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Di-Jing1994-H2AssistedCracking-HSLAWelds.pdf
Investigation on Susceptibility to HydrogenAssisted Cracking in HSLA Steel Weldments
An area of maximum stress during phase transformation contributes
to the susceptibility of hydrogen-assisted cracking
BY X. DI-JING, Q. HONG AND J. JIANMING
ABSTRACT. The effect of martensitic
transformation stress on hydrogen-assisted cracking (HAC) initiation and propagation in high-strength steel HY-80 weldments was investigated usinga new theory
of martensite phase transformation.
The results calculated by a numerical
computing program specially set up
showed that the martensitic transformation stress was not uniformly distributed
along the boundary of the martensite lath.
The magnitude and nonhomogeneity of
the distribution of the phase transformation stress increased significantly with the
increase in prior austenite grain size.
Consequently, there was a region of maximum phase transformation stress at the
frontier of the fastest growing direction of
martensite lath, and the susceptibility to
HAC in this region increased rapidly.
It was found that the behavior of the
initiation and propagation of HAC in
augmented-strain cracking test specimens of high-strength HY-80 steel
welded with the flux cored arc welding
process (FCAW) correlates with the calculated results.
The mechanism of cold cracking may
be simply started from the mechanical
aspect that a cold crack initiates while
the stress and strain induced at a point
reach critical values. But welding stress is
rather complicated. Generally, the welding stress falls into three categories: thermal stress due to the nonuniform distribution of temperature, phase transformation stress and external restrained
stress. The effect of the thermal stress and
external restrained stress on HAC initiation and propagation was studied by
many researchers. But little work was
done on phase transformation stress. The
role of phase transformation stress in
HAC initiation and propagation remained unclear until now.
It was generally observed that the
larger the grain size was, the higher the
sensitivity to HAC. Many investigations
showed that the threshold stress intensity
levels, KTh , below which neither stresscorrosion cracking nor HAC w o u l d
occur, depended upon a number of vari-
Introduction
It is well known that hydrogen-assisted cracking (HAC), which occurs bet w e e n - 1 0 0 ° to 200°C (-148°-212°F) in
HSLA steel weldments, is basically dependent upon three mutually interactive
factors: the amount of diffusible hydrogen in the weld, the level of the stress in
the weld and the susceptible microstructure in the joint.
X. DI-JING is Professor, Chairman, and Q.
HONG andj. JIANMING are Lecturers, Dept.
of Metallic Materials Science and Engineering,
Beijing Polytechnic University, Beijing, China.
KEY WORDS
Hydrogen-Assisted
Cracking
Phase Transformation
HSLA Steels
HAC Susceptibility
Hydrogen Effects
Martensitic
Transformation
Prior Austenite Grain
Crack Propagation
Heat-Affected Zone
ables, such as microstructure and grain
size (Ref. 1).
Wood (Ref. 2) has suggested that the
increasing grain size was the major variable most likely to affect the resistance to
HAC in HSLA steels.
Easterling (Ref. 3) found that cold
cracks initiated in the grain growth zone
in HAZ and the increase of grain size effectively decreased the transformation
temperature. So, in high-C eq steels, the
volume fraction of the lower temperature
transformation products, such as martensite, bainite or Widmanstatten side laths
(plate), increased. The high dislocation
density associated with these products,
together with fine carbide particle hardening, was thus likely to lead to a hard,
low ductility matrix susceptible to HAC.
It is evident that the presence of
twinned martensite is more dangerous
than that of low-carbon martensite, and
there is a certain relationship between
the phase transformation and the susceptibility to HAC.
Christian (Ref. 4) suggested that the
elastic energy of the phase transformation system uniformly distributed along
the boundaries of the growing martensite
lath. The assumption is contrary to some
important phenomena of HAC.
