Abstract
The Finite Block Method has been employed in this paper to evaluate the stress intensity factor of a bi-material plate. The complex stress intensity factor components K1 and K2 determined by the Finite Block Method is compared with an equivalent Finite Element Method (ABAQUS) analysis. The paper demonstrates the accuracy of the Meshfree approach by the Finite Block Method without the arduous demand of meshing around the crack surface as seen on standard FEM crack analysis. This paper also describes the application of the polygonal singular core and the collocations points around the interface crack. A computational example for various E1/E2 material combinations is presented.
Highlights
The analytical solution of interface crack is difficult to obtain as work produced by Williams [1], England [2], Hutchinson [3] and many others have shown
Building on the success of the Finite Element Method, the Extended Finite Element Method as proposed by Belytschko utilize interpolation functions, the concept of partition of unity and the discontinuity of near crack tip displacement fields which is deemed independent from the finite element mesh to analyse interface cracks [7]
Published under licence by IOP Publishing Ltd u(ξ,η) = ∑ ∑ F (ξ,ξi )G(η,η j )ul. In this case the number of collocation points along the two axes are represented by M and N, ul indicates the nodal value, l = ( j −1)M + i, with uniformly distributed nodes at ξi = −1+ 2(i −1) /(M −1), i = 1,2,..., M, η j = −1 + 2( j −1) /(N −1), j = 1,2,..., N, and two polynomial functions;
Summary
The analytical solution of interface crack is difficult to obtain as work produced by Williams [1], England [2], Hutchinson [3] and many others have shown. The finite element method is a popular numerical method and it has been utilised in analysing two-dimensional cracks. This has been demonstrated in recent works by Lin [4]. The Boundary Element method is another numerical method capable of evaluating stress intensity factor for bi-material. The Finite Block Method (FBM) based on the collocation method has been developed by Wen [5] for elasticity analysis. The finite block method using the polygon single core as developed by the authors is used to evaluate the stress intensity factor for bi-material interfacial problem.
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