Monte Carlo Simulation of Heat-Affected Zone Microstructure in Laser-Beam-Welded Nickel Sheet

Transcription

1 WELDING RESERCH SUPPLEMENT TO THE WELDING JOURNL, MRCH 2002 Sponored by the merican Welding Society and the Welding Reearch Council Monte Carlo Simulation of Heat-ffected Zone Microtructure in Laer-Beam-Welded Nickel Sheet Reaonable agreement wa obtained between experimental reult and imulated grain growth in the heat-affected zone BY M.-Y. LI ND E. KNNTEY-SIBU, JR. B S T RC T. The heat-affected zone grain tructure that evolve during welding of a nickel 270 heet wa imulated uing Monte Carlo technique. matrix coniting of 200 x 200 ite with 100 poible grain orientation wa ued for the imulation, and the temperature hitorie meaured during welding were ued a input to perform the imulation. The unit length of each ite i 10 µm, with the overall imulation region being 2 x 2 mm. The imulation pertained to microtructure in the vertical plane where the temperature were meaured, i.e., along the welding direction. The grain ize throughout the heataffected zone, a obtained by imulation, howed reaonable agreement with the experimental reult obtained from metallographic examination. The difference in average grain ize meaurement obtained experimentally and by imulation were 12.9% and 5.8% at location 1.26 mm and 1.70 mm below the weld centerline, repectively. The advantage of uing thi imulation method are to predict grain ize ditribution in the HZ. The reult could ubequently be ued for predicting other mechanical propertie of a weldment. Introduction In their claic work, Burke and Tu r n- bull propoed a parabolic grain growth M. -Y. LI, Ph.D., i with TWB Co., Monroe, Mich. E. KNNTEY-SIBU, JR., i a Profe o r, Department of Mechanical Engineering, The Univerity of Michigan, nn rbor, Mich. relationhip, hypotheizing that grain growth i the reult of grain boundary migration (Ref. 1), and auming urface tenion of the boundarie i the driving force for grain growth after recrytallization. imilar relationhip wa ubequently developed by Feltham (Ref. 2), Hillert (Ref. 3), and Saetre, et al. ( Ref. 4). Thi parabolic relationhip ha been verified experimentally in nickel (Ref. 5), copper (Ref. 6), and alpha brae ( Ref. 7). The propertie of a material are not only affected by the ize of it grain but alo by the geometry (hape and orientation) of the grain (Ref. 8). To predict grain geometry and grain ize, ue of topological imulation method i neceary. Monte Carlo-baed grain growth imulation technique wa developed by Srolovitz, nderon, and their coworker (Ref. 9, 10). Their algorithm provide a nondimenional imulation applicable only to iothermal grain growth. Gao and Thompon developed a real-time, KEY WORDS HZ Heat-ffected Zone Monte Carlo Grain Growth Nickel Sheet Ni 270 Temperature Hitory Simulation temperature-dependent technique uing iothermal matrice to predict grain ize at different temperature (Ref. 11). Defining a probability of MCS(x)/ M C S m a x for grain growth imulation and uing the Roenthal equation for calculating temperature cycle, Radhakrihnan and Zacharia predicted the grain growth of the HZ of Cr-Mo-V teel (Ref. 12). In thi reearch, a matrix containing ite with a ditributed temperature i conidered neceary for predicting the HZ microtructure. Toward thi end, a dimenionalized imulation method ha recently been developed (Ref. 13) to imulate grain growth in the heat-affected zone. Thi imulation require temperature hitorie at variou location of the heat-affected zone a input. The unit length of the imulation matrix i determined by the region of interet, being 10 µm for a 2 x 2 mm region. Meaurement of temperature hitorie during laer beam welding i a difficult proce. Moon and Metzbower imbedded thermocouple in a laerbeam-welded teel plate and meaured the peak temperature in the molten metal (Ref. 14 and 15). In thi reearch, temperature hitorie at different ditance from the root of a weld centerline were meaured by imbedding thermocouple into the pecimen to different depth from the root ide. Background Theory Grain growth i the proce by which WELDING JOURNL 37-S

