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Nucleation and growth conditions of single-crystallinity control are convincingly elaborated by multi-scale mathematical modeling of heat and mass transport to totally abate undesirable weld defects, e.g. disoriented crystal and hot cracking inside molten pool of nonequilibrium crystallization, in order to illustrate the usefulness of predictive capability through theory and experiment procedures. Crystal growth is complicated by crystallinity-dependent thermal and chemical driving forces in front of dendrite tip during viable laser surface modification of Ni-based single-crystal superalloy. These two thermal metallurgical determinants play crucial role in crack-insusceptible columnar crystal growth, which is favorably oriented throughout weld depth. There is particular challenge in complete elimination of disoriented crystal, i.e. stray grain formation, for acceptable surface quality. Conservative (001)/[100] crystalline orientation is desired to diminish Al concentration and supersaturation, and morphologically satisfy epitaxial growth kinetics to successfully lessen central cracking with satisfactory variability of laser power and welding speed. Comparatively, (001)/[110] crystalline orientation is disadvantageous to asymmetrically augment Al concentration and supersaturation and aggressively increase interface instability, microstructure heterogeneity and hot cracking vulnerability along disoriented crystal boundaries. Disoriented crystal is increasingly withstood if the Al concentration and supersaturation in front of dendrite tip are low enough and crack-unsusceptible part is relatively large enough in case of attractive (001)/[100] crystalline orientation with optimal range of heat input to ameliorate microstructure homogeneity. Crystalline orientation region varies with diverse welding configurations, and epitaxy across solid/liquid interface is also sensitive to heat input of laser processing, which necessitate high efficient welding conditions optimization. Considerable effort is made to distinguish diffusion-driven crystal growth between a series of combinations of multiple welding conditions, such as critical welding configuration and heat input. Metallographically, the morphologies of crystal growth and hot cracking are experimentally observed to consistently support kinetics calculation result and well explain correlation between solidification behavior and crystal growth.

When multicomponent molten pool nonequilibrium solidification, the interrelationship of location-dependent dendrite tip undercooling on low heat input and optimal growth crystallography is progressively discussed over planar interface morphology stability range to unidirectionally facilitate epitaxial growth by single-crystallinity control during laser repair of nickel-based superalloy to inhibit microstructure heterogeneity. Suppression of disoriented dendrite growth and crystallography orientation deviation along columnar interface is necessary for crackless repair. Axis-symmetrical (001)/[100] welding configuration kinetically reduces dendrite tip undercooling, nucleation and subsequent disoriented dendrite growth rather than unsymmetrical (001)/[110] welding configuration. When comparison between low heat input, within which laser power is limited and welding speed is rapid, and high heat input, within which laser power is considerable and welding speed is insignificant, the former attenuates dendrite tip undercooling and morphology transition between columnar and equiaxed dendrites to stabilize epitaxy and ameliorate dendrite growth with advantageous solidification conditions, especially drastic temperature gradient and small dendrite growth velocity. Axis-symmetrical growth crystallography and low heat input are favored to mitigate size of high-undercooling region, where stray grain formation are dominant, for homologous single-crystallization of epitaxial growth with satisfactory growth kinetics of dendrite tip, and are capable of elimination of undercooling-induced overgrowth for high quality weld, instead of aggressive unsymmetrical growth crystallography and high heat input. Additionally, the achievement of low heat input with axis-symmetrical welding configuration possesses stronger resistance to unstable interface morphology and solidification cracking. When comparison between growth regions of [100] and [010] crystalline orientation, where identical heat input is kept on both sides, wider dendrite tip undercooling is mainly located on the right side than left side to insidiously exacerbate crack-vulnerable dendrite growth, which is a ubiquitous phenomenon in the adverse (001)/[110] welding configuration. The effect of low heat input on dendrite tip undercooling is spontaneously smaller than growth crystallography. Hence, during nonequilibrium solidification of weld pool, the important mechanism of crystallography-induced microstructure heterogeneity obviation due to undercooling-limited epitaxial growth is consequently provided. The theoretical predictions cogently explain the experiment results in a concise way to properly illustrate microstructure degradation phenomena in the both sides of weld by reproducible calculation of mathematical modeling.

