Elastic-viscoplastic field at mixed-mode interface crack-tip under compression and shear

For a compression-shear mixed mode interface crack, it is difficult to solve the stress and strain fields considering the material viscosity, the crack-tip singularity, the frictional effect, and the mixed loading level. In this paper, a mechanical model of the dynamic propagation interface crack for the compression-shear mixed mode is proposed using an elastic-viscoplastic constitutive model. The governing equations of propagation crack interface at the crack-tip are given. The numerical analysis is performed for the interface crack of the compression-shear mixed mode by introducing a displacement function and some boundary conditions. The distributed regularities of stress field of the interface crack-tip are discussed with several special parameters. The final results show that the viscosity effect and the frictional contact effect on the crack surface and the mixed-load parameter are important factors in studying the mixed mode interface crack- tip fields. These fields are controlled by the viscosity coefficient, the Mach number, and the singularity exponent.     

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.     

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.     

Elastic-viscoplastic fields near the tip of a propagating crack under anti-plane shear

The elastic-viscoplastic model proposed by Bingham was used to analyse the stress and strain surrounding the tip of a propagating crack under antiplane shear. The proper displacement pattern was given ; the asymptotic equations were derived and solved numerically. The analysis and calculation show that for smaller viscosity the crack-tip possesses logarthmic singularity, and for larger viscosity it possesses power-law singularity.In critical case, the two kinds of singularity are consistent with each other. The result revealed the important role of viscosity for crack-tip field.     

VISCOPLASTIC FIELD NEAR A PROPAGATING CRACK-TIP

An elastic-viscoplastic constitutive model is proposed instead of the usual elastoplasticmodel.It is assumed tha when crack-tip is approached the viscosity coefficient tends tozero(η=η_0r).Asympto-c analysis of the dynamic field near a propagating crack-tip isgiven,and the uniparameter solution is obtained.The numerical result is given for variousMach number and viscosity coefficient,Based on the asymptotic solution,a fracturecriterion is proposed and the stability of crack propagation is discussed.     

ASYMPTOTIC DYNAMIC SOLUTION TO THE MODE Ⅰ PROPAGATING CRACK-TIP FIELD IN ELASTIC-VISCOPLASTIC MATERIAL

A new elastic-viscoplastic mode was proposed to analyze the stress and strain fields surrounding the tip of a propagating mode Ⅰ cracks. A proper displacement pattern was suggested and asymptotic equations were derived, and numerical solutions were illustrated. The analysis and calculation show that the crack-tip field is of logarithmic singularity for smaller viscosity, however no solution exists for large viscosity. By a careful analysis and comparison, it is found that the present results retain all merits of those given by Gao Yu-chen, while removing existing problems.     

Interface crack problems for mode II of double dissimilar orthotropic composite materials

The fracture problems near the similar orthotropic composite materials are interface crack tip for mode Ⅱ of double disstudied. The mechanical models of interface crack for mode Ⅱ are given. By translating the governing equations into the generalized hi-harmonic equations, the stress functions containing two stress singularity exponents are derived with the help of a complex function method. Based on the boundary conditions, a system of non-homogeneous linear equations is found. Two real stress singularity exponents are determined be solving this system under appropriate conditions about bimaterial engineering parameters. According to the uniqueness theorem of limit, both the formulae of stress intensity factors and theoretical solutions of stress field near the interface crack tip are derived. When the two orthotropic materials are the same, the stress singularity exponents, stress intensity factors and stresses for mode II crack of the orthotropic single material are obtained.     

VISCOPLASTIC SOLUTION TO FIELD AT STEADILY PROPAGATING CRACK TIP IN LINEAR- HARDENING MATERIALS

An elastic-viscoplastic constitutive model was adopted to analyze asymptotically the tip-field of moving crack in linear-hardening materials under plane strain condition. Under the assumption that the artificial viscosity coefficient was in inverse proportion to power law of the rate of effective plastic strain, it is obtained that stress and strain both possess power law singularity and the singularity exponent is uniquely determined by the power law exponent of the rate of effective plastic strain. Variations of zoning structure according to each material parameter were discussed by means of numerical computation for the tip-field of mode Ⅱ dynamic propagating crack, which show that the structure of crack tip field is dominated by hardening coefficient rather than viscosity coefficient. The secondary plastic zone can be ignored for weak hardening materials while the secondary plastic zone and the secondary elastic zone both have important influence on crack tip field for strong hardening materials. The dynamic solution approaches to the corresponding quasi-static solution when the crack moving speed goes to zero, and further approaches to the HR (Hui-Riedel) solution when the hardening coefficient is equal to zero.     

双材料界面Ⅰ型扩展裂纹尖端的弹黏塑性场

双材料界面中存在材料黏性效应, 对界面裂纹尖端场的分布和界面本身性能 的变化起着重要的影响. 考虑裂纹尖端的奇异性, 建立了双材料界面扩展裂纹尖端的弹黏塑 性控制方程. 引入界面裂纹尖端的位移势函数和边界条件, 对刚性-弹黏塑性界面I型界面 裂纹进行了数值分析, 求得了界面裂纹尖端应力应变场, 并讨论了界面裂纹尖端场随各影响 参数的变化规律. 计算结果表明, 黏性效应是研究界面扩展裂纹尖端场时的一个主要因素, 界面裂纹尖端为弹黏塑性场, 其场受材料的黏性系数、马赫数和奇异性指数控制.     

压-剪混合型定常扩展裂纹尖端的弹黏塑性场

假定黏性系数与塑性等效应变率的幂次成反比,考虑其黏性和裂纹面摩擦接触效应 建立了压-剪混合型定常扩展裂纹尖端弹黏塑性场的渐近方程,求得了裂纹尖端场不含应力、应变间 断的数值解. 并讨论了压-剪混合型裂纹数值解随各个参数的变化规律,计算结果 和分析表明,压-剪混合型裂纹尖端场是满塑性的,不含有弹性卸载区,黏性效应是研究扩展裂纹尖端场时的一个重要因素. 无论混合裂纹趋近I型还是趋近II型,静水压力随摩擦系数的增加都是增加的,裂纹面摩擦 效应是阻止裂纹扩展速度的因素,且摩擦作用越强,裂纹尖端场的韧性越高.     

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.     

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。     

黏弹性材料界面裂纹应力场奇性分析

研究两半无限大黏弹性体间Griffith界面裂纹在简谐载荷作用下裂纹尖端动应力场的奇异特性.通过引入裂纹张开位移和裂纹位错密度函数,相应的混合边值问题归结为一组耦合的奇异积分方程.渐近分析表明裂尖动应力场的奇异特征完全包含在奇异积分方程的基本解中.通过对基本解的深入分析发现黏弹性材料界面裂纹裂尖动应力场具有与材料参数和外载荷频率相关的振荡奇异特性.以标准线性固体黏弹材料为例讨论了材料参数和载荷频率对奇性指数和振荡指数的影响.     

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.