2 WELDING RESERCH B Fig. 1 triangular lattice; B an element at location (i,j) with ix nearet neighbor, where S ij i the orientation of ite (i,j) and S n ij i the orientation of it n-th neighbor. the average ize of crytal in a ytem increae. The driving force for grain growth i the decreae of free energy in the ytem and i aociated with reorientation of the atom. Therefore, the average grain ize of a microtructure increae by ome of the grain conuming other grain, thereby reducing the number of grain in a pecific aggregate. Tw o grain-growth mechanim have been widely tudied: normal and abnormal grain growth. Normal grain growth ha a relatively narrow range of grain ize and hape. However, unlike normal grain growth, abnormal grain growth uually ha a wide range of grain ize and hape. bnormal grain growth, ometime called econdary recrytallization, i uually caued by heterogeneou ytem energy ditribution or the exitence of impuritie. Mot normal grain growth theorie aume negligible heat tranfer, o the proce may be conidered to be iothermal. uming olid-tate tranformation in a pure ubtance tart from a table pherical nucleu in which grain boundary energy i iotropic, and neglecting urface energy or capillary effect, and finally, auming that growth occur continuouly on the grain boundary where the atom can uccefully attach themelve, the expreion for normal grain growth can be written a (Ref. 1) G = exp E E 1 exp RT RT (1) where G i the growth rate, λ i the atomic pacing, ν i the jump frequency of the ytem, E i the energy barrier for grain growth per mole atom, Ε i the average free energy change per mole atom during grain growth, T i the abolute temperature, and R i the univeral ga contant. uming the energy change Ε << RT during iothermal grain growth at high enough temperature, the lat term of Equation 1, may be approximated a uing exponential erie and neglecting higher order term. Equation 1 then reduce to the form E = C 0 V RT (2) Now and where C 0 i a contant, γ i the grain boundary interfacial energy, V i the volume per mole atom, and r i the grain boundary radiu (Ref. 1). Equation 2 then become dr dt = C 0 RT Equation 3 can be rewritten a dr G = 1 exp E RT, E RT exp E RT V r exp E RT (3) dt = M r (4) where M i defined a the atomic mobility and i contant for an iothermal ytem. M = C 0 V RT exp E RT (5) For iothermal grain growth, Equation 4 can be integrated to give r 2 r 0 2 = 2M t E RT, G = dr dt (6) where r 0 i the initial average grain radiu. Grain Growth Simulation Dimenionle Simulation The dimenionle Monte Carlo grain growth imulation employ a twodimenional triangular lattice in which each ite ha ix nearet neighbor at identical ditance. Each ite i initially aigned a random orientation S ij. grain i defined by a group of contiguou ite with the ame grain orientation S ij. Grain boundarie are aumed to exit between grain with different orientation. The imulation tart by electing a random orientation S ij, from 1 to Q, where Q i the number of poible orientation for a randomly elected ite (i, j). In their reearch, nderon, et al. (Ref. 10), found that for Q 30, the grain ize ditribution from Monte Carlo imulation approache a limit form. Therefore, Q = 100 i ued in thi reearch. N reorientation trial are referred to a a Monte Carlo tep (MCS), where N i the number of ite in the matrix. in the cae of Srolovitz, et al. (Ref. 9), the grain boundary energy E i j i the driving force for the motion of a grain boundary and i defined a m n =1( ) E ij = J ij ij n 1 (7) n where ij ij i the Kronecker delta and m i the number of nearet neighbor n ite, ij. m = 6 for a triangular lattice Fig. 1. J i the ytem energy contribution from two nearet neighbor ite with different orientation, and it i a poitive contant. The value of J i not neceary for the dimenionalized imulation ince the probability P 2 (to be defined later) 38-S MRCH 2002

