Material deformation and removal due to single particle impacts on ductile materials using smoothed particle hydrodynamics

Abstract

Smoothed particle hydrodynamics (SPH) was used to simulate the impact of single angular particles on Al6061-T6 targets, and the implications for solid particle erosion were discussed. The results of the simulations were verified by comparison to measurements obtained from impact experiments performed using a gas gun which was specifically designed to accelerate angular particles without disturbing their orientation with respect to the target. Both the simulations and the experiments showed that an increase in impact angle and initial orientation of the particle altered the deformation mechanism of the target material, as noted by other investigators. For impact angles close to normal, a significant amount of target material was extruded and piled up at the edge of the impact craters, due to the limited strain hardening of Al6061-T6. However, for certain combinations of incident parameters, the particle machined the surface and a chip was removed. With appropriate constitutive and failure parameters, SPH was demonstrated to be suitable for simulating all of the relevant damage phenomena, including crater formation, material pile-up and chip separation.

Introduction

The study of the impact of small particles at relatively low velocities (<500 m/s) on ductile materials has implications for many industrial processes in which the resulting removal of the material may be viewed as either destructive (e.g. fluidized bed erosion [1]) or constructive (e.g. blast cleaning [2]). Although most solid particle erosion phenomena involve the repeated impacts of a jet of small particles, the study of the impact of a single particle can be useful for understanding the mechanisms of material deformation and removal, e.g. ploughing, cutting, cracking, etc., and their dependency on impact parameters such as impact velocity, impact angle and particle shape [3], [4], [5], [6]. A single particle impact analysis can also provide an initial validation of the applicability, robustness and accuracy of the material models and numerical techniques that can be used [7] to analyse erosion due to jets of particles.

While most practical solid particle erosion processes involve granular particles, experimental, analytical and numerical studies of single particle impact have been mostly limited to spherical particles (e.g. [3], [8], [9], [10], [11]). Bitter [12] argued that if one assumes that small non-spherical particles have rounded edges, it is likely that only the rounded portion penetrates into the surface. However, other investigators [13], [14] have shown that angular particles can perform pure machining in which a chip of material is removed by a single particle. Although evidence exists that in some cases the same deformation pattern exists on impacted surfaces when angular or spherical particles are used [8], [15], it has also been found that the shape of particles can strongly affect the impact angle dependency of erosion [16]. Experiments using a centrifugal accelerator type erosion tester have also revealed a large difference in measured erosion rate between angular and spherical particles, particularly at low impact angles with respect to the target surface [17]. Moreover, it has also been found that the effect of particle size on erosion rate is different for spherical and angular particles [18], and can result in different erosion mechanisms [19].

It is thus clear that the shape and the angularity of particles should be considered for a better understanding of the micro-mechanisms responsible for material removal during solid particle erosion. However, relatively few experimental and analytical studies involving well controlled single angular particle impacts exist. Experiments by Hutchings with square particles on low-carbon steel identified two classes of impacts, resulting from different combinations of the impact angle and initial orientation of the particle with respect to the target [13]. The most probable impact involved forward rotation of the particle during impact, and resulted in target material extruded to the rim of the impact crater but no material removal. A backwards rotation of the particle with a pure machining and removal of a chip of material was also observed, but much less often [13]. These observations were also confirmed by Papini and Dhar [14], who also reported another type of material removal when conducting experiments with much sharper particles. The leading edge of these sharp particles were sometimes found to tunnel below the surface, leading to the prying off a chip of material before completion of the cutting process, forming a crater with a jagged edge.

Rigid-plastic models that predict the trajectory of non-deforming particles as they impact perfectly plastic targets, have been proposed and extended by Hutchings [13], Finnie [20], and Papini and Spelt [21], [22]. Although such models can provide good estimates of the impact crater shapes, they neglect the material-pile up at the edge of the crater. This makes it impossible to determine how the piled-up material is actually removed from the target by subsequent impacts, despite the fact that this may be a primary material removal mechanism for ductile materials [23], [24]. Therefore, these models, developed for single particle impact, cannot be easily extended to the multiple particle impact case.

Lagrangian finite element (FE) methods have been found to be appropriate to model the impact of small spherical particles on relatively hard materials [9], [25], [26]. However, traditional Lagrangian FE methods are not suitable for the modeling of angular particle impacts on ductile materials, due to the distorted and tangled elements that result from the very large plastic deformations induced in the target [7]. Element deletion and adaptive remeshing techniques have been suggested to overcome the element distortion problems encountered during the simulation of angular particle impacts [7]. Although element deletion can be used to ensure elimination of highly distorted elements, it is not a physical procedure since in some cases, e.g. the simulation of ploughing, target material is removed from the model which physically would not be removed [27]. The adaptive remeshing technique, on the other hand is computationally expensive, and can lead to numerical instabilities and unexpected termination of the simulation [7], [28] when attempting to model machined target chip separation.

Smoothed particle hydrodynamics (SPH) which is a meshless method may have significant advantages over FE methods for the simulation of angular particle impacts because it does not involve the use of elements which can deform, tangle, and distort. Wang and Yang [29] investigated the use of SPH for the simulation of multiple impacts of spherical particles on Ti–6Al–4V, a relatively hard material, and found that predictions of the effect of impact angle and impact velocity on the resulting impact crater depth agreed well with experiments.

In summary, it appears that no analytical or numerical studies of single angular particle impacts on ductile targets exist that can account for both chip separation and pile-up formation at the crater edge. The present work investigates the applicability of SPH to address these problems, thus providing a basis for future multi-particle simulations of solid particle erosion phenomena involving angular particles.