2 - A Coupled Finite Element and Mesh Free Analysis of Erosive Weae - Wang - Yang
2 - A Coupled Finite Element and Mesh Free Analysis of Erosive Weae - Wang - Yang
2 - A Coupled Finite Element and Mesh Free Analysis of Erosive Weae - Wang - Yang
Tribology International
journal homepage: www.elsevier.com/locate/triboint
a r t i c l e in fo abstract
Article history: Erosive wear is a kind of material degradation, which is largely involved in many industries, and
Received 2 August 2007 caused a series of serious problems and economic loss. Many theoretical models and numerical
Received in revised form models have been established to study the erosion phenomena. In this study, a coupled finite
13 June 2008
element and meshfree model was developed for the simulation and prediction of erosive wear. By
Accepted 18 July 2008
Available online 3 September 2008
utilizing the meshfree technique, the error due to mesh distortion and tangling at impacted area
in the finite element analysis could be effectively avoided. The fundamental mechanisms of erosion
Keywords: by solid particle impact were investigated as well. Comparison against the results of analytical
Erosion model erosion models and finite element model are made. It is shown that the predicted results are in
Meshfree
agreement with reported results. The present study could be very useful and efficient in studying
Smoothed particle hydrodynamics (SPH)
erosive wear.
Finite element method (FEM)
& 2008 Elsevier Ltd. All rights reserved.
0301-679X/$ - see front matter & 2008 Elsevier Ltd. All rights reserved.
doi:10.1016/j.triboint.2008.07.009
ARTICLE IN PRESS
2. Modeling particles. The solution time is set to 1.5 t5, where t5 is the time
when the last particle contacted to the target surface.
The erosive processes are simulated using a 3-D explicit Only a half-model was evaluated, so the constrains and SPH
dynamic analysis within ANSYS/LS-DYNA. The Johnson–Cook symmetry plane were set for the FE and SPH sections at the
(J–C) [33,34] viscoplastic material model with Grüneisen equation boundaries to achieve the symmetry conditions. All of the bottom
of state (EOS) was employed to model the flow stress behavior of and outside nodes of the target materials were defined for non-
the target Ti-6Al-4V material. Johnson and Cook express the von reflecting boundaries. The SPH scheme and FE mesh of the erosion
Mises flow stress as detailed in Eq. (1): model are shown in Fig. 1.
Generally, the erosion rate (mg/g) was used to characterize the
s ¼ ðA þ Bn Þð1 þ c ln _ n Þð1 T nm Þ (1) erosion performance of the target materials. It is defined as
where A and B are yield stress constant and strain hardening Cumulative mass loss of target materialsðmgÞ
constant; n, c, m are constants; and e is the equivalent plastic Erosion rate ¼
Impact particles weight ðgÞ
strain, _ n ¼ _ =_ 0 is the dimensionless plastic strain rate for
(4)
_ 0 ¼ 1.0 m/s. T* ¼ (TTr)/(TmTr), T, Tr and Tm are the target
material temperature, room temperature and melting point of the In this study, the variation of impact angle and impact velocity
target material, respectively. in the model was achieved through ANSYS Parametric Design
A shear failure model is utilized to model the failure: the Language (APDL). The impact angle varies from 151 to 901 in
P
damage occurs when the damage parameter D ¼ De/ef reaches increments of 151. The impact velocity varies from 60 to 105 m/s
the value of 1. De is the incremental plastic strain per computa- in increments of 15 m/s.
tional cycle, and the failure strain ef is given by
Table 1
Material constants of ductile materials [35–37]
1.228e+00
1.105e+00
9.822e-00
8.594e-00
7.366e-00
6.139e-00
4.911e-00
3.683e-00
2.455e-00
1.228e-00
0.000e+00
1.710e+00
1.539e+00
1.368e+00
1.197e+00
1.026e+00
8.549e-00
6.839e-00
5.129e-00
3.420e-00
1.710e-00
0.000e+00
Fig. 3. The erosive plastic strain on the target material: (a) at 301 impact angle and (b) at 901 impact angle.
ARTICLE IN PRESS
4 8
7
3
Erosion rate (mg/g)
4
Coupling Algorithm
1 Bitter’s model
Finite element model 3
2
0
10 20 30 40 50 60 70 80
Impact angle (deg.) 1
15 30 45 60 75 90
Fig. 5. Variation of erosion rate with impact angle for ductile materials. Impact angle (deg.)
10
400
Stress (MPa)
-800
-1200
0.1 -1600
60 70 80 90 100 Distance beneath the target surface (m)
Impact velocity (m/s)
Fig. 8. The residual stress (sx) profiles after five-particle impact.
Fig. 6. Variation of erosion rate with the impact velocity for ductile materials.
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