WEAR ELSEVIER
Wear
181183
(1995) 730742
Impact wear of multiplated
electrical
contacts
Peter A. Engel, Qian Yang Mechanical
Engineering Dept., State University of New York at Binghamton,
Binghamton,
NY 13902, USA
Received 29 April 1994; accepted 3 November 1994
Abstract Multiplated electrical contacts often undergo repeated dynamic loading. In the present study, a pivotal hammering impact wear tester was used to inflict wear scars on typical layered contact configurations. The wear life was observed to consist of three main stages: the plastic deformations stage; the zero wear stage; the measurable wear stage. Experimental observations of the wear behavior aided the formulation of a predictive engineering analysis method for impact wear life. Keywords:
Contact force; Composite hardness; Impact wear; Hardness test; Modulus of elasticity; Plastic deformation
1. Introduction
Wear due to repeated dynamic loading occurs, for example, in various electrical connectors designed for the computer and telecommunication industry. The surface materials used in these devices are typically multilayered (multiplated), and tend to plastically deform during the early contact life. It is vital to know their expected wear behavior, because removal of surface films (made of noble or seminoble metals, such as Au and PdNi alloys, respectively), drastically affects operational functions (electrical conduction) as well as structural integrity and corrosion resistance. Past studies of impact wear have been performed mainly for bulk materials [1,2]. A large class of applications involved sensitive but highstrength machine surfaces which, under impact, developed Hertz contact stresses in the elastic range. Under these conditions, two consecutive regions of wear life could typically be distinguished. The first zone of “zero wear” denotes macroscopically insignificant wear with a magnitude less than half the surface roughness. Following this, during the “measurable wear” part, wear scar formation promotes ever increasing conformance between the contacting pair. Repetitive impacting at constant momentum would thus tend to go on at diminishing contact stresses. Predictive mathematical solutions for the wear curves (h vs. N) of various onebody wear configurations (e.g. hard sphere impacting a soft plane) yield a gently rising graph in the loglog representation.
00431648/95/$09.50 0 1995 Elsevier Science S.A. All rights reserved SSDI 00431648(94)07105S
In the present study of the repetitive impacting of multilayered media, not two but three stages of wear life were evident. A first, initial stage (1
implied, hammer wear was negligible, satisfying the onebody wear condition. The impact wear testing apparatus is centered on electrically driven pivotal hammers [l], with adjustable
P.A. Engel
Q. Yang / Wear 181183
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manner (Fig. 1). A schematic of the device is shown in Fig. 2. A programmable real time computer generated the digital signal of electrical pulse, converted to an analogue signal by a D/A converter. After amplified by a coil driver, the signal would fire the hammer by moving the armature of an electromagnet. The system was based on an IBM mechanical printer. It could provide a stably repeated impulse at constant impact velocity during the test run. Impact force ranged between 10200 N (240 lbs). 2.2. Hammer The hammers were formed from IBM print hammers. An original flat rectangular striking face was outfitted with a steel ball of diameter D=O.8 or 1 mm (0.032 Because the or 0.040 in), and hardness R,, S60. hardness of the hammer is much higher than that of the specimen, we can consider the hammer as a nonwearing body relative to the specimen. In actuality, the wear of a hammer was negligible even after an accumulated lo9 cycles of impact. The equivalent hammer mass was 0.25 g, which is calculated from I/r? I is the moment of inertia about the pivot, and r the pivot to striking point distance.
Fig. 1. Photo of impact wear apparatus.
loading parameters (normal speed, repetition rate, striking face, etc.) The specimens had plating combinations of Au, Pd, PdNi, Ni, Cu, in the 0.130 ,um thickness range. The depth or volume of impact dents or wear scars were obtained by stylus profilometry; no repositioning was attempted. Optical and scanning electron microscopy was used to get closer information on wear surface behavior. The combined observational and analytical treatment attempted to create an engineering theory and method for impact wear analysis and design.
