Modeling Primary Dendrite Arm Spacings in Resistance Spot Welds Part II Experimental Studies

Transcription

1 WELDING RESEARCH SUPPLEMENT TO THE WELDING JOURNAL, MAY 994 Sponsored by the Amercan Weldng Socety and the Weldng Research Councl Modelng Prmary Dendrte Arm Spacngs n Resstance Spot Welds Part II Expermental Studes Experments on sheet steel of three dfferent thcknesses and yeld strengths verfy models for predctng prmary dendrte spacngs BYJ. E.GOULD ABSTRACT. Hold tme senstvty s a potental concern when cold-rolled hghstrength low-alloy sheet steels are used n resstance spot welded applcatons. Hold tme senstvty s defned by crackng, whch occurs along the fayng surface of the weld on peel testng when conventonal hold tmes are used, and does not occur when reduced hold tmes are used. Hold tme senstvty s related to soldfcaton crackng n the steel; however, t s beleved that steel hardenablty may also play a role. As an ad to understandng of soldfcaton crackng n resstance spot welds, t s necessary to have an understandng of how the soldfcaton structure develops. In ths work, soldfcaton structures n resstance spot welds have been characterzed by the prmary dendrte spacng. In Part I of ths work, prmary dendrte spacngs were modeled by usng a combnaton of numercal thermal modelng and closedform prmary dendrte spacngs modelng. Numercal thermal modelng was used to predct soldfcaton condtons n these welds. These soldfcaton condtons were then used n the prmary dendrte spacngs model to predct the local spacngs. In ths paper, expermental studes were conducted to examne j. E. GOULD s wth the Edson Weldng Insttute, Columbus, Oho. the valdty of the modelng descrbed n the prevous paper. Expermentally, prmary dendrte spacngs were characterzed for three grades of cold-rolled HSLA steel wth nomnal compostons of 0.05C-0.3Mn, 0. C- Mn and 0.5C-.5Mn. For each steel, three separate thcknesses (nomnally 0.8,.25 and 2.0 mm) were nvestgated. Prmary dendrte spacngs were determned at nomnally the weld fayng surface from deep-etched mcrographs usng an area-averagng technque. Emprcally, the observed prmary dendrte spacngs were found to ncrease wth ncreasng gauge. Also, prmary dendrte spacngs were found to ncrease KEY WORDS Resstance Spot Weld Modelng Dendrte Arm Spacng Hold Tme Senstvty HSLA Soldfcaton Num. Therm. Modelng Structural Modelng Steel Thcknesses Steel Composton wth ncreases n composton. Prmary dendrte spacngs n the ndvdual steel types were found to correlate well wth the predcted soldfcaton condtons (taken from the numercal thermal model). Correlatons were done between as a power relatonshp wth ether G x R or G x R"-. Both fts appeared equally good, and the predcted exponents n ether case are consstent wth other efforts n ths area. Correlatons were establshed between prmary dendrte spacng, soldfcaton condtons and steel composton usng ether of two spacngs models. In order to apply these models, the steels under study must have soldfcaton events defned by a sngle alloy addton. A careful examnaton of the materal and composton terms used n these models, as well as the compostons of the actual steels used, showed that soldfcaton was domnated by C addton. As such, for the purpose of ths soldfcaton modelng, the steels were treated as essentally Fe-C bnary alloys. These results ndcate that the prmary dendrte spacngs n these welds correlate well wth the predcted soldfcaton condtons and bulk C content. Predcted exponent n the ft was very close to that predcted n ether of the prmary dendrte spacngs models consdered. Note was taken that hold tme sens- WELDING RESEARCH SUPPLEMENT I 9-s

2 Table Types, Gauges and Detaled Compostons of the Steels Used n Ths Study Materal 0.05C-0.3Mn 0.05C-0.3Mn 0.05C-0.3Mn 0.0C-Mn 0.0C-Mn 0.0C-Mn 0.5C-.5Mn 0.5C-.5Mn 0.5C-.5Mn Gauge C Mn P S S Al tvty generally ncreases wth both decreasng gauge or ncreasng composton. However, the prmary dendrte spacngs apparently decrease wth decreasng gauge, and ncrease wth ncreasng composton. As such, hold tme senstvty does not drectly correlate wth prmary dendrte spacng. It s beleved that soldfcaton crackng wll generally ncrease wth ncreasng prmary dendrte spacngs; however, the lghter gauges (wth greater coolng rates) result n greater contractual stresses, ncreasng the lkelhood of soldfcaton crackng (and hold tme senstvty). To fully understand hold tme senstvty n resstance spot welds, more detaled thermomechancal modelng wll be requred. Introducton Hold tme senstvty s consdered a crtcal aspect of resstance spot weldng cold-rolled hgh-strength sheet steels (Refs. -5). Prevous work has documented that a major cause of hold tme senstvty s soldfcaton related crackng (hot crackng) (Ref. 4). Ths study was ntated to understand relatonshps between steel composton, steel gauge and susceptblty to hold tme senstvty. The basc approach has been to examne these relatonshps through modelng the