Engineering Approximations in Welding: Bridging the Gap ... · PDF fileas a basis, most welding and materials engineers have developed engineering tools to ... mately 0.15 to 1 mm

Introduction Throughout their careers, weldingengineers and welding metallurgistsare often confronted with weldingprocess and properties questions thaton the surface and to those not famil-iar with welding appear to be simple,clear, and direct. Typical examples ofthese kinds of questions might be: “We need to make a laser spot weldnext to an extremely heat-sensitive

component — will welding damage it?” “We are going to make this assem-bly out of an alloy we’ve never weldedbefore — will the welds crack?” “We’d like to use this new alloy tomake a welded structural part for aone-off test — will it be strongenough?” Of course, these questions are any-thing but simple and the complexityassociated with the scientific princi-ples underlying each of them can be

quite daunting, especially to the newwelding or materials engineer. Scien-tific research and applied developmentstudies have been conducted since be-fore the American Welding Society wasfounded to develop the basic under-standing, experimental data, and ana-lytical and computational tools neededto provide complete and quantitativesolutions to welding problems. Syn-thesizing that information into day-to-day problem-solving tools can bechallenging since it often requires anin-depth familiarity with subjects asdiverse as laser and arc physics, heatand fluid flow, solidification dynamics,phase transformations, strengtheningmechanisms, simulation methods, andmany others. Moreover, the highly dy-namic and nonlinear nature of weldingmakes observation and intuitive as-sessment of these processes difficult,so that guesswork and overly simpli-fied rules of thumb can be misleadingor worse. In addition to their complexity, manyquestions of this type are accompaniedwith short timelines and limited re-sources, so that the opportunity to con-duct in-depth studies is often not avail-able, and the specific nature of the prob-lem often means that it has not beendirectly addressed or studied in the lit-erature. Under these constraints, mostwelding and materials engineers relyon their experience base or that of col-leagues to address the issue. For thosecases where at least some resourcesand time are available, or where thequestions are recurring and general in

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JANUARY 2016 / WELDING JOURNAL 1-s

SUPPLEMENT TO THE WELDING JOURNAL, JANUARY 2016Sponsored by the American Welding Society and the Welding Research Council

Engineering Approximations in Welding: Bridgingthe Gap between Speculation and Simulation

The author presents working approaches to welding problems from process physics to materials/process interactions

BY C. V. ROBINO

ABSTRACT During the course of their careers, welding engineers and welding metallurgists areoften confronted with questions regarding welding processes and properties that on thesurface appear to be simple and direct, but are in fact quite challenging. These questionsgenerally mask an underlying complexity whose underpinnings in scientific and appliedresearch predate even the founding of the American Welding Society, and previousComfort A. Adams lectures provide ample and fascinating evidence of the breadth anddepth of this complexity. Using these studies or their own experiences and investigationsas a basis, most welding and materials engineers have developed engineering tools toprovide working approaches to these daytoday questions and problems. In this article,several examples of research into developing working approaches to welding problemsare presented. The examples were selected to span a range of problems from processphysics, to materials/process interactions, and finally to weld properties development.The examples include timeresolved measurement of energy absorption in laser spotwelding, assessment of the dynamics of solidification hot cracking in nickelbased alloys,and evaluation of the heataffected zone softening in a modern ultrahighstrength steelalloy. From these evaluations, some physical insight and comparatively simple phenomenological criteria and assessment methods are developed, and their use in daytodayproblems are outlined.

KEYWORDS • Laser Welding • Modeling • Hot Cracking • HighStrength Steel • HeatAffected Zone

C. V. ROBINO is with Sandia National Laboratories, Albuquerque, N.Mex. Based on the 2015 AWS Comfort A. Adams Lecture delivered duringFABTECH in Chicago, ILL.

Robino 1-16.qxp_Layout 1 12/11/15 3:42 PM Page 1

nature, most welding and materialsengineers have developed engineeringtools that provide workable approach-es and solutions. In this article, severalexamples of the latter from the au-thor’s experience and applied researchare presented. The examples were se-lected in an attempt to span a range ofproblems from process physics, to ma-terials/process interactions, and final-ly to weld properties development. Itis hoped that within these examples ageneral audience can find specific topi-cal areas of interest. The examples in-clude time-resolved measurement oflaser energy absorption and applica-tion to laser spot welding, assessmentof the dynamics of weld hot crackingin nickel-based alloys, and estimationof the heat-affected zone softening ina modern ultrahigh-strength steel alloy.

Energy Absorption inPulsed Laser Welds Considering the first questionposed above, power and energy trans-fer are fundamental aspects of anywelding process and are needed formeaningful estimation of weldingtemperatures. As a result, power andenergy transfer are key elements ofprocess selection, process modeling,and process optimization. With re-spect to pulsed laser welding, because

of the highly dynamicand short duration ofthe process, characteri-zation of these efficien-cies is challenging(Refs. 1–5). Fuer-schbach and Eisler(Ref. 2) characterizedpulsed laser weld ener-gy absorption throughcalorimetry by usinghundreds of bead-on-plate spot welds made in rapid succes-sion. As the welds cooled to room tem-perature, the energy released wasmeasured by calorimetry. The total en-ergy was then divided by the numberof welds to yield the average energyabsorbed per weld and was found torange from 40 to 65% of the deliveredpulse energy. Temporal resolution isnot obtained by this method and forlow-pulse-energy welds, measurementuncertainty increases. The authorsalso considered the complicating fac-tor of weld spatter and the uncertaintyit causes. Differential microcalorime-try was used by Perret et al. (Refs. 3, 4)and indicated energy transfer efficien-cies in the range 32–80% dependingon process parameters. Notably, Perretet al. (Refs. 3, 4) also used high-speedflash x-ray radiography to study thetime-resolved keyhole formation in atitanium alloy, and observed that thekeyhole forms very early in the pulse(on the order of 1 ms) and, for pulse

times up to 5 ms, continues to growthroughout the duration of the pulse. In lieu of calorimetry, Cremers etal. (Ref. 5), determined energy absorp-tion by measuring the thermal expan-sion of welded metal samples. Thetransient displacement of the weldedsample was evaluated through inter-ferometry complemented by a secondmethod that monitored coaxial dis-placements using a linear variable dif-ferential transformer (LVDT). In the approach discussed here,Norris et al. (Refs. 1, 6) developed anew method for determination oftransfer efficiencies in pulsed laserwelding. This approach is describedand results are presented for a rangeof welding parameters in order to gainan understanding of the dynamics andphenomenology of energy transfer inlaser spot welding. In turn, these ob-servations provide a basis for engi-neering assessments of welding tem-peratures as well as an engineering ba-sis for welding parameter selection.

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Fig. 1 — Schematic drawing of energy absorption apparatus includingenergy balance. Energy absorbed by the weld and beam splitter are denoted with subscripts W and BS, respectively. Subscripts P and T indicatethat passed through and turned, respectively, by the beam splitter.

Fig. 2 — Typical delivered pulse profiles for A — power andB — energy for 3 kW (set power), 6 ms, 9.5 J pulse using aLasag SLS C16 fiber delivered 40W average power pulsedNd:YAG laser.