2.3. Specimens 2. Experimental details
The specimens used were multiplated circuit boards of typical surface roughness 6< 1 pm. Two particular sandwiches were used for this study. The first sandwich (designated III1 #l) had, from top to bottom, a 0.1 ,um (4 pin) soft Au layer, a 1.5 pm (60 (uin) PdNi
2.1. Ekperimental apparatus The impact wear tests employed a light pivotal hammer normally hitting the specimen in a repetitive
Armature
electromagnet real time computer
push
rod hammer
GPIB
specimen PC
Fig. 2. Schematic of impact wear apparatus.
force
transducer
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P.A. Engel, Q. Yang / Wear 181183
Table 1 Intrinsic and composite hardness of materials tested, from Ref. [5] Material
Cu (metal and pp) Ni 70Pd30Ni SOPd20Ni Soft Au Hard Au Fiberglass (z)
Poisson’s ratio
Hardness,
Young’s
H
(u)
(MPa)
modulus, E @Pa)
0.33 0.29 0.28 0.28 0.42 0.40 0.43
1225 2253 3919 3919 834.3 1958 460
119 207 220 220 68.9 68.9 7.1
(1995) 730742
load, based on knowledge of the intrinsic hardnesses (HJ, elastic properties (Ei, pi) and thickness (ti) of the constituent layers [3,4]. We note that our nomenclature counts layers i = 1n starting from the one above the substrate, increasing toward the top of the sandwich. The iterative process of computation hinges on two equations (Eq. (1) and Eq. (3)). Firstly, by a generalization based on Ref. [6], we write for the composite hardness:
(1) The blunt indenter
layer and a 10 pm (400 pin) Cu layer; the second sandwich (III1 #6) had a 1 pm (40 pin) soft Au layer, a 3.75 pm (150 pin) PdNi layer, a 2.5 pm (100 pin) Ni layer and a 10 pm (400 pin) Cu layer. Both were plated to a 25 pm (1000 pin) “peelapart” Cu layer, the latter in turn attached to a 1.9 mm thick segment of an epoxyglass printed circuit board. The intrinsic Vickers hardnesses of these platings, and the composite hardnesses of the sandwiches are shown in Table 1. 2.4. Impact wear tests The specimen was adhered directly on the top of a Kistler 9202 force transducer, and a laser displacement sensor was fixed above the hammer. Thus the force and velocity were monitored during the process. All specimens were cut from one large piece of board in order to keep uniformity. Wear curves were put together from wear tests running up to a certain cycle number; no repositioning was attempted. 2.5. Measurements A Tencor Instruments (Mountain View, CA) profilometer AlphaStep 200 was used to measure wear scars and a computer connection was provided, to compose 3D plots of the wear scars from parallel profiles, as shown in Fig. 3. Scanning electron micrography (SEM) was used for imaging the wear scar and analyzing its components. Figs. 4(a)4(c) are the images of wear scars for specimen III1 #6 impacted at V, = 1 m sl at impact cycles N=2000, 180 000 and 1 500 000 respectively. Figs. 5(a)5(d) show SEM component analysis of the III1 #6 specimens, at various spots and cycle number N during the wear history. 3. Plastic deformation 3.1. Static indentation The static composite hardness of a multilayered sandwich may be calculated quite accurately at a given
(Fig. 6) equation is adapted [7]
E tan p/Y= 6( 1  v)(2c/d,)3  4( 1 2~)
(2)
whence the distance of the plasticelastic c=d,/2{(3E
tan p/H+4(12v))/6(1
,)}I/3
boundary: (3)
where we substitute E and H as a composite Young modulus and composite hardness respectively; p = 22” for the Vickers indenter, and tan p=d,l(D2d,2)1n for the Meyer (spherical) indenter. The plastic strain E,,= l/c yields the compressed total layer thickness ~C7i=t(1  ?? ,). Assuming the compressive deformation of each layer to be inversely proportional to its intrinsic hardness, the loadcarrying area of each layer and of the substrate are then determined. The iterations are performed to reconcile Eqs. (1) and (3). 3.2. Dynamic indentation Dynamic hardness has been defined in several ways. Martel [8], considered a “dynamic hardness number” as the ratio of the kinetic energy of the indenter immediately before impact to the volume of the indentation; this ratio has the units of a stress. Shore [9] used the height of rebound as a measure of hardness, keeping the height of drop constant. We may assume that the mechanism involved in the dynamic indentation (i.e. impact) is essentially the same as that which occurs under static conditions, and that Young’s modulus for the specimen is essentially the same as for static conditions. The hardness (force per projected area of indentation), related to yield strength, has been observed to be higher [lo], however, at high speeds of indentation; hence our definition of dynamic hardness. Tabor [lo] divided quasistatic impact into four main stages. At first, the contact is deformed elastically, according to Hertz theory. The second stage occurs when the mean pressure exceeds l.lY. Some plastic deformation would take place. At higher energies of impact the deformation rapidly passes over to a condition of “full” plasticity (stage 3) and plastic deformation proceeds until all the kinetic energy of the indenter is consumed. Finally, a release of elastic stresses in
PA.
