Wear258(2005)
339–348merged
Micro-contact bad modelling of abrasive wear
M.A.Man∗,M.B.de Rooij,D.J.Schipper
Faculty of Engineering Technology,Surface Technology and Tribology,University of Twente,P.O.Box217,7500AE Enschede,The Netherlands
Received22December2003
Available online18October2004
Abstract
A model that describes the abrasive wear between a hard and rough surface and a softer and smooth surface is developed.The contact between the two solids is modelled bad on micro-contacts[M.A.Man,M.B.de Rooij,Abrasive wear between rough surfaces in deep drawing,in: Proceedings of the6th Austrib Tribology Conference,Perth,Australia,2002,pp.601–608],instead of the more conventional summits-bad modelling[J.A.Greenwood,J.J.Wu,Surface roughness and contact:
an apology,Meccanica36(6)(2001)617–630;J.A.Greenwood,J.B.P. Williamson,Contact of nominallyflat surfaces,Proc.R.Soc.London A295(1966)300–319].Using3D surface roughness measurements, the hardness of both surfaces and process parameters as applied load,a collection of micro-contact spots is identified and subquently the surface to surface approach is calculated.The micro-contact spots act as abrasive entities,resulting in wear of the softer contact partner. On a pin-on-disk tribometer the abrasive action of a single micro-contact,or asperity,at different loads is experimentally investigated.An expression for the verity of wear as a function of the indentation depth is obtained by applying a curve-fit through experimentally obtained data.When the indentation depth of a micro-contact spot into the counter surface,as well as the material properties are known,the wear caud by a single micro-contact is obtained.The macroscopic wear volume is found by summing the volumetric wear of each individual micro-contact.
©2004Elvier B.V.All rights rerved.
Keywords:Asperity;Micro-contact;Contact model;Abrasive wear;Sheet metal forming;Tailor welded blanks
1.Introduction
Recent trends in industrial sheet metal forming lead to an incread tribological verity of the process and hence a possible initiation of wear process like galling and abra-sion.It needs no explanation that the wear process should be avoided as they cau poor product quality and higher costs due to an increa in scrap,additional maintenance of the tools and standstill of the production line.The sub-jects of galling and adhesive wear in deep drawing pro-cess have been discusd extensively,e for instance [4,5].
This work focus on the abrasive wear of deep drawing tools,as occurs low-cost tooling applications and the processing of tailor welded blanks.A tailor welded blank
∗Corresponding author.Tel.:+31534894390;fax:+31534894784.
preciousE-mail address:m.a.man@ctw.utwente.nl(M.A.Man).consists of veral plates which are connected by a lar weld. In the investigated situation,this weld has a higher surface roughness and both the weld and its heat affected zone show incread hardness.As known from industrial practice,in deep drawing of tailored blanks,the hard and rough weld might initiate abrasive wear of the relatively soft tool material, e also[6].
