A new computational approach for three-dimensional singular stress analysis of interface voids

Zhang, Yuxuan; Ping, Xuecheng; Wang, Congman; Xiao, Zhongmin; Yang, Jiyuan; Chen, Mengcheng

doi:10.1007/s00707-020-02842-0

Cited by 8 publications

(2 citation statements)

References 45 publications

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“…In recent years, Chen and Ping 43–45 have developed a 2D hybrid crack‐tip singular element by using the numerical eigensolution of the singular stress field on the basis of the one‐dimensional (1D) finite element eigenanalysis method, which avoids difficulty in accessing exact analytical solutions for asymptotic displacement and stress fields. Ping et al 46,47 and Zhang et al 48 extended this singular element to three‐dimensional (3D) fracture mechanics problems. The singular stress field characteristics of complex defects such as V‐shaped notch, hole corner, multiphase material interface edge, inclusion corner, and interface crack are analyzed.…”

Section: Introductionmentioning

confidence: 99%

A novel crack‐tip singular element for extended finite element analysis

Wang

Ping

Wang

et al. 2023

Fatigue Fract Eng Mat Struct

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The traditional extended finite element method (XFEM) is suitable for simulating crack growth, but the crack‐tip stress field analysis still depends on the enriched function. In this paper, based on the numerical eigensolution of the singular displacement and stress field together with the Hellinger–Reissner (H–R) variational principle, a novel crack‐tip singular element is established to replace the enriched element in the crack‐tip region in the traditional XFEM. The stress field inside the element adopts a series expression instead of only including the leading‐order terms. The element only requires Gaussian integration at the element boundary and avoids mesh refinement in the crack‐tip region. The element can be used to analyze cracks in anisotropic materials, interface cracks, and cracks terminating at the bimaterial interface. The numerical solutions of the singular stress field in various crack forms are presented through numerical examples, which proves the effectiveness and versatility of the novel crack‐tip singular element.

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Section: Introductionmentioning

confidence: 99%

A novel crack‐tip singular element for extended finite element analysis

Wang

Ping

Wang

et al. 2023

Fatigue Fract Eng Mat Struct

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“…Akisanya et al [7][8][9][10] employed complex potential method proposed by Muskhelishvili to derive the stress and displacement solutions at the interface junction of two dissimilar materials in the form of series expansions, and then utilized the contour integral method to evaluate the coefficient of the singular term. While majority of research studies are dedicated to the evaluation of the coefficient of the singular term, [11][12][13][14][15][16] some recent studies have highlighted the importance of first non-singular term in the accurate assessment of stress distribution around bi-material notches. For instance, Mirsayar et al 17 and Malíkov a et al 18 demonstrated the considerable role of first non-singular term in fracture initiation angle in bi-material and composite notches.…”

Section: Introductionmentioning

confidence: 99%

On the effects of higher order stress terms in pure mode III loading of bi‐material notches

Bahrami

Ayatollahi

Mehraban

et al. 2022

Fatigue Fract Eng Mat Struct

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The effects of higher order terms (HOTs) on the stress distribution at the vicinity of the sharp corner of two bonded dissimilar materials were investigated under pure out‐of‐plane (mode III) loading. To achieve this aim, finite element (FE) analysis in conjunction with the over‐deterministic technique were performed for two specimens, each containing four different notch opening angles. The coefficients of singular and non‐singular stress terms were then computed from the displacement field determined from the FE analysis. The elastic stresses obtained directly from the FE analysis were compared with those reconstructed from the truncated series expansions, in order to validate the accuracy of the calculated coefficients. The numerical results show that although the contribution of HOTs in the out‐of‐plane stress field is less than that of the in‐plane notch problems, ignoring their effects can lead to considerable errors in the stress field estimation. The magnitude of numerical error depends on the geometry and loading conditions of the bi‐material notch.

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