Deng (Ref. 5) proposed a new theory
for thermoelastic transformation, he suggested that the controlling factor of the
phase transformation, in the radial and
the thickening directions of the grain
growth of martensite, is the localized
equilibrium between chemical-free energy and the elastic energy in the growing frontier. Consequently, this theory
provided the possibility for further study
of the effect of martensitic transformation
on HAC in the micro-area.
W E L D I N G RESEARCH SUPPLEMENT I 285-s
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r (relative units)
A single growing martensite plate is
under consideration. The cooling rate is
slow enough that thermoelastic equilibrium can be reached at any temperature.
The free energy change of the system AG
is
AG = AG c h + AG e + AG S + AG o t
where AG c h is the change of chemicalfree energy; AG e is the change of elastic
energy; AGS is the change of interfacial
energy; and AG o t is the change of other
kinds of energies, such as acoustic emission, external fields, and friction of the interphase boundary motion.
Among all these terms, the chemicalfree energy and the elastic energy are the
most important because the former is the
driving factor for the transformation and
the latter is the main hindering factor. The
relationship between them basically determines martensite phase growth behavior. For a specific alloy composition,
the change of total chemical-free energy
depends on temperature and the volume
of the martensite.
Estimation of elastic energy is much
more difficult than that of chemical-free
energy. Direct experimental measurements of elastic energy have not been reported, and the theoretical calculations
depend strongly on the details of the
model adopted. Average elastic energy
286-s I DECEMBER 1 9 9 4
10.20
10.30
10.40
c (relative units)
F/g. / — Elastic energy in the radial frontier E' (Ref. 51.
Theoretical M o d e l and
Calculation Formulas
10.10
frontier Ec (Ref. 5).
Fig. 2 — Elastic energy in the thickening
can be used to calculate the elastic energy term in the formula above to estimate if a certain macroprocess is possible. But it is not suitable to describe the
micro-process of martensitic transformation, and the distribution of elastic energy
must be taken into account.
The essential assumption of the
micro-area model for the martensitic
transformation is that the controlling factor of the phase transformation, in the radial and the thickening directions of the
growth of martensite, is the local equilibrium between chemical-free energy
and the elastic energy in the growing
frontier area, i.e., the region near the interphase boundary. Esheby's continuum
elasticity theory was chosen by Deng as
the theoretical basis to calculate the local
elastic energy (Ref. 5). According to the
equations deduced by Deng, the elastic
displacement tender at the growing frontier area caused by the martensite growth
1 = 1-2v
Ujk
r = \r -r'\
=
XM) 2
ll=[xi-x'i)/r
, / = 1, 2, 3
f' = 1, 2, 3
The calculation of elastic energy,
stress and strain in frontier area from the
displacement is a standard procedure in
elastic mechanics. Let
tensor, then
IJ
2
'duf(r)
<9x,
be the strain
duf(r)
dx i
(2)
Uf(r)
.
• „
, can be written as the following
formula, which is very convenient for numerical computing:
dv
r ;d
Uf(
y ijk
J«1-
where,
du f(r)
dx.
dx.
are the disand
placement components in different d i rections at the growing frontier area. Let
of,
be the stress tensor, then
where -jk is elastic strain tensor in a
free transformation, which is to be distinguished from the strain that occurs
when the transformed region is constrained by the surrounding matrix.
ofj=Xe§8,j+2nefj
(3)
where X is the lame constant, and p is the
shear modules. Then, the change of elastic energy , G e , is
29.00
30.00
1—
31.00
1
32.00
33.00
9
1—
S
—
i2
'c
^*>~
/
o
^
3
CO
>
ro
cu
'
8
c
o
o
8
d
d 4.00
r (relative units)
(4)
The detail of the calculation procedure and the selection of the parameter
was listed as Deng's computing program.
Calculation Results
The calculation of the local elastic energy in the radial growth frontier, Er, and
that in the thickening frontier, Ec, were
done by Deng. Figures 1 - 4 show the calculated results.
