PSI - Issue 13

Danilo D’ Angela et al. / Procedia Structural Integrity 13 (2018) 939–946 Danilo D’Angela and Marianna Ercolino / Structural Integrity Procedia 00 ( 2018) 000 – 000

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Low-Cycle Fatigue (LCF) involves early achievement of plastic strain due to high amplitude or lower frequency cycles and failure occurs at a relatively reduced number of cycles (Stephens and Fuchs, 2001). In ABAQUS, LCF analysis is a tool (London et al., 2015) finalised to simulate stabilized cyclic response of the structure (Simulia, 2016). The behavior of the structure is evaluated at discrete points of the loading history and the damage at the next cycles interval is predicted (Simulia, 2016) by using such degraded response. Such prediction method significantly reduces the computational time of the analysis without losing accuracy of the outcomes (Simulia, 2016). A two dimensional FE model is implemented in ABAQUS in order to simulate a fatigue test on metal CT specimens made of 7% Nickel steel (Kim et al., 2015). The model is developed according to the linear elastic fracture mechanics using XFEM technology. Direct cyclic analysis step is performed with the LCF approach. Room and cryogenic temperature tests are simulated and both plane stress and plane strain conditions are considered. The cyclic load frequency is 10 Hz, the peak load P is equal to 18 kN and the R ratio is equal to 0 (i.e., minimum-to-maximum load/stress ratio). The geometry of the model is shown in Fig. 3. Node A (B) is coupled to the upper (lower) half surface of the plate by a continuum distributing coupling. Node B is pinned, whereas a vertical roller restraint is assumed for the node A. The vertical load (i.e., P ) is applied at the node A. A linear elastic response is assigned to the material (London et al., 2015). The fracture propagation process is modelled by using the Paris law (Eq. 5); this latter is implemented in ABAQUS considering ΔG instead of ΔK , and ( c 3 , c 4 ) instead of ( c, m ). Mixed-mode power law (Eq. 5) models the occurring of the critical condition (Simulia, 2016; Wu and Reuter, 1965). = ( ) + ( ) + ( ) (5) G IC , G IIC and G IIIC are critical G for the three modes; a m , a n and a o are the related exponents. The G equiv -to-G equivC ratio controls the fracture process. The fatigue response evolves on the Paris law path until G equiv is contained in the range defined by G thresh and G pl . When G equiv reaches G pl the fracture proceeds at an accelerated rate, leading to the failure. The main parameters assigned to the model are reported in Table 1. A partitioned quadrilateral free mesh was assigned using CPS4R and CPE4R elements (Simulia, 2016) for plane stress and plane strain conditions, respectively. The size of the mesh in the vicinity of the crack length is equal to 0.15 mm, according to the results of a convergence analysis. 2. Finite Element model

Fig. 3. Sample features (dimensions in mm) and boundary conditions.