3 only conider it ene. E i j i poitive when the two nearet neighbor ite are of unlike orientation and zero otherwie. The um i taken over all nearet neighbor ite. The energy change aociated with a reorientation i calculated a WELDING RESERCH E ij = E ij,new E ij, old (8) where E ij,new i the energy of ite (i,j) after reorientation and E ij, old i the energy of ite (i,j) before reorientation. probability P wa introduced by nderon, et al. (Ref. 10), and defined a P = 1 if E ij 0 exp E ij if E RT ij >0 (9) poitive E ij indicate the ytem energy change increae after reorientation. On the other hand, a negative E ij indicate a decreae of ytem energy after reorientation. Thu, thi probability can be modified and defined a probability P 2 P 2 = 0 if Eij > 0 {1 if E ij 0 (10) Fig. 2 Procedure of dimenionle Monte Carlo normal grain growth imulation. The probability P 2 force the imulation to accept only thoe reorientation trial aociated with decreaing total ytem energy. reorientation trial i accepted if thi probability criterion i atified. flow chart of the imulation procedure i hown in Fig. 2. Dimenionalized Simulation Simulation lgorithm The iothermal imulation algorithm developed by nderon and coworker ( Ref. 10) wa modified to incorporate temperature variation by uing the original Burke and Turnbull grain growth theory. Figure 3 how the modified procedure. Unlike the dimenionle imulation, a new probability term P 1 wa introduced to incorporate abolute temperature into the new imulation. Conidering Equation 2, P 1 i determined by P 1 = exp E RT (11) Fig. 3 Procedure of dimenionalized Monte Carlo normal grain growth imulation. where E i the activation energy for grain growth. P 1 repreent the probability that an atom will overcome the energy barrier of grain growth E. imulation trial atifying the P 1 criterion implie that the atom overcome the energy barrier and ha a potential to change it orientation. mentioned in the preceding ection, another probability term P 2 i conidered when an atom attempt to change it location relative to it neighboring atom, by which the grain orientation i changed, after atifying the P 1 criterion. The new orientation i accepted when P 2 i alo atified, i.e., the ytem total energy i lowered. Therefore, a reorientation trial i ucceful when both criteria P 1 and P 2 are atified. Grain Growth Exponent n and Coefficient K for Simulation In addition to temperature, two other parameter are required for dimenionalization, viz. temporal and patial parameter. Iothermal imulation at variou WELDING JOURNL 39-S

4 WELDING RESERCH Table 1 Parameter Ued in the Simulation Symbol Unit Value Decription δ µm 10 Unit length of the imulation matrix K 0 m 2 / (Ref. 16) 1.36 x 10 3 Grain growth coefficient of nickel E kcal/(mol 0 K) 27.5 Normal grain growth activation energy of nickel (Ref. 16) K δ 2 /MCS Grain growth coefficient for imulation t 1.11 x 10 9 The time each MCS repreent. Q N 100 Number of poible orientation temperature were therefore undertaken to determine the grain growth parameter of the following equation: D n D n 0 = K P 1 t (12) where D and D 0 are the final and initial average grain ize of the imulation, repectively, n i the grain growth exponent [n = 2 for nickel (Ref. 16)], K i the grain growth coefficient of the Monte Carlo imulation with unit δ 2 /MCS, δ i the unit length of the imulation matrix, t i the number of imulation tep, and P 1 i the probability term introduced in Equation 11. Figure 4 how the reult of iothermal imulation with P 1 equal to 1.0 and 0.1. The matrix i a triangular lattice with 200 x 200 element and 100 poible orientation randomly ditributed at the beginning of the imulation. From thee imulation, the grain growth exponent for imulation wa determined a dicued in the following paragraph. From Equation 6 and 12, the mobility M can be aumed to be given by M = K P 1 (13) M i then given by the lope of the plot of D n n D 0 againt t. Taking the natural logarithm on both ide of Equation 13 give 