prmary dendrte spacngs n resstance spot welds on a range of HSLA steels. Ths modelng coupled predctons of soldfcaton condtons n spot welds taken from an exstng numercal model (Ref. 4) wth a closed-form soluton predctng dendrte spacngs as a functon of Table 2 Weldng Condtons Used for the Three Gauges of Steel under Study Weld Current Nomnal Electrode Weld Weld (approx- Gauge Dameter Tme Force mate) (cycles) (kn) (ka) these soldfcaton condtons. Detals of the modelng work were presented n Part I of ths work (Ref. 6). Included n Part I were detals of the numercal smulaton, approaches for modelng prmary dendrte spacngs and detals for adaptng the numercal modelng results to specfc spot weld geometres. Also detaled n Part I were examples of varatons n soldfcaton condtons over the freezng cycle of spot welds made on some representatve gauges of steels. In ths work, soldfcaton condtons were found to be extremely senstve to both the gauge of the steel beng welded, and the relatvedegreeof soldfcaton of the weld nugget. Typcally, condtons followng the onset of soldfcaton (mmedately after termnaton of the weld current) showed the hghest soldfcaton rates and steepest thermal gradents. Also, welds made on lghter gauges of steel throughout soldfcaton of the weld nugget showed hgher soldfcaton rates and steeper thermal gradents. Based on the prmary dendrte spacngs modelng results presented n the pror work, ncreasng dendrte spacngs were predcted for both the advancng soldfcaton front and for thcker gauges of steels. Increased compostons were also nferred to result n ncreased prmary dendrte spacngs. In ths part of the work, expermental examnatons were done to verfy the relatonshps suggested by the modelng detaled n Part I. Here, prmary dendrte spacngs n spot welds on nne varatons of steels were examned. These ncluded three gauge varatons (nomnally, 0.8,.25 and 2.0 mm) and three composton varatons (nomnally 0.05%C 0.3%Mn, 0. %C -.0%Mn and 0.5%C -.5%Mn steels). Prmary dendrte spacngs for spot welds on each steel were characterzed along the fayng surface by careful sectonng polshng and etchng. Actual prmary dendrte spacngs were determned from mcrographs usng a space fll assumpton. Results were then correlated wth the modelng results as detaled n Part I to determne the valdty of ths approach for understandng soldfcaton structure varatons, as well as ther re atonshp to hold tme senstvty n resstance spot welds. Expermental In ths study, three separate types of contnuously annealed HSLA steels were used. "These nomnally conformed to classfcatons of 280, 350 and 560 MPa yeld strength steels. To acheve these strength levels, each of these steels employed dfferng levels of C, Mn and S addtons. Nomnal compostons for each of these steels s as follows: 280 MPa (40 ks), 0.05C-0.3Mn; 350 MPa (50 ks), 0. 0C- Mn-0.3S; 560 MPa (80 ks), 0.5C-.5Mn-0.3S. In these experments, three separate thcknesses of each steel were employed. These ncluded thcknesses of nomnally 0.8,.25 and 2.0 mm (0.030, and n.). Types, thcknesses and detaled compostons of each of the steels used are gven n Table. Weldng was done on a 00-kVA Scaky press-type sngle-pont resstance spot weldng machne. Weldng current was montored usng a Duffers 820 current meter. Weldng condtons, ncludng the type of electrode used, were taken from the approprate Ford Motor Co. specfcaton (Ref. 7). Electrodes were all of the truncated cone geometry. The lghtest gauge steel (nomnally 0.8 mm) used an electrode wth a 6.4-mm (0.25- n.) face and a 90-deg ncluded angle. The heaver gauge steels used an electrode wth a 7.9-mm (0.3-n.) face and a 20-deg ncluded angle. In all weldng trals, electrodes were dressed and subjected to 25 break-n welds pror to any testng. Current levels for these test welds were then determned by ncreasng the weldng current (all other process condtons remanng constant) untl condtons just below expulson were acheved. Separate trals were made for each combnaton of steel type and steel thckness. Actual weldng condtons for each case are gven n Table 2. Welds were then used for the subsequent sectonng descrbed below. Two sample welds from each comb- 92-s I MAY 994

3 m*' ^JM M-T^ Fg. I End-on dendrte morphologes for the 0.05C-0.3Mn steel spot weld. A sample; C nomnally 2.0-mm-thck sample. Nomnally 0.8-mm-thck sample; B nomnally.25-mm-thck naton of materal type and steel thckness were subjected to sectonng and metallurgcal examnaton. The frst was sectoned normal to the centerlne or fayng surface of the weld n order to reveal the degree of penetraton of the weld, and any ndentaton of the electrodes nto the sheets. The second was sectoned along the fayng surface. Ths was used for end-on examnaton of the dendrte spacngs. For ths set of samples, the weld was sectoned slghtly to one sde of the partng surface of the sheets (at the fayng surface). The sample was then ground back to a pont just across the fayng