Diffusion W e l d i n g of Reactive and
Refractory Metals to Stainless Steel
Use of the proper filler metal permits the joining of
Types 430 and 321 stainless steel to
titanium,
tantalum and other refractory base metals
BY R. LISON A N D ). F. STELZER
Introduction
The utilization of costly metals and
alloys is increasing. As a result, there is
a demand for methods to join these
expensive metals with the more c o m monly used metals. This requirement
is not always caused by cost, but also
by the desire for new, basically
improved structures.
A precondition for the utilization of
the advantageous properties of dissimilar metals w i t h i n one structure is the
generation of transition joints which
fulfill proposed requirements; these
include a long lifetime at high temperatures for gas turbines or neutron
compatibility and corrosion resistance
in nuclear technology. Joining dissimilar metals enables us to use the most
suited material for each part of the
structure.
There is a growing demand also for
suitable joining methods, because of
the increasing variety of metals and
their improved properties. There are
cases where a mechanical construction suffices, but frequently welding is
inevitable. Each welding process raises
specific problems.
Welding Dissimilar Metals' *
In the case of fusion welding, the
structure and properties of the base
metals are changed. Even if similar
metals are fusion welded, a deviation
of the o p t i m u m parameters causes a
deterioration of the properties of the
joint. In the case of dissimilar metals,
welding parameter compromises are
necessary; these mostly are unfavor-
306-s I O C T O B E R 1979
able to the transition zone.
When using fusion welding, the
generation of an alloy of the base
metals cannot be suppressed in the
region of melting. If metallurgical
incompatibility occurs, either suitable
interlayers or specially alloyed filler
metals are employed. Thus, a composition of the joint w i t h acceptable properties is accomplished.
Well suited for this purpose are the
gas tungsten arc process and, even
better, electron beam- welding. Here
the possibility is given for the precise
regulation of both the weld energy
level and beam location; this permits
close control of the weld shape and
the ratio of the two base metals in the
weld metal. The high energy density
enables narrow welds. Therefore, it is
possible to insert one or more interlayers w i t h o u t the need for much
space.
Solid State Welding
The group of processes that constitute solid state welding is even better
suited to the joining of dissimilar
metals, because no alloy is generated
in the liquid state.
Diffusion Welding
This process offers the advantage of
Paper presented at the Ninth International
AWS-WRC Brazing Conference held in New
Orleans, Louisiana, during April 4-6, 1978.
R. LISON and '. F. STELZER are with the
Nuclear Research Establishment, luelich.
West Germany.
precisely dimensioned interlayers (filler metals) and the formation of very
thin intermetallic layers between the
dissimilar base metals. This leads to
the most important theme in the context of diffusion welding.
The parameters during the fabrication of such a joint change the properties of the base metals. Often c o m promises are necessary and a certain
deterioration of the properties of the
transition zone must be accepted. This
zone is a narrow layer of an alloy
generated by the movement of atoms
at the interface through the heated but
still solid metal. The vicinity of this
zone is also subjected to residual stress
during cooling, which is determined
by the thermal expansion properties
and Young's moduli.
Due to this, and also metallurgical
reasons, not every random pair of
metals delivers a satisfactory joint.
Therefore, the use of one or several
intermediate metals is advisable. The
thermal coefficients of expansion of
these filler metals and of the base
metals should have a uniform change
from one base metal to the other.
These filler metals should have good
mutual solubility, but the occurrence
of intermetallic phases should be
suppressed as far as possible.
Although the generated diffusion
zone is not required for the completion of a joint, 3 it can scarcely be
avoided. Compared to fusion welding,
diffusion welding offers the advantage
of limiting the thickness of the transition zone according to the time and
temperature of welding. Thus, it is
possible
to avoid
concentrations
which exceed the solubility and often
exhibit the formation of intermetallic
phases.
