PSI - Issue 28

Ping Zhang et al. / Procedia Structural Integrity 28 (2020) 1176–1183 P. Zhang et al. / Structural Integrity Procedia 00 (2019) 000–000

1179

4

0 t    

dt 

(7)

ICSS

.



The slip system with the highest ICSS value is chosen to be the representative one of an element and its associated normal direction vector is considered as the normal of the corresponding slip plane. When its ICSS exceeds a critical value, fracture occurs and the crack will propagate along the relevant crystallographic direction. 3. Computational approach Fatigue tests on crack propagation were performed by Zhang et al. (2019) using an in-situ SEM approach. Shown in Fig. 1a, specimens machined from [111] or [001] orientated single-crystal rod have a gauge length of 5 mm and a cross section of 2×1 mm 2 , containing a U-shape notch with a depth of 0.4 mm and a radius of 0.16 mm in the middle section. At both 24 °C and 650 °C, the applied cyclic load was of a sinusoidal waveform of 10 Hz frequency, with peak stress of 560 MPa ([001]) or 680 MPa ([111]) and a loading ratio of 0.1. Conducted in vacuum conditions, tests were paused at various intervals for SEM imaging to measure the crack length.

Fig. 1. (a) The geometry of specimens (Zhang et al., 2019); (b) boundary conditions description along with geometrical details of crack propagation model.

To simulate the crack propagation, a 2D plane strain model was developed for the notched region of the specimen in ABAQUS (Fig. 1b) with a size of 2000×5000 μm 2 . Since the focus is on the early stage of crack propagation, a dense mesh was created for a specified XFEM domain near the notch root, in which the crack can grow to a horizontal length of 110 μm. Inside the XFEM domain there are 3850 quadrilateral linear plane strain (CPE4) XFEM elements with an average size of ~2.5 μm while 360 CPE4 elements as well as 1713 triangular linear plane strain elements (CPE3) are used in the rest of the model. Besides, a predefined crack was introduced to the centre of the notch matching the initial crack observed experimentally (see the magnified section in Fig. 1b). The bottom and left sides of the model were constrained in their respective normal directions to prevent rigid body movement. Moreover, the critical value of ICSS was chosen as 0.026 for 24 °C and 0.020 for 650 °C according to our observations in the simulations. Considering that the activity of different slip systems was relatively stable at the crack tip after the first or second loading cycle, 0.026 was chosen for 24 °C to allow us to obtain the crack growth rate with