surface, polshed and examned. Followng polshng, all metallographc samples were subjected to deep etchng n a saturated pcrc acd soluton. Ths etchant was found to be very effectve n revealng soldfcaton structures n steel welds. Resultng samples were characterzed usng ether optcal or scannng electron mcroscopy (SEM). SEM was used where resoluton of the soldfcaton structure was dffcult. Where possble, however, optcal mcroscopy was used. Results Observatons of Prmary Dendrte Structures Each of the metallographc specmens used for end-on observaton of the dendrtes was examned wth the approprate nstrument (optcal mcroscope or SEM) for best revealng these structures. Generally, the ease wth whch the structures could be resolved was a functon of two (probably compounded) factors; the degree of resdual segregaton n the structure, and the dendrte spacng tself. The end-on soldfcaton structures for the three thcknesses of the 0.05C- 0.3Mn steel are presented n Fg.. Parts A, B and C of Fg. represent the soldfcaton structures for the 0.8-,.25- and 2.0-mm-thck steels, respectvely. For these steels, the degree of resdual segregaton was relatvely small, so SEM was requred to reveal the underlyng structure. The soldfcaton structure, n ths orentaton and for ths composton of steel, appears as an array of shallow ndentatons. These ndentatons are beleved to represent nterdendrtc regons, however, ther exact nature s not clear from the mcrographs. These mcrographs do ndcate clearly the effect steel thckness has on the scale of the prmary dendrte spacngs; ncreasng thcknesses correspond to ncreasng spacngs. An nterestng facet of these mcrographs s the apparent washng out of the underlyng mcrostructure. The outlnes of pror austente grans can be observed and, to some degree, relatonshps between the pror gran structure and prmary dendrte structure can be examned. However, evdence of the 0 A B Fg. 2 End-on dendrte morphologes for the 0.C-I.OMn steel spot welds. A Nomnally 0.8-mm-thck sample;, sample; C nomnally 2.0-mm-thck sample. nomnally.25-mm-thck WELDING RESEARCH SUPPLEMENT I 93-s

4 * -. -? M 5-- L -..» > ^T»'- W* l $«utv ««* - " %" " <B f^^ "Ty-% t * '" j? -v v^» '' m%w^l *HKI *» ' «"- - # m ' t 2u * V % r ' ^?... *.*,. A B C F/g. 3 End-on dendrte morphologes for the 0.5C-.5Mn steel spot welds. A 0.8-mm-thck sample; B nomnally.25-mm-thck sample; C nomnally 2.0-mm-thck sample. % f - * - ' 4 a» * -r 4 fe underlyng transformed structure s dffcult to observe. Ths s an ndcaton of why ths etchant was used; there s a strong tendency to etch even small varatons n composton, rather than structural heterogenetes n the steel. End-on vews of the soldfcaton structure for the three gauges of 0.0C- Mn steel are presented n Fg. 2. Agan, n order to adequately reveal the structure, SEM was used. These soldfcaton structures dffer from those observed n the 0.05C-0.3Mn steel n two major respects. Frst, the apparent degree of resdual segregaton was much greater. Ths was evdent both from the fact that the dendrte structure was much easer to reveal on etchng, and the appearance of "etch pts" located at dendrte trple ponts. These etch pts are undoubtedly the result of segregated C, whch s preferentally attacked by the pcrc acd durng etchng. The second feature whch dstngushes these results from those for the 0.05C-0.3 Mn steel s the scale of the soldfcaton structure. In ths case, the scale of the structure was great enough that t could be revealed at half the magnfcaton. Otherwse, the results are qute smlar to those presented for the 0.05C- 0.3Mn steel. Agan, there s an apparent ncrease n the scale of the soldfcaton structure wth ncreasng gauge of the steel. Also, preferental etchng of the soldfcaton structure apparently has agan obscured much of the underlyng mcrostructure. End-on vews of the soldfcaton structures for the three gauges of the 0.5C-.5Mn steel are presented n Fg. 3. In ths case, the prmary dendrte spacngs were so large and the degree of etchng so pronounced, that optcal mcroscopy could be used. In optmzng the mcroscope to reveal the prmary dendrte structure, t was found useful to completely close down the aperture, and slghtly devate from proper focus. By defocusng the mcroscope, the "valleys" assocated wth the nterdendrtc regons could be resolved. However, ths often reduced the overall qualty of the mage -Fg. 3B. Compared to the other two steels, the apparent degree of segregaton s agan greater. Ths s clear from the sze and frequency of the etch pts and the well demarked lnes ndcatng the boundares of the ndvdual dendrtes or cells. The scale of the soldfcaton structure s here also clearly greater than for the other two Table 3 Postons of the Polshed Surfaces for Dendrte Spacngs Evaluatons, as Well as Local Calculated Soldfcaton Condtons for Each Materal and Gauge Studed n Part II Steel 0.5C-0.3Mn 0.5C-0.3Mn 0.5C-0.3Mn 0.0C-Mn 0.0C-Mn 0.0C-Mn 0.5C-.5Mn 