solidificacao de aço

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SOLIDIFICAÇÃO

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Qual a temperatura de fusão dos elementos puros? Qual a temperatura de fusão da liga Pb40wt%Sn?

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v  Solidificação

L

G1

L

S

G2 = G1+ΔG

T

G

T Tf

ΔT

ΔGv

Gsólido

Glíquido

Temperatura de fusão = T de solidificação?

interface

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v  Solidificação Nucleação homogênea

G2=VSGsv+ VLGL

V +ASLγSL

Para uma particula esférica:

ΔGr=-4/3πr3 ΔGv + 4 πr2 γSL

Para reduzir energia do sistema: r* = núcleo crítico: núcleo < r* redução; núcleo>r* crescimento

TLTr

S

m

ΔΔ

−=

γ2*

ΔLS = calor latente de solidificação

Tm = temperatura de fusão

γ = energia livre da superfície

ΔT = Tm - T = super-resfraimento

r* = raio critico

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During Solidification the atomic arrangement changes from a random or short-range order to a long range order or crystal structure.

Nucleation occurs when a small nucleus begins to form in the liquid, the nuclei then grows as atoms from the liquid are attached to it.

The crucial point is to understand it as a balance between the free energy available from the driving force, and the energy consumed in forming new interface. Once the rate of change of free energy becomes negative, then an embryo can grow.

Nucleação homogênea

Para reduzir energia do sistema: r* = núcleo crítico: núcleo < r* redução; núcleo>r* crescimento

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Raio critico r* diminui com o aumento de ΔT

Quanto maior o super-resfriamento menor serão r* e ΔGv*

Efeito do super-resfriamento sobre o raio critico

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Taxa de nucleação

Depende do número de aglomerados de átomos com raio r e

da frequência com um átomo se agregam a este aglomerado

É necessário um super-resfriamento mínimo para que se inicie a nucleação

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Nucleação Heterogênea

Condição necessária para que a nucleação seja eficiente:

γSI < γIL + γSL

No equilibrio:

γIS = γIL + (γSL cos θ)

0 < θ <90° a condição de molhabilidade é satisfeita, já para θ > 90° não é.

Ocorrendo molhabilidade, um núcleo com um raio de curvatura igual ao raio critico em nucleação homogênea pode ser formado a partir de um número muito menor de átomos do que seria necessário para a formação de um núcleo livre no seio do líquido.

super-resfriamento necessário para a nucleação heterogênea é muito menor do que o necessário para a nucleação homogênea.

ΔGhet=VSΔGv+ASLγSL+ASIγSI -ASLγSL

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Nucleação homogênea vs nucleação heterogênea

Variação de energia livre para o mesmo r*

Taxa de nucleação

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Nucleação em trincas – o angulo de contato pode ser bem diferente da consição anterior; super-resfriamento é muito menor A trinca tem de ter largura suficiente para permitir o crescimento do sólido Nucleação na fusão

�

Nhet = f1C1e−ΔGhet

∗

kT nuclei /m3

�

n∗

= n1e−ΔGhet

∗

kT

number of atoms in contact with nucleating agent surface

number of atoms in contact with nucleating agent surface per unit volume

Mould walls not flat

�

ΔG∗

=1

2V

∗ΔG

v

Exercise show that

Critical radius

for solid

for cracks to be effective the crack opening should be large enough to allow the solid to grow out without the radius of the solid/liquid interface decreasing below r*

Nucleation in cracks occur with very little undercooling

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Solidificação:

- nucleação

- crescimento

Temperatura

sólido líquido

Temperatura

sólido líquido a) b)

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v  Solidificação Crescimento do sólido depende da interface:

Rugosa (metais) – transição L/S é gradual em várias camadas atômicas; controlada pelo escoamento de calor (metais puros) ou difusão de soluto (ligas); átomos chegam no cucleo em qualquer localização – crescimento continuo

Lisa (não metais) – atomicamente plana e compacta;

Nucleação na superfície

Crescimento em espiral Crescimento lateral

Influência do super-resfriamento da interface S/L na taxa de crescimento para diferentes interfaces

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v  Solidificação Crescimento – influência do escoamento de calor

