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A.S.D’Oliveira
SOLIDIFICAÇÃO
A.S.D’Oliveira
Qual a temperatura de fusão dos elementos puros?
Qual a temperatura de fusão da liga Pb40wt%Sn?
A.S.D’Oliveira
v Solidificação
L
G1
L
S
G2 = G1+ΔG
T
G
T Tf
ΔT
ΔGv
Gsólido
Glíquido
Temperatura de fusão = T de solidificação?
interface
A.S.D’Oliveira
v Solidificação
Nucleação homogênea
G2=VSGs
v+ 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
TL
T
r
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
A.S.D’Oliveira
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
A.S.D’Oliveira
v Solidificação
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
A.S.D’Oliveira
v Solidificação
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
A.S.D’Oliveira
v Solidificação
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
A.S.D’Oliveira
v Solidificação
Nucleação homogênea vs nucleação heterogênea
Variação de energia livre para o mesmo r*
Taxa de nucleação
A.S.D’Oliveira
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
/m3
with
with
unit
Mould walls not flat
Critical radius
for solid
Nucleation in cracks occur with very little
undercooling
A.S.D’Oliveira
v Solidificação
Solidificação:
- nucleação
- crescimento
Temperatura
sólido líquido
Temperatura
sólido líquido
a) b)
A.S.D’Oliveira
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
A.S.D’Oliveira
v Solidificação
Crescimento – influência do escoamento de calor
Crescimento planar
Crescimento não planar
A.S.D’Oliveira
Crescimento dendritico
Crescimento não planar
v Solidificação
A.S.D’Oliveira
Crescimento em ligas metálicas - Equilibrio
v Solidificação
Para a liga Pb30wt%Sn qual a composição das fases nas temperaturas
220C
200C
190C
A.S.D’Oliveira
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
A.S.D’Oliveira
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
A.S.D’Oliveira
Desenvolvimento de dendritas
Segregação do soluto no
desenvolvimento de dendrítas
Dendritas de um sistema Ni-Al
José Eduard/oUnicamp
v Solidificação
A.S.D’Oliveira
v Solidificação
Crescimento celular - Frente
de solidificação não planar
A.S.D’Oliveira
v Solidificação
Efeito do super-resfriamento
constitucional na morfologia de
solidificação.
A.S.D’Oliveira
v Solidificação
Formação de uma estrutura dendritica
Relação com a estrutura de grão
Resistência mecânica é proporcional ao espaçamento entre
braços secundários das dendritas
A.S.D’Oliveira
v Solidificação
Formação de grãos em um metal fundido
A.S.D’Oliveira
v Solidificação
Crescimento dendritico em um sistema eutético Al-Ni
Com autorização de José
Eduardo/Unicamp
A.S.D’Oliveira
v Solidificação
Microestrutura de solidificação no equilibrio e resfriadas
fora do equilibrio?
A.S.D’Oliveira
v Solidificação
Liga hipo-eutética
A.S.D’Oliveira
v Solidificação
Liga peritética
A.S.D’Oliveira
v Solidificação
A.S.D’Oliveira
v Solidificação
Solidificação eutética L -> α + β
Eutético divorciado – volume de uma das fases é muito pequeno
Eutético lamelar
A.S.D’Oliveira
v Solidificação
Solidificação de lingotes
Zona
equiaxial
Zona
colunar
Zona
coquilhada
Direção de crescimento em metais cúbicos <100>
A.S.D’Oliveira
v Solidificação
Solidificação em soldagemSolidificação 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
A.S.D’Oliveira
Solidificação em soldagem
v Solidificação
Os parâmetros Ks, v, t e q irão determinar a
morfologia da solidificação
Condutividade
Velocidade
espessura
A.S.D’Oliveira
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 Solidification
John N. DuPont, Lehigh University
MICROSTRUCTURAL EVOLUTION dur-
ing solidification of the fusion zone represents
one of the most important considerations for
controlling the properties of welds. A wide
range of microstructural features can form in
the fusion zone, depending on the alloy compo-
sition, welding parameters, and resultant solidi-
fication conditions. The primary objective of
this article is to review and apply fundamental
solidification concepts for understanding micro-
structural evolution in fusion welds.
