WELDING RESEARCH SUPPLEMENT TO THE WELDING JOURNAL, SEPTEMBER 1973 Spnsred by the American Welding Sciety and the Welding Research Cuncil ("Rtj Weld Cling Rates and Heat-Affected Zne Hardness in a Carbn Steel Study shws that hardness is related t cling rate at a particular temperature and cnsiders the implicatins fr welding BY B. A. GRAVILLE ABSTRACT. Cling rates have been widely used as a means f relating weld and heat-affected zne (HAZ) hardness t welding parameters. There is, hwever, n agreement n which temperature shuld be used fr measuring cling rates and in sme instances difficulties have arisen because f the particular temperature chsen. Accrdingly, experiments have been carried ut t prvide sme experimental justificatin fr the assumptin that hardness can be related t cling rate at sme temperature and t determine that temperature fr a carbn steel. Studies f cling behavir and weld metal and heat affected zne hardness as a functin f energy input and thickness have been made. The results shw that cling behavir changes during transfrmatin and in thick plate (3D cling) this is equivalent t an increase in the thermal cnductivity belw abut 450 C. Data is presented enabling cling rates at a variety f temperatures t be determined fr bth thick and thin (3D and 2D) plate cnditins. The results f hardness tests shw that fr a range f hardnesses (275-375 HV) the temperature f crrelatin is abut 400-450 C but decreases t abut 300 C when hardnesses f 400-425 HV are prduced in the HAZ. Intrductin The prperties f welded jints and the pssibility f cracking depends t a great extent n the cling rate after B. A. GRAVILLE is Supervisr, Technical Research, Dminin Bridge C., Ltd., Lachine, P.Q., Canada. Paper was selected as alternate fr the 54th A WS Annual Meeting in Chicag during April 2-6, 1973. welding. The cncept f critical cling rates has been used in attempts t predict safe welding prcedures (i.e., preheat, energy input, etc., t avid cld cracking) fr carbn and lw ally steels. Cttrell (Ref.1) fr example fund a relatin between the ccurrence f cld cracking and the cling rate at 300 C. It and Bessy (Ref. 2) have related the ccurrence f cracking in restrained butt welds t the cling time between 300-100 C. Recently, Bailey (Ref. 3) has presented a system fr determining safe welding prcedures based n a critical heat-affected zne (HAZ) hardness criterin. He used the cling rate at 300 C t relate t the hardness. Bailey encuntered certain difficulties with this apprach when preheat was used. It became apparent that fr sme f his steels the hardness was determined by the cling rate at a temperature higher than 300 C and it was necessary t apply a crrectin factr. Many ther suggestins have been put frward fr ways f characterizing the cling cycle, (such as cling time between 800-500 C, cling rate at 540 C) s as t relate t the resulting hardness althugh there has been n experimental basis fr any f these. Cling rates have been measured by a number f wrkers, and recently Signes (Ref. 4) has presented data cvering a wide range f thicknesses, energy inputs and preheat levels. Mst f these wrkers have fund that cling rate data fit the frm f the theretical equatins quite well but with different values fr the cnstants. N wrk is knwn where the cling rates ver a range f temperatures were studied. In the present wrk an attempt is made t prvide sme experimental justificatin t the assumptin that hardness in the heat-affected zne and weld metal can be related t cling rate and t determine at what temperature the cling rate shuld be measured. The wrk als presented the pprtunity f studying cling rates at varius temperatures and this has prved useful in crrelating data in