Issue 50

A. Sarkar et alii, Frattura ed Integrità Strutturale, 50 (2019) 86-97; DOI: 10.3221/IGF-ESIS.50.09 91 Figure 4 : Crack growth behavior at  t /2 LCF : ±0.6% and  t /2 HCF : ±0.1% , T: 573 K. Predicted value of a cr is marked in the figure. The arrow indicates possible LCF-HCF interaction through a sequence of LCF followed by HCF. As indicated earlier, the crack propagation behavior under a given strain amplitude can be expressed through the following mathematical relation: da/dN = A (Δ Ɛ in ) n a (2) where da/dN = crack propagation rate, Δ Ɛ in = inelastic strain range, a = instantaneous crack length and n & A=material constant. Under loading conditions involving extensive creep and ratcheting deformation, the foregoing treatment can be modified by making a minor revision to Eqn. (2) as detailed below. Significant plastic deformation occurs at higher temperatures like 823 and 923 K leading to accumulation of permanent strain through plastic ratcheting through the mean strain acting on the specimen. This imparts a loss of residual ductility in the material. Thus, Eqn. (2) can be revised as follows, incorporating the damage contributions from plastic ratcheting (induced through presence of mean strain) by introducing a parameter δ c which is the ratcheting strain accumulated per cycle: ( ) n in c da A a dN D    + = (3a) where δ c = strain accumulated per cycle through ratcheting, D = material ductility. By integrating Eqn. (3a), a ‘ductility normalized equation’ can be naturally derived when δ c is zero, as follows: 1 ln( ) ( ) f n in f i a N A a D   = (3b) where a f = final crack length and a i = initial crack length. However, for a loading condition where δ c >0, the life prediction equation can be derived from Eqn. (3a) as: , 1 1 ( ) ( ) ln( ) ln( ) f f n n in inc f in c i i eqi a a N D A a A a       =   + (3c)