Microstructural Features in Fusion
Welds
Figures 1 through 3 schematically demon-
strate the important microstructural features
that must be considered during solidification
in fusion welds (Ref 1, 2). On a macroscopic
scale, fusion welds can adopt a range of grain
morphologies similar to castings (Fig. 1), in
which columnar and equiaxed grains can poten-
tially form during solidification. The final grain
structure depends primarily on alloy composi-
tion and the heat-source travel speed. Although
some of the concepts applicable to grain struc-
ture formation in castings apply to welds, there
are also some unique differences. While the
columnar and equiaxed zones can form in
cooled below its liquidus temperature due to
compositional gradients in the liquid. The
extent of constitutional supercooling in the
weld is determined by the alloy composition,
welding parameters, and resultant solidification
parameters. Lastly, the distribution of alloying
elements and relative phase fractions within
the substructure (Fig. 3) are also important
microstructural features that strongly affect
weld-metal properties. The particular example
shown in Fig. 3 represents a case in which
extensive residual microsegregation of alloying
elements exists across a cellular substructure
after nonequilibrium solidification. This micro-
segregation, in turn, produces a relatively high
fraction of intercellular eutectic and associated
secondary phase. The microsegregation behav-
ior and concomitant amount of secondary phase
that forms can each be understood with solute
redistribution concepts. Lastly, dendrite tip
undercooling can become important at
high solidification rates associated with high-
energy-density welding processes. Tip under-
cooling can lead to significant changes in the
primary solidification mode, distribution of sol-
ute within the solid, and final phase fraction
balance. Rapid solidification concepts are
needed to understand these phenomena. All
of these fundamental solidification concepts
(nucleation, competitive grain growth, constitu- Fig. 1 Types of grain morphologies that can form in
ASM Handbook, Volume 6A, Welding Fundamentals and Processes
T. Lienert, T. Siewert, S. Babu, and V. Acoff, editors
Copyright # 2011 ASM InternationalW
All rights reserved
www.asminternational.org
A.S.D’Oliveira
v Solidificação em soldagem
Nucleação -> Crescimento epitaxial
Metal de base apresenta uma coerência cristalográfica quase
que perfeita; não existe barreira para a nucleação
Grain Structure of Fusion Welds
As described previously, the weld-metal
grains will grow epitaxially from the preexist-
ing base-metal grains. However, not all of these
grains will be favorably oriented for continued
growth. Two primary factors control the
continued competitive growth of weld-metal
grains:
This is shown schematically in Fig. 10 (Ref
6). Grains at the fusion line may initially be ori-
ented in a favorable direction for growth, but
their direction may become unfavorable as the
curved solid/liquid interface changes its posi-
tion. These grains may then eventually be
overgrown by other grains that exhibit more
favorable orientation for growth as the solid/liq-
uid interface sweeps through the weld. An
example of this is shown on a weld in nearly
pure (99.96%) aluminum in Fig. 11(a) (Ref 7).
Fig. 9 Example of epitaxial growth from the fusion line
in an electron beam weld of alloy C103.
Original magnification: 400Â. Source: Ref 5
Fig. 10 Schemat
growth
near the fusion line.
orientated grains at a
Fig. 8 Comparison of free-energy changes associated
with homogeneous nucleation, heterogeneous
nucleation, and fusion welding
Grãos na poça de fusão crescem diretamente sobre grãos pre-
existentes no metal-base orientados favoravelmente
A.S.D’Oliveira
v Solidificação em soldagem
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)
atching. An example of this in a fusion weld
ade with the electron beam process is shown
Fig. 9 (Ref 5). Note that there are no fine
quiaxed grains at the fusion line, as often
bserved in the chill zone of castings. Instead,
e weld-metal grains grow directly from the pre-
xisting base-metal grains. As a result, there is no
arrier to formation of the solid. This condition is
ferred to as epitaxial growth, because growth
ccurs directly from the preexisting solid without
e need for nucleation. Therefore, there is no
ndercooling required to initiate solidification
the fusion line, and solidification commences
the liquidus temperature of the alloy. It should
e noted that undercooling can still occur near the
eld centerline due to the process of constitu-
onal supercooling, as explained in more detail
ter. This can lead to the formation of the central
quiaxed zone often observed in fusion welds.
ndercooling can also be required for nucleation
new phases during solidification.
