Welding - Analysis _ Modeling----iiiiidf

welding analysis

1. WELDING – ANALYSIS & MODELING
Acknowledgement: Prof. Sandip Kumar Saha
1

2. CONDUCTION - Transfer of Thermal Energy
between one part of a body and an Adjacent
part of the same body or between one body and
another which is in physical contact with it.

CONVECTION - Transfer of Thermal Energy
through mass movement.

RADIATION - Transfer of Thermal Energy by
the emission and absorption of Electromagnetic
Radiation.


Modes of Heat Transfer
In Welding
Heat source to work-piece : Radiative or Non-Radiative (FSW)
Work-piece to Atmosphere : Radiation and Convection
Within the Work-piece : Conduction
THERMAL EVOLUTION GOVERNS THE MICROSTRUCTURAL EVOLUTION
WHICH IN TURN DETERMINES THE MATERIAL PROPERTIES


2

3. Water :Water Level:: Heat :Temperature
Heat Transfer Analogy
3

4. �
�
Heat Transfer in Welding
�=�������
�
�=���� ��������
�=�����������
�=������� ������������
� =??????��������� ���� ���������� ����

�=���� �������� �����������
�
∞=??????������ �����������
�
�=������� �����������
�=�������
′
� ��������
�=����������
�
��??????=�������������
Conduction:
??????
??????�
��
��=�.���+�
Convection: �
���??????=�(�
�−�
∞)
Radiation: �
�??????�=��(�
�
4
−�
��??????
4
)
Through the Bulk
From the Surface
To the Surface
Heat flux: Typically Gaussian, e.g.
��,�,�=
3�
��
2
���−3
�−��
2
+�
2
�
2

z, x= welding and transverse directions, v =
source velocity, Q = heat transfer rate, c =
effective radius of the heat source.
For Friction-Stir Welding:
�∝�??????�?????????????????? �??????��????????????�� for �≤�
??????
4

5. Welding Heat Sources
Source Type Example Heat Intensity
(W/m
2
)
Electrical Arc Welding, Resistance Welding, Electroslag 10
6
−10
8

Chemical Oxy-fuel Gas Welding, Thermite Welding 10
6
−10
8

High Energy Laser Beam Welding, Electron Beam Welding 10
10
−10
12

Mechanical Friction-stir welding, Ultrasonic Welding, Explosion
Welding
10
4
−10
6

Others Diffusion Welding −
5

6. Power Density in GTAW
As the electrode tip becomes blunter, the diameter of the arc decreases
and the power density distribution increases
6

7. Weld Thermal Cycle
For a point situated at a higher distance from the
weld centerline:

•Peak temperature is low
•Heating and cooling rates are low
•Time taken to achieve the peak temperature is
high
7

8. Question !
8

9. Solution !
A
Finite Thermal Diffusivity
�=
�
��
�
Diffusivity is halved, lag will increase
9

10. Question !
Is it ever possible for a welding sample that
two points on a transverse line which are
equidistant from the weld-centerline but
situated on different sides, have different
thermal cycle?
10

11. Answer !
Yes, it is possible when two pieces which are being
welded together have different thermal diffusivities.
Example: Dissimilar Metal Welding

Is it ever possible for a welding sample that two points on a transverse line
which are equidistant from the weld-centerline but situated on different
sides, have different thermal cycle?
11

12. Weld Thermal Cycle
•Thermal Excursion- Weld temperature ranges from the ambient
temperature of the work environment to above the liquidus temperature
and possibly to boiling point and above for some very high energy
density processes
•The severity of this excursion in terms of the
Temperature reached
Time taken to reach them
Time remain at them
completely determines the effects on structure (both microstructural for
material changes and macrostructural for distortion)
•To quantify the thermal cycle mathematically, we need temperature
distribution in time and space coordinates

12

13. Thermal Cycle: Characterization via Thermocouples
13

14. •Thermocouples → at various points along weld path
•Approach of the heat source → rapid rise in temperature to a peak → a very short hold
at that peak → then a rapid drop in temperature once the source has passed by
•A short time after the heat from the source begins being deposited, → the peak
temperature & rest of the thermal cycle, reaches a quasi-steady state
•Quasi-steady state → balance achieved between the rate of energy input and the rate of
energy loss or dissipation
•Quasi-steady state → temperature isotherms surrounding a moving heat source remain
steady and seem to move with the heat source (away from edges)
Thermal Cycle: Quasi-Steady State
14