Figure 1 shows the relationship between the elastic energy in the radial
growth frontier area, Er, and martensite radius, r, on conditions that a disk-shaped
martensite is embedded in an infinite parent phase and its radius, r, is much larger
than its semithickness, c, i.e., r/c >100.
These conditions are consistent with reported observations. Calculations on different shapes, including the oblate one,
yields curves with the same tendency,
i.e., Er increases with r increase.
Figure 2 shows that the local elastic
energy in the thickening frontier area, Ec,
increases with the increase of the semithickness of martensite lath, c.
It is worthwhile to notice the influence
of radial growth on the local elastic energy in the thickening frontier area, i.e.,
the relationship between Ec and r with a
constant c. Ec is slightly reduced when r
increases, as shown in Fig. 3. Generally,
•
12.00
i
16.00
20.00
c (relative units)
Fig. 3 — The relationship between Ec and r (Ref. 5).
= 0.5Jefs ofj dv
i
8.00
Fig. 4 — Nonhomogenous
the growth velocity in the radial direction
of martensite is different from that in the
thickening direction, the former is much
larger than the latter. Hence, the ratio r/c
is very high. Thus, Er will be much larger
than Ec . This means that the elastic energy of the phase transformation system
nonuniformly distributes along the growing boundaries of martensite lath. When
n is the ratio of Er to Ec , then n is an indicator of nonhomogeneity of the elastic
energy distribution. Figure 4 shows the relationship between n and r; n goes up
with the radial growth. The value of local
elastic energy in the radial growing frontier of the martensite lath is higher than
that in other areas.
n changes with radius r (Ref. 5).
The martensitic transformation stress is
closely related to elastic energy of the
transformation system. Since the value of
local elastic energy in the radial growing
frontier area of the martensite lath, i.e., the
martensite lath tip, is higher than that in
other areas, the tip of the martensite plate
or lath will become the region of the maximum martensitic transformation stress.
martensite lath. It strongly affects the
magnitude of the local elastic energy in
the growing frontier of the martensite
lath, as well as the nonhomogeneity of
the elastic energy distribution. O b v i ously, the coarser the prior austenite
grain, the larger is the phase transformation stress in the fastest growth direction,
i.e., the radial direction of the martensite
lath, and the higher is the nonhomogeneity of the distribution of the phase
transformation stress.
Calculation of the martensitic phase
transformation stress of prior austenite of
different grain sizes in high-strength HY80 steel FCA welded was carried out by
using a specially designed computer program in this investigation. Parameters for
HY-80 are as follows:
Young's Modules: E = 200 GPa (2.04
x 10 6 kg/cm 2 )
Shear Modules: p = 74 GPa (0.75 x
10 6 kg/cm 2 )
Poisson's Ratio: v = 0.33
Normal Strain Component: c\„ = 0.09
Shear Strain Component: £;s = 0.1 9
It has been confirmed that the possible maximum magnitude of martensite
lath mainly depends upon the size of the
prior austenite grain from w h i c h the
martensite lath formed because martensite lath grows rapidly during the phase
transformation process until it reaches
the boundary of the prior austenite grain.
Therefore, the prior austenite grain size
determines the value of r and r/c of the
The habit plane of the lath martensite
is close to {111).