Grain Structure of Fusion Welds
As described previously, the weld-metal
ains will grow epitaxially from the preexist-
g base-metal grains. However, not all of these
ains will be favorably oriented for continued
owth. Two primary factors control the
ontinued competitive growth of weld-metal
ains:
to the solid/liquid interface. The second crite-
rion results from the preferred crystallographic
growth direction, which, for cubic metals, is
along the [100] directions. By combining these
two criteria, it can be seen that grains that have
their easy-growth direction most closely
aligned to the solid/liquid interface normal will
be most favorably oriented to grow, thus
crowding out less-favorably-oriented grains.
This phenomenon accounts for the columnar
grain zone that is often observed in castings,
shown schematically in Fig. 5. In this case,
the grains that nucleated near the mold wall
and have their easy-growth direction aligned
normal to the mold/casting interface outgrow
the less-favorably-oriented grains, leading to
the 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 (Ref
6). Grains at the fusion line may initially be ori-
ented in a favorable direction for growth, but
their direction may become unfavorable as the
curved solid/liquid interface changes its posi-
tion. These grains may then eventually be
overgrown by other grains that exhibit more
favorable orientation for growth as the solid/liq-
uid interface sweeps through the weld. An
example of this is shown on a weld in nearly
pure (99.96%) aluminum in Fig. 11(a) (Ref 7).
to the growth rate. Because the growth rate is
highest at the weld centerline, the release rate
of latent heat is also highest at the weld center-
line. However, the temperature gradient is at a
Schematic illustrations of competitive grain
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
v Solidificação em soldagem
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 difficult
to transport the latent heat away from the pool
to permit solidification. This causes elongation
of the pool near the weld centerline and leads
to the teardrop shape. In this case, the direction
of grain growth does not change (because the
solid/liquid interface is no longer curved), and
the grains grow straight toward the weld center-
line until grains growing from each side of the
weld intersect. This process typically leads to
a centerline grain boundary, as shown in
Fig. 11(b) (Ref 7).
Axial grains that grow along the direction of
heat-source travel can also occasionally be
observed in fusion welds. The various types of
grain morphologies are summarized in Fig. 12
(Ref 6). Examples of grain structures produced
with elliptical and teardrop-shaped weld pools
were shown in Fig. 11. Figures 12(c) and (d) rep-
resent conditions in which an axial grain grows
along the direction of the heat-source travel.
These grains form in the region where the solid/
liquid interface is generally perpendicular to the
direction of heat-source travel, so that it becomes
favorable for one or more grains to grow in this
direction. The width of this zone can depend on
the pool shape. The region of the interface that
is perpendicular to the heat-source direction is
relatively small in an elongated weld pool, so
the width of axial grains will also be small. By
comparison, this perpendicular region is rela-
tively larger for an elliptical pool, so the axial
grain region can also be larger.
The large columnar grains and the potential
presence of centerline grain boundaries are gen-
erally undesirable from a weldability and
mechanical property point of view. Centerline
grain boundaries can often lead to solidification
cracking associated with solidification shrinkage
and low-melting-point films that become concen-
trated at the centerline. Fine, equiaxed grains are
desired over coarse columnar grains for improve-
ments in both cracking resistance and mechanical
properties (at low temperature). One effective
means for minimizing or eliminating the coarse
columnar grains is through manipulation of the
pool shape. Figure 13 shows an example of a
weld in which the arc was oscillated at a fre-
quency of 1 Hz in a direction normal to the
heat-source travel (Ref8). In this case, the contin-
uously changing direction of the solid/liquid
interface makes it difficult for the columnar
grains to extend over large distances, thus
providing a degree of grain refinement. Grain
size reduction can also be achieved through the
use of inoculants. This process takes advantage
of heterogeneous nucleation (discussed previ-
ously) and liquid undercooling that occur due to
constitutional supercooling. This topic is
morphologies within the grains that can be cel-
lular, columnar dendritic, or equiaxed dendritic.
