Comparative analysis of stress state in the vicinity of the crack-tips and notches using truncated Williams series expansion

In the present study the asymptotic analysis of the multi-parameter Williams series expansion of the stress-strain state in the vicinity of seven different configurations is performed. The aim of the asymptotic analysis is to educate the sensitivity of different cracked and notched configurations to the number of kept terms in Williams series expansion. It is shown that all configurations with the concentrated forces possess the more sensitivity to the number of terms in the truncated Williams series expansions and, therefore, require the more terms in the series expansion. The cracked configurations with distributed loadings are less sensitive to the number of terms in Williams series expansion. As a whole, it is demonstrated that high order terms have principal role in the description of the stress-strain in the vicinity of the crack tip.