Development of a constitutive model for erosion based on dissipated particle energy to predict the wear rate of ductile metals
Introduction
There are many erosion models available that can calculate and predict the erosion rate [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13]. Most of the models considered the impact parameters such as impact velocity and angles [1], [3], [4], [6], [7]. However, some models considered impacting particle and impacted surface material properties [1], [2], [8], [9], [10], [11], [12], [14], [15]. It is clear from the previous studies that a single mechanism of material removal cannot be applied to all the different wear situations.
In early erosion research, Finnie [8] proposed the expressions for the volume loss of surface material, V due to the moving action of a single particle that has a mass m, velocity v, impact angle , and depth of cut ψ, as is presented below.
Eq. (1) applies to lower impact angles, and Eq. (2) relates to the higher impact angles below and above a threshold angle based on the parameter k (the ratio of vertical to horizontal force components on the particle). In another paper, Finnie [7] also explained that the surface area in which the particle contacts is approximately twice the depth of the associated erosive cut, and described another wear model as:Where I is the moment of inertia of the particle, r is average particle radius, p is the parallel component of flow pressure, c is the fraction of particles, and xt is the parallel velocity of a particle when cutting occurs.
Following the analysis of Finnie's model [8], Bitter [9] reported that the wear mainly occurs by two distinct mechanisms: deformation wear and cutting wear. Bitter [9] first expressed the unit volume loss due to deformation wear, WD, is:Where WD is the unit volume loss of surface material, K is maximum impact velocity in which the impact is purely elastic, and ε is the deformation energy factor (energy needed to remove a unit volume of material from the surface due to deformation process).
Subsequently, Bitter [10] said that the cutting wear occurs if a particle impacts on a surface at an oblique angle, and he introduced a cutting energy factor, ϕ (energy needed to remove a unit volume of material from the surface through cutting action).Where WC is the volume loss of material by cutting mechanism.
Subsequently, Neilson and Gilchrist [12] simplified Bitter's wear model and proposed that the cutting wear mechanism and the deformation wear mechanism are both involved in the erosion process simultaneously where one mechanism is more dominant than another. They proposed a relationship for erosive wear loss, W below:
Tilly [16] described a two-step mechanism for erosion of ductile materials. In the first step, the impacting particle strikes the surface to produce an indentation and eliminate a metal chip. The second step is the fracture of particle and the fragments are radially projected from the main site. By the combination of both steps, the total erosion is expressed as:Where W1 is primary erosion and W2 is secondary erosion. Both are measured at reference velocity vr, velocity v, particle size d, Fd,v is the degree of fragmentation, K is the threshold velocity below which the impact is purely elastic, and d0 is the minimum particle size below which no erosion occurs.
Hutchings et al. [1] proposed a model of crater formation that accurately predicts the volume of material displaced and the energy lost by the sphere of impact. They found that at a 30° impact angle, the mass of material removed varies under the following relationship:Where W is the mass loss of target material per mass of impacting particles, and v is the impact velocity (ms−1). Hutchings [17] also demonstrated another equation by equating the initial kinetic energy of the impacting particle with the work done in creating the indentation:Where W is erosion, α is the impact angle, ρt is the density of the surface material, σ is the plastic flow stress, εc is the erosion ductility, and Ht is the hardness of the impacted surface material. B. F. Levin et al. [15] presented another energy based erosion model for normal impact that incorporates the surface material properties as below:Where W is erosion rate, T is the tensile toughness, L is plastic-zone size, Vi is initial particle velocity, H is the material hardness.
Subsequently, many researchers [18], [19], [20], [21] have attempted to develop the parametric model for predicting erosion rate. But they did not consider the energy factor which is very important for predicting erosion. In recent years, using modern numerical analysis, new research investigating the erosion phenomena has occurred [22], [23], [24], [25], [26], [27], [28], [29]. Most of these research papers have used the Johnson-Cook visco-plastic failure model [30] for the analysis. All these studies could help to understand the behaviour of target material during impact and distinguish the erosion mechanisms instead of determining erosion rate at a specific condition that was the purpose of this study.