Cellular and columnar dendritic morphologies
develop due to breakdown of the initially planar
solid/liquid interface that forms at the fusion
line, while equiaxed dendrites form by nucle-
ation of solid in undercooled liquid, typically
near the weld centerline. Formation of these
features can be understood with the concept of
constitutional supercooling. The basics of this
topic 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 solute
into the liquid. The extent of solute enrichment
in the liquid progresses as solidification pro-
ceeds and the liquid composition follows the
liquidus line. The solute rejected by the solid
at the solid/liquid interface must be transported
away from the interface by diffusion and/or
convection in the liquid. If the solid/liquid
interface growth rate is relatively high (which
leads to a high rate of solute rejection) and/or
the 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 the
solid/liquid interface. Because solute enrich-
ment leads to a reduction in the liquidus tem-
perature (for an element that partitions to the
liquid), it follows that the presence of a solute
Fig. 13 Grain structure in a fusion weld of alloy 2014
made 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 a
welding speed of 250 mm/min (10 in./min). The weld in
(b) was made at a welding speed of 1000 mm/min (40
in./min). Source: Ref 7
100 / Fundamentals of Fusion Welding
minimum at the weld centerline, so it is difficult
to transport the latent heat away from the pool
to permit solidification. This causes elongation
of the pool near the weld centerline and leads
to the teardrop shape. In this case, the direction
of grain growth does not change (because the
solid/liquid interface is no longer curved), and
the grains grow straight toward the weld center-
line until grains growing from each side of the
weld intersect. This process typically leads to
a centerline grain boundary, as shown in
Fig. 11(b) (Ref 7).
Axial grains that grow along the direction of
heat-source travel can also occasionally be
observed in fusion welds. The various types of
grain morphologies are summarized in Fig. 12
(Ref 6). Examples of grain structures produced
with elliptical and teardrop-shaped weld pools
were shown in Fig. 11. Figures 12(c) and (d) rep-
resent conditions in which an axial grain grows
along the direction of the heat-source travel.
These grains form in the region where the solid/
liquid interface is generally perpendicular to the
direction of heat-source travel, so that it becomes
favorable for one or more grains to grow in this
direction. The width of this zone can depend on
the pool shape. The region of the interface that
is perpendicular to the heat-source direction is
relatively small in an elongated weld pool, so
the width of axial grains will also be small. By
comparison, this perpendicular region is rela-
tively larger for an elliptical pool, so the axial
grain region can also be larger.
The large columnar grains and the potential
presence of centerline grain boundaries are gen-
erally undesirable from a weldability and
mechanical property point of view. Centerline
grain boundaries can often lead to solidification
cracking associated with solidification shrinkage
and low-melting-point films that become concen-
trated at the centerline. Fine, equiaxed grains are
desired over coarse columnar grains for improve-
ments in both cracking resistance and mechanical
properties (at low temperature). One effective
means for minimizing or eliminating the coarse
columnar grains is through manipulation of the
pool shape. Figure 13 shows an example of a
weld in which the arc was oscillated at a fre-
quency of 1 Hz in a direction normal to the
heat-source travel (Ref8). In this case, the contin-
uously changing direction of the solid/liquid
interface makes it difficult for the columnar
grains to extend over large distances, thus
providing a degree of grain refinement. Grain
size reduction can also be achieved through the
morphologies within the grains that can be cel-
lular, columnar dendritic, or equiaxed dendritic.
Cellular and columnar dendritic morphologies
develop due to breakdown of the initially planar
solid/liquid interface that forms at the fusion
line, while equiaxed dendrites form by nucle-
ation of solid in undercooled liquid, typically
near the weld centerline. Formation of these
features can be understood with the concept of
constitutional supercooling. The basics of this
topic 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 solute
into the liquid. The extent of solute enrichment
in the liquid progresses as solidification pro-
ceeds and the liquid composition follows the
liquidus line. The solute rejected by the solid
at the solid/liquid interface must be transported
away from the interface by diffusion and/or
convection in the liquid. If the solid/liquid
interface growth rate is relatively high (which
leads to a high rate of solute rejection) and/or
the 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 the
solid/liquid interface. Because solute enrich-
ment leads to a reduction in the liquidus tem-
perature (for an element that partitions to the
liquid), it follows that the presence of a solute
Fig. 13 Grain structure in a fusion weld of alloy 2014
made 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 a
welding speed of 250 mm/min (10 in./min). The weld in
(b) was made at a welding speed of 1000 mm/min (40
in./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
v Solidificação em soldagem
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
v Solidificação em soldagem
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
Fig. 15 Schematic illustrations showing (a) stability of a pla
temperature gradient and (b) breakdown of a plana
temperature gradient
G/R – super-
resfriamento
v Solidificação em soldagem
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
v Solidificação
A.S.D’Oliveira
2.4mm
substrato
Vergara, V.M., Tese de doutorado 2007
v Solidificação em soldagem
Descrever solidificação do
revestimento
A.S.D’Oliveira
v Solidificação
Ni12wt%Al
Ni30wt%Al
Explique o desenvolvimento das estruturas de solidificação considerando
que o desenvolvimento do composto intermetálico é exotérmico

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solidificacao de aço

  • 2. A.S.D’Oliveira Qual a temperatura de fusão dos elementos puros? Qual a temperatura de fusão da liga Pb40wt%Sn?