15. Time-Temperature Curves
15

16. •The peak temperature decrease with increasing distance from the source, and
more or less abruptly
•The maximum temperatures reached (T
mA ,T
mB, T
mc) decrease with distance
from the weld line and occur at times (t
mA, t
mB, t
mc) that increase. This allows the
peak temperature, T
p to be plotted as a function of time
•Peak temperature separates the heating portion of the welding thermal cycle
from the cooling portion
•At a time when points closest to a weld start cooling, the points farther away are
still undergoing heating. This phenomenon explains
– certain aspects of phase transformations that go on in the heat-affected zone,
– differential rates of thermal expansion/contraction that lead to thermally
induced stresses and, possibly, distortion
Time-Temperature Curves
16

17. Spatial Isotherms
17

18. Time-Temperature Curves
•Temperature distribution→ Controls microstructure, residual stresses and
distortions, and chemical reactions (e.g., oxidation)
•The influencing parameters
– the solidification rate of the weld metal
– the distribution of peak temperature in the Heat Affected Zone (HAZ)
– the cooling rates in the fusion and HAZ
– the distribution of heat between the fusion zone and the heat-affected
zone
•Requires mathematical formulation to quantify the influence of these
parameters
18

19. Time-Temperature Curves for Various Welding
processes
19

20. Multiple-Pass Weld-Cycle
20

21. Generalized Heat Flow Equation
This general equation needs to be solved for one, two, or three
dimensions depends on
oWeld geometry
oWhether the weld penetrates fully or partially
oParallel sided or tapered
oRelative plate thickness
1-D solution → thin plate or sheet with a stationary source or for
welding under steady state (at constant speed and in uniform cross
sections remote from edges) in very thin weldments
2-D solution → in thin weldments or in thicker weldments where the
weld is fully penetrated and parallel-sided (as in EBW) to assess both
longitudinal and transverse heat flow
3-D solution → thick weldment in which the weld is partial penetration
or non-parallel-sided (as is the case for most single or multipass welds
made with an arc source)
�
��
��
��=�.���+�
21

22. a)2-D heat flow for full-penetration welds in thin plates or sheets
b)2-D heat flow for full-penetration welds with parallel sides (as in EBW and
some LBW)
c)3-D heat flow for partial penetration welds in thick plate
d)3D, condition for near-full penetration welds
Weld Geometry and Dimensionality of Heat Flow
22

23. Question !
Initial Temperature = T
o
Heat Transfer Coefficient= h

23

24. Answer !
� − �??????
�����−�
∞ =
�
��
(�.��
2
.2��
��(�))
⇒� −�??????
����−�
∞=2���
2
��
�
��
��

Rate of Heat in – Rate of Heat Out = Rate of Heat Accumulation
⇒
�??????
� −�??????
���??????−??????∞
??????=??????
�??????�??????�
??????=??????�
=
1
2���
2
??????????????????
��
�=
2??????R
??????
�=0


Where ??????
���=��
2
+��
2
+2��2�=2��(�+2�)
Welding time
Final Temperature
Integrate and solve for T
final
It is very simplified case when the thermal diffusivity is infinite. However in reality there
are thermal gradients in the sample due to finite thermal diffusivity which makes the
mathematical treatment more complicated as it introduces
??????
2
??????�
2
term as well apart from the
??????
??????�

term.
24

25. Rosenthal’s Simplified Approach
•Assumption 1→ Energy input from the heat source is uniform and moves with a constant
velocity v along the x-axis of a fixed rectangular coordinate system. The net heat input to
the weld under these conditions is:
�=
??????��
�

where ?????? is the transfer efficiency of the process. E and I are the welding voltage (in V) and
current (in A), respectively, and v is the velocity of welding source (in m/s).
•Assumption 2 → Heat source is a point source, with all of the energy being deposited into
the weld at a single point which avoids complexities with density distribution of the
energy from different sources and restricted heat flow analysis to the heat-affected zone,
beyond the fusion zone or weld pool boundary.
•Assumption 3 → The thermal properties (thermal conductivity, density and specific heat)
of the material being welded are constants
•Assumption 4 → Modify the coordinate system from a fixed system to a moving system
25

