Numerical Simulation of Solid Particle Erosion of Alumina by Overlapping Irregular-Shaped Particle Impacts

Abstract

Strength degradation of aluminum oxide under successive impingements of small particles is a destructive process occurring in many applications, especially when using alumina coatings to improve the solid particle erosion resistance of metals. Solid particle erosion of alumina has been mostly studied either experimentally or analytically, and the existing numerical studies generally consider a low number of modeled impacts of over-simplified abrasive geometries. In this work, the erosion of an alumina target after the impact of 160 irregular-shaped silicon carbide (SiC) abrasive particles at perpendicular and oblique incidence was modeled. A Johnson–Holmquist material model (JH-2) with a finite element (FE) decomposition method was used, and it was found to be more suitable than a smoothed particle hydrodynamics (SPH) method. A dynamic tensile strength was implemented and simply related to the Hugoniot elastic limit (HEL) of the material. Once the failure strain was tuned using experimental data obtained at perpendicular incidence, the model was able to accurately predict the measured erosion at all the tested oblique incidences (predicted values within ~ 4% of measured). The effect of particle velocity on the erosion rate was predicted to be a well-known power law with a velocity exponent of 1.8, which agreed reasonably well with the measured value of 2.01. The angle dependency of the alumina erosion rate was predicted as a typically brittle response with a maximum at perpendicular incidence. Finally, the simulated erosion mechanisms were compared with those observed from the experiments. No ploughing was observed or predicted, and the alumina was mainly removed by chip removal. The depths of the craters created by individual non-overlapping impacts were predicted to within 10% of those seen experimentally.

Appendices

Appendix A: Decomposition Method and Computational Cost

In preliminary modeling, the use of the FE method to represent the alumina plate was compared to the use of SPH. The SPH target formulation was used with the same impacting particles, number of impacts, target dimensions, target material, and damage model as was used in the FE model described in Sect. 3. To be consistent with the element size used in the FE model (Appendix B), the SPH particles on the alumina target were spaced 5.55 µm apart. For the target modeled using SPH, Fig. 16a shows that the sharp SiC abrasive particles penetrated unrealistically into the SPH nodes representing the alumina plate, resulting in cutting and ploughing behaviors (Fig. 16b) which were more consistent with the ductile erosion mechanisms seen in, e.g., an epoxy polymer model [81]. This is also consistent with the work of Lv et al. [38] who reported that, at best, the SPH modeling overestimated the penetration of even a spherical projectile into a brittle target by approximately 20%. In the solid particle erosion of brittle materials like alumina, cutting and ploughing actions have little effect on the resulting erosion rate, while propagation of lateral cracks (microcracking and microchipping) is the main removal mechanism [22,23,24].

Fig. 16

a The contact behavior of the alumina SPH nodes with the sharp irregular-shaped SiC abrasives in preliminary modeling, and b the resulting plowed surface after 160 particle impacts

For several reasons, the runtime of the otherwise identical single particle impact simulations using the JH-2/SPH method was approximately twice that when using the JH-2/FEM method. Firstly, the SPH particles representing a target chip that is removed by an impact are only deactivated when the erosion criteria are satisfied. Therefore, it is possible for SPH particles to separate from the target material while still remaining active. In the FE method, on the other hand, execution time is saved because the target elements can be immediately deleted by means of a failure strain or other failure criterion. Such an option does not exist with the SPH method. Secondly, in LS-DYNA, one can define either a contact or a deletion box around the target such that whenever the separated parts of the target material exit the box, the contact with the abrasive particles will no longer be active. This can be implemented successfully using the FE method, but in the case of SPH, it caused all the SPH particles to be deactivated after only one particle exited out of the box. Thirdly, although implementation of the non-reflecting boundary condition (Sect. 3.1.3) was available for both SPH and FE, definition of non-reflecting boundary surfaces was much more easily implemented in the latter than the former. Finally, a Full Restart option for SPH particles could only be used when implementing the double-precision Dyna solver which increased the runtime by ~ 30–60%. Taking all these issues into account, FEM was preferred to SPH in the present work.

Appendix B: Sensitivity Tests

Before tuning the material model representing the alumina target, the sensitivity of the predicted erosion rate to target thickness and area, as well as the FE mesh size was assessed using the same number of impacts and conditions described at the beginning of Sect. 3. Since this step was before the tuning process, two arbitrary values of 0.01 and 7.5 GPa were used for failure strain, ${FS}$, and Hugoniot Elastic Limit, ${HEL}$, respectively. All other material and damage properties were taken from the literature as provided in Sect. 3.1.2. As Figs. 17 and 18 indicate, both the target thickness and the area did not significantly affect the erosion rate. The predicted erosion rate at a thickness of 100 µm was similar to that for the much thicker substrates. The $350\times 350$ µm² target area also yielded the same erosion rate as with much larger areas. Therefore, a $350\times 350\times 100$ µm³ target dimension was used in the models to predict the erosion rate. The relative insensitivity of the erosion rate to the target dimensions may be due to the use of non-reflecting boundary conditions on the side and bottom nodes. Figure 19 illustrates that at mesh size lower than 5.55 µm, the erosion rate tended to level out. Therefore, the element size was selected as 5.55 µm.

Fig. 17

Effect of target thickness on predicted erosion rate for an abrasive size and impact angle of 152 µm and 90°, respectively. The target area and the element size were $350\times 350$ µm² and 5.55 µm, respectively

Fig. 18

Effect of target area on predicted erosion rate for an abrasive size and impact angle of 152 µm and 90°, respectively. The thickness and the element size were 100 µm and 5.55 µm, respectively

Fig. 19

Effect of element size on predicted erosion rate for an abrasive size and impact angle of 152 µm and 90°, respectively. The target size was $350\times 350\times 100$ µm³