A theoretical study on wear simulation in metal forming processes

Journal of Materials Processing Technology, 34 (1992) 233-240

233

Elsevier

A theoretical study on wear simulation in metal forming processes T. Sobis, U. Engel and M.Geiger Chair of Manufacturing Technology, University Erlangen-Niirnberg, Postfach 3429 D-8520 Erlangen, Germany

Abstract

One of the main reasons of tool failure in industrial application of metal forming technologies is wear. Typical for this kind of failure is that it affects not only the costs of the process but also the tolerances of the formed parts. The only way to control these features is to develop methods which allow prediction of wear and which are suited to be used in the design stage in order to optimize the process. Starting with a survey of prediction methods, a new concept for the simulation of wear is presented in this paper.

INTRODUCTION The handling of wear problem can be classified broadly into two categories: prevention and prediction. It is rather amazing that wear prediction and thereby the wear theory at all are at a relative early stage of development, although the wear problems are accompanying any process in which things are in motion. This is true also in metal forming, which is probably the latest technological field of interest. The problems of wear prediction had to await the fifties until a number of scientists take up this subject [1]. The explanation of this situation may be found in general principles which control the approach to any technological problem: first - to solve it it at all, second - to do it in a way which is safe for human being, and third - to do it on an economic, effective way. The second and third principle are basically the motives for the development of theoretical background of technological problems. Because wear almost never threatens human life directly, the second principle is not so decisive, yielding a rather delayed development of wear theory if it is compared to other kinds of failure such as deformation or fracture. In Figure 1 the development of wear theories is shown in the historical background of deformation and fracture theories. Another reason for the inadequate developement of wear theory may be found in the first of the above mentioned principles: the complexity of the wear process aggravates any attempt to solve the problem on a more universal level. This especially is true in metal forming processes, which are characterized by extremely high contact pressures between the tool and billet. Therefore it is not surprising that only a small number of publications considering these problems can be found. In contrast to the theory the practical methods of wear prevention have a quite longer tradition and have reached today a relative high level of development. Similarly to the lubrication technology, the use of prevention methods can be characterized by the fact that 0924-0136/92/$05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.

234

they belong to the most closely guarded secrets of the whole operation. This is not surprising, because they are developed by experiments and experiences, which reflects of course in very high costs. The way to reduce these costs is to improve and even, if needed, to develop more advanced theoretical methods of wear prediction.

....................

~

n Adhesion Theory

....... ~ _ _ _ (^,~,d} I Frocture ~eory

~1921 / ~

___

1963 Fotigue Fracture

/ J Strain Criterion ( (

1632

Sheerin9 Stress "lheory 1776

Distortion-Energy Criterion

1904

Time

I~

Figure 1. Historical background of development of wear theory.

1. P R E D I C T I O N O F W E A R - STATE O F T H E A R T In order to illustrate the complexity of the problem, fist some experimental results of Westheide [3] should be discussed. In this investigation the wear profiles of flat dies were measured which were used for upsetting of cylindrical billets. Taking a common tool steel as die material, a wear profile is found as shown in Figure 2a. Using surface treated dies (nitrogen hardened), a quite different profile results, Figure 2b, although all the other process conditions (roughness, lubrication etc) were not changed. From this it can be stated that there is no definite correlation between friction and wear which aggravates the problem of wear prediction. On the other hand these results imply that the problem of wear cannot be considered separately from other tribological phenomena such as friction and lubrication, which both may influence the wear in very complex way. Because of its simplicity upsetting of a cylindrical billet is a common process to study wear of forming tools experimentally as well as theoretically [4,5]. For other metal forming processes it is very difficult to measure wear as a function of the place. In these cases only a average value of wear can be determined. Eg Nehl [6] determined such a value in backward cup extrusion measuring the change of punch diameter. Besides this, there are no experimental works known to the authors, which handle wear of metal forming tools with complex geometry as a time- and place-dependent phenomena. With respect to the theoretical treatment of wear in metal forming most of the publications proceed from the Arehard's wear model [7,8,9,10]. Based on Holm's theory, Archard