The above topics were the subject of
experimental
and
theoretical
research.
more filler metals are necessary. Case
b2 occurs when the welding temperature for joining one base metal to the
adjacent filler metal exceeds the melting point of the other base metal or
one of the remaining filler metals. Also
belonging to case b2 are joints w i t h
filler metals deposited by electrolytic
or vapor deposition methods.
Figure 1 shows ranges of temperatures recommended by Kasokov 5 for
the welding of some metals. Wide
overlapping, as in the cases of Ti-Zr or
Ta-Cb, points to favorable conditions
for the welding of these combinations.
Yet metallurgical compatibility must
also be present, since joint strength
largely depends on this factor.
The diffusion zone shows o p t i m u m
properties if a combination forms a
complete series of solid solutions, e.g.,
C u - N i , A g - A u , M o - T i , V-Cb. The j o i n ing of these combinations is relatively
easy to control, since the thickness of
the diffusion zone does not have an
appreciable influence on the mechanical properties.
The properties become less favorable if intermetallic phases occur, as in
binary alloys w i t h limited solubility , e.
g., Ti-Fe, Zr-Fe, Al-Fe. In some cases
(e.g., Al-Fe), it is possible to succeed in
Diffusion W e l d i n g Research
Experiments were performed concerning the diffusion welding of metals of the groups IVa (Ti, Zr), Va (Cb,
Ta, V) and Via (Mo) w i t h AISI Types
430 and 321 stainless steel. The physical properties of the dissimilar base
metals are very different, e.g., the
melting point range is as high as 1000 C
(1832 F). W e found that the following
classification of the joints is appropriate: a—directly weldable metals;
b—joints w i t h one or more filler metals, b1— producible in one operation,
and b2—producible in t w o or more
operations.
To the first group belong pairs of
metals which yield a metallurgically
satisfactory joint produced at a given
temperature
where
the
residual
stresses remain tolerable.
The second group includes base
metals w i t h very different chemical
and physical properties. Here one or
obtaining a useful joint by applying
precise control and appropriate j o i n ing geometry. 6 There are still other
structures w i t h i n the transition zone,
whose properties lie between those of
solid
solutions
and
intermetallic
phases.
Before starting experimental work it
was important to obtain information
about the expected properties in the
transition zone. Criteria were found in
the literature. 78
Compatibility of Base Metals and Choice
of Suitable Filler Metals
In the periodic system of elements,
those w i t h similar properties are in the
same column and are designated as
groups numbered from I to VIII.
Figures 2 and 3 show the thermal
expansion coefficients and the melting
points of the metals in the groups. It
can be seen that Fe, contained in many
alloys, and the metals of groups IVa, Va
and Via differ widely in these properties. They do not match the requirement for direct welding. For the choice
of the filler metal, t w o well k n o w n
approximation equations are given.
For metals w i t h cubic lattice:"
TBa ca 0.02
where Ts = melting point in °K;
a = thermal expansion coefficient.
From this follows that for a pair of
metals:
T»i
ct2
T,2 ~~ a,
If the thermal expansion coefficient
of a filler metal lies between that of
the base metals, the melting point of
the filler metal should also lie between
those of the base metals. This is valid
for metals w i t h a cubic lattice but not
for those of group Via w i t h a hexagonal lattice.
The second equation" is:
Tantalum
Vanadium
k
Molybdenum
R„' E
Tungsten
Chromium
Gold
Silver
Palladium
Platinum
~\
i
600
i
i
800
i
i
1000
i
i
1200
i
i
HOC
i
i
1600
i
i
1800
i
i
i
23X
i
i
i
2200 2400
i
i
i
i
2600 2800
i
i
i
r
3000 3200
l l l l
3400
T K
327
527
727
927
1127 1327
1527
1727
1927 2127
2327 2527
2727 2927
t °c
TD = ( 0 , 5 3 - 0 , 8 8 ) T s
O
Melting point (Ts)
Fig. 1-Temperature ranges recommended for diffusion brazing
3600
where
k = Boltzmann's
constant;
R„ = interatomic distance at equilibrium; E = Young's modulus.