  • 3. A.S.D’Oliveira v Solidificação L G1 L S G2 = G1+ΔG T G T Tf ΔT ΔGv Gsólido Glíquido Temperatura de fusão = T de solidificação? interface
  • 4. A.S.D’Oliveira v Solidificação Nucleação homogênea G2=VSGs v+ 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 TL T r 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
  • 5. A.S.D’Oliveira 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
  • 6. A.S.D’Oliveira v Solidificação 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
  • 7. A.S.D’Oliveira v Solidificação 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
  • 8. A.S.D’Oliveira v Solidificação 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
  • 9. A.S.D’Oliveira v Solidificação Nucleação homogênea vs nucleação heterogênea Variação de energia livre para o mesmo r* Taxa de nucleação
  • 10. A.S.D’Oliveira 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 /m3 with with unit Mould walls not flat Critical radius for solid Nucleation in cracks occur with very little undercooling
  • 12. A.S.D’Oliveira 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
  • 13. A.S.D’Oliveira v Solidificação Crescimento – influência do escoamento de calor Crescimento planar Crescimento não planar
  • 15. A.S.D’Oliveira Crescimento em ligas metálicas - Equilibrio v Solidificação Para a liga Pb30wt%Sn qual a composição das fases nas temperaturas 220C 200C 190C
  • 16. A.S.D’Oliveira 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
  • 17. A.S.D’Oliveira 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
  • 18. A.S.D’Oliveira Desenvolvimento de dendritas Segregação do soluto no desenvolvimento de dendrítas Dendritas de um sistema Ni-Al José Eduard/oUnicamp v Solidificação
  • 19. A.S.D’Oliveira v Solidificação Crescimento celular - Frente de solidificação não planar
  • 21. A.S.D’Oliveira v Solidificação Formação de uma estrutura dendritica Relação com a estrutura de grão Resistência mecânica é proporcional ao espaçamento entre braços secundários das dendritas
  • 23. A.S.D’Oliveira v Solidificação Crescimento dendritico em um sistema eutético Al-Ni Com autorização de José Eduardo/Unicamp
  • 24. A.S.D’Oliveira v Solidificação Microestrutura de solidificação no equilibrio e resfriadas fora do equilibrio?
