AIR FORCE CAMBRIDGE RESEARCH LABORATORIES. Shear Strength of Twelve Grossly Deformed Metals at High Pressures and Tomperatures

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' IS AFCRL AUGUST 967 ENVIRONMENTAL RE5FARCH PAPERS, NO. 273 CO AIR FORCE CAMBRIDGE RESEARCH LABORATORIES L. G. HANSCOM FIELD, BEDFORD, MASSACHUScTTS 'i; Shear Strength f Twelve Grssly Defrmed
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' IS AFCRL AUGUST 967 ENVIRONMENTAL RE5FARCH PAPERS, NO. 273 CO AIR FORCE CAMBRIDGE RESEARCH LABORATORIES L. G. HANSCOM FIELD, BEDFORD, MASSACHUScTTS 'i; Shear Strength f Twelve Grssly Defrmed Metals at High Pressures and Tmperatures R. E. RIECKER L. C. TOWLE T P. ROONEY This wrk wus supprted by the Advanced Research Prject» Agency under ARPA Prject 867 OFFICE OF AEROSPACE RESEARCH United States Air Frce D CLEARINGHOUSE c ^ 'S BEST AVAILABLE COPY tf0m Ä ) - ' l Distributin f this dcument is unlimited. It may be released t tiie] Clearinghuse, Department f Cmmerce, fr sale t the general public. Qualified requestrs may btain additinal cpies frm the Defense Dcumentatin Center. AU thers shuld applj t the Clearinghuse fr Federal Scientific and Technical Infrmatin. r AFCRL AUGUST 967 ENVIRONMENTAL RESEARCH PAPERS, NO. 273 J AIR FORCE CAMBRIDGE RESEARCH LABORATORIES TERRESTRIAL iciences LABORATORY PROJECT 7639 L. G. HANSCOM FIELD. BEDFORD, MASSACHUSETTS Shear Strength f Twelve Grssly Defrmed Metals at High Pressures and Temperatures R.E. RIECKER L C. TOWLE* T. P. ROONEY *U.S. Naval Research Labratry, Wthingtn,. .C. This wrk was supprted by the Advanced Research Prjects Agency under ARPA Prject 867 Distributin f this dcument is unlimitad. It may be released t the Claaringhuse, Department f Cmmerce, fr sale t the general public. OFFICE OF AEROSPACE RESEARCH United States Air Frce Abstract The shear strength f grssly defrmed tungsten, germanium, nickel, beryllium, uranium, cpper, gld, silver, aluminum, magnesium, bismuth, and tin was measured in an ppsed anvil shear apparatus at pressures up t 50 kb at 27 0 C, andfrgld, silver, and cpper t a maximum f 900 C. The shear data agree with independent strength measurements at lw pressures, but differ significantly frm high-pressure shear-strength measurements made by ther investigatrs. The data n the nble metals als fit a simple empirical frmula relating the temperature and pressure dependence f the shear strength. iii BLANK PAGE Cntents. INTRODUCTION 2. EXPERIMENT AL 2 3. THEORETICAL MODEL 5 4. RESULTS 9 5. CONCLUSIONS 22 ACKNOWLEDGMENTS 23 REFERENCES 25 illustratins Trque-Time Curve Shwing Schematically That a Significant Transient State Always Exists 3 Metallgraphic Crss Sectin Thrugh Defrmed Wafer Shwing Undefrmed Segment * Metallgraphic Crss Sectin Thrugh Defrmed Wafer Shwing Mst Severely Defrmed Periphery 4 Metallgraphic Crss Sectin Thrugh Defrmed Wafer at Center 4 Schematic Shwing Relatin Between Observed Data and Idealized Mdes f Behaviui, Internal Shear, and Surficial Slip 8 Pressure Distributin vs Radial Psitin f Defrmed Wafer 8 Shear Curves fr Tungsten. Uranium, and Nickel at 27 C and a Strain Rate f 0 sec Shear Curves fr Beryllium, Cpper, Silver, and Gld at 27 0 C and a Strain Rate f 0 _ sec -! Shear Curves fr Aluminum, Magnesium, Bismuth, and Tin at 27^ and a Strain Rat«f 0 sec -' lllustrcriins 0. Observed Shear Curves f Cpper, öilver, and Gld at 27 C Shwing Zer Pressure Strength 