Deformation twinning and its effect on crack extension

Deformation twinning near a crack tip is observed in b.c.c. metal Mo based on molecular dynamics simulation at temperature T = 50 K and loading rate (K) over dot(II) = 0.0706 MPa m(1/2)/ps. The defor mation twinning is closely controlled by both the crystal geometry orientation and the stress distribution. The width of the deformation twin band is affected by the distance between the upper and lower crack surfaces. The twin plane and twin direction are (<1(1)over bar>2) and [(1) over bar 11], respectively. The initial crack extension occurs in the deformation twin region near the crack tip. The simulation shows that the extension direction of the crack is changed as the crack propagates over the twinning boundary.

Dynamic SIF of interface crack between two dissimilar viscoelastic bodies under impact loading

In this paper, the transient dynamic stress intensity factor (SIF) is determined for an interface crack between two dissimilar half-infinite isotropic viscoelastic bodies under impact loading. An anti-plane step loading is assumed to act suddenly on the surface of interface crack of finite length. The stress field incurred near the crack tip is analyzed. The integral transformation method and singular integral equation approach are used to get the solution. By virtue of the integral transformation method, the viscoelastic mixed boundary problem is reduced to a set of dual integral equations of crack open displacement function in the transformation domain. The dual integral equations can be further transformed into the first kind of Cauchy-type singular integral equation (SIE) by introduction of crack dislocation density function. A piecewise continuous function approach is adopted to get the numerical solution of SIE. Finally, numerical inverse integral transformation is performed and the dynamic SIF in transformation domain is recovered to that in time domain. The dynamic SIF during a small time-interval is evaluated, and the effects of the viscoelastic material parameters on dynamic SIF are analyzed.

A crack perpendicular to and terminating at a bimaterial interface

Using dislocation simulation approach, the basic equation for a finite crack perpendicular to and terminating at a bimaterial interface is formulated. A novel expansion method is proposed for solving the problem. The complete solution to the problem, including the explicit formulae for the T stresses ahead of the crack tip and the stress intensity factors are presented. The stress held characteristics are analysed in detail. It is found that normal stresses sigma(x) and sigma(y) ahead of the crack tip, are characterised by Q fields if the crack is within a stiff material and the parameters \p(T)\ and \q(T)\ are very small, where Q is a generalised stress intensity factor for a crack normal to and terminating at the interface. If the crack is within a weak material, the normal stresses sigma(x) and sigma(y) are dominated by the Q field plus T stress.

Ice induced low temperature fatigue crack propagation in offshore structural steel A131

To investigate the low temperature fatigue crack propagation behavior of offshore structural steel A131 under random ice loading, three ice failure modes that are commonly present in the Bohai Gulf are simulated according to the vibration stress responses induced by real ice loading. The test data are processed by a universal software FCPUSL developed on the basis of the theory of fatigue crack propagation and statistics. The fundamental parameter controlling the fatigue crack propagation induced by random ice loading is determined to be the amplitude root mean square stress intensity factor K-arm. The test results are presented on the crack propagation diagram where the crack growth rate da/dN is described as the function of K-arm. It is evident that the ice failure modes have great influence on the fatigue crack propagation behavior of the steel in ice-induced vibration. However, some of the experimental phenomena and test results are hard to be physically explained at present. The work in this paper is an initial attempt to investigate the cause of collapse of offshore structures due to ice loading.

Large strain field near a crack tip in a rubber sheet

The distribution of stress-strain near a crack tip in a rubber sheet is investigated by employing the constitutive relation given by Gao (1997). It is shown that the crack tip field is composed of two shrinking sectors and one expanding sector. The stress state near the crack tip is in uniaxial tension. The analytical solutions are obtained for both expanding and shrinking sectors.

Plastic constitutive behavior of short-fiber/particle reinforced composites

A cylindrical cell model based on continuum theory for plastic constitutive behavior of short-fiber/particle reinforced composites is proposed. The composite is idealized as uniformly distributed periodic arrays of aligned cells, and each cell consists of a cylindrical inclusion surrounded by a plastically deforming matrix. In the analysis, the non-uniform deformation field of the cell is decomposed into the sum of the first order approximate field and the trial additional deformation field. The precise deformation field are determined based on the minimum strain energy principle. Systematic calculation results are presented for the influence of reinforcement volume fraction and shape on the overall mechanical behavior of the composites. The results are in good agreement with the existing finite element analyses and the experimental results. This paper attempts to stimulate the work to get the analytical constitutive relation of short-fiber/particle reinforced composites.

Dislocations emission and crack extension at the atomistic crack tip in body-centered-cubic metal Mo

The behaviors of a crack in body-centered-cubic metal Mo under different loading modes were studied using the molecular dynamics method. Dislocation emission was observed near the crack tip in response to mode II loading with theta = 0 degrees in which theta is the inclination angle of the slip plane with respect to the crack plane, and two full dislocations were observed at the stress level of K-II = 1.17 MPa m(1/2) without any evidence of crack extension. Within the range of 0 degrees less than or equal to theta less than or equal to 45 degrees, crack extension was observed in response to mode I loading, and the effect of crystal orientation on the crack propagation was studied, The crack propagated along the [111] slip direction without any evidence of dislocations emission.