To pertinently balance growth kinetics, solidification thermodynamics and dendrite expitaxy of multicomponent nickel-based single-crystal supralloy during laser processing, effect of thermometallurgy determinant factors, including laser power, welding speed and welding configuration, on solidification behavior, such as nonequilibrium solidification temperature range, and dendrite growth, such as dendrite trunk spacing, are progressively advanced to forestall solidification cracking phenomena. Symmetric developments of dendrite trunk spacing and solidification temperature range alongside solid/liquid interface are crystallographically driven by useful (001)/[100] welding configuration to auspiciously bring about crack-insusceptible and well-oriented dendrite growth. Dissimilarly, unsymmetrical developments of dendrite trunk spacing and solidification temperature range alongside solid/liquid interface are crystallographically driven by (001)/[110] welding configuration to insidiously favor crack-unresistant and disoriented dendrite growth. Higher heat input thermodynamically and kinetically boosts wide solidification temperature range, appalling stray grain growth with excess of solute ahead of dendrite tip and large size of crack-unresistant region to thermometallurgically disintegrate epitaxial growth for untoward solidification cracking, and therefore should be strictly withstood. Although geometry of symmetrical weld pool both sides is the same in infelicitous (001)/[110] welding configuration, [100] region of dendrite growth is more liable to ruinous stray grain growth and extensive solidification temperature range than [010] region of dendrite growth to complicate dendrite growth and exacerbate weld integrity. The determinant mechanism of crystallography-aided amelioration of solidification cracking resistance as result of kinetics-and thermodynamics-driven dendrite growth is propitiously proposed. Furthermore, the credible and understandable theoretical predictions are in conformity with the experiment results.

The effect of thermo-metallurgical factors, such as heat input and welding configuration, on solidification cracking driving forces nearby dendrite tip, such as solidification temperature range and columnar/equiaxed transition (CET) was thermodynamically and kinetically discussed with aid of comprehensive numerical analysis for multicomponent melt-pool solidification during laser processing under non-equilibrium solidification conditions to better understand problematical solidification cracking phenomena. By using (001)/[100] welding configuration, axisymmetrical distributions of columnar/equiaxed transition and solidification temperature range alongside solidification interface are homogeneously produced on both sides of weld pool. By using (001)/[110] welding configuration, nonaxisymmetrical distributions are heterogeneously produced, and are able to bring about infelicitous microstructure degradation. Unidirectional region of [001] columnar dendrite is more prone to epitaxial growth without morphology transition to conservatively better crystallography-assisted single-crystal growth. Unidirectional epitaxial growth is collapsed, and onset of stray grain nucleation and solidification cracking eventuates in [100] region of equiaxed dendrite growth. Low heat input relatively broadens portion of unidirectional columnar dendrite, where stray grain is infrequently nucleated and grown, and thus morphology transition seldom happens, as long as undercooling and solidification temperature range alongside dendrite tip are sufficient low to challengingly develop crackless dendrite growth and high-quality weld by thermometallurgy-aided single-crystallinity control. Auspicious (001)/[100] welding configuration simultaneously abates overall stray grain nucleation and constricts solidification temperature range nearby fusion boundary to wane microstructure heterogeneity. Conversely, plenteous stray grain formation is kinetically attained and extensive solidification temperature range nearby fusion boundary is thermodynamically obtained by problematical (001)/[110] welding configuration to metallurgically induce pernicious equiaxed dendrite and disintegrate dendrite growth. Moreover, the mechanism of solidification cracking diminution as consequence of appropriate optimization of thermo-metallurgical determinants during multicomponent nickel-based single-crystal superalloy melt-pool non-equilibrium solidification is also proposed. The potent consistency between the predicted and experimented results is exceedingly tenable.

