Carbon Diffusion Between the Layers in Modern Pattern-Welded Damascus Blades John D

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Carbon Diffusion Between the Layers in Modern Pattern-Welded Damascus Blades John D. Verhoeven* and Howard F. Clark† *Department Materials Science and Engineering, Iowa State University, Ames, IA 50011; and †Morgan Valley Forge, RR 1, Box 74, Runnells, IA 50237

Pattern-welded Damascus steel blades are made by forge welding together pairs of steels having low- and high-carbon compositions. It is often assumed that these blades consist of hard and soft layers owing to the carbon variations of the original steels and that it is this difference in hardness that produces the etching characteristics that give the surface patterns. Theoretical arguments are presented that show that, with the modern forging tech- niques used to make these blades, carbon diffusion should be adequate to homogenize the C level between the layers of the blades, which predicts no hardness difference between layers. Experiments are presented on several modern blades, showing that there are no hardness differences found between layers. Arguments are presented for a theory that it is the difference in alloying elements between the layers that produces the differential etching characteristics that give rise to the visual surface patterns of most contemporary pattern- welded Damascus steels. © Elsevier Science Inc., 1998

INTRODUCTION of layers have been formed. It is common to select a low-carbon and a high-carbon steel The beautiful Damascus gun barrels found for the two kinds of steels. For example, one in most large museums are an example of might start with three sheets of a 1086 steel what is often termed pattern-welded Dam- (% C, 0.86) separated with two sheets of ascus steel. These steels have an ancient 1018 steel (% C, 0.18). As the number of history, possibly having been produced as folds increases, the number of layers in the long ago as 300 B.C. [1]. In the past 15 years, forged blade rises dramatically. After 3 bladesmiths in the United States have learned folds, the 5 layers have increased to 40 lay- to produce beautiful knives of pattern- ers, after 6 to 320, and after 9 to 2560 layers. welded steels, and a market has developed To observe an attractive damask pattern on for these knives. There are some interesting the surface of the blade two conditions metallurgical aspects to these modern blades, must be satisfied: (1) the two different lay- and this paper addresses two of them. ers must etch to different gray levels so that The process for making pattern-welded the alternating layer structure is distinctly Damascus steel blades consists of stacking observed by the eye and (2) the spacing of alternating sheets of two different kinds of the layers must be in a range that also al- steels on top of each other and then forge lows the alternating layer structure to be welding them together. After this compos- distinctly observed by the eye. If the spac- ite has been forged to roughly twice its ing is too small, the eye will not be able to original length, it is folded together and distinguish the layers and one can see the forged again, thereby doubling the number surface pattern only with the aid of a mag- of layers in the composite. The folding and nifying glass. If the spacing is too large, the welding is continued until a large number surface appearance generally loses its pat- 183 MATERIALS CHARACTERIZATION 41:183–191 (1998) © Elsevier Science Inc., 1998 1044-5803/98/$–see front matter 655 Avenue of the Americas, New York, NY 10010 PII S1044-5803(98)00035-7