A

B


Experimental Procedures The basic concept behind the ab-sorption measurement method is rela-tively simple — capture and measure,in a time-resolved manner, the energyreflected from a single laser spot weldand subtract that from the energy de-livered to the part. In practice, howev-er, the method is somewhat complexand requires rigorous characterizationand calibrations. The characterizationand calibrations are described in detailin Ref. 1, and only the salient pointsare summarized here. The welds exam-ined in this work represented typicalengineering practice and weld proce-dures for sub-millimeter spot welds inan austenitic stainless steel, andranged in penetration from approxi-mately 0.15 to 1 mm (0.006 to 0.039in.). The measurement technique isbased on creating a laser weld withinthe interior of an integrating sphere,and is shown schematically in Fig. 1.An integrating sphere is an optical de-

vice that is hollow and spherical inshape and the interior is coated to pro-mote high reflectance for a given lightsource wavelength. The result, ideally,is scattering of the incoming light andisotropic illumination of the sphere’sinterior walls (Refs. 7, 8). An apertureon the side of the sphere allows thelight flux to be measured with a pho-todiode. In practice for welding experi-ments, it was found that two gold-plated integrating spheres are requiredas shown in Fig. 1. In this approach, the total scatteredenergy collected by the two spheres issubtracted from the known deliveredlaser pulse energy to determine theabsorbed energy. The two gold-platedintegrating spheres each contain a nar-row band pass photodiode filtered toinclude only the laser wavelength andthus measure the light flux as a func-tion of time. A beam splitter is used toredirect possible exiting reflectionsfrom the primary weld sphere into thesecondary sphere. The primary sphereis positioned directly beneath the laser

head assembly (light source). The weldsample (typically a 12.5-mm-diameter,3-mm-thick 304L stainless steel diskwith a surface finish of 0.8 mm RMS) iscontained within the sphere and is po-sitioned at sharp focus by an ad-justable gold-plated post. Welding isconducted in an argon atmosphere.Depending upon the state of the weldpool, light is reflected from the weld’ssurface and is either captured by theprimary weld sphere or exits throughthe sphere’s entrance opening, isturned by a partially reflective mirror,and is captured by the secondarysphere. Preliminary experiments indi-cated that due to the entrance angle ofthe primary sphere and the beam fo-cus angle, welding had to be conductedabove the centerline of the primarysphere rather than at the more opti-mal base of the sphere. Thus, a signifi-cant amount of the reflected light wasfound to escape from the entrancehole of the primary sphere, and in or-der to account for this loss, the sec-ondary sphere was added to collect

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Fig. 3 — Results of absorption measurements for a 6ms, 1585W (actual) peak power pulse (~9.5 J/pulse) spot weld. A — Individualsphere and total reflected power; B — total reflected power compared with delivered power; C — absorbed power compared with delivered power; D — time resolved delivered and absorbed energy.

A B

C D


this light. Figure 1 shows the basic en-ergy balance and losses for the meas-urement system. Characterization and calibration ofthe energy balance and measurementlosses, such as those through the turn-ing mirror and the quartz tube (in-cluded to protect the primary spherefrom spatter and metal deposition) aredescribed in detail in Ref. 1. Calibra-tions for both spheres were found tobe linear and repeatable. The result forboth spheres, in essence, is a tempo-rally resolved photodiode voltage thatvaries in amplitude directly with re-flected light intensity. Through cali-brations using power meters and fullyreflecting parts, these voltage signalscan be converted into a delivered pow-er waveform as shown in Fig. 2A. Inte-gration of the power waveform resultsin a delivered energy waveform asshown in Fig. 2B.

Results and Discussion

Typical results are presented in Fig.3A, which shows the measured reflect-ed power for a 6 ms, 1585-W (actual)peak power pulse (~9.5 J-pulse). Thegreen and red curves represent the re-

flected Nd:YAGpower through-out the durationof the pulse asdetected by theprimary and sec-

ondary spheres, respectively, while theblue curve shows the summation ofthese curves (i.e., the total reflectedpower). In Fig. 3B, the total reflectedpower is compared with the deliveredpower (note that the laser pulse profileis acquired prior to welding in a sepa-rate experiment) and, as expected, thereflected power constitutes an appre-ciable fraction of the delivered power.Subtraction of the reflected powercurve from the delivered power curveresults in the absorbed power curveshown in Fig. 3C, and integration ofthe delivered and absorbed powercurves results in the time resolved, de-livered, and absorbed energy curves inFig. 3D. These results can be interpreted interms of the weld pool formation andkeyhole growth, and are shown con-ceptually in Fig. 4. In the early stagesof the laser pulse, the majority of thereflected light exits the primarysphere and is captured by the second-ary sphere. This initially high reflec-tion not only shows low absorption oflaser power (Fig. 3A) but, since it ismostly detected by the secondarysphere, the reflection is essentiallyparallel to the incoming beam. This

implies a nearly flat, largely perpendi-cular surface such as that expected atthe onset of weld pool formation(Refs. 9–11) and shown conceptuallyin Fig. 4A. Once sufficient melting is achieved,surface tension forms a semihemispher-ical weld pool reflecting light in all direc-tions above the surface of the sample.This is evident by the rapid decrease inreflected light detected by the second-ary sphere (red curve in Fig. 3A) and in-creasing reflections captured in the pri-mary sphere (green curve). Over thenext few milliseconds, laser power ab-sorbed by the weld increases as the totalmeasured reflection decreases (bluecurve). The decrease in reflected light isbelieved to be indicative of the forma-tion of a weld pool keyhole and the rateof decrease is a measure of the rate atwhich the keyhole develops and grows,as shown conceptually in Fig. 4B. Uponkeyhole maturation at approximately3–4 ms, reflected light reaches a mini-mum and is roughly constant for theduration of the pulse — Figs. 3C and4C. Laser power reflected at this pointis ~25% of the power delivered.Through Fresnel reflections (Refs. 12,13), as the keyhole becomes deeperand its walls become more inclined(steeper), the decreased angle of inci-dence increases the number of reflec-tions that are contained and eventual-ly captured within the keyhole, there-

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Fig. 4 — Notional images of the various stages of keyhole formation. A — Initial reflection and start of melting; B — keyhole growth; C —final or steady state.

Fig. 5 — A — Effect of peak power on energy absorption in Nd:YAGlaser spot welds. Values just to the right of the curves are thepower transfer efficiencies at the end of the weld pulse; B — metallographic cross sections corresponding to the welds in A.

B

B

A

A

C


by yielding a higher net transfer inlaser power. With each reflection, en-ergy is both absorbed and reflected,and with the decreased incident beamangle, more energy is deposited at theroot of the keyhole. This drives highaspect ratio, high energy transfer effi-ciency, and high melting efficiencywelds.

The difference between the deliv-ered power and the measured reflectedpower is the power absorbed to formthe weld. This difference is presentedin Fig. 3C along with the laser pulseprofile. As before, the general condi-tion of the weld pool can be deducedfrom the temporal plot: absorption islow at the onset of melting and rapidlyincreases as a keyhole is formed. Thisplot allows the efficiency of power andenergy transfer to be characterized. At

any point along theplot of power ab-sorbed vs. time,power transfer effi-ciency is the ratioof laser power ab-sorbed to the laserpower delivered.This numeric val-ue, as already dis-cussed, is descrip-tive of the instan-taneous state ofthe weld pool. Atthe onset of weld-ing (initial meltingand conductionmode), powertransfer efficiencyis <50% and, as thekeyhole develops,

the efficiency increases to 75%. Ener-gy transfer efficiency, t, is the overallenergy efficiency of the weld and isthe ratio of energy absorbed (area un-der the weld power curve) to the ener-gy delivered (area under the pulse pro-file power curve). The energy transferefficiency for the weld shown in Fig. 3is 66%. Replicates of similar testsshowed the absorption measurementsto be very repeatable (Ref. 1) despitethe complex physics associated withlaser absorption and the chaotic na-ture of the weld pool that accompanieskeyhole mode welds (Refs. 10, 11, 14).This implies that assessments basedon these absorption measurementsare very reasonable for engineeringpurposes. The effect of peak power on energytransfer at constant pulse duration is

