Stress intensity factors and T-stresses for offset double edge-cracked plates under mixed-mode loadings

Chen, Chih‐Hao; Wang, Chein Lee

doi:10.1007/s10704-008-9276-5

Cited by 18 publications

(15 citation statements)

References 17 publications

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“…The results show that as the value R I =L e increases, the T-stress converges towards a stable value, which is just between the value given by Wang [42] and that provided by Chen and Wang [43] for each value of 2a=W . The relative errors between present results and those obtained in [42,43] are within 0.5% when the value R I =L e > 48 for the mesh used in this study. This example implies that the integral domain need to be large enough to achieve satisfactory precision.…”

Section: Example 2: An Inclined Crack In An Fgm Platesupporting

confidence: 56%

T‐stress evaluations for nonhomogeneous materials using an interaction integral method

Guo

et al. 2012

Numerical Meth Engineering

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A new equivalent domain integral of the interaction integral is derived for the computation of the T-stress in nonhomogeneous materials with continuous or discontinuous properties. It can be found that the derived expression does not involve any derivatives of material properties. Moreover, the formulation can be proved valid even when the integral domain contains material interfaces. Therefore, the present method can be used to extract the T-stress of nonhomogeneous materials with complex interfaces effectively. The interaction integral method in conjunction with the extended FEM is used to solve several representative examples to show its validity. Finally, using this method, the influences of material properties on the T-stress are investigated. Numerical results show that the mechanical properties and their first-order derivatives affect the T-stress greatly, while the higher-order derivatives affect the T-stress slightly. Nakamura and Parks [19] and Wang [20] used the method to solve the T-stress along threedimensional (3D) curved crack fronts. Jayadevan et al. [21] employed the method to evaluate the T-stress in dynamically loaded fracture specimen. Sladek and Sladek [22] and Kim et al. [23] utilized the interaction integral method for computing the T-stress of an interface crack.Functionally graded materials (FGMs), as one of the representative nonhomogeneous materials, have many advantages that make them attractive in potential applications, such as the improvement on residual stress distribution and mechanical durability. introduced the interaction integral method to compute the T-stress of 2D cracks in isotropic and orthotropic FGMs and gave a summary on the definitions of the auxiliary fields. Using the method, Shim et al. [27] conducted an investigation on the elastic and elastic-plastic fracture problems of FGMs. Sladek et al. [28] used the interaction integral method combined with a meshless method and to evaluate the T-stress in orthotropic FGMs. Recently, the interaction integral method was used for the evaluation of the T-stress in isotropic and orthotropic FGMs under thermal loading [29,30].Most of the previous work is concerned with materials with continuous and differentiable properties. Actually, there exist more or less material interfaces in various nonhomogeneous composite materials and thus, the material interfaces have to be taken into account when the fracture performance of these composites is focused. In addition, FGMs are actually two-phase or multiphase particulate composites in which material composition and microstructure vary spatially or the volume fraction of particles varies in one or several directions [31]. Therefore, in certain scales, the material interfaces should be investigated when we examine the fracture performance of FGMs. In previous works [32,33], the authors have given an effective interaction integral method for extracting the SIFs in the materials with complex interfaces. The aim of this study is to develop an interaction integral method for solving the T-str...

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Section: Example 2: An Inclined Crack In An Fgm Platesupporting

confidence: 56%

T‐stress evaluations for nonhomogeneous materials using an interaction integral method

Guo

et al. 2012

Numerical Meth Engineering

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“…where g(a) is the only unknown function of the half crack length a. Substituting equation (12) into equation 5, and assuming the stress distribution function (x) is equal to a constant value 0 , it leads to…”

Section: Weight Function Methodsmentioning

confidence: 99%

“…10,11 As is known, the SIFs, related to the crack opening displacements and the plastic zone sizes, characterize and dominate the singular stress states in the vicinity of the crack tip. 12,13 Thus, the accurate calculation of the SIF around the crack tip is of quite importance for assessing the load capacity, fatigue crack growth rate and fracture failure control of a cracked component. Although the SIFs are possibly available in some of the SIF handbooks 14 for a wide range of crack configurations and loading conditions, the documented solutions are sometimes inapplicable in practical problems due to complicated non-linear stress fields.…”

Section: Introductionmentioning

confidence: 99%

A general approach for calculations of weight functions and stress intensity factors

Fan¹,

Guo

Guohui

et al. 2016

Proceedings of the Institution of Mechanical Engineers, Part C:

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An approximate and simple expression is presented to calculate the crack face displacements of collinear cracks and center cracks by use of only one reference stress intensity factor. The crack face displacement and its partial derivative determined by the present method are in good agreement with their exact solutions. Calculations of weight functions for the center crack are reduced to the simple quadrature of the correction function and of the partial derivative of the crack face displacement. Based on the weight function method, the relationships between the stress intensity factor of the rotating blade with a center crack to the crack length, crack location, rotating speed and angular acceleration are studied. The critical rotating speed of the blade is evaluated based on the fracture law.

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“…The improved finite element method [7] divides the whole crack region into two sub-regions, namely the complementary energy sub-region around the crack tip and the potential energy sub-region of the rest regions, which is an improved method to extract the SIF by using the FEM. The particular weight function method [8] uses the specified reference loading conditions on both sides of the crack for finite element analysis, deduces the coefficients of each weight function, and then computes the SIF under loading by using the weight function.…”

Section: Introductionmentioning

confidence: 99%

Direct Evaluation of the Stress Intensity Factors for the Single and Multiple Crack Problems Using the P-Version Finite Element Method and Contour Integral Method

Zhang

Yang

2021

Applied Sciences

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Stress intensity factor (SIF) is one of three important parameters in classical linear elastic fracture mechanics (LEFM). The evaluation of SIFs is of great significance in the field of engineering structural and material damage assessment, such as aerospace engineering and automobile industry, etc. In this paper, the SIFs of a central straight crack plate, a slanted single-edge cracked plate under end shearing, the offset double-edge cracks rectangular plate, a branched crack in an infinite plate and a crucifix crack in a square plate under bi-axial tension are extracted by using the p-version finite element method (P-FEM) and contour integral method (CIM). The above single- and multiple-crack problems were investigated, numerical results were compared and analyzed with results using other numerical methods in the literature such as the numerical manifold method (NMM), improved approach using the finite element method, particular weight function method and exponential matrix method (EMM). The effectiveness and accuracy of the present method are verified.

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Stress intensity factors and T-stresses for offset double edge-cracked plates under mixed-mode loadings

Cited by 18 publications

References 17 publications

T‐stress evaluations for nonhomogeneous materials using an interaction integral method

T‐stress evaluations for nonhomogeneous materials using an interaction integral method

A general approach for calculations of weight functions and stress intensity factors

Direct Evaluation of the Stress Intensity Factors for the Single and Multiple Crack Problems Using the P-Version Finite Element Method and Contour Integral Method

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