184 J. D. Verhoeven and H. F. Clark tern. In a finished knife, the blade thickness will be in the range of 3 to 6mm (1/8 to 1/4 inch), and experience finds that one needs somewhere between 100 and 500 layers to produce attractive surface patterns. This paper is concerned with two common assumptions about welded Damascus steels that are prevalent among many prac- ticing bladesmiths: 1. It is well known that low-carbon steels are softer than high-carbon steels. There- fore, it is logical to assume that a Dam- ascus blade made from low- and high- carbon steels would consist of soft and hard layers. 2. It is also natural to assume that the different etching characteristics of the two layers result from the low- and high-car- FIG. 1. Change in carbon composition between layers bon levels in the two layers. during forging. It will be shown here that both of these fairly obvious assumptions are generally incorrect. A Ðπ2Dt ln------= ------(1) There are theoretical reasons to believe 2 Ao d that the initial carbon difference between the low- and high-carbon layers will disap- Consider the case where the A/Ao ratio has pear during the forging operation because fallen to a value of 0.01. This would mean of the relatively high diffusion coefficient that the amplitude of the carbon-composi- of C in austenite at the forging tempera- tion difference in the two layers has been tures. To illustrate this point further, con- reduced to only 1% of its original value. It sider the diagram of Fig. 1, which shows al- will be assumed that this difference is small ternating layers of 1086 and 1018 steel at enough that one may now consider the C the top with both layers having thickness d. composition to be homogenized between Initially, the carbon composition will vary the 2 layers. Therefore, Eq.1 predicts the with distance across the layers, as shown time required for homogenization of a by line labeled time ϭ 0 on the diagram. blade with a given spacing, and Fig 2 pre- Diffusion will cause the C atoms to change sents the graphic solution for forging done the composition to the sine wave profile af- at 1100ЊC(ഠ2000ЊF) and 1310ЊC (ഠ2400ЊF). ter some time (t) and eventually give com- The curves for C used D ϭ 0.12 exp plete homogenization, as shown by the (-32000/RT) [3], and for Mn used D ϭ 0.466 dashed line labeled t ϭ ∞. The maximum exp(-65950/RT) [4], where units are cm2/s composition at the center of the 1086 layer on D and cal/mol- K on R. The layer thick- after carbon diffusion is labeled A, for am- ness, d, was converted into the number of plitude. The original amplitude is labeled layers in the blade as follows. It was as- Ao, and one sees that the amplitude has sumed that the blade thickness in the forg- dropped by the ratio of A/Ao after a time t. ing step at temperature was on average The solution to Fick’s second law of diffu- 4.8mm (3/16 inch). Then the layer thick- sion for the boundary conditions shown ness was simply calculated as 0.48cm di- here at t ϭ 0 and t ϭ ∞ [2] gives the follow- vided by the number of layers in the blade. ing expression for variation of the amplitude Figure 2 shows that, in a blade with 200 ratio with t, d, and diffusion coefficient, D. layers, it will take only 2.7 s at 1100ЊC to ho-

Pattern-Welded Damascus Blades 185

FIG 2. Theoretical time required to homogenize C and Mn between the layers of a 4.8mm (3/16 inch)-thick welded Damascus blade versus the number of layers in the blade.

mogenize the carbon level between the lay- Mo, and Ni. All of these elements diffuse ers. Most modern bladesmiths use forging substitutionally in iron and are very much temperatures nearer 1310ЊC than 1100ЊC for less mobile than C and hence have much pattern-welded steels. The 1310ЊC line pre- smaller values for D. The element Mn was dicts that a 200-layer blade would homoge- chosen to illustrate the homogenization nize in 0.5 s at this temperature. On blade characteristics of these low-mobility ele- sections thinner than 4.8mm (3/16 inch), ments; the two upper curves in Fig. 1 are the times would be reduced to even smaller calculated for Mn. One sees that homogeni- values, whereas they would increase on zation times for Mn in a 200-layer blade thicker blades. However, even on thicker would range from 48h at 1100ЊC to 1.6 h at blades, the times remain small, rising only 1310ЊC. Hence, for normal forging condi- from 0.5 to 0.9 s on a 6.4mm (1/4 inch) tions, the theory predicts that, although the blade at 1310ЊC. The forging operation in- homogenization of C should be complete, volves several heat ϩ hammer steps, and that of the less-mobile elements heretofore the diffusion effect is cumulative so that the listed would not be complete. times in Fig. 2 will be overestimates of the These calculations have assumed that, actual required times for homogenization. when the C diffusion is complete, the car- Hence, the small times predicted for ho- bon composition will be the same in both mogenization in Fig. 2 show that diffusion layers. The difference in the alloying-ele- theory predicts that the forging operation ment compositions between the two layers should homogenize the carbon between the could cause a difference in C levels be- layers of pattern-welded Damascus blades. tween the two layers, owing to a ternary al- In addition to carbon, the commercial loying effect. Data are available that allow steels used to make modern pattern-welded one to estimate the magnitude of this effect Damascus blades contain various alloying [5, 6]. It is shown in the appendix that this elements that generally include Mn, Si, Cr, effect is negligible for the alloys studied

