PSI - Issue 23

Tomáš Oplt et al. / Procedia Structural Integrity 23 (2019) 101–106 Tomáš Oplt / Structural Integrity Procedia 00 ( 2019) 000 – 000 3 modelled. Central crack was advanced from initial length a 0 to final length a f = 15 mm. Initial crack length was prescribed as a 0 = a f - N c ⋅ L e , where N c stands for number of cycles and L e for element size. Since the element size L e varies with different load ratios R , a 0 could not be prescribed as a fixed parameter. Numerical model was loaded by force inducing constant stress intensity factor range ΔK = 20 MPa√m , load ratio varied from R = -1 to R = 0.1. Material model simulated behaviour of railway axle steel EA4T (see details (Pokorný et al. 2017) ], therefore it was assumed homogenous, isotropic, linear elastic-perfectly plastic with yield stress equal to cyclic yield stress σ y,c = 470 MPa , Young’s modulus E = 208 000 MPa and Poisson’s ratio ν = 0.3. Most of the input parameters were adopted from extensive 2D numerical study of Pokorny’s experiments published by (Oplt et al. 2019). 103

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Fig. 1 M(T) specimen (a) and FE model with detail

of mapped mesh in the crack advancing area (b)

Element type and its size is widely discussed topic among researchers since the beginning of PICC numerical modelling. Most of the researchers employed in 2D modelling linear four-noded elements with reduced integration, which assures that plane strain locking is avoided (Dougherty et al. 1997; Solanki et al. 2004b). Similarly, eight-noded hexahedral elements SOLID185 were employed with prescribed reduced integration. Fig. 1b presents meshed model with highly refined crack propagation area and its vicinity. Size of the element is the crucial parameter necessary for reliable description of the plastic zone development. Researchers often agree on the element size, which ensures 10 elements within forward plastic zone according to Irwin’s estimation (eq. 1) and assuming plane strain conditions (Dougherty et al. 1997; McClung and Sehitoglu 1989; Oplt et al. 2019; Solanki et al. 2004a). Although real shape of the plastic zone is different than Irwin’s suggestion (Fig. 2a), it is a convenient controlling parameter for sufficient mesh refinement. = 3 1 ( , , ) 2 (1) Element height H e (size in the direction normal to the crack face) was twice bigger H e = 2L e . In thickness direction, 30 elements were employed with the size decreasing towards the free surface by the bias factor 2 in order to capture free surface effects more accurately.

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Fig. 2 Irwin’s plastic zone size estimation compared to the real plastic zone shape under plane strain (a) and illustration of determination method monitoring the displacement of the 1 st node behind the crack tip (b)