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Bimaterial Interface

The Experts below are selected from a list of 312 Experts worldwide ranked by ideXlab platform

Roberto Ballarini – 1st expert on this subject based on the ideXlab platform

  • a cohesive zone model for cracks terminating at a Bimaterial Interface
    International Journal of Solids and Structures, 1997
    Co-Authors: Alberto Romeo, Roberto Ballarini

    Abstract:

    Abstract Linear elastic fracture mechanics (LEFM) does not provide a realistic propagation criterion for a crack tip touching a Bimaterial Interface. In fact, LEFM predicts that the crack penetrates the Interface at either zero or infinite value of the characteristic applied load, depending on the relative stiffness of the bonded materials. This paper presents a cohesive zone model that provides a propagation criterion for such cracks in terms of the parameters that define the relation between the crack opening displacement and the traction acting along the crack surfaces. Extensive numerical results are presented for the case of constant cohesive traction, σ o associated with a critical crack tip opening displacement, η c . A quantitative evaluation of the effective toughening resulting from the presence of the Interface is presented, for both small scale and large scale bridging, in terms of the Dundurs parameters (α and β), and ρ 2 / L , where ρ 2 is proportional to the small scale critical cohesive zone length and L is a characteristic length of the crack problem. In particular, universal results for small scale bridging are presented as where k c and δ c are, respectively the critical stress intensity factor and critical cohesive zone length, λ is the power of the stress singularity associated with the elastic crack touching the Interface, and A and B ∗ are universal functions. These equations generalize those derived from the Dugdale model for a homogeneous medium. It is shown through the analysis of a finite length crack that for a relatively wide range of α-β and ρ 2 / L values, the presence of the Interface has a rather insignificant effect on the critical stress, and the elastic singularity associated with a crack terminating at the Interface between two dissimilar elastic materials dominates the stress field within an extremely small near-tip region.

  • a crack very close to a Bimaterial Interface
    Journal of Applied Mechanics, 1995
    Co-Authors: Alberto Romeo, Roberto Ballarini

    Abstract:

    This paper presents the plane elastostatics analysis of semi-infinite crack perpendicular to a perfectly bonded Bimaterial Interface. Both cases of the crack approaching the Interface and penetrating the Interface are addressed. The distance from the tip of the crack to the Interface is 6. A singular integral equation approach is used to calculate the stress intensity factor, K 1 , and the crack-opening displacement at the Interface, η, as functions of 6, the Dundurs parameters a and β, and the stress intensity factor k 1 associated with the same crack terminating at the Interface (the case δ = 0). The results are presented as K I = k 1 δ 1/2-λ f(α, β) and η = Ck 1 δ 1-λ η(α, β) where λ is the strength of the stress singularity associated with δ = 0, f and η are functions calculated numerically and C is a material constant. These results can be used to determine the stress intensity factor and crack opening displacement of cracks of finite length 2a with one tip at a distance 6 from the Interface for δ/a << 1. The selected results presented for a crack loaded by a uniform far-field tension in each half-plane show that the stress intensity factors approach their limits at a relatively slow rate.

  • A Crack Very Close to a Bimaterial Interface
    Journal of Applied Mechanics, 1995
    Co-Authors: Alberto Romeo, Roberto Ballarini

    Abstract:

    This paper presents the plane elastostatics analysis of semi-infinite crack perpendicular to a perfectly bonded Bimaterial Interface. Both cases of the crack approaching the Interface and penetrating the Interface are addressed. The distance from the tip of the crack to the Interface is 6. A singular integral equation approach is used to calculate the stress intensity factor, K 1 , and the crack-opening displacement at the Interface, η, as functions of 6, the Dundurs parameters a and β, and the stress intensity factor k 1 associated with the same crack terminating at the Interface (the case δ = 0). The results are presented as K I = k 1 δ 1/2-λ f(α, β) and η = Ck 1 δ 1-λ η(α, β) where λ is the strength of the stress singularity associated with δ = 0, f and η are functions calculated numerically and C is a material constant. These results can be used to determine the stress intensity factor and crack opening displacement of cracks of finite length 2a with one tip at a distance 6 from the Interface for δ/a

Naoaki Noda – 2nd expert on this subject based on the ideXlab platform

  • Stress Concentration of an Ellipsoidal Inclusion of Revolution in the Vicinity of a Bimaterial Interface
    Transactions of the Japan Society of Mechanical Engineers. A, 2020
    Co-Authors: Naoaki Noda, Yasuhiro Moriyaam

    Abstract:

    This paper deals with a stress concentration problem of an ellipsoidal inclusion of revolution in a Bimaterial body under tension. The problem is formulated as a system of singular equations with Cauchy-type or logarithmic-type singularities, where unknowns are densities of body forces distributed in the r-and z-directions in Bimaterial boodies having the same elastic constants of those of the given problem. I order to satisfy the boundary conditions along the ellipsoidal boundary, four fundamental density functions proposed in the previous paper are used. Then the body force densities are approximated by a linear combination of fundamental density functions and polynomials. The present method is found to yield rapidly converging numerical results for stress distribution along the boundaries of both the matrix and inclusion even when the inclusion is very close to the Bimaterial Interface. Then, the effect of Bimaterial surface on the stress concentration factor is discussed with varying the distance from Bimaterial Interface, shape ratio, and elastic ratio.

