幂硬化介质中平面应力动态裂纹的尖端弹塑性场

本文采用塑性动力学方程,对幂硬化介质中平面应力动态裂纹尖端场进行了渐近分析,其结果表明:在裂纹尖端附近,应力具有的奇异性,应变具有的奇异性,其中A是一个与塑性区尺寸有关的常数因子,r是离开裂纹尖端的距离,n为硬化指数,文中给出了尖端场的控制参量D,它依赖于马赫数;并且给出了各物理量的角函数。     

Anisotropic plastic fields at a rapidly propagating crack-tip

Under the condition that all the stress components at a crack-tip are the functionsofθonly,making use of the equations of steady-state motion,stress-strain relationsand Hill anisotropic yield conditions,we obtain the general solutions at a crack-tip inboth the cases of anti-plane and in-plane strains.Applying these general solutions tothe concrete cracks,the anisotropic plastic fields at the rapidly propagating tips ofmodeⅢand modeⅠcracks are derived.     

Anisotropic plastic fields at a rapidly propagating plane-stress crack-tip

Under the condition that all the stress components at a crack-tip are the functions ofθonly,making use of the equations of steady-state motion.Hill anisotropic yield condition and stress-strain relations,we obtain the general solution of anisotropic plastic field at a rapidly propagating plane-stress crack-tip.Applying this general solution to four particular cases of anisctropy,the general solutions of these four particular cases are derived.Finally,we give the anisotropic plastic field at the rapidly propagating plane-stress modeⅠcrack-tip in the case of X=Y=Z     

Anisotropic plastic stress fields at a rapidly propagating crack-tip

All the stress components at a rapidly propagating crack-tip in an elastic perfectly-plastic material are the functions of only. Making use of this condition and the equations of steady-state motion, stress-strain relations and Hill anisotropic yield condition, we obtain the general solutions in both the cases of anti-plane and in-plane strain. Applying these two general solutions to propagating Mode III and Mode I cracks, respectively, the anisotropic plastic stress fields at the rapidly propagating tips of Mode III and Mode I cracks are derived.     

Fields near a rapidly propagating crack-tip in an elastic perfectly-plastic material

Dynamic effects are investigated for the steady-state fields of stress and deformation in the immediate vicinity of a rapidly propagating crack-tip in an elastic perfectly-plastic material. Both the cases of antiplane strain and in-plane strain have been considered. The governing equations in the plastic regions are hyperbolic in nature. Simple wave solutions together with uniform fields provide explicit asymptotic expressions for the stresses and the strains in the near-tip regions. The dynamic solutions describe a region of plastic loading which completely surrounds the propagating crack-tip.     

Antiplane shear fields near a crack-tip in a brittle damaged material

In this paper, a simplified brittle damage model is proposed according to the Mazarz-Lemaitre damage model for concrete. A closed-form solution for a mode III crack is obtained based on the simplified model under small scale damage conditions, which allows for discontinuities of displacement-gradient and tangential stress on the damage boundary. It is pointed out that the discontinuities of field variables near the tip region exist for the brittle damaged material induced by the softening effect of the material. The preoject supported by the National Natural Science Foundation of China     

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.     

PERFECTLY PLASTIC FIELDS AT A RAPIDLY PROPAGATING PLANE-STRESS CRACK TIP

Under the condition that all the perfectly plastic stress components at a crack tiP arethe functions ofθonly,making use of the Mises yield condition,steady-state movingequations and elastic perfectly-plastic constitutive equations,we derive the generallyanalytical expressions of perfectly plastic fields at a rapidly propagating plane-stress cracktip.Applying these generally analytical expressions to the concrete crack,we obtain theanalytical expressions of perfectly plastic fields at the rapidly propagating tips of,modesⅠandⅡplane-stress cracks.     

应变损伤材料I型动态扩展裂纹尖端场的渐近分析

研究了应变损伤材料Ｉ型动态扩展的裂纹尖端场。假定材料服从Ｊ２流动理论，且损伤规律以幂律应变软化的规律给出。对于塑性区引进了应力函数φ，ψ０借助于动力学方程的分析，给出了渐近方程及数值解。结果表明，对于可压缩材料Ｉ型平面应变尖端场是完全由塑性区组成，没有弹性卸载区。在裂纹尖端附近，应力和应变分别具有如下的奇异性：σ￣（ｌｎＲ／ｒ）＾－ｎ／ｎ＋１，ε￣（ｌｎＲ／ｒ）＾１／ｎ＋１。     

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.     

