On crack path stability in a layered material

Crack paths in an elastic layer on top of a substrate are considered. Crack growth is initiated from an edge crack in the layer. The plane of the initially straight crack forms an angle to the free surface. The load consists of a pair of forces applied at the crack mouth and parallel to the interface. Crack paths are calculated using a boundary element method. Crack growth is assumed to proceed along a path for which the mode II stress intensity factor vanishes. The inclination and the length of the initial crack are varied. The effect of two different substrates on the crack path evolution is demonstrated. A crack path initially leading perpendicularly to the interface is shown to be directionally unstable for a rigid substrate. Irrespective of its initial angle, the crack does not reach the interface, but reaches the free surface if the layer is infinitely long. At finite layer length the crack reaches the upper free surface if the initial crack inclination to the surface is small enough. For an inextendable flexible substrate, on the other hand, the crack reaches the interface if its initial inclination is large enough. For the flexible substrate an unstable path parallel with the sides of an infinitely long layer is identified. The results are compared with experimental results and discussed in view of characterisation of directionally unstable crack paths. The energy release rate for an inclined edge crack is determined analytically.

Wave pattern characteristics of a two-phase nozzle flow by shock propagation

In this paper, the wave pattern characteristics of shock-induced two-phase nozzle Hows with the quiescent or moving dusty gas ahead of the incident-shock front has been investigated by using high-resolution numerical method. As compared with the corresponding results in single-phase nozzle flows of the pure gas, obvious differences between these two kinds of flows can be obtained.

Dynamic analysis of arrest of buckle propagation on a beam on a nonlinear elastic foundation by FEM

Based on the dynamic governing equation of propagating buckle on a beam on a nonlinear elastic foundation, this paper deals with an important problem of buckle arrest by combining the FEM with a time integration technique. A new conclusion completely different from that by the quasi-static analysis about the buckle arrestor design is drawn. This shows that the inertia of the beam cannot be ignored in the analysis under consideration, especially when the buckle propagation is suddenly stopped by the arrestors.

The mixed-type integral equations for transient elastodynamic plane crack problems

In the present paper, by use of the boundary integral equation method and the techniques of Green fundamental solution and singularity analysis, the dynamic infinite plane crack problem is investigated. For the first time, the problem is reduced to solving a system of mixed-typed integral equations in Laplace transform domain. The equations consist of ordinary boundary integral equations along the outer boundary and Cauchy singular integral equations along the crack line. The equations obtained are strictly proved to be equivalent with the dual integral equations obtained by Sih in the special case of dynamic Griffith crack problem. The mixed-type integral equations can be solved by combining the numerical method of singular integral equation with the ordinary boundary element method. Further use the numerical method for Laplace transform, several typical examples are calculated and their dynamic stress intensity factors are obtained. The results show that the method proposed is successful and can be used to solve more complicated problems.

Fracture criteria for combined cleavage and dislocation emission

A general theory of fracture criteria for mixed dislocation emission and cleavage processes is developed based on Ohr's model. Complicated cases involving mixed-mode loading are considered. Explicit formulae are proposed for the critical condition of crack cleavage propagation after a number of dislocation emissions. The effects of crystal orientation, crack geometry and load phase angle on the apparent critical energy release rates and the total number of the emitted dislocations at the initiation of cleavage are analysed in detail. In order to evaluate the effects of nonlinear interaction between the slip displacement and the normal separation, an analysis of fracture criteria for combined dislocation emission and cleavage is presented on the basis of the Peierls framework. The calculation clearly shows that the nonlinear theory gives slightly high values of the critical apparent energy release rate G(c) for the same load phase angle. The total number N of the emitted dislocations at the onset of cleavage given by nonlinear theory is larger than that of linear theory.

Molecular dynamics simulation of interaction of a dislocation array from a crack tip with grain boundaries

The interaction of a dislocation array emitted from a crack tip under mode II loading with asymmetric tilt grain boundaries (GBs) is analysed by the molecular dynamics method. The GBs can generally be described by planar and linear matching zones and unmatching zones. All GBs are observed to emit dislocations. The GBs migrated easily due to their planar and linear matching structure and asymmetrical type. The diffusion induced by stress concentration is found to promote the GB migration. The transmissions of dislocations are either along the matched plane or along another plane depending on tilt angle theta. Alternate processes of stress concentration and stress relaxation take place ahead of the pileup. The stress concentration can be released either by transmission of dislocations, by atom diffusion along GBs, or by migration of GBs by formation of twinning bands. The simulated results also unequivocally demonstrate two processes, i.e. asymmetrical GBs evolving into symmetrical ones and unmatching zones evolving into matching ones during the loading process.

