Effect of Elastic Constants on Stress In A Composite Under Plane Deformation

Dundurs, J.

doi:10.1177/002199836700100306

Cited by 216 publications

(74 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We emphasize that the presence of logarithmic packets is ensured by a relation between the instantaneous Lamé coefficients and the coefficients of relaxation kernel. This relation resembles the famous Dundurs relation [13] providing a condition for the presence of oscillating singularities at a crack between two dissimilar isotropic elastic half-planes.…”

Section: "Pure Square-root Singularity Of Stresses Are To Be Expectedmentioning

confidence: 84%

“…[25], see also in [31], Section 7.4, and [27], it is proved that the spectrum of the associated operator pencil coincides with 13) in the general situation of the Dirichlet and Neumann problems for arbitrary selfadjoint systems which enjoy the polynomial property [26,28]. The fact that ν = 0 is well known for elasticity equations in isotropic and orthotropic materials and was established in [12] for homogeneous anisotropic elasticity.…”

Section: Mellin Transformationmentioning

confidence: 95%

“…In [9] the equality ν = 0 is proved for arbitrary Douglis-Nirenberg systems with the same boundary operators on the two crack surfaces ϕ = ±π. The situation ν = 0 occurs e.g., with a crack inside the interface between two anisotropic bodies, we refer the reader to [12,13,27] for related examples. We gather in the following lemmas the facts which we will use in our analysis.…”

Section: Mellin Transformationmentioning

confidence: 99%

“…Proof. Formula (7.11) is deduced from explicit calculations made in [12], Section 3.3 (we refer also to [13] Replacing σ k by its expression with respect to λ k and µ k :…”

Section: An Interface Crackmentioning

confidence: 99%

See 3 more Smart Citations

Analysis of crack singularities in an aging elastic material

Costabel¹,

Dauge²,

Назаров³

et al. 2006

ESAIM: M2AN

View full text Add to dashboard Cite

Abstract. We consider a quasistatic system involving a Volterra kernel modelling an hereditarilyelastic aging body. We are concerned with the behavior of displacement and stress fields in the neighborhood of cracks. In this paper, we investigate the case of a straight crack in a two-dimensional domain with a possibly anisotropic material law. We study the asymptotics of the time dependent solution near the crack tips. We prove that, depending on the regularity of the material law and the Volterra kernel, these asymptotics contain singular functions which are simple homogeneous functions of degree 1 2 or have a more complicated dependence on the distance variable r to the crack tips. In the latter situation, we observe a novel behavior of the singular functions, incompatible with the usual fracture criteria, involving super polynomial functions of ln r growing in time.Mathematics Subject Classification. 35Q72, 74D05, 74G70.

show abstract

Section: "Pure Square-root Singularity Of Stresses Are To Be Expectedmentioning

confidence: 84%

Section: Mellin Transformationmentioning

confidence: 95%

Section: Mellin Transformationmentioning

confidence: 99%

“…Proof. Formula (7.11) is deduced from explicit calculations made in [12], Section 3.3 (we refer also to [13] Replacing σ k by its expression with respect to λ k and µ k :…”

Section: An Interface Crackmentioning

confidence: 99%

See 2 more Smart Citations

Analysis of crack singularities in an aging elastic material

Costabel¹,

Dauge²,

Назаров³

et al. 2006

ESAIM: M2AN

View full text Add to dashboard Cite

show abstract

“…For a crack perpendicular to the interface and under applied load parallel to the interface, the strain energy release rates as a function of crack extension G d along the interface (deflection) and G p into the interface (penetration) are well known to be of the forms [20][21][22][23][24]:…”

Section: Crack Behavior At the Interface For Four-point Bending Condimentioning

confidence: 99%

Criteria for Crack Deflection-Penetration in EBC Coated Ceramics: A Parametric Study

Abdul-Aziz

Bhatt

Grady

2015

Mechanics of Advanced Materials and Structures

View full text Add to dashboard Cite

This article discusses results obtained from a parametric study to analytically evaluate the impingement of a crack at the interface of an environmental barrier coating (EBC) and a monolithic Silicon nitride (Si 3 N 4 ) layered ceramics substrate. The study establishes a correlation that leads to determine if the crack is arrested or advanced by either penetrating or deflecting along the EBC/substrate interface. A finite-element-based fracture mechanics methodology is utilized to perform these calculations. Critical parameters determining penetration-deflection conditions in relation to EBC's physical characteristics, such as porosity level, voids, and mini cracks, are determined for a single layer and multi-layered coating system coordinating the interactions between the EBCs (Mullite, Mullite mixture, Silicon nitride, etc.) and the substrate structure. Results showing thermo-mechanical stresses and stress/strain energy release relations with respect to crack penetration-deflection are presented and discussed as the crack is advanced. = stress at the interface r and = radial distance and the polar angle f ij ( ) = angular distribution of the singular stress field = defines the strength of stress singularity ␣ and ␤ = Dundurs bi-material parameters E' j = E j is for plane stress E' j = E j /(1 -j ) for plane strain (1 and 2 denote the material) = shear modulus [MPa] G d = (material 1) is the strain energy release rate associated with the "deflected" crack or adhesive failure G p = (material 2) is the strain energy release rate associated with the "penetrated" crack (or cohesive failure of adjacent material) G pc = cohesive or penetrated fracture energy G dc = adhesive or deflected fracture energy, respectively K 1 and K 2 = stress intensity factors for the interface crack ε = a function of material constants Keywords

show abstract

Singular Stress Behavior in a Bonded Hereditarily-Elastic Aging Wedge. Part I: Problem Statement and Degenerate Case

Mikhailov

1997

Math. Meth. Appl. Sci.

View full text Add to dashboard Cite

Stress singularity is investigated in a plane problem for a bonded isotropic hereditarily elastic (viscoelastic) aging infinite wedge. The general solution of the operator Lamé equations, which are partial differential equations in space co‐ordinates and integral equations in time, respectively, is represented in terms of one‐parametric holomorphic functions (the Kolosov–Muskhelishvili complex potentials depending on time) in weighted Hardy‐type classes. After application of the Mellin transform with respect to the radial variable, the problem is reduced to a system of linear Volterra integral equations in time. By using the residue theory for the inverse Mellin transform, the stress asymptotics and strain estimates near the singular point are presented here for non‐hereditary Dundurs parameters. The general case of the hereditary Dundurs operators is considered in Part II (see [21]). © 1997 by B.G. Teubner Stuttgart‐John Wiley & Sons, Ltd.

show abstract

Effect of Elastic Constants on Stress In A Composite Under Plane Deformation

Cited by 216 publications

References 7 publications

Analysis of crack singularities in an aging elastic material

Analysis of crack singularities in an aging elastic material

Criteria for Crack Deflection-Penetration in EBC Coated Ceramics: A Parametric Study

Singular Stress Behavior in a Bonded Hereditarily-Elastic Aging Wedge. Part I: Problem Statement and Degenerate Case

Contact Info

Product

Resources

About