Fig. 3. 3D plot of a wear
Engel, Q. Yang / Wear 181183
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733
scar.
the indenter and in the indentation takes place, causing rebound (stage 4). When a comparatively hard ball strikes a massive flat specimen, we can neglect the elastic action of the first two stages [ll]. On the basis of energy analyses, the “mean yield pressure” (dynamic hardness) is given respectively (by Refs. [10,12]):
(4) (5) where the test values of (Yfor steel and aluminum lay between 0.44 and 0.47; and by [S]
(6) We shall define the dynamic f&Or: fd =pd/ps, where ps=4Plnd2 is d ue to the static force causing an indentation d, achieved through an indenter D; fd always exceeds unity. The dynamic factor has been experimentally found to have a larger value when the impact speed is higher or the material is softer. Refs. [lO,ll] attributed this to a viscous effect. The value of fd is usually determined by experiment as the ratio of the pressures when the indentations in both cases are of the same size. Table 2 shows some published data [lo].
Some of our tested values offd for multilayered sandwich are shown in Table 3. 3.3. The first impact We assume that all the initial kinetic energy is consumed as plastic and elastic deformation when the impact indenter is at its deepest position before rebound, 1 ,mG=p,W,
(7)
where W, is the apparent paraboloidal volume of indentation, which is expressed as W, = nd4/3W, proving Eq. (6). Rearranging, we get (d/D)“p,  16mV,2/rD3 = 0
(8)
Using static indentation theory (i.e. the method of Section 3.1), and curve fitting, we can express ps (i.e. Zf, of Section 3.1) as a polynomial function of d/D for a specific D: ps =f(dlD)
(9)
Noting that pd=fdps, and substituting it into Eq. (S), the latter will become a polynomial equation of d/D. In our practical situations, d/D ranges between 0.08 and 0.46, V, between 0.1 and 2 m sl, and m between 0.20.8 g; for these values, we can usually find a reasonable root, yielding d. Substituting back into Eq. (9) ps is calculated, resulting in pd as well.
734
PA
Engel, Q. Yang 1 Wear 181183
(1995) 730742
(a)
Fig. 4.
(b)
xmtinued)
P.A. Engel, Q. Yang I Wear 181183
Fig. 4. SEM images of wear scars of III1 #6 specimen, at various stages of wear life (V,=l (c) at N=l 500 000.
When the indenter rebounds, the whole process is assumed elastic, governed by Hertz theory. The residual crater radius R and depth h can be obtained [lo]: R=
1 2 
D
37CPd
(10)
2dE
R being negative for a seat; the indentation
depth is
then h = d218R
(11)
3.4. The second and following impacts
Assume that past the first impact, the kinetic energy is also absorbed in local deformation, plastically and elastically, at the peak of indentation. However, the deformation is made in the dent left by previous impacts, rather than on the original flat surface. So we have a formula modified from Eq. (6)
(12) where d’ and R’ represent the projected indentation diameter and residual crater radius respectively, left by previous impact(s), R’ being negative for a seat. The same calculation as discussed above, expresses pS
13.5
(1995) 730742
m sl):
(a) at [email protected];
(b) at N=180
ooo;
as the polynomial function of d/D; we substitutep, =fdpS into Eq. (12), then solve the polynomial equation for d/D; whence we get d and pa, and finally R and h from Eqs. (10) and (11) respectively. An example with computational detail is given in Appendix B. 3.5. The length of plastic deformation (“initial wear”) region Ni The amount of incremental plastic deformation can be seen to be less and less with each consecutive impact [13]. So, at some point, the plastic deformation between two consecutive impacts becomes negligible comparing it to the total accumulated plastic deformation; let’s say their ratio is 1%. The impact cycle Ni at this point can be considered as the length of the plastic deformation (“initial wear”) period; now the dent geometry has the parameters Ri and hi. Further impacts are largely considered elastic. We note that no material removal (wear) has taken place up to the point Ni in wear history; the resulting dent is merely plastic deformation.