Crescimento planar

Crescimento não planar

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Crescimento dendritico

Crescimento não planar v  Solidificação

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Crescimento em ligas metálicas - Equilibrio v  Solidificação

Para a liga Pb30wt%Sn qual a composição das fases nas temperaturas 220C 200C 190C

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v  Solidificação Crescimento em ligas metálicas fora do equilibrio

Sem difusão no sólido e mistura perfeita no liquido (queda gradual de T do liq)

Desenvolvimento de dendritas Segregação do soluto

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v  Solidificação Solidificação de ligas: v Sem difusão no sólido e difusão no liquido

Ao atingir a T2 a taxa de crescimento é constante; o aumento da concentração de soluto na frente de solidificação estabiliza

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Desenvolvimento de dendritas Segregação do soluto no

desenvolvimento de dendrítas

Dendritas de um sistema Ni-Al José Eduard/oUnicamp


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Crescimento celular - Frente de solidificação não planar

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Efeito do super-resfriamento constitucional na morfologia de solidificação.

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v  Solidificação Formação de uma estrutura dendritica Relação com a estrutura de grão

Resistência mecânica é proporcional ao espaçamento entre braços secundários das dendritas

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Formação de grãos em um metal fundido

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v  Solidificação Crescimento dendritico em um sistema eutético Al-Ni

Com autorização de José Eduardo/Unicamp

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Microestrutura de solidificação no equilibrio e resfriadas fora do equilibrio?

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Liga hipo-eutética

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Liga peritética

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v  Solidificação Solidificação eutética L -> α + β

Eutético divorciado – volume de uma das fases é muito pequeno

Eutético lamelar

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Solidificação de lingotes

Zona equiaxial

Zona colunar

Zona coquilhada

Direção de crescimento em metais cúbicos <100>

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Solidificação em soldagem Solidificação em soldagem/vazamento continuo

Taxa de aporte de calor (depende do processo de soldagem e da dimensão da solda; ou do volume e temperatura do fundido, q

Velocidade do arco; velocidade de retirada do tarugo, v

Condutividade térmica do metal sendo soldado ou fundido, Ks

Espessura da placa sendo soldada ou fundida, t

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Solidificação em soldagem v  Solidificação

Os parâmetros Ks, v, t e q irão determinar a morfologia da solidificação

Condutividade

Velocidade

espessura

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v  Solidificação em soldagem

Diluição: alteração da composição química

Microestrutura/propriedades depende de:

Solidificação: parâmetros de solidificação G e R

Os parâmetros de solidificação são determinados pelos parâmetros de soldagem Tx de crescimento (R) depende da velocidade de avanço da fonte de calor e do formato da poça de fusão Tx de resfriamento (ε) e gradiente de T(G) diminuem com o aumento do aporte de calor

ε= G.R

Fundamentals of Weld SolidificationJohn N. DuPont, Lehigh University

MICROSTRUCTURAL EVOLUTION dur-ing solidification of the fusion zone representsone of the most important considerations forcontrolling the properties of welds. A widerange of microstructural features can form inthe fusion zone, depending on the alloy compo-sition, welding parameters, and resultant solidi-fication conditions. The primary objective ofthis article is to review and apply fundamentalsolidification concepts for understanding micro-structural evolution in fusion welds.

Microstructural Features in FusionWelds

Figures 1 through 3 schematically demon-strate the important microstructural featuresthat must be considered during solidificationin fusion welds (Ref 1, 2). On a macroscopicscale, fusion welds can adopt a range of grainmorphologies similar to castings (Fig. 1), inwhich columnar and equiaxed grains can poten-tially form during solidification. The final grainstructure depends primarily on alloy composi-tion and the heat-source travel speed. Althoughsome of the concepts applicable to grain struc-ture formation in castings apply to welds, thereare also some unique differences. While thecolumnar and equiaxed zones can form inwelds, the fine-grained chill zone at the moldwall represented by the fusion line is rarelyobserved in welds. Fundamental concepts asso-ciated with nucleation are needed to understandthese differences. In addition, the solid/liquidinterface in welds is typically curved and itsrate of movement is controlled by the heat-source travel speed, which leads to differencesin formation of the columnar zone withinwelds. These differences can be understoodthough application of competitive grain growthprocesses that occur during solidification.On a microscopic scale, there can also be a