1n( M ) = 1n( K ) + 1n( P 1 ) (14) Thu, the lope of a 1n(M ) v. 1n(P 1 ) plot hould be unity, and the intercept on the 1n(M ) axi, 1n(K ). The lope of the line that bet fit the data point in Fig. 4 and B are 1.58 x 10 2 and 1.57 x 10 3, repectively. dditional reult were obtained for imulation with probabilitie from 10 2 to Figure 5 how the bet-fit line for a plot of M v. P 1 on a natural log-log graph for n = 2.0. The growth coefficient K i determined by Equation 14, i.e., the intercept of the traight line and the 1n(M ) axi in Fig. 5. The equation of the line i given a 1n( M ) = n ( P 1 ) (15) Therefore, 1n(K ) = and the value of K i (unit: δ 2 /MCS) for imulation with 100 poible orientation, where δ i the unit length of the imulation matrix. Table 2 ctivation Energie for the Grain Boundary Self-Diffuion of Nickel Mifit ngle Energy (degree) Temporal and Spatial Parameter Experimental reult have hown the grain growth exponent n for nickel i 2 (Ref. 16). To incorporate the experimental data into the imulation, the grain growth exponent n = 2 wa employed. That give the unit of the experimental grain growth coefficient, K 0, a m 2 / and thoe of the imulation a δ 2 / M C S, where δ i the unit length of the matrix and MCS i the Monte Carlo Step or the imulation tep. δ i determined by the region of interet and the ize of the matrix. Since K and K 0 are equivalent, we have or MCS K m 2 o 2 K MCS K 2 m K 0 ctivation (kcal/g mole) (16a) (16b) Equation 16b determine the amount of time that an MCS repreent when the length of δ i et. For example, for a 2 x B Fig. 4 Reult of iothermal imulation baed on parabolic growth, n = 2, with different P 1 value. P 1 =1.0; B P 1 = S MRCH 2002

5 WELDING RESERCH Fig. 5 Reult of iothermal imulation with variou n value. Fig. 6 laer welding pecimen with ten hole drilled for mounting thermocouple. 2-mm region, a δ of 10 µm i elected to give a 200 x 200 matrix. Inerting δ i n t o Equation 16b give MCS K m ec 1 m K 0 (17) The grain growth coefficient K 0 of nickel i 1.36 x 10-3 m 2 / (Ref. 16). Subtituting the value of K 0 and K into Equation 17 give the equivalent time for an MCS a 1.11 x Heat-ffected Zone Microtructure Simulation The material elected for the imulation wa commercially pure nickel, Ni 270. The unit length ued in the imulation wa 10 µm, which implie a 2 x 2-mm parallelogram (200 x 200 element) with a height of mm a the imulation matrix. Temperature hitorie meaured during welding were applied to the imulation for each MCS. The location of the econd thermocouple (Fig. 6) correpond to the top of the imulation matrix. Thu, the matrix contain thermocouple 2, 3, 4, 5, and 6. The correponding temperature hitorie ued in the imulation are hown in Fig. 7. Figure 7B how the temperature hitorie uperimpoed on each other. uming quaiteady-tate welding condition, the curve in Fig. 7B correpond to the temperature hitorie at depth of 1.26, 1.70, 2.06, 2.52, 2.90, and 3.32 mm. The activation energy of grain growth E ued in the imulation wa 27.5 kcal/(mol K) and the grain growth coefficient K o wa 1.36 x 10-3 m 2 / (Ref. 16). The activation energy wa elected to be the average of activation energie with grain orientation mifit angle from 20 to 80 deg, hown in Table 2. The computation time required for a 200 x 200 matrix can be overwhelming. Thi i epecially true with the normally low probability value obtained from Equation 11. To ave computation time, a probability factor, P f a c t o r, i introduced for the imulation. The baic aumption i that the growth behavior for imulation at low probabilitie i imilar to that at high probabilitie. From Equation 12, it i evident the growth behavior i governed by the K P 1 t term. higher probability eentially reduce the time required to reach a particular grain ize. The probability factor, P factor, i then defined a (18) where P 1,new i the new probability, uually equal to 1, and P 1,old i the original probability given by Equation 11. The probability factor for welding imulation i