4. Zero impact wear stage
The plastic deformation rate, by definition, is very low at the end of the initial wear stage. The impacted
136
Fig. 5.
P.A. Engel, Q. Yang / Wear 181183
(1995) 730742
P.A. Engel, Q. Yang / Wear 181183
(1995) 730742
(d) Fig. at N
3DS 500
xment analysis of III1 #6 specimen: (a) at N= 180 000, central cracks; (d) at N= 1 500 000, nonworn area.
darken
area;
(b) at N= 1 500 000, cent] ral pitted
spots;
(cl
738
P.A. Engel, Q. Yang I Wear 181183
(1995) 730742
perimentally as 2000, and Ni < 2000, we may take the approximation: No = 2000
(13)
Because of imperfections and hysteresis, minute plastic deformations of the materials continue occurring in each impact. Therefore perfect strain reversibility is not expected to hold during the zero wear stage, and so at N,, the depth of the impact crater has been seen to have increased about 10% with respect to that at Ni. Thus, while dM is not changing much, we get h, l.lhi
Fig. 6. Geometrical
5. Measurable wear stage
relationships of Vickers indentation.
Table 2 Dynamic factors fd [lo] of some bulk metals (with the condition of 0.5 cm diameter of ball indenter drop from 300 cm) Metal
fd
Steel Brass Alalloy Lead Indium
1.28 1.32 1.36 1.58 5.0
(14)
In an elastically stressed machine contact the wear scar tends to evolve toward conformance with the mating surface. In a onebody impact wear process, the “softer” partner progressively wears toward the curvature of the nonwearing “harder” partner. A greater resistance to wear is meant here by hardness I$ it is proportional to y: H=3Y. By a geometric approximation, the volume of a paraboloidal wear crater W can be expressed as W=_~
Table 3 Dynamic factors fd of multilayered materials tested (with 1 mm diameter of spherical indenter of equivalent mass 0.25 g) Material
Velocity (vi, m s‘)
III1 III1 III1 III1
0.65 1.00 0.65 1.00
#l #l #6 #6
fd 1.6 1.8 1.5 1.67
site winds up with a dent diameter dNi at Ni. The mean flow stress at this point is a,=4P,/m1,2. After this point in wear life, a nowear period has been observed for both bulk [l] and, from the present study, multilayered metallic materials, as well. This “induction period” before the appearance of significant wear after No will, by reapplying Engel’s terminology, be called the zero impact wear stage, Fig. 8. We shall next deduce the length of this second stage, stretching from N;N,. The length of the zero wear stage, N,N,, is postulated to be fatigue dependent, and as such, we may borrow an expression from Ref. [l] valid for bulk impact wear: (NNi)ag = constant, where the constant may be taken at a reference cycle NC, producing the term NCaCg.Since a= constant = a, throughout the zero wear regime, a substitution of a, = a, will produce No  Ni =N,, and therefore N,=N,+ Ni. However, since N, is taken ex
(15)
In Ref. [l] it was argued that the optimal wearpath for Hertzian impacts requires that the crater outline coincide with the current peak contact dimensions. Then, from Hertz impact of bulk materials we get [l]: d=2K,(1+p)us
(16)
where &= 0.9406(E,‘E:mD2)1’5
(17)
(18) and then the nondimensional defined:
curvature parameter
is
(19) Now, the wear volume Eq. (15) is rewritten:
P3) The contact stress dependence of the wear mechanism is expressed in the form W=f(N,
a) =kNu’
(21)
where k is a constant, u is the peak Hertz stress.From of Eq. (21), introducing an empirical factor g, we get:
P.A. Engel, Q. Yang / Wear 181183
139
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2 OOE005
1
$
: 63E005
j :
6 OOE 006
4 CCE
006
,/’
1
,/I
4 OOE006
/ ’
OOOE+OOO
&
(b) 2 OOE005
I 60E005
i
OOE005
I
1
j : 1 20ELOO: : c 8 OOEL006
4 OOE006
Fig. 7. Comparisons m SC’; (b) III1 #l,
dW=
of analytical mode1 with experimental V, = 1 m sl; (c) III1 #6, V, =0.65
results: steel hammer of m = 0.25 g, D = 1 mm was used: m SC’; (d) III1 #6, V, = 1 m SC’.