wide range of substructural morphologieswithin the grains (Fig. 2), including planar(i.e., no substructure), cellular, columnar den-dritic, and equiaxed dendritic. The type and rel-ative extent of each substructural region isgoverned by the process of constitutionalsupercooling in which the liquid becomes

cooled below its liquidus temperature due tocompositional gradients in the liquid. Theextent of constitutional supercooling in theweld is determined by the alloy composition,welding parameters, and resultant solidificationparameters. Lastly, the distribution of alloyingelements and relative phase fractions withinthe substructure (Fig. 3) are also importantmicrostructural features that strongly affectweld-metal properties. The particular exampleshown in Fig. 3 represents a case in whichextensive residual microsegregation of alloyingelements exists across a cellular substructureafter nonequilibrium solidification. This micro-segregation, in turn, produces a relatively highfraction of intercellular eutectic and associatedsecondary phase. The microsegregation behav-ior and concomitant amount of secondary phasethat forms can each be understood with soluteredistribution concepts. Lastly, dendrite tipundercooling can become important athigh solidification rates associated with high-energy-density welding processes. Tip under-cooling can lead to significant changes in theprimary solidification mode, distribution of sol-ute within the solid, and final phase fractionbalance. Rapid solidification concepts areneeded to understand these phenomena. Allof these fundamental solidification concepts(nucleation, competitive grain growth, constitu-tional supercooling, solute redistribution, and

Fig. 1 Types of grain morphologies that can form infusion welds

Fig. 2 Types of substructure morphologies that can form within the grains of fusion welds

ASM Handbook, Volume 6A, Welding Fundamentals and ProcessesT. Lienert, T. Siewert, S. Babu, and V. Acoff, editors

Copyright # 2011 ASM InternationalW

All rights reserved

www.asminternational.org

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Nucleação -> Crescimento epitaxial Metal de base apresenta uma coerência cristalográfica quase que perfeita; não existe barreira para a nucleação

y ! cos"1gSLgSL

! "! 0 (Eq 14c)

S#y ! 0$ ! 0 (Eq 14d)

Thus, from Eq 12, the activation energy in fusionwelding (△Gfw) for nucleation is given simply by△Gfw = 0. This is compared to△Ghom and△Ghet

in Fig. 8. This can be interpreted by noting thatthe base-metal mold presents a perfect crystallo-graphicmatch for growth of the solid fusion zone.Thus, there is no solid/mold interface in fusionwelding due to this perfect crystallographicmatching. An example of this in a fusion weldmade with the electron beam process is shownin Fig. 9 (Ref 5). Note that there are no fineequiaxed grains at the fusion line, as oftenobserved in the chill zone of castings. Instead,the weld-metal grains grow directly from the pre-existing base-metal grains. As a result, there is nobarrier to formation of the solid. This condition isreferred to as epitaxial growth, because growthoccurs directly from the preexisting solid withoutthe need for nucleation. Therefore, there is noundercooling required to initiate solidificationat the fusion line, and solidification commencesat the liquidus temperature of the alloy. It shouldbe noted that undercooling can still occur near theweld centerline due to the process of constitu-tional supercooling, as explained in more detaillater. This can lead to the formation of the centralequiaxed zone often observed in fusion welds.Undercooling can also be required for nucleationof new phases during solidification.

Grain Structure of Fusion Welds

As described previously, the weld-metalgrains will grow epitaxially from the preexist-ing base-metal grains. However, not all of thesegrains will be favorably oriented for continuedgrowth. Two primary factors control thecontinued competitive growth of weld-metalgrains:

% The grains tend to grow in a direction anti-parallel to the maximum direction for heatextraction.

% The solid will grow in the “easy-growth”crystallographic directions.