determined by etting the new probability for the point that experienced the highet temperature to 1. The peak temperature of the firt curve in Fig. 7B i C ( K). Therefore, the maximum probability for thi imulation, P 1, m a x, i 3.74 x 10 5 and the P f a c t o r for thi imulation i the invere of P 1, m a x, , and thu reduce the imulation tep from 4.80 x 10 9 to 1.80 x Table 1 how the parameter ued in the i m u l a t i o n. Experiment P factor = P 1,new P 1, old Specimen Preparation The material ued in the experiment wa originally hot-rolled (in the areceived condition) nickel 270 (Ni 270), with purity 99.9% or greater, and wa tempered in the laboratory at 600 C for 30 min to relieve any reidual tree that might have been produced during manufacturing. The tempered Ni 270 wa then cold rolled from to 6.86 mm with a 50% thickne reduction and wa ubequently machined to 6.35-mm thickne, mm width, and mm length for laer beam welding. The pecimen wa firt cut to approximate dimenion on a band aw and then milled to the final dimenion. Cutting fluid, water, and cutting oil for the band aw and mill, repectively, were ued to minimize the impact of heat from material removal and to enhance the urface finih. Specimen for the normal grain growth invetigation were then ubjected to a recrytallization treatment, heated at 700 C for 30 min, to produce homogeneou grain ize ditribution in the material before laer beam welding. Specimen urface condition are important in laer beam welding. The pecimen were, therefore, dry anded uing 400-grit ilicon carbide paper to remove oxide and produce uniform cratche in the welding direction for a conitent urface condition. Ten blind hole were then drilled to different depth at different location on the back of the pecimen Fig. 6. Each hole wa initially drilled uing a regular drill bit. The root of each hole wa then flattened uing a flat-headed drill bit. The actual depth were meaured uing a microcope after welding. Laer Beam Welding utogeneou welding wa done uing a CO 2 laer at 1000-W power focued by a 125-mm (5-in.) focal length len. The out- WELDING JOURNL 41-S

6 WELDING RESERCH B C Fig. 7 Temperature hitorie meaured during laer welding; B time-hifted temperature hitorie for grain growth imulation; C cooling rate calculated from B. put beam i D-mode [combined TEM 0 0 (60%) and TEM 0 1 * (40%) mode], with a correponding beam quality M 2 of about 2.0 (Ref. 17). The focal point wa located on the pecimen top urface with a diameter of about 250 µm and an incident angle of 3 deg. The welding peed wa 5 mm/. rgon wa ued a hielding ga at a flow rate of 21 L/min. To minimize heat conduction to the ambient, the pecimen wa upported by two ceramic tube, each of mm diameter. Temperature Meaurement Temperature hitorie at variou location are neceary for dimenional grain growth imulation. K-type thermocouple (chromel-alumel) of in diameter were ued in the experiment. Thee were mounted in the plane along the welding direction, to meaure temperature vertically below the centerline of the weld Fig. 6. Bare thermocouple wire were protected by two-hole ceramic tube, mm outer diameter and mm inner diameter, mounted into the predrilled hole on the back of the pecimen. The thermocouple were welded to the flattened bottom of the blind hole by capacitive dicharge welding to firmly attach them to the pecimen. Due to the guiding two-hole ceramic tube, each thermocouple tip wa centered very well, a oberved after laer beam welding, microcopically. Each contact wa carefully examined by meauring the electric reitance between the thermocouple and the pecimen. Fig. 8 Microtructure of laer-beam-welded nickel in the plane under the weld and parallel to the welding direction. 486 PC with a 10-channel, 12-bit data acquiition ytem wa ued to record the temperature variation during welding. The channel were connected to the thermocouple at a elected ampling rate of Hz per channel. high ampling rate allowed more temperature data to be recorded during welding, en- 42-S MRCH 2002