Calculated results listed in Table 1
show that the phase transformation stress
increases significantly with the increase
of the prior austenite grain size. Because
of the great disparity in parameters of the
material selected, it was difficult to calculate accurately the value of the phase
transformation stress. Only the relative
W E L D I N G RESEARCH SUPPLEMENT I 287-s
Table 1 — Relationship between Martensitic Transformation Stress and the Prior Austenite
Grain Size
Austenite grain size
(relative units)
Table 3—Flux Cored Arc Welding
Parameters
10
Martensitic transformation
stress (relative units)
100
104
110
115
120
125
130
133
134
134
Table 2 — Chemical Compositions of the Base Metal and Undiluted Weld Metal
Base metal
(HY-80 steel)
Undiluted weld
metal
(flux cored
electrode
E90T1-K2)
C
Mn
P
s
Si
Ni
Cr
Mo
0.18
0.32
0.018
0.013
0.20
2.99
1.68
0.41
0.05
1.50
0.010
0.018
0.50
1.75
Electrode diameter, in. (mm)
VJ6 (1.6 mm)
DCEP
Polarity
75%Ar-25%C0 2
Shielding gas
35-40(16-19)
Shielding gas flow rate, cfh
L/min
210 (88.9)
Electrode feed speed, in./min
(mm/s)
Welding current, amperes (A)
200
Arc voltage, (V)
27
Travel speed, in./min (mm/s)
11 (4.66)
Heat input, kj/in. (kj/m)
29.5 (1161)
gation position of hydrogen-assisted
c r a c k i n g , the g r o w t h d i r e c t i o n of the
martensite lath, a n d the p r i o r austenite
grain b o u n d a r i e s .
E x p e r i m e n t a l Results
r e l a t i o n s h i p b e t w e e n the phase transform a t i o n stress a n d t h e p r i o r a u s t e n i t e
g r a i n size w a s f o u n d in this i n v e s t i g a t i o n .
Table 1 reveals that the phase transform a t i o n stress w i l l increase a b o u t 4 0 %
w h e n the p r i o r austenite g r a i n size i n creases ten t i m e s .
Experimental Procedures
Base Metal and Filler Metal
A n a l l o y - r i c h heat of H Y - 8 0 steel plate
and an a l l - p o s i t i o n f l u x c o r e d e l e c t r o d e
D u a l Shield II E90T1-K2 w e r e used in this
investigation. The c h e m i c a l c o m p o s i t i o n s
of the base metal and u n d i l u t e d w e l d metal
of the flux cored electrode E90T1-K2 are
listed in Table 2. Figure 5 shows the m i c r o s t r u c t u r e of t h e base m e t a l H Y - 8 0 ,
w h i c h had been q u e n c h e d in water and
then t e m p e r e d in air at 6 5 0 ° C (1202°F).
T h e microstructure is tempered martensite.
Fig. 5 — Microstructure
Picric etch, 500X.
288-s I DECEMBER
of HY-80 base metal.
1994
Specimen Preparation and
Experimental Procedure
T h e a u g m e n t e d - s t r a i n c r a c k i n g (ASC)
test samples a n d h y d r o g e n c o n t e n t a n a l y sis specimens w e r e c u t f r o m 3 8 - m m (1.5in.) plate. T h e w e l d i n g parameters used in
this investigation are listed in Table 3. T h e
h y d r o g e n c o n t e n t in the FCA w e l d m e n t
w a s increased by e x p o s i n g the e l e c t r o d e
to 1 0 0 % h u m i d i t y at 3 2 ° C (89.6°F) for
several days. Both the ASC test and hyd r o g e n c o n t e n t analysis procedures w e r e
the same as Savage's (Ref. 6).
Metallographic Examination
ASC test s p e c i m e n s w e r e r e p o l i s h e d
a n d e t c h e d for m e t a l l o g r a p h i c e x a m i n a t i o n to reveal t h e martensite m i c r o s t r u c t u r e a n d the p r i o r austenite g r a i n b o u n d aries in the H A Z of the w e l d m e n t s .
Scanning electron microscopy analysis w a s c a r r i e d o u t to e x a m i n e the relat i o n s h i p a m o n g the i n i t i a t i o n a n d p r o p a -
Hydrogen-assisted cracking was o b served in t h e ASC test s p e c i m e n s w h i c h
had h y d r o g e n c o n t e n t of m o r e t h a n 4 to
5 p p m a n d s u b j e c t e d to an a u g m e n t e d
strain e q u a l to or larger t h a n 1.1 5 % . Figure 6 reveals that t h e hydrogen-assisted
c r a c k i n g in t h e ASC test s p e c i m e n i n i t i ated m a i n l y in t h e H A Z at t h e g r a i n
b o u n d a r i e s o f the c o a r s e - g r a i n e d p r i o r
austenite, a n d p r o p a g a t e d i n t o the w e l d
metal or the base m e t a l .