186 J. D. Verhoeven and H. F. Clark here but can be important for modern pat- the forging direction and mounted and pol- tern-welded blades that utilize alloys with ished with standard metallographic tech- large alloying additions, such as stainless niques. After being etched in nital, the two steels. layers became visible under the microscope, as is illustrated in Fig. 3 for the E sample. In all cases, the oil- and water-quenched sam- EXPERIMENTS ples gave essentially the same microstructural appearance and hardness values. The To evaluate whether the predictions of hardnesses of the two layers in each sample Eq.(1) are approximated in practice, a series were measured with a microhardness tester of experiments has been carried out by us- with the use of a Knoop indenter, and Fig. ing several different types of AISI steels to 4 shows sample C with four indentations forge pattern-welded Damascus blades. In on it. The Knoop hardnesses were con- all cases, the initial composite consisted of 3 verted into Rockwell C hardness values, layers of the two types of steels shown in and the hardnesses of both layers are shown the second column of Table 1. The 2 layers in the right-hand column of Table 1. It is of the first steel shown on the left side of seen that there is no soft layer even when the column surrounded 1 layer of the steel using wrought iron. at the right side of the column. It is esti- mated that the forge welding was done in the 1200 to 1310ЊC (ഠ2200 – 2400ЊF) range. DISCUSSION The original thicknesses of the two steels are shown in the third column, and it seen It is a well established fact [7] that the hard- that, in most of the experiments, the two ness of as-quenched fully martensitic plain steels had different thicknesses. The experi- carbon steel increases with carbon content, ments also differed from the calculations as shown in Fig. 5. It is also well known of Fig. 2 in that the final blades were forged that this curve is not changed significantly to closer to 3.2mm (1/8 inch) than 4.8mm by small additions of alloying elements and (3/16 inch). These differences, in relative will apply to low-alloy steels as well as layer thicknesses and in final blade thick- plain carbon steels. Table 2 presents the ness, would be expected to make only nominal compositions of the AISI steels small changes in the predicted times for ho- used in this study, and it is seen that the mogenization shown on Fig. 2, and one level of alloying addition is relatively would predict that homogenization of the small. This means that a Damascus blade C should be complete. made from a combination of 1018 and 5160, Two samples were made of each of the such as the A blade, should have the same steels, and one was quenched in water and hardness in the 1018 layers as in the 5160 the other was quenched in oil. To evaluate layers if the C level is homogenized be- the amount of diffusion of the C between the tween the two layers, even though the Cr layers, the samples were cut transversely to alloying element will remain much higher

Table 1 Data on the Steels of This Study

Code Steel pairs Thicknesses (in.) R. Hardnesses

A 5160–1018 5/16*–3/16* 64.6–65.3 B 1086–1018 5/16–3/16 69.4–69.4 C 5160–L6 3/8*–5/16 68.9–68.6 D 52100–L6 5/16–5/16 66.7–64.2 E L6–wrought iron 5/16–3/16 63.9–64.4

*5/16 Ϸ 7.9mm, 3/16 Ϸ 4.8mm, 3/8 Ϸ 9.5mm.

Pattern-Welded Damascus Blades 187

folding, it will become 3/10. This means that, in the final blade, the steel of the original inner layer will occupy a volume fraction of only 3/13, which corresponds to 23% of the total volume. After homogenization, the %C in both layers will reach an average value over the starting sheets given as 0.77 times the %C in the outer sheets ϩ 0.23 times that in the inner sheet. For blades A and B, the expected average values turn out to be 0.50%C and 0.70%C. Figure 5 predicts that martensites of these carbon levels are expected to have Rc hardnesses of 62 and 66, respectively. It is seen that the hardness values in Table 1 are running FIG. 3. Blade E: thick layer is L6; thin layer is wrought higher than expected by about 3 points. iron. Perhaps inaccuracy of the conversion from the Knoop scale into the Rockwell C scale is causing the Rc values to be high. Indepen- in the 5160 layers. Hence, the equal hard- dent of this problem, however, the num- nesses found between the two layers of bers clearly show that there is no signifi- steels A through E in Table 1 provide very cant difference in hardness between the strong evidence that C diffusion has com- two layers after forging. pletely homogenized the C level between This conclusion means that the second the two layers during the forging operation. assumption presented at the beginning of Folding of the 3-layer initial composite the article is also incorrect: the reason that will quickly produce an alternating layer the two layers etch to different gray levels structure in which the ratio of the thickness cannot be due to a difference in the C level of the original inner sheet to original outer between the layers. The cause of the differ- sheets will be reduced from the initial ent etching characteristics must be related value. For example, starting with an inner to the difference in the alloying elements. sheet of 3/16-inch thickness and outer There are two mechanisms by which the al- sheets of 5/16 inches, the original sheet- loying-element difference could produce thickness ratio will be 3/5, whereas, after different etching characteristics. Mecha- nism (1): they could change the hardenability of the two layers such that martensite forms on quenching in the high-alloy layer and a nonmartensite structure, such as pearlite or bainite, forms in the low-alloy layer. Mechanism (2): If martensite forms in both layers, then the alloying elements must be changing the etching characteristics of the martensite. The equal hardnesses in the layers indi- cates that mechanism 1 is not occurring here. Additionally, it is possible to deter- mine if mechanism 1 is operating from a simple microscopic examination of the polished and etched samples. Examination of all of the samples of this study at higher FIG. 4. Blade C: thick layer is 5160; thin layer is L6. magnifications than shown in Figs. 3 and 4

