缓慢扩展裂纹尖端的各向异性塑性应力场
Anisotropic Plastic Stress Fields at a Slowly Propagating Crack Tip
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摘要: 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.Abstract: Under the condition that any perfeetly plastic stress components at a crack tip are nothing but the Junctions of 0 only, making use of equilibriumequations,Hill ani.sutropic yield condition and unloading stress-strain relations, in this paper, we derive the general analytical expressions of anisotropic plastiestress Jields at the slowly steadyhe slowly steady propagatin tips of plane and anti-phane strain,Applying these general analytical expressions to the concrete cracks the attchvtical expressions of anisotropie plastic stress fields at the slowly steady propagating tips of Motle I and Motle III cracks are obtained. For the isolropic plastic material, the anisotropic plastic stress fields at a slowly propagating crack tip become the perfeeby plastic mress fields.
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[1] Chitalcy,A.P.and F.A.McClinlock,Elastic-Plastic mechanics of steady crack growth under anti-plane strain,J.Mech.Phys.Solids.19,3(1971),147-163. [2] Слепян Л.И.,Растущая трещина лри плоской деформации упруго-пластическоготел,Изэ.АН СССР МТТ,9,1(1974)57-67 [3] Rice J.R.,W.T.Drugan and T.L.Sham,Elastic-plastic analysis of growing crack,ASTM STP 700(1980),189-221. [4] 高玉臣,理想塑性介质中裂纹定常扩展的弹塑性场,力学学报,1(1980),18-56 [5] Hill,R..The Mathematical Theory of plasticity,Oxford(1950). -
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