illustrated in Fig. 5. At 500 W (greencurve), a relatively constant absorp-tion profile is observed throughoutthe weld pulse, yielding a power trans-fer and energy efficiency on the orderof 47%. As might be expected, themetallographic cross section of thatweld (Fig. 5B) reveals a low aspect ra-tio conduction mode weld. For a deliv-ered peak power of 1033 W (redcurve), a keyhole is formed as impliedby the increased power absorption andthe parabolic shape of the absorptioncurve as discussed earlier. Powertransfer efficiency starts below 50%and increases to 63% at the end of thepulse, yielding a total energy transferefficiency of 54%. Further increases inthe delivered power to 1585 W (bluecurve) yields, upon keyhole matura-tion, an even higher power transfer ef-ficiency of 73% for an overall energytransfer efficiency of 66%. Compari-son of the 1033 and 1585 W curvesshows the rate of keyhole maturation(time to maximum power transfer) tobe nearly equivalent and occurs atabout 4 ms. The relatively constantpower transfer from 4 to 6 ms impliesan essentially fully developed and quasi-stable keyhole. Although bothwelds are effectively keyhole modewelds, the maximum power transferefficiency at 1585 W is greater thanthat at 1033 W. The lower peak powertransfer of the 1033-W weld implies aless acute keyhole with fewer internalreflections and thus lower transfer ef-ficiency. In support of this interpreta-tion, the corresponding metallograph-ic sections show a lower weld aspectratio for the 1033-W weld. Logically,

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Fig. 7 — Energy transfer efficiency as functions of average delivered power and pulse length for square (SQR) and controlledramp down (CRD) pulse shapes.

Fig. 6 — A — Effect of pulse duration on energy absorption in Nd:YAG laser spot welds; B — metallographic cross sections correspondingto the welds in A.

BA


the high-aspect-ratio 1585-W weld im-plies that upon keyhole maturation, adeeper, more inclined keyhole wasformed and resulted in the highermaximum power transfer value and ul-timately more efficient overall energytransfer. Similarly, the effect of pulse dura-tion at constant power can be evaluat-ed and is shown in Fig. 6. In this case,the absorption profile for each weldoverlaps as pulse time increases. At 2ms, there is insufficient time for com-plete keyhole development and this re-sults in a low transfer efficiency weldwith power and energy transfer lessthan 50%. As pulse time increases(from 4 to 8 ms), the relative amountof time spent in keyhole mode increas-es, thereby yielding a greater overallenergy transfer effeciency. A peakpower transfer effeciency of approxi-mately 77% is reached and is relativelyconstant after 4 ms. At 4, 6, and 8 ms,energy transfer efficiency increasesfrom 61% to 66% to 70%, respectively.Evaluation of the metallographic crosssections in Fig. 6B reveals the progres-sion of the weld as pulse time, energy,and efficiency increase. Each weld issimilar in overall shape, with weld sizeincreasing with pulse duration. Inter-estingly, after 4 ms, a single pore of

roughly common size is seen (root-type pores such as these are commonin keyhole mode laser welds and aregenerally formed by the collapse of theweld pool keyhole, Ref. 10). From Figs. 3–6, it is clear that in-creasing energy transfer efficiency isachieved by increasing either pulsetime or delivered power, and this isparticularly the case for keyhole modewelds. This is discussed in more detailin Ref. 1, but can be summarized asshown in Fig. 7. Here, energy transferefficiency is shown as a function ofpulse time and delivered power (or av-erage power in the case of nonsquarewave pulses discussed below) for arange of typical Nd:YAG welding pa-rameters with a 150-mm focal lengthlens. These conditions produce spotwelds in 304L ranging from 0.15 to 1mm in depth and are typical of actualengineering practice. Although thedata is somewhat scattered, it is clearthat increasing power yields greater ef-ficiency. In contrast, however, if pulsetime is too short, thereby inhibitingkeyhole formation (i.e., 2 ms – blackcurve Fig. 7), only moderate increasesin efficiency can be expected regard-less of increasing output power.

These measurements of energytransfer efficiency for milliscale stain-

less steel welds are comparable tothose presented by Fuerschbach andEisler (Ref. 2), and by Cremers et al.(Ref. 5), and therefore appear to bereasonably general. In terms of engi-neering approximations, therefore, arelatively simple correlation that com-bines the effects of power and pulseduration on energy transfer can be de-rived from Fig. 7. For delivered aver-age power levels above 500 W andpulse durations greater than 4 ms, areasonable approximation is that en-ergy transfer efficiency increases fromabout 0.45 at 500 W at a rate of about0.002 per watt. Of course, adjust-ments to this need to be made for dif-ferent lenses (spot sizes) and lasercharacteristics, but if little else isknown (in the manner of the questionposed in the Introduction of this arti-cle) such an approximation provides amethod for assessing energy transferand temperatures adjacent to spotwelds. Melting efficiency, or that por-tion of delivered energy that is actu-ally used to create a molten zone, isanother key characteristic of weldprocess selection and, in conjunctionwith transfer efficiencies, can also beassessed for these spot welds. Thistopic is addressed in more detail inRefs. 1–5. As a general engineeringrule, however, it is clear that for agiven-sized weld, higher power pulsesare generally preferred as they achievehigher energy transfer efficienciessooner, and thus are likely to provide amore efficient (lower overall tempera-ture, lower distortion, etc.) weld. Finally, the time resolved absorp-tion measurements can be used as anaid in other aspects of process selec-tion. Observation of Figs. 5B and 6Bshows that for high powers and squarepulse shapes, weld root porosity is atypical result. A common approach tolimiting root porosity in spot welds(Ref. 9) is through control of the weldpulse shape, with the goal of impart-ing a more gradual collapse of the key-hole at the end of the weld cycle. Com-parisons of energy absorption deter-minations and weld defect levels forsquare (SQR) and controlled rampdown (CRD) pulse shapes are shown inFigs. 8 and 9. As shown, the 6-ms, 4.2-J CRD pulse produces a weld of similarpenetration and size to that of a 6-ms,4.7-J SQR pulse, but without rootporosity. In this case, the CRD pulse isboth more efficient (by 10%) than theSQR pulse and less prone to defects.As shown in Fig. 9, this is essentiallybecause the higher power during the

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Fig. 8 — A — Pulse shape and absorption for a square 6ms, 4.7J spot welding pulse; B —pulse shape and absorption for a controlled ramp down 6ms, 4.2J spot welding pulse; C— cross section of weld in A; D — cross section of weld in B.

A

C

B

D


initial portion of the CRD pulse morerapidly establishes the keyhole and thepenetration depth, while at a latertime smoothly decreases the power fora less abrupt collapse of the keyhole.Thus, the absorption measurementsprovide an engineering basis that canbe used as a guide to understandingand utilizing the interplay betweenthermal constraints, penetration, andweld defect formation. In summary,when combined with methods for esti-mating welding temperatures, the ab-sorption and efficiency determina-tions provide the required informationneeded to answer the first questionposed in the Introduction, and at thesame time provide interesting insightto the welding process and keyhole de-velopment and control.

