幂硬化粘塑性材料动态扩展裂纹尖端场的渐近解

采用弹性－粘塑性本构模型，对幂硬化粘塑性介质中反平面剪切动态扩展裂纹尖端的应力，应变场进行了渐近分析，给出了反平面剪切动态扩展纹尖端场的渐进方程。分析结果表明，在裂纹法端应力具有（ｌｎＲ／ｒ）１／ｎ－１的奇异性，应变具有（ｌｎＲ／Ｒｎ／ｎ－１的奇异性。从而提示了幂硬化粘塑材料反平面剪动态扩展裂纹尖端场的渐近行为。     

Mode I and mixed mode crack-tip fields in strain gradient plasticity

Strain gradients develop near the crack-tip of Mode I or mixed mode cracks. A finite strain version of the phenomenological strain gradient plasticity theory of Fleck-Hutchinson (2001) is used here to quantify the effect of the material length scales on the crack-tip stress field for a sharp stationary crack under Mode I and mixed mode loading. It is found that for material length scales much smaller than the scale of the deformation gradients, the predictions converge to conventional elastic-plastic solutions. For length scales sufficiently large, the predictions converge to elastic solutions. Thus, the range of length scales over which a strain gradient plasticity model is necessary is identified. The role of each of the three material length scales, incorporated in the multiple length scale theory, in altering the near-tip stress field is systematically studied in order to quantify their effect.     

The influence of a rate sensitive effect of material for a propagating crack-tip field

The elastic-viscoplastic model proposed in [1] is used in this paper to analyze the quasi-statically growing crack field and dynamic propagating crack-tip field of mode III. By analysis, we obtained more reasonable results than those of an elastic-plastic material. When the effect of rate sensitivity of a material is considered, it is found that only the quasi-statically growing crack-tip field is the special case of dynamic propagating crack-tip field when Mach numberM approaches zero.     

Perfect elastic-viscoplastic field at mode Ⅰ dynamic propagating crack-tip

The viscosity of material is considered at propagating crack-tip. Under the assumption that the artificial viscosity coefficient is in inverse proportion to power law of the plastic strain rate, an elastic-viscoplastic asymptotic analysis is carried out for moving crack-tip fields in power-hardening materials under plane-strain condition. A continuous solution is obtained containing no discontinuities. The variations of numerical solution are discussed for mode Ⅰ crack according to each parameter. It is shown that stress and strain both possess exponential singularity. The elasticity, plasticity and viscosity of material at crack-tip only can be matched reasonably under linear-hardening condition. And the tip field contains no elastic unloading zone for mode Ⅰ crack. It approaches the limiting case, crack-tip is under ultra-viscose situation and energy accumulates, crack-tip begins to propagate under different compression situations.     

Perfect elastic-viscoplastic field at mode I dynamic propagating crack-tip

The viscosity of material is considered at propagating crack-tip. Under the assumption that the artificial viscosity coefficient is in inverse proportion to power law of the plastic strain rate, an elastic-viscoplastic asymptotic analysis is carried out for moving crack-tip fields in power-hardening materials under plane-strain condition. A continuous solution is obtained containing no discontinuities. The variations of numerical solution are discussed for mode I crack according to each parameter. It is shown that stress and strain both possess exponential singularity. The elasticity, plasticity and viscosity of material at crack-tip only can be matched reasonably under linear-hardening condition. And the tip field contains no elastic unloading zone for mode I crack. It approaches the limiting case, crack-tip is under ultra-viscose situation and energy accumulates, crack-tip begins to propagate under different compression situations.     

The anti-plane shear field in an infinite slab of elasto-damaged material with a semi-infinite crack

This paper deals with an infinite slab with a semi-infinite crack, which is subjected to the anti-plane sheark _III field at infinity. The slab is made of an elasto-damaged material. Analytical solution is obtained by use of conformal mapping. The shape of damaged-zone, the dissipative energy, the shear opening displacement on the crack surface and several stress distribution curves are given. The far field condition is checked, The asymptotic behavior near the crack-tip is given. The project supported by National Natural Science Foundation of China     

Non-elliptic deformation field near the tip of a mixed-mode crack in a compressible hyperelastic material

This paper gives an asymptotic analysis of the deformation field near the tip of an arbitrary mixed-mode crack in a compressible hyperelastic harmonic material which loses ellipticity at sufficiently large deformations. It is found that the near-tip deformation field is characterized by a localized non-elliptic deformation band issuing from the crack-tip and bounded by two curves of discontinuous deformation gradient. Explicit expression for the near-tip deformation field is obtained both inside and outside the localized deformation band. In particular, a simple relation is derived that determines the orientation of the deformation band in terms of two complex governing parameters of the near-tip fields inside and outside the deformation band, respectively.     