The first criterion results from the need totransport the latent heat of solidification downthe temperature gradient into the cooler basemetal. Because the temperature gradient ishighest in a direction perpendicular to thesolid/liquid interface, the resultant heat-flowrate is also highest in this direction. Thus, thegrains tend to grow in a direction perpendicularto the solid/liquid interface. The second crite-rion results from the preferred crystallographicgrowth direction, which, for cubic metals, isalong the [100] directions. By combining thesetwo criteria, it can be seen that grains that havetheir easy-growth direction most closelyaligned to the solid/liquid interface normal willbe most favorably oriented to grow, thuscrowding out less-favorably-oriented grains.This phenomenon accounts for the columnargrain zone that is often observed in castings,shown schematically in Fig. 5. In this case,the grains that nucleated near the mold walland have their easy-growth direction alignednormal to the mold/casting interface outgrowthe less-favorably-oriented grains, leading tothe columnar region.The situation is slightly more complex in

fusion welding, because the pool shape pro-duces a curved solid/liquid interface that is con-stantly in motion as it follows the heat source.This is shown schematically in Fig. 10 (Ref6). Grains at the fusion line may initially be ori-ented in a favorable direction for growth, buttheir direction may become unfavorable as thecurved solid/liquid interface changes its posi-tion. These grains may then eventually beovergrown by other grains that exhibit morefavorable orientation for growth as the solid/liq-uid interface sweeps through the weld. Anexample of this is shown on a weld in nearlypure (99.96%) aluminum in Fig. 11(a) (Ref 7).

As may be expected, the pool shape can havea strong influence on competitive grain growthand the resultant grain structure of the weld.In turn, the pool shape can be influenced bythe welding parameters. At low-to-moderateheat-source travel speeds, the pool shape is gen-erally elliptical and typically produces the grainstructure pattern shown in Fig. 11(a). However,at higher travel speeds, the pool shape becomeselongated into a teardrop shape in which thesolid/liquid interface is straight. This elongatedshape is attributed to the low thermal gradientand high growth rate that exist at the weld cen-terline. The release of latent heat is proportionalto the growth rate. Because the growth rate ishighest at the weld centerline, the release rateof latent heat is also highest at the weld center-line. However, the temperature gradient is at a

Fig. 9 Example of epitaxial growth from the fusion linein an electron beam weld of alloy C103.

Original magnification: 400&. Source: Ref 5

Fig. 10 Schematic illustrations of competitive graingrowth in welds. (a) Early growth of grains

near the fusion line. (b) Continued growth of favorably-orientated grains at a later time. Source: Ref 6

Fig. 8 Comparison of free-energy changes associatedwith homogeneous nucleation, heterogeneous

nucleation, and fusion welding

Fundamentals of Weld Solidification / 99

Grãos na poça de fusão crescem diretamente sobre grãos pre-existentes no metal-base orientados favoravelmente

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Crescimento: Ø Grãos crescem perpendicularmente a

interface S/L sendo a extração de calor é máxima (calor escoa pelo substrato)

Ø Sólido cresce na direção cristalográfica que for mais fácil ( metais cubicos [100] – grãos com [100] orientados perpendicularmente a interface vão crescer)

y ! cos"1gSLgSL

! "! 0 (Eq 14c)

S#y ! 0$ ! 0 (Eq 14d)

Thus, from Eq 12, the activation energy in fusionwelding (△Gfw) for nucleation is given simply by△Gfw = 0. This is compared to△Ghom and△Ghet

in Fig. 8. This can be interpreted by noting thatthe base-metal mold presents a perfect crystallo-graphicmatch for growth of the solid fusion zone.Thus, there is no solid/mold interface in fusionwelding due to this perfect crystallographicmatching. An example of this in a fusion weldmade with the electron beam process is shownin Fig. 9 (Ref 5). Note that there are no fineequiaxed grains at the fusion line, as oftenobserved in the chill zone of castings. Instead,the weld-metal grains grow directly from the pre-existing base-metal grains. As a result, there is nobarrier to formation of the solid. This condition isreferred to as epitaxial growth, because growthoccurs directly from the preexisting solid withoutthe need for nucleation. Therefore, there is noundercooling required to initiate solidificationat the fusion line, and solidification commencesat the liquidus temperature of the alloy. It shouldbe noted that undercooling can still occur near theweld centerline due to the process of constitu-tional supercooling, as explained in more detaillater. This can lead to the formation of the centralequiaxed zone often observed in fusion welds.Undercooling can also be required for nucleationof new phases during solidification.