S c a n n i n g e l e c t r o n m i c r o s c o p e (SEM)
analysis of s p e c i m e n s d e m o n s t r a t e d dist i n c t l y that t h e i n i t i a t i o n a n d p r o p a g a t i o n
positions of H A C w e r e c l o s e l y related t o
t h e g r o w t h d i r e c t i o n of t h e m a r t e n s i t e
l a t h . A c o n s i d e r a b l e n u m b e r of o b s e r v a tions revealed that H A C i n i t i a t e d often at
the g a t h e r i n g region of the radial f r o n t i e r
of the martensite lath, i.e., the g a t h e r i n g
r e g i o n at t h e t i p of t h e martensite l a t h , at
the
coarse-grained
prior
austenite
b o u n d a r i e s — Fig. 7. Frequently, the d i r e c t i o n of H A C i n i t i a t i o n a n d p r o p a g a -
Fig. 6 — Hydrogen-assisted cracks. A — Initiated at the coarse-grained prior austenite boundaries
in the HAZ, picric etch, 400X; B — propagated along the coarse-grained prior austenite boundaries, picric etch, 500X, SEM (BE).
fS^^HmWv
> t/ll
"' "•" " F I B
1 ,11
^ "
^wif
R
v ^ l l 0» V .V
*
i ^ i ^ ,^**»*2L* *tJ
^' 11' ; ! y, /w
I&
Fig. 7 — The relationship between HAC and
the radially growing frontier of martensite lath,
Vi lel la's etch, WOX, SEM (SE).
Fig. 8 — Relationship between HAC and the
radially growing frontier of the martensite lath,
Vi lel la's etch, 1000X, SEM (BE).
tion was roughly perpendicular to the radial direction of the martensite lath. The
orientation of HAC would change if the
direction of the martensite lath changed
- F i g . 8.
Generally, the HAC occurred at the
prior austenite grain boundaries, which
were the thickening frontier of the growing martensite. Accidentally, HAC propagated through the prior austenite grains.
The propagation would be diminished
gradually — Fig. 9.
The size of the prior austenite grain
size was estimated by the Intercept
Method. The coarse-grained prior
austenite had the ASTM grain size number of 3 (from 63.5 to 222 pm), and the
prior austenite in the base metal and the
fine-grained area of the HAZ had the
ASTM grain size number of 7 (from 25.4
to 44.4 pm). This meant that the prior
austenite grain size in the coarse-grained
area in the HAZ increased 2.5 to 5 times
as compared with the fine prior austenite. As described earlier in this paper, the
possible maximum magnitude of the
martensite lath was approximately equal
to the size of the prior austenite grain.
more than that at the boundary of the
fine-grained prior austenite.
Although the martensitic transformation stress forms mainly at the interface of
t w o phases, the parent prior austenite
and the transformation product, martensite, the existence of the retained austenite will keep the stress until room temperature. In addition, at the prior
austenite grain boundaries, phase transformation stress is in a very complex state
because of the different orientation of the
martensite lath in different prior austenite grains. Therefore, the martensitic
transformation stress will not vanish after
the transformation process.
Moreover, the orientation of the HAC
initiation and propagation is usually perpendicular to the radial direction of the
martensite lath, i.e., perpendicular to the
shear stress component of the martensitic
transformation stress. It is considered that
under the action of the shear stress component, the grain boundary will slip and
vacancies w i l l gather up at the grain
boundaries. If the number of the vacancies reaches a certain level, the fissures
will form and become the source of HAC
initiation. The normal stress component
of the martensitic transformation stress
will add to the external stress and decrease the energy required and the critical size, r, for forming a platelet hydrogen
cluster (Ref. 6). The experimental and
calculated results described above fully
proved that the martensitic transformation stress plays an important role in HAC
initiation and propagation.