Dynamics of Weld HotCracking Considering the second questionposed in the Introduction of this arti-cle regarding the cracking tendency ofwelds, a common method for assessingthe susceptibility of alloys to crackingis through weldability testing. Thereare many forms of weldability tests de-signed to evaluate the various types ofweld cracking (Refs. 15, 16) and otherdefects. In the present discussion, thehot cracking susceptibility of nickel al-loys as evaluated by the longitudinalVarestraint test is of specific interest. The longitudinal Varestraint test

(Refs. 17, 18) has long been used to as-sess the relative hot cracking suscepti-

bility of alloys. In thistest, a gas tungsten arcweld is produced alongthe longitudinal center-line on the top side of arectangular plate orsheet, beginning at anunsupported end andmoving toward a fixedend mounted over acurved die block. Whenthe welding arc reachesa predetermined loca-tion over the die block,the bar is rapidly bentto conform to the radiusof the block. This bend-ing induces an aug-mented strain (i.e. anadditional strain that is superimposedon the normal solidification and ther-mal shrinkage strains). The augment-ed strain is inversely proportional tothe radius of the block, and, on thewelded side of the bar can produce so-lidification hot cracks that typicallyform in the partially molten zone adja-cent to the trailing edge of the weldpool. Various die block radii are usedto characterize the strain level atwhich cracking becomes evident, andtotal crack length, number of cracks,or maximum crack length are used asthe comparative measures of weldabil-ity. A key (though occasionally over-looked) characteristic of this test isthat, in practice, straining of the sam-ple cannot occur instantaneously, butrather the strain increases over timeduring the test. Thus, the dynamics ofthe test are extremely complex, with

time varying augmented and shrink-age strains superimposed onto a mov-ing temperature field and moving so-lidification front. Qualitatively, thiscomplexity has been addressed by re-stricting hot cracking susceptibilitycomparisons to those determined un-der identical conditions of samplegeometry, weld size, travel speed,straining rate, etc., but a more usefulaspect of the test is the insight it pro-vides into the phenomenology that oc-curs during solidification cracking.

In order to gain a better under-standing of the dynamics of hot crack-ing and the hot ductility of semi-molten alloys in general, Matsuda andcoworkers (Refs. 19–22) used high-speed cinematography to observecrack formation and growth in thesemimolten region of welds. Thesestudies used tensile straining trans-

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Fig. 9 — Comparison of absorption profiles for square 6 ms, 4.7 Jand controlled ramp down 6ms, 4.2J spot welding pulses.

Fig. 10 — A — Varestraint imaging setup; B — image takenfrom video at a late stage in the Varestraint testing of lowcarbon Alloy 718 showing hot cracks and the weld pool inthe upper left of the image. Scribe marks used for longitudinal strain measurement are shown on the right side ofthe image.

A

B


verse to the welding direction andclearly demonstrated the utility ofhigh-speed photometric methods forquantifying ductility and cracking be-havior. In addition to developing in-situ strain measurement techniques,hot ductility curves for a wide range ofsemimolten alloys were constructed.These observations led to a number ofproposed modifications to Borland’s(Ref. 23) theory of super-soliduscracking. In referenced work (Ref. 24) andthe discussion following, the tech-

niques developed by Matsuda andcoworkers (Refs. 19–22) are applied tothe longitudinal Varestraint test in or-der to gain understanding of the dy-namics of the test and some of thephenomenology of hot cracking. Ob-servations made with high-speedvideography are described and inter-preted with the aid of solidificationmodels. From these observations andestimates, criteria defining the impor-tant cracking events such as initiation,growth, and crack backfilling are de-veloped. These criteria provide a basisfor engineering assessments of hotcracking in alloys similar to those evaluated.

Experimental Procedures

Imaging experiments (Ref. 24) wereconducted on subsize Varestraint testsof low- and high-carbon versions ofthe nickel-based Alloy 718 with thecompositions shown in Table 1. Basedon the compositions, the high-carbonalloy was expected (Ref. 25) to exhibit

eutectic backfilling of hot cracks dur-ing Varestraint testing, while the low-carbon alloy was not. The sampleswere 165 ¥ 25 ¥ 3.2 mm (6.5 ¥ 1 ¥0.125 in.) and welding parameterswere 100 A electrode negative, 12.5 V,3.3 mm/s, (8.8 in./min) with Arshielding. All imaging experimentswere conducted at an augmentedstrain of 3.5%. A photograph of the setup used forthe imaging experiments is shown inFig. 10A. For these imaging experi-ments, the welding head was angledrelative to the sample to facilitate im-aging of the trailing edge of the weldpool. Video records were generally cap-tured at a rate of 1000 frames/s usinga Speed Vision HGTX 2000 camera fit-ted with a Navitar Zoom 6000 lens. Animage taken from a video record at alate stage in a test is shown in Fig.10B. Longitudinal strain measure-ments were made by using scribemarks in the region adjacent to theweld. Following the methods describedby Matsuda et al. (Ref. 19), local strainmeasurements were made in the par-tially molten zone by using dendriticfeatures visible on the weld surface.

Results and Discussion

Figure 11 shows several images tak-en from the video record of a Vare-straint test. These images correspondto 37, 47, and 77 ms from the initia-tion of sample bending and the trail-ing edge of the weld pool is visible inthe first two photos. The arrowsshown on each image mark the loca-tion of the crack initiation on the sur-face of the weld, which occurred at ap-proximately 37 ms. As shown, the hotcrack grows in both advancing (in theweld travel direction) and retreatingdirections from the initiation site. From each of the video images, a

variety of dimensions were measuredand the convention used for thesemeasurements is shown in Fig. 12. Themeasurements included longitudinalstrain, measured from scribe markoutside of the weld path; local strain,measured approximately perpendicu-lar to the crack from visible image fea-tures; advancing crack length; and re-treating crack length. The horizontalline is referenced to a scribe mark andwas used to locate the crack initiation

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Table 1 — Compositions of Alloys Used in Varestraint Cracking Study

Element Alloy 718 LowCarbon wt% Alloy 718 HighCarbon wt%

Fe 19.21 19.19 Cr 17.41 17.19 Nb 5.11 5.07 Mo 2.87 2.86 Ti 0.90 0.90 Al 0.44 0.42 C 0.04 0.09 Ni Bal Bal

Fig. 11 — Selected images taken fromvideo record of Varestraint test. Fromfront to rear, the images correspond to37, 47, and 77 ms from the initiation ofbending.

Fig. 12 — Image showing the measurements taken from each image in the videorecord. The circle shows the crack initiationlocation and is referenced to a position relative to the scribe lines. A — Baseline forlongitudinal strain; B — baseline for localstrain; C — retreating crack length; D —advancing crack length.

Fig. 13 — Local strain, longitudinal strain,and total crack length for lowcarbonAlloy 718 test at 3.5% augmented strain.