Grain Structure of Fusion Welds

As described previously, the weld-metalgrains will grow epitaxially from the preexist-ing base-metal grains. However, not all of thesegrains will be favorably oriented for continuedgrowth. Two primary factors control thecontinued competitive growth of weld-metalgrains:

% The grains tend to grow in a direction anti-parallel to the maximum direction for heatextraction.

% The solid will grow in the “easy-growth”crystallographic directions.

The first criterion results from the need totransport the latent heat of solidification downthe temperature gradient into the cooler basemetal. Because the temperature gradient ishighest in a direction perpendicular to thesolid/liquid interface, the resultant heat-flowrate is also highest in this direction. Thus, thegrains tend to grow in a direction perpendicularto the solid/liquid interface. The second crite-rion results from the preferred crystallographicgrowth direction, which, for cubic metals, isalong the [100] directions. By combining thesetwo criteria, it can be seen that grains that havetheir easy-growth direction most closelyaligned to the solid/liquid interface normal willbe most favorably oriented to grow, thuscrowding out less-favorably-oriented grains.This phenomenon accounts for the columnargrain zone that is often observed in castings,shown schematically in Fig. 5. In this case,the grains that nucleated near the mold walland have their easy-growth direction alignednormal to the mold/casting interface outgrowthe less-favorably-oriented grains, leading tothe columnar region.The situation is slightly more complex in

fusion welding, because the pool shape pro-duces a curved solid/liquid interface that is con-stantly in motion as it follows the heat source.This is shown schematically in Fig. 10 (Ref6). Grains at the fusion line may initially be ori-ented in a favorable direction for growth, buttheir direction may become unfavorable as thecurved solid/liquid interface changes its posi-tion. These grains may then eventually beovergrown by other grains that exhibit morefavorable orientation for growth as the solid/liq-uid interface sweeps through the weld. Anexample of this is shown on a weld in nearlypure (99.96%) aluminum in Fig. 11(a) (Ref 7).

As may be expected, the pool shape can havea strong influence on competitive grain growthand the resultant grain structure of the weld.In turn, the pool shape can be influenced bythe welding parameters. At low-to-moderateheat-source travel speeds, the pool shape is gen-erally elliptical and typically produces the grainstructure pattern shown in Fig. 11(a). However,at higher travel speeds, the pool shape becomeselongated into a teardrop shape in which thesolid/liquid interface is straight. This elongatedshape is attributed to the low thermal gradientand high growth rate that exist at the weld cen-terline. The release of latent heat is proportionalto the growth rate. Because the growth rate ishighest at the weld centerline, the release rateof latent heat is also highest at the weld center-line. However, the temperature gradient is at a

Fig. 9 Example of epitaxial growth from the fusion linein an electron beam weld of alloy C103.

Original magnification: 400&. Source: Ref 5

Fig. 10 Schematic illustrations of competitive graingrowth in welds. (a) Early growth of grains

near the fusion line. (b) Continued growth of favorably-orientated grains at a later time. Source: Ref 6

Fig. 8 Comparison of free-energy changes associatedwith homogeneous nucleation, heterogeneous

nucleation, and fusion welding

Fundamentals of Weld Solidification / 99

Fonte de calor em movimento – interface S/L curva e em movimento Grãos que inicialmente exibem orientação favorável podem perder esta condição

Crescimento normal as isotermas; ajuste a velocidade da fonte de calor

A.S.D’Oliveira


O aspecto geométrico da poça de fusão determina a forma da interface S/L e depende dos parâmetros de soldagem

minimum at the weld centerline, so it is difficultto transport the latent heat away from the poolto permit solidification. This causes elongationof the pool near the weld centerline and leadsto the teardrop shape. In this case, the directionof grain growth does not change (because thesolid/liquid interface is no longer curved), andthe grains grow straight toward the weld center-line until grains growing from each side of theweld intersect. This process typically leads toa centerline grain boundary, as shown inFig. 11(b) (Ref 7).Axial grains that grow along the direction of