7. Shear Strength vs Reduced Temperature Plt f Cpper, Silver, and Gld 9 2. Shear Curve fr Germanium at 27 C and a Strain Rate f 0' sec Tables. Test Cnditins fr Tungsten 2. Test Cnditins fr Uranium 3. Test Cnditins fr Nickel 4. Test Cnditins fr Beryllium 3 5. Test Cnditins fr Cpper 3 6. Test Cnditins fr Silver 3 7. Test Cnditins fr Gld 3 8. Test Cnditins fr Aluminum 5 9. Test Cnditins fr Magnesium 5 0. Test Cnditins fr Bismuth 5. Test Cnditins fr Tin 5 2. Rm Temperature Parameters 6 3. Summary f Shear Strengths at Varius Temperatures fr Cpper, Silver, and Gld 8 4. Test Cnditins fr Germanium 2 5. Summary f Physical am', Mechanical Prperties fr Twelve Elements 22 vi Shear Strength f Tw Ive Grssly Defrmed Metals at High Pressures and Temperatures I. INTRODUCTION The sliear strength f pure, single-phase metals depends principally n temperature, pressure, dislcatin density, and strain-rate. In general, dislcatin density is nt an independent variable, since it depends n the detailed histry f the material. Hwever, when a metal defrms cntinuusly at a cnstant strain-rate, temperature, and pressure, the dislcatin density appraches a saturatin value apprpriate t the dynamic equilibrium cnditins that prevail. Under these circumstances ne wuld hpe that the shear strength wuld depend n te^.perature, pressure, and strain-rate thrugh sme relatively sim le relatinship. The shear strength f a metal in the grssly defrmed state represents the maximum that can be btained by wrkhardening. Thus the study f grssly defrmed metpls is f bth theretical and practical interest. The shear stre gth f pure tungsten, germanium, nickel, beryllium, uranium, cpper, gld, silver, aluminum, magnesium, bismuth, and tin was measured in an ppsed anvil shear press frm 0 kb t a maximum f 50 kb at 27 0 C, and high-temperature tests t a maximum f 900 C were made n the nble elements cpper, silver, and gld. The results exhibit internal cnsistency and agree with independent measurements made at lw pressures. The new data n the nble metals als fit a recently reprted emperical relatinship giving the temperature and pressure dependence f the shear strength f grssly (Received fr publicatin 4 August 967) defrmed materials (Twle, '967). The present results differ significantly frm earlier rm-temperature measurements by Bridgman (935, 937) in the limited pressure range t 50 kb and by Vereshchagin and Shapchkin (960) t 50 kb. 2. EXPERIMENTAL The shear press used in the testp reprted herpin is similar t that emplyed riginally by Bridgman (935, 937) and t a mre recent design f Vereshchagin et ai. (960). We aescribed the apparatus in detail elsewhere (Riecker, 9S4a; 9f! 4b). The essential features include a 0.25-in. -diam, 0.00-in. -thick sample wafer that is cmpressed by a hydraulic ram between a pair f tungsten carbide anvils having in. -diam. flat circular faces. The upper anvil is rtated at cnstant speed by a variable-speed mtr thrugh a gear train, A lever arm prevents rtatin f the lwer anvil and is anchred t the press frame thrugh a strain-gage lad cell. tin heating f the anvils. High-temper at jre peratin is achieved by external induc- The directly bserved physical quantities include: anvil temperature, T; nrmal lad applied t the anvils. N; rtatin rate f the upper anvil, R; end the frce applied thrugh the lad cell t prevent rtatin f the lwer anvil, F. An infrared pyrmeter recrds the temperature