  • 28. A.S.D’Oliveira v Solidificação Solidificação eutética L -> α + β Eutético divorciado – volume de uma das fases é muito pequeno Eutético lamelar
  • 30. A.S.D’Oliveira v Solidificação Solidificação em soldagemSolidificação 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
  • 31. A.S.D’Oliveira Solidificação em soldagem v Solidificação Os parâmetros Ks, v, t e q irão determinar a morfologia da solidificação Condutividade Velocidade espessura
  • 32. A.S.D’Oliveira 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 Solidification John N. DuPont, Lehigh University MICROSTRUCTURAL EVOLUTION dur- ing solidification of the fusion zone represents one of the most important considerations for controlling the properties of welds. A wide range of microstructural features can form in the fusion zone, depending on the alloy compo- sition, welding parameters, and resultant solidi- fication conditions. The primary objective of this article is to review and apply fundamental solidification concepts for understanding micro- structural evolution in fusion welds. Microstructural Features in Fusion Welds Figures 1 through 3 schematically demon- strate the important microstructural features that must be considered during solidification in fusion welds (Ref 1, 2). On a macroscopic scale, fusion welds can adopt a range of grain morphologies similar to castings (Fig. 1), in which columnar and equiaxed grains can poten- tially form during solidification. The final grain structure depends primarily on alloy composi- tion and the heat-source travel speed. Although some of the concepts applicable to grain struc- ture formation in castings apply to welds, there are also some unique differences. While the columnar and equiaxed zones can form in cooled below its liquidus temperature due to compositional gradients in the liquid. The extent of constitutional supercooling in the weld is determined by the alloy composition, welding parameters, and resultant solidification parameters. Lastly, the distribution of alloying elements and relative phase fractions within the substructure (Fig. 3) are also important microstructural features that strongly affect weld-metal properties. The particular example shown in Fig. 3 represents a case in which extensive residual microsegregation of alloying elements exists across a cellular substructure after nonequilibrium solidification. This micro- segregation, in turn, produces a relatively high fraction of intercellular eutectic and associated secondary phase. The microsegregation behav- ior and concomitant amount of secondary phase that forms can each be understood with solute redistribution concepts. Lastly, dendrite tip undercooling can become important at high solidification rates associated with high- energy-density welding processes. Tip under- cooling can lead to significant changes in the primary solidification mode, distribution of sol- ute within the solid, and final phase fraction balance. Rapid solidification concepts are needed to understand these phenomena. All of these fundamental solidification concepts (nucleation, competitive grain growth, constitu- Fig. 1 Types of grain morphologies that can form in ASM Handbook, Volume 6A, Welding Fundamentals and Processes T. Lienert, T. Siewert, S. Babu, and V. Acoff, editors Copyright # 2011 ASM InternationalW All rights reserved www.asminternational.org
  • 33. A.S.D’Oliveira v Solidificação em soldagem Nucleação -> Crescimento epitaxial Metal de base apresenta uma coerência cristalográfica quase que perfeita; não existe barreira para a nucleação Grain Structure of Fusion Welds As described previously, the weld-metal grains will grow epitaxially from the preexist- ing base-metal grains. However, not all of these grains will be favorably oriented for continued growth. Two primary factors control the continued competitive growth of weld-metal grains: This is shown schematically in Fig. 10 (Ref 6). Grains at the fusion line may initially be ori- ented in a favorable direction for growth, but their direction may become unfavorable as the curved solid/liquid interface changes its posi- tion. These grains may then eventually be overgrown by other grains that exhibit more favorable orientation for growth as the solid/liq- uid interface sweeps through the weld. An example of this is shown on a weld in nearly pure (99.96%) aluminum in Fig. 11(a) (Ref 7). Fig. 9 Example of epitaxial growth from the fusion line in an electron beam weld of alloy C103. Original magnification: 400Â. Source: Ref 5 Fig. 10 Schemat growth near the fusion line. orientated grains at a Fig. 8 Comparison of free-energy changes associated with homogeneous nucleation, heterogeneous nucleation, and fusion welding Grãos na poça de fusão crescem diretamente sobre grãos pre- existentes no metal-base orientados favoravelmente
  • 34. A.S.D’Oliveira v Solidificação em soldagem 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) atching. An example of this in a fusion weld ade with the electron beam process is shown Fig. 9 (Ref 5). Note that there are no fine quiaxed grains at the fusion line, as often bserved in the chill zone of castings. Instead, e weld-metal grains grow directly from the pre- xisting base-metal grains. As a result, there is no arrier to formation of the solid. This condition is ferred to as epitaxial growth, because growth ccurs directly from the preexisting solid without e need for nucleation. Therefore, there is no ndercooling required to initiate solidification the fusion line, and solidification commences the liquidus temperature of the alloy. It should e noted that undercooling can still occur near the eld centerline due to the process of constitu- onal supercooling, as