Modelling of contact interface oxidation , ECCOMAS ...

European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012) J. Eberhardsteiner et.al. (eds.) Vienna, Austria, September 10-14, 2012

MODELLING OF CONTACT INTERFACE OXIDATION PROCESS AT ASPERITY SCALE Jan Maciejewski1,2, Marcin Białas2, and Zenon Mróz2 1

Institute of Construction Machinery Engineering, Warsaw University of Technology Narbutta 84 St., 02-524 Warsaw, Poland e-mail: [email protected] 2

Institute of Fundamental Technological Research, Polish Academy of Sciences Pawińskiego 5B St., 02-106 Warsaw, Poland {mbialas,zmroz}@ippt.gov.pl

Keywords: frictional sliding, bulk and flash temperatures, oxidation, asperity scale Abstract. Wear and oxidation processes at contact interfaces in FGM systems are coupled with several thermo-mechanical phenomena such as: variation of friction coefficient with contact stress and temperature, variation of mechanical properties with temperature, local temperature distribution affected by frictional sliding and oxidation kinetics. The solution of thermo-mechanical coupling on a macro scale does not explain the oxidation mechanism. Thus, the oxidation problem should be treated using two scale modelling approach. The first scale is the macroscopic level, corresponding for example to ball on disc test or a braking system, the second scale is the asperity micro scale level. In this paper, the oxidation problem will be considered on the asperity micro scale level using the finite element method. Representative volume element is modeled based on the actual surface topography . Assuming thermo-elastic material properties, the calculation on the asperity scale are performed in two steps. Firstly, the mechanical contact between two surface is calculated. As a result, the relation between the global load and micro stress distribution is obtained. Next, for a given stress load and slip velocity, FEM thermal analysis is performed. In the present analysis asperity is simplified to have a conical shape. It is assumed that the real contact zone can be treated as an axisymmetric cell with the contact slip generating heat flux. The temperature fluctuations on the asperity are used for the calculation of averaged wear-oxidation parameters (friction coefficient, oxidation activity factor).

Jan Maciejewski, Marcin Białas, and Zenon Mróz

1.

INTRODUCTION

Wear and oxidation processes at contact interfaces in FGM systems are connected with several thermo-mechanical phenomena such as: variation of friction coefficient with contact stress and temperature, variation of mechanical properties with temperature, local temperature distribution affected by frictional sliding induced oxidation. Wear coupled with thermo-mechanical effects was analysed by a number of researchers, see for example [1-3]. In these papers configurational changes were considered for different boundary conditions and, in particular, for those resembling ball on disc tests. Using finite elements or other numerical methods evolution in stress state and temperature field due to wear was modelled. The contact shape evolution during wear process of two bodies in relative sliding motion was usually simulated numerically by integrating the wear rate expressed in terms of the relative sliding velocity and the contact pressure. A steady state was then predicted in the case of constant contact zone by the incremental integration procedure accounting for contact shape and pressure variation. A more effective procedure was developed in [1,2] by postulating minimization of the contact response functional. It was demonstrated that the stationary conditions of the total wear dissipation power at the contact interface provide the pressure distribution in the steady wear and generate the coaxiality rule requiring the wear rate vector to be collinear with the wear velocity vector consistent with the boundary conditions allowing for a rigid body motion induced by the wear process. The considerations on temperature distribution in asperities in micro scale are not widely represented in the literature. The survey of some existing solutions can be found in [4], where it is clearly seen, that the influence of surface roughness on oxidation has not been satisfactory explained yet. In tribology it is common to distinguish three temperatures: the bulk temperature, the average surface temperature and the flash temperature. Bulk temperature is the temperature averaged over the bulk of one of the contact bodies; surface temperature is the temperature averaged over the thin surface layer of a body; flash temperature is the local increment of temperature at the contact of micro asperities on the rubbing surfaces. The notion of flash temperature reflects the discrete nature of frictional contact. Since the area of real contact of bodies is three-four orders of magnitude lower than the nominal contact area, the heat generated in the friction zone is concentrated on small contact spots. Owing to this, the heat-flow density on these spots can be very high and result in short-time temperature elevation by hundreds of degree. The solution of thermo-mechanical coupling on a macro scale does not explain the oxidation mechanism. Thus, the oxidation problem should be treated using two scale modelling. The first scale is the macroscopic level, corresponding, for example, to ball on disc test or braking system. The second scale is the asperity micro scale level. In the following, the oxidation problem will be treated on asperity micro scale level using the finite element method. 2.