7 WELDING RESERCH B Fig. 9 Monte Carlo imulation reult of the heat-affected zone microtructure. Before welding; B after welding. abling moother temperature hitorie. The temperature hitorie were then applied to the ubequent HZ microtructure imulation. Reult and Dicuion Due to the low heat input rate (1000 W), only conduction mode of fuion wa oberved in the weld. That i, no keyhole formation wa obtained. Figure 7 how the temperature hitorie at eight location, channel one through eight. The dicontinuity oberved in the firt channel wa due to the fact the thermocouple mounted in that hole melted during welding. Subequent cro-ectional examination howed the actual depth of that thermocouple wa 1.08 mm, and that wa very cloe to the fuion zone, 0.98 mm deep. Figure 7B how the modified temperature hitorie obtained by hifting each temperature hitory toward the econd channel by an amount of time equal to it ditance to the econd channel divided by the welding peed. For example, channel 3 wa hifted 1 econd while channel 4 wa hifted 2 econd to the left. Under quai-equilibrium welding condition, it i aumed each point of the ame depth, except thoe point near the end of the pecimen, experienced the ame temperature hitory following a certain amount of time delay. Therefore, the curve in Fig. 7B relate to temperature hitorie at the location of depth equal to 1.26, 1.70, 2.06, 2.52, 2.90, and 3.32 mm. Thee depth were determined after welding uing a microcope at 100X magnification, to meaure the cro-ection of the ample along the center of the weld line. Temperature at ite located between two thermocouple were approximated by linear interpolation for the Monte Carlo imulation. Cooling rate for the temperature hitorie in Fig. 7B were calculated and are hown in Fig. 7C. Each data point in the cooling rate chart (Fig. 7C) wa calculated by taking the average of 11 conecutive cooling rate data point, 5 before and 5 after the point of interet. From the cooling rate profile, it wa found channel 3 and 4 reached their peak temperature at about the ame time. Thi might have reulted from a mall contact area between the joint nugget of the third thermocouple (channel 3) and the pecimen. The actual contact area could not be meaured. Figure 8 how an optical micrograph of the microtructure of the vertical croection located under the weld and parallel to the welding direction. The pecimen wa etched uing an etchant containing 50% nitric acid and 50% glacial acetic acid. Location 1, 2, 3, and, 4 correpond to the location of thermocouple 1, 2, 3, and 4, repectively. verage grain ize at each location wa meaured by the Heyn lineal intercept method (Ref. 18) with at leat 50 interception on an intercept line, uing an optical microcope at a magnification of 100. Each grain ize value of the imulation reult wa taken a an average of five meaurement around the location of interet. Figure 9, imulated with a homogeneou temperature ditribution Fig. 10 Grain ize ditribution from experiment and imulation. tarting with a randomly oriented matrix, illutrate a typical initial grain tructure before welding, and Fig. 9B how the heat-affected zone grain tructure obtained by Monte Carlo imulation after welding. The location of the econd thermocouple hown in Fig. 6 i the top of the imulation matrix hown in Fig. 9. Therefore, the matrix of the imulation contain thermocouple 2, 3, 4, 5, and 6. Temperature at ite located between two thermocouple were approximated by linear interpolation. The average initial grain ize of the material (obtained after the recrytallization treatment) wa µm, taken from three meaurement in the unaffected zone, while the average initial grain ize obtained for the imulated microtructure wa µm. The light difference in the two average initial grain ize i due to the fact that it wa WELDING JOURNL 43-S

