Welding: Solidification and microstructure

Abstract

Parameters that control the solidification of castings also control the solidification and microstructure of welds. However,
various physical processes that occur due to the interaction of the heat source with the metal during welding add a new dimension
to the understanding of the weld pool solidification. Conventional theories of solidification over a broad range of conditions
can be extended to understand weld pool solidification. In certain cases, because of rapid cooling rate effects, it is not
unusual to observe nonequilibrium microstructures. Recent developments in the application of computational thermodynamics
and kinetic models, studies on single-crystal welds, and advanced in-situ characterization techniques have led to a better
understanding of weld solidification and microstructures.

Full text

Welding: Solidification and Microstructure
S.A. David, S.S. Babu, and J.M. Vitek
Parameters that control the solidification of castings also control the solidification and
microstructure of welds. However, various physical processes that occur due to the
interaction of the heat source with the metal during welding add a new dimension to the
understanding of the weld pool solidification. Conventional theories of solidification over a
broad range of conditions can be extended to understand weld pool solidification. In certain
cases, because of rapid cooling rate effects, it is not unusual to observe nonequilibrium
microstructures. Recent developments in the application of computational thermodynamics
and kinetic models, studies on single-crystal welds, and advanced in-situ characterization
techniques have led to a better understanding of weld solidification and microstructures.
INTRODUCTION
In welding, as the heat source interacts with the material,
the severity of thermal excursions experienced by the
material varies from region to region, resulting in three
distinct regions in the weldment (Figure 1). These are the
fusion zone (FZ), also known as the weld metal, the heat-
affected zone (HAZ), and the unaffected base metal (BM).
The FZ experiences melting and solidification, and its
microstructural characteristics are the focus of this article.
The microstructure development in the FZ depends on the
solidification behavior of the weld pool. The principles of
solidification control the size and shape of the grains,
segregation, and the distribution of inclusions and porosity.
Solidification is also critical to the hot-cracking behavior of
alloys. Sometimes, it is convenient to consider the FZ as a
minicasting. Therefore, parameters important in determining microstructures in casting, such
as growth rate (R), temperature gradient (G), undercooling (∆T), and alloy composition
determine the development of microstructures in welds as well. Comprehensive reviews of
weld pool solidification based on these parameters are available in the literature.1,2
Figure 1. A schematic diagram
showing the interaction between
the heat source and the base metal.
Three distinct regions in the
weldment are the fusion zone, the
heat-affected zone, and the base
metal.
Most knowledge of weld pool solidification is derived from the extrapolation of the
knowledge of freezing of castings, ingots, and single crystals at lower thermal gradients and
slower growth rates.1–6 In addition, rapid solidification theories have been extended to welds
solidified at very high cooling rates.7–14However, microstructure development in the FZ is
more complicated15,16because of physical processes that occur due to the interaction of the
heat source with the metal during welding, including re-melting, heat and fluid flow,
vaporization, dissolution of gasses, solidification, subsequent solid-state transformation,
stresses, and distortion. These processes and their interactions profoundly affect weld pool
solidification and microstructure. In recent years, phenomenological modeling of welding
processes has provided unprecedented insight into understanding both the welding process
and the welded materials. A variety of sophisticated models that employ analytical and

numerical approaches are capable of describing many physical processes that occur during
welding.15–25
During the past 15 years, significant progress has been made in understanding the
solidification behavior of the weld pool and the evolution of microstructure in the FZ. The
application of computational thermodynamic and kinetic tools has enhanced the
understanding of weld solidification behavior of complex multi-component systems.
Advanced in-situ characterization techniques have enabled the characterization of phase
formation and non-equilibrium effects during weld pool solidification. The use of model
alloy single crystals resulted in new insight into the role of weld pool geometry and dendrite
growth selection processes in the development of weld microstructure. This overview will
address some of the current progress in understanding weld pool solidification.
WELD POOL SHAPE
An important aspect of weld solidification is the dynamics
of weld pool development and its steady-state geometry.
Weld pool shape is important in the development of grain
structure and dendrite growth selection process.6, 26-
29Thermal conditions in and near the weld pool and the
nature of the fluid flow have been found to influence the
size and shape of the weld pool.16–18,24,25Significant advances have been made in recent years to
understand, in greater detail, the dynamics of the heat and fluid flow in the weld and the
subsequent development of the pool shape. To a large extent, convective flow in the weld
pool determines weld penetration. For arc-welding processes, convection in the weld pool is
mainly controlled by buoyancy, electromagnetic forces, and surface-tension forces. In
actuality, depending on the interplay between various driving forces, the convective flow
could be simple or more complex with a number of convective cells operating within the
weld pool, as shown in Figure 2.
Figure 2. The calculated fluid-flow
pattern in a stainless-steel
stationary arc weld pool 25 s after
the initiation of the arc.
Recent theoretical developments include the formulation of a free-surface computational
model to investigate coupled conduction and convection heat-transfer models to predict not
only weld pool geometry but also thermal profiles to estimate thermal gradients and cooling
rates critical to determining solidification structure.25 In addition to computational models,
neural net models have been applied to predict weld pool geometry.30 These models, which
are empirical in nature, are useful when applied to complex welding processes such as hybrid
laser-arc welding.30
MICROSTRUCTURE
Unlike in casting, during welding, where the molten pool is moved through the material, the
growth rate and temperature gradient vary considerably across the weld pool. Geometrical
analyses have been developed that relate welding speed to the actual growth rates of the solid
at various locations in the weld pool.1,2,27

