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Effect of rhenium coatings on the mechanical properties of molybdenum wires
ELSEVIER
Surface and Coatings Technology 72 (1995) 43-50
Effect of rhenium coatings on the mechanical properties of molybdenum wires A.G. Kolmakov *, V.N. Geminov *, G.V. Vstovsky, V.F. Terent'ev *, V.T. Zabolotny, E.E. Starostin A.A. Baikov Institute of Metallurgy, Russian Academy of Sciences, Leninsky Prospect 49, I 17911 Moscow, Russian Federation Received 24 September 1993; accepted in final form 4 June 1994
Abstract The dependence of the mechanical properties of rhenium-coated, commercially pure molybdenum wires 1 mm in diameter on the rhenium coating thickness w = 0.4-4.2 p.m was studied. The coatings were deposited by vacuum electron beam evaporation with simultaneous Ar ion irradiation (ion-beam-assisted deposition method). The increases in elasticity limit or(e) and yield stress a(0.2%) due to the coating were found to be about 28% and 12% in comparison with uncoated wire. Maximal property increments occur when the ratio of coating thickness to wire diameter is w/d = 0.001-0.002. Fractographic features were investigated by means of multifractal analysis.
Keywords: Molybdenum; Strengthening; Surface effects; Rhenium coatings
1. Introduction The general deformation kinetics of metals is substantially influenced by the state and behaviour of thin surface layers [ 1-4]. The evolution of dislocation structure begins in these layers before the substrate region. At the microplastic stage of specimen deformation the surface layer deforms in a plastic manner and this deformation-hardened layer acts as a barrier for dislocation glide in the main volume of metal; macroscopic yielding takes place as a result of the breakage of innervolume dislocation pile-ups through this layer [2]. Therefore modification of the surface layer behaviour by means of alloying or coating deposition may lead to alteration of the macroplastic characteristics of the metal [1,3,5 7]. The purpose of this investigation was to reveal the effect of coating thickness on the mechanical properties of rhenium-coated molybdenum wires.
2. Materials and techniques 2.1. Materials The investigation was carried out on commerically pure molybdenum wires 1 m m in diameter in the * Corresponding authors. 0257-8972/95/$09.50 © 1995 ElsevierScience S.A. All rights reserved SSDI 0257-8972(94)02329-0
as-drawn condition. The chemical analysis of the Mo wire is given in Table 1. After the removal of drawing defects with emery paper the specimens were electropolished in a solution of 95% H e S O 4 + 5% ethanol; the total thickness of the removed layer was 20 25 p.m. The coatings were deposited by vacuum electron beam evaporation with simultaneous Ar ion irradiation (ionbeam assisted deposition (IBAD) method). The treatment conditions (temperature and ion and atom beam energies) were optimized for the predomination of mixing during the radiation-stimulated diffusion and for the creation of metastable solid solutions a few nanometres thick over the coating-matrix interface. The specimen temperature during the treatment did not exceed 80 °C. The coating thickness was in the range 0.4-4.2 p.m.
2.2. Mechanical testing The mechanical properties of the wires were determined by tensile testing specimens 1 m m in diameter and 50 m m in active length with an initial strain rate of 3.3 × 10 -3 s 1 on an Instron T T - D M machine. Scanning electron microscopy (SEMi was used for fractographic analysis. Conversion and normalization of the elongation [8] were carried out. Direct comparison of the natural
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A.G. Kolmakov et al./Surface and Coatings Technology 72 (1995) 43 50
Table 1 ,Chemical analysis of molybdenum wires Element
C
N
S
Ti
Ni
Fe
AI
Cu
Cr
Mn
Mg
Mo
Amount (mass%)
0.025
0.005
0.001
0.16
0.02
0.012
0.008
0.005
0.014
0.0025
0.0025
Bal.
elongation Al/l with the length-to-diameter ratio l/d for specimens of different length does not give enough useful information or even gives erroneous results. However, it is possible to use the standard lid ratios instead of nonstandard data. The most convenient method is the comparison of two tensile diagrams for specimens with different lid irrespective of specimen sizes. This method is based on the following obvious assumptions. (1) The neck (the deformation instability zone) does not depend on the specimen length, i.e. lid or A(i)= const.; Ud is invariant. (2) The total specimen length increment A is the sum of the uniformly elastic and necking length increments, i.e. A = A(e) + A(i). (3) The ratio of elastic length increments of two specimens is proportional to their length ratio, i.e. A(el )/A(e2) = l( 1 )/l(2). We can deduce the universal formula connecting elongations of three specimens with different length-todiameter ratios l/d = m, n(1) and n(2) as 3(m) =
3(1) [n(2)/m - 1 ] - 6(2) [n(2)/m -- n(2)/n( 1 )] n(2)/n(1)-
1
The experimental ratios n(1) and n(2) are selected arbitrarily; from tensile diagrams we have 6 ( 1 ) = A(1)/I(1) and 3 ( 2 ) = A(2)/1(2); 6(m) is calculated for the standard ratio m = lid = 5 or m = lid = 10. 2.3. Multifractal analysis Fractal geometry, despite its very short history, turns out to be extremely effective for searching for new ways of describing, forecasting the behaviour, etc. of objects under investigation in various branches of science [e.g. 9-12]. However, it is now well known that knowledge of only one fractal dimension is not sufficient for a detailed description of the self-similarity of the natural and numerous model fractal structures. A multifractal formalism (MF) [13,14] provides more opportunities for such a description. MF, being one of the new branches of statistical physics, enables to carry out analyses of the structures of complex systems, their evolution and measurement processes on them. Many modern alloys, composite materials, nanocrystalline materials, etc. have supercomplicated structures and their adequate description demands a significant revision of the conventional approaches in materials science. In particular, the latter provide no means for quantitative evaluation of the complexity and ordering of material
structures. Some progress in this direction can be achieved using MF. M F could also find in the future an effective application in materials science for the quantitative analysis of structures and their dynamic evolution, surface relief, surface energy, etc. In this work M F was used to evaluate the distinctions between fracture surfaces quantitatively rather than by eye. The authors do not know of any analogous works apart from the rather artificial Williford fracture model for AISI 4340 steel [15], which is interesting nevetheless. The multifractal description is based on the generation (in one way or another) of a measure due to the partition of the space embedding the object under consideration into boxes, the object being called a measure support. An investigation of the scaling properties of the measure correlation function (under some assumptions about the scaling of every measure) enables one to ascribe to the object some statistical quantities to characterize it and to compare it with other similar ones, which provides a rather subtle identification [16 19]. Consider some strange (irregular, porous, rough, etc.) object embedded in euclidean space and divide it into N boxes of sizes I/(i) <~ l, i = 1. . . . . N, 1 being a characteristic size. Such a partition enables one to ascribe to the boxes their measures ("weights") according to the nature of the object. For example, if one studies a fractal aggregate of overall mass M, the measures may be the parts of the mass in the boxes, p(i) = m(i)/M, re(i) being the mass of the ith box [ 18]. If one investigates a strange attractor of some dynamical system, then the measures may be constructed using the numbers of times (n(i)) the trajectory in the phase space passes through each box during some sufficiently long period of time: p(i) = n(i)/Z~=ln(i). The distributed square on the plane [19,20], normalized Fourier spectra [21,22], fracture energy parts [15] and other continuous and discrete distributions can be used to generate the measure. The latter examples bear witness that the multifractal description based on a quite general concept of measure is very flexible. Avoiding the mathematical details, the multifractal formalism (MF) is as follows. For the generated (in one way or another) measure p(i) a partition function can be calculated as F(q, z, l ) =