0.5C-.5Mn 0.5C-.5Mn Gauge Poston Fract G (C/mm) R (mm/s) CXR (C/mm) 0, , C X R /2 (C/mm X s) materals. As for the other two materals, observed cell or dendrte spacng clearly ncreased wth ncreases n the gauge of the steel used. Measurements of Prmary Dendrte Spacngs In ths work, an averaged prmary dendrte spacng was estmated from each mcrograph. The basc approach for producng these estmates s shown n Fg. 4. Bascally, the assumpton s made that the dendrtes, end-on, are confgured n a two-dmensonal closedpacked array. Wth ths assumpton, the average prmary dendrte spacng (D) over the mcrograph can be estmated from the measured area of the mcrograph (A meas ), the number of dendrtes n the mcrograph (N) and the magnfcaton of the mcrograph (MAG), usng the followng equaton: A. X '3 NxMAG \ (D As cescrbed above, the actual condtons governng soldfcaton vary sgnfcantly wth poston n the weld. As such, the actual locatons of the planes of polsh used to measure these prmary dendrte spacngs must be documented for correlaton wth the estmated soldfcaton condtons. Ths has been done for each of the metallographc samples and tabulated as the fractonal poston back nto the sheet n Table 3. Estmates of the prmary dendrte spacngs made from the mcrographs of the three gauges of 0.05C-0.3Mn steel are presented n lable 4. Included on ths table s the gauge of the steel, the measured erea of the mcrograph, the magn- 94-s I MAY 994

5 r Y Y N d = Prmary Dendrte Spacng Ameas = Measured Area of the Mcrograph N = Number of Prmary Dendrtes n the Mcrograph MAG = Magnfcaton of the Mcrogaraph v X X y - ( * * \ /2 Ameas \ N * MAG 2 / Fg. 4 Method of estmatng prmary dendrte spacngs from the mcrographs taken n ths study. fcaton of the mcrograph, the number of dendrtes counted n the mcrograph and the estmated dendrte spacng. As descrbed above, each mcrograph was capable of yeldng one estmate of the prmary dendrte spacng. Therefore, n order to provde some assessment of reproducblty, a mnmum of fve mcrographs were used to characterze each metallographc sample. Ths, n turn, yelded fve separate estmates of the dendrte spacng. The ndvdual sets of prmary dendrte spacngs measurements for each gauge of the 0.05C-O.3Mn steel are qute consstent. Spacngs for the 0.8-mm materal range from 4.42 to 4.62 um, those for the.25-mm steel range from 6.5 to 7.00 pm, and those for the heavy gauge of steel range from 8.23 to 8.83 pm. The dependence of gauge can also be seen, wth spacngs n the heaver gauge steel nearly double those n the lghter gauge materal. Estmated prmary dendrte spacngs for the three gauges of 0.0C-Mn steel are presented n Table 5. Agan, n order to provde some estmate or reproducblty, a mnmum of fve ndependent mcrographs were used to estmate the dendrte spacng for each sample. Agan, the estmates of prmary dendrte spacng from a specfc sample were relatvely consstent wth spacngs ncreasng as a functon of base metal thckness. Estmated spacngs for the 0.8-mm-thck materal ranged from 3.82 to 4.44 pm, those for the.25-mm-thck materal ranged from 6.55 to 7.05 pm and those for the 2.0-mm materal ranged from Table 4 -- Prmary Dendrte Spacngs Measurements for the 0.5C-0.3Mn Steel Gauge Poston Area (mm 2 ) Magnfcaton Table 5 Prmary Dendrte Spacngs Measurements for the 0.0C-Mn Steel Gauge Poston Area (mm 2 ) Magnfcaton N N d ( Mm) d (Mm) WELDING RESEARCH SUPPLEMENT I 95-s

6 Table 6 Prmary Dendrte Spacngs Measurements for the 0.5C-.5Mn Steel Gauge Poston Area (mm 2 ) to 9.33 pm. In ths last case, wth the excepton of the sngle observaton of 7.42 pm, the spacngs were relatvely more consstent, rangng only from 8.57 to 9.33 pm. In general, the spacngs (for specfc gauges of steel) were greater for the 0.C- Mn steel than for the 0.05C-0.3Mn steel, though there was consderable overlap. Ths was not the case only for the nomnally 0.8-mm samples, where the 0. C- Mn steel had an average spacng of about 4.2 pm, compared to an average spacng of 4.5 pm for the 0.05C- 0.3Mn steel. Ths apparent dscrepancy s probably due to a slght gauge varaton between the two steels (about 0.8 mm for the 0.05C-0.3Mn steel compared to about 0.7 mm for the 0. C- Mn steel) Magnfcaton N d (jm) as well as the apparent deeper secton nto the sheet on the 0. C- Mn steel (shown n Table 3). Estmated prmary dendrte spacngs for the three gauges of the 0.5C-,5Mn steel are presented n Table 6. As for the other steels, a mnmum of fve mcrographs per sample were used to estmate prmary dendrte spacngs. Ths agan provded some estmate of the reproducblty of the estmate. As n the prevous cases, estmated dendrte spacngs appeared to ncrease monotoncally wth ncreases n steel gauge. Also, the ndvdual estmates were qute consstent. The ranges of these estmates ncluded 5.64 to 6.39 pm for the 0.8-mm steel, 8.93 to 0.73 pm for the.25-mm steel and 4.6 to 5.94 pm for the 2.0-mm steel. Estmated prmary dendrte spacngs for ths materal are about 