Intersonic crack growth under time-dependent loading

The problem investigated in this paper is a mode II crack extending at a uniform intersonic speed in an otherwise unbounded elastic solid subjected to time dependent crack-face tractions. The fundamental solution for this problem is obtained analytically, which is then used to construct the general solution for an intersonic crack subjected to arbitrary time-dependent loading. For time-independent loading, this solution reduces to Huang and Gao’s [J. Appl. Mech 68 (2001) 169] fundamental solution. We have also studied two crack-face loadings that are of interest for engineering applications.     

Dynamic crack growth under stress wave loading

The crack growth process has been analysed on the basis of a fracture criterion of a dynamic stress intensity factor when a crack in an infinite plate was subjected to a pulse type of stress wave. The crack velocity and the amount of crack extension were related to the constant amplitude and the duration of the stress pulse. The calculated amount of crack extension was well in agreement with the experimental one for the polymer material Acrylite (which is similar to polymethylmethacrylate) found by the authors, thus indicating the validity of the present approach.     

A partially insulated interface crack between a graded orthotropic coating and a homogeneous orthotropic substrate under heat flux supply

In this paper, thermal response of an orthotropic functionally graded coating-substrate structure with a partially insulated interface crack under heat flux supply is considered. It is assumed that there exists thermal resistance to heat conduction through the crack region. The mixed boundary value problems are reduced to a system of singular integral equations and solved numerically. Higher order asymptotic terms for the singular integral kernels are considered to improve the accuracy and the convergence efficiency of the numerical integrals. Numerical results are presented to show the effects of the orthotropy parameters, thermo-elastic nonhomogeneity parameters, and dimensionless thermal resistance on the temperature distribution and the thermal stress intensity factors (SIFs).     

Modelling of crack growth under cyclic contact loading

The paper describes a general computational model for modelling of subsurface fatigue crack growth under cyclic contact loading of mechanical elements. The model assumes that the initial fatigue crack develops along the slip line in a single crystal grain at the point of the maximum equivalent stress. The position and magnitude of the maximum equivalent stress are determined with the Finite Element Analysis of the equivalent contact model, which is based on the Hertzian contact conditions with the addition of frictional forces. The Virtual Crack Extension method is then used for simulation of the fatigue crack propagation from the initial to the critical crack length, when the surface material layer breaks away and a pit appears on the surface. The pit shapes and relationships between the stress intensity factor and the crack length are determined for various combinations of contacting surface curvatures and contact loadings. The computational results show that the model reliably simulates the subsurface fatigue crack growth under contact loading and can be used for computational predictions of surface pitting for various contacting mechanical elements.     

A moving interface crack between two dissimilar functionally graded piezoelectric layers under electromechanical loading

The dynamic propagation of an interface crack between two dissimilar functionally graded piezoelectric material (FGPM) layers under anti-plane shear is analyzed using the integral transform method. The properties of the FGPM layers vary continuously along the thickness. The properties of the FGPM layers vary differently and the two layers are connected weak-discontinuously. A constant velocity Yoffe-type moving crack is considered. Fourier transform is used to reduce the problem to two sets of dual integral equations, which are then expressed to the Fredholm integral equations of the second kind. Numerical values on the dynamic energy release rate (DERR) are presented for the FGPM to show the effects on the electric loading, gradient of material properties, crack moving velocity, and thickness of layers. Followings are helpful to increase of the resistance of the interface crack propagation of FGPM: (a) certain direction and magnitude of the electric loading; (b) increase of the gradient of material properties; (c) increase of the material properties from the interface to the upper and lower free surface; (d) increase of the thickness of FGPM layer. The DERR increases or decreases with increase of the crack moving velocity.     

Two dimensional numerical simulation of crack kinking from an interface under dynamic loading by time domain boundary element method

The hybrid time-domain boundary element method, together with the multi-region technique, is applied to simulate the dynamic process of propagation and/or kinking of an interface crack in a two-dimensional bi-material. The whole bi-material is divided into two regions along the interface. The traditional displacement boundary integral equations are employed with respect to each region. However, when the crack kinks into the matrix material, the non-hypersingular traction boundary integral equations are used with respect to the part of the crack in the matrix. Crack propagation along the interface is numerically modelled by releasing the nodes in the front of the moving crack-tip controlled by the fracture criterion. Kinking of the interface crack is controlled by a criterion developed from the quasi-static one. Once the crack kinks into the matrix, its propagation is modeled by adding new elements of constant length to the moving crack-tip controlled by a criterion extended from the quasi-static maximum circumferential stress. The numerical results of the crack growth trajectory for different material combinations are computed and compared with the corresponding experimental results. Good agreement between numerical and experimental results implies that the present boundary element numerical method can provide an excellent simulation for the dynamic propagation and deflection of an interface crack.     

