Finite difference method for solving crack problems in FGM

What is it about?

This work demonstrate how to solve crack problems in a functionally graded material with the simple finite difference method. It also demonstrate the extraction of the stress intensity factor (SIF), which shows the severity of the stresses near the crack tip. First, the linear elastic two-dimensional formulation for functionally graded materials is presented. Then the formulation and boundary conditions are transformed into orthogonal curvilinear co-ordinate system. The transformation is done for enabling solutions in any curvilinear coordinates (for example, rectangular or cylindrical coordinates) and to increases the capability of refining the mesh at areas of stress concentration. The method is applied for solving a long layer containing an edge crack in which it is assumed that the Young's modulus varies continuously along its width. The extraction of the SIF is done by three integral methods which are known to be more accurate : J line and two versions of a modified conservative J integral for graded materials.

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Why is it important?

It enriches the number of tools that can be used to solve complicated problems of singularities in FGM's. It encourages further application of the method for problems involving crack closure which include the combined intricate fields of fracture mechanics and frictional receding contact.

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