26. Rosenthal’s Simplified Approach (Contd…)
•The moving coordinate system → replace x with ??????, where ?????? is the distance of
the point heat source from some fixed position along x axis, depending on the
velocity of welding, v

•Hence, ??????=�−��, (where t is the time)
�
2
�
�??????
2
+
�
2
�
��
2
+
�
2
�
��
2
=−
���
�
�
��
�??????
+
�
�
�
��
��


•This equation can be further simplified, in accordance with Rosenthal, if a
quasi-stationary temperature distribution exists.
•Temperature distribution around a point heat source moving at constant
velocity will settle down to a steady form, such that
??????T
??????�
=0, for
�
??????
=��������.
�
2
�
�??????
2
+
�
2
�
��
2
+
�
2
�
��
2
=−
���
�
�
��
�??????

26

27. Rosenthal’s Solution
•For thin plates (line source model):
�−�
�=−
�
2�k
�
−
????????????
2??????�
���/2�

�=
????????????�
??????
= Heat input from the welding source (in J/m)
k=Thermal conductivity (in J/m s
-1
K
-1
)
�=
�
�??????
�
= Thermal diffusivity (in m
2
/s)
�=√(??????
2
+�
2
+�
2
)= The distance from the heat source to a
particular fixed point (in m)
�
�= Bessel function of the first kind, zero order

•For thick plates (point source model):
�−�
�=−
�
2�kd
�
−
????????????
2??????
�
−
??????�
2??????
�


where �=depth of the weld (which for
symmetrical welds is half of the weld width
27

28. Rosenthal’s Solution: Simplified Form
Above equations can each be written in a simpler form, giving the
time-temperature distribution around a weld when the position from
the weld centerline is defined by a radial distance, r, where
�
2
=�
2
+�
2

•For thin plates:
�−�
�=−
�
�
�√(4�k��
��)
�
−
�
2
4??????�
•For thick plates:
�−�
�=−
�
�
2���
�
−
�
2
4??????�
28

29. Dimensionless Weld Depth vs. Dimensionless
Operating Parameter
•Based on Rosenthal’s solution of the simplified three dimensional heat flow
equation, Christiansen et al. (1965) derived theoretical relationships between
a weld bead’s cross-sectional geometry and the welding process operating
conditions using dimensionless parameters.
•Dimensionless weld width, D and dimensionless operating parameter, n are,
�=
��
2�
�
��� �=
��
4���
��
�
2
(�
�−�
�)

•Data obtained from different materials and processes can be interrelated
through the dimensionless parameters for weld depth and weld operating
parameter
29

30. �=
��
2�
�

�=
��
4���
��
�
2
(�
�−�
�)


D vs. n
d = depth of penetration of the weld,
v = welding speed (m/s),
�
�= thermal diffusivity of the base
material (as a solid),
Q = rate of heat input to the workpiece
(J/s),
T
m = melting point of the base material
(the workpiece), and
T
o = temperature of the workpiece at the
start of welding.
For a symmetrical weld bead the width
of the weld bead w = 2d→ Cross-
sectional area of the weld bead can be
determined
Can be applied to the heat-affected zone by simply
substituting T
H for T
m where T
H is the temperature of
some relevant phase transformation that could take
place
30

31. Cooling Rate vs. n
31

32. Simplified Equations for Approximating
Welding Conditions: Peak Temperatures
Predicting metallurgical transformations (melting, austenitization,
recrystallization of cold-worked material, etc.) at a point in the solid
material near a weld requires some knowledge of the maximum
temperature reached (�
�) at that specific location.

For a single-pass, full-penetration butt weld in a sheet or a plate, the
distribution of peak temperatures (T
p) in the base material adjacent to
the weld is given by:
1
�
�−�
�
=
��
���2��
�
+
1
�
�−�
�

t = Thickness of the base material (mm)
y = 0 at the fusion zone boundary and where T
p = T
m
32

33. Question !
33

34. 1
�
�−�
�
=
��
���2��
�
+
1
�
�−�
�

Answer !
�=�
��
�
=720
�
��

34

35. •Peak temperature equation can be used to calculate the width of the
HAZ.