Along the fusion line the growth rate is low while the temperature gradient is steepest. As the
weld centerline is approached, the growth rate increases while the temperature gradient
decreases. Consequently, the microstructure that develops varies noticeably from the edge to
the centerline of the weld. Most of these microstructural features can be interpreted by
considering classical theories of nucleation and growth.
In welds, weld pool solidification often occurs without a nucleation barrier. Therefore, no
significant undercooling of the liquid is required for nucleation of the solid. Solidification
occurs spontaneously by epitaxial growth on the partially melted grains. This is the case
during autogenous welding. In certain welds, where filler metals are used, inoculants and
other grain-refining techniques are used in much the same way as they are in casting
practices. In addition, dynamic methods for promoting nucleation such as weld-pool stirring
and arc oscillation have been used to refine the weld metal solidification structure.2 Although
the mechanisms of nucleation in weld metal are reasonably well understood, not much
attention is given to modeling this phenomenon. Often, weld solidification models assume
epitaxial growth and for most of the cases the assumption seems to be appropriate. However,
to describe the effects of inoculants, arc oscillations, and weld pool stirring, heat and mass
transfer models18,24,25 have to be coupled with either probabilistic models such as cellular
automata31–33or deterministic models using the fundamental equations of nucleation as
described elsewhere.34
Figure 3. A scanning-electron micro
g
raph showin
g
the development of dendrites in a nickel-based
superalloy single-crystal weld.
Figure 4. An optical micrograph shows the change in
dendrite morphology from cellular to dendritic as the
growth velocity increases toward the center of spot weld
(from bottom to top) after the spot weld arc is
extinguished.
During growth of the solid in the weld pool, the shape of the solid-liquid interface controls
the development of microstructural features. The nature and the stability of the solid-liquid
interface is mostly determined by the thermal and constitutional conditions (constitutional
supercooling) that exist in the immediate vicinity of the interface.35,36 Depending on these
conditions, the interface growth may occur by planar, cellular, or dendritic growth. Dendritic
growth of the solid, with its multiple branches, is shown in Figure 3. Another example of

changes in solidification morphology directly related to welding conditions is shown in
Figure 4. This figure shows a spot weld on a nickel-based superalloy in which the
morphology changes from cellular to dendritic as the growth velocity increases toward the
center of the spot weld after the spot weld arc is extinguished. The micrograph also shows the
elimination of a poorly aligned dendrite, which is discussed in greater detail later. The
criterion for constitutional supercooling for plane front instability can be mathematically
stated as:
plane front will be stable (1)
planar instability will occur (2)
where GL is the temperature gradient in the liquid, R is the solidification front growth rate,
∆TO is the equilibrium solidification temperature range (at composition CO), and DL is the
solute diffusion coefficient in liquid.
The temperature gradient and growth rate are important in the combined forms GR (cooling
rate) and G/R since they influence the scale of the solidification substructure and
solidification morphology, respectively. Although the method of using GR and G/R relations
to understand the solidification modes is simple and elegant, modeling of solidification
morphology in a typical weld must consider other factors such as fluid flow and the effect of
base plate texture. Recent work on the in-situ observation of weld pool solidification using a
transparent analog-metal system has produced a greater understanding of the evolution of
growth morphology in welds.37
Solute distribution during weld pool solidification is an important phenomenon resulting in
segregation that can significantly affect weldability, microstructure, and properties. Studies
extending different solidification models to describe solute distribution during weld
solidification are summarized elsewhere.2 In describing the solute distribution under dendritic
growth conditions, consideration should be given to redistribution at the dendrite tip and in
the interdendritic regions. In welds, since the microstructures are much finer in scale than in
castings, the contribution to the total tip undercooling due to the curvature effect is
significant.2 The effect of increased undercooling at the dendrite tip would be to solidify at a
composition closer to the overall composition and thus reduce the extent of microsegregation.
Dendrite tip undercoolings in welds have been estimated by measuring dendrite core
compositions for Al-Cu and Fe-Nb systems after welding.38 For solute distribution in the
interdendritic regions it may be sufficient to extend the solidification models for
microsegregation in castings to welds. This can be achieved by the Schiel equation39 or
modified Schiel equation that considers the diffusion in the solid during welding.38,40
As mentioned earlier, since solidification of the weld metal proceeds spontaneously by
epitaxial growth of the partially melted grains in the base metal, the FZ grain structure is
mainly determined by the base metal grain structure and the welding conditions.2
Crystallographic effects will influence grain growth by favoring growth along particular

