension specimen subjected to a controlled displacement and corresponding load within a cohesive model framework. The model is able to capture the material response while the Fracture Process Zone is being developed, obtaining the evolution of multiple variables such as the crack opening and the cohesive stresses, for an arbitrary Cohesive Law shape. The crack growth prediction based on the R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}

Micromechanical Analysis of Mode I Crack Growth in Carbon Fibre Reinforced Polymers

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A continuum damage model for composite laminates: Part I - Constitutive model

\end{document}-curve and the nominal strength prediction based on Bažant’s Size Effect Law have been implemented using the output variables available from the proposed analytic model. The minimum specimen size has been found in order to properly apply R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}