p(i) q i=a l(i) ~
(1)
where the sum is over the boxes with non-zero measure (as everywhere below as well) and q and r are real numbers. In the case of singular behaviour of the
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A.G. Kolmakov et aL/Surface and Coatings Technology 72 (1995) 43 50
measure, i.e. p(i)oc[l(i)] ~,
tively. For the uniform measure one has e>0
I--*0,
(2)
it can be shown [13,14,23] that there exists a unique function r(q) such that the function F ( q , z ( q ) , l ~ O ) is finite. Given q, for ~ ' > r(q) or z ' < z(q), F(q, ~', l--,O) is infinite or zero respectively. The equality F(q, r(q), l ~ 0 ) = 1 gives the definition of fractal dimension in the case of equiboxed partition, l(i)= I, and uniform measure, p(i) = 1/N(l), i = 1. . . . . N(1), N ( l ) being the number of boxes covering the support, as log[N(/)] D = lim i~o log(i/l)
r q- 1
and one can set for the arbitrary partition and measure also F(q, z(q), l--, O} = 1
(3)
For a generalized correlation function z(q) one has N
z ( q ) = ~ p(i)qocY (°),
(4a)
l~O
i-1
In [z(q)] r(q) = l i r a l=o In(l)
(4b)
Thus, by constructing an appropriate measure, one can ascribe to the object under consideration some real function z(q) uniquely. The sum over the boxes in (4a) can be replaced by an integration over the measure singularity exponents (see Eq. (2)) p(i) q o(L l(i)~q: z(q): fd~[pte)l
m'W],
l--,0
(5)
where p(c~)l-ml de is the probability that an arbitrarily chosen value ~' is between e and e + de; p(e) is a nonsingular smooth function. Thus the first interpretation of M F is such that the measure of support is modelled by a collection of interwoven sets of singularities of strength e, each having its own dimension f(e) [13]. The dependence f(e) is called a spectrum of singularities or an f(e) spectrum. In the limit l--.0 the integral value (5) is determined by such an e that qe - f(c0 = min; then z(e) and f(e) are related by the Legendre transform z(q) = qe - . f ( e ) ,
e -
dr dq
(6)
Owing to the normalization condition E~=~p(i)= 1 and Eqs. (4), r( 1) = 0, which can be expressed explicitly as z(q) = (q -- 1 )D(q)
(7)
It can be shown that D(q) are the so-called Renyi dimensions (entropies) and D(0) >~ D(1) ~> D(2) are the fractal, information and correlation dimensions respec-
D(q) = D(1) = D(0) = e(max) = e(min) = f(e),
(8) r(q) = ( q - - 1)D(1) The quantity ~ can be interpreted as an average over an ensemble of sets of isosingularities [ 19], i.e. e - dz dq -
f
z(q)
= (e')
(9)
and f ( ( c ( ) ) as a fractal dimension of the set that best approximates z(q) for corresponding q. Thus these quantities can be considered as the thermodynamic quantities in the canonical ensemble and this is another interpretation of MF. Here we have used the practical algorithm proposed in Ref. [24]. The 64 x 64 gm 2 near-surface and internal fracture regions were divided into 64 x 64 square boxes, each of which was marked by 1 if it was located in the domain of the fracture surface (almost perpendicular to the wire axis) and by 0 otherwise. This initial 64 x 64 partition was used to produce eight more rough partitions by integrating the "atomic" boxes into larger boxes of sizes l(k) x l(k), l(k) = 4, 6, 8, 10, 12, 16, 21, 32, k = l . . . . . 8. For each such partition the measure was built up simply by summing the unities in each box and dividing this sum by the overall sum of unities over the photograph. The approximation of the dependences of lg[z(q)] on lg[l(k)] for each given q • [ - 3 0 , 40] by the least-squares method (the correlation coefficients were always greater than 0.99) produced the slope r(q), which was used to calculate the multifractal spectra f(e) and the Renyi dimensions D(q) via Eqs. (6) and (7). These calculations were conceived to make clear the possibility of distinguishing the fracture surfaces quantitatively by exactly the same computer algorithm rather than having to develop a method of exact evaluation of fractal characteristics. Arguments can easily be put forward [24,25] to interpret DD = D( 1 ) - D(40) as a quantitative measure of the order of fracture surfaces and f ( e ( q = 40)) - - f ( 4 0 ) as a measure of the homogeneity of distribution. Together these quantities can be considered as characteristics of the complexity of the fracture surface structure. The calculations were carried out on a PC/AT-286/287 "WYSE" computer in Turbo-Pascal 6.0 using "extended" real numbers, which allowed us to use q in the range [ - 3 0 , 4 0 ] . Nevertheless, one obtained value o f f ( 4 0 ) was small and negative. Since f ( e ( q ) ) must be non-negative for any q, we can consider the small negative value as an estimation of the calculation accuracy and the corresponding .1"(40) is taken to be zero.
3. Results A summary of the mechanical properties as functions of coating thickness is presented in Table 2 and Fig. 1.
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A. G. Kolmakov et aL/Surface and Coatings Technology 72 (1995) 43 50
Table 2 Tensile properties of molybdenum wires Characteristic
Specimen Uncoated
a(e) (MPa) a(0.2%) (MPa) UTS (MPa)
With coating thickness w (Ixm)
810 1213 1460
,~(5) (%) 5(10) (%)
(%)
0.4
0.8
2.4
3.2
4.2
983 1290 1441
1010 1027 1015 1033 1307 1333 1327 1355 1445 1485 1492 1484 1.6-2 6-8 46-53
200 150
2
r,
~100 ~o 4
I ",--,..~-~ 1 -50 m
2
3
I 4
3 I 5
W (Re),am
Fig. 1. Changes in tensile properties of molybdenum wires: 1, elasticity limit a(e); 2, yield stress a(0.2%), 3, UTS; w is the rhenium coating thickness.
Along with the original properties - - elasticity limit a(e), yield strength a(0.2%), ultimate tensile strength (UTS), area reduction and elongation - - for the investigated length-to-diameter ratio of 50, i.e. 6(50), conversion to the standard value 6(10) was carried out [-8]. M i c r o p h o t o g r a p h s of the fracture patterns of wires are shown in Figs. 2-6. The multifractal characteristics for the investigated areas of fracture surfaces are given in Table 3. O n e particular case, the change in correlation dimension D(2) with coating thickness w, is shown in Fig. 7. The correlation between the relative increments of elasticity limit a(e) and yield stress a(0.2%) and some M F characteristics is shown in Fig. 8. The character of changes in uniformity f ( 4 0 ) and hidden periodicity D D = D(1) - D(40) of the wire fracture surfaces of near-surface layers in relation to the presence and thickness of coatings as well as to the main volume fracture surface is shown in Fig. 9; see also Ref. [ 2 5 ] .
Fig. 2. General view of wire specimens: (a) uncoated; (b) with rhenium coating 0.4 ~tm thick; (c) with rhenium coating 3.2 lam thick.
4. Discussion The increase in plasticity (elongation 6 and area reduction ~b) was shown to be negligible; no appearance of a physical yield point was established, a(e) rises by
Fig. 3. Neck region of coated wire specimen after fracture.