site from image to image. Both longi-tudinal and local strain measurementswere based on lengths determinedwhen the trailing edge of the poolcrossed (what would eventually be-come) the crack initiation site. Figure 13 shows the time evolutionof strain and total crack length for theVarestraint test of the low-carbon Al-loy 718. The longitudinal strain (theaugmented strain applied duringbending plus shrinkage strain) increas-es only slightly during the first 35 ms,then increases approximately linearlyto 4% at about 140 ms. The localstrain (a measure of the augmentedplus shrinkage strains across the cracklocation) increases to 10% over a simi-lar time scale, which is equivalent to astrain rate of approximately 1/s in thevicinity of the crack. Cracking initiatesat 37 ms and a local strain level ofabout 1%, and the total crack growthis roughly linear with time. The crack growth rates for the ad-vancing and retreating portions of thecrack in a fixed frame of reference areshown in Fig. 14A. Crack initiation oc-

curs close to the trailing edge of theweld pool (about 0.396 mm, 0.016 in.,from the visible solidification front),and both the advancing and retreatingcracks are observed to grow sporadi-cally with some periods of inactivityfollowed by periods of rapid growth.On average, however, the advancingcrack grows roughly linearly with time.The retreating crack grows somewhatparabolically until growth ceases atabout 150 ms. By using the velocity ofthe trailing edge of the pool, the ad-vancing and retreating crack lengthdata can be used to assess the crackgrowth relative to the moving refer-ence of the weld pool. This assessmentis shown in Fig. 14B and several obser-vations are immediately apparent. As before, growth of the crack inboth advancing and retreating direc-tions is somewhat erratic, with peri-ods of rapid growth followed by peri-ods of stagnation (which may be relat-ed to the occurrence of neighboringcracks). Second, the advancing cracktip remains, on average, at an essen-tially constant distance behind the

weld pool. This implies that the ad-vancing crack is tied to an isothermwithin the mushy zone, and it is essen-tially the same isotherm in which thecrack initiates (in this case about0.396 mm from the trailing edge). Inaddition, since it grows in anisotherm, it is also growing in a regionof constant fraction liquid. This is animportant engineering observationand implies that, in a longitudinalVarestraint test, the advancing cracktip is the most similar to a “real” hotcrack in a structural weld, and that“real” hot cracks probably grow at thetravel speed and essentially trail theweld as they are formed. The retreat-ing crack tip, while interesting, proba-bly does not represent the behavior ofcracks in “real” welds (i.e., welds inwhich the strain is not artificially aug-mented). The retreating crack tipmoves in the direction of decreasingtemperature behind the pool, and thusinto a region of decreasing fraction liq-uid. It would appear the augmentedstrain plays a key (if somewhat artifi-cial) role in the retreating portion ofthe Varestraint crack growth. Turning now to tests on the high-carbon Alloy 718, a late time video im-age and a scanning electron micro-scope (SEM) secondary electron imageof the test sample are shown in Fig.15. In this case, analysis of the videorecords showed that the crack initiatedat a local stain level similar to that forthe low-carbon alloy, but at a distancebehind the pool of 0.217 mm (0.009in.) compared with 0.396 mm for thelow-carbon alloy. Moreover, the initia-tion location corresponded to the loca-tion where backfilling starts — thecracking initiated at the apex of theangled crack near the center of theSEM image in Fig. 15B. In otherwords, although it is very difficult tocapture in video images, it appearsthat backfilling occurs simultaneouslywith the movement of the advancingcrack tip, and may be more appropri-ately described as infilling of the ad-vancing crack as it opens. It is knownthat backfilling in Alloy 718 consistsof an NbC/austenite terminal eutecticconstituent (Refs. 24, 25). In order to rationalize these obser-vations, it is necessary to determinethe temperatures and liquid fractionsassociated with the various key eventsduring the test. The first requires esti-

WELDING RESEARCH


Fig. 14 — A — Advancing and retreating crack tip positions as a function of time relativeto the position of the S/L interface at crack initiation in the lowcarbon Alloy 718. B —Advancing and retreating crack tip positions as a function of time relative to the trailingedge of the weld pool.

Fig. 15 — A — Image taken from video at a late stage in the Varestraint testing of highcarbon Alloy 718 showing hot cracks and the weld pool in the upper right of the image;B — SEM image of approximately the same area showing crack backfilling associatedwith the advancing portion of the crack. Arrow on B shows location of crack initiation.

A B

A B


mation of the temperature gradientbehind the weld pool and this can beobtained through numerical modeling(Ref. 24) or by various analyticalmethods (Ref. 26). Estimates of thesegradients from Ref. 24 for the two al-loys are shown in Fig. 16A. Estimationof the liquid fraction requires a solidi-fication model for the alloys. Amethod for estimating the fraction liq-uid and terminal constituent forma-tion as a function of temperature forcomplex nickel alloys has been devel-oped by DuPont and coworkers (Refs.25, 27–29), and results for the two al-loys using this method are shown inFig. 16B. Combination of the two setsof curves in Fig. 16 results in the frac-tion liquid vs. distance curves shownin Fig. 17. The figure also shows theposition at which cracking was ob-served to initiate in the high-speedvideo as well as the estimated locationat which the NbC/austenite eutecticbegins to form in the two alloys. Although several models and meas-urements were combined to constructFig. 17 and there is appreciable uncer-tainty in all of these, in conjunctionwith the other video observations andstrain measurements, the assessment

provides the basis for several usefulphenomenological descriptions andengineering approximations concern-ing hot cracking in nickel alloy welds.The phenomenological description isillustrated in Fig. 18. First, for bothunfilled and backfilled cracks, crackinginitiates at a fraction liquid of about10% and a local strain of about 1%.These local strain values are very con-sistent with those determined by Mat-suda and coworkers (Refs. 19–22) fornickel alloys. In a manner similar tosolidification cracks in real welds, theadvancing crack tip grows sporadicallybut remains an approximately con-stant distance behind the pool, andthus the crack tip is at constant tem-perature and presumably constant lo-cal strain conditions. For conditionswhere the formation of eutectic liquidprecedes the above strain and fractionliquid conditions, the advancing crackinfills with eutectic liquid as it opens.Conversely, it can be surmised that foralloys where the eutectic solidificationdoes not initiate until after the criticalstrain/fraction liquid condition isreached, the likelihood that the crackwill backfill is small. The retreatingcrack tip grows into a region of de-

creasing fraction liquid, and presum-ably terminates as the strain field de-grades or it intersect the solidus. To the author’s knowledge, there areno widely accepted methods by whichsolidification crack initiation can be pre-dicted from first principles. Althoughthere are clearly many simplifying as-sumptions in the above analysis and nu-merous physical phenomena are in-volved in weld solidification cracking,from the perspective of estimatingcracking susceptibility in welding thesesimple criteria provide a means to de-fine those conditions (at least for nickelsuperalloys and similar alloys). Ofcourse, application of these criteria re-quires assessment of the thermal,strain, and metallurgical conditions inthe vicinity of welds, but as these meth-ods become increasingly available to thepracticing welding engineer, it is be-lieved that these criteria can be used ina predictive manner and as an engineer-ing method to assess the potential forhot cracking in real welds.

HeatAffected Zone Softening in a HighStrength Steel Turning now to the final questionposed in the Introduction to this arti-cle, weldment properties, this sectionprovides an illustration of relativelysimple methods to assess weldmentproperties in an ultrahigh-strengthsteel alloy. This section is based on acomprehensive report on the fabrica-tion and service weldability of Aer-Met® 100 alloy (Ref. 30). AerMet® 100

WELDING RESEARCH


Fig. 18 — Phenomenology of Varestraint solidification hot cracking of Alloy 718.

Fig. 17 — Estimation of fraction liquid as a function of distance and NbC/austenite eutecticstart position behind the weld pool in the Varestraint tests. Also shown are the measuredcrack initiation positions for the two alloys.

Fig. 16 — A — Estimation of temperature behind the weld pool for the Varestrainttests of the two alloys; B — estimation of fraction liquid and NbC/austenite eutecticstart temperatures for the two alloys.