the literature and in explaining sme f the anmalies. Methd f Apprach Fr a bead-n-plate test with a given energy input the cling rate will increase as the thickness increases. Abve a certain thickness, hwever, the cling rate becmes independent f the thickness. This thickness can be termed the 'saturatin thickness'. The saturatin thickness will depend n the energy input and n the temperature at which the cling rate is measured. Fr a high temperature the saturatin thickness wuld be quite small whereas fr a lw temperature it wuld be greater. In a similar manner the hardness (in the HAZ r the wel metal) will increase as the thickness increases (at least fr thse steels in which hardness varies with cling rate. This includes C, C-Mn and lw ally steels). Again there will be a saturatin thickness abve which the hardness will nt increase. In essence the prgram cnsists f measuring the saturatin thickness fr hardness and cmparing it with the saturatin thickness fr cling rates measured at different temperatures. The prgram therefre falls int tw parts: firstly, the study f cling rates in welds ver a range f thicknesses and energy inputs and secndly, the study f HAZ and weld metal hardnesses as a functin f thickness and energy input. In this study n attempt was made t examine the effect f preheat. WELDING RESEARCH SUPPLEMENT! 377-s
500 Fig. 2 The mean f the maximum HAZ hardness in thick plate as a functin f energy input fr SA W and SMA W depsits 500 TT 450 I 2 s LU z Q 5 3 S 400 350 2 300 Manual Sub-arc I I I _ I 80 60 40 30 20 10 8 ENERGY INPUT kj/in 80 70 60 50 ENERGY INPUT kj/in Fig. 1 Maximum hardness f the HAZ f submerged arc welds pltted as a functin f energy input fr several thicknesses NOTATION T = Temperature T 0 = Initial plate temperature K = Thermal cnductivity C = Specific heat P = Density P = Thickness P = Rate f heat input E = Energy input H = Heat input (H=TJE where 17 is arc efficiency) P s = Saturatin thickness t = Time \ = p /2K V = Welding speed h = Cefficient t surface transfer r = (X 2 +Y 2 )' 7 ' crdinates Theretical Backgrund The theretical basis f heat flw in welding has been available fr sme time (Refs. 5,6) and has recently been summarized (Ref. 7). In thin plates, heat flw cnditins are tw dimensinal (2D) and the cling rate n the weld centerline is given by: (?), = 2TT Kp C P2 (T - T V 378-s l SEPTEMBER 1973 In thick plate cnditins are three dimensinal (3D) and the cling rate is given by: \ 2-K (T - T ) 2 H (2) In plates f intermediate thickness the cnditins are termed 2.5D and charts (Ref. 8) have been presented t describe this regin. The saturatin thickness (p s ) can be defined as the thickness at which equatins (1) and (2) give the same cling rate. Equating (1) and (2) gives: Pi = H pc(t-t 0 ) These equatins assume that the physical prperties (C, p, K) f the material d nt change with temperature. In practice it is knwn that they are dependent n temperature and this makes it difficult t predict accurate values f cling rate using these equatins. In general, t, at high energies and particularly in thin plates, there will be significant lsses f heat by surface transfer. Integratin f equatin (1) shws that the time t fr the weld t cl t temperature T under 3D cnditins is where A 3D is a cnstant dependent n the heat input, H, and the ther cnstant depends n the chice f rigin. Likewise the time fr a weld under 2.D cnditins t cl t temperature T will be: t = 1 T -T J + Cnst + Cnst (3) (4) in general a weld will start t cl under 3D cnditins and change t 2D cnditins at a lwer temperature. Analyzing a cling curve in the frm f equatins (3) and (4) thus prvides a ready way f determining the mde f heat flw at any temperature.