The second equation shows that
metals with a small thermal expansion
coefficient have a large Young's m o d ulus. If they are joined to a metal w i t h
a high thermal expansion coefficient,
considerable residual stress is developed. This concerns principally combinations with M o or W. The criteria
shown in the literature 7 - 8 for the formation of binary systems indicate,
when compared to Figs. 2 and 3, that
the elements forming solid solutions
W E L D I N G RESEARCH S U P P L E M E N T I 307-s
4000-,
3500-
*
3000
c
°- 2500H
O
C
I
20001500-
1000-
500-
i—i—i—i—r^r~i—i—i—i—i—i i r
I A mA :EA Y i i A w f A I B m B ^ B
Group of t h e periodic System
Fig- 2—Mean linear expansion
the periodic system
coefficient
of the metals
0
I
I I I
I I I I I I
IA JI1AYAYJ1A-^AIB
I I I I
IHB YB
Group of t h e periodic System
within
Fig. 3—Melting
temperatures
of metals within
the periodic
system
<As)-Fe
,-Fe
/J-Ti
!
^
complete solubility
eutectic alloy
limited solubility
no mutual effect
intermetalic phases
•
Fig. 4-Mutual
system
effects
of Ti with
308-s j OCTOBER 1979
•
•
of the
eutectic alloy
limited solubility
no mutual effect
intermetalic phases
not examined
the elements
complete solubility
periodic
Fig. 5-Mutual
system
effects
•
of Fe with
not examined
the elements
of the
periodic
w i t h another element are to be found
in the same group or an adjacent
group of the periodic system. These
metals do not differ much in their
melting points or thermal expansion
coefficients.
Joints Between Stainless Steel (AISI Types
321 or 430) and Metals of Group IVa
Stainless Steel with Titanium. This
joint may serve as representative of
this joint family. The solubility of Fe in
a-Ti lies between 0.05 and 0.1 wt-%. If
the Fe content increases, the intermetallic phases TiFe and TiFe, form; this
causes a change of the mechanical
properties. A Ti-Fe alloy w i t h 0.14 wt-%
Fe has a hardness of 199 VHN and
tensile elongation of 18.5%. At 2.5
wt-% Fe, the hardness increases to 450
V H N and elongation decreases to
2.5%. This is a disadvantageous condition for a direct joint and is made
worse by a ratio of 2 for the thermal
expansion coefficients.
In our experiments it was basically
possible to join pure Ti w i t h AISI Type
321 stainless steel directly. But when
preparing the specimens for tensile
testing, seven of eight specimens
broke. The intact specimen showed a
tensile strength of 28 MPa (4.01 ksi).
The brittle behavior of this combination indicates a need for intermediate
metals.
Suitable Filler Metals. The mutual
effects of Ti w i t h other elements are
given in Fig. 4. 1 " The t w o modifications, hexagonal alpha-Ti and cubic
beta-Ti, display different alloying characteristics.
The beta-Ti forms a complete range
of solid solutions with the elements V,
Cb and Ta, whereas the behavior of
alpha-Ti is more limited in this respect.
At 700 C (1292 F), 3 wt-% V can be
dissolved in alpha-Ti. Vanadium dissolves 87 wt-% Ti at this temperature.
These promising properties are further
enhanced by thermal expansion coefficients which form a ratio (Ti:V) of
8.5:8.3. Thus, V seems to be a suitable
filler metal.
The compatibility of V w i t h the
other base metal-AISI Type 321 stainless steel—is now considered. Vanadium forms only w i t h alpha-Fe a
complete series of solid solutions. In
gamma-Fe its solubility is limited, (Fig.
5), and intermetallic phases are pres-
ent. W i t h regard to the alloying
elements in stainless steel, only Cr is of
unlimited solubility in V, whereas Ni
has only a limited solubility. In the
solid state the phases VNL,, VNL and
V 3 Ni are found. 1 " Although the carbon
content of the given steel is low, there
exists the possibility of diffusion into
the V. In this case vanadium carbides
w o u l d appear. We learned in a series
of experiments that it is apparently not
possible to obtain useful joints between V and AISI Type 321 stainless
steel. Additional filler metals are
necessary.