where g is characteristic of the wear process, and as such, should be determined experimentally.By Hertz relationships, (T is of the form +p)“S
(a) III1 #l,
V, = 0.65
results, subject to the initial condition existing at the end of the zero wear stage:
!$N+ggINdo= $dN+gFdo (22)
a=K,(l
4>,‘:
N=N,,,
h=h,
(26)
The nondimensional curvature p0 at the zero wear limit can be obtained from known ho by solving the equation deduced from Hertzian contact theory:
(23)
ho= CSp,(l+p0)4’5
(24)
where C, is the “stress severity factor” for spherical geometry:
(27)
where KI =O.l907(E:l+rD
‘)l”
Combining Eqs. (1%23), an ordinary equation dealing with N and p:
53P(1+9g) +_ 5PQ+p)
cw N
differential
(25)
C, = 0.77( V$z2E, ‘R; ‘)lA The relationship from Eq. (25)
(28)
between N and p is finally obtained
740
PA.
Engel, Q. Yang I Wear 181183
zero wear stage
Fig. 8. Schematic
N+lo
of impact
wear
history.
WJfJY
(3 l+p
A+B
l+Po
where A=l,
B= ; (1+9g)
The physical depth of the wear scar is calculated from p similar to Eq. (27): h= C,p(l+p)4’5
(31)
6. Results and discussion The preponderance of initial plastic deformations fundamentally sets apart the impact wear phenomena of multiplated electrical contacts from those of precision machine surfaces. In the present work the wear history of the former was seen to be divisible into three stages: the initial (plastic deformation) stage, the zero wear stage and the measurable wear stage. The wear accrued in the measurable wear stage is superimposed on top of the plastic deformation derived from the first, initial stage. These stages were characterized by the profilometrically measured shapes of wear scars, and the microscopically observed textures and debris seen on their surfaces. Figs. 7(a)7(d) plotted of four experimental wear histories demonstrate the three stages of
(1995) 730742
wear formation. The material configurations used are described in Section 2.3. The impact wear theory emerging for both electrical and machine contacts is essentially a geometric one. For example, in the present study, spherical, negligibly wearing steel impact hammer faces induce a wear scar which tends to gradually conform to the impactor with the added cycles. Fig. 3 is a computer graphics rendition of an evolving wear scar, the paraboloidal nature of which may represented by its radius of curvature and crater depth. This makes the results amenable to analysis: by dynamic plasticity relations [8121 in the first stage, and by Engel’s Hertzian wear theory [1,2] in the latter two wearhistory stages. Analysis of the plastic deformation range is aided by static indentation theory of multilayer contacts, developed through Refs. [5,4,3] in chronological order. This general theory has been experimentally well substantiated, and applies to practically all indenter shapes. Its basic ingredients are: (a) the generalized composite hardness Eq. (l), originally applied to twomaterial Vickers indentations [6]; (b) the distance to the plasticelastic zone, involving blunt indenters [7]. Experimental wear curves were obtained (see Fig. 7) for two types of multiplated sandwiches, designated III1 #l and III1 #6. In these tests, the impact velocity was varied from V, = 0.65 m SC’ (26 in SC’) to V,=l m s’ (40 in sl). The new analytical formulation procedures were also applied to the parameters of these test runs, thus permitting comparison of theory vs experiment. The first, plastic deformation stage, is short, of the order of Ni= 1020, but the depth of the dent quite rapidly increases. During the zero wear stage a very slight increase in the scar depth (perhaps amounting to 10%) indicates further small hysteretic deformation, but no wear debris