A.G. Kolmakov et aL/Surface and Coatings Technology 72 (1995) 43 50
47
201~m I Fig. 6. Fragment of inner-side fracture pattern for uncoated specimen. Table 3 Some multifractal characteristics of fracture surfaces Characteristic
Coating thickness w (~tm) 0.4
0
D(0) =.f(max) ~(0) D(1)=~(I) = f(1) D(2) ~(2) f(2) D(40) ~(40) f(40)
1.94123 1.97419 2.01693 2.02177 1.88251 1.93930 1.84388 1.91810 1.81144 1.90079 1.77901 1.88348 1.61599 1.77926 1.57538 1.73931 -0.00847 0.18128 1 . 4 0 9 3 6 1.33244
DD=D(1)--D(40)
1.96
3.2
Internal volume
1.96775 2.00285 1.94142 1.92461 1.91053 1.89646 1.80206 1.76684 0.39363 1.00156
1.97799 2.00703 1.95597 1.94157 1.92937 1.91717 1.83859 1.80846 0.63323 0.99242
n
Internal v o l u m e s .
Fig. 4. Fracture surface of near-surface layer of wire specimens: (a) uncoated; (b) with rhenium coating 0.4 lam thick; (c) with rhenium coating 3.2 ~tm thick.
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#
1.92 v
El 1.88
1.84( 0
I
I
1
2 W (Re), ~m
Fig. 7. Dependence of correlation dimension D(2) thickness w.
Fig. 5. Fracture surface of inner volume of wire specimen.
on
coating
28%, ~r(0.2%) by 12% and UTS only slightly. These results are in accordance with Kramer's work [6,7], where a markedly higher rise in ~(e) in comparison with a(0.2%) and UTS was found for Ti-6A1-4V additionally alloyed with Cr and Ni over the surface.
48
A. G. Kolmakov et al./Surface and Coatings Technology 72 (1995) 43 50
1.2
. o
(0.2%)
(~ (e) zx
A
~1.1
Pi
1.0
I 1.0
1.1
1.2
1.3
A~
Fig. 8. Correlation between relative increases in elasticity limit a(e) and yield strength a(0.2%) and some multifractal characteristics: D, AD(40); A, Act(40).
[]
internal
volume
0.6-
~0.4 -
OW=3.21.tm
N--
0.2 -
~W=0.4gm
~ 0.10
=
0
1
I
I
0.15
0.20
DD
.
t
m
1" 0 - . 0.25
Fig. 9. Changes in uniformity f(40) and hidden structure periodicity DD of wire fracture surfaces of near-surface layers in relation to presence and thickness of Re coating.
Very satisfactory adhesion properties of coatings were achieved: no delamination occurred and visible damage was detected only in the vicinity of the border of the fracture surface (Fig. 2). The fracture path of wires is normal to the tensile axis; the specific fracture pictures through the neck (Fig. 2) and longitudinal section (Fig. 3) show evidence of intergranular fracture. Such a mechanism is typical for Mo and its alloys in the temperature interval from 250 to 500 K and is analysed in detail in Refs. [26,27]. Crack-like circumferential patterns on the specimen surface are revealed in the vicinity of the neck both with and without the coating (Fig. 2). The dimensions of the crack-like fragments diminish and their number increases for thicker coatings (in the examined range of 0.4-
4.2 gm). The appearance of the crack-like relief for thickcoated specimens is nearly the same as for uncoated specimens. We consider the crack-like relief existence in the neck area as evidence of the initiation of surface damage leading to fracture. The distinction between deformation patterns in the near-surface and innervolume regions is established for both uncoated and coated specimens. The fracture surface of uncoated specimens has a distinctive outer layer and its deformation and fracture patterns are very different in comparison with the inner volume (Figs. 2(a), 3 and 5). The side view of the inner longitudinal fracture of the near-surface interface layer is shown in Fig. 6. The characteristic band structure is clearly visible. Such band structures (like the dislocationless channels) with additional rotational deformation modes should appear in the near-surface layers of b.c.c. metals during the evolution of dislocation structures under both static and cyclic loading at the pre-fracture stage [ 3]. The fracture surface pictures in the near-surface and inner-volume regions of coated and uncoated specimens are very different (Figs. 3 and 5), but they are the same in the inner volumes of all specimens (i.e. they are coating independent). Moreover, the differences between the near-surface and inner-volume fracture structures for Re-coated Mo specimens are less important (Figs. 2, 4 and 5) and vanish with an increase in coating thickness; for the thickest coatings the two structures are very similar (Fig. 5). The visually established differences between fracture surface patterns can be quantified (parametrized) by means of multifractal analysis of fractographs. In Table 3 several multifractal characteristics of the investigated fracture areas are presented. The multifractal indices D(q), c~(q) and f(q) for the near-surface layers increase with coating thickness w and approach the indices for the inner volumes. The character of multifractal characteristic changes as a function of coating thickness w shows a good correlation with the corresponding mechanical property dependences (see Figs. 1, 7, and 8) and with the visual appearance of fracture surfaces. The most important multifractal characteristics are f(40) and DD. The parameter f(40) characterizes the structure homogeneity and its value increases for more homogeneous structures. The parameter DD characterizes the relative presence of periodic and chaotic components. It rises with an increase in periodic counterpart. For the near-surface zone of fracture surfaces the values of DD are higher in comparison with the inner-volume fractures, but with an increase in coating thickness w the DD values diminish (see Fig. 9). This evidences the higher level of dislocation structure evolution in the nearsurface zones at the pre-rupture stage. The rhenium coating impedes the dislocation structure evolution in surface layers and this effect increases with w. In contrast,
A.G. Kolmakovet al./Surface and Coatings Technology72 (1995) 43-50 the f(40) values are lower for near-surface regions than for inner volumes but they increase with w. The higher deformation homogeneity in the inner volumes of specimens in comparison with near-surface regions at the pre-rupture stage is clear. Thus we can conclude that rhenium coating leads to deformation homogenization in near-surface layers. The revealed peculiarities of the effect of coatings on the fracture appearance of near-surface layers and mechanical properties can be attributed to a combination of the well-known afore-cited effects of dislocation structure evolution advancing in the near-surface specimen layers, surface layer existence with enhanced mechanical properties and barrier impediment of dislocations on the interfaces. The strength of Re exceeds that of Mo and the strain-hardening exponent of Re is nearly three times as high as for Mo [28]. Taking into account the general theory of dislocation structures advancing in the near-surface layers [ 1 - 5 ] , the highhardened Re coating should act as an effective barrier that hinders the escape of individual dislocations and their pile-ups from the inner volume to the surface. The thin interlayer between matrix and coating, which consists of M o - R e alloy with highly complex mechanical properties, acts as an additional barrier [28]. Thus the processes of surface microyielding at the macroelastic deformation stage and advanced surface yielding at the plastic stage act mainly in the surface and transitional interlayer. This complexity of the processes leads, as can be supported, to the suppression of differences between dislocation structures formed in the near-surface layer of the molybdenum matrix and in the inner volume and therefore to a diminishment of the difference in evolution rates of dislocation structures. This effect increases with the coating thickness increasing to some limit only: the surface processes concentrate in the Re coating and interlayer; therefore for thick coatings the mechanical properties of the wires vary only slightly (the saturation effect). These deductions were verified experimentally (Fig. 1). The non-monotonic appearance of UTS changes with coating thickness changes can be explained with the aid of fractographic examinations. For the Re coating thickness in the range 0.4-1 gm the surface roughness and possible variations in coating thickness lead to the origination of circumferential cracks in the weakest region of the coating at the necking stage (Fig. 2). These local cracks promote the main crack development and hence the UTS diminishment. The surface cracking appearance for the thicker coatings is nearly the same as for uncoated wires (Fig. 2) owing to the diminishment of the relative influence of coating thickness and surface state; the differences in the dislocation structure evolution rates in the outer and inner volumes of specimens are small. In this connection some increase in UTS of