From the literature, 3 some useful
filler metals for the combination V-Fe
are known. Besides copper bronze,
preproduced sheets of three-layer VNi-Cu are recommended. In our experiments, in addition to the V-Ni-Cu, a
sheet of three-layer V-Cu-Ni was
inserted because of the better order of
the thermal expansion coefficients.
Also, from the metallurgical point of
view, the latter series offers an advantage in that V has only a limited solubility for Ni;" 1 if this solubility is
exceeded, the phases VNL, V 3 Ni and
VNL form. Copper also has only a
Titanium
Fig. 6—Diffusion braze between Ti and AISI 430 via filler metals
W E L D I N G RESEARCH S U P P L E M E N T I 309-s
Titanium
^^mWim^lW 'AISI430
Fig. 7-Diffusion
braze between
Ti and AISI 430 via filler
metals
^H
AISI 321
Fig. 8—Diffusion
Zr2Sn
braze between
310-sl OCTOBER 1979
Zr2Sn (Zircaloy
2) and AISI 321 via filler
metals
complete solubility
Fig. 9—Exhibition example for joints ol
stainless steel to reactive and refractory
metals
limited solubility in V but the system
remains free of intermetallic phases.
Nickel and Cu form an uninterrupted series of solid solutions. The
segregation of a NiCu : , phase in the
solid state is controversial. 1 "" The
solubility of Cu in Fe is limited, but
intermetallic phases do not appear.
=
eutectic alloy
limited solubility
no mutual effect
intermetalic phases
not examined
Fig. 10-Mutual effects of Mo with elements of the periodic system
Nickel and gamma-Fe form a complete
range of solid solutions. The solubility
of Ni in alpha- and delta-Fe is limited,
to about 10 atomic-% at 200 C (392 F).
A higher Ni content causes a segregation of Fe.,Ni, FeL,Ni and FeNi :i phases.
Preproduced three-layer filler metal
sheets, as well as separately intro50 p i
321
lM.iii,.i|ii»tim^pqTOiBiitwp<\wiyBitii^
_;
,l,.,,l,..,l...,l„,,>imt.«»V»«V>MAw)
Fig. 11-Diffusion braze between Mo and AISI 321 via filler metals
W E L D I N G RESEARCH S U P P L E M E N T I 311-s
in the transition zones. But the insertion of an additional metal (Ti) is not
favorable for other reasons.
Joints Between Stainless Steel (AISI Type
321 or 430) with Metals of Group Va
There are three metals in this group:
V, Cb and Ta. The transition from V to
steel has already been described above
and needs no further discussion. The
other t w o metals, Cb and Ta, form
with V a complete series of solid solutions, 10 w i t h the system Ta-V segregating TaV, in the solid state. This
compound does not have an appreciable influence on the properties of the
joint.
The same transition series as described above can be inserted from V
to steel. Diffusion welded joints of
Va-metals w i t h stainless steel are
exhibited in Fig. 9.
Joints Between Stainless Steel (AISI Type
321 or 430) with a Metal of Group Via
Fig. 12— Finite element model for stress calculations
duced metals of the given sequence,
were satisfactory for diffusion welding
of Ti to ferritic or austenitic stainless
steels. Success was also achieved w i t h
the application of preproduced t w o layer V-80Cu20Ni and V-Ni15Cr7Fe filler metals. Figures 6 and 7 show such
combinations.
The filler metals were preproduced
from sheets w i t h thicknesses between
1 and 5 mm (0.04 and 0.20 in.) if no
foils were available. Later on, foils of
0.1 mm (0.04 in.) thickness were also
successfully used.
Stainless Steel with
Zr2Sn. This
combination is of special interest in
nuclear technology. Since Zr also
belongs to group IVa, similar properties are to be expected as for Ti.