A B


alloy is a 0.23 wt-%C, 13.4 wt-%Co,3.1 wt-%Cr, 11.1 wt-%Ni, 1.2 wt-%Moproprietary steel alloy (Refs. 31, 32)designed by Carpenter TechnologyCorp. for aerospace structural applica-tions. The alloy exhibits a favorablecombination of high strength, highfracture toughness, and exceptionalresistance to stress corrosion cracking.The nominal properties for the alloyare 1965 MPa (285 ksi) ultimate ten-sile strength, 126.4 MPa√m (115ksi√in) KIc, and 38.5 MPa√m (35ksi√in) KIscc in a 3.5% NaCl solution,and these make it a candidate for ap-plications such as navel aircraft land-ing gear. The alloy is the most recentdevelopment in the family of second-ary (precipitation) hardening Ni-Co-Crsteels that includes HY180 andAF1410 alloys. Following normal heat treatment(solution treating, quenching, and ag-ing), these alloys are low-carbon, Fe-Ni

lath martensitic alloys that attaintheir properties through the precipita-tion of M2C (where M is Mo and Cr)carbides during aging. AerMet® 100 al-loy has a high hardenability, and wasdesigned to be air cooled from the so-lution treatment temperature in sec-tion sizes up to 51 mm (2 in.). Thenormal heat treatment for this alloyconsists of solution treatment at885°C (1625°F) for 1 h, air cooling, re-frigeration at –73°C (–100°F) for 1 h,air warming, and aging at 482°C(900°F) for 5 h. In comparison to other types ofhigh-strength steels, such as thequenched and tempered grades, thegeneral weldability of the secondaryhardening Ni-Co-Cr steels is usuallyconsidered to be quite good (Ref. 33).This improvement results primarilyfrom the fact that the low-carbonmartensite that forms in these alloysis relatively soft and ductile. Thus, in

the as-quenched condition, which typ-ifies much of the weld fusion and heat-affected zones, the Ni-Co-Cr steels areresistant to the problems (particularlycold cracking) that are often associat-ed with welding of high-strengthquenched and tempered steels. A com-plete discussion of welding response,weldment properties, and postweldheat treatment of AerMet® 100 Alloyis provided in Ref. 30, but a key issueassociated with welding of precipita-tion hardening Ni-Co-Cr steels is over-aging and softening in the heat-affect-ed zone (HAZ). This softening is illustrated in Fig.19, which shows the as-welded struc-ture and a microhardness traverse(converted to Rockwell C) across a sin-gle bead-on-plate gas tungsten arc(GTA) weld in aged AerMet® 100 Alloyplate. Several important regions areapparent in the hardness traverse. Inthe fusion zone the hardness is rela-tively low, and the microstructure con-sists essentially of fresh martensite.Thus, the hardness is similar to thatfor solution-treated base metal andthe fusion zone can be expected (aswas observed in Ref. 30) to respond topostweld aging treatments as illustrat-ed by the dashed green line on theplot. The near weld interface region ofthe HAZ between about 1.5 and 3 mm(0.060 and 0.12 in.) also consists offresh martensite and responds to post-weld aging. In locations further out inthe HAZ, the hardness steadily in-creases toward the unaffected agedbase plate, but there is a trough in thehardness in the range of approximate-ly 3.5–4.5 mm (0.14–0.18 in.). The re-gion adjacent to, and within thistrough is particularly important be-cause it does not respond to postweldaging heat treatments. As a result, theprimary emphasis of the analysis de-scribed below was placed on character-ization of the microstructure andproperties evolution in this region ofthe HAZ. This characterization includ-ed determination of the temperaturesand microstructures associated withthe trough, as well as development ofkinetic descriptions of the softeningand reaustenitization processes. Gleeble simulations were used todetermine the temperatures associat-ed with the hardness trough in theHAZ. For these simulations, thermalcycles similar to those shown in Fig.

WELDING RESEARCH


Fig. 19 — A — GTA weld in aged AerMet® 100alloy plate showing location of microhardnesstrace in B; B —microhardness trace from weldin A.

Fig. 20 — A — Typical thermal cycle used for Gleeble HAZ simulations; B — hardness as afunction of peak temperature for aged base plate showing softened trough and hardnessafter postsimulation aging.

A B

A B


20A were used. The results of the ther-mal cycle simulations on pre-aged baseplate are shown in Fig. 20B. For thesesimulations, the minimum in hardnessoccurs for the 710°C (1310°F) peaktemperature thermal cycle. In addi-tion, as discussed previously, postsim-ulation aging does not affect the levelor temperatures associated with thehardness trough. This implies that thesoftening is associated with overaging,although it is also conceivable that theformation of reverted austenite (dis-cussed in more detail following) alsocontributes to the softening. The in-crease in hardness at peak tempera-tures of 760°C (1400°F) and above isassociated with the formation of newaustenite and fresh martensite oncooling. Microstructural analysis ofthe Gleeble samples (Ref. 30) generallyconfirmed the overaging of the hard-ening precipitates at peak tempera-tures near 710°C and the formation ofnew fresh martensite for peak temper-atures of 760°C and above.

Overaging Model Description of the overagingprocess in the HAZ of AerMet® 100 Al-loy requires a numerical model thatcan be applied to the rapid thermal cy-cle associated with the weldingprocess. In this section, a semiempiri-cal engineering model is developedand applied to the thermal cycles usedin the HAZ simulations. Since mostavailable data are in the form of hard-ness as a function of time and temper-ature for simple, isothermal aging con-ditions, the parameter is first devel-oped for AerMet® 100 Alloy hardnessdata (Ref. 34), and then shown to beapplicable to strength data. It is first assumed that hardness isproportional to shear strength andthat analysis for the strengthening ef-fect of incoherent precipitates (Ref.35) applies,

(1)

where H is the hardness, is the shearstrength, is a geometric factor, m isthe shear modulus, b is the burgersvector, and l is the interparticle spac-ing. For overaging, the volume fractionof precipitates is assumed constant, sothat l r, where r is the precipitate ra-dius and the precipitates are assumedto be spherical. Thus, in the overagingregime,

(2)During aging, the precipitates are as-sumed to follow classical coarseningkinetics (Ref. 35) (i.e., Lifshitz and V.V. Slyozov (Ref. 36), and Wagner (Ref.37), commonly known as LSW kinet-ics), so that

(3)where r0 is the mean initial particle ra-dius and rt is the particle radius attime t. Through direct measurementsof carbide size during isothermal heattreatment, Yoo et. al. (Ref. 38) and Leeet. al. (Ref. 39) have shown that thecarbide coarsening kinetics in AerMet®100 Alloy are well approximated by thecubic dependence of Equation 3. Thecoefficient K in Equation 3 is generallygiven by an equation of the form

(4)where D is the diffusivity, is the in-terfacial energy, Vm is the molar vol-ume of precipitate, C() is the solu-bility of the solute, R is the ideal gasconstant, T is the temperature, andf() is a function that depends on theparticular coarsening theory (f() = 1for the LSW theory). If it is assumed

r t3 = r 0

3 + Kt

H � 1r�

H �� = �μb�

K = 89D�VmC� �( )

RTf �( ),

WELDING RESEARCH


Fig. 21 — A — Plot of hardness vs. optimized K2 for isothermally aged (Ref. 34) AerMet®100 alloy. Dashed lines are 90% prediction limits; B — plot of ultimate tensile strength vs.optimized K2 for isothermally aged (Ref. 34) AerMet® 100 Alloy. Dashed lines are 90% prediction limits.

Fig. 23 — A — Typical dilatation curve for solutiontreated AerMet® 100 alloy in the onheating austenite transformation temperature range. Inset shows entire heating andcooling curve; B — apparent austenite fraction as determined by lever rule conversion ofdilatation data for several heating rates.

Fig. 22 — Comparison of model predictionsand measured hardness for HAZ simulations in aged base plate. Dashed lines are90% prediction limits.

