Evaluation of the stress singularities of plane V-notches in bonded dissimilar materials

Niu, Zhongrong; Da-li, GE; Cheng, Changzheng; Ye, Jianqiao; Récho, Naman

doi:10.1016/j.apm.2008.03.007

Cited by 54 publications

(25 citation statements)

References 29 publications

(53 reference statements)

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“…The interpolating matrix method 30 proposed by the authors before is introduced to solve the established characteristic ordinary differential equations to determine the singularity orders. The governing equations for the notch in a plate are transformed into the characteristic ordinary differential equations with respect to the singularity orders.…”

Section: Introductionmentioning

confidence: 99%

Singularity analysis near the vertex of the V‐notch in Reissner's plate by coupling the asymptotic expansion technique with the interpolating matrix method

Chen

Han

Wang

et al. 2014

Fatigue Fract Eng Mat Struct

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A new numerical method for calculating the singularity orders of V‐notches in Reissner's plate is proposed in this paper. By introducing the asymptotic expansion of the generalised displacement field at the notch tip into the equilibrium equations of a plate, a set of characteristic ordinary differential equations with respect to the singularity order are established. In addition, by adopting the variable substitution technique, the obtained non‐linear characteristic equations are transformed into linear ones, which are solved by the interpolating matrix method. The singularity orders of moments and shear forces can be obtained simultaneously and can be distinguished from the corresponding characteristic angular functions conveniently. Four types of boundary conditions are proposed to investigate the influence of boundary conditions on the singularity order values. The effect of the Poisson's ratio on the singularity orders of the V‐notch in Reissner's plate is discussed. The present method is versatile for the singularity analysis of single material V‐notches and bi‐material V‐notches, and can be easily extended to multi‐material V‐notches.

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Section: Introductionmentioning

confidence: 99%

Singularity analysis near the vertex of the V‐notch in Reissner's plate by coupling the asymptotic expansion technique with the interpolating matrix method

Chen

Han

Wang

et al. 2014

Fatigue Fract Eng Mat Struct

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“…Because the other parameters, i.e., λ k ,ũ ikR (θ ),ũ ikI (θ )(i=ρ, θ),σ ikR (θ ), σ ikI (θ )(i = ρρ, θ θ, ρθ ), have been calculated by the interpolate matrix method (Niu et al 2009a), the displacement and stress field at the V-notch tip can be obtained from Eqs. (3) and (4) respectively.…”

Section: Maximum Energy Release Rate (Merr) Criterionmentioning

confidence: 99%

“…By the interpolate matrix method developed by Niu et al (2009a), the singularity order λ kR , λ kI and associatedũ ikR (θ ),ũ ikI (θ ) (i=ρ, θ) can be acquired. σ ikR (θ ),σ ikI (θ ) (i=ρρ, θ θ, ρθ ) are the linear combination ofũ ikR (θ ),ũ ikI (θ ) (i=ρ, θ) and their derivatives.…”

Section: Evaluation Of Non-singular Stress At the V-notch Tipmentioning

confidence: 99%

“…Chen and Sze (2001); Chen and Ping (2007); Ping et al (2008) proposed a hybrid finite element with asymptotic expansion to determine the stress exponents and stress distributions of bonded bimaterial V-notches. Because the stress singularity orders and associated eigenvectors of the displacement and stress at the two-dimensional V-notch tip region have been determined by means of the interpolating matrix method proposed by Niu et al (2009a), the stresses at V-notch tip regions can be expressed as the linear combination of the series expansion including two singular terms and several non-singular terms. The stress field far from the V-notch tip is modeled by the conventional boundary element method.…”

Section: Introductionmentioning

confidence: 99%

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Effect of non-singular stress on the brittle fracture of V-notched structure

2012

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The traditional brittle fracture criteria for V-notched structures are established on the base of the singular stress field at a V-notch tip where only two singular stress terms are adopted. The non-singular stress terms also play a significant role in determining the stress and strain fields around a V-notch tip, which in turn could affect the fracture character of V-notched structures predicted by the fracture mechanics criteria. In this paper, the effect of the non-singular stress on the brittle fracture properties for the V-notch problem is discussed. Firstly, the stress field around a V-notch tip is described by the Williams asymptotic expansions. At the same time, the stress field far from the V-notch tip is modeled by the conventional boundary element method since there is no stress singularity. By the combination of the Williams asymptotic expansions and the boundary integral equations, the complete stress field at a V-notch tip including several non-singular stress terms can be obtained. Then, three different brittle fracture criteria are introduced to predict the critical loading and initial crack propagation direction of V-notched structures under mixed-mode loading. Comparing with the existed experimental results, it can be found that the degree of accuracy of the predicted results when taking into account the non-singular stress terms is much higher than the predicted ones neglecting the non-singular stress.

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“…Some excellent numerical methods have been developed to solve the ordinary different equations. A method named the interpolate matrix method 22 is introduced to solve the above eigen‐value problem. By the interpolate matrix method, all the main eigen‐values and associated eigen‐functions , with their derivatives can be obtained at the same time.…”

Section: Eigen‐analysis At the Crack Tip Regionmentioning

confidence: 99%

Analyse the role of the non‐singular stress in brittle fracture by BEM coupled with eigen‐analysis

Chen

Niu

Récho

et al. 2012

Fatigue Fract Eng Mat Struct

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A coupled model resulting from the boundary element method and eigen‐analysis is proposed in this paper to analyse the stress field at crack tip. This new combine method can yield several terms of the non‐singular stress in the Williams asymptotic expansion. Then the maximum circumferential stress (MCS) criterion taken the non‐singular stress into account is introduced to predict the brittle fracture of cracked structures. Two earlier experiments are re‐examined by the present numerical method and the role of the non‐singular stress in the brittle fracture is investigated. Results show that if more terms of non‐singular stress are taken into account, the predicted crack propagation direction and the critical loading by MCS criterion are much closer to the existing experimental results, especially for dominating mode II loading conditions. Moreover, numerical results manifest that Williams series expansion can describe the stress field further from the crack tip if more non‐singular stress terms are adopted.

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Evaluation of the stress singularities of plane V-notches in bonded dissimilar materials

Cited by 54 publications

References 29 publications

Singularity analysis near the vertex of the V‐notch in Reissner's plate by coupling the asymptotic expansion technique with the interpolating matrix method

Singularity analysis near the vertex of the V‐notch in Reissner's plate by coupling the asymptotic expansion technique with the interpolating matrix method

Effect of non-singular stress on the brittle fracture of V-notched structure

Analyse the role of the non‐singular stress in brittle fracture by BEM coupled with eigen‐analysis

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