Zirconium in alpha-Fe has a solubility
of only 0.35 atomic-%; alpha-Zr at 800
C (1472 F) can dissolve 4 atomic-%
Fe.
During
solidification,
ZrFe,,
is
formed, which converts to Zr4Fe in the
solid state. The eutectic existing at the
Zr side shows a melting point of 934 C
(1713 F). Zirconium cannot dissolve
appreciable amounts of the alloying
elements Cr and Ni, and vice versa.
Zirconium forms intermetallic phases
with both elements. The ratio of thermal expansion coefficients Zr/AISI
Type 321 stainless steel is 6.5/18; for
AISI Type 430 stainless steel it is 6.5/12.
Making a direct joint by welding is,
therefore, not advisable and filler
metals should be used.
Suitable Filler Metals. Again V, being
located in a neighboring group, offers
limited solubility w i t h o u t intermetallic
phases in the solid state.' 0 The transition from V to stainless steel is accomplished as described above.
Figure 8 illustrates a diffusion weld
between stainless steel and Zr2Sn
using filler metals of V-Cu-NL Also,
the sequence Zr2Sn-Ti-V w o u l d be
satisfactory because of the formation
of a complete series of solid solutions
Table 1-Meehan cal Properties of th 3 Materials Joined in the Calcu ation Example
Young's m o d u us,
MPa
Th ?rmal expansion
coefficient,
1/K
Poisson's
ratio
140.000
127.000
175.000
8.3 -10-"
17.7-10-"
18-103
0.35
0.34
0.3
Vanadium
Copper
AISI 321
312-s I O C T O B E R 1979
From this group M o was chosen for
examination as the most widely used
metal of the group. Its thermal expansion is 30% of that of austenitic steel
and 40% of that of ferritic stainless
steel. The melting points of the base
metals are 1000 C (1800 F) apart.
The binary system Fe-Mo contains
limited solubilities and intermetallic
phases. M o dissolves 16.7 Fe at 1480 C
(2696 F) and 4.5 atomic-% at 1100 C
(2012 F). W i t h further decreases in
temperature, the solubility also decreases. O n the other hand, the solubility of M o in Fe amounts to 26
atomic-% at 1450 C (2642 F), but
gamma-Fe dissolves only 4 atomic-%.1'3
The system Mo-Fe contains the phases
M0;,Fe3 and MoFe.
From the presented points of view,
the welding of M o directly to an Fe
alloy does not appear promising. Filler
metals are necessary. Figure 10 exhibits
the mutual effects of M o with the
elements of the periodic system. Vanad i u m , Cb and Ta of group IVa display
attractive alloying behavior w i t h Mo.
Unfortunately, welds between M o
and V failed. Apparently the reason is
to be sought in the thermal expansion
ratio of 5.1/8.3 for M o / V , which leads
to excessive residual stresses during
cooling, augmented by the high
Young's modulus of M o .
The next experiments concerned Ta
as a filler metal. The ratio of the thermal expansion coefficients is at 5.1/6.5
for M o / T a more promising. The further transition to the stainless steel has
already been described above. The
widely diverging melting points do not
allow the production of the joint at
one temperature. The transition of
Mo-Ta-V-Ni-Cu-AISI 321 was joined in
two operations. The first accomplishes
REFERENCE 5TRE55
REFERENCE 5TRE55
Fig. 13—Reference stress field in a joint ol stainless steel and V with
a thick copper filler metal
t h e c o m b i n a t i o n M o - T a - V at 1500 C
(2732 F) in 40 m i n u t e s ( m i n ) . 1 3 This
c o m b i n a t i o n is t h e n j o i n e d t o stainless
steel i n a s e c o n d o p e r a t i o n w i t h f o i l s
of N i a n d C u at 850 C in 20 m i n . To
save t i m e , h o w e v e r , t w o
Mo-Ta-V
c o m b i n a t i o n s m a y be p l a c e d t o g e t h e r
w i t h t h e i r V surfaces s e p a r a t e d by a
p a r t i n g c o m p o u n d ; this p r e v e n t s t h e
j o i n i n g of t h e t w o V - l a y e r s . In t h i s w a y
o n l y 1.5 j o i n i n g o p e r a t i o n s are n e c e s sary f o r e a c h M o - T a - V c o m b i n a t i o n .