crystallographic directions, namely the easy growth
directions.35,36,41 For cubic metals, these easy
directions are <100>. Which of these <100>
directions will be selected, a fundamental question
that is important when welding single crystals, will
be addressed later. Conditions for growth are
optimum when one of the easy growth directions
coincides with the heat-flow direction. Thus,
among the randomly oriented grains in a
polycrystalline specimen, those grains that have one
of their <100> crystallographic axes closely aligned
with heat-flow direction will be favored. Without
additional nucleation, this will promote a columnar
grain structure. Figure 5 shows clearly the grain
growth selection process in an iridium alloy weld.
Under certain conditions it is also possible to
change the epitaxial columnar growth to equiaxed growth by inoculation or changing welding
conditions.28,42,43
Figure 5. Epitaxial and columnar growth
near the fusion line in an iridium alloy
electron-beam weld. The figure also shows
the grain-growth selection process of the
grains from the fusion line.
SOLIDIFICATION OF SINGLE-CRYSTAL WELDS
Studies on Fe-15Ni-15Cr single-crystal welds carried out during the last ten years have
advanced significantly the fundamental understanding of weld pool solidification.27–29 These
studies have identified the effect of crystallography on the development of FZ microstructure.
A geometrical model has been developed that provides a three-dimensional relationship
between travel speed, solidification velocity, and dendrite growth velocity that predicts stable
dendrite growth directions as a function of weld pool shape and weld orientation. The regions
of differently oriented dendrites develop because growth occurs along the preferred <100>
growth directions, and the choice of which growth direction will prevail among the six
possible variants is based on the relation between weld pool shape and dendrite orientation.
The model’s capability to predict microstructural features in an Fe-15Ni-15Cr singlecrystal
electron beam weld made along [100] on (001) plane is shown in Figures 6a and 6b.
a b
Figure 6. (a) An Fe-15Cr-15Ni single-crystal electron-beam weld
made along [100] direction on (001) plane, and (b) the calculated
dendritic growth pattern for a similar weld orientation in (a).
Figure 7. An optical micrograph of overlapping
laser spot welds on PWA-1480 single-crystal
nickel-based superalloy showing the formation of
stray grains at the center of the weld.
Recently, these basic concepts have been extended to commercial nickel-based superalloy
single-crystal technology technology used in jet and land-based turbine engines.44–46 Unlike in
Fe-15Ni-15Cr single-crystal welds where the single crystallinity of the weld was maintained,