Finite Element Solutions for Plane Strain Mode I Crack with Strain Grading Effect

In this paper, a new phenomenological theory with strain gradient effects is proposed to account for the size dependence of plastic deformation at micro- and submicro-length scales. The theory fits within the framework of general couple stress theory and three rotational degrees of freedom omega(i) are introduced in addition to the conventional three translational degrees of freedom mu(i). omega(i) is called micro-rotation and is the sum of material rotation plus the particles' relative rotation. While the new theory is used to analyze the crack tip field or the indentation problems, the stretch gradient is considered through a new hardening law. The key features of the theory are that the rotation gradient influences the material character through the interaction between the Cauchy stresses and the couple stresses; the term of stretch gradient is represented as an internal variable to increase the tangent modulus. In fact the present new strain gradient theory is the combination of the strain gradient theory proposed by Chen and Wang (Int. J. Plast., in press) and the hardening law given by Chen and Wang (Acta Mater. 48 (2000a) 3997). In this paper we focus on the finite element method to investigate material fracture for an elastic-power law hardening solid. With remotely imposed classical K fields, the full field solutions are obtained numerically. It is found that the size of the strain gradient dominance zone is characterized by the intrinsic material length l(1). Outside the strain gradient dominance zone, the computed stress field tends to be a classical plasticity field and then K field. The singularity of stresses ahead of the crack tip is higher than that of the classical field and tends to the square root singularity, which has important consequences for crack growth in materials by decohesion at the atomic scale. (C) 2002 Elsevier Science Ltd. All rights reserved.

Torsional impact of transversely isotropic solid with functionally graded shear moduli and a penny-shaped crack

The torsional impact response of a penny-shaped crack in an unbounded transversely isotropic solid is considered. The shear moduli are assumed to be functionally graded such that the mathematics is tractable. Laplace transform and Hankel transform are used to reduce the problem to solving a Fredholm integral equation. The crack tip stress fields are obtained. Investigated are the influence of material nonhomogeneity and orthotropy on the dynamic stress intensity factor. The peak value of the dynamic stress intensity factor can be suppressed by increasing the shear moduli's gradient and/or increasing the shear modulus in a direction perpendicular to the crack surface.

The scattering of general SH plane wave by interface crack between two dissimilar viscoelastic bodies

The scattering of general SH plane wave by an interface crack between two dissimilar viscoelastic bodies is studied and the dynamic stress,intensity factor at the crack-tip is computed. The scattering problem can be decomposed into two problems: one is the reflection and refraction problem of general SH plane waves at perfect interface (with no crack); another is the scattering problem due to the existence of crack. For the first problem, the viscoelastic wave equation, displacement and stress continuity conditions across the interface are used to obtain the shear stress distribution at the interface. For the second problem, the integral transformation method is used to reduce the scattering problem into dual integral equations. Then, the dual integral equations are transformed into the Cauchy singular integral equation of first kind by introduction of the crack dislocation density function. Finally, the singular integral equation is solved by Kurtz's piecewise continuous function method. As a consequence, the crack opening displacement and dynamic stress intensity factor are obtained. At the end of the paper, a numerical example is given. The effects of incident angle, incident frequency and viscoelastic material parameters are analyzed. It is found that there is a frequency region for viscoelastic material within which the viscoelastic effects cannot be ignored.

Interface crack problems with strain gradient effects

In this paper, the strain gradient theory proposed by Chen and Wang (2001 a, 2002b) is used to analyze an interface crack tip field at micron scales. Numerical results show that at a distance much larger than the dislocation spacing the classical continuum plasticity is applicable; but the stress level with the strain gradient effect is significantly higher than that in classical plasticity immediately ahead of the crack tip. The singularity of stresses in the strain gradient theory is higher than that in HRR field and it slightly exceeds or equals to the square root singularity and has no relation with the material hardening exponents. Several kinds of interface crack fields are calculated and compared. The interface crack tip field between an elastic-plastic material and a rigid substrate is different from that between two elastic-plastic solids. This study provides explanations for the crack growth in materials by decohesion at the atomic scale.

Asymptotic analysis for a crack on interface of damaged materials

An asymptotic analysis for a crack lying on the interface of a damaged plastic material and a linear elastic material is presented in this paper. The present results show that the stress distributions along the crack tip are quite similar to those with HRR singularity field and the crack faces open obviously. Material constants n, mu and mo are varied to examine their effects on the resulting stress distributions and displacement distributions in the damaged plastic region. It is found that the stress components sigma(rr), sigma(theta theta), sigma(r theta) and sigma(e) are slightly affected by the changes of material constants n, mu and m(0), but the damaged plastic region are greatly disturbed by these material parameters.