Experimental Cling Rates The cling cycles f bead-nplate welds using the submerged arc prcess were measured using Pt- Pt/13% Rh thermcuple. The plates were a minimum f 12 in. wide which allwed temperatures dwn t 100 C t be measured withut edge effects. The thermcuple was manually inserted int the weld pl thrugh the slag immediately behind the arc and the utput f the thermcuple was recrded n a fast respnse strip chart recrder. The lse flux and slag were nt remved frm the weld during the cling perid. Mst f the heat used t melt the flux is cnducted int the weld at high temperature because f the intimate cntact between the metal and the slag and because f the insulating effect f the lse flux abve the slag. The heat remaining in the slag when it detaches frm the weld is small cmpared with the ttal heat input and thus the submerged arc prcess has a high efficiency (-95%). Thicknesses frm 0.24 in. t 4 in. and energy inputs frm 4.4 t 126 kj/in. were cvered. The weld metal was a cnventinal silicn killed C/Mn weld metal giving an apprximate chemistry f 0.1%C, 1.0%Mn, 0.3%Si. Hardness Measurements The steel chsen fr the hardness measurements was ASTM A515 Grade 70 with a cmpsitin f 0.24C, 0.87Mn, 0.19Si. The steel was chsen because a wide range f HAZ hardnesses can be achieved ver a relatively narrw range f cling rates. The wide range f hardnesses is necessary because f the inherent inaccuracies in measuring hardness. Beads were depsited in shallw grves n the surface f a tapered plate. The plate was 36 in. by 36 in. and tapered frm 3 in. thick at ne end t 0.25 in. thick at the ther. Five beads using the submerged arc prcess (dc electrde +ve) and five using E7018 manual electrdes (ac) were depsited. The energy inputs f the ten beads are shwn in Table 1. Sectins were cut transverse t the beads at different thicknesses and hardness measurements were made in the HAZ and weld metal. At least five indentatins clse t the fusin bundary in the HAZ and tw in the weld metal were made using a Vickers hardness machine with a 10 kg. lad. The maximum value f the five was taken as the maximum HAZ hardness fr that particular sectin. Ten f the sectins were at the thick end f the taper and the HAZ hard- Table 1 Cnditins Used in the Hardness Test Submerged arc welding: Weld n. S1 32 S3 S4( a >. S5 Amp 300 300 300 500 400 Arc vltage 26 26 26 27 27 Shielded metal-arc welding (E7018 electrdes): Weld n. M1 (dc) M1 (ac) b ' M2 (ac) M3 (ac) M4 (ac) M5 (ac) Amp 79 90 116 112 166 166 Vltage 19 21 22 2-2 22 22 Speed,. ipm 48.6 24.3 19.5 21.0 22.4 Speed, ipm 10 10 8 6.5 8 6.5 Energy, kj/in. 9.7 19.3 24.0 38.6 29.0 Electrde size, in. 3/32 3/32 1/8 5/32 5/32 Energy, kj/in. 8.8 11.3 19.2 22.8 27.4 34.0 (a) S4 weld was restricted t the thick end t avid tempering f adjacent beads. (b) M1 (ac) was a shrt run at the thick end f M1, The plate was allwed t cl cmpletely between runs. ness in each bead was expected t be cnstant. These values were thus averaged t give a gd estimate f the maximum HAZ hardness n thick plate fr each bead. The values als prvided a measure f the accuracy f measurement f hardness values. The results were pltted as HAZ hardness against energy input fr each thickness. Sme f the results are shwn in Fig. 1 and cmplete results are listed in Tables 2, 3 and 4. The mean f the maximum hardness values fr the thick end are pltted in Fig. 2, fr the submerged arc and the manual prcess. Higher hardnesses are achieved at the same energy input in the manual prcess because f its lwer arc efficiency. T make the curves cincide a value f abut 60% fr the efficiency f the manual prcess relative t that f the submerged arc wuld have t be used. This lw efficiency is in agreement with ther wrk (Ref. 4) but might als be partly attributable t the