49
specimens is established when the coating thickness exceeds 1.5 lam. The Re coating thickness that corresponds to negligible changes in mechanical properties is in the range 1-2 lam; consequently, the critical ratio of coating thickness to wire diameter is w/d = 0.001-0.002 and it can be assumed that this is a critical point (taking into account some other experiments not considered here). The following calculations were carried out for additional confirmation of the fact that the changes in the mechanical properties of the coated specimens under study are due to the changes in the structure evolution processes in the near-surface layers rather than the decrease in specimen cross-section due to the large surface microdefects or due to the increase in the overall strength of specimens because of the addition of the hardened volume component to the surface (the coating), i.e. owing to the composite effect. The specimen surfaces were investigated by light microscopy. It turned out that in a band of width equal to double the size of the maximal defect and perpendicular to the wire axis there were no more than two large enough defects, usually in the form of blisters, the depth of the largest surface defects being (equal to their width R) less than 0.7 lam for uncoated specimens and significantly smaller for coated specimens. Taking this into account, the assumption was made that no more than four large surface defects may be concentrated in the plane of one cross-section. The change in the defect size cannot be more than the size of every defect. Thus for the last two cases - - when one specimen has no surface defects and the second has the largest surface defects the ratio of cross-section squares is S(*)/S(O)= I S ( 0 ) - s ] / S ( O ) , where S(0) is the cross-section of the specimen without defects, S(*)= S ( O ) - s is the crosssection in the presence of defects and s ~ 4 R 2 is the square of defects. The ratio S(*)/S(O} is the reverse of the relative change in stress, i.e. the possible relative change in stress due to the increase in size of microdefects must be a(0)/a(*)= S(O)/[S(O)- s]. The calculated relative change in stress via this formula for s = 4R ~ = 2 I.tm 2 and S(0) = 800000 gm 2 must be a(0)/~r(*) = 1.00001. For the composite material, assuming the equality of deformation rates of the composite as a whole and for its particular layers, the rule of mixture holds, i.e. cs=a(Mo)f(Mo)+a(c)f(c), where ~r, rr(Mol and ~r(c) are the actual stresses in the specimen as a whole, the molybdenum and the coating respectively and f ( M o ) and f(c) are the corresponding volume parts. For the tensile tension of a cylinder specimen with a uniform coating the fs should be equal to the parts of the square of the specimen cross-section; i.e. cr = a(Mo)[S(Mo)/S] +a(c)[S(c)/S], where S, S(Mo) and S(c) are the overall cross-section, that of molybdenum and that of the coating respectively. Introducing a factor n such that or(c)= ha(Mot, using the relation S(c)=
50
A. G Kolmakov et al./Surface and Coatings Technology 72 (1995) 43-50
S-S(Mo)
and taking into account that S(Mo)/S= {d(Mo)/[d(Mo) + 2w]} z (d is the wire diameter and w is
References
the coating thickness), after simple calculations one can obtain a/a(Mo) = n - ( n - 1 ) { d ( M o ) / [ d ( M o ) + 2w]} 2. For the investigated coatings with n ~ 1.6 (which is greater than the value in Ref. [28]), d = 1 mm and w = 4 ~tm the above formula gives for the maximal possible relative change in stress due to the composite effect the value 1.01. The relative changes in stress obtained experimentally are 1.28 and 1.12 for a(e) and a(0.2%) respectively, i.e. at least 12 times greater than the values calculated above. This uniquely bears witness to the fact that the changes in the mechanical properties of Mo due to Re coatings are the result of the influence of the structure evolution in the near-surface layer. However, the insufficient change in UTS is of the same order as the calculated value.
[1] I.R. Kramer, in Advances in the Mechanics and Physics of Surface, Vol. 3, Academic Press, New York, 1986, p. 109. [2] V.F. Terent'ev, L.G. Orlov and V.G. Pojda, Probl. Prochn. (USSR), 9 (1972) 34. [3] V.S. Ivanova, V.F. Terent'ev, I.S. Kohan et al., Phys. Chem. Mater. Treat., (2) (1979) 136. [4] V.P. Alechin and M.N. Shorshorov, Phys. Chem. Mater. Treat., (4) (1974) 107. [5] M.N. Shorshorov and V.P. Alechin, Phys. Chem. Mater. Treat., (1) (1976) 61. [6] I.R. Kramer, Influence of solid films on the creep behavior of metals, Naval Air Systems Command, N-0019-69-c-01, 1969. [7] I.R. Kramer and A. Kumar, Study of effects of diffused layers on the fatigue strength of commercial titanium alloys, US Air Force Tech. Rep. AFML-TR-70-185, 1970. [8] V.N. Geminov and A.G. Kolmakov, Ind. Lab, 5 (1993) 32. [9] L. Pietronero and L. Tosatti (eds.), Fractals in Physics, NorthHolland, Amsterdam, 1986. [10] A. Aharony and J. Feder (eds.), Fractals in Physics, NorthHolland, Amsterdam, 1989. [11] R.W. Chan, Nature, 338 (1989) 201. [12] Ph. Davy, Nature, 348 (1990) 56. [13] H.G.E. Hentschel and I. Procaccia, Physica D, 8 (1983) 435. [14] T.C. Helsey et al., Phys. Rev. A, 33 (1986) 1141. [15] R.E. Williford, Scr. Metall., 22 (1988) 1749. [16] G. Paladin and A. Vulpiani, Phys. Rep., 156 (1987) 147. [17] A. Aharony, Physica A, 168 (1990) 479. [18] T. Vicsek, Physica A, 168 (1990) 490. [19] J.L. McCauley, Int. J. Mod. Phys. B, 3 (1989) 821. [20] G.V. Vstovsky, Phys. Lett. A, 168 (1992) 41. [21] M. Giona, P. Piccirili and V. Cimagalli, J. Phys. A: Math. Gen., 24 (1991) 367. [22] C. Godreche and J.M. Luck, J. Phys. A: Math. Gen., 23 (1990) 3769. [23] J. Feder, Fractals, Plenum, New York, 1988. [24] G.V. Vstovsky, A.G. Kolmakov and V.F. Terent'ev, Russ. Metall., 4 (1993) 164. [25] G.V. Vstovsky and I.G. Bunin, J. Adv. Mater., 1 (1994). [26] J.C. Thorniey and A.S. Wronsky, Acta Metall., 18 (1970) 1053. [27] V.V. Rybin and A.N. Vergazov, Phys. Met. Mater. Sci. (USSR), 4 (1977) 43. [28] E.E. Savizky and G.S. Burchanov, Metallscience of High Melted and Rare Metals, Nauka, Moscow, 1971, p. 354.
5. Conclusions (1) The dependence of the mechanical properties of molybdenum wires 1 mm in diameter on the thickness of rhenium coatings deposited by vacuum electron beam evaporation with simultaneous argon ion irradiation (IBAD method) was investigated. It was established that the elasticity limit a(e) and yield stress a(0.2%) rise by 28% and 12% respectively in comparison with uncoated specimens with the coating thickness increasing from 0.4 to 4.2 ~tm; the UTS changes only slightly; the plastic characteristics remain invariant. (2) The dependence of the mechanical properties on the coating thickness is non-monotonic. The maximum changes are revealed for ratios of coating thickness to wire diameter of w/d --- 0.001-0.002. (3) It is confirmed experimentally that the effective depth of the hardened near-surface layer at the microyielding stage is a few microns.