The order of the thermal expansion
c o e f f i c i e n t s f o r t h e c o m b i n a t i o n of
M o - T a - V - N i - C u - A I S I T y p e 321 s t a i n less steel is 5 . 1 - 6 . 5 - 8 . 3 - 1 3 . 3 - 1 7 . 7 - 1 8
a n d s h o w s a d e s i r a b l e u n i f o r m i t y of
c h a n g e f r o m o n e base m e t a l t o t h e
o t h e r . Such a j o i n t is s h o w n in Fig.
11.
Mechanical
Property
Predictions
f o r Dissimilar M e t a l Joints
Theoretical examinations were cond u c t e d to f i n d a m e t h o d t o p r e d i c t t h e
m e c h a n i c a l b e h a v i o r of d i s s i m i l a r m e t al j o i n t s w i t h f i l l e r m e t a l s . For c o n s i d eration w e chose cylindrically shaped
specimens consisting of V and stainless steel (AISI T y p e 321) d i f f u s i o n
w e l d e d w i t h Cu filler metal. This structure was subjected to c o m p u t e r analysis u s i n g f i n i t e e l e m e n t s . T h u s , its
r e s i d u a l stress f i e l d s a n d t h e c o n s e q u e n t stored potential energy could
be r e v e a l e d .
W e a n a l y z e d several cases w i t h d i f f e r e n t ratios o f l e n g t h t o d i a m e t e r ,
varying the filler metal thicknesses and
the temperature changes.
Model
Fig. 14.—Reference stress field in a joint
with a thin copper filler metal
of stainless steel and V
thus producing compressive
forces
w i t h n e g a t i v e stress. T h e m e t a l w i t h
the lower expansion coefficient behaves in t h e o p p o s i t e m a n n e r . 1 1 • "
Results are g r a p h i c a l l y p r e s e n t e d in
Figs. 13 a n d 14. T h e p a t t e r n s of refere n c e stresses are p l o t t e d v e r t i c a l l y o v e r
the upper section corresponding to
Fig. 12. B o t h cases refer t o a c y l i n d e r of
125 m m (4.9 in.) l e n g t h a n d 25 m m (1
in.) d i a m e t e r , b u t d i f f e r in t h e t h i c k ness of t h e c o p p e r f i l l e r m e t a l . T h e
t h i c k n e s s e s are 5 a n d 0.1 m m (0.2 a n d
0.04 in.) in t h e cases o f Figs. 13 a n d Fig.
14,
respectively.
The
temperature
c h a n g e is 10 K (10 C, 18 F) in b o t h
cases.
c y l i n d e r s u f f i c e d b e c a u s e of s y m m e t r y .
This is s u b d i v i d e d i n t o f i n i t e e l e m e n t s
as d i s p l a y e d in Fig. 12. In t h e v i c i n i t y o f
t h e filler m e t a l , t h e e l e m e n t d i m e n sions p e r p e n d i c u l a r t o t h e j o i n t are
r e d u c e d in o r d e r to o b t a i n
more
d e t a i l e d i n f o r m a t i o n in t h i s area w h e r e
t h e stress is c o n c e n t r a t e d .
T h e m e c h a n i c a l p r o p e r t i e s of base
m e t a l s a n d t h e f i l l e r m e t a l are listed in
Table 1.
Stress Fields
For ease of p r e s e n t a t i o n in t h i s
context,
we
deal
with
reference
stresses, w h i c h are p u t t o g e t h e r f r o m
t h e six n o r m a l stresses a c c o r d i n g t o
t h e v o n M i s e s h y p o t h e s i s . T h e refere n c e stress is a l w a y s p o s i t i v e , c o n c e a l i n g t h e f a c t t h a t t h e n o r m a l stresses
s h o w t h e p o s i t i v e sign i n s o m e r e g i o n s
and in others, t h e negative sign.