explained in more detail ter. This can lead to the formation of the central quiaxed zone often observed in fusion welds. ndercooling can also be required for nucleation new phases during solidification. Grain Structure of Fusion Welds As described previously, the weld-metal ains will grow epitaxially from the preexist- g base-metal grains. However, not all of these ains will be favorably oriented for continued owth. Two primary factors control the ontinued competitive growth of weld-metal ains: to the solid/liquid interface. The second crite- rion results from the preferred crystallographic growth direction, which, for cubic metals, is along the [100] directions. By combining these two criteria, it can be seen that grains that have their easy-growth direction most closely aligned to the solid/liquid interface normal will be most favorably oriented to grow, thus crowding out less-favorably-oriented grains. This phenomenon accounts for the columnar grain zone that is often observed in castings, shown schematically in Fig. 5. In this case, the grains that nucleated near the mold wall and have their easy-growth direction aligned normal to the mold/casting interface outgrow the less-favorably-oriented grains, leading to the 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 (Ref 6). Grains at the fusion line may initially be ori- ented in a favorable direction for growth, but their direction may become unfavorable as the curved solid/liquid interface changes its posi- tion. These grains may then eventually be overgrown by other grains that exhibit more favorable orientation for growth as the solid/liq- uid interface sweeps through the weld. An example of this is shown on a weld in nearly pure (99.96%) aluminum in Fig. 11(a) (Ref 7). to the growth rate. Because the growth rate is highest at the weld centerline, the release rate of latent heat is also highest at the weld center- line. However, the temperature gradient is at a Schematic illustrations of competitive grain 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
  • 35. A.S.D’Oliveira v Solidificação em soldagem 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 difficult to transport the latent heat away from the pool to permit solidification. This causes elongation of the pool near the weld centerline and leads to the teardrop shape. In this case, the direction of grain growth does not change (because the solid/liquid interface is no longer curved), and the grains grow straight toward the weld center- line until grains growing from each side of the weld intersect. This process typically leads to a centerline grain boundary, as shown in Fig. 11(b) (Ref 7). Axial grains that grow along the direction of heat-source travel can also occasionally be observed in fusion welds. The various types of grain morphologies are summarized in Fig. 12 (Ref 6). Examples of grain structures produced with elliptical and teardrop-shaped weld pools were shown in Fig. 11. Figures 12(c) and (d) rep- resent conditions in which an axial grain grows along the direction of the heat-source travel. These grains form in the region where the solid/ liquid interface is generally perpendicular to the direction of heat-source travel, so that it becomes favorable for one or more grains to grow in this direction. The width of this zone can depend on the pool shape. The region of the interface that is perpendicular to the heat-source direction is relatively small in an elongated weld pool, so the width of axial grains will also be small. By comparison, this perpendicular region is rela- tively larger for an elliptical pool, so the axial grain region can also be larger. The large columnar grains and the potential presence of centerline grain boundaries are gen- erally undesirable from a weldability and mechanical property point of view. Centerline grain boundaries can often lead to solidification cracking associated with solidification shrinkage and low-melting-point films that become concen- trated at the centerline. Fine, equiaxed grains are desired over coarse columnar grains for improve- ments in both cracking resistance and mechanical properties (at low temperature). One effective means for minimizing or eliminating the coarse columnar grains is through manipulation of the pool shape. Figure 13 shows an example of a weld in which the arc was oscillated at a fre- quency of 1 Hz in a direction normal to the heat-source travel (Ref8). In this case, the contin- uously changing direction of the solid/liquid interface makes it difficult for the columnar grains to extend over large distances, thus providing a degree of grain refinement. Grain size reduction can also be achieved through the use of inoculants. This process takes advantage of heterogeneous nucleation (discussed previ- ously) and liquid undercooling that occur due to constitutional supercooling. This topic is morphologies within the grains that can be cel- lular, columnar dendritic, or equiaxed dendritic. Cellular and columnar dendritic morphologies develop due to breakdown of the initially planar solid/liquid interface that forms at the fusion line, while equiaxed dendrites form by nucle- ation of solid in undercooled liquid, typically near the weld centerline. Formation of these features can be understood with the concept of constitutional supercooling. The basics of this topic 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 solute into the liquid. The extent of solute enrichment in the liquid progresses as solidification pro- ceeds and the liquid composition follows the liquidus line. The solute rejected by the solid at the solid/liquid interface must be transported away from the interface by diffusion and/or convection in the