f the sample; it is calibrated with chrmel-alumel thermcuples placed in exact duplicates f the anvils. Observed temperatures are accurate within ± 2 percent. Pressure applied t the sample is calculated frm the frce per unit sample area. Reprducibility appraches ± 3 percent, as determined using bismuth I-II and thallium II-III phase transitins t calibrate the press. A Variac mtr-speed cntrl calibrated under lads t 200 kb determines the anvil rtatin rate. A strip-chart recrder mnitrs the lad cell utput frce, and when multiplied by the lever arm lengtn, L, gives a cntinuus recrd f the trque M, required t prevent rtatin f the lwer anvil. Measuremen*s were made n samples having purities f percent r better btained frm the Lawrence Radiatin Labratry. Each metal, except fr Bi and SN, was crss-rlled t a thickness f in, and then annealed fr t 2 hr at 500 C. We btained all data at a cnstant rtatin-rate f 0 revlutins per hur, which crrespnds t an average strain-rate f abut 0 The metals were sheared fllwing applicatin f pressure and temperature. A fresh sample was used fr each datum pint, except v here nted. This prcedure prevented frequei t anvil-t-anvil cntact at the sampl? periphery which wuld have led t errneus results. In previus shear measurements n silicate insulating materials (Riecker and Hney, 965; 966), we mnitred the electrical resistance between anvils as a means f detecting anvil-t-anvil cntact. After shearing a sample?.t ne sec Drssure, anvil-t-anvil cntact usually develped if we attempted t shear the samp.e ag?in at a higher pressure. Cntact frequently caused a 2- r 3-fld increase in shearing trque. Cnsequently, we used fresn spmples fr each datum pint. Sir.ce resistance mnitring is nt pssible with metallic samples, the trque-time recrds were carefully inspected t verify that anvil-t-anvil cntact had nt ccurred. In spite f the use f a fresh sample in each test, a few spurius results attributable t cntact were discvered and rejected. A typical trque-time curve is shwn schematically in Figure. The figure shws an initial transient state that persists thrugh an angle f abut C deg, after which a steady state develps. During the transient perid the sample reaches an equilibrium thickness, wcrkhardens, and devel'^s sme preferred rientatin. Only the steady-state trque value is used in the shear-strength calculatins. Evidence supprting the behavir f the grssly deirmed wafers during the transient perid is prvided by bservatins made n micrhardness, thickness prfile, and metallgraphic textures f sheared wafers. The typical thickness f defrmed cpper wafers varies frm in. in virgin metal t in. (Figure 2) at the wafer periphery (Figure 3), and in. at the center (Figure 4). Virgin cper grain size averages abut 0.00 in. in diameter, but drps t less than in. in defrmed regins. Sme grains shw extreme flattening in directins nrmal t the applied lad (F'gure 3).» Stedy State 7 ML' t Figure. Trque-Time Curve Shwing Schematically That a Significant Transient State Always Exists. Wrkhardpning ccurs during this perid regardless whether the final steady-state is ne f surficial slip r internal shear Kigure 2, Metallgraphie Crss Sectin Thrugh Defrmed Wafer Shwing Undefrmed Segment. Nte thickness f specimen and lai-ge grain size. Axis f nrmal pressure lcated veitically. Scale line is i. n Figure 3. Metallgraphie Crss Sectin Thrugh Defrmed Wafer Shwing Mst Severely Defrmed