Antiplane stress analysis of an isotropic wedge with multiple cracks

Faal, R.T.; Fotuhi, Ali Reza; Fariborz, S.J.; Daghyani, Hamid Reza

doi:10.1016/j.ijsolstr.2004.03.005

Cited by 35 publications

(16 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As mentioned previously, the stress components (19) have Cauchy-type singularity in the vicinity of a dislocation point, therefore we may conclude that k ij ðs; tÞ has also the Cauchy-type singularity for i = j as t ? s. The dislocation density functions b zj ðtÞ are expressed in terms of the function g zj ðtÞ with various types of weight functions as follows [15].…”

Section: The Coated Circular Plane With Multiple Crackssupporting

confidence: 58%

“…where c ¼ GÀ1 Gþ1 : Making use of the formulas given in Appendix A of the report [19], and substituting Eqs. (18) into (17), the stress components are summed in the whole region, leading to …”

Section: Analysis Of Domain With Screw Dislocationmentioning

confidence: 99%

“…(19). First, since the functions E m and F m converge very rapidly for large values of m. Also for special case, G ¼ 1 (isotropic material), the terms of stress components including E m and F m are vanished for all m -0: For isotropic circular plane (G 1 ¼ G 2 ¼ l), we set G ¼ 1 and R 2 ¼ R; therefore the stress field (19) is simplified as follows …”

Section: Analysis Of Domain With Screw Dislocationmentioning

confidence: 99%

“…The traction on the surface of the ith crack generated by the presence of the former distribution of dislocations, via employing Eqs. (19) and (31), leads to …”

Section: The Coated Circular Plane With Multiple Cracksmentioning

confidence: 99%

See 3 more Smart Citations

Anti-plane stress analysis of cracked circular regions with outer coating

Faal

Alimardani

2015

Applied Mathematical Modelling

View full text Add to dashboard Cite

a b s t r a c tFirst, using the finite Fourier sine transform, the stress solution of a coated circular plane with a screw dislocation is achieved. In special case of study, namely an isotropic circular plane with a screw dislocation, the solution is validated using the method of images. After that, anti-plane deformation analysis of an intact coated circular plane under self-equilibrating traction is accomplished and the resulting stress field is computed. Also, via dislocation solution and the stress field of the intact coated circular plane under traction, integral equations are formulated for the same circular plane weakened by several cracks. The resulting singular integral equations, which are of Cauchy types, are solved numerically with the aim of finding the dislocation density functions on crack surfaces. The dislocation density functions on crack surfaces are used to determine the stress intensity factors (SIFs) of the tips of the cracks. The paper is furnished with several examples of a single crack and multiple cracks. For isotropic cases, the solution is validated by the published results in the literature. Effect of material properties of circular plane and its coating, thickness of coating as well as the crack location on the ensuing stress intensity factors at crack tips are studied.

show abstract

Section: The Coated Circular Plane With Multiple Crackssupporting

confidence: 58%

Section: Analysis Of Domain With Screw Dislocationmentioning

confidence: 99%

Section: Analysis Of Domain With Screw Dislocationmentioning

confidence: 99%

“…The traction on the surface of the ith crack generated by the presence of the former distribution of dislocations, via employing Eqs. (19) and (31), leads to …”

Section: The Coated Circular Plane With Multiple Cracksmentioning

confidence: 99%

See 2 more Smart Citations

Anti-plane stress analysis of cracked circular regions with outer coating

Faal

Alimardani

2015

Applied Mathematical Modelling

View full text Add to dashboard Cite

show abstract

“…Shahani (2003) derived analytical expressions for the mode III stress intensity factor (SIF) of circular shafts with edge cracks, bonded half planes containing an interfacial edge crack, bonded wedges with an interfacial edge crack and also DCB's with different boundary conditions. Anti-plane stress analysis for an infinite isotropic wedge weakened with a screw dislocation was accomplished by Faal et al (2004) using the Mellin transform. The problem of finite annular dissimilar composite wedges with equal apex angles subjected to anti-plane concentrated loadings was considered by Lin and Ma (2004).…”

Section: Introductionmentioning

confidence: 99%

Analysis of anisotropic sector with a radial crack under anti-plane shear loading

Shahani

Ghadiri

2010

International Journal of Solids and Structures

View full text Add to dashboard Cite

a b s t r a c tIn this paper, the anti-plane shear deformation of an anisotropic sector with a radial crack is investigated. The traction-traction boundary conditions are imposed on the radial edges and the traction-free condition is considered on the circular segment of the sector. A novel mathematical technique is employed for the solution of the problem. This technique consists of the use of some recently proposed finite complex transforms (Shahani, 1999), which have complex analogies to the standard finite Mellin transforms of the first and second kinds. However, it is essential to state the traction-free condition of the crack faces in the form of a singular integral equation which is done in this paper by describing an exact analytical method. The resultant dual integral equations are solved numerically to determine the stress intensity factors at the crack tips. In the special cases, the obtained results coincide with those cited in the literature.

show abstract

Closed‐form solution for an orthotropic elastic strip with a crack perpendicular to the edges under arbitrary anti‐plane shear

Li¹,

Lee

2009

Z Angew Math Mech

View full text Add to dashboard Cite

A cracked orthotropic elastic strip of finite width is analyzed under antiplane shear loading. For four frequently encountered constraint edges, i.e. free-free, clamped-clamped, free-clamped, or clamped-free edges, the Fourier series method is used to reduce triple series equations, and then to a mixed boundary value problem associated with a mode-III crack for each case to a singular integral equation. Closed-form solutions are derived for the resulting equations, and formulae for calculating stress intensity factors are obtained for an internal crack and edge cracks subjected to arbitrarily varying loading. Numerical results of the stress intensity factors for an eccentric, central, and edge crack are shown graphically for the case of uniform loading at the crack faces. Obtained formulae for determining stress intensity factors can be taken as a benchmark of numerical evaluations. The derived results are also applicable to an isotropic elastic strip with an anti-plane shear crack normal to the edges.

show abstract

Antiplane stress analysis of an isotropic wedge with multiple cracks

Cited by 35 publications

References 10 publications

Anti-plane stress analysis of cracked circular regions with outer coating

Anti-plane stress analysis of cracked circular regions with outer coating

Analysis of anisotropic sector with a radial crack under anti-plane shear loading

Closed‐form solution for an orthotropic elastic strip with a crack perpendicular to the edges under arbitrary anti‐plane shear

Contact Info

Product

Resources

About