Analysis of bonded anisotropic wedges with interface crack under anti-plane shear loading

The antiplane stress analysis of two anisotropic finite wedges with arbitrary radii and apex angles that are bonded together along a common edge is investigated. The wedge radial boundaries can be subjected to displacement-displacement boundary condi- tions, and the circular boundary of the wedge is free from any traction. The new finite complex transforms are employed to solve the problem. These finite complex transforms have complex analogies to both kinds of standard finite Mellin transforms. The traction free condition on the crack faces is expressed as a singular integral equation by using the exact analytical method. The explicit terms for the strength of singularity are extracted, showing the dependence of the order of the stress singularity on the wedge angle, material constants, and boundary conditions. A numerical method is used for solving the resul- tant singular integral equations. The displacement boundary condition may be a general term of the Taylor series expansion for the displacement prescribed on the radial edge of the wedge. Thus, the analysis of every kind of displacement boundary conditions can be obtained by the achieved results from the foregoing general displacement boundary condition. The obtained stress intensity factors （SIFs） at the crack tips are plotted and compared with those obtained by the finite element analysis （FEA）.     

A numerical study for three-dimensional viscoelastic flow inspired by non-linear radiative heat flux

Present article examines the three-dimensional flow of upper-convected Maxwell (UCM) fluid over a radiative bi-directional stretching surface. Novel non-linear Rosseland formula for thermal radiation is utilized in the formulation of energy equation. The conventional transformations lead to a strongly non-linear differential system which is treated numerically through Runge–Kutta integration procedure together with the shooting approach. We found that heat transfer rate from the sheet has inverse as well as non-linear relationship with wall to ambient temperature ratio. Moreover an increase in viscoelastic fluid parameter (Deborah number) corresponds to a decrease in the fluid velocity and the boundary layer thickness.     

Interaction between a rigid inclusion and a line crack under uniform heat flux

The thermoelastic displacement boundary value problem for a rigid inclusion interacting with a line crack in an infinite plane subjected to a uniform heat flux is studied, in which the rigid body rotation of the inclusion is considered. To solve the prescribed problem, we use the principle of superposition to decompose it into two groups of problems, which are further reduced to several basic subproblems including Green’s functions of edge dislocation and heat source couple, as well as the problem of a plane containing the inclusion under uniform heat flux and the problem of the inclusion subjected to a small rotation. The problems are solved using the complex variable method along with the rational mapping function technique. The variations of the stress intensity factors at the crack tips and the rigid body rotation angles with various crack lengths and heat flux angles are shown. The effects of the inclusion shape and size are also investigated.     

Prediction models of fatigue crack closure and growth under random loading

The effects of plastic zones both in front of and behind crack tip on crack closure have been analysed. The total residual deformations of crack surfaces involve two parts, that is, the amount of plastic blunting of crack tip and the residual deformation in the wake of the tip. This paper presents a fatigue crack closure model in which the influences of compressive load on closure stress are discussed. The model is applied to random loading conditions by the assumption of limited memory properties. The fatigue lives are predicted using the proposed crack growth model for CCT plane stress specimen cut from 2219-T851 aluminum alloy under flight spectrum loadings, and the prediction values agree with the test results.The project was supported by the natural science foundation of China.     

Elastic-plastic crack growth on plane strain bimaterial interface

Finite element computation are carried out to simulate plane strain crack growth on a bimaterial interface under the assumption of small scale yielding. The modified Gurson constitutive equation and the element vanish technique introduced by Tvergaard et al. are used to model the final formation of an open crack. It is found from the calculation that the critical fracture toughness for crack growth is much lower in bimaterials than that in homogeneous material. The critical fracture toughness is strongly dependent on material properties of the bimaterial pair and the mixed mode of remote loads. The interface crack grows in the more compliant (lower hardening) material or in the weaker (lower yield strength) material. In Mode-I loading, the crack grows zigzag along the interface. Project supported by Fok Ying-Tung Education Foundation and National Natural Science Foundation of China.     

Fatigue crack growth in high and low strength steel under torsional loading

During loading of a crack in mode III the crack surfaces in contact slide against each other giving rise to friction, abrasion and mutual support, thereby reducing the effective stress at the crack tip (“sliding mode crack closure”). This phenomenon was investigated in a high strength steel (AISI 4340) and in a low strength steel (AISI C1018) in circumferentially notched specimens under pure cyclic torsion and combined loading (cyclic torsion plus static axial load). The influence of sliding mode crack closure on fatigue crack propagation is shown and “true” crack growth values (without the sliding mode crack closure influence) are determined on the basis of an extrapolation procedure. Explanations are given for causes of the various fracture modes observed, such as “factory roof” fracture, macroscopically flat mode III fracture and “lamella” fracture. Finally the scientific and technical importance of sliding mode crack closure is demonstrated.     