use f ac fr the manual tests where the pwer factr may have been lw. Results Cling Rates The time and temperature data frm the cling curves was analyzed in a cmputer in the fllwing way. Fllwing equatins 3 and 4, the curves 1/(T-T 0 ) versus t and 1/(T-T 0 ) 2 versus t were generated. The slpes f these curves (A 3D and A 2D ) were then determined as a functin f temperature. The results were pltted ut graphically by the cmputer and this enabled the heat flw mde t be determined at any temperature. A typical cling curve fr thick plate (4 in.) in which 3D cnditins btain almst ver the entire temperature range is shwn in Fig. 3, pltted in the frm 1/(T-T 0 ) versus t. T a gd apprximatin, the curve can be cnsidered as being cmpsed f tw lines with a fairly rapid change f slpe at a temperature f abut 450 C. This behavir was nt bserved in an austenitic weld metal and is therefre assumed t be assciated with the transfrmatin f the steel. The slpes f the curves 1/(T-T 0 ) versus t at different temperatures fr thick plate are pltted fr five different energy inputs in Fig. 4. The change in cling behavir fr the lwest energy inputs is sharper and ccurs at a slightly lwer temperature than fr the high energy inputs. This is cnsistent with the idea that the change results frm the transfrmatin since the start f transfrmatin decreases with increasing cling rate. The temperature at which the change in behavir ccurs wuld be expected t depend n the cmpsitin f the weld metal. Frm equatin 1 fr 3D cnditins, the slpes (A 3D ) f the graphs 1/(T- T 0 ) versus t wuld be expected t depend n the energy input E in the frm A 3D = B 3D /E where B 3D is a cnstant and the arc efficiency is assumed cnstant. Such a plt is shwn in Fig. 5 fr results at 700 C where a large number f the tests were in the 3D regin. Gd lines were btained fr ther temperatures althugh as nted abve the cling behavir started t change at a lwer temperature fr the lwer energy inputs. Fr practical purpses, hwever, the difference was small, and lines culd be drawn thrugh all the data at each temperature. The resulting values f B 3 D are pltted against temperature in Fig. 6. WELDING-RESEARCH SUPPLEMENT! 379-s
This enables the cling rate at any temperature t be determined frm the equatin dt dt B3D (T - T 0 ) 2 (5) x Time t ( sec s ) Fig. 3 Cling curve fr a submerged arc weld (Energy input 29.4 kj/in.) n 4 in. thick plate pltted in the frm 1/(1'-T) versus t. 3D cnditins prevail almst ver the entire range Fig. 4 Slpes A 3 DOI the curves 1/(T-T) versus t pltted as a functin f temperature fr five submerged arc depsits n 4 in. thick plate 1 X I OJ in T O 0 Q 4 3 2 0 1 1 1 t * * 1 1 ^, - - ' ' / ^. * 1 1 1 T / - kj/in,52 l i 1 1 1 1 1 1 800 600 400 200 Temperature T C /' / / /-'- 2 0-3 ^... 29 4 ^ - """" 40 5. 126 - - fr 3D cnditins fr submerged arc welding. These values cmpare quite well with thse f Signes. Data fr 2D cnditins, were analyzed in essentially the same way except that all data were crrected fr surface transfer lsses accrding t the methd in the appendix. Fllwing equatin 4 the slpes A 20 f the plts 1/(T-T 0 ) 2 versus t were pltted against P 2 /E 2. This is shwn in Fig. 7 fr a temperature f 200 C where a large number f tests were in the 2D regin. The slpe f these curves (divided by 2 which cmes frm the differentiatin) are pltted as a functin f temperature in Fig. 8. These values enable the cling rate t be determined frm the equatin dt dt = B. (T - T 0 f (6) fr 2D cnditins. These values agree well with ther published data. Equatins 5 and 6 enable the saturatin thickness P s t be determined as a functin f energy input at each temperature. Equating 5 and 6 leads t the relatin: P/ = B, (T-T 0 ) where B 3D and B 2D are taken frm Figs. 6 and 8 respectively. This relatin