188 J. D. Verhoeven and H. F. Clark

pearlitic or bainitic, whereas the alloy layer will be martensitic. For a light etch, this produces a change in the overall gray level along a band running in from the cutting edge. The band extends in from the edge to a line where the blade thickness is roughly a constant value. A change in the gray level is evident to the eye along this line. Deep etching has been found to reduce the change in gray level along this line. Mechanism 2 requires that the etching characteristics of the martensite be strongly affected by the level of alloying elements. Experience with the effect of tempering on the etching characteristics of martensite il- lustrates that the gray level of polished and FIG. 5. Increase in Rockwell C hardness of fully mar- etched martensite can be changed dramati- tensitic steels versus carbon content (from [7]). cally. It is well known that as-quenched martensite (so-called fresh martensite) etches white in nital, whereas tempered showed that all of the samples were fully martensite etches dark in nital. On temper- martensitic in both layers. Mechanism 1 ing, very fine carbides form in the fresh can, however, sometimes be operative. A martensite, and the formation of these car- recent paper on a welded Damascus mate- bides affects the etching pattern on the pol- rial [8] made with layers of W2 and A203E ished surface, apparently causing the sur- presented metallographic evidence of this face to become more roughened and mechanism. The paper also presented mi- darkening its appearance to the eye be- croscopic evidence that the C level was ho- cause of the increased light scattering from mogenized, and chemical analysis with the the roughened condition. Alloying ele- use of an electron microprobe showed that ments affect the composition and the chem- the Ni layer was not homogenized; both of ical reactivity of both the carbides and the these conclusions are consistent with this martensite. They also tend to delay the for- study. It is a common experience of blade- mation of carbides during tempering. smiths to observe an etching effect due to Therefore, it seems likely that it is the dif- mechanism 1 on lightly etched Damascus ference in alloy content between the two blades. After quenching, both layers of the layers of a Damascus blade that produces damask are fully martensitic near the thin the different etching characteristics of the edge of the blade, but, as one moves away martensite in the two layers of fully marten- from the edge into the thicker region of the sitic blades. The changes in etching charac- blade, the plain carbon layer will become teristics would be expected to be increased

Table 2 Standard Compositions of AISE Steels Used in This Work

Steel C Mn Cr Ni Mo

1018 0.18 0.75 ——— 1086 0.86 0.40 ——— 5160 0.60 0.87 0.80 —— 52100 1.04 0.35 1.45 —— L6 0.70 0.55 0.75 1.5 (0.3)

To a first approximation all of the steels are expected to have roughly the same low levels of residual elements, Si, S, and P.