The dependency of morphology development and dendrite growth on welding conditions (laser power, welding speed and welding configuration) is numerically analyzed to decrease nucleation and growth of stray grain formation during laser processing aerospace component surface of ternary Ni-Cr-Al single-crystal superalloy. Proper (001)/[100] welding configuration crystallographically initiates three axisymmetrical distributions of microstructure development, i.e. stray grain formation, morphology development and dendrite trunk spacing, alongside the advancing solid/liquid interface of molten pool, whereby metallurgical properties are increased. Unpromising (001)/[110] welding configuration tends to crystallographically possesses unaxisymmetrical microstructure development to favor substantial crack-vulnerable dendrite size and morphology. Epitaxial [001] columnar dendrite growth region is favored for single-crystal dendrite growth, while vulnerable [100] equiaxed dendrite growth region is more susceptible to solidification cracking. The lower heat input is used, the smaller stray grain formation, negligible columnar/equiaxed transition (CET) and finer dendrite trunk spacing are consistently promoted by narrower constitutional undercooling ahead of solid/liquid interface to improve crack-resistant microstructure development and weld integrity. When comparing between [100] dendrite growth region on the right side and [010] dendrite growth region on the left side, (001)/[110] welding configuration spontaneously engenders severer stray grain formation, insidious columnar/equiaxed transition and coarser dendrite trunk spacing on the right side to deteriorate microstructure development with restriction of the same heat input on both sides of weld pool. The mechanism of asymmetrical solidification cracking as result of crystallography-induced microstructure degradation is therefore proposed. The theoretical predictions of asymmetrical solidification cracking susceptibility are comparable with experiments.

When three welding conditions, including welding configuration, welding speed and laser power, are sequentially altered, supersaturation of liquid aluminum is crystallography-dependently determined to limit growth kinetics of dendrite tip with decease of thermo-metallurgical factors for solidification cracking to salvage the weld properties during emerging laser welding repair of multicomponent nickel-based single-crystal superalloy. After comparing growth crystallography between right side and left side of weld, the distribution of supersaturation of liquid aluminum is axis- symmetrically developed by favorite (001)/[100] dendrite growth kinetics, while the distribution is nonaxisymmetrically developed by detrimental (001)/[110] dendrite growth kinetics. High heat input is inappropriately procured by either high laser power or slow welding speed to insidiously boost supersaturation of liquid aluminum, worsen alloying partition and solute copiousness, heterogeneously exacerbate morphology and size of dendrite growth, whereby stray grain formation is strongly produced. In order to ameliorate dendrite growth, low heat input is usefully rendered by either low laser power or high welding speed to attenuate supersaturation of liquid aluminum, narrow solidification temperature range and obviate dendrite tip undercooling alongside columnar interface in order to augment crack-resistant dendrite of epitaxial growth. The overall supersaturation of liquid aluminum is crystallography-dependent. During across whole melt-pool solidification interface, supersaturation of nonsymmetric (001)/[110] welding configuration is not as small as symmetric (001)/[100] welding configuration under well-controlled heat input, thereby fosters the kinetic factors for stray grain development to obstruct columnar dendrite and consequently weaken unidirectional morphology. It is crystallographically favorable for relief of supersaturation with axis- symmetrical dendrite growth. The mechanism of crack-vulnerable dendrite growth elimination through circumspect improvement of supersaturation-controlled growth kinetics is constructively proposed for feasible crackless rejuvenation of laser welding or laser cladding. The theoretical predictions are scrupulously supported by corroborative metallograph observation.

Two important thermometallurgical factors, i.e. aluminum redistribution and dendrite tip undercooling, are numerically analyzed to better understand growth kinetics of microstructure development with favorable and unfavorable crystallographic orientations in three dimensions during advancement of Ni-Cr-Al ternary single-crystal melt-pool solidification interface to optimize microstructure stability within gamma γ phase. Inappropriate growth crystallography dominates profiles of aluminum redistribution and undercooling of dendrite tip in the crack-susceptible region, simultaneously. For beneficial (001)/[100] growth crystallography, the profiles of solid aluminum concentration and undercooling ahead of dendrite tip are clearly symmetrical throughout solidification interface. For detrimental (001)/[110] growth crystallography, the profiles of solid aluminum concentration and undercooling ahead of dendrite tip are quite asymmetrical within two sides of weld, and this asymmetrical phenomenon is of particular interest. The same energy of heat input is accessible to each half of molten pool, however, the difference of dendrite growth driving forces between right side and left side of weld pool kinetically exacerbates microstructure development. The complexity of (001)/[110] welding configuration is consistently attributable to larger overall solid aluminum concentration and undercooling of dendrite tip in [100] dendrite region than that of [010] dendrite region. In the two welding configurations, the size and shape of [001] dendrite growth region modifies growth kinetics of dendrite tip to extend columnar morphology of epitaxial growth for crack-resistant microstructure development with smaller solid aluminum concentration and narrower dendrite tip undercooling by either decrease of laser power or further increase of welding speed, while [100] dendrite growth region preferentially aids columnar/equiaxed transition (CET) with severe aluminum redistribution and wider dendrite tip undercoolig. The smaller heat input is imposed, the smaller solid aluminum concentration and narrower dendrite tip undercooling are crystallographically induced that is capable of elimination of metallurgical contributing factors for microstructure anomalies and vice versa. Optimum (001)/[100] growth crystallography and low heat input with decrease of laser power and increase of welding speed minimize columnar/equiaxed transition and stray grain formation, improve resistance to solidification cracking and ameliorate weld integrity, while (001)/[110] growth crystallography and high heat input with increase of laser power and decrease of welding speed significantly contribute to weldability exacerbation and microstructure degradation. The crystallography-dependent mechanism of efficient microstructure anomalies reduction, which is attributed to decreasing aluminum enrichment and undercooling ahead of dendrite tip, is therefore proposed. Consequently, comparison between calculation results and experiment results is plausible and acceptable. The usefulness application of this numerical analysis improves predictive capability and enables attractive microstructure control of single-crystal superalloys with similar materials properties.