50% greater than for the other two materals. Ths appears to be true for each of the three thcknesses of steel studed. There may be two contrbutng factors to ths. Frst, the steel s unquestonably rcher n composton, and based on Equatons 2 and 3 n Part I of ths study, ths wll lead to greater dendrte spacngs. In addton, however, the actual thcknesses of the matera s used were somewhat thcker for each of the three gauge classfcatons. Ths, as sclearfrom the results presented above, also leads to larger prmary dendrte spacngs. Dscusson Relatonshps between Prmary Dendrte Spacngs and Soldfcaton Condtons for the Varous Steels As descrbed above, dendrte spacngs are typcally correlated wth soldfcaton condtons (G and R) n some sort of power relatonshp. To understand the relatonshps between prmary dendrte spacngs and soldfcaton condtons for each of the steels studed, results are presented both as a functon of G x R and G x R" 2 on log-log plots. Regresson analyses were done n all cases both to assess the qualty of ft, and provde a quanttatve estmate of the governng power relatonshps. Log-log plots showng the relatonshps between the prmary dendrte spacng and the two groupngs of soldfca- 0.0 STEEL % CARBON AND 0.3% Mn 0.0 STEEL % CARBON AND 0.3% Mn o < CL CO CE LU CO LU I G tmes R (C/mm) G tmes FT /2 (C/(mrTTsecr/2) Fg. 5 Varaton n prmary dendrte spacngs for the 0.05C-0.3Mn steel as a functon of G x R. Fg. 6 Varaton n prmary dendrte spacngs for the 0.05C-0.3Mn steel as a functon of G x R /2. 96-S I MAY 994

7 WELDING RESEARCH SUPPLEMENT I 97-s Table 7 Regresson Analyses of Prmary Dendrte Spacngs as a Functon of G X R and G X R /2 for the 0.5C-0.3Mn Steels 0.0 STEEL - 0.% CARBON AND.0% Mn Exponent Pre-exponent R 2 F Standard Error Degrees of Freedom GX R % n 5 G XR ' % n 5 (Results are tor dendrte spacngs measured n nm. G measured n "C/mm and R n mm/s.) Table 8 Regresson Analyses of the Prmary Dendrte Spacngs as a Functon of G X R and G X R /2 for the 0.C-.0Mn Steels S o o < CL ro LU t 5 5 G X R G XR Exponent Pre-exponent R 2 F Standard Error Degrees of Freedom % (Results are for dendrte spacngs measured n * n C/mm and R n mm/s.) % /* 5, G measured ton condtons (G x R and G x R" 2 ) are presented n Fgs. 5 and 6. Included on these plots are regressed lnear fts ndcatve of a power relatonshp. In both cases, a hgh degree of lnearty s apparent. In fact, from these results, power relatonshps wth both G x R and G x R ' 2 appear equally applcable. Ths dffculty n dentfyng dfferences between the two relatonshps s not surprsng. Apparently, the change n the exponent on the soldfcaton rate (R) s not a sgnfcant enough factor to apprecably affect the relatonshp on a log-log plot. The accompanyng regresson analyses for these plots are presented n Table 7. As suggested from the plots presented above, the fts are very good, wth.r 2 values of almost 98%. Interestngly, both fts show vrtually dentcal values for the three estmators of ft (R 2, error of the Y estmate and F statstc), agan showng the dffculty n assessng the preferred predctng relatonshp. The actual predcted relatonshps from these fts are as follows: As a functon of G x R: d =282x(GxR) As a functon of G x R l/2 : (2) G tmes R (C/mm) where d s n mcrons, G s n C/mm and R s n mm/s. Most nterestng to note are the estmated exponents on these relatonshps. In Equaton 2, a value of 0.45 s estmated. Ths s very close to the exponents estmated n other works (Refs. 8-0). In Equaton 3, an exponent of 0.60 s estmated. Ths compares very favorably wth the value of '/.> suggested by both the Hunt and Kurz-Fsher relatonshps descrbed n Part I. Log-log plots graphcally showng the relatonshps between the prmary dendrte spacngs and the two groupngs of soldfcaton condtons are presented n Fgs. 7 and 8. Agan, ncluded on these o ro STEEL - 0.% CARBON AND.0% Mn Fg. 7 Varaton n prmary dendrte spacngs for the 0. C- Mn steel as a functon ofgxr. plots are the regresson lnes representng the best ft power expresson. As wth the 0.05C-0.3Mn steel results, the data appear to be well ft by both groupngs of soldfcaton condtons. Detals of the regresson analyses are presented n Table 8. Agan, correlatons for the two sets of groupngs are smlar n all major statstcs (R 2, error of the Y estmate and F value). There s some ndcaton that the G x R groupng may provde a better ft, but the dfference s not consdered sgnfcant. Estmated power relatonshps based on the regresson analyses for the two groupngs are as follows: Fg. 8 Varaton n prmary dendrte spacngs for the 0. C- Mn steel as a functon of G x RW. d=532x GxR~ 2 (3) G tmes FT /2 (C/(mnrsecr /2)