In any contact between two rough contact partners, actual surface to surface contact only occurs at l
ocalid spots.The micro-contacts cau the abrasive action of the macroscopic contact and therefore the behaviour of a single micro-contact should be investigated in order to be able to describe the macroscopic contact.This paper focus on the determination of the contact and wear behaviour of a single micro-contact.In[1]the developed micro-contact model is implemented in a macroscopic model for abrasive wear in which it is assumed that a micro-contact is a single entity that does not interfere with any of its neighbouring micro-
0043-1648/$–e front matter©2004Elvier B.V.All rights rerved. doi:10.1016/j.wear.2004.09.009
340M.A.Man et al./Wear258(2005)339–348
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coverletterNomenclature
a radius of the contact area(m)
A contact area(m2)
A g frontal area of wear groove(m2)
A s frontal area of side ridges(m2)
d indentation depth(m)
D p degree of penetration
E complete elliptic integral of the cond kind
E i Young’s modulus of body i(Pa)
E*reduced Young’s modulus(Pa)
H hardness(Pa)
k average contact pressure factor
K complete elliptic integral of thefirst kind
N normal load(N)
¯p average contact pressure(Pa)
q wear per unit scratch length(m2)
R radius of contact partner(m)
R*reduced radius(m)
w width of the wear groove(m)
z(x,y)function describing indenter
Greek symbols
αdimensionless radius of the contact ellip(–)γdimensionless normal approach(–)
δrelative elastoplastic indentation depth(–)
θorientation of indenter,angle between minor axis and sliding direction(◦)
κellipticity ratio of the contact area(–)
λellipticity ratio of the contacting bodies;gap curvature ratio(–)
νi Poisson’s ratio of body i(–)
ξdegree of wear(–)
Suffixes
d erning sliding contact
e elastic
ep elastoplastic
e,trans value at elastic–elastoplastic transition
p plastic
p,trans value at elastoplastic–plastic transition
s arbitrary value;ud in text
x in x-direction
x in sliding direction
y in y-direction
contacts.However,the growth of individual micro-contacts with increasing load and merging of adjacent micro-contacts has to be taken into account.In the model the macroscopic behaviour is determined by simply adding the results for all individual micro-contacts.2.Micro-level
In the investigated situation of a hard and rough tailor welded blank against a softerflat tool,a micro-contact can be reprented by a rigid protuberance in contact with a de-formingflat.The shape of this protuberance is reprented by a paraboloid,and its size and shape are determined by curvefitting of the surface micro-geometry inside the micro-contact.In the following,the paraboloidal geometrical body reprenting the surface micro-geometry will be called an asperity.In Section2.1an elastic–elastoplastic–plastic con-tact model is derived for the contact between a moving hard asperity and a deformingflat and soft body.The contact model provides a relation between the contact load and the indentation depth.Subquently,single asperity wear exper-iments are described,resulting in an empirical relation be-tween indentation depth and volumetric wear.Finally,this empiric relation is theoretically extended to describe wear by paraboloidal shaped asperities.Thefinal result is a model that describes the volumetric wear due to the sliding mo-tion of a paraboloidal shaped asperity at a given contact load.
2.1.Sliding contact
In the deep drawing process the contact at micro-level is a combination of elastic and plastic material behaviour.There-fore a contact model incorporating both elastic and plastic deformation is applied.However,pure elastic contact hardly ever occurs.Following the approach of Zhao et al.[7]the contact model includes a relatively large intermediate regime between pure elastic and fully plastic deformation.Equations for the elastic–elastoplastic–plastic contact between aflat sur-face and a moving paraboloidal shaped asperity are derived in Appendix A.The elastic contact situation is described using the theory of Hertz[8],while the fully plastic contact is dis-cusd according to Johnson[9].For the intermediate elasto-plastic deformation mode a third order polynomial template between the elastic and fully plastic asymptotes is applied, similar to Zhao et al.[7],resulting in Eqs.(1)and(2)for the elastoplastic contact area and the elastoplastic contact load in sliding contact:
A ep,d=A e,d+(A p,d−A e,d)·(−2·δ3+3·δ2)(1)
N ep,d={A e+(A p,d−A e)·(−2·δ3+3·δ2)}
×
H−H·(1−k)·ln d p,trans
−ln d
ln d p,trans−ln d e,trans
(2)
in whichδreprents the relative elastoplastic indentation depth:
δ=
d−d e,trans
p,trans e,trans
(3)
It is shown that the transition from the elastoplastic to the fully plastic deformation mode occurs at an indentation
M.A.Man et al./Wear 258(2005)339–348
341
Fig.1.Size of the elastic–plastic transitional regime.