Periphery. Sample was riginally same size as that in Figure 2. Nte grain distrtin and cmminutin. Nrmal pressure axis lcated vertically. Scale line is 0.05 mm Figure 4. Metallgraphie Crss Sectii Thrugh Defrmed vvafer at Center. Nrmal pressure axis lcated vertically. Scale is 0.05 mm The severe distrtinal changes and cmminutin in grains graphically illus- ti ate the magnitude f the induced strain, Knp micr'iardness tests made alng diametial crss sectins als quantitatively shw the degree f strain hardening that develps during grss shear. ber f 63. Virgin cpper gives a diamnd pyramidal num- Hardness at the periphery f defrmed wafers is 00 r mre, while hardness at the wafer center ranges frm 80 t 90. These measurements shw that the metal wafers receive grss strain, and that the nistal strainhardens in respnse t grss shear. The frictinal stress at the sample-anvil interface is given by ^P where ß is the cefficient f frictin and P is nrmal pressure. At lw pressures ;ip S, where S is the shear strength f the sample, and therefre surficial slippage must ccur. Hcrvever, np nrmally increases with pressure faster than S, ani eventually a pressure is reached ax which the defrmatin mechanism switches t internal shear. tained with this apparatus. It is nly at high pressures that useful data are b- Onset f anvil-t-anvil cntact in the slip regime has little effect n the trque, since the frictic-.i cefficient is nt greatly altered. I*' cntact ccurs in the shear- ing regime where fip S, then trque rises sharply. Hwe er, cnsistent anvil cntact prduces nrmal lking trque-time cur-'es, evtn tnugh the steady-state trque may be errneusly large. As a cnsequence, when a single sample is repeatedly sheared thrugh the entire pressure range, as was dne by Bridgman and ] y VereshJiagin and Shtpchkin, anvil-t-anvil cntact can easily escape unnticed. Hence, sme f their measurements are pen t serius questin. 3, THEORETICAL MODEL rue analysis f shear measurements is based n a mdel riginally prpsed by Bridgman (935, 937). In rder t avid misinterpretatins, we indicate the majr apprximatins made in deriving the calculated shear strength frm the bserved quantities. The relatin f rtatin angle t applied strain is btained by cnsidering the trsin f a shrt circular cylinder. Shear strain y relates t the angle f rtatin 0 by the expressin v = K e (i) where h is the height f the cylinder and r is the radius at which the strain is calculated. Strain increases I'uarly frm zer at the symmetry axis t a maximum at the periphery. Fr the sample gemetry emplyed here, y ~ at the periphery, that is, extremely large strains are applied by small angels f rtatin. The trque required t prevent rtatin f the lwer anvil is given by M = L X F. This restraining mment can als be expressed by the integral a M = T X r X 2ir rdr (2) / where T is the shear stress at the distance r frm the axis f rtatin, and 2» rdr is an annular element f area in the sample wafer. The value assumed by the shear stres - depends n the defrmatin mechanism which prevails. The mecnanism can br either surficial slip at the sample-anvil interfaces, r internal shear within the sample. The mechanism i equiring the lwer activatin stress prevails. In the lw pressure surficial slip regime, T = /ip, and the restraining trque is M = 2^ MP (3) i where a is the anvil radius. In the high pressu-e regime, T = S(T, P), where the pssible dependence