heat-source travel can also occasionally beobserved in fusion welds. The various types ofgrain morphologies are summarized in Fig. 12(Ref 6). Examples of grain structures producedwith elliptical and teardrop-shaped weld poolswere shown in Fig. 11. Figures 12(c) and (d) rep-resent conditions in which an axial grain growsalong the direction of the heat-source travel.These grains form in the region where the solid/liquid interface is generally perpendicular to thedirection of heat-source travel, so that it becomesfavorable for one or more grains to grow in thisdirection. The width of this zone can depend onthe pool shape. The region of the interface thatis perpendicular to the heat-source direction isrelatively small in an elongated weld pool, sothe width of axial grains will also be small. Bycomparison, this perpendicular region is rela-tively larger for an elliptical pool, so the axialgrain region can also be larger.The large columnar grains and the potential

presence of centerline grain boundaries are gen-erally undesirable from a weldability andmechanical property point of view. Centerlinegrain boundaries can often lead to solidificationcracking associated with solidification shrinkageand low-melting-point films that become concen-trated at the centerline. Fine, equiaxed grains aredesired over coarse columnar grains for improve-ments in both cracking resistance andmechanicalproperties (at low temperature). One effectivemeans for minimizing or eliminating the coarsecolumnar grains is through manipulation of thepool shape. Figure 13 shows an example of aweld in which the arc was oscillated at a fre-quency of 1 Hz in a direction normal to theheat-source travel (Ref 8). In this case, the contin-uously changing direction of the solid/liquidinterface makes it difficult for the columnargrains to extend over large distances, thusproviding a degree of grain refinement. Grainsize reduction can also be achieved through theuse of inoculants. This process takes advantageof heterogeneous nucleation (discussed previ-ously) and liquid undercooling that occur due toconstitutional supercooling. This topic isdescribed in more detail in the next section.

Substructure Formation in FusionWelds

As shown previously in Fig. 2, grains inwelds typically exhibit various substructural

morphologies within the grains that can be cel-lular, columnar dendritic, or equiaxed dendritic.Cellular and columnar dendritic morphologiesdevelop due to breakdown of the initially planarsolid/liquid interface that forms at the fusionline, while equiaxed dendrites form by nucle-ation of solid in undercooled liquid, typically

near the weld centerline. Formation of thesefeatures can be understood with the concept ofconstitutional supercooling. The basics of thistopic are described first, followed by applica-tion of the theory to understanding the substruc-ture formation in fusion welds.

Constitutional Supercooling

As shown by the phase diagram in Fig. 14(a),formation of a solid leads to rejection of soluteinto the liquid. The extent of solute enrichmentin the liquid progresses as solidification pro-ceeds and the liquid composition follows theliquidus line. The solute rejected by the solidat the solid/liquid interface must be transportedaway from the interface by diffusion and/orconvection in the liquid. If the solid/liquidinterface growth rate is relatively high (whichleads to a high rate of solute rejection) and/orthe transport of solute into the liquid by diffu-sion or convection is low, then a solute bound-ary layer can develop in the liquid near thesolid/liquid interface. Because solute enrich-ment leads to a reduction in the liquidus tem-perature (for an element that partitions to theliquid), it follows that the presence of a solute

Fig. 12 Summary of various grain morphologies that can form from weld pools of different shapes. Source: Ref 6

Fig. 13 Grain structure in a fusion weld of alloy 2014made with transverse arc oscillation. Source:

Ref 8

Fig. 11 Examples of (a) competitive grain growth and(b) a centerline grain boundary forming on a

weld in 99.96 % Al. The weld in (a) was made at awelding speed of 250 mm/min (10 in./min). The weld in(b) was made at a welding speed of 1000 mm/min (40in./min). Source: Ref 7