depth d p,trans ,in which for simplicity it is assumed that the elastic–elastoplastic and elastoplastic–plastic transitions do not change due to the he stress distribution in the contact is not affected by the friction.In Fig.1the relative size of the elastoplastic regime,defined as d p,trans /d e,trans in Eq.(4)is expresd:
d p,trans d e,trans =400·k ·√
λ1+λ·E (1−κ2)
κ·K (1−κ2)(4)The figure illustrates that the boundaries of the elastoplastic regime depend on the ellipticity ratio λ=R x /R y of the asper-ity.The relation between the nominal contact pressure and the contact area in sliding contact is shown in Fig.2.The figure clearly points out that the elastoplastic deformation mode provides a smooth transition between the elastic and fully plastic asymptotes.2.2.Wear
In the previous subction a micro-level model for the contact between a hard rough surface and a softer deforming flat body was derived.This contact model compris three deformation regimes:elas
tic,elastoplastic and fully plastic.When the contact pressure is high enough for elastoplastic or fully plastic deformation to occur,the sliding contact between a rigid asperity and a flat results in a wear groove in the flat body,as illustrated in Fig.3(a).Part of the material from the wear groove is transferred to the side ridges and part of the material is removed as wear debris (cf.[11–15]).The degree of wear ξas defined in Eq.(5)describes the relative amount of material that is actually removed from the groove and hence can be en as the efficiency of the material
removal
nubar
Fig.2.Average contact pressure for the elastic,plastic and elastoplastic regime.
process:ξ=thomson reuters
A g −A s
A g
(5)
The total volumetric wear per unit length q equals the volume per unit length of the wear groove minus the volume per unit length of the side ridges and can now be expresd according to Eq.(6):
q =A g −A s =ξ·A g
(6)
In the equations A g reprents the frontal area of the groove and A s the frontal area of the side ridges.In pure ploughing all material from the groove is transferred to the side ridges (A g =A s )and hence ξ=0.In pure cutting all material from the groove is removed as wear debris and no side ridges are formed (A s =0),so ξ=1.The value of ξdepends on the abra-sive verity of the contact,which is reprented by the degree of penetration D p (e Fig.3(b)):D p =
d a
(7)
The relation between D p and ξis studied by Kayaba et al.[13]who distinguished three wear modes;ploughing,wedge for-mation and cutting,each with a corresponding characteristic value of ξ(0.0,0.50and 0.875,respectively).Bad on the experimental work of Kayaba et al.,Jiang and Arnell [16]de-rived a relation for ξin the wedge formation regime bad on a low-cycle fatigue wear mechanism.Becau ξdepends on many variables,[12],in this work values are obtained using scratch
experiments.
Fig.3.(a)Geometry of the wear scar and (b)degree of penetration.
342M.A.Man et al./Wear258(2005)
339–348
Fig.4.Typical scratched surface.
2.2.1.Scratch experiments on nodular cast iron
The investigated situation is the abrasive wear of deep
drawing tools,which are usually made of nodular cast
iron.This material is characterid by a number of graphite
spheres,ranging in diameter from10to50m that are en-
clod in the metal.The average Vickers hardness of the ma-
terial is about340HV.
Single pass scratch experiments were executed on a pin-
on-disk tester,using a diamond indenter with a tip-radius
of25m.Experiments were carried out at loads between
0.17and1.3N,corresponding to a degree of penetration
0.15≤D p≤0.52.The rotational speed of the disk is about 200m/s.The geometry of the scratch and its surrounding
area is measured using an interference microscope.A typical
result is shown in Fig.4,where both the scratch and the car-
bon nodules are clearly visible.In this image it can be en
that both the groove and the side ridges are not constant in
size,and hence the value ofξis not constant over the mea-
sured scratch.It can be concluded that the wear process is
not stationary,which is a result of a combination of factors,
like the tested material which is inhomogeneous,the stiff-
上海英语培训
ness of the experimental t-up and the predominant wear
mechanism which is not necessarily stationary.
From a surface height measurement the visible carbon
nodules are neglected and the remaining intact profiles per-
pendicular to the wear scar are analyd.From each profile
the tilt is removed and the location and boundaries of the
wear scar are determined by calculating the deviation from
the mean line.This is illustrated in Fig.5,showing a scratched
surface as well as the boundary of the wear scar.In the
wear
Fig.5.Wear scar and
boundary.
Fig.6.Fraction of removed material as a function of the degree of penetra-
tion.
scar the groove and the side ridges are defined as the loca-
tions where the surface data has,respectively,negative and
positive values.Combining the results for each profile of the
surface gives the size of the groove and of the side ridges.
