Stress-based Insertion in Angled Interface Specimen

As yet another test of the stress based insertion method, we attempt to simulate the effect of crack propagation and deflection at interfaces in homogeneous materials. This analysis is a numerical example of recent work performed by Xu, Huang and Rosakis (2001). Their research has shown that an initial crack, under mode I loading, propagates at various speeds towards inclined interfaces of various strengths. Depending on the interface strength as well as the interfacial angle, the crack may become trapped along the interface or simply pass right through it.

For our comparison, we use an interfacial angle of degrees and apply a shear velocity loading of $1.6$ $m/s$ along the left sides of the specimen, as presented in Figure 4.31. The bulk material is Homalite-100 with Young's modulus $E = 3.45$ $GPa$, density $\rho = 1230$ $kg/m^3$, and Poisson's ratio of $\nu = 0.35$. The cohesive elements used in the bulk material are given the properties of Homalite-100 presented in Table 4.6.

Figure 4.31: Schematic representation of interface test specimen with boundary conditions.

The simulation is run for $70000$ time steps ( $\Delta t = 7.0 \times 10^{-9}$ $s$), for both a weak interface of Loctite-384 and a strong interface of Weldon-10. The constitutive properties of these materials are also presented in Table 4.6. and a strong interface.

Table 4.6: Constitutive cohesive element properties of the bulk material and the weak and strong interfaces.

	Homalite-100	Loctite-384 (weak)	Weldon-10 (strong)
	Kobayashi and Mall (1978)	Xu et al., (2001)	Xu et al., (2001)
$\sigma_{max} (MPa)$	11.0	7.74	6.75
$\tau_{max} (MPa)$	25.0	22.0	7.47
$G_{Ic} (J/m^2)$	250.0	199.7	41.9
$G_{IIc} (J/m^2)$	568.0	568.0	46.4

The experimental results for both the weak and strong interfaces, described above, have shown that the crack becomes trapped along the interface for a short duration before turning back into the bulk material. The weak interface traps the crack for a longer distance as we have verified in Figure 4.34, while the stronger interface almost immediately turns the crack back in to the system (see Figure 4.35). Close-ups of these cracks are presented in Figures 4.36 and 4.37 for the weak and strong interfaces, respectively.

Figures 4.32 and 4.33 present the crack length and crack speed for the weak interface problem. From these figures, we can see that the initial mode I crack travels at near constant speed until it reaches the interface. At this time, it becomes a mixed-mode interfacial crack whose crack speed is increased while traveling along the interface. Comparison of these results, with those presented in Figure 13 by Xu et al. (2001), shows good agreement to the general profiles of the crack lengths and speed curves. Since we were unable to match all the necessary parameters of the experimental setup, we used our best judgment to duplicate the problem. The actual crack speeds found in our results are nearly twice as great as those presented in the experimental results. This is most likely due to the application of the boundary conditions used to mimic the effect of the impact on the wedge.

Figure 4.32: Crack length history for a weak 60 degree interface.
Figure 4.33: Crack speed history for a weak 60 degree interface.

Figure 4.34: Mode I crack trapped along the weak Loctite-384 interface for a 45% stress-based insertion (no exaggeration) (edge key: thin = normal edge, dark = cohesive element, dashed = failing cohesive element, bold = failed cohesive element).

Figure 4.35: Mode I crack trapped along the strong Weldon-100 interface for a 45% stress based insertion (no exaggeration) (edge key: thin = normal edge, dark = cohesive element, dashed = failing cohesive element, bold = failed cohesive element).

Figure 4.36: Close-up of crack region along a weak interface (no exaggeration).
Figure 4.37: Close-up of crack region along a strong interface (no exaggeration).