Surface and Coatings Technology 72 (1995) 43-50
Effect of rhenium coatings on the mechanical properties of molybdenum wires A.G. Kolmakov *, V.N. Geminov *, G.V. Vstovsky, V.F. Terent'ev *, V.T. Zabolotny, E.E. Starostin A.A. Baikov Institute of Metallurgy, Russian Academy of Sciences, Leninsky Prospect 49, I 17911 Moscow, Russian Federation Received 24 September 1993; accepted in final form 4 June 1994
Abstract The dependence of the mechanical properties of rhenium-coated, commercially pure molybdenum wires 1 mm in diameter on the rhenium coating thickness w = 0.4-4.2 p.m was studied. The coatings were deposited by vacuum electron beam evaporation with simultaneous Ar ion irradiation (ion-beam-assisted deposition method). The increases in elasticity limit or(e) and yield stress a(0.2%) due to the coating were found to be about 28% and 12% in comparison with uncoated wire. Maximal property increments occur when the ratio of coating thickness to wire diameter is w/d = 0.001-0.002. Fractographic features were investigated by means of multifractal analysis.
Keywords: Molybdenum; Strengthening; Surface effects; Rhenium coatings
1. Introduction The general deformation kinetics of metals is substantially influenced by the state and behaviour of thin surface layers [ 1-4]. The evolution of dislocation structure begins in these layers before the substrate region. At the microplastic stage of specimen deformation the surface layer deforms in a plastic manner and this deformation-hardened layer acts as a barrier for dislocation glide in the main volume of metal; macroscopic yielding takes place as a result of the breakage of innervolume dislocation pile-ups through this layer [2]. Therefore modification of the surface layer behaviour by means of alloying or coating deposition may lead to alteration of the macroplastic characteristics of the metal [1,3,5 7]. The purpose of this investigation was to reveal the effect of coating thickness on the mechanical properties of rhenium-coated molybdenum wires.
2. Materials and techniques 2.1. Materials The investigation was carried out on commerically pure molybdenum wires 1 m m in diameter in the * Corresponding authors. 0257-8972/95/$09.50 © 1995 ElsevierScience S.A. All rights reserved SSDI 0257-8972(94)02329-0
as-drawn condition. The chemical analysis of the Mo wire is given in Table 1. After the removal of drawing defects with emery paper the specimens were electropolished in a solution of 95% H e S O 4 + 5% ethanol; the total thickness of the removed layer was 20 25 p.m. The coatings were deposited by vacuum electron beam evaporation with simultaneous Ar ion irradiation (ionbeam assisted deposition (IBAD) method). The treatment conditions (temperature and ion and atom beam energies) were optimized for the predomination of mixing during the radiation-stimulated diffusion and for the creation of metastable solid solutions a few nanometres thick over the coating-matrix interface. The specimen temperature during the treatment did not exceed 80 °C. The coating thickness was in the range 0.4-4.2 p.m.
2.2. Mechanical testing The mechanical properties of the wires were determined by tensile testing specimens 1 m m in diameter and 50 m m in active length with an initial strain rate of 3.3 × 10 -3 s 1 on an Instron T T - D M machine. Scanning electron microscopy (SEMi was used for fractographic analysis. Conversion and normalization of the elongation [8] were carried out. Direct comparison of the natural
44
A.G. Kolmakov et al./Surface and Coatings Technology 72 (1995) 43 50
Table 1 ,Chemical analysis of molybdenum wires Element
C
N
S
Ti
Ni
Fe
AI
Cu
Cr
Mn
Mg
Mo
Amount (mass%)
0.025
0.005
0.001
0.16
0.02
0.012
0.008
0.005
0.014
0.0025
0.0025
Bal.
elongation Al/l with the length-to-diameter ratio l/d for specimens of different length does not give enough useful information or even gives erroneous results. However, it is possible to use the standard lid ratios instead of nonstandard data. The most convenient method is the comparison of two tensile diagrams for specimens with different lid irrespective of specimen sizes. This method is based on the following obvious assumptions. (1) The neck (the deformation instability zone) does not depend on the specimen length, i.e. lid or A(i)= const.; Ud is invariant. (2) The total specimen length increment A is the sum of the uniformly elastic and necking length increments, i.e. A = A(e) + A(i). (3) The ratio of elastic length increments of two specimens is proportional to their length ratio, i.e. A(el )/A(e2) = l( 1 )/l(2). We can deduce the universal formula connecting elongations of three specimens with different length-todiameter ratios l/d = m, n(1) and n(2) as 3(m) =
3(1) [n(2)/m - 1 ] - 6(2) [n(2)/m -- n(2)/n( 1 )] n(2)/n(1)-
1
The experimental ratios n(1) and n(2) are selected arbitrarily; from tensile diagrams we have 6 ( 1 ) = A(1)/I(1) and 3 ( 2 ) = A(2)/1(2); 6(m) is calculated for the standard ratio m = lid = 5 or m = lid = 10. 2.3. Multifractal analysis Fractal geometry, despite its very short history, turns out to be extremely effective for searching for new ways of describing, forecasting the behaviour, etc. of objects under investigation in various branches of science [e.g. 9-12]. However, it is now well known that knowledge of only one fractal dimension is not sufficient for a detailed description of the self-similarity of the natural and numerous model fractal structures. A multifractal formalism (MF) [13,14] provides more opportunities for such a description. MF, being one of the new branches of statistical physics, enables to carry out analyses of the structures of complex systems, their evolution and measurement processes on them. Many modern alloys, composite materials, nanocrystalline materials, etc. have supercomplicated structures and their adequate description demands a significant revision of the conventional approaches in materials science. In particular, the latter provide no means for quantitative evaluation of the complexity and ordering of material
structures. Some progress in this direction can be achieved using MF. M F could also find in the future an effective application in materials science for the quantitative analysis of structures and their dynamic evolution, surface relief, surface energy, etc. In this work M F was used to evaluate the distinctions between fracture surfaces quantitatively rather than by eye. The authors do not know of any analogous works apart from the rather artificial Williford fracture model for AISI 4340 steel [15], which is interesting nevetheless. The multifractal description is based on the generation (in one way or another) of a measure due to the partition of the space embedding the object under consideration into boxes, the object being called a measure support. An investigation of the scaling properties of the measure correlation function (under some assumptions about the scaling of every measure) enables one to ascribe to the object some statistical quantities to characterize it and to compare it with other similar ones, which provides a rather subtle identification [16 19]. Consider some strange (irregular, porous, rough, etc.) object embedded in euclidean space and divide it into N boxes of sizes I/(i) <~ l, i = 1. . . . . N, 1 being a characteristic size. Such a partition enables one to ascribe to the boxes their measures ("weights") according to the nature of the object. For example, if one studies a fractal aggregate of overall mass M, the measures may be the parts of the mass in the boxes, p(i) = m(i)/M, re(i) being the mass of the ith box [ 18]. If one investigates a strange attractor of some dynamical system, then the measures may be constructed using the numbers of times (n(i)) the trajectory in the phase space passes through each box during some sufficiently long period of time: p(i) = n(i)/Z~=ln(i). The distributed square on the plane [19,20], normalized Fourier spectra [21,22], fracture energy parts [15] and other continuous and discrete distributions can be used to generate the measure. The latter examples bear witness that the multifractal description based on a quite general concept of measure is very flexible. Avoiding the mathematical details, the multifractal formalism (MF) is as follows. For the generated (in one way or another) measure p(i) a partition function can be calculated as F(q, z, l ) =