8 very difficult getting the average grain ize of the imulated microtructure to a pecific value that would exactly match that of the actual material. The imulated grain ize ditribution at channel 2, 3, 4, and 5 are hown in Fig. 10. Compared to the experimental reult, the imulation error in average grain ize were 12.9%, 5.8%, 5.0%, and 9.2% at location 1.26, 1.70, 2.06, and 2.52 mm below the weld centerline, repectively. The larger error of the imulation reult at location cloe to the fuion zone boundary i due to the miing of the peak temperature at the econd channel. Thi reulted in a maller total heat input to the correponding location in the imulation. The econd reaon cauing the deviation of the imulation reult from experimental reult wa a light difference in compoition for the material ued for the experiment and the imulation. The experimental material wa a commercially pure nickel, Ni 270. However, due to the unavailability of all the data needed for thi material, the activation energy E and grain growth coefficient K value ued for the imulation were thoe of nickel bicrytal with a mall amount of aluminum inide the crytal. Depite the light difference in material propertie, the reult how reaonably good agreement on grain ize prediction, with the imulation and experimental reult following the ame trend. Concluion Normal grain growth wa aumed to be the major growth mechanim in the heat-affected zone during welding for a commercially pure annealed nickel. Compared to the experimental reult, WELDING RESERCH the imulation error in average grain ize were 12.9 and 5.8% at location 1.26 and 1.70 mm below the weld centerline, repectively. The trend of grain ize ditribution i imilar in both experimental and imulation reult. Complete development of the grain growth imulation methodology will enable it to be applied to other manufacturing procee that involve high temperature, uch a heat treatment. Thi i provided the temperature hitory i either available or predictable and the grain growth propertie (uch a activation energy and grain growth coefficient) of the material are available. Reference 1. Burke, F. E., and Turnbull, D Recrytallization and grain growth. Progre in Metal Phyic 3: Feltham, P Grain growth in metal. cta Metallurgica 5(2): Hillert, M On the theory of normal and abnormal grain growth. cta Metallurgica, 13(3): Saetre, T. O., Hunderi, O., and Ryum, N Modeling grain growth in two dimenion. cta Metallurgica 37(5): Hoffman, R. E., Piku, F. W., and Ward, R Self-diffuion in olid nickel. Tranaction IME Journal of Metal, pp Feltham, P., and Copley, G. J Grain-growth in a-brae. cta Metallurgica 6: Ghauri, I. M., Butt, M. Z., and Raza, S. M., Grain growth in copper and alphabrae. Journal of Material Science 2 5 : Srivatan, T. S Microtructure, tenile propertie and fracture behaviour of aluminium alloy Journal of Material Science 27: Srolovitz, D. J., nderon, M. P., and Sahni, P. S Computer imulation of grain growth II: Grain ize ditribution, topology, and local dynamic. cta Metallurgica 3 2 ( 5 ) : nderon, M. P., Srolovitz, D. J., Gret, G. S., and Sahni, P. S Computer imulation of grain growth I: Kinetic. cta Metallurgica 32(5) Gao, J., and Thompon, R. G Real time-temperature model for Monte Carlo imulation of normal grain growth. cta Metallurgica 44: Radhakrihnan, B., and Zacharia, T Monte Carlo imulation of grain boundary pinning in the weld heat affected zone. Metallurgical and Material Tranaction 26: Li, M. Y., and Kannatey-ibu, Jr., E Computational heat-affected zone microtructure imulation normal grain growth. Proceeding of the Laer Material Proceing Conference, ICLEO 94, 79: Metzbower, E.., and Moon, D. W Laer beam welding of STM -36 teel. Proceeding Laer in Metallurgy, 110th IME nnual Meeting, Chicago, Ill., pp Metzbower, E Laer beam welding: Thermal profile and HZ hardne. Welding Journal 69(7): 272- to Upthegrove, W. R Grain boundary and lattice elf-diffuion of nickel. Doctoral diertation, The Univerity of Michigan, pp PRC Corp., manufacturer pecification, PRC, Landing, N.J. 18. STM nnual Book of STM Standard Metal Tet Method and nalytical Procedure. STM, 3.3: S MRCH 2002