Correlation between welding conditions, such as laser power, welding speed and welding configuration, microstructure anomalies, including columnar/equiaxed transition (CET) and stray grain formation, and metallurgical factors, such as aluminum redistribution and supersaturation near dendrite tip, is elucidated by thorough numerical analysis to explain prevalent phenomenon of insidious microstructure development and face the challenge of microstructure amelioration as well as solidification cracking resistance improvement during course of ternary single-crystal Nickel-Chromium-Aluminum superalloy melt-pool solidification for crack-free laser surface modification. Metallurgical factors of γ gamma phase microstructure development strongly depend on welding configuration, and heat input is not as important as welding configuration. Although melted-pool center region is susceptible to microstructure anomalies, (001)/[100] welding configuration possesses auspicious growth crystallography under which the bimodal profiles of solid aluminum concentration and liquid aluminum supersaturation ahead of dendrite tip are symmetrically distributed to potentially decrease solute redistribution and increase resistibility to solidification cracking. Dissimilarly, (001)/[110] welding configuration possesses insidious growth crystallography under which the profiles of solid aluminum concentration and liquid aluminum supersaturation ahead of dendrite tip are asymmetrically distributed to preferably facilitate alloying plentiful enrichment and differentiate problematical microstructure instability on half side of molten pool. In the bottom of molten pool, beneficial Al-barren [001] dendrite is kinetically driven by homologous single-crystal epitaxial growth without columnar/equiaxed transition. On the right side of molten pool, detrimental Al-rich [100] dendrite is spontaneously susceptible to stray grain formation with equiaxed morphology. Symmetrical microstructure development is more enrichment-resistant than asymmetrical microstructure development, which is crystallographically ascribable to favorable thermo-metallurgical factors, i.e. aluminum redistribution mitigation and supersaturation relief, and substantially reduce metallurgical degradation and microstructure failure. The faster welding speed and the lower laser power are used, the smaller aluminum concentration and supersaturation ahead of dendrite tip are kinetically incurred to suppress columnar/equiaxed transition and stray grain formation with a number of thermometallurgical factors contribution to considerable microstructure amelioration and increasingly improve solidification cracking resistance and vice versa. Shallow molten-pool shape with symmetrical growth crystallography efficiently advances anomalies-resistant microstructure development with diminution of partition driving forces for solute redistribution and supersaturation during nonequilibrium solidification instead of deep molten-pool shape with asymmetrical growth crystallography. The latter importantly aggravates stray grain formation. Useful combination of optimum solidification conditions and favorable growth crystallography predominantly minimizes diffusion-controlled solute deviation and microstructure anomalies for excellent single-crystal superalloy laser processing without cracking, and possesses tenable relationship between welding conditions, solute redistribution and microstructure anomalies. The mechanism of crystallography-aided concentration fluctuation and copious supersaturation behind prominent phenomenon of microstructure anomalies, where nucleation and growth of stray grain formation near dendrite tip are activated, is consequently proposed. The comparison between numerical analyses and experiment results are valid and satisfactory. Microstructure anomalies are predictable for proper understanding of multicomponent microstructure development in the interior of fusion zone. The theoretical methodology is reproducible as consequence of availability of thermodynamic and kinetic properties of Nickel-based or Iron-based single-crystal superalloys.