Pattern-Welded Damascus Blades 189

by tempering and, indeed, it is our experi- teristics. Hence, it would not be surprising ence that the pattern development of Dam- if the relative contrast of modern Damsacus ascus blades is improved by tempering. blades made from steel pairs involving In the present experiments, the samples plain carbon steels would vary signifi- were subjected to a low level of tempering, cantly, depending on the batch of steel that corresponding to the 10-minute hold at happened to be used in the blades. 250ЊF produced during the plastic mount- ing operation. The proposed theory for mechanism 2 predicts that (A) unalloyed CONCLUSIONS layers should etch more darkly and (B) the largest contrast between layers should ap- Experiments on modern pattern-welded pear in blades having steel pairs with the Damascus steel blades have provided biggest difference in compositions of alloy- strong evidence to support the following ing elements. The contrast on blade E of two theories on these blades. Fig. 3 is consistent with prediction A, as 1. There are generally no soft and hard lay- one sees that the wrought iron layers have ers near the cutting edge of a modern, etched more darkly. Examination of the quenched, pattern-welded Damascus compositions of the steels used here and blade made from high- and low-carbon given in Table 2 reveals that prediction B AISI plain carbon and alloy steels. Car- also appears to be the case. Blade E (Fig. 3) bon diffusion is sufficiently rapid during should have the biggest alloy-composition the forging conditions used to make difference between the layers because there these blades that the layers become ho- are essentially no alloying elements in the mogeneous with respect to C composi- wrought iron layer. Blade E did display the tion. Because the hardness of martensite largest interlayer contrast of the five steel is controlled by C composition, the lay- pairs that were studied, as is partly illus- ers have equal hardnesses. trated by comparing Fig. 1 with blade C of 2. In fully hardened blades, the etching dif- Fig. 4 and blade B of Fig. 6. The next high- ference between the layers results from est contrast blade was A, not shown, which differences in alloying elements present had an interlayer contrast difference inter- in two different steels used to make the mediate between blade E and the two blades. These substitutional elements have blades B and C. The interlayer contrast of much lower diffusion coefficients than blade D was small, a bit less than that of does C and do not homogenize in the blade B of Fig. 6. These variations in interlayer contrast with alloy differences between the layers are qualitatively consistent with the theory. In the one blade that used a pair of plain carbon steels, blade A with 1086 and 1018, it is apparently the difference in Mn content that produces the interlayer contrast. It may well be, however, that things are more complicated than this. Virtually all modern plain carbon steels contain residual elements of Cr, Ni, Mo, and Cu in the 0.01 to 0.12% range, and large variations from batch to batch within this range are possible, particularly if large volumes of scrap are used in the refining process. It seems likely that variations even in this small range of 0.01 to 0.12% could produce significant effects on etching charac- FIG. 6. Blade B: thick layer is 1086; thin layer is 1018. 190 J. D. Verhoeven and H. F. Clark

forging process. They cause contrast dif- ment additions on C diffusion in iron [5, ference on etching, and these differences 6]. Strips of an Fe-C alloy were welded in quenched blades are enhanced on around a strip of Fe-X alloy, where X was a tempering. substitutional alloying addition of one of the following elements: Si, Ni, Co, Mn, and Previous studies [8] have shown that it is Cr. Diffusion of C was studied at 1050ºC, possible to obtain hard and soft layers in where C atoms migrated between strips and pattern-welded Damascus blades owing to the substitutional alloying elements did not. the hardenability variations between the The strips were analyzed after the C flux layers produced by the difference in alloy- had become zero, a condition termed tran- ing elements. This phenomenon was not sient equilibrium. It was found that, at tran- found in any of the blades studied here and sient equilibrium, the C level in the FeX strip would not be expected to occur near blade differed from that in the surrounding FeC edges where cooling rates on quenching strips by an amount that will be called ᭝C , become extremely high. c defined here as (% C in FeC strips) – (% C Another possible way that hard and soft in FeX strip). A ternary diffusion analysis is layers might be produced in welded Dam- presented in terms of the diffusion coeffi- ascus blades in by tempering adequately to cients D and D , which shows that the ratio drop the as-quenched hardness signifi- 11 12 of these two coefficients for their experiment cantly. The hardness loss on tempering can should be given by the following relation: be greatly reduced and even reversed by allowing additions [7]. Hence, strongly al- D ⁄ D = ∆C ⁄ C (2) loyed layers in tempered blades may retain 12 11 c x higher hardnesses than plain C steel layers. where C is % alloying element in the FeX This possibility was not investigated in the x strip. The D /D ratio was determined present study. 12 11 from the experiments, and the data are Calculations are presented in the appen- shown in Fig. 7, where % C of the abscissa dix, showing that soft and hard layers may is the average value of the terms in ᭝C also result in as-quenched blades owing to c. The D /D ratio was shown to be inde- ternary allowing effects if large differences 12 11 pendent of temperature for Ni over the in certain alloying elements are present be- range studies, 810 to 1050ºC, and theoreti- tween the layers. The experiments of cal reasons are presented to show that the Kirkaldy [5, 6] predict that Cr and Si are the ratio should be temperature independent. most potent common alloying elements for The correlation presented in Fig. 7 appears this effect. For example, blades layers of to be very good. The C diffusion process high Cr (e.g., stainless steel) against layers occurring during the forge welding of of plain C steel should produce hard and Damascus blades is quite similar to that oc- soft variations between layers. curring in these experiments. Hence, the data of Fig. 7 may be used with Eq.(2) to The authors would like to acknowledge helpful predict a value of ᭝C between the layers of discussions with A. H. Pendray. The work by c welded Damascus blades. J. D. V. was supported by the U. S. Department Equation (2) and the data of Fig. 7 were of Energy, Ofﬁce of Basic Energy Sciences, used to calculate the expected % C differ- through the Ames Laboratory, Iowa State ence in the two layers of some of the blades University, Contract No. W-7405-ENG-82. studied here, and then the difference in hardness between the two layers was calculated by using the data of Fig. 5. Consider APPENDIX blade A as an example. It was assumed that the %Mn in the two layers was essentially Kirkaldy and co-workers have studied the the same and had no effect on D12/D22, effect of some common steel alloying ele- which was therefore taken from Fig. 7 at the Pattern-Welded Damascus Blades 191

