ANISOTROPIC PLASTIC STRESS FIELDS AT A SLOWLY PROPAGATING CRACK TIP

Under the condition that any perfectly plastic stress components at a crack tip are nothing but the functions ofθonly,making use of equilibrium equations,Hill anisotropic yield condition and unloading stress-strain relations,in this paper,we derive the general analytical expressions of anisotropie plastic stress fields at the slowly steady propagating tips of plane and anti-plane strain.Applying these general analytical expressions to the concrete cracks,the analytical expressions of anisotropic plastic stress fields at the slowly steady propagating tips of ModeⅠand Mode Ⅲ cracks are obtained.For the isotropic plastic material,the anisotropic plastie stress fields at a slowly propagating crack tip become the perfectly plastic stress fields.     

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.     

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.     

缓慢扩展裂纹尖端的各向异性塑性应力场

在裂纹尖端的理想塑性应力分量都只是θ的函数的条件下,利用平衡方程、Hill各向异性屈服条件及卸载应力应变关系,我们导出了缓慢定常扩展平面应变裂纹和反平面应变裂纹的尖端的各向异性塑性应力场的一般解析表达式.将这些一般解析表达式用于具体裂纹,我们就得到缓慢定常扩展Ⅰ型和Ⅲ型裂纹尖端的各向异性塑性应力场的解析表达式.对于各向同性塑性材料,缓慢扩展裂纹尖端的各向异性塑性应力场就变成理想塑性应力场.     

静止裂纹尖端的理想塑性应力场

在裂纹尖端的理想塑性应力分量都只是θ的函数的假设下,利用平衡方程和屈服条件,本文导出了裂纹尖端的理想塑性应力场的一般解析表达式.将这些一般解析表达式用于具体裂纹,我们就得到Ⅰ型,Ⅱ型,Ⅲ型及Ⅰ-Ⅱ复合型裂纹尖端的理想塑性应力场.     

The mixed mode brittle fracture criteria in siliding mode fracture

It is well-known that the present mixed mode brittle fracture criteria are all theopening mode fracture criterion.We consider that mixed mode brittle fracture of slidingmode fracture exists too.Hence we propose three criteria of mixed mode brittle fracture ofsliding mode fracture;:the radial shearing stress criterion,the maximum shearing stresscriterion and the distortional strain-energy-density criterion.Thus,we can overall explainthe phenomena of brittle fracture in the structural elements with cracks.     

平面应变和反平面应变复合型裂纹尖端的理想塑性应力场

在裂纹尖端的理想塑性应力分量都只是θ的函数的条件下.利用平衡方程.应力应变率关系、相容方程和屈服条件,本文导出了平面应变和反平面应变复合型裂纹尖端的理想塑性应力场的一般解析表达式.将这些一般解析表达式用于复合型裂纹.我们就可以得到Ⅰ-Ⅲ、Ⅱ-Ⅲ及Ⅰ-Ⅱ-Ⅲ复合型裂纹尖端的理想塑性应力场的解析表达式.     

The strain energy criterion of mixed-mode brittle fracture

In this paper, we proposed a new cr tenon or mixea-moae brittle fracture, i.e., the strain energy criterion, which can be stated as (K_Ⅰ/K_Ⅰc)² +(K_Ⅰ/K_Ⅰc)²+(K_Ⅱ/K_Ⅱc)²=1. This criterion is shown to be in good agreement with known experimental data.In this paper, an experimental criterion:(K_Ⅰ/K_Ⅰc)^m+(K_Ⅱ/K_Ⅱc)ⁿ=1, 1≤_n^m≤2.is also proposed.     

高速扩展平面应力裂纹尖端的各向异性塑性场的补充研究（I）

献〔１〕的结果对于β≥２的情形不适用。为此，我们用献〔１〕和〔２〕的方法导出了β＝２和β〉２两的高速扩展平面应力裂纹尖端的各向异性塑性场的一般表达式。     

THE STRAIN ENERGY CRITERION OF MIXED-MODE BRITTLE FRACTURE

In this paper, we proposed a new criterion of mixed-mode brittle fracture, i.e., the strain energy criterion, which can be stated as This criterion is shown to be in good agreement with known experimental data. In this paper, an experimental criterion: is also proposed.