•Define �
�=�
�������??????���??????����

•Width of the HAZ is determined by the value of y that yields a T
p
equal to the pertinent transformation temperature (recrystallization
temperature, austenitizing temperature, etc.).

•Equation cannot be used to estimate the width of the fusion zone,
since it becomes unsolvable when

�
�=�
�������
Simplified Equations for Approximating
Welding Conditions: HAZ Width
35

36. Question !
(a)Estimate the width of Heat affected zone if �
�������??????���??????����=730
�
�
(b)Estimate the width of Heat affected zone if the sample plate was tempered at 430
�
�
as well as preheated at 200
�
�
(c)Estimate the width of Heat affected zone if the sample plate was tempered at 430
�
�
without preheating
(d)Estimate the width of Heat affected zone if the sample plate was tempered at 430
�
�
without preheating but the heat input rate is increased by 50%

36

37. �=�
��
�
=720
�
��

Answer !
37

38. •The rate at which weld metal solidifies can have a profound effect on its
microstructure, properties, and response to post weld heat treatment

•The solidification time can be approximated as:
�
� =
��
���
2����
��
�−�
�
2
����� �=������ ����

•The solidification rate, which is derived from the solidification time, helps
determine the nature of the growth mode (with temperature gradient) and the
size of the grains
Simplified Equations for Approximating
Welding Conditions: Solidification Rate
38

39. Question !
39

40. �
� =
??????���??????
2���C�??????�−??????�
2
����� �=������ ����
Answer !
40

41. •The rate of cooling influences
coarseness or fineness of the resulting structure
homogeneity, distribution and form of the phases and constituents in the
microstructure, of both the FZ and the HAZ for diffusion controlled
transformations
•Cooling rate determines which transformation (phase) will occur and, thus,
which phases or constituents will result.
•If cooling rates are too high in certain steels → hard, untempered martensite →
enbrittling the weld → adds susceptibility to embrittlement by hydrogen.
•By calculating the cooling rate, it is possible to decide whether undesirable
microstructures are likely to result.
•Preheat → To reduce the cooling rate. Cooling rate is primarily calculated to
determine the need for preheat.
Simplified Equations for Approximating Welding
Conditions: Cooling Rates
41

42. •For thick plates
R=
2���
�−�
�
2
H
net

•For thin plates

R=2����
��
�−�
�
3
�
H
net
2

Simplified Equations for Approximating
Welding Conditions: Cooling Rates (Contd…)
�=������� ���� �� ��� ���� ����������
�
�=���� ��������
�
�=����������� �� ����� ��� ������� ���� �� ����������
�=������� ������������
�=��������� �� ��� ���� �����
�
�=������� �����������


Increasing initial temperature, T
o or applying preheat, decreases the cooling rate
42

43. Relative Plate Thickness Factor (??????)
??????=�
��
��
�−�
�
�
���
0.5

??????<0.75⇒&#3627408455;&#3627408469;&#3627408470;&#3627408475; &#3627408451;&#3627408473;&#3627408462;&#3627408481;&#3627408466; &#3627408440;&#3627408478;&#3627408482;&#3627408462;&#3627408481;&#3627408470;&#3627408476;&#3627408475; &#3627408444;&#3627408480; ??????&#3627408462;&#3627408473;&#3627408470;&#3627408465;
??????>0.75⇒&#3627408455;&#3627408469;&#3627408470;&#3627408464;&#3627408472; &#3627408451;&#3627408473;&#3627408462;&#3627408481;&#3627408466; &#3627408440;&#3627408478;&#3627408482;&#3627408462;&#3627408481;&#3627408470;&#3627408476;&#3627408475; &#3627408444;&#3627408480; ??????&#3627408462;&#3627408473;&#3627408470;&#3627408465;

43

44. Question !
44

45. Answer !
45

46. Answer ! (Contd…)
46

47. Heat Source Efficiency
oLBW: High reflectivity of metal surfaces causes loss
oPAW: Much higher than LBW because reflectivity is not a problem.
oGTAW: No heat losses from arc plasma to water-cooled constricting torch nozzle. With DCEN,
imparting electrons are a major source of heat transfer to the workpiece.
oGMAW, SMAW: Heat transfer to the electrode can be transferred back to the workpiece through metal
droplets
oSAW: Arc is covered with a thermally insulating blanket of molten slag and granular flux.
oEBW: Keyhole in EBW acts like a “black body” trapping the energy from the electron beam.
47