f shear strength n temperature and pressure is recgnized. Fr grss defrmatin, S will nt depend n strain. Furthermre, Bridgman (937) shwed that the shear strength f cpper and high-melting-pint materials varies nly mderately with strain-rate. Thus, we als assume that S is independent f y in what fllws. In principle, hydrr-tatic pressure shuld increase the strength f materials. Hwever, the bserved increases nrmally are quite small. Cnventinal engineering practice assu les that shear strength is independent f pressure. We will assume that shear strength can be expanded in a Taylr's Series expansin n the pressure variable and retain nly the linear term. Thus, S = Sj + ap (4) where S. is the shear strength at atmspheric pressure. The shearing trque then becmt's M = ^fr-fsj + a P). (5) It is cmmn practice t iivide tue bserved restraining trques by the numerical factr 27ra' /3 and call the result the shear strength. The data are then pltted as shwn by the heavy curve in Figure 5. Figure 5 apprximates the idealized curves at very lw and very high pressures where Eqs. (3) and (5) apply. The idealized curves intersect at the pressure P. fr which fip = S, that is, P,, = ^. (6) When we cnsider the effects f pressure gradients in the sample, the transitin frm surficial slip t internal shear ccurs smthly, as indicated by the knee in the heavy curve. Therefre, the data btained at lw pressures, t J the left i the knee, bear n immed'ste relatin t the s.ear strength f the material. Figure ( shws schema.ically the pressure distributin acrss the anvil radius. It varies gradually ver the central prtin f the sample and changes rapidly near the periphery. Figure 6 reveals that internal shear ccurs after sme minimum threshld pressure develps at the center f the sample. With further increases in lad, the bundary between shear and slip regimes, r, increases rather rapidly until it falls between r and a. This bundary then mves utward very slwly wich increased pressure In principle, slip always ccurs in a small annular regin arund the periphery regardless f the pressure applied. This nnunifrm pressure distributin leads t a smth transitin frm the slip t internal shear. The effects f incrprating a realistic pressure rradient int tie derivatin given abve were cnsidered in detail elsewhere by Twle and Riecker (966). Fr large lads where r r and the bulk f the sample shears internally, the errr incurred by neglecting th~ pressure gradient is typically less than 5 percent. Three characteristics f shear measurements in ppsed anvil devices shuld be emphasized: () valh shear-strength data can be btained nly abve a threshld pressure that may be qaite high fr materials that are intrinsically strng r that wrkharden extensively. This threshld cm bs estimated frm Eq. (6) and is typically in ihc range frm 0 t 50 kb; (2) useful data are btained nly in the steadystate cnditin after the sample has been grssly defrmed; (3) sample defrmatin and wrkhardening ccur under all pressure cnditins in metals, as evidenced by the transient prtin f the trque-time curves, althugh surficial slip dminates the final behavir at lw pressures. in x h- z UJ tr h- Idealizeci Shearing Curve Slpe = ds/dp~.oi / Idealized Slippage Curve Slpe=/i.