prvides the lines drawn in Figs. 10 and 11 fr several temperatures. The saturatin thickness may be useful fr determining cling rates in the 2 and 2.5D regin where greater accuracy may be required. Fr a given energy the saturatin thickness may be determined frm Figs. 10 r 11. Fr a given plate thickness P the term (P/Ps) 2 becmes equivalent t Adam's relative thickness term and can be used directly (in Fig. 1 f Ref. 8) t calculate cling rates in the 2 and 2.5D regin. It was interesting t nte frm the results that transitin frm 3D behavir t 2D ccurred quite sharply generally in a range less than 100 C. Within the limits f experimental errr in these tests all f the data culd be treated as either 3D r 2D (with surface transfer crrectin), and the use f slutins fr the 2.5D regin was nt warranted. Analysis f Hardness Data In the thin end f the taper, where the hardness depends n thickness, 380-s I SEPTEMBER 1 973
2D heat flw cnditins exist at the temperature f interest. The cling rate is thus given by: dj^ dt B, P 2 (T-T 0 ) 3 E 2 Q ro r i O Fig. 5 Parameter A 3D x in Q r CD 1/ E (kj/in) X 10 at 700 C pltted as a functin f energy input If the hardness can be uniquely related t cling rate at a particular temperature then cnstant hardness wuld imply cnstant cling rate. Thus at cnstant hardness P 2 /E 2 is cnstant r P is prprtinal t E. Drawing a hrizntal line thrugh Fig. 1 at cnstant hardness prvides values f P and E. These are pltted in Fig. 9 fr ne particular hardness. A gd straight line relatinship results and indicates that hardness can be uniquely related t cling rate at sme temperature. Gd lines were btained in all cases (with crrelatin cefficient greater than 0.95 in mst cases). The line shuld g thrugh the rigin but there is a small psitive intercept. A similar value f intercept was fund n all such plts but the physical significance f this is nt knwn. At larger thicknesses the hardness becmes independent f the thickness and depends nly n the energy input. This value is knwn quite accurately since the mean f ten values in the thick regin are taken. The intersectin f the lines gives the saturatin pint and the saturatin thickness fr hardness fr the particular energy. The results fr several hardness levels in the HAZ are pltted in Fig. 10. Cmparisn with the cling rate data indicates that fr the range f hardnesses 275-375 HV the hardness can be uniquely related t the cling rate when measured at a temperature at abut 400-450 C. Fr higher hardnesses (400 and 425 HV) a lwer temperature f crrelatin is required. This crrespnds t a decrease in the start f transfrmatin, when substantial amunts f martensite are frmed. The tw pints f 400 and 425 HV are cnfirmed by the results f the manual tests when accunt is taken f the difference in arc efficiency. A similar analysis was applied t the weld metal hardness results, and are shwn in Fig. 11. These indicate a slightly higher temperature f crrelatin which wuld be expected frm the lwer carbn cntent. N hardnesses ver 350 HV were btained in the weld metal. 800 600 400 T empera ture C Fig. 6 Parameter B 3D pltted as a functin f temperature 200 General Discussin It is apparent frm the graphs that the theretical frm f the cling rate equatins may be used t predict cling rate if the apprpriate values f the cnstants are chsen. The data WELDING RESEARCH SUPPLEMENTl 381-s
