Fg. Yuan et S. Yang, CRACK-TIP FIELDS IN ELASTIC-PLASTIC MATERIAL UNDER PLANE-STRESS MODE-I LOADING, International journal of fracture, 85(2), 1997, pp. 131-155
Results on the crack-tip fields in an elastic power-law hardening mate
rial under plane stress mode I loading are presented. Using a generali
zed asymptotic expansion of the stress function, higher-order terms ar
e found which have newly-discovered characteristics. A series solution
is obtained for the elastic-plastic crack-tip fields. The expansion o
f stress fields contains both the r(ti)sigma(pq)((i))(theta; t(i)) and
Re[r(tk)sigma(rs)((k))(theta; t(k))] terms where t(i) is real and t(k
) is complex; the terms sigma(pq)((i))(theta; t(k)) and sigma(rs)((k))
(theta; t(k)) are real and complex functions of theta respectively. Co
mparing the results with that for the plane strain mode I loading show
s that: (I) the effect of higher-order solutions on the crack-tip fiel
ds is much smaller; and (2) the path independent integral J also contr
ols the second-order or third-order term in the asymptotic solutions o
f the crack-tip fields for most of the engineering materials (1 < n <
11) in plane stress, while the J-integral does not control the second
and the third-order terms for the plane strain mode I case for n > 3.
These theoretical results imply that the crack-tip fields can be well
characterized by the J-integral, and can be used as a criterion for fr
acture initiation under plane stress mode I loading. This is in agreem
ent with existing full field solutions and experimental data that J at
crack growth initiation is essentially independent of in-plane specim
en geometry. The comparison confirms the theoretical asymptotic soluti
ons developed in this study.