Subquently the value ofξis determined using Eq.(5).
The experimental results are shown in Fig.6,where the
fraction of removed material is plotted against the degree
of penetration.The plotted values are the average of three
measurements,with the error bars indicating the deviation.
The expected increa ofξwith increasing D p is visible until
knife什么意思D p=0.30.Above this,the degree of wear starts tofluctuate
heavily with increasing D p,while values obtained at the same
degree of penetration show a large deviation.At the con-
ditions a wear track as depicted in Fig.7is visible,which
explains the obtained values:at high values of D p the pre-
dominant wear mechanism is cutting,so the material from
the groove is removed by a chip.However,due to the duc-
tility of the material,the chips do not break off and con-
quently are not removed from the surface but remain next to
the track,resulting in an underestimation of the value ofξ.In
the following the results for D p≥0.35are neglected.
The dotted lines in Fig.8show the relation betweenξ
and D p for various heat treated ball bearing steels as exper-
imentally obtained by Kayaba et al.[13].Bad on this,the
degree of wear is expected to increa from0to a maximumindependenceday
value following an S-shaped curve,with the maximum value
depending on the hardness of the scratched material.
Such
Fig.7.Chips next to the wear groove.
M.A.Man et al./Wear258(2005)339–348
343
Fig.8.Corrected experimental results and results reported in literature. an S-curve can be described using various functions,like a
third order polynomial or a hyperbolic tangent.In this work
the latter is applied becau a tanh-function incorporates the
asymptotic behaviour of the curve.The dashed line in Fig.8
reprents the experimental results as shown in Fig.6,from
which a value ofξmax≈0.8can be estimated.Bad on this maximum and the constraining valueξ=0at D p=0the re-
maining degrees of freedom are obtained using a least squares
fitting procedure on the experimental data.The resulting re-
lation between degree of wear and degree of penetration is
given in Eq.(8)and is shown as the solid line in Fig.8:
ξ=0.4·tanh(12.3·D p−3.0)+0.4(8)
2.2.2.Theoretical extension to wear by paraboloidal shaped asperities
The experimental results reported before are obtained us-ing spherical shaped indenters,as paraboloidal or ellipsoidal shaped indenters are,to the author’s knowledge,not commer-cially available.A translation to ellipticity of the asperities is made by adjusting the value of the degree of penetration and by introducing the orientationθof the asperity with respect to the sliding direction x’.It is assumed that except its influence on the degree of penetration and hence onξ,the orientation has no additional effects on the wear volume(Fig.9).
The degree of penetration according to Fig.3was defined
in Eq.(7)as the ratio of the indentation depth and the
mi-
Fig.9.Elliptic contact spot:a x and a y denote the mi-minor and mi-major axis,respectively,and x the sliding
direction.
Fig.10.Groove width w as a function of orientationθ.
axis of the contact spot in sliding direction.The latter can be expresd in terms of the mi-major and mi-minor axes of the contact spot and the orientation of the asperity,repre-nted by the angleθbetween the sliding direction and the minor axis of the contact ellip:
a x =
a2x·a2y
a2x·sin2θ+a2y·cos2θ
(9) With this,Eq.(7)becomes
新gre考试流程D p=
d
a2x·a2y/(a2x·sin2θ+a2y·cos2θ)
(10)
The frontal area of the wear groove A g from Eq.(6)can be approximated by Eq.(11)(e also[1])in which d reprents the indentation depth and w the width of the wear track,which depends on the orientation and the major and minor axes of the contact area as shown in Fig.10:
A g≈2
3
·w·d+
d3
2·w
(11) 2.3.Results of the micro-level contact and wear model
In this paragraph some results of the developed model for the abrasive action of a sliding indenter in contact with a deformingflat are prented.Unless stated otherwi in the figures,the calculation parameters as listed in Table1are
Table1
Calculation parameters for the prented results
R*(m)50 E indenter(GPa)3400νindenter0.4 E cast iron(GPa)220νcast iron0.3 H cast iron(MPa)3334(=340HV) E*(GPa)228 F(N)5λ0.5θ(◦)30
