Opening and closure of short cracks has been examined experimentally using small strain gauges fixed to unnotched specimens very close to short fatigue cracks. The results of completely reversed tension+ompression constant amplitude tests are that crack opening stresses decrease with increasing stress amplitude and that crack closure occurs at nearly the same strain as crack opening. In variable amplitude loading the crack is subjected to a low crack opening level resulting from larger cycles. Based on the results of this experimental investigation some simple approximation formulas are proposed with which decrease as well as increase of crack opening levels can be described. Using these formulas it is possible to compute crack opening strains for any load sequence. The findings of the investigations have been merged to build an algorithm for the prediction of fatigue lives to initiation of cracks of technical sizes in case of variable amplitude loading. The improvement in accuracy of life predictions compared to results of an existing damage accumulation concept is demonstrated for two materials and two load sequences. NOMENCLATURE a = crack length b = fatigue strength exponent c = fatigue ductility exponent C = constant in crack growth law I) =contribution to the damage sum E = Young's modulus FA = fade away constant G = shear modulus h = frequency of occurrence of cycles within a load sequence J = J-integral K = stress intensity factor K' = cyclic hardening coefficient K, = stress concentration factor m = exponent in crack growth law n = number of cycles n' = cyclic hardening exponent N = number of cycles to initiation of cracks of technical size P = damage parameter Q = constant in the damage parameter life curve R = stress ratio in constant amplitude tests K = stress ratio of the largest cycle in a variable amplitude load sequence S = nominal stress S = crack tip opening displacement L = strain E ; = fatigue ductility coefficient v = Poisson's ratio u = stress u,, = average yield stress u ; = fatigue strength coefficient uu = ultimate tensile strength uys = yield strength, 0.2% offset 205 206 M. VORMWALD and T. SEEGER NOMENCLA TURE-continued Indices 0 = initial value a = amplitude cl = closure eff = effective el = elastic op = opening pl = plastic th = threshold f = final value upper = value at the upper reversal point lower = value at the lower reversal point
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.