Issue 38

R. Shravan Kumar et alii, Frattura ed Integrità Strutturale, 38 (2016) 19-25; DOI: 10.3221/IGF-ESIS.38.03 20 In the present work, the stress state dependent model along with an irreversible damage parameter is implemented as cohesive element. A cohesive model for a plane strain modified CT specimen analyzed for fatigue failure is presented for an aluminum alloy material. The mechanical properties and the corresponding cohesive properties for the monotonic nature of the traction separation law are taken from monotonic fracture properties of aluminum. The fatigue crack growth predictions of the model for different fatigue parameters are presented. The effect of the cohesive fatigue parameters on crack growth curves is established. S TRESS - STATE DEPENDENT COHESIVE MODEL FOR FATIGUE n the present work, the simulation of fatigue crack initiation in a modified compact test specimen and its continued growth is based on the fatigue cohesive model proposed by Jha and Banerjee [2]. The model assumes that the damage mechanisms that lead to failure are localized in a thin layer (process zone). The constitutive behavior of this thin layer is represented by a triaxiality dependent cohesive law that is updated with an irreversible damage parameter to account for the progressive cyclic damage. The triaxiality dependent relation between the traction, n T , and the normalized separation,  n  , are taken to have three distinct expressions to represent linear, hardening and softening behavior for increasing separation between the bounding surfaces as: n o T , = (1+  eff n E H 2 3  ) 3        0 <  n  ≤  n 1  = (1+ eff H 3  ) y 3   n n y E 2 3            n 1  ≤  n  ≤  n 2  =    n n max n exp 4 2 2 0.01                        n 2  ≤  n  ≤  n 2 10  where  n 1  = y E 3 2  and  n 2  = 3 2 H y eff Ce E 1.5          . Here, eff H is an effective triaxiality parameter defined to incorporate the effects of triaxiality [7], and C and S are model parameters that are used to define upper and lower bounds on the equivalent plastic strain required for failure during monotonic fracture respectively. To incorporate the accumulation of incremental damage due to cyclic loading, a damage evolution law proposed by Roe and Siegmund [1] was used. The accumulation of damage parameter was taken to start once a deformation measure, accumulated separation ( n  ), is greater than a critical magnitude ( o  ), which is implemented through Heaviside function. The accumulated separation is calculated by n n dt ˙     and the critical magnitude ( o  ) is the separation at maximum stress ( max  ). The increment of damage is related to the increment of deformation weighted by the current load level while the incremental deformation is normalized by accumulated cohesive length (   ). Also, the model assumes that there exists an endurance limit, F  , which is a stress level below which cyclic loading can proceed infinitely without failure. The evolution equation for the damage parameter is taken to be: n n n F c max max o o T D H ˙ ˙ , | |  1                          Cohesive endurance limit, F  and accumulated cohesive length,   are two fatigue parameters of this model. max  is the current maximum stress that can be taken by the process zone after the onset of damage accumulation. It is calculated by max  =   max o c D ,  1   . Then the damage is translated as the degradation of the process zone by updating its constitutive I