Fig.1 Line plot of I-shaped specimen and demonstration of the effect of \(\mathbf{q}\)parameter in the completeness of failure. (blue dashes), crack propagation direction (black dashes)
From Fig.1, it can be seen that the variation of \(q\) parameter affects the stage of fracture process in terms of the crack path. In addition, the \(q\) parameter controls the stability of the crack propagation. For I-shaped specimens in plane-strain conditions, experimental data indicates that the crack forms in the middle of the specimen with an inclination of about \(\pm 45\ \) in relation to the main stress direction.47
Miehe et al 8 suggested using the viscosity parameter to overcome the instability of crack growth. In the proposed model in this study, this is done by reducing the computational complexity by introducing the q parameter. The results of investigations on the q parameter have shown that the use of high values for this parameter leads to divergence of analysis. As such for q=1, the crack grows to the middle of the sample and then diverges. While for q=0.2, the crack growth is complete and the results agree very well with other similar works. The corresponding load-displacement curve is shown in Fig.2. The sudden drop in the curve is due to the onset of crack phase-field localization.