T h e r e is l i t t l e d i f f e r e n c e b e t w e e n
t h e t w o cases in t h e m a g n i t u d e a n d
c o n t o u r o f stresses. T h e
maximum
stress a p p e a r s in t h e V a n d i m m e d i a t e
p r o x i m i t y t o t h e f i l l e r m e t a l . H e r e , if
a n y , a c r a c k w o u l d p r e f e r e n t i a l l y set i n .
C h a r a c t e r i s t i c stress v a l l e y s o c c u r in
t h e base m e t a l p a r a l l e l t o t h e f i l l e r
m e t a l at a s h o r t d i s t a n c e f r o m t h e
transition.
During heating, the metal w i t h the
h i g h e r t h e r m a l e x p a n s i o n c o e f f i c i e n t is
restrained f r o m
normal
expansion,
Table 2—Potential Energy in N m m Stored in a Cylinder Structure (125 m m Long, 25 m m
Diameter) Consisting of AISI Type 321 Stainless Steel, Copper and Vanadium,
Temperature Change of 10 °K
Filler metal
thickness,
mm
Vanadium length.
mm
Case
Steel length,
mm
1
2
60
62.45
Case
Energy in
steel,
Nmm
Energy in
filler metal,
Nmm
Energy in
vanadium,
Nmm
Sum,
Nmm
1
2
8.349
8.69
0.488
7.8-10-'
1.42
1.478
10.25
10.16
60
62.45
5
0.1
To f o r m the m o d e l , a quarter of the
WELDING
R E S E A R C H S U P P L E M E N T I 313-s
Stored Potential Energy
The amount of potiential energy
equals the deformation load on a
stressed structure. If it exceeds a
certain limit, the structure will fail. The
potential energy W is commonly written as:
W = Vi
cr S € dV
(1)
with 0" = stress; S € = variation of
strain; and V = volume.
In the finite element analysis, the
potential energy is treated as:
W = '/> { u } T [k] {u},
(2)
where { u } is the displacement vector
of the nodes of the net and [k] is the
stiffness matrix of the structure.
This value was calculated for each
parametrical case. It agrees very well
w i t h the results gained by the reduced
method of summing each of the individually integrated potential energies
of the adjacent metals:
W
T' A
2 , a? L, Ei,
2
T3 A [a-;
—-|_-T(L-s)
2'
E, + a ; s
a: E , + a; E.,
(5)
where the indices 1 and 2 identify the
base metals.
(3)
Conclusion
w i t h T = temperature change; A =
cross section; a = thermal coefficient
of expansion; L = length of individual
pieces; E = Young's modulus; and
i = numbering index of joint metals.
The temperature change can be
treated as a constant, since it is
normally uniform over the entire structure in length and cross section. The
number i increases from three, in the
case of one filler metal joining t w o
base metals, to five, if three filler
metals are used. In the case of the
above treated example, equation (3)
becomes:
W
only slightly on the filler metal thickness, s, in the special case of Table 2.
The considerable decrease of energy in
the very thin filler metal of case 2
shows only a slightly reduced total
energy content, as compared w i t h case
1. This however, is not generally valid.
In other cases, w e found that w i t h a
decrease of the filler metal, an increase
of the total potential energy took
place. Therefore, the decision on an
optimum thickness lies in an individual match of the variables in equation 3
for each joint under consideration.
Concerning the "ideal filler metal
(ifm)," it can be said, from the
mechanical point of view, that the
filler metal properties should approach
as nearly as possible to:
ai
E , + -2
(L-s)Ej
The results of the present investigation show the possibilities of joining
stainless steel w i t h the reactive and
refractory metals. Because of the
diverging physical and metallurgical
properties, filler
metal
must
be
used.
The laws of metal science serve for
the choice of filler metals. To assess
the mechanical behavior of the joint
and to choose the filler metal thicknesses, it is w o r t h w h i l e to calculate
the stress distribution by determining
the potential energy.