p(i) q i=a l(i) ~
(1)
where the sum is over the boxes with non-zero measure (as everywhere below as well) and q and r are real numbers. In the case of singular behaviour of the
45
A.G. Kolmakov et aL/Surface and Coatings Technology 72 (1995) 43 50
measure, i.e. p(i)oc[l(i)] ~,
tively. For the uniform measure one has e>0
I--*0,
(2)
it can be shown [13,14,23] that there exists a unique function r(q) such that the function F ( q , z ( q ) , l ~ O ) is finite. Given q, for ~ ' > r(q) or z ' < z(q), F(q, ~', l--,O) is infinite or zero respectively. The equality F(q, r(q), l ~ 0 ) = 1 gives the definition of fractal dimension in the case of equiboxed partition, l(i)= I, and uniform measure, p(i) = 1/N(l), i = 1. . . . . N(1), N ( l ) being the number of boxes covering the support, as log[N(/)] D = lim i~o log(i/l)
r q- 1
and one can set for the arbitrary partition and measure also F(q, z(q), l--, O} = 1
(3)
For a generalized correlation function z(q) one has N
z ( q ) = ~ p(i)qocY (°),
(4a)
l~O
i-1
In [z(q)] r(q) = l i r a l=o In(l)
(4b)
Thus, by constructing an appropriate measure, one can ascribe to the object under consideration some real function z(q) uniquely. The sum over the boxes in (4a) can be replaced by an integration over the measure singularity exponents (see Eq. (2)) p(i) q o(L l(i)~q: z(q): fd~[pte)l
m'W],
l--,0
(5)
where p(c~)l-ml de is the probability that an arbitrarily chosen value ~' is between e and e + de; p(e) is a nonsingular smooth function. Thus the first interpretation of M F is such that the measure of support is modelled by a collection of interwoven sets of singularities of strength e, each having its own dimension f(e) [13]. The dependence f(e) is called a spectrum of singularities or an f(e) spectrum. In the limit l--.0 the integral value (5) is determined by such an e that qe - f(c0 = min; then z(e) and f(e) are related by the Legendre transform z(q) = qe - . f ( e ) ,
e -
dr dq
(6)
Owing to the normalization condition E~=~p(i)= 1 and Eqs. (4), r( 1) = 0, which can be expressed explicitly as z(q) = (q -- 1 )D(q)
(7)
It can be shown that D(q) are the so-called Renyi dimensions (entropies) and D(0) >~ D(1) ~> D(2) are the fractal, information and correlation dimensions respec-
D(q) = D(1) = D(0) = e(max) = e(min) = f(e),
(8) r(q) = ( q - - 1)D(1) The quantity ~ can be interpreted as an average over an ensemble of sets of isosingularities [ 19], i.e. e - dz dq -
f
z(q)
= (e')
(9)
and f ( ( c ( ) ) as a fractal dimension of the set that best approximates z(q) for corresponding q. Thus these quantities can be considered as the thermodynamic quantities in the canonical ensemble and this is another interpretation of MF. Here we have used the practical algorithm proposed in Ref. [24]. The 64 x 64 gm 2 near-surface and internal fracture regions were divided into 64 x 64 square boxes, each of which was marked by 1 if it was located in the domain of the fracture surface (almost perpendicular to the wire axis) and by 0 otherwise. This initial 64 x 64 partition was used to produce eight more rough partitions by integrating the "atomic" boxes into larger boxes of sizes l(k) x l(k), l(k) = 4, 6, 8, 10, 12, 16, 21, 32, k = l . . . . . 8. For each such partition the measure was built up simply by summing the unities in each box and dividing this sum by the overall sum of unities over the photograph. The approximation of the dependences of lg[z(q)] on lg[l(k)] for each given q • [ - 3 0 , 40] by the least-squares method (the correlation coefficients were always greater than 0.99) produced the slope r(q), which was used to calculate the multifractal spectra f(e) and the Renyi dimensions D(q) via Eqs. (6) and (7). These calculations were conceived to make clear the possibility of distinguishing the fracture surfaces quantitatively by exactly the same computer algorithm rather than having to develop a method of exact evaluation of fractal characteristics. Arguments can easily be put forward [24,25] to interpret DD = D( 1 ) - D(40) as a quantitative measure of the order of fracture surfaces and f ( e ( q = 40)) - - f ( 4 0 ) as a measure of the homogeneity of distribution. Together these quantities can be considered as characteristics of the complexity of the fracture surface structure. The calculations were carried out on a PC/AT-286/287 "WYSE" computer in Turbo-Pascal 6.0 using "extended" real numbers, which allowed us to use q in the range [ - 3 0 , 4 0 ] . Nevertheless, one obtained value o f f ( 4 0 ) was small and negative. Since f ( e ( q ) ) must be non-negative for any q, we can consider the small negative value as an estimation of the calculation accuracy and the corresponding .1"(40) is taken to be zero.
3. Results A summary of the mechanical properties as functions of coating thickness is presented in Table 2 and Fig. 1.
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A. G. Kolmakov et aL/Surface and Coatings Technology 72 (1995) 43 50
Table 2 Tensile properties of molybdenum wires Characteristic
Specimen Uncoated
a(e) (MPa) a(0.2%) (MPa) UTS (MPa)
With coating thickness w (Ixm)
810 1213 1460
,~(5) (%) 5(10) (%)
(%)
0.4
0.8
2.4
3.2
4.2
983 1290 1441
1010 1027 1015 1033 1307 1333 1327 1355 1445 1485 1492 1484 1.6-2 6-8 46-53
200 150
2
r,
~100 ~o 4
I ",--,..~-~ 1 -50 m
2
3
I 4
3 I 5
W (Re),am
Fig. 1. Changes in tensile properties of molybdenum wires: 1, elasticity limit a(e); 2, yield stress a(0.2%), 3, UTS; w is the rhenium coating thickness.
Along with the original properties - - elasticity limit a(e), yield strength a(0.2%), ultimate tensile strength (UTS), area reduction and elongation - - for the investigated length-to-diameter ratio of 50, i.e. 6(50), conversion to the standard value 6(10) was carried out [-8]. M i c r o p h o t o g r a p h s of the fracture patterns of wires are shown in Figs. 2-6. The multifractal characteristics for the investigated areas of fracture surfaces are given in Table 3. O n e particular case, the change in correlation dimension D(2) with coating thickness w, is shown in Fig. 7. The correlation between the relative increments of elasticity limit a(e) and yield stress a(0.2%) and some M F characteristics is shown in Fig. 8. The character of changes in uniformity f ( 4 0 ) and hidden periodicity D D = D(1) - D(40) of the wire fracture surfaces of near-surface layers in relation to the presence and thickness of coatings as well as to the main volume fracture surface is shown in Fig. 9; see also Ref. [ 2 5 ] .
Fig. 2. General view of wire specimens: (a) uncoated; (b) with rhenium coating 0.4 ~tm thick; (c) with rhenium coating 3.2 lam thick.
4. Discussion The increase in plasticity (elongation 6 and area reduction ~b) was shown to be negligible; no appearance of a physical yield point was established, a(e) rises by
Fig. 3. Neck region of coated wire specimen after fracture.