may als be useful in cnverting cling rates at ne temperature t thse at anther. The data cntained in Fig. 6 are useful in explaining sme f the anmalies in the literature. Fr example, Bradstreet (Ref. 9) presents data fr cling rates at 540 C which crrespnd t a value f B 3 D equal t 5.2 X 10 3 kj/in./sec/c deg. This value is clser t the values at 300 C in the present wrk. If the cmpsitin f this weld metal was such that transfrmatin was ccurring at higher temperatures, then the value f B 3D wuld be btained at higher temperatures. The variatin f B2D with temperature is nt the same as B 3 D althugh there is an increase thrugh the transfrmatin. The decrease at lwer temperatures may have resulted frm errrs intrduced by the surface transfer crrectin r may result frm the decreasing specific heat f the steel. The gd crrelatin btained in the cnstant hardness plts (Fig. 9) prvides justificatin fr using cling rate measured at a temperature fr relating t hardness. It is pssible that an equally gd crrelatin may have been btained by using the time t cl ver a certain range f temperatures such as 800-500 C. The effect f using a temperature range wuld be t 'rund ff the transitin between the 2D and 3D parts in Fig. 9. If the temperature range were large then there wuld be a gradual curve in Fig. 9 as it appraches thick cnditins. Frm the plts f the types shwn in Fig. 9, it can be inferred that in rder t accunt fr the relatively sharp transitin bserved, gd crrelatin wuld nly be achieved if the temperature range were less than abut 300 C. Furthermre, misleading results wuld be btained if the temperature range verlapped the start f the transfrmatin. Figure 10, shwing the temperature f crrelatin, indicates that fr a wide range f hardness (275-375 HV) the pints lie clse t a single temperature between 400-450 C. Likewise, all the pints fr the weld metal results lie between 400-500 C. The pints fr HAZ hardnesses f 400-425 HV (bth frm submerged arc welds and manual welds) lie clse t 300 C. It is interesting t speculate that Cttrell fund gd crrelatin between cracking and cling rate at 300 C because cracking was ccurring when hardnesses f 400 HV and greater were frmed. Certainly the recent evidence f Bailey suggests that under similar cnditins a hardness f 400 HV r mre wuld be required fr cracking. The fact that the temperature f crrelatin falls within the transfrmatin range where cling behavir is changing presents sme prblems in recmmending temperatures fr measuring cling rates. Since the transfrmatin range wuld be cmpsitin dependent, different cling rates wuld be btained fr different steels fr the same welding cnditins. Since the bject f specifying Table 2 Hardness Results, a Thickness in. 3.125 2.938 2.688 2.313 1.938 1.500 1.375 1.250 1.125 1.000 0.875 0.750 0.727 0.662 0.625 0.601 0.528 0.500 0.450 0.402 0.375 0.328 0.287 9.7 498 446 450 446 459 453 (b > 417 478 468 514 433 304 287 cling rates wuld be t characterize the welding cnditins irrespective f steel cmpsitin (at least ver a limited range) either the cling rate wuld have t be measured abve the transfrmatin r, if quted at lwer temperatures, use values f B 3D, B i2d frm higher temperatures where they HAZ f SAW Welds Made with Varius Energy Inputs Energy input, kj/in. 19.3 394 425 446 450 416 b» 383 390 376 357 281 287 230 224 24.0 394 360 376 351 383 (b 360 354 317 297 276 272 242 221 221 227 29.0 370 306 339 390 336 350 (b) 348 283 281 254 266 249 225 232 228 201 209 232 38.6 304 322 309 307 (b (a) The figures are the Vickers hardness numbers with 10 kgm lad. Each figure is the maximum f five readings taken in the HAZ clse t the fusin bundary. (b) Mean value f the figures listed abve, i.e., the figures fr "thick" sectins. Table 3 Hardi riess Results, Inputs Thickness. in. 3.125 2.938 2.688 2.313 1.938 1.500 1.375 1.250 1.125 1.000 0.875 0.750 0.727 0.662 0.625 0.601 0.528 0.500 0.450 0.402 0.375 0.328 0.287 9.7 342 348 348 361 363 380 366 355 tb» 339 294 366 363 383 231 342 327 276 270 242 Weld Metal f SAW Energy input, 19.3 285 264 270 279 279 270 285 285 283 276 (b» 262 264 247 268 225 216 206 205 201 kj/in. 24.0 276 260 268 253 253 272 230 254,b, 225 242 201 249 228 212 235 212 201 196 202 Welds Made with Varius Energy 29.0 253 251 247 243 262 240 266 243 248 (b) 225 233 219 209 215 187 213 194 193 188 215 38.6 254 247 242 230 227 240 (b) (a) The figures are Vickers Hardness numbers with 10 kgm lad. Each figure is the higher f tw readings in the weld metal, (b) Mean value f the figures listed abve, i.e.. the figures fr "thick sectins." 382-s I SEPTEMBER 1 973