Upon consideration of all mechanisms and models for erosion described above, it is clear that erosion is a very complex phenomenon that simultaneously involves many factors during the wear cycle. To date, some satisfactory predictive energy based erosion models have been developed; however, the influence of many factors and methods in the erosion process remains undefined. Indeed, in many cases, even the removal mechanisms of the materials are not clear; for example, there is no adequate description in the literature of how energy factors are related to the wear process. Besides, the influence of kinetic energy dissipation on the surface (based on the varying of impact angles) has not been described explicitly by any of the models [8], [9], [10], [12], [15]. The models consider that the total wear is solely deformation wear at 90° impact angles; however, it is known from the literature that both deformation and cutting wear are simultaneously involved in wear processes.
Therefore, there is a gap in the literature concerning the dissipation of kinetic energy in the surface material during erosion at different impact angles and the relevant surface material parameters such as elastic-plastic properties, coefficient of restitution, surface heating and microstructure that require more thorough investigation. Research is also required to correlate deformation and cutting mechanisms with various impact angles and velocities.
In this study, an energy-based erosion model has developed with respect to impact parameters, surface material properties and energy factors. The challenging issues surrounding the modelling of small particle impacts are also discussed in detail. More precisely, the study described how the energy is being transmitted into the material surface from the impacting particle. Steady-state experimental erosion rates were also determined in this study to compare with the developed model. The developed model can also be used to determine the particle-impact strain rate, dynamic pressure, and coefficient of restitution.
Section snippets
Materials and methodology
In this study, the erosion testing was carried out to measure the erosion rate. Subsequently, the experimental results were compared with the theoretical erosion rate that was determined from the developed model in this study. The materials selection and testing procedure are described below:
Erosion modelling
It is now well known that the erosion occurs by different mechanisms at different impact condition. Bitter [9] stated that erosion occurs by two distinct mechanisms; deformation and cutting mechanisms depending on the impact condition. Neilson and Gilchrist [12] combined Bitter's erosion models and explained that erosion occurs by the combination of deformation and cutting wear mechanisms where a single mechanism is more dominant than another. Both models considered that the deformation and
Calculation of steady-state erosion rate using impact kinetic energy
In the initial comparative work, it is assumed that all the kinetic energy is used to erode the surface, as such, the full impact energy value is used in the modelling. Subsequently, the steady-state erosion rates were calculated using the developed model (Eq. (32)) that considers energy factors and impacted material properties and compared with the experimental results.
In this study, alumina (Al2O3) particles with an average size of 120 µm were used for erosion tests on aluminium and mild
Model improvements and extensions
The newly developed model provides useful information for the prediction of erosion rate of ductile metal. The current structure of the model encapsulates the energy dispersed into the surface, which provides an important theoretical framework for erosion determination. However, there are two distinct inputs that currently are experimentally based, which require further research, namely, rebound velocity and unit energy factors of cutting and deformation.
The rebound velocity component is an
Conclusions
In this study, a new erosion model was developed based on surface material properties, impact parameters and impact energy factors. The surface material properties used the modulus of elasticity and Poisson's ratio. Impact parameters were mean particle size, particle mass, impact velocity, impact angle, rebound velocity (i.e. to determine dissipation energy), elastic modulus and Poisson's ratio of the particle and the dynamic pressure at impact. Deformation and cutting energy factors were also
Acknowledgement
This work was carried out in the Centre for Bulk Solids and Particulates Technologies laboratory at The University of Newcastle, Australia and was supported by Cooperative Research Centre for Infrastructure and Engineering Asset Management (CIEAM). It is also acknowledged that the content presented in this paper is a part of the first author's PhD thesis [36] that is deposited at the University of Newcastle (UoN), Australia. Lastly, the authors would like to thank Dr Mohammad Mainul Hoque for
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