A.G. Kolmakov et aL/Surface and Coatings Technology 72 (1995) 43 50
47
201~m I Fig. 6. Fragment of inner-side fracture pattern for uncoated specimen. Table 3 Some multifractal characteristics of fracture surfaces Characteristic
Coating thickness w (~tm) 0.4
0
D(0) =.f(max) ~(0) D(1)=~(I) = f(1) D(2) ~(2) f(2) D(40) ~(40) f(40)
1.94123 1.97419 2.01693 2.02177 1.88251 1.93930 1.84388 1.91810 1.81144 1.90079 1.77901 1.88348 1.61599 1.77926 1.57538 1.73931 -0.00847 0.18128 1 . 4 0 9 3 6 1.33244
DD=D(1)--D(40)
1.96
3.2
Internal volume
1.96775 2.00285 1.94142 1.92461 1.91053 1.89646 1.80206 1.76684 0.39363 1.00156
1.97799 2.00703 1.95597 1.94157 1.92937 1.91717 1.83859 1.80846 0.63323 0.99242
n
Internal v o l u m e s .
Fig. 4. Fracture surface of near-surface layer of wire specimens: (a) uncoated; (b) with rhenium coating 0.4 lam thick; (c) with rhenium coating 3.2 ~tm thick.
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#
1.92 v
El 1.88
1.84( 0
I
I
1
2 W (Re), ~m
Fig. 7. Dependence of correlation dimension D(2) thickness w.
Fig. 5. Fracture surface of inner volume of wire specimen.
on
coating
28%, ~r(0.2%) by 12% and UTS only slightly. These results are in accordance with Kramer's work [6,7], where a markedly higher rise in ~(e) in comparison with a(0.2%) and UTS was found for Ti-6A1-4V additionally alloyed with Cr and Ni over the surface.
48
A. G. Kolmakov et al./Surface and Coatings Technology 72 (1995) 43 50
1.2
. o
(0.2%)
(~ (e) zx
A
~1.1
Pi
1.0
I 1.0
1.1
1.2
1.3
A~
Fig. 8. Correlation between relative increases in elasticity limit a(e) and yield strength a(0.2%) and some multifractal characteristics: D, AD(40); A, Act(40).
[]
internal
volume
0.6-
~0.4 -
OW=3.21.tm
N--
0.2 -
~W=0.4gm
~ 0.10
=
0
1
I
I
0.15
0.20
DD
.
t
m
1" 0 - . 0.25
Fig. 9. Changes in uniformity f(40) and hidden structure periodicity DD of wire fracture surfaces of near-surface layers in relation to presence and thickness of Re coating.
Very satisfactory adhesion properties of coatings were achieved: no delamination occurred and visible damage was detected only in the vicinity of the border of the fracture surface (Fig. 2). The fracture path of wires is normal to the tensile axis; the specific fracture pictures through the neck (Fig. 2) and longitudinal section (Fig. 3) show evidence of intergranular fracture. Such a mechanism is typical for Mo and its alloys in the temperature interval from 250 to 500 K and is analysed in detail in Refs. [26,27]. Crack-like circumferential patterns on the specimen surface are revealed in the vicinity of the neck both with and without the coating (Fig. 2). The dimensions of the crack-like fragments diminish and their number increases for thicker coatings (in the examined range of 0.4-
4.2 gm). The appearance of the crack-like relief for thickcoated specimens is nearly the same as for uncoated specimens. We consider the crack-like relief existence in the neck area as evidence of the initiation of surface damage leading to fracture. The distinction between deformation patterns in the near-surface and innervolume regions is established for both uncoated and coated specimens. The fracture surface of uncoated specimens has a distinctive outer layer and its deformation and fracture patterns are very different in comparison with the inner volume (Figs. 2(a), 3 and 5). The side view of the inner longitudinal fracture of the near-surface interface layer is shown in Fig. 6. The characteristic band structure is clearly visible. Such band structures (like the dislocationless channels) with additional rotational deformation modes should appear in the near-surface layers of b.c.c. metals during the evolution of dislocation structures under both static and cyclic loading at the pre-fracture stage [ 3]. The fracture surface pictures in the near-surface and inner-volume regions of coated and uncoated specimens are very different (Figs. 3 and 5), but they are the same in the inner volumes of all specimens (i.e. they are coating independent). Moreover, the differences between the near-surface and inner-volume fracture structures for Re-coated Mo specimens are less important (Figs. 2, 4 and 5) and vanish with an increase in coating thickness; for the thickest coatings the two structures are very similar (Fig. 5). The visually established differences between fracture surface patterns can be quantified (parametrized) by means of multifractal analysis of fractographs. In Table 3 several multifractal characteristics of the investigated fracture areas are presented. The multifractal indices D(q), c~(q) and f(q) for the near-surface layers increase with coating thickness w and approach the indices for the inner volumes. The character of multifractal characteristic changes as a function of coating thickness w shows a good correlation with the corresponding mechanical property dependences (see Figs. 1, 7, and 8) and with the visual appearance of fracture surfaces. The most important multifractal characteristics are f(40) and DD. The parameter f(40) characterizes the structure homogeneity and its value increases for more homogeneous structures. The parameter DD characterizes the relative presence of periodic and chaotic components. It rises with an increase in periodic counterpart. For the near-surface zone of fracture surfaces the values of DD are higher in comparison with the inner-volume fractures, but with an increase in coating thickness w the DD values diminish (see Fig. 9). This evidences the higher level of dislocation structure evolution in the nearsurface zones at the pre-rupture stage. The rhenium coating impedes the dislocation structure evolution in surface layers and this effect increases with w. In contrast,
A.G. Kolmakovet al./Surface and Coatings Technology72 (1995) 43-50 the f(40) values are lower for near-surface regions than for inner volumes but they increase with w. The higher deformation homogeneity in the inner volumes of specimens in comparison with near-surface regions at the pre-rupture stage is clear. Thus we can conclude that rhenium coating leads to deformation homogenization in near-surface layers. The revealed peculiarities of the effect of coatings on the fracture appearance of near-surface layers and mechanical properties can be attributed to a combination of the well-known afore-cited effects of dislocation structure evolution advancing in the near-surface specimen layers, surface layer existence with enhanced mechanical properties and barrier impediment of dislocations on the interfaces. The strength of Re exceeds that of Mo and the strain-hardening exponent of Re is nearly three times as high as for Mo [28]. Taking into account the general theory of dislocation structures advancing in the near-surface layers [ 1 - 5 ] , the highhardened Re coating should act as an effective barrier that hinders the escape of individual dislocations and their pile-ups from the inner volume to the surface. The thin interlayer between matrix and coating, which consists of M o - R e alloy with highly complex mechanical properties, acts as an additional barrier [28]. Thus the processes of surface microyielding at the macroelastic deformation stage and advanced surface yielding at the plastic stage act mainly in the surface and transitional interlayer. This complexity of the processes leads, as can be supported, to the suppression of differences between dislocation structures formed in the near-surface layer of the molybdenum matrix and in the inner volume and therefore to a diminishment of the difference in evolution rates of dislocation structures. This effect increases with the coating thickness increasing to some limit only: the surface processes concentrate in the Re coating and interlayer; therefore for thick coatings the mechanical properties of the wires vary only slightly (the saturation effect). These deductions were verified experimentally (Fig. 1). The non-monotonic appearance of UTS changes with coating thickness changes can be explained with the aid of fractographic examinations. For the Re coating thickness in the range 0.4-1 gm the surface roughness and possible variations in coating thickness lead to the origination of circumferential cracks in the weakest region of the coating at the necking stage (Fig. 2). These local cracks promote the main crack development and hence the UTS diminishment. The surface cracking appearance for the thicker coatings is nearly the same as for uncoated wires (Fig. 2) owing to the diminishment of the relative influence of coating thickness and surface state; the differences in the dislocation structure evolution rates in the outer and inner volumes of specimens are small. In this connection some increase in UTS of