100 / Fundamentals of Fusion Weldingminimum at the weld centerline, so it is difficultto transport the latent heat away from the poolto permit solidification. This causes elongationof the pool near the weld centerline and leadsto the teardrop shape. In this case, the directionof grain growth does not change (because thesolid/liquid interface is no longer curved), andthe grains grow straight toward the weld center-line until grains growing from each side of theweld intersect. This process typically leads toa centerline grain boundary, as shown inFig. 11(b) (Ref 7).Axial grains that grow along the direction of

heat-source travel can also occasionally beobserved in fusion welds. The various types ofgrain morphologies are summarized in Fig. 12(Ref 6). Examples of grain structures producedwith elliptical and teardrop-shaped weld poolswere shown in Fig. 11. Figures 12(c) and (d) rep-resent conditions in which an axial grain growsalong the direction of the heat-source travel.These grains form in the region where the solid/liquid interface is generally perpendicular to thedirection of heat-source travel, so that it becomesfavorable for one or more grains to grow in thisdirection. The width of this zone can depend onthe pool shape. The region of the interface thatis perpendicular to the heat-source direction isrelatively small in an elongated weld pool, sothe width of axial grains will also be small. Bycomparison, this perpendicular region is rela-tively larger for an elliptical pool, so the axialgrain region can also be larger.The large columnar grains and the potential

presence of centerline grain boundaries are gen-erally undesirable from a weldability andmechanical property point of view. Centerlinegrain boundaries can often lead to solidificationcracking associated with solidification shrinkageand low-melting-point films that become concen-trated at the centerline. Fine, equiaxed grains aredesired over coarse columnar grains for improve-ments in both cracking resistance andmechanicalproperties (at low temperature). One effectivemeans for minimizing or eliminating the coarsecolumnar grains is through manipulation of thepool shape. Figure 13 shows an example of aweld in which the arc was oscillated at a fre-quency of 1 Hz in a direction normal to theheat-source travel (Ref 8). In this case, the contin-uously changing direction of the solid/liquidinterface makes it difficult for the columnargrains to extend over large distances, thusproviding a degree of grain refinement. Grainsize reduction can also be achieved through theuse of inoculants. This process takes advantageof heterogeneous nucleation (discussed previ-ously) and liquid undercooling that occur due toconstitutional supercooling. This topic isdescribed in more detail in the next section.

Substructure Formation in FusionWelds

As shown previously in Fig. 2, grains inwelds typically exhibit various substructural

morphologies within the grains that can be cel-lular, columnar dendritic, or equiaxed dendritic.Cellular and columnar dendritic morphologiesdevelop due to breakdown of the initially planarsolid/liquid interface that forms at the fusionline, while equiaxed dendrites form by nucle-ation of solid in undercooled liquid, typically

near the weld centerline. Formation of thesefeatures can be understood with the concept ofconstitutional supercooling. The basics of thistopic are described first, followed by applica-tion of the theory to understanding the substruc-ture formation in fusion welds.

Constitutional Supercooling

As shown by the phase diagram in Fig. 14(a),formation of a solid leads to rejection of soluteinto the liquid. The extent of solute enrichmentin the liquid progresses as solidification pro-ceeds and the liquid composition follows theliquidus line. The solute rejected by the solidat the solid/liquid interface must be transportedaway from the interface by diffusion and/orconvection in the liquid. If the solid/liquidinterface growth rate is relatively high (whichleads to a high rate of solute rejection) and/orthe transport of solute into the liquid by diffu-sion or convection is low, then a solute bound-ary layer can develop in the liquid near thesolid/liquid interface. Because solute enrich-ment leads to a reduction in the liquidus tem-perature (for an element that partitions to theliquid), it follows that the presence of a solute

Fig. 12 Summary of various grain morphologies that can form from weld pools of different shapes. Source: Ref 6

Fig. 13 Grain structure in a fusion weld of alloy 2014made with transverse arc oscillation. Source:

Ref 8

Fig. 11 Examples of (a) competitive grain growth and(b) a centerline grain boundary forming on a

weld in 99.96 % Al. The weld in (a) was made at awelding speed of 250 mm/min (10 in./min). The weld in(b) was made at a welding speed of 1000 mm/min (40in./min). Source: Ref 7

100 / Fundamentals of Fusion Welding

250mm/min

1000mm/min

Liberação de calor latente de solidificação é proporcional a tx de crescimento (R) que é máxima no centro do cordão; mas o gradiente térmico (G) é minimo on centro do cordão o que dificulta a transferencia de calor – provoca o alongamento da poça – interface S/L reta Contorno no meio do cordão é indesejável