  • Variations of the stress intensity factors for a planar crack parallel to a Bimaterial Interface
    Structural Engineering and Mechanics, 2008
    Co-Authors: Chunhui Xu, Li Yuan, Naoaki Noda

    Abstract:

    Stress intensity factors for a planar crack parallel to a Bimaterial Interface are considered. The formulation leads to a system of hypersingular integral equations whose unknowns are three modes of crack opening displacements. In the numerical analysis, the unknown displacement discontinuities are approximated by the products of the fundamental density functions and polynomials. The numerical results show that the present method yields smooth variations of stress intensity factors along the crack front accurately. The mixed mode stress intensity factors are indicated in tables and figures with varying the shape of crack, distance from the Interface, and elastic constants. It is found that the maximum stress intensity factors normalized by root area are always insensitive to the crack aspect ratio. They are given in a form of formula useful for engineering applications.

  • stress intensity factors of an inclined elliptical crack near a Bimaterial Interface
    Engineering Fracture Mechanics, 2006
    Co-Authors: Naoaki Noda, Takao Kouyama, Yositomo Kinoshita

    Abstract:

    Abstract In this paper the stress intensity factors are discussed for an inclined elliptical crack near a Bimaterial Interface. The solution utilizes the body force method and requires Green’s functions for perfectly bonded semi-infinite bodies. The formulation leads to a system of hypersingular integral equation whose unknowns are three modes of crack opening displacements. In the numerical calculation, unknown body force densities are approximated by using fundamental density functions and polynomials. The results show that the present method yields smooth variations of stress intensity factors along the crack front accurately. Distributions of stress intensity factors are presented in tables and figures with varying the shape of crack, distance from the Interface, and elastic modulus ratio. It is found that the inclined crack can be evaluated by the models of vertical and parallel cracks within the error of 24% even for the cracks very close to the Interface.

Xu Wang – 3rd expert on this subject based on the ideXlab platform

  • a bridged crack perpendicular to a Bimaterial Interface
    Acta Mechanica, 2018
    Co-Authors: Moxuan Yang, Xu Wang

    Abstract:

    We consider the contribution of fully or partially crack bridging to a mode I or mode II crack perpendicular to a Bimaterial Interface. The crack faces are subjected to both shear and normal bridging forces, and the bridging stiffnesses are allowed to vary arbitrarily along the crack. The resulting singular integral equations are solved numerically by combining the Chebyshev polynomials and the collocation method. The proposed method is proved reliable and efficient for the bridged crack problem under consideration. It is observed that the stress intensity factors at the two crack tips and the crack opening displacement are suppressed due to the toughening and stiffening effects of crack bridging, respectively. In particular, when the crack is embedded in the right stiffer (or softer) half-plane and is only partially bridged at its left (or right) portion, new phenomena can be observed. More specifically, with suitably chosen bridging zone and bridging stiffness, the behavior of the stress intensity factors and the crack opening displacement for a bridged crack can be quite different from those for an unbridged crack, and the crack can even propagate toward the opposite direction to that for an unbridged crack.

  • a screw dislocation interacting with a Bimaterial Interface incorporating surface strain gradient elasticity
    European Journal of Mechanics A-solids, 2015
    Co-Authors: Xu Wang, Peter Schiavone

    Abstract:

    Abstract We present an analytical solution in terms of the exponential integral of the problem associated with the interaction of a screw dislocation near a Bimaterial Interface incorporating surface strain gradient elasticity. Three intrinsic material lengths are identified as a result of the introduction of the surface strain gradient elasticity for the Interface. The size-dependent image force acting on the screw dislocation is also obtained. The stiffening effect of the Interface can be clearly seen from the image force expression.

  • interaction between a screw dislocation and a viscoelastic piezoelectric Bimaterial Interface
    International Journal of Solids and Structures, 2008
    Co-Authors: Xu Wang

    Abstract:

    The complex variable method is employed to derive analytical solutions for the interaction between a piezoelectric screw dislocation and a Kelvin-type viscoelastic piezoelectric Bimaterial Interface. Through analytical continuation, the original boundary value problem can be reduced to an inhomogeneous first-order partial differential equation for a single function of location z = x + iy and time t defined in the lower half-plane, which is free of the screw dislocation. Once the initial, steady-state and far-field conditions are known, the solution to the first order differential equation can be obtained. From the solved function, explicit expressions are then derived for the stresses, strains, electric fields and electric displacements induced by the piezoelectric screw dislocation. Also presented is the image force acting on the screw dislocation due to its interaction with the Kelvin-type viscoelastic Interface. The derived solutions are verified by comparing with existing solutions for the simplified cases, and various interesting features are observed, particularly for those associated with the image force.