is generated yet. The length of this stage is found to be of the order of No=2000 cycles, from considerations of composite hardness H, = 3Y, surrounding Eq. (13); this follows from analogy with impact wear theory of bulk elastic materials. The experimental values of No (Figs. 7(a)7(d)) quite well confirm this value. For the third, measurable wear stage, the wear constant g (see Eqs. (22) and (25)) can be derived from experiments. The flatter the wear curve, the greater the value of g found by fitting the curve. Figs. 7(a)7(d) indicate that g= 1 is a reasonable value for most specimens, but depending on conservatism, the range 0.51gl2 serves well for design [14], in general. A large number of SEM readings were taken of wear scars at various stages (Figs. 4(a)4(c). Fig. 4(a) showed that at the zero wear limit, No= 2000, only plastic indentation existed. Only the unbroken top Au film was seen on the surface. At N=180 000, cracks were visible on the wear scar, but component analysis (Fig. 5(a)) showed that Au alone was still the dominant
P4. Engel, Q. Yang / Wear 181183
element found on the surface. At N= 1 500 000 cycles, the cracks were extended, and some flakes and pitted spots appeared in the central area of the scar. Component analysis indicated that the pitted spots had PdNi (Fig. 5(b)), and even Cu protruded through the cracks caused by the fracture of the intermediate hard layer (PdNi), (Fig. 5(c)). In the meantime, a thin Au film stayed on the surface. This supports the existence of an upsurgence phenomenon [5]. The component spectra for wear scars (Figs. 5(a)5(c)) should be compared to the original, unworn surface spectrum of Fig. 5(d), showing a sole Au peak.
7. Conclusions The impact wear development of plastically deformed materials can be divided into three stages: plastic deformation (or initial wear), zero wear and measurable wear. Only the last stage yields wear debris, i.e. leading to removal of mass. The concept of dynamic hardness combined with the general theory of static indentation of multilayered materials was used for predicting deformation in the initial wear stage. The semiempirical zero impact wear relation for bulk materials was extended to apply to multilayer specimens, with known composite hardness properties. Geometric measurable wear relations for bulk materials were also useful to describe the ensuing wear range for multiplated contacts.
Acknowledgement The assistance of Z. Zhao, D. Rattazzi and S. Lin in experimental data collection and handling is gratefully acknowledged.
(1995) 730742
741
fd
Dynamic factor Equivalent hardness Composite hardness K H,, Hi Intrinsic hardness of substrate, and ith layer of material respectively h Depth of the wear crater Depth of the wear crater at the end of zero ho wear stage Depth of the wear crater at the end of initial hi wear stage Mass moment of inertia Vickers indentation depth Equivalent mass of the indenter/impactor Number of impact cycles Number of impact cycles at the end of zero wear Number of impact cycles at the end of initial wear Number of layers above the substrate : Applied load on indenter Peak impact force p, Dynamic indentation pressure Pd Static indentation pressure (equivalent to the PS hardness) R Radius of residual impact crater t Thickness of plated layers before plastic deformation, t = Xti Thickness of the ith layer before plastic deti formation Impact velocity Wear scar volume Yield stress Indenter angle (Vickers: p = 22”) Plastic strain Equivalent (bulk) Poisson’s ratio of the material Poisson’s ratio of the ith layer material Peak maximum contact pressure Thickness of the ith layer after plastic deformation H
Appendix A: Nomenclature A A,, Ai