ASYMPTOTIC ANALYSIS OF MODE Ⅱ STATIONARY GROWTHCRACK ON ELASTIC-ELASTIC POWER LAWCREEPING BIMATERIAL INTERFACE

A mechanical model was established for mode Ⅱ interfacial crack static growingalong an elastic-elastic power law creeping bimaterial interface. For two kinds of boundaryconditions on crack faces, traction free and frictional contact, asymptotic solutions of thestress and strain near tip-crack were given. Results derived indicate that the stress andstrain have the same singularity, there is not the oscillatory singularity in the field; thecreep power-hardening index n and the ratio of Young‘s module notably influence the crack-tip field in region of elastic power law creeping material and n only influences distribution ofstresses and strains in region of elastic material. When n is bigger, the creepingdeformation is dominant and stress fields become steady, which does not change with n.Poisson‘s ratio does not affect the distributing of the crack-tip field.     

The plane stress crack-tip field for an incompressible rubber material

ＴＨＥＰＬＡＮＥＳＴＲＥＳＳＣＲＡＣＫ－ＴＩＰＦＩＥＬＤＦＯＲＡＮＩＮＣＯＭＰＲＥＳＳＩＢＬＥＲＵＢＢＥＲＭＡＴＥＲＩＡＬＧａｏＹｕ－ｃｈｅｎ（高玉臣）,ＳｈｉＺｈｉ－ｆｅｉ（石志飞）（ＨａｒｂｉｎＳｈｉｐｂｕｉｌｄｉｎｇＥｎｇｎｅｅｒｉｎｇＩｎｓｔ...     

Dynamic crack-tip fields in rate-sensitive solids

The asymptotic stress and strain fields near the tip of a crack which propagates dynamically in a rate-sensitive solid are obtained under anti-plane shear and plane strain conditions. The problem is formulated within the context of a small-strain theory for a solid whose mechanical behavior under high strain rates is described by an elastic-viscoplastic constitutive relation. It is shown that, if the stresses are singular at the crack-tip, the viscoplastic relation is equivalent asymptotically to an elastic-non-linear viscous relation. Furthermore, for a certain range of the material parameter which characterizes the rate-sensitivity of the material, the elastic strain-rates near the propagating crack tip are shown to have the same asymptotic radial dependence near the propagating crack-tip as the inelastic strain-rates. This determines the order of the stress singularity uniquely. The governing equations for anti-plane shear and plane strain are then derived. The numerical results for the stress and strain fields are presented for anti-plane shear and plane strain. For the present model, the results suggest that under small-scale yielding conditions, there exists a minimum velocity for stable steady crack propagation. The implication that a terminal velocity for a running crack may exist is also discussed.     

On the driving force for crack growth during thermal actuation of shape memory alloys

The effect of thermomechanically induced phase transformation on the driving force for crack growth in polycrystalline shape memory alloys is analyzed in an infinite center-cracked plate subjected to a thermal actuation cycle under mechanical load in plain strain. Finite element calculations are carried out to determine the mechanical fields near the static crack and the crack-tip energy release rate using the virtual crack closure technique. A substantial increase of the energy release rate – an order of magnitude for some material systems – is observed during the thermal cycle due to the stress redistribution induced by large scale phase transformation. Thus, phase transformation occurring due to thermal variations under mechanical load may result in crack growth if the crack-tip energy release rate reaches a material specific critical value.     

Quasi-static and dynamic crack growth along bimaterial interfaces: A note on crack-tip field measurements using coherent gradient sensing

The paper presents a preliminary experimental investigation of crack-tip deformation fields near quasistatically and dynamically growing cracks in bimaterial interfaces. A three-point-bend bimaterial specimen with a relatively large stiffness mismatch between the two materials is studied. A recently developed optical method of coherent gradient sensing (CGS) is used to map crack-tip deformation fields.The quasi-static measurements are interpreted using plane-stress, singular-field solution for the interface crack tip. Results are compared with two-dimensional finite-element computations performed on identical specimen geometries and material mismatch.³² Impact studies conducted with bimaterial specimens provide the first experimental results of deformation fields near dynamically growing cracks along interfaces. Very high crack velocities, up to 80 percent of the Rayleigh wave speed for the less stiffer material of the two, are observed.     