235

Final Geometry

Initial Geometry

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b

t

2000pm

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] I

I I

I ,

il llw

)

l

w, i

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Figure 2. Different wear profiles by the same metal forming process [3]. proposed the adhesion theory of wear in dry rubbing [11]. There as a central presupposition the assumption is used that the wear rate is proportional to the true contact area. In [12] he interpreted his model as an universal theory valid for all wear mechanism, ie adhesion, abrasion, fatigue and chemical reaction. The comparison of the experimental and theoretical wear profiles, which were calculated on the basis of Archard's model, yields a rather good qualitative agreement, Figure 3. On the other hand it seems to be very surprising that due to its complexity the tribological phenomena can be described by such a simple "wear rule". It must be noted that Archard's model takes into account as parameters of the tribological system only the sliding length, the load of contact and the hardness with the additional restriction that only the softer of both the contacting bodies is considered. The explanation for this coincidence can be found in the selected forming process itself, which in case of upsetting is characterized by the simple geometry of contact. It can be shown that in comparison to the contact stress, which is rather homogeneously distributed, the sliding length is the wear-controlling parameter, since its profile coincides with the measured wear profile [9,10]. However, the observed coincidence gets a more casual character if the experimental result of Figure 2b is considered. In order to overcome these inconsistencies the local contact phenomena must be taken into account. Two extremely different states of contact are shown in Figure 4 using the example

Initial Geometryof the Billet Final Geometry'~ \l 0

, .

'l

.

.

Relative Wear Rate wt/w,,~,

.

J

',

t

i

,

0 ReferencePoint Coordinater .

{

I

Experimental [Westheide]

Calculated

Figure 3. Comparison between measured and calculated wear profiles in upsetting.

236 of deep drawing of a cylindrical cup. The situation of boundary lubrication is shown at point B. The contact mechanism is determined by solid contact intermitted by small fluid pockets. In the following these fluid films are called microscopic lubricant pockets. At extremely severe conditions, eg for high values of local pressure, the solid contact may significantly predominate the area of the microscopic lubricant pockets. In this case the corresponding ratio reaches the value of 1 and describes the state of dry rubbing.

MacroscopicLubricantP o c k e t ~ Blank Holder

.,~'~-~~'~ , ~

;/),2~.¢

MicroscopicLubricontPocket Figure 4. State of contact in deep drawing.

Figure 5. Modelling a macroscopic lubricant pocket by the Rastegaev test.

The other extreme, ie ratio equal 0, is illustrated by point A in Figure 4. This is the appearance of the so called macroscopic lubricant pocket which in fact is a kind of fluid lubricant film coveting a small but macroscopic area. However, it is worth noting that this situation is not the same as in the well-known case of self-acting hydrodynamic lubrication, for which the tribological conditions are too severe especially in case of non-stationary forming processes [2]. A comparable situation can be modelled by the Rastegaev test, ie by upsetting of a rimmed specimen, Figure 5. In this test a macroscopic lubricant pocket arises, which causes a complete separation from the contact surfaces. The applied upsetting load is transmitted predominantly via the lubricant film. The friction contribution can be assumed to be low enough to be negligible. Therefore the sliding length of the workpiece on the die reaches its maximum value. This extreme situation, where the contact surfaces are obviously not affected by wear, represents a further example for the insufficienciy of Archard's model. Since in this approach wear is controlled mainly by the sliding length, which reaches maximum values as discussed above, the calculation of wear must result in maximum values, too. The reason for this is that Archard's theory ignores the existence of the macroscopic lubrication pocket. From this the significance of the real contact area in treating wear problems again must be emphasized. As mentioned above this fact was recognized by Archard too, but his theory was derived under rather restrictive assumptions as given by the dry rubbing problem. A more general definition of the real contact area has to make use of the lubrication controlled contact which for two characteristic situations was discussed by Figure 4 and 5. Moreover it must be taken into account that such situations are functions of place and time, ie the contact phenomena must be treated as place- and time-dependent problem. Summarizing this section following features characterizing the state of the art can be emphasized:

237

-

-

-

Archards model enables a qualitative good description of wear distribution in case of geometrically simple operation such as upsetting, in Archard's model the formulation of real area of contact (being the central concept of wear theory) is insufficient due to the complexity of the wear process, there are no formulations of real area of contact which takes into account the lubrication controlled contact, there are neither experimental nor theoretical researches, which investigate the wear process of tools with complex geometry as a time- and place-dependent phenomena.