Empirical modelling of subcritical crack growth size and profile under continued loading

During continued loading the slow crack growth regions at the crack tip assume different shapes and sizes. Two different crack front profiles may be identified in practice depending on the extent of crack growth. They may be approximated as parabolic and semi-circular in shape. Crack fronts tend to be semi-circular for relatively large extent of crack growth and parabolic during the early stages of crack growth. Modelling of crack growth size and profile for each crack growth increment is carried out by two approaches; namely, offset measurement and area consideration. The variation of average crack growth size as well as the convergence of as a function of measurement number is studied. The difference in the values obtained by the offset method and area method is also investigated in addition to the influence of specimen thickness and maximum crack growth on ø. Experimental verification of crack growth front profiles and the change in the value with ø is carried out. It suffices to consider eight to ten measurements for modelling crack growth size and profile in commonly used specimen thickness.     

Stable growth of penny-shaped crack in viscoelastic composite material under time-dependent loading

Considered is the long-term cracking of the three-dimensional fiber-reinforced viscoelastic composite with a plane penny-shaped crack under time-dependent loading. The composite has a hexagonal structure and consists of elastic isotropic fibers and viscoelastic isotropic matrix. The material is modeled by transversally isotropic homogeneous linearly viscoelastic medium with some averaged characteristics. The crack propagation planecoincides with the plane of isotropy. A ring-shaped yield zone in front of the moving crack is modeled as a Dugdale's zone with time-dependent stresses. Crack growth under deformation of the composite occurs by application of a slowly increasing tensile load; it is normal to the plane of crack propagation. A convolution-type time operator describes the viscoelastic properties of the matrix material. Use is made of the Volterra principle and the theory of long-term cracking of viscoelastic bodies. The irrational function of integral operator associated with the viscoelastic crack opening expression is expanded into a continued fraction of operators. The solution is reduced to the nonlinear integral equations of crack growth. Numerical results are obtained for a specific material. Crack growth kinetics is discussed in connection with the onset of stable crack growth and crack border stress intensity factor.     

Mode-III crack kinking under stress-wave loading

A horizontally polarized step-stress wave is incident on a semi-infinite crack in an elastic solid. At the instant that the crack tip is struck, the crack starts to propagate in the forward direction, but under an angle κπ with the plane of the original crack. In this paper a self-similar solution is obtained for the particle velocity of the diffracted cylindrical wave field. The use of Chaplygin's transformation reduces the problem to the solution of Laplace's equation in a semi-infinite strip containing a slit. The Schwarz-Christoffel transformation is employed to map the semi-infinite strip on a half-plane. An analytic function in the half-plane which satisfies appropriate conditions along the real axis, can subsequently be constructed. The Mode-III stress-intensity factor at the tip of the kinked crack has been computed for angles of incidence varying from normal to grazing incidence, for angles of crack kinking defined by -0.5?κ?0.5, and for arbitrary subsonic crack tip speeds.     

Three-dimensional elliptic crack under impact loading

The dynamic stress intensity factor of a three-dimensional elliptic crack under impact loading is determined with the finite element method. The computation results can take into account the influence of time and the ratio of the wave speeds on the stress intensity factor. The present method is suitable not only for three-dimensional dynamic crack, but also for three-dimensional dynamic contact. Project supported by the National Natural Science Foundation of China (No. K19672007).     

Subcritical crack growth in weak interface under mixed mode in two dimension

Constitutive equations, which govern subcritical crack growth within a weak brittle interface, are derived assuming mixed-mode loading, i.e., both tensile and shear stresses acting at the crack tip. The subcritical crack growth is assumed to be caused by the classical activation mechanism of fluctuation fracture kinetics. To derive the constitutive equations, two approaches are developed. The first approach is process-zone-detail-independent (PZI), which ignores any details of the process zone, i.e., a near-crack-tip zone of significant damage resulting in fracture, and takes into account only the process zone length. The second approach is process-zone-detail-dependent (PZD), which takes into account some details of the process-zone structure. After some general considerations including 3D case, the detailed consideration is given for 2D case, particularly, for plane strain. Illustrative calculated examples of the obtained theoretical results are presented.     

Analysis of a Griffith crack at the interface of two piezoelectric materials under anti-plane loading

The main objective of this work is the contribution to the study of the piezoelectric structures which contain preexisting defect (crack). For that, we consider a Griffith crack located at the interface of two piezoelectric materials in a semi-infinite plane structure. The structure is subjected to an anti-plane shearing combined with an in-plane electric displacement. Using integral Fourier transforms, the equations of piezoelectricity are converted analytically to a system of singular integral equations. The singular integral equations are further reduced to a system of algebraic equations and solved numerically by using Chebyshev polynomials. The stress intensity factor and the electric displacement intensity factor are calculated and used for the determination of the energy release rate which will be taken as fracture criterion. At the end, numerical results are presented for various parameters of the problem; they are also presented for an infinite plane structure.