MACRO SCALE CALCULATIONS

Figure 1 represents schematically ball on disc test. We model the part of the disc only in the vicinity of the ball. The arrow indicates direction of ball movement. The wear process is modeled using modified Archard’s law: w i 

 H

( n ) vt 

 H

(  n ) vt

(1)


where n, n are the shear and normal stress, vt is the sliding velocity, H is hardness and  is material parameter. The friction coefficient  is calculated using two scale model. Generally, it is a function of normal stress n and the global temperature T.

Figure 1: Schematic representation of ball and the disc. One-half setup due to the symmetry.

The disc profile changes are affected by frictional wear and oxide layer growth. The oxidation process takes place at different rates at the contact zone and in the non-contact area, where it depends on the temperature distribution. For the description of oxidation of FGM composite in the non-contact area we use the following formula:

ho  Av (T )Af  ( Ai  Af ) exp(  A3t )

(2)

,

where Av(T) is the temperature dependant oxidation activity factor controlling the oxidation process and has the form:

0 k   T  Tmin    Av (T )   A0  T  T min    max  A0

T  Tmin Tmin  T  Tmax

(3)

T  Tmax

In equations (2) and (3) ho is the growth rate of the oxide height, Af, Ai, A3, k are model parameters, Tmin is a minimal temperature for the oxidation to take place and Tmax is the saturation temperature. Equation (2) ensures that during the oxidation process, the initial oxide thickness growth rate AvAi decreases to the asymptotic value AvAf. The proposed oxidation model correctly fits in the experimental data obtained from TGA tests for Cu alloys and composites [5,6]. In the tribological tests such as ball on disk test, evolution of the stress and temperature are cyclic, as presented in Figure 2. A point on the disc upper surface is in contact with the ball between time values t1 and t2, as indicated by the yellow area. For the sliding velocity Vt and length R from the disc center to the ball, time required for one complete cycle is equal to t=2R/Vt. In this particular case, the thickness changes due to wear and oxidation processes are given by g ( y) 

 w  h dt   h dt   w  h dt   h dt t1

0

t

t2

0

t0

t2

0

t1

0

t3

(4)


26 25

200 normal stress 150

24

temperature 23

100 22 50

temperature [C]

normal stress [MPA]

250

21

0

t1 t2

t0 t

t

20

t3

time

t

Figure 2: Stress and temperature evolution for a given point on the disc upper surface in contact with the ball.

The calculation procedure is as follows:  slide the ball until temperature steady state in the disc is reached,  use the obtained contact stress distribution to calculate wear and oxidation rates according to formulas (1) and (2),  modify mesh using equation (3),  repeat the whole procedure for a desired number of cycles. initial

worn-out surface

(a)

(b)

Figure 3: (a) Normal contact stress and (b) temperature distribution for initial and worn out surfaces (steady state).

Performed finite element simulation of wear and oxidation processes used adaptive meshing capabilities offered by Abaqus through the user subroutine UMESHMOTION. Based on


steady state contact stresses and applying modified Archard’s law, rate of nodal displacements is calculated for each nodal streamline. Figure 3 presents stress and temperature distribution in initial configuration and after wear process. We see that the macroscopic temperatures reaching the maximal value of 25C are to small for oxidation process to start. Micro modelling at the asperity scale is needed. 3.

MICRO SCLAE CALCULATIONS

Real view of surface topography in initial configuration is presented in Figure 4(a). The microscopic problem is solved for a unit cell, as indicated in Figure 4(b), which is assumed to be representative for the entire rough surface. Its dimensions are 200x200 m. Its height h, equal to 100 m, is assumed to be sufficiently large, so that the results are not affected by its finite value. In Figure 4(b) the 3D mesh approximation with roughness topography is magnified 10 times in the vertical direction. Simulation of heat conduction through a surface with a real roughness is considered in [7]. Figure 5 presents sample distributions of normal stress (microcontact zones) for the unit cell during the loading exerted by pressing a rigid flat surface. In the course of loading the real contact area increases. The fraction of real contact area is defined by =Ar/A0, where A0 is the nominal surface area and Ar is the real contact area. µm 1.12 1.08 1.04 1 0.96 0.92 0.88 0.84 0.8 0.76 0.72 0.68 0.64 0.6 0.56 0.52 0.48 0.44 0.4 0.36 0.32 0.28 0.24 0.2 0.16 0.12 0.08 0.04 0

Figure 4: (a) Actual view of surface topography; (b) finite element mesh representation of a unit cell.

Figure 5: Normal stress in the representative unit cell due to pressing of a rigid flat surface.

The mean stress acting within the representative element is presented in Figure 6 for different wear stages. The parameter Ra presents the arithmetic mean values of profile roughness.