nickel-based superalloys are extremely prone to stray grain formation (as shown in Figure 7).
This phenomenon can be attributed to constitutional supercooling46,47or dendrite
fragmentation48 ahead of the dendritic front that may nucleate new grains. Recent studies
suggest that the constitutional supercooling may be the controlling mechanism for straygrain
formation.44,47
NONEQUILIBRIUM SOLIDIFICATION
Because of the rapid cooling rates encountered during welding, especially during high-power-
density processes such as electron and laser-beam welding, it is not uncommon to observe
nonequilibrium solidification effects. Most nonequilibrium features in welding can be
associated with two phenomena that take place as the solidification growth velocities
increase. First, the partitioning of solute between solid and liquid, described by the
partitioning coefficient k (= solid composition/liquid composition, both at the solid/liquid
interface), is affected by growth rate such that, as the growth velocity increases, k deviates
from the equilibrium value and approaches a value of 1. Second, high growth velocities can
lead to a change in the solidification mode and result in nonequilibrium phase formation. It is
noteworthy that these phenomena are closely interrelated.
As discussed earlier, the solidification morphology also changes with growth velocity and is
influenced by the extent of solute partitioning and the phase that forms. In this section,
nonequilibrium solute partitioning will be addressed, but even equilibrium solute partitioning
can lead to nonequilibrium phase formation because of residual microsegregation; this can be
evaluated by the Scheil equation and its variants.
A b
Figure 8. Photomicrographs of high-speed laser welds showing (a) fully ferritic microstructure in
type-312 stainless steel with negligible secondary austenite formation and (b) nonequilibrium
austenitic microstructure in type-308 stainless steel without any ferrite formation.
Theories have been developed to relate the degree of partitioning to the growth rate.14 For
high growth rates that may be prevalent during welding, reduced solute partitioning resulting
from a change in k can lead to a variety of effects including morphological changes to plane
front solidification, changes in the solidification phase, and less segregation in the weld
microstructure. An example is shown in Figure 8a, where an autogenous laser weld was made
on a 312 stainless-steel weld overlay pad. The laser-weld microstructure is fully ferritic,
which reflects the fact that minimal partitioning during solidification prevented secondary
austenite formation, as found in the weld overlay. In this case, the rapid cooling conditions
during laser welding also prevented solid-state transformation of the solidified ferrite to
austenite.
Numerous examples of nonequilibrium solidification in austenitic stainless steels have been
documented over the years.8–11,49 An example is shown in Figure 8b. In this case, the
micrograph is of an autogenous laser weld on a 308 stainless-steel weld overlay. The base
material (weld overlay), shown on the left, shows the typical weld microstructure in this

material consisting of austenite and residual ferrite. This is produced by primary ferrite
solidification followed by secondary austenite solidification and ferrite transformation to
austenite during solid-state cooling. The laser-weld microstructure is completely different. It
is a fully austenitic microstructure produced by nonequilibrium primary austenite
solidification.
Another example of nonequilibrium solidification in a low-alloy steel is presented in the
section on in-situ observations. It is also noteworthy that the laser-welded microstructure
does not show any dendritic structure; this is another example of the solidification
morphology changing to planar solidification at high growth rates. Extremely high growth
rates are not necessary to produce nonequilibrium solidification. A series of experiments in
which welds were made across dissimilar stainless steels showedthat nonequilibrium
solidification can be found even under less extreme solidification conditions.50 Current
research focuses on the quantitative prediction of these transitions from equilibrium to
nonequilibrium conditions by numerical modeling of weld solidification in
multicomponentalloys.
MODELING WELD SOLIDIFICATION
A b
C d
Figure 9. Quasi-binary diagrams showing liquid, austenite, and δ-ferrite phase regions in Fe-Cr-Ni
alloy systems with (a) 0.01 wt.% nitrogen and (b) 0.1 wt.% nitrogen. The calculated variation of
phase fraction as a function of cooling time from 1,750 K using a diffusion-controlled growth model
for Fe-Cr-Ni alloy systems with (c) 0.01 wt.% nitrogen and (d) 0.1 wt.% nitrogen.
In addition to heat and fluid-flow models used for welding, additional modeling techniques
are now available that can help describe the phase evolution during weld solidification.
Foremost among these are computational thermodynamic models for multicomponent
systems that can predict the primary solidification phases, the solidification phases that may
form as a result of solute partitioning during solidification, and the stability of these phases as
the weldments are cooled to room temperature. For example, one such program,
ThermoCalc,51 has been used to calculate a phase diagram for a hypothetical Fe-20Cr-8Ni-xN
(wt.%) alloy as a function of temperature and chromium content for two different nitrogen
concentrations, x = 0.01% and x = 0.1% (Figure 9a and Figure 9b, respectively). The plots
show that at 20% chromium, for both 0.01% nitrogen and 0.1% nitrogen, the primary
solidification will occur by δ-ferrite. However, the phase stability following solidification is

