On the inclined crack problem in an orthotropic medium under biaxial loading

Nobile, Lucio; Piva, A.; Viola, Erasmo

doi:10.1016/s0013-7944(03)00051-1

Cited by 22 publications

(18 citation statements)

References 16 publications

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“…(4) and A 2 ÀC 22 /C 11 in Eq. (3) are positive, therefore, p 1 and p 2 become real positive numbers, as discussed by Carloni and Nobile [6], Carloni et al [7] and Nobile and Carloni [8]; applicable for most composites [9].…”

Section: Mechanics Of Orthotropic Materialsmentioning

confidence: 92%

Crack analysis in orthotropic media using the extended finite element method

Asadpoure

Mohammadi

Vafai

2006

Thin-Walled Structures

123

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Section: Mechanics Of Orthotropic Materialsmentioning

confidence: 92%

Crack analysis in orthotropic media using the extended finite element method

Asadpoure

Mohammadi

Vafai

2006

Thin-Walled Structures

123

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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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“…Investigations related with the inclined crack problem in an orthotropic medium have been carried out by Carloni et al (2004), Nobile et al (2004) and others. This paper is also related to the studies performed by Federici et al (2001) and Piva et al (2005Piva et al ( , 2006, about the dynamic problem of crack propagation in non isotropic media.…”

Section: Introductionmentioning

confidence: 99%

A non-conventional approach for crack problems in piezoelectric media under electromechanical loading

2009

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In this paper the elastostatic solution of an inclined crack problem has been analyzed. The approach is analogous to the one proposed over the past years for orthotropic materials by Piva and Viola (1988) (Eng Fract Mech, 29: 535-548), and it may be considered an alternative to the mathematical formalisms currently used. A general expression of the stress field is determined in terms of complex potentials. The stress distribution and the displacement field in the proximity of the crack tip are finally obtained. An expression of the energy release rate is provided in terms of the field intensity factors. Numerical results are presented and discussed under different remote electro-mechanical loading conditions and varying the crack inclination. Particular attention has been focused on the effect of the lateral load on the fracture quantities and on the direction of the incipient branching angle.

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On the inclined crack problem in an orthotropic medium under biaxial loading

Cited by 22 publications

References 16 publications

Crack analysis in orthotropic media using the extended finite element method

Crack analysis in orthotropic media using the extended finite element method

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

A non-conventional approach for crack problems in piezoelectric media under electromechanical loading

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