are nt influenced by the transfrmatin. One pssible apprach wuld be t standardize n ne temperature (say 540 C) which is clse t, but abve, the start f transfrmatin fr many carbn manganese and lw ally steels. Fr thicknesses that wuld invlve 2D heat flw the effective cling rate wuld be determined using Adams' graphs but using the term (P/P s ) 2 fr relative thickness where Ps is taken frm the hardness data in Figs. 10 r 11, rather than the cling rate data. In this way crrect welding prcedures can be determined n a critical hardness criterin. Althugh theretically nt very elegant, this apprach is simple and appears t wrk quite well in practice. Cnclusins The results f a study f weld cling rates and heat-affected zne and weld metal hardnesses have led t the fllwing cnclusins. 1. The cling behavir changes abruptly as the weld metal transfrms. The change is equivalent t an increase in the thermal cnductivity f the steel fr 3D heat flw cnditins. 2. The frm f the theretical equatins may be used with the cnstants determined experimentally. 3. Heat-affected zne and weld metal hardness can be uniquely related t weld cling rate at a temperature. The temperature depends n the level f hardness but is apprximately cnstant fr a wide range f hardnesses. Table 4 Hardness Results,( a > HAZ f SMAW Welds Made with Varius Energy Inputs Thickness in. 3.125 2.938 2.688 2.313 1.938 1.500 1.375 1.250 1.125 1.000 0.875 0.750 0.728 0.679 0.625 0.577 0.550 0.500 0.486 0.426 0.375 0.351 0.287 8.8 (dc) 49 8 (b) b» 514 473 483 503 488 514 483 4861 > 478 493 498 483 508 498 548 409 Energy 19.2 (ac) 493 468 503 478 503 473 469 c > 413 417 351 473 459 376 463 376 281 281 268 input, KJ/in. 22.8 (ac) 478 508 446 444 () 421 319 360 363 274 251 27.4 (ac) 413 413 421 394 473 383 415( > 380 327 254 294 228 232 232 (a) Each figure is the maximum f five readings in the HAZ clse t the fusin bundary. (b) These were welded with ac energy, 11.3 kj/in. (c) Mean value f the figures listed abve, i.e., the figures fr "thick sectins." 50 40 30 1 I MINI 34.0 (ac) 409 380 383 360 380 370 394 W 421 325 283 276 253 224 230 233 Acknwledgements The authr wuld like t thank Mr. L. Bigras and Mr. G. Mntpetit fr help with the experimental wrk, NRC (Canada) fr financial assistance and Dminin Bridge Cmpany Limited fr permissin t publish. Appendix Crrectin fr surface transfer At the lwer temperatures particularly n the thinner material significant heat lsses ccur by surface transfer. Since the data was being analyzed in terms f cnductin, it was necessary t crrect sme f the lw temperature data. This was nly dne fr the 2D analysis since slutins were readily available fr this case (Ref. 5). The temperature distributin arund a mving arc fr the 2D mde where surface transfer heat lsses are ccurring is: (0 \! c 20 10 5 4 3 CvJ 0-5 0 4 A _LL 3-4 -5 2 3 4 5 10 20 30 40 50 K 0 (6) -» exp (-5 ) (2- (*)" Fig. 7 Parameter A 20 p 2 /E 2 in 4, kj" 2 X I0" 4 at 200 C pltted as a functin f thickness, and energy input WELDING RESEARCH SUPPLEMENT! 383-s
