Elastic plastic analysis of growing cracks
Elastic plastic analysis of growing cracks
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DOI：
10.1520/stp36972s
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发表时间：
1980
期刊：
影响因子：
--
通讯作者：
J. Rice;WJ Drugan;T. Sham
中科院分区：
文献类型：
--
作者：
J. Rice;WJ Drugan;T. Sham
在理想塑性固体中，裂纹尖端的弹塑性应力场和变形场在平面应变作用下表现为小尺度屈服条件。渐近分析结果表明，裂纹尖端存在与经典普朗特场相似的应力状态，但在中心扇区和尾部恒应力塑性区之间存在弹性卸载区。在离生长尖端距离r处，张开位移δ速率的近尖端表达式为delta-。=…cap alpha…J -。/sigma/下标0 / +…（∑/下标0 //E） a-。ln（R/ R）但是弹性楔的存在导致。。修正后的值为5.08(泊松比…= 0.3);（a =裂纹长度，sigma/sub o/ =屈服强度，E =弹性模量，J为远场值），(1-…/sup 2/)K/sup 2//E为考虑的小规模屈服条件。参数…cap alpha…和R不能从渐近分析中确定，但与有限元解的比较表明，对于少量的增长，…R随塑性区尺寸增大而增大，约增大15% ~ 30%。对于大规模产量，类似的形式适用于…和. .β. .，在裂纹尖端保持三轴约束的情况下。在完全屈服的情况下，R预计与未裂韧带的尺寸成正比。模型裂纹扩展准则要求在尖端的某个固定r处有一个临界增量，根据更精确的解重新检查。结果表明，描述生长的J与δ的关系取决于产量的程度。有人建议，如果在所有情况下都保持类似的三轴约束，这种依赖性可能对高延展性材料较小。«少
The elastic--plastic stress and deformation fields at the tip of a crack which grows in an ideally plastic solid under plane strain, shows small scale yielding conditions. Results of an asymptotic analysis suggests the existence of a crack tip stress state similar to that of the classical Prandtl field, but containing a zone of elastic unloading between the centered fan region and the trailing constant stress plastic region. The near tip expression for the rate of opening displacement delta at distance r from the growing tip is found to have the form delta-. = ..cap alpha.. J-./sigma/sub o/ + ..beta..(sigma/sub o//E) a-. ln(R/r) but the presence of the elastic wedge causes ..beta.. to have the revised value of 5.08 (for Poisson ratio ..nu.. = 0.3); also, (a = crack length, sigma/sub o/ = yield strength, E = elastic modulus, and J denotes the far-field value), and (1-..nu../sup 2/)K/sup 2//E for the small scale yielding conditions considered. The parameters ..cap alpha.. and R cannot be determined from the asymptotic analysis, but comparisons with finite element solutions suggest that, for small amounts of growth, ..cap alpha.. is approximately the same for stationary and growing cracks, and R scales approximately with the sizemore » of the plastic zone, being about 15% to 30% larger. For large scale yielding, a similar form applies with possible variations in ..cap alpha.. and ..beta.., in cases which maintain triaxial constraint at the crack tip. In the fully yielded case R is expected to be proportional to the dimension of the uncracked ligament. Model crack growth criterion requiring a critical delta at some fixed r from the tip, is re-examined in light of the more accurate solution. Results suggest that the J versus ..delta..a relation describing growth is dependent on the extent of yielding. It is suggested that this dependency might be small for highly ductile materials, provided that a similar triaxial constraint is maintained in all cases.« less