Abstract
This paper presents the numerical prediction of stress intensity factors (SIFs) of 2-D inhomogeneous functionally graded materials (FGMs) by an enriched Petrov-Galerkin natural element method (PG-NEM). The overall trial displacement field was approximated in terms of Laplace interpolation functions, and the crack tip one was enhanced by the crack-tip singular displacement field. The overall stress and strain distributions, which were obtained by PG-NEM, were smoothened and improved by the stress recovery. The modified interaction integral M ˜ ( 1 , 2 ) was employed to evaluate the stress intensity factors of FGMs with spatially varying elastic moduli. The proposed method was validated through the representative numerical examples and the effectiveness was justified by comparing the numerical results with the reference solutions.
Highlights
In the late 1980s, a new material concept called functionally graded material (FGM) was proposed to resolve the inherent problem of traditional lamination-type composites [1]
This paper introduces an enriched Petrov-Galerkin natural element method (PG-natural element method (NEM)) to explore whether and how much the enrichment of interpolation function increases the prediction reliability of stress intensity factors for
An enriched PG-NEM was introduced for the reliable crack analysis of inhomogeneous functionally graded materials (FGMs)
Summary
In the late 1980s, a new material concept called functionally graded material (FGM) was proposed to resolve the inherent problem of traditional lamination-type composites [1]. To evaluate the stress intensity factors of FGMs with cracks, one can consider the use of the well-known J− or M−integral methods These conventional indirect integral methods cannot reflect the spatially varying material properties of FGMs. The studies on the fracture mechanics of inhomogeneous bodies were initiated in the 1970~80s by assuming the spatially varying elastic modulus as an exponential function [17,21]. Laplace interpolation functions provide the high smoothness of C1 -continuity, there is still room for further improvement in capturing the high stress singularity at the crack tip In this context, this paper introduces an enriched PG-NEM to explore whether and how much the enrichment of interpolation function increases the prediction reliability of stress intensity factors for FGMs. The validity of enrichment was reported for homogeneous materials [31,32], but it was rarely reported for inhomogeneous materials. The proposed method was validated through the illustrative numerical examples and its effectiveness was quantitatively evaluated
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