Journal of Materials Processing Technology 73 (1998) 200 – 205
Energy partitioning in elasto-plastic impact by sharp abrasive
particles in the abrasive water jet machining of brittle materials
S. Paul *, A.M. Hoogstrate, C.A. van Luttervelt, H.J.J. Kals
Laboratory for Flexible Production Automation, Faculty of Mechanical Engineering and Marine Technology, Delft Uniersity of Technology,
Landbergstraat 3, 2628 CE Delft, The Netherlands
Received 24 February 1996
Abstract
In the abrasive water jet machining (AWJM) of brittle materials, the stress wave energy, associated with the impact of abrasive
particles, plays an important factor in material removal by fracture. The models currently available are idealised and simplified
and cannot take into account the particle shape or size. The present paper addresses the problem of taking into consideration the
size and shape of the particles. The results indicate that use of spherical blunt particles in the AWJM of brittle materials will lead
to more fracture. © 1998 Elsevier Science S.A.
Keywords: Abrasive water jet machining; Brittle materials; Energy partitioning; Total depth of cut
1. Introduction
Abrasive water jet machining (AWJM) is an upcom-
ing technology which is finding applications in cutting,
pocket milling, turning and other machining operations
for both ductile and brittle materials. The mechanism
of material removal in ductile materials seems to be
micro-cutting by the free flowing abrasive particles,
accompanied by a large amount of plastic deformation
[1].
However in the case of the AWJM of very brittle
materials such as ceramics, cemented carbides, glasses
etc. the stress wave energy associated with the impact
by the abrasive particles causes fracture [2–4] in addi-
tion to micro-cutting and gross plastic deformation.
One of the main problems in modelling the total depth
of cut achieved in the AWJM of brittle materials is to
determine the stress wave energy as a percentage of the
total energy [3,5].
Zeng and Kim [4] proposed a model to determine the
stress wave energy as a percentage of the total energy
for impact by a solid particle at a low angle. No
considerations were given to the shape and size of the
abrasive particles. The analysis assumed the abrasive
particles to be spherical (i.e. having no sharp corners).
However, the common abrasive particles used in
AWJM such as garnets and more recently alumina and
silicon carbide particles, are non-spherical and do have
sharp cutting edges [1].
The objective of the present study is to determine
analytically the stress wave energy associated with a
single impact by an abrasive particle, which might be
non-spherical and might have sharp cutting edges, at
any angle of impact in relation to the AWJM of brittle
materials.
2. Modelling
In 1904 Lamb [6] investigated for the first time the
propagation of stress waves in an isotropic elastic semi-
infinite solid due to point loading. Much later in the
mid 1950s Miller and Pursey [7,8] studied wave propa-
gation and energy partitioning for different cases such
as a circular disc of finite diameter imparting cyclic
loading normal to the free surface of an isotropic
semi-infinite solid. Hunter [9] utilised the work of
Miller and Pursey [7,8] and proposed a mathematical
* Corresponding author. Present address: Department of Mechani-
cal Engineering, Indian Institute of Technology, Kharagpur, West
Bengal 721 302, India. Fax.: + 91 3222 55303; e-mail:
spaul@mech.iitkgp.ernet.in
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