Field structure at mode III dynamically propagating crack tip in elastic-viscoplastic materials

An elastic-viscoplastic mechanics model is used to investigate asymptotically the mode Ⅲ dynamically propagating crack tip field in elastic-viscoplastic materials. The stress and strain fields at the crack tip possess the same power-law singularity under a linear-hardening condition. The singularity exponent is uniquely determined by the viscosity coefficient of the material. Numerical results indicate that the motion parameter of the crack propagating speed has little effect on the zone structure at the crack tip. The hardening coefficient dominates the structure of the crack-tip field. However, the secondary plastic zone has little influence on the field. The viscosity of the material dominates the strength of stress and strain fields at the crack tip while it does have certain influence on the crack-tip field structure. The dynamic crack-tip field degenerates into the relevant quasi-static solution when the crack moving speed is zero. The corresponding perfectly-plastic solution is recovered from the linear-hardening solution when the hardening coefficient becomes zero.     

Field structure at mode Ⅲ dynamically propagating crack tip in elastic-viscoplastic materials

An elastic-viscoplastic mechanics model is used to investigate asymptotically the mode Ⅲ dynamically propagating crack tip field in elastic-viscoplastic materials. The stress and strain fields at the crack tip possess the same power-law singularity under a linear-hardening condition. The singularity exponent is uniquely determined by the viscosity coefficient of the material. Numerical results indicate that the motion parameter of the crack propagating speed has little effect on the zone structure at the crack tip. The hardening coefficient dominates the structure of the crack-tip field. However, the secondary plastic zone has little influence on the field. The viscosity of the material dominates the strength of stress and strain fields at the crack tip while it does have certain influence on the crack-tip field structure. The dynamic crack-tip field degenerates into the relevant quasi-static solution when the crack moving speed is zero. The corresponding perfectly-plastic solution is recovered from the linear-hardening solution when the hardening coefficient becomes zero.     

I型定常扩展裂纹尖端的弹黏塑性场

考虑材料在扩展裂纹尖端的黏性效应，假设黏性系数与塑性应变率的幂次成反比，对幂硬化材料中平面应变扩展裂纹尖端场进行了弹黏塑性渐近分析，得到了不含间断的连续解，并讨论了I型裂纹数值解的性质随各参数的变化规律. 分析表明应力和应变均具有幂奇异性，并且只有在线性硬化时，尖端场的弹、黏、塑性才可以合理匹配. 对于I型裂纹，裂尖场不含弹性卸载区. 当裂纹扩展速度趋于零时，动态解趋于准静态解，表明准静态解是动态解的特殊形式；如果进一步考虑硬化系数为零的极限情况，便可退化为Hui和Riedel的非线性黏弹性解.     

粘弹塑性材料动态裂纹尖端场

本文采用一种弹性/粘塑性模型,对扩展裂纹尖端应力应变场进行了渐近分析。文中假定,弹性阶段的粘性效应可以略去,仅在塑性应变中粘性才起作用。对这种模型,文中导出了一种率敏感型的本构关系。并进一步导出了裂纹尖端应力应变场的动力学方程。通过量级分析,给出了尖端场的应力应变奇异性指数。并且讨论了弹性,塑性及粘性三者的匹配条件。对Ⅲ型裂纹进行了具体的分析计算。对各个不同参数的选取进行了详细的分析,讨论了解的性质随各参数的变化规律。     

Suppressed plastic deformation at blunt crack-tips due to strain gradient effects

Large deformation gradients occur near a crack-tip and strain gradient dependent crack-tip deformation and stress fields are expected. Nevertheless, for material length scales much smaller than the scale of the deformation gradients, a conventional elastic–plastic solution is obtained. On the other hand, for significant large material length scales, a conventional elastic solution is obtained. This transition in behaviour is investigated based on a finite strain version of the Fleck–Hutchinson strain gradient plasticity model from 2001. The predictions show that for a wide range of material parameters, the transition from the conventional elastic–plastic to the elastic solution occurs for length scales ranging from 0.001 times the size of the plastic zone to a length scale of the same order of magnitude as the plastic zone.     

Effect of T-stress on branch angle of moving cracks

The effects of the T-stress on Yoffe crack propagation are analyzed. Using a maximum k_I fracture criterion near the kink of a moving crack tip, a branch angle is determined via asymptotic crack-tip field containing two fracture parameters related to singular and constant terms. Results indicate that crack speeds decrease the T-stress. The crack-tip field and the branch angle depend on the T-stress, especially for higher crack velocities. The critical speed for crack bifurcation is independent of remote transverse loading if neglecting the T-stress. Otherwise, the crack branch speed is reduced or raised, depending on positive or negative transverse loading, respectively.