A.S.D’Oliveira


Desenvolvimento de sub-estruturas – diferente morfologias dentro de um grão

Celular/colunar dendritico/equiaxial dendritico

Interrupção da interface plana Nucleação de sólido no liq super-resfriado

Relações que determinam as caracteristicas da estrutura/propriedades G/R -> tipo de estrutura

G.R -> refino da estrutura

Propriedades dependem do espaçamento entre braços das dendritas que é proporcional a tx de resfriamento; determina pelo aporte de calor

A.S.D’Oliveira

Valores de G e R mudam contantemente em direções opostas em torno da interface S/L Linha de fusão:

- alto gradiente térmico (G) e baixa taxa de crescimento (R) pode ter uma estrutura planar

Centro do cordão: - baixo gradiente térmico (G) e alta taxa de crescimento (R)

Crescimento mais rápido no centro e mais lento nas bordas


Relação entre taxa de crescimento e velocidade de soldagem (v)

R=v.cosΘ R≈0, linha de fusão R≈v ,linha central

A.S.D’Oliveira 38

G decreases as the weld centerline isapproached because the molten pool is in con-tact with resolidified weld metal that wasalready heated well above the liquidus tempera-ture. An opposite trend exists for the growthrate. Figure 17 shows the relation betweenthe heat-source travel speed (S) and growthrate (R) in terms of the angles a and b, where

a represents the angle between the weldingdirection and normal to the solid/liquid inter-face, and b represents the angle betweenthe welding direction and [100] growth

direction (for a cubic metal). The growth rateR is given by:

R ! S cosacos a" b# $ (Eq 20)

In many cases, the value of (a – b) is smallso that cos(a – b) % 1, and the relation betweenthe growth rate and heat-source travel speed isgiven simply as:

R ! S cosa (Eq 21)

From this it can be seen that R % 0 at the fusionline and R % S at the weld centerline. Thus, thevalue of G/R is very high at the fusion line anddecreases appreciably as the weld centerline isapproached. This can be portrayed on the G-Rdiagram as shown in Fig. 16. As a result,the fusion zone initially forms as a planar inter-face, which breaks down into cellular andcolumnar dendritic morphologies as the center-line is approached. If enough undercooling isobtained, an equiaxed zone can form in the cen-terline of the weld. The relative positions ofthese substructural morphologies are shownschematically in Fig. 2. An example of theequiaxed zone is shown in Fig. 18 (Ref 2).It is interesting to note that the planar zone

typically occupies a very small fraction of thefusion zone. This suggests that the planar

Fig. 15 Schematic illustrations showing (a) stability of a planar interface for a condition in which the actual temperature gradient in the liquid is greater than the liquidustemperature gradient and (b) breakdown of a planar interface for a condition in which the actual temperature gradient in the liquid is lower than the liquidus

temperature gradient

Fig. 16 Schematic illustration of a G-R diagramshowing regions of various substructural

morphologies Fig. 17 Schematic illustration showing the relationbetween the heat-source travel speed (S) and

growth rate (R) in terms of the angles a and b, where arepresents the angle between the welding direction andnormal to the solid/liquid interface, and b represents theangle between the welding direction and [100] growthdirection (for a cubic metal)

102 / Fundamentals of Fusion Welding

G/R – super-resfriamento


Desenvolvimento da estrutura na poça de fusão G/R muito alto na linha de fusão e vai diminuindo até a linha central

Sequencia de solidificação

Estrutura planar

Celular

Colunar dendritica

Equiaxial dendritica (Alto super-resfriamento

constitucional)

Linha de fusão

Centro do cordão

A.S.D’Oliveira

Considere as aletas de turbinas abaixo. Assumindo que todas foram produzidas com a mesma liga de Ni, descreva como se desenvolvem as 3 estruturas de solidificação


A.S.D’Oliveira

2.4mm

substrato Vergara, V.M., Tese de doutorado 2007


Descrever solidificação do revestimento

A.S.D’Oliveira


Ni12wt%Al

Ni30wt%Al

Explique o desenvolvimento das estruturas de solidificação considerando que o desenvolvimento do composto intermetálico é exotérmico

solidificacao de aço

Education

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