Non-Singular Term Effect for the Inclined Crack Extension in Anisotropic Solids under Uniaxial Loading

Lim, Won-Kyun; Sankar, Bhavani V.

doi:10.1177/0021998302036017251

Cited by 5 publications

(3 citation statements)

References 8 publications

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“…where X T , Y T are longitudinal and transverse tensile strengths. Lim and Bhavani 6,7 used anisotropic strength equation for inclined crack extension in anisotropic material under uni‐axial and biaxial loading and they also determined the effect of non‐singular second‐order term on crack extension in anisotropic material. The hoop stress σ θθ in the polar coordinate system is given by …”

Section: Theorymentioning

confidence: 99%

The characteristics of an inclined crack in anisotropic paperboard under biaxial loading

Ahmad

Park

2013

Fatigue Fract Eng Mat Struct

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In this paper, a fracture mechanics method was applied for the evaluation of crack behaviour in anisotropic paperboard subjected to biaxial uniform loading. The experiment was performed to determine the crack propagation angle and the fracture strength of paperboard under biaxial loading with the cruciform specimen optimized by FEM simulation. The effects of biaxial loads on the critical stress ratio and crack propagation angle for various inclination angles were investigated. The experimental results were compared with theoretical results, which were calculated by using the Normal Stress Ratio Criteria. The experimental results for crack propagation angle and critical stress show good agreement with theoretical results.

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Section: Theorymentioning

confidence: 99%

The characteristics of an inclined crack in anisotropic paperboard under biaxial loading

Ahmad

Park

2013

Fatigue Fract Eng Mat Struct

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“…Lim et al (2001) have estimated the influence of second-order terms originated from load biaxiality on the stress and displacement fields in the vicinity of the crack tip under mode I in anisotropic materials and investigated their effects on the predicted crack growth direction. This analysis has been extended to the case of mixed-mode cracks by Lim and Sankar (2002), Carloni and Nobile (2002), Carloni et al (2003), Nobile et al (2004), Nobile and Carloni (2005) and Viola et al (2008). Numerical analysis for cracked orthotropic bodies was provided by Saouma and Sijiotis (1986), Boone et al (1987) and Garcia et al (2004), where they computed the coefficients of the first-order terms by employing the singular crack-tip element.…”

Section: Introductionmentioning

confidence: 99%

Determination of Second-Order term Coefficients for the Inclined Crack in Orthotropic Plate using Singular Finite Elements

Lim

2010

Int J Fract

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The finite element method with quarter-point crack-tip elements is used and a simple formula for obtaining the coefficients of the second-order terms in the series expansion for near crack tip stresses in orthotropic materials under biaxial loading is presented. This formula is obtained by comparing the variation of the displacements along the crack tip element with the elastic field solution for the crack tip. Numerical examples are given for the validity of the present formulation. The results obtained are compared with the theoretical ones and a good agreement between the two solutions is obtained.Keywords: orthotropic plate, inclined crack, biaxial loading, stress intensity factor, second-order term coefficient, finite element analysis.1. Introduction. The importance of the second-order term of the series expansion for crack tip stresses and displacements is evident in the case of a flat crack under tensile loads in normal and tangential directions where the effect of the tangential stress appears only in the second term, and is thus completely omitted in the first-term formula. Omitting this term not only denies the physical presence of such a load, but also misleads one into thinking that load biaxiality does not affect the prediction of crack growth direction. The second-order term is therefore quantitatively significant for fracture mechanics analysis. Concerning the problem of cracked anisotropic materials, Yuan (2000a, 2000b) have investigated the effects of higher-order terms on the expression for crack-tip stresses. They derived the second and third terms of the crack tip stress field as additional parameters in characterizing the behavior of the crack. Lim et al (2001) have estimated the influence of second-order terms originated from load biaxiality on the stress and displacement fields in the vicinity of the crack tip under mode I in anisotropic materials and investigated their effects on the predicted crack growth direction. This analysis has been extended to the case of mixed-mode cracks by Lim and Sankar (2002), Carloni and Nobile (2002), Carloni et al (2003), Nobile et al (2004), Nobile and Carloni (2005) and Viola et al (2008).Numerical analysis for cracked orthotropic bodies was provided by Saouma and Sijiotis (1986), Boone et al (1987) and Garcia et al (2004), where they computed the coefficients of the first-order terms by employing the singular crack-tip element. However, to the best of the author's knowledge, little work has been done so far to obtain the coefficients of the secondorder terms for cracked orthotropic materials by using the finite element method(FEM). In this paper, the correct form of the second-order terms near a crack in orthotropic materials under biaxial loading is given. It is shown that the FEM with quarter-point singular crack-tip elements can be used to obtain the coefficients of the second-order terms. Special formulae

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“…Obviously, the fracture behaviour of anisotropic materials under mixed mode loading cannot be predicted by the same criteria that are developed for the isotropic materials and, therefore, when using the MTS and S-criterion some modifications must be made to include the effects of anisotropy [15][16][17][18][19][20][21]. This paper shows the advantage of using the boundary element shape sensitivities for prediction of the crack growth over other existing methods, both in terms of the computational modelling and numerical accuracy.…”

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confidence: 99%

Simulation of crack propagation in anisotropic structures using the boundary element shape sensitivities and optimisation techniques

Tafreshi

2011

Engineering Analysis with Boundary Elements

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Using the boundary element shape sensitivities of multi-region domains coupled with an optimization algorithm and an automatic mesh generator, the crack kink angle and propagation path in anisotropic elastic solids are predicted. The maximum strain energy release rate criterion, best suited for the composite structures, has been employed. In contrast to the J-integral method, which would require the computation of stresses and strains at a series of internal points, here by direct differentiation of the structural response the strain energy release rates at the existing crack tip and new cracks for the period of crack growth are determined. The length of each kinked crack is treated as the shape design variable. The shape variable is then associated with the coordinates of a series of boundary nodes located on the new crack surface. Thus, the relevant velocity terms are applied together in the sensitivity analysis with respect to that variable to determine the energy release rate, which is the derivative of the total strain energy with respect to the crack length extension. Wherever possible the results are compared with the existing experimental, analytical and/or numerical results reported in the literature, in which good agreement is observed. It is shown that the present method is computationally more accurate and efficient. Two example problems with different anisotropic material properties are presented to validate the applications of this formulation. The results show that material anisotropy has a profound influence on the crack propagation of composites.

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Non-Singular Term Effect for the Inclined Crack Extension in Anisotropic Solids under Uniaxial Loading

Cited by 5 publications

References 8 publications

The characteristics of an inclined crack in anisotropic paperboard under biaxial loading

The characteristics of an inclined crack in anisotropic paperboard under biaxial loading

Determination of Second-Order term Coefficients for the Inclined Crack in Orthotropic Plate using Singular Finite Elements

Simulation of crack propagation in anisotropic structures using the boundary element shape sensitivities and optimisation techniques

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