quite different. In the case of the low-nitrogen stainless steel, at 800°C, a mixture of ferrite
and austenite is expected while a fully austenitic structure is predicted for the high-nitrogen
alloy in equilibrium at the same temperature. Such calculations are simple and can be used to
identify the effect of alloy composition on the phase stability during and after weld
solidification. Perhaps the greatest benefit that results from these models is that the
calculations can be performed easily for complex multicomponent systems with ten or more
constituents.
Kinetics models based on diffusion-controlled growth can be integrated with computational
thermodynamics models to provide valuable information on the time evolution of the
microstructure.52 For example, in the case of welding, calculations can be made to identify the
effect of cooling rate on the final microstructure.
Such calculations were made for the two Fe-20Cr-8Ni-xN alloys described above. The
calculations assumed a half-dendrite arm spacing of 100 µm and a cooling rate of 10 Ks–1.
The model considered a peritectic solidification mode, with primary ferrite formation and
secondary austenite formation at the ferrite/liquid interface. The results of the calculations are
shown in Figure 9c and Figure 9d, where the phase fractions are plotted versus time. In the
case of the high-nitrogen welds, the austenite growth into ferrite phase was found to increase
rapidly after ~35 s. Thus, the diffusion-controlled growth models allow the calculation of the
amount of δ-ferrite that may be retained after solidification and the description of the weld
microstructure evolution in stainless steels to a certain extent. These calculations can be
repeated for different weld cooling rates and dendrite arm spacings to evaluate the effect of
welding process parameters on the microstructure
As noted in the previous section, nonequilibrium solidification may take place at higher
cooling rates and solidification growth rates. Recent advances in interface-response function
models53 can be used to evaluate the phase selection during solidification in multicomponent
steels by coupling them with computational thermodynamic software. The interface-response
function model evaluates the dendrite tip radius, tip temperature, and partition coefficients as
a function of interface velocity for various competing phases and determines which
solidification phase is kinetically favored. The next step in the modeling of weld
solidification is to couple computational thermodynamic, diffusion-controlled growth models,
crystallographic geometry models,27 and cellular automata54 models to depict the fine details
of microstructure morphology as a function of composition and welding process parameters.
IN-SITU OBSERVATIONS
Modeling activities must be accompanied by careful experimental measurements in order to
validate the models. Traditionally, the evaluations of models have been made by post-weld
characterization of solidification microstructures using optical microscopy and analytical
electron microscopy. However, interpretation of weld behavior by examination of welds at
room temperature is often incomplete and complicated by phase transformations that take
place upon cooling. There is a growing need to monitor solidification microstructure in-situ
during weld cooling. Many techniques are currently available to observe the weld
solidification features in-situ, including high-speed, high-resolution photography on real
materials55 or on metal analog transparent systems,37 and time-resolved x-ray diffraction
(TRXRD) with synchrotron radiation.56

Recent results from metal analog transparent systems, combined with detailed numerical heat
transfer models and solidification theories, led to the identification and analysis of
instabilities at the liquid-solid interface while welding at high speeds.37 Additional work has
focused on nonequilibrium phase selection during weld solidification in an Fe-C-Al-Mn steel
by means of in-situ observations using the TRXRD technique.57,58 In this research, the
equilibrium primary solidification phase is δ-ferrite and this was confirmed by TRXRD
measurements on slowly cooled spot welds. However, under rapid cooling conditions, the
TRXRD measurements showed the formation of primary austenite (Figure 10). Research in
stainless steels has shown that it is possible to form nonequilibrium primary austenite under
rapid solidification conditions but this is the first time such a phenomenon was observed in a
low-alloy steel. In these steels, in-situ measurements are particularly valuable since behavior
at elevated temperatures is masked by subsequent solid-state transformation of ferrite to
austenite and austenite to martensite. Time-resolved x-ray diffraction measurements have
proven to be ideal for identifying competing phase-transformation mechanisms under
nonequilibrium weldcooling conditions. This technique has been applied to other alloy
systems and exciting new insight into issues relating to weld solidification issues is being
achieved.59
Figure 10. An image representation of time-resolved x-ray
diffraction data that shows the formation of primary
austenite (fcc) from liquid during rapid cooling.
ACKNOWLEDGEMENTS
This research is sponsored by the Division of Materials Sciences and Engineering, Office of
Basic Energy Sciences, U.S. Department of Energy, under Contract DE-AC05-00OR22725
with UT-Battelle, LLC.

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For more information, contact S.A. David, Oak Ridge National Laboratory, Metals &
Ceramics Division, Building 4508, MS 6095, Oak Ridge, Tennessee 37831-6095; (865)
574-4804; fax (865) 574-4928; e-mail Davidsa1@ornl.gov.
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