Micromechanics analyses of interface crack

A new mechanics model based on Peierls concept is presented in this paper, which can clearly characterize the intrinsic features near a tip of an interfacial crack. The stress and displacement fields are calculated under general combined tensile and shear loadings. The near tip stress fields show some oscillatory behaviors but without any singularity and the crack faces open completely without any overlapping when remote tensile loading is comparable with remote shear loading. A fracture criterion for predicting interface toughness has been also proposed, which takes into account for the shielding effects of emitted dislocations. The theoretical toughness curve gives excellent prediction, as compared with the existing experiment data.

The annular crack in a nonhomogeneous matrix surrounding a fiber under torsional loading .2. The crack going through the bimaterial interface into the fiber

The axisymmetric problem of an elastic fiber perfectly bonded to a nonhomogeneous elastic matrix which contains an annular crack going through the interface into the fiber under axially symmetric shear stress is considered. The nature of the stress singularity is studied. It is shown that at the irregular point on the interface, whether the shear modulus is continuous or discontinuous the stresses are bounded. The problem is formulated in terms of a singular integral equation and can be solved by a regular method. The stress intensity factors and crack surface displacement are given.

Transient effect on ideally plastic stationary crack-tip fields

This paper analyses the transient effect on ideally plastic stationary crack-tip fields under mode I plane strain conditions, when the inertial forces are not negligible. It is shown that the governing equation for such a problem can be expressed in formal simplicity when referred to a system of moving curvilinear coordinates, which is a generalization of the system defined by the slip-line field in quasi-static plasticity. A perturbation method of solving the equations is described and illustrated by application to problems of ideally plastic stationary crack-tip fields when the inertia forces are not negligible.

Transient effect on ideally plastic stationary crack-tip fields

This paper analyses the transient effect on ideally plastic stationary crack tip fields under mode I plane strain conditions, when the inertial forces are not negligible. It is shown that the governing equation for such a problem can be expressed in formal simplicity when referred to a system of moving curvilinear coordinates, which is a generalization of the system defined by the slip-line field in quasi-static plasticity. A perturbation method of solving the equations is described and illustrated by application to problems of ideally plastic stationary crack tip fields when the inertial forces are not negligible.

Molecular dynamics simulation of crack-tip processes in copper

The crack tip processes in copper under mode II loading have been simulated by a molecular dynamics method. The nucleation, emission, dislocation free zone (DFZ) and pile-up of the dislocations are analyzed by using a suitable atom lattice configuration and Finnis & Sinclair potential. The simulated results show that the dislocation emitted always exhibits a dissociated fashion. The stress intensity factor for dislocation nucleation, DFZ and dissociated width of partial dislocations are strongly dependent on the loading rate. The stress distributions are in agreement with the elasticity solution before the dislocation emission, but are not in agreement after the emission. The dislocation can move at subsonic wave speed (less than the shear wave speed) or at transonic speed (greater than the shear wave speed but less than the longitudinal wave speed), but at the longitudinal wave speed the atom lattice breaks down.

Dislocation nucleation and emission from crack-tip

The problems of dislocation nucleation and emission from a crack tip are analysed based on Peierls model. The concept adopted here is essentially the same as that proposed by Rice. A slight modification is introduced here to identify the pure linear elastic response of material. A set of new governing equations is developed, which is different from that used by Beltz and Rice. The stress field and the dislocation density field can be expressed as the first and second Chebyshev polynomial series respectively. Then the opening and slip displacements can be expanded as the trigonometric series. The Newton-Raphson Method is used to solve a set of nonlinear algebraic equations. The new governing equations allow us to extend the analyses to the case of dislocation emission. The calculation results for pure shearing, pure tension and combined tension and shear loading are given in detail.

Elastodynamic stress-intensity factors for a semiinfinite crack under 3-d combined mode loading

The dynamic stress intensity factor histories for a half plane crack in an otherwise unbounded elastic body are analyzed. The crack is subjected to a traction distribution consisting of two pairs of suddenly-applied shear point loads, at a distance L away from the crack tip. The exact expression for the combined mode stress intensity factors as the function of time and position along the crack edge is obtained. The method of solution is based on the direct application of integral transforms together with the Wiener-Hopf technique and the Cagniard-de Hoop method, which were previously believed to be inappropriate. Some features of solutions are discussed and the results are displayed in several figures.