Green’s functions for a bi-material problem with interfacial elliptical rigid inclusion and applications to crack and thin rigid line problems

Prasad, Parmeshwar; Hasebe, Norio; Wang, X.F.; Shirai, Yasuo

doi:10.1016/j.ijsolstr.2004.07.014

Cited by 16 publications

(2 citation statements)

References 27 publications

(33 reference statements)

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“…Issues such as interfacial fracture and crack problems in bi-material systems are at the forefront of many investigations (Lambros and Rosakis, 1995). The reader is referred to Wu et al (2003) and Prasad et al (2005) for an extensive list of work in this area. The problem of accurate prediction of interfacial stresses is also a major concern for researchers working on composite laminates (Noor and Burton, 1990).…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional dynamic Green’s functions in transversely isotropic bi-materials

Khojasteh

Rahimian

Pak

2008

International Journal of Solids and Structures

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a b s t r a c tBy virtue of a complete representation using two displacement potentials, an analytical derivation of the elastodynamic Green's functions for a linear elastic transversely isotropic bi-material full-space is presented. Three-dimensional point-load Green's functions for stresses and displacements are given in complex-plane line-integral representations. The formulation includes a complete set of transformed stress-potential and displacement-potential relations, within the framework of Fourier expansions and Hankel integral transforms, that is useful in a variety of elastodynamic as well as elastostatic problems. For numerical computation of the integrals, a robust and effective methodology is laid out which gives the necessary account of the presence of singularities including branch points and pole on the path of integration. As illustrations, the present Green's functions are analytically degenerated to the special cases such as half-space, surface and full-space Green's functions. Some typical numerical examples are also given to show the general features of the bi-material Green's functions.

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Section: Introductionmentioning

confidence: 99%

Three-dimensional dynamic Green’s functions in transversely isotropic bi-materials

Khojasteh

Rahimian

Pak

2008

International Journal of Solids and Structures

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“…A dislocation emission mechanism for micro-crack initiation at the tip of a semi-infinite rigid line inhomogeneity in a piezoelectric solid was considered by Xiao et al [15]. Applying a complex variable method and conformal mapping technique, Prasad et al [16] obtained the Green's functions for a point force and dislocation interacting with interfacial elliptical rigid inclusion in a bonded bimaterial system and examined the problem of an internal crack or thin rigid line interacting with the interfacial inclusion. Xiao et al [17] derived an analytical closed-form solution for a screw dislocation interacting with collinear rigid lines along the interface of two dissimilar piezoelectric media.…”

Section: Introductionmentioning

confidence: 99%

Interaction of an anti-plane singularity with interfacial anti-cracks in cylindrically anisotropic composites

Liu

Fang

2007

Arch Appl Mech

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Anti-plane problem for a singularity interacting with interfacial anti-cracks (rigid lines) under uniform shear stress at infinity in cylindrically anisotropic composites is investigated by utilizing a complex potential technique in this paper. After obtaining the general solution for this problem, the closed solution for the interface containing one anti-crack is presented analytically. In addition, the complex potentials for a screw dislocation dipole inside matrix are obtained by the superimposing method. Expressions of stress singularities around the anti-crack tips, image forces and torques acting on the dislocation or the center of dipole are given explicitly. The results indicate that the anisotropy properties of materials may weaken the stress singularity near the anti-crack tip for the singularity being a concentrated force but enhance the one for the singularity being a screw dislocation and change the equilibrium position of screw dislocation. The presented solutions are valid for anisotropic, orthotropic or isotropic composites and can be reduced to some new or previously known results.

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Interfacial Cracks Emanating from Partially Debonded Subsurface Circular Elastic Inclusions

Prasad¹

Fracture of Nano and Engineering Materials and Structures

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The problem of a sub-surface circular elastic inclusion with single interfacial debond in plane elasticity is considered in the present work. The sub-surface defect is modeled as elastic circular inclusion lying at some distance from the free surface. The presence of such defects is critical to the life of components subjected to high contact stresses. The question of the presence of free boundary on the stress intensity factors (SIF) of interfacial arc crack under remote uniform stress fields is addressed in this study. By varying the elastic modulus of inclusion, three cases of elastic mismatch are considered: 1) inclusion is hard corresponding to sub-surface rigid inclusion, 2) inclusion is soft corresponding to sub-surface hole, 3) and, inclusion has same material properties as surrounding matrix (equivalent to sub-surface arc crack in elastic half-plane). Half plane is simulated by means of long crack in the vicinity of the circular elastic inclusion so that half-plane boundary conditions are represented locally. Singular integral equation is setup to simulate half-plane boundary. SIF at arc-crack tip closest to the half-plane is evaluated to study its variation as the inclusion approaches half-plane.

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Green’s functions for a bi-material problem with interfacial elliptical rigid inclusion and applications to crack and thin rigid line problems

Cited by 16 publications

References 27 publications

Three-dimensional dynamic Green’s functions in transversely isotropic bi-materials

Three-dimensional dynamic Green’s functions in transversely isotropic bi-materials

Interaction of an anti-plane singularity with interfacial anti-cracks in cylindrically anisotropic composites

Interfacial Cracks Emanating from Partially Debonded Subsurface Circular Elastic Inclusions

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