8 Table 9 Regresson Analyses of Prmary Dendrte Spacngs as a Functon of G X R and G X R /2 for the 0.5C-.5Mn Steels Exponent Pre-exponent R 2 F Standard Error Degrees of Freedom (Results are for dendrte spacngs n C/mm and R n mm/s.) GXR % M 6 GXR % 77.02/J 6 measured n nm G measured Table 0 Freezng Ranges (Ato) of Bnary Fe-X Alloys, Where X Is the Alloyng Addton of Interest, of Compostons Observed n the Alloys Used Alloy Addton C (d) MnM SM p(a) S<"» Mnmum Composton (a) Data estmated from phase dagrams n Ref. 4. (b) Data estmated from phase dagrams n Ref. 5. Maxmum Composton Mnmum AT C Maxmum AT ( C) AT 0/wt-% As a functon of G x R: d = 28x(Cxtf) (4) As a functon of G x R" 2 : c/=70.2x GxR (5) where d, G and R agan have unts of mcrons, C/mm and mm/s, respectvely. Interestngly, the exponents for these expressons are somewhat less than those for Equatons 2 and 3 above. It s not known, however, whether ths dfference s sgnfcant. Stll, the exponent of Equaton 4 s wthn the range of values reported n the lterature (Refs. 8-0). The exponent of Equaton 5 s notceably less than the value of V- suggested by the Hunt and Kurz-Fsher expressons. Log-log plots showng the relatonshps between prmary dendrte spacngs and the groupngs of soldfcaton condtons for the 0.5C-.5Mn steel are presented n Fgs. 9 and 0. As wth the results for the other two steels, regresson lnes representng best ft power expressons are ncluded on each fgure. Agan, both fts show a hgh degree of lnearty, and t s dffcult to dstngush dfferences n ft for the two groupngs of soldfcaton condtons. Regresson analyses of the power expresson fts are presented n Table 9. The degree of ft for these expressons s agan qute smlar, however, the fts are the poorest for the three steels studed. The reasons for ths are not clear. Based on these fts, the estmated power expressons are as follows: As a functon of G x R: d = 603 x(gxr) -0.5 (6) As a functon of G x R ' 2 : ( \ 0b7 d =50x GxR (7) where d, G and R have the same unts as prevously descrbed. In ths case, the results were qute consstent wth those for the 0.05C-0.3Mn steel. Exponents were roughly the same, and the pre-exponental terms were larger, presumably the effect of the rcher composton. Ths latter aspect s suggested both from prevous expermental work (Refs. 8-0), as well as the Hunt and Kurz-Fsher analyses. Combned Effects of Composton and Soldfcaton Condtons on the Prmary Dendrte Spacngs Applcaton of ether the Hunt or Kurz-Fsher models, combned wth the 00.0 STEEL - 0.5% CARBON AND.5% Mn 00.0 STEEL - 0.5% CARBON AND.5% Mn b E CO 5 z _J 0.0 o h g a z CL ro UJ t- z lu G tmes R (C/mm) G tmes R~/2 (C/(mm*secn/2) Fg. 9 Varaton n prmary dendrte spacngs for the 0.5C-l.5Mn steel as a functon of GxR. Fg. 0 Varaton n prmary dendrte spacngs for the 0.5C-.5Mn steel as a functon of G x /?'/-'. 98-s I MAY 994

9 predcted soldfcaton condtons from the numercal thermal model, provdes an opportunty for also characterzng compostonal effects on the prmary dendrte spacng. Unfortunately, the Hunt and Kurz-Fsher models have been constructed only for bnary systems. To apply these models to the steels studed here, the alloys must be consdered as pseudo bnary systems. Ths s a reasonable assumpton, provded that the varous alloy addtons has a reasonably domnant nfluence on the development of the soldfcaton structure. Prmary dendrte spacngs are, n general terms, consdered a functon of the freezng range of the alloy, or AT. As such, an estmate of the effects of each of these addtons on AT 0 wll ndcate ther nfluence on the prmary dendrte spacng. For the steels studed, the ranges of AT 0 s assocated wth each alloy addton are lsted n Table 0. AT 0 s for carbon and sulfur are most domnant. However, gven the low sulfur contents t s clear that the AT s for sulfur n these alloys are smaller and do not vary over the range of the AT () s for carbon. In addton, the varaton n AT D s are random over the alloys studed, whle those for carbon vary at defned levels over these materals studed. As such, the system here s consdered to act as a seres of pseudo bnary Fe-C alloys wth dfferng carbon contents. Assumng that the steels studed here durng soldfcaton act as Fe-C bnary alloys, prmary dendrte spacngs can be correlated by a combnaton of the estmated soldfcaton condtons and thec content. Both the Hunt and Kurz-Fsher analyses then predct that the dendrte spacng can be expressed as a power functon of the followng lumped parameter: where c A log r- GxR (8) s the bulk C content of the steel, 'og plot showng the prmary dendrte spacngs measured n ths work as a functon of ths parameter s presented n Fg.. Ths plot ncludes each of the roughly fve estmatons of prmary dendrte spacngs for each steel type and thckness. Lnearty of the data on ths plot ndcates good adherence to a power relatonshp. These results ndcate reasonably good ft to the power relatonshp over a varaton of roughly an order of magntude of the lumped parameter. Ths plot also ndcates consderable overlap of the data for the ndvdual steel types. The ftted power expresson s also ncluded on ths plot for comparson. The results of the regresson analyss I % (J z I ro LU E a. z LU STEEL - ALL TYPES AND GAUGES ' O 006 O