Abstract
The bi-material interface arc crack has been the focus of interest in the composite community, where it is usually referred to as the fiber-matrix interface crack. In this work, we investigate the convergence properties of the Virtual Crack Closure Technique (VCCT) when applied to the evaluation of the Mode I, Mode II and total Energy Release Rate of the fiber-matrix interface crack in the context of the Finite Element Method (FEM). We first propose a synthetic vectorial formulation of the VCCT. Thanks to this formulation, we study the convergence properties of the method, both analytically and numerically. It is found that Mode I and Mode II Energy Release Rate (ERR) possess a logarithmic dependency with respect to the size of the elements in the crack tip neighborhood, while the total ERR is independent of element size.
Highlights
Bi-material interfaces represent the basic load transfer mechanism at the heart of Fiber Reinforced Polymer Composite (FRPC) materials
The application of the Virtual Crack Closure Technique to the calculation 285 of Mode I, Mode II and total Energy Release Rate was analyzed in the context of the Finite Element solution of the bi-material circular arc crack, or fibermatrix interface crack
A synthetic vectorial formulation of the Virtual Crack Closure Technique (VCCT) has been proposed and its usefulness exemplified in the analysis of the mesh dependency
Summary
Bi-material interfaces represent the basic load transfer mechanism at the heart of Fiber Reinforced Polymer Composite (FRPC) materials. The problem was first addressed in the 1950’s by Williams [3], who derived through a linear elastic asymptotic analysis the stress distribution around an 10 open crack (i.e. with crack faces nowhere in contact for any size of the crack) between two infinite half-planes of dissimilar materials He found the existence of a strong oscillatory behavior in the stress singularity at the crack tip of the form. The same problems exposed previously for the open straight bi-material crack were shown to exist for the open fiber-matrix interface crack: the presence of strong oscillations in the crack tip singularity and onset of crack face interpenetration at a critical flaw size.
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