Supplementary study on anisotropic plastic stress fields at a stationary plane-stress crack-tip

The results in Ref.[1]are not suitable for the cases of a≥2 .For this reason,we use the method in Ref.[1]to derive the general expressions of the anisotropic plastic stress fields at a stationary plane-stress crack-tip for both of the cases of a=2 and a>2 .As an example,we give the analytical expressions of the anisotropic plastic stress fields at the stationary tips of modeⅠand modeⅡplane-stress cracks for the case of a=2.     

A SUPPLEMENTARY STUDY OF ANISOTROPIC PLASTIC FIELDS AT A RAPIDLY PROPAGATING PLANE－STRESS CRACK－TIP（I）

ＡＳＵＰＰＬＥＭＥＮＴＡＲＹＳＴＵＤＹＯＦＡＮＩＳＯＴＲＯＰＩＣＰＬＡＳＴＩＣＦＩＥＬＤＳＡＴＡＲＡＰＩＤＬＹＰＲＯＰＡＧＡＴＩＮＧＰＬＡＮＥ－ＳＴＲＥＳＳＣＲＡＣＫ－ＴＩＰ（Ｉ）ＬｉｎＢａｉｓｏｎｇ（林拜松）（ＲｅｃｅｉｖｅｄＪｕｌｙ１５．１９９４...     

幂软化损伤材料Ⅲ型动态裂纹尖端的渐近场

利用幂软化损伤模型，对Ⅲ型裂纹进行了详细的研究。给出了本构方程及渐近方程。位移、应变和应力用对数级数展开，揭示了场的渐近特性。其结果表明，应力和应变分别具有如下的奇异性：σ－（ｌｎＲ／ｒ）＾１／ｎ＋１，ε－（ＬｎＲ／ｒ）＾ｎ／ｎ＋１。     

应变损伤材料平面应力动态裂纹尖端场的渐近解

采用塑性动力学方程,对应变损伤材料的平面应力动态裂纹尖端场进行了渐近分析。假定损伤规律服从反比例关系,对平面应力问题,导出了本构方程,并给出了动态弹塑性场的渐近解,揭示了场的渐近特性。     

复合材料切口应力奇性指数计算

提出一种计算广义平面应交状态下复合材料切口应力奇性指数的新方法.在切口尖端的位移幂级数渐近展开式被引入正交各向异性材料的物理方程后,将用位移表示的应力分量代入切口端部柱状邻域的线弹性理论控制方程,切口应力奇性指数的计算被转化为常微分方程组特征值的求解.采用插值矩阵法求解该常微分方程组,可一次性地获取切口尖端多阶应力奇性指数.本法适合平面和反平面应力场耦合或解耦的情形,并可退化计算裂纹或各向同性材料切口的应力奇性指数.算例表明,所提方法对分析复合材料切口应力奇性指数是一种准确有效的手段.     

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

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

Singular fields of a mode III interface crack in a power-law hardening bimaterial

A high order of asymptotic solution of the singular fields near the tip of a mode III interface crack for pure power-law hardening bimaterials is obtained by using the hodograph transformation. It is found that the zero order of the asymptotic solution corresponds to the assumption of a rigid substrate at the interface, and the first order of it is deduced in order to satisfy completely two continuity conditions of the stress and displacement across the interface in the asymptotic sense. The singularities of stress and strain of the zeroth order asymptotic solutions are −1/(n ₁+1) and −n/(n ₁+1) respectively. (n=n ₁,n ₂ is the hardening exponent of the bimaterials.) The applicability conditions of the asymptotic solutions are determined for both zeroth and first orders. It is proved that the Guo-Keer solution^[10] is limited in some conditions. The angular functions of the singular fields for this interface crack problem are first expressed by closed form. The project supported by National Natural Science Foundation of China     

Near-tip fields for a crack growing along an elastic perfectly plastic interface

The stress and deformation fields near the tip of an anti-plane crack growing quasi-statically along an interface of elastic perfectly plastic materials are given in this paper. A family of solutions for the growing crack fields is found covering all admissible crack line shear stress ratios. The project supported by the National Natural Science Foundation of China     

The asymptotic solution to the antiplane shear dynamic crack-tip field in an elastic strain-softening viscoplastic material

ProjectsupportedbytheNationalNaturalScienceFoundationofHeilongiianginP.R.ChinaI.Introductionlnthatengineering,thereisakindofmaterials.Somesofteninganddamagephenomenaa1waysappearwhenthedeformationbecomeslargeenough.Forstudyingthisprocess.asofteningmode1oft…