A B

A B

--


that all factors other than the diffusiv-ity are not functions of temperatureand the temperature dependence of Dcan be represented by

(5)then Equation 4 can be written as

(6)where K1 is a constant. Combinationof Equations 3 and 6 yields an expres-sion for the coarsening rate as a func-tion of time and temperature:

(7)Substitution of Equation 7 into 2(with rt = r) and rearranging leads tothe result

(8)where K2 has the form

(9)and a plot of H vs. K2 should be linear.The most direct means to apply thismethodology to isothermal aging datais to search for values of r0, K1, and Q,which maximize the linearity of such aplot. This searching can easily be ac-complished in a spreadsheet applica-tion. Alternatively, if values for any ofthe three parameters are known, suchas an initial precipitate size or the acti-vation energy for the diffusion of a

known precipitating species, these canbe used to reduce the number ofsearch parameters. The procedure described above wasused to fit the isothermal aging datafor AerMet® 100 given by Novotny(Ref. 34), and the results are shownin Fig. 21A. The optimized fit param-eters for this data set are r0 = 2.47 ¥10–8 m, K1 = 0.02718 m3 K/s, andQ/R = 38990, and the hardness canbe represented by a line of the form.

HRC =38.18 + 4.690 ¥ 10-7 (K2) R2 = 0.9559 (10)

These parameters linearize thedata over a wide range of aging condi-tions, including those conditions nearpeak hardening and overaged. The ap-parent activation energy for the soft-ening, 324,130 J/mole (77,470cal/mole), is higher than that whichmight be expected for coarsening ofalloy carbides in AerMet® 100. For ex-ample, the activation energy for thediffusion of Mo in ferrite is given(Ref. 40) as 241,420- 251, J/mole(57,700–60,000 cal/mole). However,given other assumptions inherent inthe model (Ref. 30), such as sphericalprecipitates, invariant carbide compo-sition, temperature independence ofinterfacial energies, etc., this discrep-ancy is not thought to be a majordrawback with respect to applicationof the model. Moreover, the fitting isnot exceptionally sensitive to the ac-tivation energy within a specificrange, and additional tests of themodel are described in Ref. 30. Asshown in Fig. 21B, aging data for

strength (Ref. 34) can be treated in asimilar way.

Application to Thermal Cycles Application of the overaging modelto weld HAZs requires a means to esti-mate the cumulative effect of the ther-mal cycle on the kinetics. A commonlyused approach for estimating this ef-fect is the additivity principle (Refs.41, 42). To apply the additivity princi-ple, a thermal cycle is modeled as a se-ries of small isothermal steps. At eachstep, the time elapsed is a fraction ofthe time required, at that temperature,to achieve a given amount of transfor-mation or in this case, hardness. Whenthese fractions sum to unity, the givenhardness has been achieved. Formally,this can be written as

(11)where t is the time and ta(T) is thetime to reach the given hardnessisothermally. For discrete time steps,Equation 11 can be written in thesummation form, or

(12)From Equation 10, H = H0 + mK2,where H0 and m are the intercept andslope of the fit to the isothermal agingdata, respectively, it is apparent that

(13)

dtta T( )

0

t

� = 1 ,

r t3 = r 0

3 + K1

exp�QRT

��

��

Tt,

H �K2

K 2 = r03 +

K1t exp�QRT

��

��

T

�

�

��

�

�

��

�1/3

D = D0 exp�QRT

��

�� ,

K = K1

exp�QRT

��

��

T,

�tta T( )0

t

� = 1

H=H0 + m r03 +

K1 texp�QRT

��

��

T

�

�

��

�

�

��

�1/3

WELDING RESEARCH


Fig. 24 — Continuous heating transformation diagram for solutiontreated AerMet® 100 for heating rates from 50 to2500°C/s. Error bars for 100°C/s are ± 2 standard deviations.

Fig. 25 — Combined plot of hardness, overaging model predictions, and austenite formation data for HAZ simulations in AerMet® 100 Alloy plate.

-

-


or, upon rearranging

(14)For an isothermal hold, Equation 14represents the time required to reach agiven hardness, H, at a given tempera-ture, T. Using a series of small isother-mal steps to represent a thermal cycle,the summation of Equation 12 can besolved by using a goal-seeking routineto find the hardness that satisfies thesummation for that thermal cycle. Al-ternatively, the summation can besolved sequentially by calculating thesoftening during a given time step, ad-justing the temperature to the temper-ature associated with the next timestep and adjusting the start time tothat which it would have been had thetemperature always been at the newtemperature, and iterating this proce-dure over the entire thermal cycle. Using Equations 12 and 14, togeth-er with the coefficients derived in Fig.21A and the actual thermal cycle fromthe Gleeble HAZ simulations, thehardness for the HAZ simulations canbe estimated. The results of these esti-mates are shown in Fig. 22 and theagreement between predicted andmeasured hardness is quite good. Thus, the overaging model, devel-oped from isothermal aging data andapplied to weld thermal cycles throughthe use of the additivity principle, ap-pears to provide an appropriate meansfor estimating the HAZ softening inAerMet® 100 Alloy. However, it shouldalso be noted that the accuracy of pre-dictions based on this model is de-pendent on the accuracy to which thethermal cycle at any HAZ location isknown. For the Gleeble simulations inFig. 22, the thermal cycle is directlymeasured and therefore accuratelyknown. For general application towelds, the thermal cycle at a givenHAZ location must be estimated fromthermal models of the weld processand parameters, and in these cases theaccuracy is therefore partially depend-ent on the accuracy of the thermalmodel. In addition, real welds, and inparticular multipass welds, can havemultiple thermal cycles and complexresidual stress distribution within theHAZ. Although the model should be

capable of treating the multiple ther-mal cycles, the potential effect ofresidual stresses on the softening be-havior is not incorporated here. As discussed above, the high-temperature edge of the HAZ softenedregion is bounded by the formation ofnew, transformable austenite. For thisreason, it is important to develop a de-scription of the austenite formationkinetics at rapid heating rates. In thisportion of the work, the austenite for-mation kinetics were empirically ex-amined by Gleeble dilatometry atheating rates in the range of 0.1 to2500°C/s (0.18 to 4500°F/s). Figure23A shows the typical dilatation re-sponse of solution-treated AerMet®100 Alloy for a heating rate of 100°C/s(180°F/s). In principle, the lower andupper critical temperatures can be es-timated from these curves by deter-mining the initial departure from, andfinal approach to, the linear portionsof the curve associated with the low-and high-temperature constituents,respectively. In practice, these temper-atures were determined as the temper-atures at which the difference in di-latation between the curve and the ex-trapolated linear fit of the curve pre-ceding the initial contraction was ei-ther 2 or 98% of the dilatation differ-ence between the low- and high-tem-perature linear extrapolations (i.e,. alever rule approach). A similar approach can be used toestimate the apparent fraction trans-formed over the entire transformationrange. However, for these determina-tions, it should be noted that the con-version of dilatation data to fractiontransformed is very approximate sincethe austenite that forms is likely tohave a composition that depends ontemperature (as does the decomposingmartensite/ferrite), and therefore alever rule estimation of the fractiontransformed is not strictly correct. Inaddition, heating rates of 200°C/s(360°F/s) and higher were found to ex-hibit unusual features, which furthercomplicate interpretation of the di-latation data (Ref. 30). Figure 23B shows the apparentaustenite fraction (determined bylever rule conversion of the dilatationdata) for several representative heat-ing rates. From these curves, severaltrends are apparent. First, the lowercritical temperature initially increases