Diffusion welding is well suited for
the production of dissimilar metal
joints w i t h selected filler metals.
H)
References
where s = filler metal thickness.
Results
The total potential energy depends
1. Rabkin, D. M., Ryabov, W. R., and
Gurevitsch, S. M., Welding of Dissimilar
Metals, Technique Publishers, Kiev, 1975 (in
Russian).
2. Tscharuchina, K. E., Golovanenko, S.
A., Masterov, W. A., and Kasakov, N. F.,
loints of Dissimilar Metals, Metallurgy
Publishers, Moscow, 1970 (in Russian).
3. Metzger, G., and Lison, R., "Dissimilar
Metal Welding With Metals of Importance
in Nuclear Technology," Juel-Report 1011,
Kernforschungsanlage juelich, 1973 (in German).
4. Metzger, G., and Lison, R., "Electron
Beam Welding of Dissimilar Metals," We/ding lournal, 55(8), Aug. 1976, Research
Suppl., pp. 230-s to 240-s.
5. Kasakov, N. F., Diffusion Welding of
Materials, Mechanical Engineering Publishers, Moscow, 1976 (in Russian).
6. Lison, R., "Diffusion Welding and Its
Application-Examples from Nuclear Technology," Schw. u. Schn., Vol. 23 (1971), pp.
304-308 (in German).
7. Voschvischenski, W. M., Possibilities
oi Predicting Binary Phase Diagrams Using
Statistical Criteria, Metallurgy Publishers,
Moscow, 1975 (in Russian).
8. Lison, R., "Problems of Dissimilar
Metal Welding by Fusion Welding Processes," Schw. u. Schn., Vol. 28 (1976), pp.
89-92 (in German).
9. Savitzki, E. M., and Burchanov, G. S.,
Metal Science of Metals With High Melting
Points, Science Publishers, Moscow, 1967
(in Russian).
10. Kornilov, J. )., Mateeveeva, N. M.,
Pryachina, L. (., and Polyakova, R. S.,
Metallo-chemical Properties of the Elements of the Periodic System, Science
Publishers, Moscow, 1966 (in Russian).
11. Hansen, M., Constitution of Binary
Alloys, McGraw-Hill, New York, 1958.
12. Morginova, N. N., Klypin, B. A., Byarschinov, V. A., Tarakonov, L. A., and
Mangein, ]. V., Alloys of Molybdenum,
Metallurgy Publishers, Moscow, 1975 (in
Russian).
13. German Welding Society joint Project 01, "Technology of Diffusion Welding," Final Report, Kernforschungsanlage
juelich (in German).
14. Stelzer, j . F., "Calculation of Thermoelastic Deformations and Stresses in
Two-Component
Structures,"
Welding
lournal, 55(8), Aug. 1976, Research Suppl.,
pp. 249-s to 252-s.
15. Stelzer, J. F., "Calculation of Thermal
Stresses in a Pipe of Clad Metal," Schw. u.
Schn., Vol. 29 (1977), pp. 217-220.
WRC Bulletin 245
January 1979
A Fracture-Mechanics Evaluation of Flaws in Pipeline Girth Welds
by R. P. Reed, H. I. McHenry and M. B. Kasen
Fracture-mechanics methods were used to provide a basis for assessing the significance of flaws in girth welds
in a buried arctic oil pipeline. The objective was to illustrate the approach based on current knowledge and to
define areas where further work will increase the validity of such analyses. Various fracture-mechanics analyses
were used to calculate a series of allowable flaw-size curves in accordance with worst case requirements set by the
Office of Pipeline Safety Operations (OPSO).
Publication of this bulletin was sponsored by the Weldability Committee of the Welding Research Council.
The price of WRC Bulletin 245 is $11.00 per copy. Orders should be sent with payment to the Welding Research
Council, 345 East 47th St., New York. NY 10017.
314-s I O C T O B E R 1979