The work of Kirkaldy [5, 6] predicts that it should be possible to make Damascus blades that do have hard and soft layers if the proper alloying elements are employed. The data of Fig. 7 show that Cr and Si have the largest effects. Consider as an example a welded Damascus blade made up of equal volumes of AISI 1060 and the stainless steel AISI 405. It is seen in Eq.(2) that the large Cx , value of 13 wt.% Cr (13.8 at. %) in the 405 will produce large values of ᭝Cc. And, interestingly, although nearly all C originates in the 1060 steel layers, most of it will end up in the 405 layers after transient equilibrium is achieved. The calculation predicts final C levels of 0.11 and 0.50 wt.% in the 1060 and 405 layers, respectively, which corresponds to a significant hardness difference of about 24 Rc points. FIG. 7. Experimental data on variation in ratio of dif- Hence, it is predicted that hard and soft fusion coefficients with average percent carbon (from layers could appear in welded Damascus [5, 6]). blades with proper choice of the alloys used for the steel pairs. It is also possible to obtain hard and soft layers by using pure value for the 0.8 wt.% Cr of 5160. The value Ni for one of the layers or by using thin of ᭝Cc was then calculated from Eq.(2). pure Ni foil between the layers, as is some- From the known volume fraction of the two times done by U. S. bladesmiths. layers and the original C level in each layer, the average C composition of the blade was calculated, which allowed calculation of the References % C in each layer using ᭝Cc. It was neces- sary to utilize at.% with Eq.(2). For blade A, 1. M. Sachse: Damascus Steel: Myth, History, Technol- the calculation predicted the Cr layers to ogy Applications, Verlag Stahleisen, Dusseldorf, Germany (1994). reach a C composition of 0.55 wt.% and the 2. J. D. Verhoeven: Fundamentals of Physical Metal- Fe-C layers 0.49 wt.%, which corresponds to lurgy. Wiley, New York, p. 297 (1975). ϭ hardnesses of Rc 62 and 60, respectively, a 3. W. Jost: Diffusion in Solids, Liquids and Gases. Aca- difference of only 2 points. For blade B, the demic Press, New York (1952). calculation was made by using the Mn dif- 4. J. Fridbery, L. D. Torndahl, and M. Hillert: Diffu- ference of 0.35 wt.% as a method of approx- sion in iron. Jernkont. Ann. 153:263–276 (1969) imating D12/D22 from Fig. 7, and the pre- 5. J. S. Kirkaldy and G. R. Purdy: Diffusion in multi- component metallic systems. Can. J. Phys. 40:208– dicted Rc difference was less than 1 point. The remaining blades all involve L6, which 217 (1962). contains several alloying elements, and the 6. L. C. Brown and J. S. Kirkaldy: Carbon diffusion in dilute ternary austenites. Trans Metall. Soc. AIME estimation of D12/D22 becomes extremely 230:223–226 (1964) approximate because it is not clear how the 7. G. Krauss: Steels: Heat Treatment and Processing alloying elements might interact. However, Principles. American Society for Metals Interna- the results for blades A and B predict Rc dif- tional, Metals Park, OH, Chapter 6 (1990) ferences of 2 points at most, which is in rea- 8. B. Lacey and C. Brooks: Microstructural analysis sonable agreement with the observed data, of a welded Damascus knife blade billet. Mater. Char. 29:243–248 (1992). in view of the difficulty of measuring Rc more accurately than 2 points. Received December 1997; accepted April 1998.