A discrete element model to investigate sub-surface damage due to surface polishing

Abstract

Large high-power laser facilities such as megajoule laser (LMJ) or National Ignition Facility (NIF) are designed to focus about 2 MJ of energy at the wavelength of 351 nm, in the center of an experiment chamber. The final optic assembly of these systems, operating at 351 nm is made of large fused silica optics working in transmission. When submitted to laser at the wavelength of 351 nm, fused silica optics can exhibit damage, induced by the high amount of energy traversing the part. The created damage is a set of micro-chips that appear on the optic surface. Current researches have shown that this damage could be initiated on pre-existing sub-surface damages created during the optics manufacturing process. It is then very important to understand, for various set of manufacturing parameters, what are the key parameters for sub-surface damage. The presented work details the development of a simplified model to investigate the polishing process. Both silica (the material to be polished) and the abrasive particles are modeled using a discrete element approach. This numerical tool allows following the evolution of micro-cracks inside the material during the abrasion process. It is shown how the mechanical properties (pressure), the abrasive properties (shape and quantity of abrasive particles) and the system properties (filtration) have an influence on the sub-surface properties at the end of the process.

Introduction

When submitted to high fluences (>5–10 J/cm²) at the wavelength of 351 nm, transmission fused silica optics such as lenses, windows can exhibit damage similar to micro-chipping. Damage is induced by the high amount of energy traversing the part. An example of such laser damage is shown in Fig. 1.

Consequently, lifetime in the UV of fused silica optics used on large high-power laser facilities such as megajoule laser (LMJ) [1] or National Ignition Facility (NIF) [2] has been the subject of extensive studies. It has been shown that at the wavelength of 351 nm, the lifetime of fused silica optics is determined by both surface damage initiation and damage growth [3]. Hence, strategies developed to improve lifetime rely on reducing initiator density and using mitigation techniques to inhibit growth of damage sites induced by residual initiators [4].

As for the nature of damage initiators, it has been shown that damage initiation can occur on local absorption of contaminants coming from polishing slurries buried into the fused silica optics interface [5]. Sub-surface cracks, such as the ones present in sub-surface damage (SSD) layer of conventionally polished optical parts, are also possible damage initiators [6], [7]. SSD is created during the first steps of the optic manufacturing [8]. Sawing and grinding involve hard abrasive grains put in contact with the optical part to remove material in brittle mode. Generated cracks can then extend far below the surface. Loose abrasive grinding and polishing can also damage the optical surface as well. SSD depth is also greatly process dependent [9]. Creation of SSD during fused silica grinding and polishing can be seen as the action of multiple loaded hard particles on a brittle material. Therefore, most of the models developed to understand the creation of SSD is based on basic fracture relationship (single static indent, trailing indent, etc.) combined with experimental data. It leads to an estimation of a maximal depth of SSD for given manufacturing parameters (load, particle diameter, etc.) but does not give a complete understanding of the abrasion phenomenon. Our aim is to get a better physical understanding of the grinding process. Hence, the present work is based on the development of a three-dimensional discrete element simulation (DES) of the grinding step, an early step of the fused silica optic polishing process. This study focuses on SSD.

In 1995, taking into account existing wear models, Meng and Ludema [10] proposed to abandon efforts to model wear in terms of known wear mechanisms and develop full descriptions of the progression of macroscopic events on sliding surfaces. This included a description of the formation and movement of fragmented particles in the interface region. This recalls the work of Godet and co-workers [11], [12], [13], who developed the concept of the third body in the 1970s, aware of the lack of conceptualization concerning dry contacts. The underlying idea was to use the same approach in order to study lubricated and dry contact. For this, Godet defines the third body as the medium at the interface of two bodies in contact. To study the behavior of the third body inside and outside the contact, Berthier proposed [14] the tribological circuit which brings into play all the third body flows and thus provides a very general view of the problem. This makes it applicable to a wide range of tribological situations. Based on this tribological circuit and coupling DESs to experimental, but simplified, wear studies, Fillot et al. [15], [16], [17] proposed a set of equations that allows a qualitative modeling of wear as a mass balance in the contact area. Iordanoff and Charles [18] showed how abrasion process can be studied as a particular and controlled wear process. Two-dimensional DESs were used. This study outlined the effects of abrasion process (free or fixed abrasive, re-circulating or loosed abrasive flow) on both removal material rate and sub-surfaced damage. This preliminary work has been carried out to outline the possibility of using DEM simulation for the study of SSDs. The model is based on micro-mechanical laws. The laws chosen for this study have been greatly simplified. The next step is to find the contact laws and link laws that allow a quantitative comparison between the presented results and classical results from the fracture mechanics literature [19], like the linear elastic F.M. Such comparison between discrete approach and continuous approach has been carried out for the study of silicon carbide by Ippolito et al. [20].