Fig. 8 Parameter Bz pltted as a functin f temperature T (x.y)~" 277-KP -S-exp (A VX)K {{ X2V2 VJ } Fr large values f the argument 5 the Bessel functin K 0 (5)can be apprximated. i O K 0 tf)-*exp(-»(-i-)* CO Making this apprximatin and assuming X 2 V 2»2h/KP and, cnsidering the weid centerline where y = 0 and x = r, we have CM _ T (x.y) s e x p 2irKP r Ts, = T 2D e *P O OJ OD 800 600 400 200 where T 2 D is the temperature that wuld have resulted if there had been n surface lsses. The equatin can be further mdified by eliminating the term r which in general is nt knwn. This gives: T emperature '2D ST exp 27rKPVCpVT 2D Pi 50 40 Thus the temperature T 2D that wuld have resulted in the absence f surface lsses may be fund frm the real temperature TST frm the abve equatin. This was dne by iteratin and by assuming reasnable 'values fr the ther terms. Fr h, a value f 0.0004 cal/sec/cm 2 /C deg was used having been determined in a separate experiment. References Q. Z a Ul 2 30 20 / 1. Cttrell, C. L. M., Jacksn, D. M., Whitman, J. G., Welding Research, 1951, 5, (4), 201 r. 2. It, Y., and Bessy, K., "A predictin f welding prcedure t avid heat af- 10 HARDNESS = 300 Hv 0-4 0-6 THICKNESS (Ins) 1-0 1-2 Fig. 9 Plt f energy input against thickness fr cnstant hardness f 300 HV. Results frm the HAZ f submerged arc depsits. The line marked "Thick" is the energy input giving a hardness f 300 HV n thick plate and is the mean f ten values. The intersectin f the lines represents the saturatin pint and gives the saturatin thickness fr the crrespnding energy
c UJ 2 0 Sturatin Thickness (ins) Fig. 10 Energy input as a functin f saturatin thickness. The lines are derived frm the cling rate data and the pints frm hardness data. Results are fr the HAZ f SAW and SMAW depsits Saturatin Thickness (ins) Fig. 11 Similar plt t Fig. 10 fr results frm submerged weld metal arc fected zne cracking," IIW Dcument N. IX-631-69. 3. Bailey, N., "Welding Prcedures fr lw ally steels," Welding Institute, July 1970. 4. Signes, E., "A Simplified Methd f Calculating Cling Rates in Mild and Lw Ally Steel Weld Metals," Welding Jurnal, 51, (10) Research Suppl., 473-s t 484-s, 1972. 5. Carslaw, M. S., and Jaeger, J. C, Cnductin f heat in slids, Secnd editin, Oxfrd Press, Lndn, U.K. (1959). 6. Rsenthal, D., ASME Trans., 849-866 (Nvember) 1946. 7. Myers, P. S., Uyehara, O. A., and Brman, G. L., Welding Research Cuncil Bulletin, N. 123, (July) 1967. 8. Jhaveri, P., Mffatt, W. G., and Adams, C. M., Welding Jurnal, Vl. 41,(1) Research Suppl., 12-s t 16-s (1962). 9. Bradstreet, B. J., Welding Jurnal, Vl. 34, (11) Research Suppl., 499-s t 504-s (1969). Stress Indices and Flexibility Factrs fr Mment Ladings n and Curved Pipe Elbws by W. G. Ddge and S. E. Mre WRC Bulletin N. 179 Dec. 1972 Flexibility factrs and stress indices fr elbws and curved pipe laded with an arbitrary cmbinatin f in-plane, ut-f-plane and trsinal bending mments are develped fr use with the simplified analyses prcedures f present-day design cdes and standards. An existing analytical methd was mdified fr use in calculating these factrs, the equatins were prgrammed fr the IBM-360 cmputer and cmputed results were cmpared with experimental data t establish the adequacy f the mdified methd. Parametric studies were then perfrmed t btain desired infrmatin. The results are presented in bth tabular and graphical frm. Apprximate equatins f best fit, develped frm the tabulated values, are presented in a frm which can be used directly in the cdes and standards. The present equatins are slightly mre cnservative than the nes in current use. Hwever, experimental and analytical studies nw in prgress may indicate further mdificatins in the stress indices and flexibility factrs fr elbws. The research presented in this paper was spnsred by the U.S. Atmic Energy Cmmissin under cntract with the Unin Carbide Crpratin. Publicatin was spnsred by the Pressure Vessel Research Cmmittee f the Welding Research Cuncil. The price f WRC Bulletin 179 is $3.50 per cpy. Orders shuld be sent t the Welding Research Cuncil, East 47th Street, New Yrk, N.Y. 10017.