2. REAL AREA OF CONTACT AS A CENTRAL CONCEPT OF WEAR The central concept of Archards adhesion theory of wear in dry rubbing [11] is the assumption that the volumetric wear rate Wv/s, ie worn volumen per unit sliding length s, is proportional to the real contact area A w.

o, a

(1)

Assuming that the real contact area A is proportional to the ratio of normal load Fn and hardness H of the softer of the two contacting bodies A - Fn

(2)

H

he obtalnes the linear wear rate Wv,, ie depth of wear W~per unit sliding length s :

p

(3)

where p is the nominal pressure on contact surface (the load Fn devided by the apparent area

A o ) and K the wear coefficient. Equation (2) was the theoretical basis of the developed system for simulation of wear distribution on the upsetting die, Figure 3. [10]. The calculation of wear follows in two steps. In the first step the boundary conditions, ie the contact stresses and the sliding distance, are determined via a finite element analysis (FEM). There are two ways to realize this step [13]: the coupled analysis, ie the modelling of the whole workpiece-tool system, and so called de-coupled analysis, which is used in the present work. In the decoupled analysis first the material flow is simulated by FEM too, presupposing a rigid tool, followed by a transfer process of data from the surface of the workpiece onto the surface of the tool [13]. This procedure was applied to calculate the wear of the upsetting die [10], Figure 6. The calculated wear profile is given by Figure 3. As mentioned above a good qualitative agreement with experimental results, taken from investigations of Westheide [3], can be stated. The second step is the quantitative description of the real area of contact, which is the most important task of wear approach. Hereafter, the problems arising by solving this task are briefly summarized.

238 In Figure 7 the experimental results of investigations on real contact area in relation to contact pressure are shown [14]. As it appears, the description of the real area of contact with the relation (2) is satisfactory only in the region of small contact stresses. In ease of high contact stresses, which are typical for metal forming processes, equation (2) yields insufficient results. Additionally, it must be noted that the relation (2) was derived for steady-state contact processes of dry rubbing, ie without consideration of lubricant existence. Thus, it would be very difficult to describe a real contact area for complex contact processes, as for example shown in Figure 4, via equation (2). 1

H: Hordness l / :ContactLoad / p: ContectPressure ~ e q

o

J

14 Initial 0eome[ry.

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Final Geometry\ i

-~- r

~ I0q

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Reference Point

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• Tin • Silver • Aluminium 10

Retotive C0nt0ct Stress p/H Figure 6. Upsetting of a cylindrical billet between two flat dies.

Figure 7. Relation between real area of contact and contact pressure [14].

3. MECHANICAL-RHEOLOGICAL CONCEPT OF REAL AREA OF CONTACT The basic idea of the new, mechanical-rheological concept [15] is to quantify the real contact area considering the lubrication controlled contact as discussed in chapter 2. Hereafter, a brief introduction of this concept has been done in three steps: (i) idealisation of contact mechanism, (ii) physical criterion, (iii) way of solution and first results. It was assumed that any process of contact can be idealised by three contact mechanism, which are illustrated in Figure 4 and 8. The first one is the solid contact, which is the main subject of contact mechanics. Reviews to this subject, beginning from the classical paper of Hertz, have been given, for example, by Johnson [16], Thomas [17], Schey [1] and Wear Control Handbook [12]. The earlier mentioned microscopic lubricant pocket represents the basis of two next contact mechanisms: a static lubricant pocket, which is a known mechanism of transmission of contact forces [1] and a dynamic lubricant pocket, which should not be confound with a self-acting hydrodynamic lubrication. The latter mechanism is introduced to describe the time-dependence of the contact processes. The fundamental condition for any contact process, as illustrated in Figure 9, is the equilibrium between external force F, acting on the apparent contact area and the sum of forces representing the three contact mechanism, as mentioned above, ie force F of solid body, force F, acting on the static lubricant pocket and force F d acting on the dynamic lubricant pocket, and may be written:

239

(4)

F,,(x) = F(x) + F,,(x) + Fa(x)

where x is the ratio of the indentation d to the maximum height of equivalent roughness of contact bodies h ~ and is called relative indentation. In the apparent area a steady-state tribological system is assumed to exist. In order to solve equation (4) the forces must be defined. The external force is known from the simulation of material flow [13], the other forces are unknown variables. The force of solid contact can be defined following one of the earliest study on statistical models of surface roughness in elastic contact conducted by Greenwood and Williamson (GVO [16,17]. The force F, acting on the static lubricant pocket can be calculated with the help of a model represented in Figure 8 by a spring of modulus K. The force Fa, which exists in a dynamic lubricant pocket, can be defined by a Maxwell model, Figure 8, ie a spring of modulus K in series with a dashpot of viscosity ~/. For a given apparent area characterized by the parameters of roughness geometry, and Initial Model

