Higher-Order Analysis of Crack-Tip Fields in Power Law Hardening Materials

In this paper,we present an exact higher-order asymptotic analysis on the near-crack-tip fields in elastic-plastic materials under plane strain,Mode 1.A four- or five-term asymptotic series of the solutions is derived.It is found that when 1.6 < n≤2.8 (here,n is the hardening exponent),the elastic effect enters the third-order stress field; but when 2.8< n≤3.7 this effect turns to enter the fourth-order field,with the fifth-order field independent.Moreover,if n>3.7,the elasticity only affects the fields whose order is higher than 4.In this case,the fourth-order field remains independent.Our investigation also shows that as long as n is larger than 1.6,the third-order field is always not independent,whose amplitude coefficient K3 depends either on K1 or on both K1 and K2 (K1 and K2 arc the amplitude coefficients of the first- and second-order fields,respectively).Finally,good agreement is found between our results and O'Dowd and Shih's numerical ones by comparison.

In this paper,we present an exact higher-order asymptotic analysis on the near-crack-tip fields in elastic-plastic materials under plane strain,Mode 1.A four- or five-term asymptotic series of the solutions is derived.It is found that when 1.6 &lt; n≤2.8 (here,n is the hardening exponent),the elastic effect enters the third-order stress field; but when 2.8&lt; n≤3.7 this effect turns to enter the fourth-order field,with the fifth-order field independent.Moreover,if n&gt;3.7,the elasticity only affects the fields whose order is higher than 4.In this case,the fourth-order field remains independent.Our investigation also shows that as long as n is larger than 1.6,the third-order field is always not independent,whose amplitude coefficient K3 depends either on K1 or on both K1 and K2 (K1 and K2 arc the amplitude coefficients of the first- and second-order fields,respectively).Finally,good agreement is found between our results and O’Dowd and Shih’s numerical ones by comparison.