It can be observed that the mean stress is strongly dependent on the wear level and, consequently on the roughness parameter Ra. FGM I Cu_Al2O3 (No128)

mean [MPa] 4000 3000

Ra [m] 0.021 (Fn=3N, t=3h)

worn-out surface

0.044 (Fn=6.7 N, t=3h)

2000

0.101 (initial)

1000 0

0

0.2

0.4

0.6

0.8

1

1.2

real contact area fraction  [-]

Figure 6: Mean stress evolution versus real contact area ratio  for different wear stages.

In the present analysis the simplification of asperity shape is applied. It is assumed that the real contact zone can be treated as an axisymmetric cell with the contact slip generating heat flux. The simplified representative contact element is presented in Figure 7(a). The stress distribution for various real contact areas for this RVE is presented in Figure 7(b). These distributions are used for the description of the equivalent heat flux intensity through the following equation: q  f nVt  f nVt

(5)

where q is the heat flux and f=0.5 is a fraction of frictional contact heat distributed into the disc. (a)

(b)  [MPa]

8000

Cu-Al2O3 equivalent stress distribution  n

0.985 0.976 0.944 0.851 0.523 0.317 0.174

4000

0 0

0.2

0.4

0.6

0.8

1

Radius of substitute RVE

Figure 7: (a) Simplified asperity within the representative unit cell. (b) Equivalent stress on the cylindrical RVE cell for different value of real contact area .

Surface heat flux is distributed at the top of the asperity, corresponding to the equivalent stress value. As an example, temperature distribution obtained at steady-state for =0.4 and slip velocity equal to 0.02 m/s is presented in Figure 8(a). Asperity is made of copper alloys (density: 8.92 g/m3, thermal conductivity: 385 W/m K, specific heat: 0.385 J/g K) and ambient temperature of 20 C is assumed. It can be seen, that temperature reaches high values directly under heat flux surface and decreases rapidly to ambient on the surfaces not subject to


heating. Temperature distribution at asperity surface is presented in Figure 8(b) for different values of real contact area fraction , in contact with surface load. It can be seen, that its peak values are reached directly on the heat flux surface and decrease to ambient on the surfaces which are directly not subject to heating. We see that the temperature values are substantially bigger than those on the macro scale and can induce oxidation process. (a)

(b)

Figure 8. (a) Temperature distribution in RVE; (b) Temperature at upper surface for different value of of real contact area fraction .

4.

MICRO -MACRO TRANSITION

The micro-macro transition is performed through the averaging of oxidation factor on the micro scale level through the equation 1

 Av (T ) 

1 Av (T )dS  2 Av (T )rdr S 0

(6)

where S is the contact area of the axisymmetric simplified unit cell. The growth of the oxide layer should now be calculated from the formula

ho  Av (T )  Af  ( Ai  Af ) exp(  A3t )

(7)

being basically the same as equation (2), except for the fact that oxide growth is controlled by the homogenized activity factor. Figure 9 presents average oxidation activity factor versus mean surface temperature for various real contact area fractions. The activity factor for uniform surface temperature is presented in blue. It is clearly seen, that for frictional contact slip, the oxidation process starts at a lower temperature than in TGA experiments (simultaneous thermo-gravimetric analysis), where the temperature is uniform. 5.

CONCLUSIONS

Wear and oxidation processes at contact interfaces in FGM systems are coupled with several thermo-mechanical phenomena such as: variation of friction coefficient with contact stress and temperature, variation of mechanical properties with temperature, local temperature distribution affected by frictional sliding and oxidation kinetics. The solution of thermomechanical coupling on a macro scale does not explain the oxidation mechanism. Thus, the oxidation problem should be treated using two scale modelling approach. The first scale is the macroscopic level, corresponding for example to ball on disc test or a braking system, the second scale is the asperity micro scale level. Using finite element method, calculations of


temperature distribution on the asperity scale were performed. It was shown that the temperature values are substantially bigger than those on the macro scale and can induce oxidation process. It is clearly seen, that for frictional contact slip, the oxidation starts in a lower temperature than in TGA experiments. 1.40E-03

mean activity factor

1.20E-03 1.00E-03 8.00E-04

0.01

6.00E-04

0.1 0.4

4.00E-04

T=const.

2.00E-04 0.00E+00 0

200

400

600

800

1000

1200

m ean surface tem perature

Figure 9: Variation of averaged activity factor versus macro scale temperature.

Acknowledgements This work was supported by the EU FP7 Project “Micro and Nanocrystalline Functionally Graded Materials for Transport Applications“ (MATRANS) under Grant Agreement No. 228869.

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