liquid. If the solid/liquid interface growth rate is relatively high (which leads to a high rate of solute rejection) and/or the 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 the solid/liquid interface. Because solute enrich- ment leads to a reduction in the liquidus tem- perature (for an element that partitions to the liquid), it follows that the presence of a solute Fig. 13 Grain structure in a fusion weld of alloy 2014 made 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 a welding speed of 250 mm/min (10 in./min). The weld in (b) was made at a welding speed of 1000 mm/min (40 in./min). Source: Ref 7 100 / Fundamentals of Fusion Welding minimum at the weld centerline, so it is difficult to transport the latent heat away from the pool to permit solidification. This causes elongation of the pool near the weld centerline and leads to the teardrop shape. In this case, the direction of grain growth does not change (because the solid/liquid interface is no longer curved), and the grains grow straight toward the weld center- line until grains growing from each side of the weld intersect. This process typically leads to a centerline grain boundary, as shown in Fig. 11(b) (Ref 7). Axial grains that grow along the direction of heat-source travel can also occasionally be observed in fusion welds. The various types of grain morphologies are summarized in Fig. 12 (Ref 6). Examples of grain structures produced with elliptical and teardrop-shaped weld pools were shown in Fig. 11. Figures 12(c) and (d) rep- resent conditions in which an axial grain grows along the direction of the heat-source travel. These grains form in the region where the solid/ liquid interface is generally perpendicular to the direction of heat-source travel, so that it becomes favorable for one or more grains to grow in this direction. The width of this zone can depend on the pool shape. The region of the interface that is perpendicular to the heat-source direction is relatively small in an elongated weld pool, so the width of axial grains will also be small. By comparison, this perpendicular region is rela- tively larger for an elliptical pool, so the axial grain region can also be larger. The large columnar grains and the potential presence of centerline grain boundaries are gen- erally undesirable from a weldability and mechanical property point of view. Centerline grain boundaries can often lead to solidification cracking associated with solidification shrinkage and low-melting-point films that become concen- trated at the centerline. Fine, equiaxed grains are desired over coarse columnar grains for improve- ments in both cracking resistance and mechanical properties (at low temperature). One effective means for minimizing or eliminating the coarse columnar grains is through manipulation of the pool shape. Figure 13 shows an example of a weld in which the arc was oscillated at a fre- quency of 1 Hz in a direction normal to the heat-source travel (Ref8). In this case, the contin- uously changing direction of the solid/liquid interface makes it difficult for the columnar grains to extend over large distances, thus providing a degree of grain refinement. Grain size reduction can also be achieved through the morphologies within the grains that can be cel- lular, columnar dendritic, or equiaxed dendritic. Cellular and columnar dendritic morphologies develop due to breakdown of the initially planar solid/liquid interface that forms at the fusion line, while equiaxed dendrites form by nucle- ation of solid in undercooled liquid, typically near the weld centerline. Formation of these features can be understood with the concept of constitutional supercooling. The basics of this topic 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 solute into the liquid. The extent of solute enrichment in the liquid progresses as solidification pro- ceeds and the liquid composition follows the liquidus line. The solute rejected by the solid at the solid/liquid interface must be transported away from the interface by diffusion and/or convection in the liquid. If the solid/liquid interface growth rate is relatively high (which leads to a high rate of solute rejection) and/or the 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 the solid/liquid interface. Because solute enrich- ment leads to a reduction in the liquidus tem- perature (for an element that partitions to the liquid), it follows that the presence of a solute Fig. 13 Grain structure in a fusion weld of alloy 2014 made 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 a welding speed of 250 mm/min (10 in./min). The weld in (b) was made at a welding speed of 1000 mm/min (40 in./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
  • 36. A.S.D’Oliveira v Solidificação em soldagem 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
  • 37. 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 v Solidificação em soldagem Relação entre taxa de crescimento e velocidade de soldagem (v) R=v.cosΘ R≈0, linha de fusão R≈v ,linha central
  • 38. A.S.D’Oliveira 38 Fig. 15 Schematic illustrations showing (a) stability of a pla temperature gradient and (b) breakdown of a plana temperature gradient G/R – super- resfriamento v Solidificação em soldagem 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
  • 39. 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 v Solidificação
  • 40. A.S.D’Oliveira 2.4mm substrato Vergara, V.M., Tese de doutorado 2007 v Solidificação em soldagem Descrever solidificação do revestimento
  • 41. A.S.D’Oliveira v Solidificação Ni12wt%Al Ni30wt%Al Explique o desenvolvimento das estruturas de solidificação considerando que o desenvolvimento do composto intermetálico é exotérmico