; di
d
E Ei e
Projected area of indentation Projected loadcarrying area of substrate and the ith layer, respectively Plasticelastic boundary Diameter of spherical indenter Vickers, projected indentation diagonal of the ith layer; Meyer’s, projected indentation diameter of the ith layer Vickers, projected superficial indentation diagonal; Meyer’s, projected superficial indentation diameter Equivalent (bulk) Young’s modulus of the material Young’s modulus of the ith layer material Coefficient of restitution
Appendix B: Example of impact deformation calculation in initial wear stage Take specimen III1 #6 impacting at velocity V, = 0.65 m s’ as example: Using static indentation theory (the method of Ref. [3], described in Section 3.1), and curve fitting, we can express ps = H,: ps = 
7933(d/D)3 + 11869(d/O)’
 4976(d/D) + 1292 (MPa)
(RI)
Noting that pd =fd ps = 1.5 ps, m = 0.25 g, D = 1 mm, VI = 0.65 m SK’, and substituting into Eq. (S), the latter will become a polynomial equation of d/D:
742
P.A. Engel, Q. Yang I Wear 181183
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References  11899.5(~f/D)~+ 17803.5(d/D)6  7464(~UD)~ + 1938(d/D)”  0.538 = 0
(B2)
In our practical situations, d/D ranges between 0.08 and 0.46; we solve Eq. (B2) in this range, and obtain d/D =0.1458. Substituting back into Eq. (Bl), p,=794
(MPa)
and pd= 1.5p,= 1191 (MPa)
(B3)
By the method of Ref. [4], we calculated the equivalent Young’s modulus E 30 GPa, substituting this value into Eq. (lo), we can then obtain the residual crater radius R and depth h: R=
I21 131
[41
PI
PI [71
1 2 D
Ill
= 3nPd

1.2 mm
(B4)
PI
2dE 191 [101 WI
and h= d21SR=2.2 pm
(W
Let R’= R, d’=d and pd = 1.5p,, where ps is in the form of Eq. (Bl), and substitute into Eq. (12). Making Eq. (12) a polynomial equation of d/D having the form of Eq. (B2), and by using similar steps as above, we can obtain d, R and h of the second impact, and of consecutive impacts. The analytical curve of Fig. 7(c) for the region 1
WI
[I31
u41
P.A. Engel, Impact Wear of MateriaLr, Elsevier, Amsterdam, 1976. P.A. Engel, Impact Wear, in ASM Metals Handbook Friction, Lubrication and Wear Technology. Sktion III, Wear, Vol. 18, 1992, pp. 263270. P.A. Engel and Q. Yang, General microhardness indentation theory for multilayer contacts, ASME Water Ann. Meet., Book PED Vol. 67, TRIB Vol. 4, 1993, pp. 912. P.A. Engel, Q. Yang and K.R. Wu, Microhardness evaluation for multiplated electrical contacts, Proc. Eumtrib ‘93, 6th Int. Congr. T&&l., Budapest, Hungary, Vol. 3, 1993, pp. 268273. P.A. Engel, E.Y. Hsue and R.G. Bayer, Hardness, friction and wear in multiplated electrical contacts, Wear, 162I& (1993) 538551. B. Jonsson and S. Hogmark, Hardness measurements of thin tilms, ThinSolid Film, 181 (1984) 257269. K.L. Johnson, Contact Mechanics, Cambridge University Press, 1986. R. Martel, Sur la mesure de la durete des metaux, Commission des M&ho&s d’Essai des Matkaux de Construction,, Section A (M&au), Paris, 3 (1895) 261277. J. Shore, Iron St. Inst., 98 (1918) 59. D. Tabor, The Hardness of Metals, Clarendon, Oxford, 1951. C.H. Mok and J. [email protected], The behavior of metals at elevated temperatures under impact with a bouncing ball, Znt. J. Mech. Sci., 6 (1964) 161. C.H. Mok and J. D&y, The dynamic stressstrain relation of metals as determined from impact tests with a hard ball, ht. J. Mech. Sci., 7 (1965) 355371. K. Wellinger and H. Breckel, Kenngroessen und Verschleiss beim Stoss Metallischer Werkstoffe, Wear, 13 (1969) 257281 (in German). H.L. Milligan, B.M. Johnson and P.A. Engel, Wear analysis of BjorkShiley Delrin tilting disc heart valves, ASTM/. Testing Evaluation, 22 (5) (1994) 476486.