49
specimens is established when the coating thickness exceeds 1.5 lam. The Re coating thickness that corresponds to negligible changes in mechanical properties is in the range 1-2 lam; consequently, the critical ratio of coating thickness to wire diameter is w/d = 0.001-0.002 and it can be assumed that this is a critical point (taking into account some other experiments not considered here). The following calculations were carried out for additional confirmation of the fact that the changes in the mechanical properties of the coated specimens under study are due to the changes in the structure evolution processes in the near-surface layers rather than the decrease in specimen cross-section due to the large surface microdefects or due to the increase in the overall strength of specimens because of the addition of the hardened volume component to the surface (the coating), i.e. owing to the composite effect. The specimen surfaces were investigated by light microscopy. It turned out that in a band of width equal to double the size of the maximal defect and perpendicular to the wire axis there were no more than two large enough defects, usually in the form of blisters, the depth of the largest surface defects being (equal to their width R) less than 0.7 lam for uncoated specimens and significantly smaller for coated specimens. Taking this into account, the assumption was made that no more than four large surface defects may be concentrated in the plane of one cross-section. The change in the defect size cannot be more than the size of every defect. Thus for the last two cases - - when one specimen has no surface defects and the second has the largest surface defects the ratio of cross-section squares is S(*)/S(O)= I S ( 0 ) - s ] / S ( O ) , where S(0) is the cross-section of the specimen without defects, S(*)= S ( O ) - s is the crosssection in the presence of defects and s ~ 4 R 2 is the square of defects. The ratio S(*)/S(O} is the reverse of the relative change in stress, i.e. the possible relative change in stress due to the increase in size of microdefects must be a(0)/a(*)= S(O)/[S(O)- s]. The calculated relative change in stress via this formula for s = 4R ~ = 2 I.tm 2 and S(0) = 800000 gm 2 must be a(0)/~r(*) = 1.00001. For the composite material, assuming the equality of deformation rates of the composite as a whole and for its particular layers, the rule of mixture holds, i.e. cs=a(Mo)f(Mo)+a(c)f(c), where ~r, rr(Mol and ~r(c) are the actual stresses in the specimen as a whole, the molybdenum and the coating respectively and f ( M o ) and f(c) are the corresponding volume parts. For the tensile tension of a cylinder specimen with a uniform coating the fs should be equal to the parts of the square of the specimen cross-section; i.e. cr = a(Mo)[S(Mo)/S] +a(c)[S(c)/S], where S, S(Mo) and S(c) are the overall cross-section, that of molybdenum and that of the coating respectively. Introducing a factor n such that or(c)= ha(Mot, using the relation S(c)=
50
A. G Kolmakov et al./Surface and Coatings Technology 72 (1995) 43-50
S-S(Mo)
and taking into account that S(Mo)/S= {d(Mo)/[d(Mo) + 2w]} z (d is the wire diameter and w is
References
the coating thickness), after simple calculations one can obtain a/a(Mo) = n - ( n - 1 ) { d ( M o ) / [ d ( M o ) + 2w]} 2. For the investigated coatings with n ~ 1.6 (which is greater than the value in Ref. [28]), d = 1 mm and w = 4 ~tm the above formula gives for the maximal possible relative change in stress due to the composite effect the value 1.01. The relative changes in stress obtained experimentally are 1.28 and 1.12 for a(e) and a(0.2%) respectively, i.e. at least 12 times greater than the values calculated above. This uniquely bears witness to the fact that the changes in the mechanical properties of Mo due to Re coatings are the result of the influence of the structure evolution in the near-surface layer. However, the insufficient change in UTS is of the same order as the calculated value.
[1] I.R. Kramer, in Advances in the Mechanics and Physics of Surface, Vol. 3, Academic Press, New York, 1986, p. 109. [2] V.F. Terent'ev, L.G. Orlov and V.G. Pojda, Probl. Prochn. (USSR), 9 (1972) 34. [3] V.S. Ivanova, V.F. Terent'ev, I.S. Kohan et al., Phys. Chem. Mater. Treat., (2) (1979) 136. [4] V.P. Alechin and M.N. Shorshorov, Phys. Chem. Mater. Treat., (4) (1974) 107. [5] M.N. Shorshorov and V.P. Alechin, Phys. Chem. Mater. Treat., (1) (1976) 61. [6] I.R. Kramer, Influence of solid films on the creep behavior of metals, Naval Air Systems Command, N-0019-69-c-01, 1969. [7] I.R. Kramer and A. Kumar, Study of effects of diffused layers on the fatigue strength of commercial titanium alloys, US Air Force Tech. Rep. AFML-TR-70-185, 1970. [8] V.N. Geminov and A.G. Kolmakov, Ind. Lab, 5 (1993) 32. [9] L. Pietronero and L. Tosatti (eds.), Fractals in Physics, NorthHolland, Amsterdam, 1986. [10] A. Aharony and J. Feder (eds.), Fractals in Physics, NorthHolland, Amsterdam, 1989. [11] R.W. Chan, Nature, 338 (1989) 201. [12] Ph. Davy, Nature, 348 (1990) 56. [13] H.G.E. Hentschel and I. Procaccia, Physica D, 8 (1983) 435. [14] T.C. Helsey et al., Phys. Rev. A, 33 (1986) 1141. [15] R.E. Williford, Scr. Metall., 22 (1988) 1749. [16] G. Paladin and A. Vulpiani, Phys. Rep., 156 (1987) 147. [17] A. Aharony, Physica A, 168 (1990) 479. [18] T. Vicsek, Physica A, 168 (1990) 490. [19] J.L. McCauley, Int. J. Mod. Phys. B, 3 (1989) 821. [20] G.V. Vstovsky, Phys. Lett. A, 168 (1992) 41. [21] M. Giona, P. Piccirili and V. Cimagalli, J. Phys. A: Math. Gen., 24 (1991) 367. [22] C. Godreche and J.M. Luck, J. Phys. A: Math. Gen., 23 (1990) 3769. [23] J. Feder, Fractals, Plenum, New York, 1988. [24] G.V. Vstovsky, A.G. Kolmakov and V.F. Terent'ev, Russ. Metall., 4 (1993) 164. [25] G.V. Vstovsky and I.G. Bunin, J. Adv. Mater., 1 (1994). [26] J.C. Thorniey and A.S. Wronsky, Acta Metall., 18 (1970) 1053. [27] V.V. Rybin and A.N. Vergazov, Phys. Met. Mater. Sci. (USSR), 4 (1977) 43. [28] E.E. Savizky and G.S. Burchanov, Metallscience of High Melted and Rare Metals, Nauka, Moscow, 1971, p. 354.
5. Conclusions (1) The dependence of the mechanical properties of molybdenum wires 1 mm in diameter on the thickness of rhenium coatings deposited by vacuum electron beam evaporation with simultaneous argon ion irradiation (IBAD method) was investigated. It was established that the elasticity limit a(e) and yield stress a(0.2%) rise by 28% and 12% respectively in comparison with uncoated specimens with the coating thickness increasing from 0.4 to 4.2 ~tm; the UTS changes only slightly; the plastic characteristics remain invariant. (2) The dependence of the mechanical properties on the coating thickness is non-monotonic. The maximum changes are revealed for ratios of coating thickness to wire diameter of w/d --- 0.001-0.002. (3) It is confirmed experimentally that the effective depth of the hardened near-surface layer at the microyielding stage is a few microns.