Ml 00 C -.0 Mn O 6 C -.6 Mn 8... h s I.O CO" /2/(G*FT /2) ((wt%-mm-sec) /2)/C for the ftted power relatonshp are presented n Table. The statstcs characterzng the degree of ft (R 2, standard estmate of the Y, and F statstc) all agan ndcate a relatvely hgh level of correlaton. The exact ftted relatonshp s as follows: f Y>-48 d =447x GxR 2 (9) The most nterestng characterstc of ths equaton s that the predcted exponent s extremely close to that by both the Hunt and Kurz-Fsher models. The results then appear to valdate two assumptons made n ths approach: that soldfcaton condtons could be estmated wth the one-dmensonal thermal model, and the materals could be effectvely treated as pseudo-bnary Fe-C alloys. Interestngly, what these results do not do s provde defnte data for dscernng the relatve applcablty of the Hunt vs. Kurz-Fsher models. To characterze ths dfference, t would be necessary to examne alloys whose soldfcaton s domnated by addtons wth dfferng partton ratos (k). Ths, as mentoned prevously, has been examned elsewhere for welds on T alloys (Ref. ). Relatonshps between Prmary Dendrte Spacngs, Soldfcaton Crackng and Hold Tme Senstvty The results presented n ths work suggest the followng trends wth respect to the prmary dendrte spacng: c a. Fg. 7 Varatons n prmary dendrte spacngs for all the steels studed as a functon of the lumped parameter c 0 W(C x R)V2. ) Hgher C contents lead to coarser dendrte spacngs n RSW. 2) RSW n thcker secton steels have coarser dendrte spacngs. However, these do not correlate wth the trends for soldfcaton crackng and hold tme senstvty. Hgher C contents do appear to lead to ncreased soldfcaton crackng and hold tme senstvty; however, thcker secton steels typcally show reduced ncdences of these types of problems. Clearly then, the prmary dendrte spacng s, of tself, not a drect measure of crackng senstvty. Soldfcaton crackng and hold tme senstvty are beleved to be a complex nteracton between the prmary dendrte spacng and stress state actve n the weld. Coarser prmary dendrte spacngs are consdered detrmental to the crackng senstvty for two reasons. Frst, the larger spacngs nfer a greater degree of segregaton. The dstance between the dendrte cores s greater, so based on a smple Shel (Ref. 2) analyss, there wll be a greater degree of solute buldup n the nterdendrtc regons. Second, a coarser dendrte spacng also reduces the degree of nterdendrtc surface area n Table Regresson Analyses of the Prmary Dendrte Spacngs as a Functon of C 0 /2 /(G X R /2 ) for all Steels Exponent Pre-exponent R 2 F Standard Error Degrees of Freedom % f 48 (Results are for dendrte spacngs measured n frm, C measured n C/mm and R n mm/s.) WELDING RESEARCH SUPPLEMENT I 99-s

10 00-s I MAY 994 the weld. As such, there s a greater tendency to collect crtcal levels of lqud along the fayng surface (fnal regon to soldfy) and back between the dendrtes, resultng n crackng. Certanly, ncreasng the prmary dendrte spacng by ncreasng the C content has the effect of ncreasng crackng susceptblty. That a smlar effect s not seen as the dendrte spacng ncreases wth steel thckness s beleved related to the developng stress state n the weld. Prevous work (Ref. 3) has shown that coolng rates and thermal gradents n the workpece ncrease markedly wth reduced steel thcknesses. As the thermal gradents and coolng rates ncrease, so wll the tendency for dfferental thermal contracton n the weld. It s beleved that n the lghter gauge steels the soldfed materal smply contracts at an accelerated rate, leavng vods both at the weld centerlne as well as back n between the dendrtes. Forthe lghter gauge materals, t s beleved these contracton effects swamp the benefts of a refned soldfcaton structure, ncreasng the weld crack susceptblty. Clearly, to understand these effects wll requre more sophstcated modelng capable of characterzng these contractual stresses as well as the prmary dendrte spacng. Conclusons In ths work, prmary dendrte spacngs n resstance spot welds have been studed through a combnaton of numercal process modelng and exstng structural development modelng. In a prevous artcle (Part I), numercal thermal modelng of the resstance spot weldng process was used to estmate soldfcaton condtons n resstance spot welds. These soldfcaton results were then used wth exstng closed-form prmary dendrte spacngs models to predct spacngs n spot welds. In ths paper, the modelng results were correlated wth prmary dendrte spacngs measurements on three steels of progressvely ncreasng C and Mn contents. Three thcknesses of each steel type were used. From ths work, the followng conclusons were drawn: ) Method of Estmatng Prmary Dendrte Spacngs. Prmary dendrte spacngs were estmated from mcrographs taken end-on by assumng a closed packed dstrbuton. Ths technque proved to be qute reproducble on multple mcrographs from the same sample. 