with heating rate, and then becomesessentially constant at the higherheating rates. The behavior of the up-per critical temperature with heatingrate is not, however, as clearly defined.Finally, a relatively sharp and repro-ducible break occurs in the curve for300°C/s (550 °F/s) near a fractiontransformed of 0.8 and was observedfor all tests with heating rates of200°C/s (360°F/s) and above (Ref. 30).Note that at temperatures above thebreak in the 300°C/s curve shown, thecurve becomes extremely jagged. How-ever, this is not thought to be real, butrather appears to be an artifact of thedata collection equipment. As is discussed in more detail inRef. 30, it is believed that the breakthat occurs for heating rates of200°C/s and above is the terminationof the formation of austenite, and thatthe approach to the final expansionline is homogenization of the austen-ite by diffusional adjustments. For thisreason, in the continuous heatingtransformation (CHT) diagram pre-sented below, the upper critical tem-perature for heating rates above200°C/s is depicted as the tempera-ture at which the break in the curveappears. The temperature at which thedilatation reaches the high-tempera-ture expansion line is depicted as aseparate point on the diagram. Figure 24 shows the CHT diagramfor solution-treated AerMet® 100 Al-loy for heating rates in the range of 0.1to 2500°C/s. The diagram for this alloyis extremely complex, and appears toconsist of two distinct heating rate re-gions. The first of these is the lowerheating rate range from 0.1 to 25°C/s(0.18 to 45°F/s), and the other is therange including 50°C/s (90°F/s) andabove. These regions are believed toconstitute different mechanisms ofaustenite formation, and are discussedin detail in Ref. 30. For the purposesof the present article, the CHT dia-gram provides a means for estimatingthe temperature (location) of the hightemperature extreme of the softenedregion of welds’ HAZs. This estimationcan be accomplished simply by super-imposing the dilatation curve or criti-cal temperatures from the CHT dia-gram onto the peak temperature vs.position curve for a weld HAZ. A plotof this type for the HAZ simulationsdiscussed above (which used a heating

t=ta T( ) =T

mH-Ho

��

��

3

� r 03

�

��

�

��

K1exp�QRT

��

��

WELDING RESEARCH



rate of approximately 100°C/s ) isshown in Fig. 25. As shown, the data from the CHTdiagram provides a reasonable esti-mate of the high-temperature limit ofthe softened region. The green frac-tion austenite curve shown in Fig. 25is not intended to imply an estimationof hardness due to the formation ofthe austenite, but rather that the soft-ening due to overaging is supersededby the formation of austenite. As withthe model for overaging, the accuracyof estimates for austenite formationbased on the CHT diagram is depend-ent to some extent on the accuracy towhich the thermal cycle is known. Inthis case, however, the relative insen-sitivity of the critical temperatures atheating rates associated with weldingimplies that this should not be a majorlimitation for estimates of weldmentbehavior. For those cases where an ex-perimental CHT diagram is not avail-able, computational databases are be-coming increasingly available and ca-pable of predicting steel phase trans-formation temperatures and kinetics.In terms of engineering approxima-tions, the methods and analyses em-ployed in the construction of Fig. 25provide an engineering basis that canbe used as a reasonably quantitativeguide for estimating properties ofwelds in similar Fe-Ni-Co or other precipitation-hardening alloys.

Summary and Conclusions This article has described a series ofevaluations aimed at developing engi-neering approaches to common weld-ing process and welding metallurgyquestions. The examples were selectedto illustrate a range of welding topicsfrom process physics, to materials/process interactions, and finally toweld properties development. The ex-amples included time-resolved meas-urement of laser energy absorption,assessment of the dynamics of weldhot cracking in nickel-based alloys,and estimation of the heat-affectedzone softening in a modern ultrahigh-strength steel alloy. The measurements of energy ab-sorption in laser spot welding providequalitative and quantitative insightinto spot weld keyhole phenomenaand indicate that keyhole-mode welds

separate into three regions of energytransfer: <50% during initial melting,50–70% during keyhole formation,and >75% for a mature keyhole. Forlow-power (conduction mode) welds,transfer efficiency is low, <50%, andremains low throughout the weldingpulse. The balance of transfer andmelting efficiencies can be manipulat-ed with pulse shape, thereby providinga basis for optimization of penetra-tion, defect mitigation, and control ofweld thermal effects. High-speed video records of Vare-straint tests, coupled with thermal,strain and solidification models, pro-vide interesting insight into weldcracking phenomenology. Crack initia-tion occurs at a fraction liquid of about0.10 and local strains on the order of1%, and these values provide a reason-able solidification crack initiation cri-teria for nickel alloys similar to Alloy718. The advancing crack tip growssporadically but remains an approxi-mately constant distance behind theweld pool, and thus the crack propa-gates at constant temperature andconstant local strain conditions. Forconditions where the formation of eu-tectic liquid precedes the above strainand fraction liquid conditions, the ad-vancing crack appears to infill with eu-tectic liquid as it opens. The softened region in AerMet®100 alloy heat–affected zones is con-trolled by precipitate overaging andaustenite formation, and the overag-ing process can be reasonably de-scribed by a simple model based onparticle strengthening and coarsening.Weld HAZ softening can be estimatedby combination of the overaging mod-el and the additivity rule. In turn,when this estimation is combined withempirical (or numerical) determina-tions of the on-heating transforma-tion behavior, a reasonably quantita-tive estimation of the depth and ex-tent of the softened region in the HAZof this and similar Fe-Ni-Co steels canbe made. It is recognized that the examplesprovided here only scratch the surfaceof the essentially infinite variety ofphenomena, questions, and challengesthat underlie the fields of welding sci-ence and engineering, but it is hopedthat within these examples the readerfound some specific areas of interest.

The author gratefully and sincerelyacknowledges the many people whohave contributed, throughout his ca-reer, to his continuing education inthe field of welding. Professional inter-actions are of course key elements ofany research endeavor, but far moreimportant are the personal interac-tions and learning that accompany ashared interest and goals. At the riskof inadvertently neglecting someoneand in no particular order, the authorexpress his gratitude for the friend-ship and support provided by JohnDuPont, Phil Fuerschbach, Mike Cies-lak, Mike Maguire, Joe Puskar, JeromeNorris, Don Susan, Mark Reece, DanMacCallum, Jeff Rodelas, Matt Perri-cone, Brian Damkroger, Stan Pierce,Paul Moniz, Greg Shelmidine, and Jer-ry Knorovsky. The encouragement andthoughtful reviews of this manuscriptprovided by Mike Maguire, Don Susan, and Jeff Rodelas is greatly appreciated. Sandia National Laboratories is amultiprogram laboratory managedand operated by Sandia Corp., a whollyowned subsidiary of Lockheed MartinCorporation, for the U.S. Departmentof Energy’s National Nuclear SecurityAdministration under Contract DE-AC04-94AL85000.

1. Norris, J. T., Robino, C. V., Perricone,M. J., and Hirschfeld, D. A. 2010. Develop-ment of a time-resolved energy absorptionmeasurement technique for laser beamspot welds. Welding Journal 89(4): 75-s to81-s. 2. Fuerschbach, P. W., and Eisler, G. R.2002. Effect of laser spot weld energy andduration on melting absorption. Scienceand Technology of Welding and Joining 7(4):241–246. 3. Perret, O., Naudy, P., and Bizouard,M. 1999. Keyhole formation study inpulsed Nd:YAG laser welding. ICALEO Pro-ceedings, Vol. 87, Sec D: 177–186. 4. Jouvard, J. M., Girard, K., and Perret,O. 2001. Keyhole formation and powerdeposition in ND:YAG laser spot welding.J. Phys D: Appl. Phys. 34: 2894–2901. 5. Cremers, D. A., Lewis, G. K., and Ko-rzekwa, D. R. 1991. Measurement of ener-gy deposition during pulsed laser welding.

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