The Experts below are selected from a list of 312 Experts worldwide ranked by ideXlab platform
Roberto Ballarini - One of the best experts on this subject based on the ideXlab platform.
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a cohesive zone model for cracks terminating at a Bimaterial Interface
International Journal of Solids and Structures, 1997Co-Authors: Alberto Romeo, Roberto BallariniAbstract: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.
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a crack very close to a Bimaterial Interface
Journal of Applied Mechanics, 1995Co-Authors: Alberto Romeo, Roberto BallariniAbstract: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.
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A Crack Very Close to a Bimaterial Interface
Journal of Applied Mechanics, 1995Co-Authors: Alberto Romeo, Roberto BallariniAbstract: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
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a rigid line inclusion at a Bimaterial Interface
Engineering Fracture Mechanics, 1990Co-Authors: Roberto BallariniAbstract:A solution is presented for the plane elastostatics problem of a rigid line inclusion at a Bimaterial Interface. Explicit expressions are derived for the complex potentials. The complex stress intensity factors at the tip of the rigid line are compared with those for the corresponding crack problem. It is found that the nature of the singularities differ. Furthermore, unlike the crack problem, the singularity for the rigid line inclusion depends on the stresses parallel to the Interface.
Naoaki Noda - One of the best experts on this subject based on the ideXlab platform.
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Stress Concentration of an Ellipsoidal Inclusion of Revolution in the Vicinity of a Bimaterial Interface
Transactions of the Japan Society of Mechanical Engineers. A, 2020Co-Authors: Naoaki Noda, Yasuhiro MoriyaamAbstract: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.
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Variations of the stress intensity factors for a planar crack parallel to a Bimaterial Interface
Structural Engineering and Mechanics, 2008Co-Authors: Chunhui Xu, Li Yuan, Naoaki NodaAbstract: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.
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stress intensity factors of an inclined elliptical crack near a Bimaterial Interface
Engineering Fracture Mechanics, 2006Co-Authors: Naoaki Noda, Takao Kouyama, Yositomo KinoshitaAbstract: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.
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elastic stress concentration of an ellipsoidal inclusion of revolution in the vicinity of a Bimaterial Interface
Journal of Engineering Materials and Technology-transactions of The Asme, 2004Co-Authors: Naoaki Noda, Yasuhiro MoriyamaAbstract: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 integral equations with Cauchy-type or logarithmic-type singularities, where unknowns are densitics of body forces distributed in the r and z-directions in Bimaterial bodies having the same elastic constants of those of the given problem. In 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 Interface on the stress concentration factor is discussed with varying the distance from the Interface, shape ratio, and elastic ratio.
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analysis of an elliptical crack parallel to a Bimaterial Interface under tension
Mechanics of Materials, 2003Co-Authors: Naoaki Noda, Ruri Ohzono, Mengcheng ChenAbstract:Abstract In this paper an elliptical crack parallel to a Bimaterial Interface is considered. The solution utilizes the body force method and requires Green’s functions for perfectly bonded elastic half planes. The formulation leads to a system of hypersingular integral equations whose unknowns are three modes of crack opening displacements. In the numerical calculation, fundamental density functions and polynomials are used to approximate unknown body force densities. The results show that the present method yields smooth variations of stress intensity factors along the crack front accurately. The stress intensity factors are indicated in tables and figures with varying the shape of crack, distance from the Interface, and elastic constants. The root area parameter proposed by Murakami is found to be effective for engineering use because different shaped cracks have almost the same values.
Xu Wang - One of the best experts on this subject based on the ideXlab platform.
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a bridged crack perpendicular to a Bimaterial Interface
Acta Mechanica, 2018Co-Authors: Moxuan Yang, Xu WangAbstract: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.
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a screw dislocation interacting with a Bimaterial Interface incorporating surface strain gradient elasticity
European Journal of Mechanics A-solids, 2015Co-Authors: Xu Wang, Peter SchiavoneAbstract: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.
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interaction between a screw dislocation and a viscoelastic piezoelectric Bimaterial Interface
International Journal of Solids and Structures, 2008Co-Authors: Xu WangAbstract: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.
A J Rosakis - One of the best experts on this subject based on the ideXlab platform.