2) Varaton n Prmary Dendrte Spacngs as a Functon of Gauge. Prmary dendrte spacngs were consstently found to ncrease wth steel gauge for the three steel compostons under study. 3) Varaton n Prmary Dendrte Spacngs as a Functon of Composton. Steels of progressvely hgher C and Mn contents were found also to have progressvely larger prmary dendrte spacngs. 4) Estmaton of Soldfcaton Condtons for the Samples under Study. Based on the ntal geometry of the weld confguraton, and degree of maxmum nugget penetraton, soldfcaton condtons representatve of the postons n the weld from whch the prmary dendrte spacngs measurements were taken could be calculated. 5) Prmary Dendrte Spacngs vs. C x R and G x /?'/-'. Usng the varaton n gauge to provde the varaton n soldfcaton condtons, prmary dendrte spacngs were found to correlate very well wth ether G x R or G x R 2 n a power relatonshp. Ths was true for all three compostons of steel studed. Estmates of the exponents n these power relatonshps were consstent wth other works. It was not possble, however, to determne whch relatonshp was more applcable for predctng prmary dendrte arm spacngs. 6) Treatment of These Alloys as a Pseudo Fe-C Bnary System for Soldfcaton. Based on estmates of the materal-dependent parameters n ether the Hunt or Kurz-Fsher models (k A T or A Tyk, respectvely), t was found that C was the domnant compostonal varable affectng soldfcaton. As such, the steels used n ths study were consdered as pseudo-bnary Fe-C alloys for examnng soldfcaton characterstcs. 7) Prmary Dendrte Spacngs vs. the,/2 Lumped Parameter c 0 AG x Fl / 2 ). Usng the pseudo-bnary approxmaton for these steels, prmary dendrte spacngs results for all nne varatons of steel (three gauges, three compostons) could be ft to the same power relatonshp. Ths relatonshp correlates the prmary dendrte spacng wth a lumped parameter c /2 0 /(G x R" 2 ).Ths relatonshp s predcted from both the Hunt and Kurz- Fsher models. A hgh degree of ft was noted, and the predcted exponent was nearly dentcal to that suggested by ether model. 8) Relatonshps between the Prmary Dendrte Spacng, Soldfcaton Crackng and Hold Tme Senstvty n Spot Welds. Prmary dendrte spacng as a functon of gauge and composton dd not vary n a way consstent wth prevous work on soldfcaton crackng and hold tme senstvty. As such, the prmary dendrte spacng can, of tself, not be consdered an ndcator of these problems. It s beleved that soldfcaton crackng and hold tme senstvty n spot welds s a functon both of the prmary dendrte spacng and the rate of thermal contracton of the soldfed weld metal durng soldfcaton. Therefore, t s beleved more detaled modelng, capable of predctng both prmary dendrte spacngs and thermal contracton effects wll be requred to detal soldfcaton crackng and hold tme senstvty n resstance spot welds. Acknowledgments The author would lke to thank the Inland Steel Co. under whose employ the bulk of ths work was conducted. Also, to P.-H. Chang for hs contrbutons. Dscussons wth A. Preban, R. Rvett and M. Krnch are also acknowledged. Fnally, the author would lke to acknowledge Neal Saooff who conducted the bulk of the expermental work n ths program. References. Fne, T. E., and Fostn, R. V Spot weldablty of hgh strength, cold rolled steels. SAE Techncal Paper 79005, SAE, Warrendale, Pa. 2. Sawhll, ). M., Jr., and Furr, S. T Weldablty consderatons n the development of hgh strength sheet steels. Weldng Journal 63(7):203-s to 2 2-s. 3. Goodman, S. R., and Doms, W. F Effects of carbon, phosphorus and sulfur content on the tensle propertes and spot weldablty of hgh-strength cold-rolled sheet. SAE Techncal Paper , SAE, Warrendale, Pa. 4. Gould, J. E Unpublshed research, Inland Steel Company. 5. Baker, R. G., and Newman, R. P Crackng n welds. Metal Constructon and Brtsh Vodng journal 6(2): Gould, ). E Modelng prmary dendrte arm spacngs n resstance spot welds, part I modelng studes. Weldng lournal 73(4) Ford Laboratory Test Methods, Schedule BAI Spttle, J. A., and Lloyd, D. M Dendrte arm spacngs n hypoeutectc Pb-Sb alloys drectonally soldfed under steady and nonsteady condtons. Soldfcaton and Castng of Metals, conference proceedngs, pp Rohatg, P. K., and Adams, C. M., Jr Dendrtc soldfcaton of alumnum copper alloys. Transactons of the Metallurgcal Socety of AIME, 234( ): Young, K. P., and Krkwood, D. H The dendrte arm spacngs of alumnum copper alloys soldfed under steady state condtons. Metallurgcal Transactons, 6A( ): Gould, J. E Effect of composton and weld process on the structure of ttanumalloy welds. Ph.D. dssertaton, Carnege-Mellon Unversty. 2. Flemngs, M. C Soldfcaton Processng, McGraw Hll, New York, N.Y. 3. Gould, J. E An examnaton of nugget development durng spot weldng, usng both expermental and analytcal technques. Weldng journal 66( ):-s to 0-s. 4. Bnary Alloy Phase Dagrams nd Ed., Vols. and 2. ASM Internatonal Pubs., Materals Park, Oho. 5. Metals Handbook, Vol th Ed., ASM Pubs., Materals Park, Oho.