48. Reinforcement
Heat
Affected
Zone
Melted Base Metal
A
w = Cross Section of Weld = A
m + A
r
For Autogenous Weld (no filler metal) A
w = A
m

Melting efficiency is the fraction of the net energy input that is used for
actually melting material.
Q =
Heat Required to elevate
solid to melting point
+ Latent Heat
of Fusion
Heat Required to melt
a Given Volume of Weld
=
Melting Efficiency
48
where V is the welding speed, H
base = the energy required to raise a unit volume of base metal to the melting point
and melt it, and H
filler = the energy required to raise a unit volume of filler metal to the melting point and melt it.

49. Melting Efficiency (Contd…)
49

50. Parameters Affecting Welding
•The shape of the melt, size & heat
distribution, is a function of
– Material (&#3627409148;)
– Welding speed
– Welding power/energy density
– Weldment plate thickness
•Increasing thermal conductivity
– tends to cause deposited heat to
spread
– Smaller welds for a given heat
input and melting temperature
•For a given heat input, the lower
the melting point, the larger the
weld
50

51. Effect of Heat-Flow Paths
51

52. Effect of Welding Parameters on Temperature
Gradient
1100 aluminum: (a) higher welding speed and heat input; (b)
lower welding speed and heat input.
52

53. Effect of Power Density on the Weld Shape
53

54. Effect of Welding Parameters on Grain Structure
GTAW of 6061 aluminum: (a) 70A & 11V heat
input and 5.1 mm/s welding speed; (b) 120A &
11V heat input and 12.7 mm/s welding speed
Low welding speed and heat input  Low
constitutional supercooling  Columnar grain
formation

High welding speed and heat input  Less thermal
gradient and high solidification rate 
Heterogeneous nucleation aided by high
constitutional supercooling at the end of the weld
pool  Formation of equaixed grains near weld
centerline and usual formation of columnar grains
away from the weld centerline
54

55. Velocity 0 Low Medium High Very High
Plan View Circle Elliptical Elongated
Ellipse
Tear Drop Detached
Tear Drop
3D View Hemi-
Spherical
Prolate
Spheroidal
Elongated
Prolate
Spheroidal
3D Tear
Drop
3D Tear
Drop
Effect of Welding Speed on HAZ
•For a stationary (spot) weld, the shape, is round (plan view), and approximately
hemispherical in 3-D
•Once the source is moved with constant velocity, the weld pool and surrounding
HAZ become elongated to an elliptical shape (plan view), and prolate
spheroidal in 3-D
•With increased velocity, these zones become more and more elliptical
•At some velocity (for each specific material), a tear drop shape forms, with a
tail at the trailing end of the pool. 55

56. Tear Drop Formation
•Increasing velocity →elongates the
teardrop more and more, narrows
the fusion and heat affected zone
→ overall melted volume constant
•Very high welding speeds → the
tail of the teardrop weld pool
detaches → isolate regions of
molten metal → lead to shrinkage-
induced cracks along the centerline
of the weld
56

57. Effect of Weldment Thickness
Thick weldment →Small weld pool and heat affected zone
57

58. Effect of Energy Density
•Increased energy density → increases the efficiency of melting →
increases the amount of melting (especially in the depth direction)
→ decreases the heat-affected zone.

•Shape of weld pool & HAZ will be distorted by any asymmetry
around the joint.

•Asymmetry might be the result of the relative thermal mass (e.g.
thickness) of the joint elements as well as their relative thermal
properties (T
m, k & C
p)
58

59. Summary
•Heat transfer in welding is a function of welding parameters
•Choice of welding heat source makes a difference in the input heat intensity
and its distribution
•Heat transfer determines the thermal cycle at any given point in the sample
which in turn governs the phase transformation and hence the final
microstructure
•Rosenthal’s approach for heat transfer in welding is the most simplified one
•Rosenthal’s analytical solution leads to approximated formulae of
temperature distribution, solidification time, cooling rates, peak temperatures,
HAZ width for thermally thin and thick plates and helps in choosing the
correct set of parameters

59

60. Thank you
60