Static Lubricant Pockets

]

D)~amic Lubricant Pockets

I p, p, p,

lp, ,,~ Equilibrium of Forces:

I~-o

F.=F+F,+F d

Ao~

v

go- Apparent Area (~

Solid C o n t o c t . ~ . . . / ~

K

~

K

°'

PAd- Area ol D~nic Lubricant Pocket

P'S - - 7 - - 7 " (~A

Figure 8. Contact mechanisms in mechanical-rheological concept of real contact area.

0.8 <1~ II ._o

As - Area of StQtic Lubricant Pocket

k - Area of Solid Contact

Figure 9. Equilibrium of forces in contact area.

MechanicaI-RheologicalConcept: ElasticSolidContact of Greenwood & Williomsen

0".

0.6

(Non-RealisticModel)

0.4 g

Dry Rubbing..~._~_~

0.2 0

I

0

500

\ Lubricated I 1000 1500 2000 MPo Contact Stress ~, I

I

/

3000

Figure 10. Relation between relative real contact area and contact stress resulting from mechanical-rheological concept.

240 additionally by the lubricant parameters as viscosity ~/and modulus K, the relation between the ratio of real contact area and contact stress can be calculated, Figure 10. Despite of the non-realistic elastic GW model of solid contact, these first results show that the effect of stress as well as of lubricant on the real contact area can be modelled in a qualitatively correct way.

4. CONCLUSION The significance of the real contact area for wear prediction is outlined. The limits of Archard's model assuming proportionality between wear and real contact area are discussed. In case of simple metal forming processes such as upsetting, it is possible to obtain reasonable results for wear distribution. In case of more complex processes this model must fail, because the lubricant controlled contact is not taken into account. Therefore a new concept defining the real contact area is proposed which is based a mechanical-rheological model. Three contact mechanisms are considered: solid body contact, static and dynamic lubricant pocket. The applicability of this concept can be confirmed by first results.

ACKNOWLEDGEMENT: This research is part of joint project PSU, which is supported by the Volkswagen-Foundation, Hannover. REFERENCES

1 2 3

4 5 6 7 8 9 10 11 12 13 14 15 16 17

J.A.Schey, Tribology in Metalworking, ASM Metals Park: Ohio 1984 B.Avitzur, Wear 126(1988) 227-249 H.Westheide, EinfluB von Oberfl~ichenbeschichtungen af den WerkzeugverschleiB bei der Massivumformung, Berichte aus d. Inst. F. Umformtechnik, Universit~t Stuttgart, Nr. 87, Springer 1986 L.N.Mironov, Kuznecno-stampovocnoe Proizvodstvo, 6 (1975) 21-29 M.Weiergr~iber, WerkzeugverschleiB in der Massivumformung. Berichte aus d. Inst. F. Umformtechnik, Universi~t Stuttgart, Nr. 73, Springer 1983 E.Nehl, ICFG Birmingham, 7 (1985) 144-150 J.F.Renaudin et al, 11.Internationale Gesenkschmiedetagung, K61n 1983 W.K6nig, K.Steffens, Ind. Ariz. 107 (1985) 26, 22-26 P.H.Hansen, N.Bay, Proc. 3rd Int.Conf.Technology of Plasticity, Kyoto, 1990, 19-26 U.Engel, M.H~insel, T.Sobis, M.Geiger, Werkstatt und Betrieb 125 (1992) 6 J.F.Archard, J. Appl. Phy., 24 (1953) 981-988 M.B.Peterson, W.O.Winer (eds), Wear Control Handbook, ASME New York 1980 T.Sobis, U.Engel, M.Geiger, 4th Int.Conf.Num.Methods Ind.Form.Processes, NUMIFORM'92, France, September 14-18, 1992, acc.for pub. A.Uppal, S.D.Propert, Wear 23(1973)2, 173-184 T.Sobis, A Concept of Real Area of Contact at High Pressure, to be published in: Wear K.L.Johnson, Contact Mechanics. Cambridge University Press 1985 T.R.Thomas, Rough Surfaces. Longman Group Limited 1982