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effect of loading and geometry on the subsonic intersonic transition of a Bimaterial Interface crack
Engineering Fracture Mechanics, 2003Co-Authors: O Samudrala, A J RosakisAbstract:Abstract An experimental investigation was conducted to study the nature of intersonic crack propagation along a Bimaterial Interface. A single edge notch/crack oriented along a polymer/metal Interface was loaded predominantly in shear by impacting the specimen with a high velocity projectile fired from a gas gun. The stress field information around the propagating crack tip was recorded in real time by two different optical techniques––photoelasticity and coherent gradient sensing, in conjunction with high speed photography. Intersonic cracks on polymer/metal Interfaces were found to propagate at speeds between the shear wave speed (cs) and 2 c s of the polymer. The nature of the crack tip fields during subsonic/intersonic transition and the conditions governing this transition were examined. Experimental observations showed the formation of a crack face contact zone as the interfacial crack speed exceeds the Rayleigh wave speed of the polymer. Subsequently, the contact zone was observed to expand in size, shrink and eventually collapse onto the intersonic crack tip. The recorded isochromatic fringe patterns showed multiple Mach wave formation associated with such a scenario. It is found that the nature of contact zone formation as well as its size and evolution differ substantially depending on the sign of the opening component of loading.
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effect of elastic mismatch in intersonic crack propagation along a Bimaterial Interface
Engineering Fracture Mechanics, 1998Co-Authors: W Wang, Yonggang Huang, A J RosakisAbstract:Abstract Recent experiments showed that the speed of a crack tip propagating along a Bimaterial Interface can exceed the shear wave speed of the more compliant constituent in the Bimaterial. This experimental observation has motivated analytical and numerical investigation on fast crack growth. Among these investigations, Huang et al. obtained a simple, analytic full-field solution for an elastic/rigid Bimaterial with crack-face contact. Although this solution compares quite favorably with all available experimental data, it is not clear which Bimaterial can be approximated by the elastic/rigid model. In this paper, we use the method of analytical continuation to obtain the asymptotic stress fields near the crack tip and near the trailing end of the contact zone. It is established that the elastic/rigid model is an excellent approximation to all Bimaterials that have been used in fast crack growth experiments. Therefore, the simple, analytic solution of elastic/rigid model provides a useful means for analyzing experimental fringe patterns and data. It is shown that, as the elastic mismatch decreases, the elastic/rigid model may become invalid.
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highly transient elastodynamic crack growth in a Bimaterial Interface higher order asymptotic analysis and optical experiments
Journal of The Mechanics and Physics of Solids, 1993Co-Authors: John Lambros, A J RosakisAbstract:A higher Order asymptotic analysis of the transient deformation field surrounding the tip of a crack running dynamically along a Bimaterial Interface is presented. An asymptotic methodology is used to reduce the problem to one of the Riemann-Hilbert type. Its solution furnishes displacement potentials which are used to evaluate explicitly the near-tip transient stress field. Crack-tip fields corresponding to crack speeds up to the lower of the two shear wave speeds are investigated. An experimental study of dynamic crack growth in PMMA steel Interfaces using the optical method of CGS and high speed photography, is also described. Transonic terminal speeds (up to 1.4cPMMAS) and initial accelerations ($108 ms2) are reported and discussed. Transient effects are found to be severe and more important than in homogeneous dynamic fracture. For subsonic crack growth, these experiments arc used to demonstrate the necessity of employing a fully transient expression in the analysis of optical data to predict accurately the complex dynamic stress intensity factor history.
Shintaro Tamura - One of the best experts on this subject based on the ideXlab platform.
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numerical study of splay faults in subduction zones the effects of Bimaterial Interface and free surface
Journal of Geophysical Research, 2011Co-Authors: Shintaro TamuraAbstract:[1] Splay faults are a characteristic branching fault system in some subduction zones. We model a megathrust earthquake rupture with a branching fault, inhomogeneous media, and a free surface, using a spontaneously propagating mode II crack on a Bimaterial Interface. For this purpose, we develop an explicit finite element code to solve the elastodynamic equations and a slip-weakening friction law on the fault plane. In a homogeneous prestress condition, the rupture on the branching fault is enhanced when the upper medium is more compliant. Even when the upper medium is less compliant, a fast rupture propagating at a velocity close to the generalized Rayleigh velocity produces the strong dynamic stress around the rupture front and activates the branching fault. When prestress linearly increases with depth from zero at the free surface, only a slight change of normal stress that is due to seismic waves causes an initiation of rupture on the branching fault at the free surface, and this rupture propagates downward on the branching fault. The arrival of this descending rupture at the branching point greatly changes the stress field in the surrounding area. It affects the slip distribution on the main fault and even terminates the main rupture propagation if it occurs before the arrival of the main rupture on the branching point.