~ O.I UJ I in Internal Shearing /ip S Surficial Slippage/iP S P K PRESSURE P F igure 5. Schematic Shwing Relatin Between Observed Data and Idealized Mdes f Behavir, Internal Shear, and Surficif! Slip Surficiül Slippage RADIUS r Figure 6. Pressure Distributin vs Radial Psitin f Defrmed Wafer. Surficial slip always ccurs at periphery f wafer where frictinal stress drps belw the shear strength f the sample I. RESULTS Figures 7, 8, and 9 shw the shear-strength nrmal-pressure curves btained t rm temperature fr tungsten, uranium, nickel, beryllium, cpper, silver, gld, aluminum, magnesium, bismuth, and tin. Tables thrugh give the teat cnditins and shear-s'rength values bserved Sme elements were nt sheared t 50 kb due t excessive anvil failure. The curves in Figures 7, 8, and 9 clearly snw the qualitative frm anticipated by the theretical mdel indicated in Figure 5. 0 O AFCRL 967 * BRIOGMAN NORMAL PRESSURE kb I ISO URANIUM 238-9=?- O AFCRL 966 BRIOGMAN 937 ] _i_ -L. _L MO NORMAL PRESSURE kb O AFCRL 967 BRiDGMAN K MO ISO NORMAL PRESSURE kb Figure 7. Shear Curves fr Tungsten, Uranium, and Nickel at 27 C and a Strain Rate f 0 sec . Test cnditins given in Tables,2, and 3 ' - ir tf cn^rt CO O OJ m c- a ^ridcööio O ^--«-^ PJ Oi? W N ä O CO c c id t, u IM m c a c U ta 0 h c 4j M B 3 - B C X! B c U in - re h CO PI 3 a E V h a u p p m 3 E w w ec 'f TT 3 S ai S «^ ^f n en TI- 3 O m O m a) ^r C) -f O' ^r OT * 03 M in ^ *JI c m -' w PJ v i ci r- cmt^rin 0OO3 i i i i iii II & c 0» 0 3 O JE _.. P PPDPP DPP ai OJ OJ CTJ CD e M url- Url-2 Url-3 Url-4 Url-5 O C-J t-* 8 E 2 c t- CQ ci 00 3 ll i g a w ID P E t a en ~* cncncin c-ra)^ ODTCT. 2= fpj ^«eßo virtttt- r-ca: s M ^ OB O 03 in? en N -T W M «J'«NWiD-* * OOO u Of CO ^(M ai^f,^. ^ftfoc t^v 'rc CO r- N»- -'- «-«OOOC OOO CD* cd «3«3 w c 0 Q M c cfl -n 3 * 5 s ^ O H k n tn ) tn t ifioioo) a «r ai nr us ^ en n is air- ciicr- 'C'tntnrj- «rnm j»; *«w CTJOJ asiftoi iffict) ii 03 PH a; -fl.- ^j ^-. -ntcf-aji O M j^ Ö t. Ji z i. u CO 0) O a e u t 0) h h cfl 3 m c M O CO.- ^ - - ' 00 N n j «0 h. I m m «^ V m td r- e tr 0 i* 0' O 0' «/) ^- -H -^ r-. M S 00 k O 3 0 w It 8 «Kn O -f ^ as tc 0 M O (C OO t OJ «c» 00 « a 0 e e .- T in T T *^ R cr J) O* O 0 -- O* O* O O e 0* 0 0* 0 '' r Oi t- O w C4 5 s c 'S b y t) If O ~ 2 c CO «m tn 0 a «r A i# fö e«cc m t- t- t COiO n ^ ^ n NO» * ö- 0 -..^ e» en' O) O) O) Ol OJ 05 OJ' OJ' a» Oi OJ 0)0) C4 M ^. m tr- 00 OJ O ^ M ««r m i i * u S i % E S 7T 0 - Ol «* t r- { «J r- a) OJ «5? z 'A % ^ ^ c: z! ^ ^3 - ctd^th^i --j»»as zzzzz zsiszz KZ a H, _ 0 'S «E P r-c4^' 9*m «r-cf H ^ ui tot-aso) ^.^-^.-,«r^^ K S5 S55S SS5S5 555 'S) 2 O «FCRL 9*6 BRIOGMAN 937 NORMAL PRESSURE kb IZC ISO 0 20 SO O AFCRL 966 BRIOGMAN 937 A VERESHCHAGMI960 J U ISO NORMAL»RtSSURE kb O AFCRL 966 BRIOGMAN 937 A VEHESHCHAGN 960 J! J L SO ISO NORMAL PRESSURE kb O AFCRL 966 BRIOGMAN ( ISO NORMAL PRESSURE kb Figure 8. Shear Curves fr Beryllium, Cpper, Silver and Gld at 27 e C and a Strain Rate f lo sec'l. Test cnditins given in Tables 4 thrugh 7 ! '3 u m a U m fi O -» d U M m 0) H in () 3 T * is,»», »,-v«v»«v «fi?' * ( i is ig.. --,,.- a, - u -:.. n- JJ T -^ M. «^ si - ^! ««P P «S * i s Is d - b b e b b b b b b b - 3 ' q - _ O ' r 5 6 f m m (J:- i'sss ;ssss s;g; sss s i L, O OD' C»' B at ai ai ai» b b b b i c. a b b - (SitM * m m io t- nii-i w * P si- It d ' 3 ^ 6S 2 ll '- '3-3'3'3 iiiii -jiii hii 3 ÜÜUU uuuuu uu uuu u «i i i i Eu Ü t c. T3 c U IT. V H 0) I ««Ü v I«b ä 5 P- Ken ^^HrHcsj (MeMMMn n m m vs * i (003^ Mm wm Q N M «mwcf V'^m^n^' c^'»'cr
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