The nonuniform distribution of the
phase transformation stress will lead to a
nonuniform distribution of the diffusible
hydrogen concentration. The larger the
phase transformation stress is in a local
area, the higher is the local hydrogen
concentration. The maximum of the
local hydrogen concentration will appear in the vicinity of the prior austenite
grain boundary in the radial growing
Discussion
Experimental results indicated that
the coarse-grained prior austenite
boundaries along which HAC initiated
and propagated were just the same as the
fastest growing frontier (radial direction)
of martensite lath, and were consistent
with the region of calculated maximum
martensitic transformation stress. For the
HAZ investigated, the size of coarsegrained prior austenite is 2.5 to 5 times
the grain size of the fine-grained prior
austenite. According to the calculated result shown in Table I, the martensitic
transformation stress in the radial growing frontier of the martensite lath, at the
boundary of the coarse-grained prior
austenite, increases approximately 20%
Fig. 9 — Hydrogen-assisted crack penetrated
into the prior austenite grain, picric etch,
500X.
frontier of martensite lath, which is the
region of the maximum phase transformation stress. Thereby, some parts of the
prior austenite grain boundaries possess
sufficient conditions for HAC initiation.
The increase in prior austenite grain
size will also cause the Ms to decrease,
and then the elastic energy and the local
phase transformation stress to increase.
The phase transformation stress of
high-carbon martensite is generally
larger than that of low-carbon martensite
because the high-carbon martensite has
the higher carbon supersaturation level,
the ratio of lattice constant c/a and the
larger volume difference between
martensite and austenite. Obviously, a
high-phase transformation stress level
must accompany the forming process of
high-carbon martensite.
Of course, the HAC initiation and
propagation processes are very complex.
Other controlling factors for HAC initiation and propagation, such as external
stress, local hydrogen concentration, the
nonhomogeneity of the chemical composition, microstructure and the existence of micro defects, will affect the susceptibility to HAC.
The mechanics of the current HAC
micromodel can be explained clearly
from the sources of stress, considering
the role of local martensitic transformation stress in HAC initiation and propagation. Some strange phenomena of the
HAC with orientations that do not coincide with the macrostresses, i.e., thermal
stress and external restrained stress, can
also be well explained.
Conclusions
Martensitic transformation stress is
distributed nonuniformly along the
martensite lath boundary. Its magnitude
and nonhomogeneity increase with the
increase of prior austenite grain size.
There is a maximum region at the coarse-
W E L D I N G RESEARCH SUPPLEMENT I 289-s
g r a i n e d p r i o r austenite b o u n d a r i e s o n t h e
r a d i a l l y g r o w i n g frontiers o f t h e m a r t e n site laths.
T h e H A C in FCA w e l d s o n H Y - 8 0 steel
i n i t i a t e d m a i n l y in t h e r e g i o n o f m a x i m u m m a r t e n s i t i c t r a n s f o r m a t i o n stress i n
the H A Z .
The m i c r o m e c h a n i c s of the current
H A C initiation and propagation microm o d e l c a n be e x p l a i n e d c l e a r l y f r o m t h e
sources o f stress b y using t h e t h e o r y o f
thermoelastic martensitic transformation.
Acknowledgments
This w o r k w a s c a r r i e d o u t m a i n l y in
the D e p t . o f M a t e r i a l s E n g i n e e r i n g , Rensselaer P o l y t e c h n i c I n s t i t u t e , Troy, N.Y.
T h e authors e x t e n d t h e i r a p p r e c i a t i o n t o
Dr. C . S. A n s e l l , Dr. E. F. N i p p e s , a n d
M e t a l l o g r a p h e r N . J. G e n d r o n for t h e i r
enthusiastic h e l p a n d s u p p o r t .
References
1. Gerberich, W. W., and Lessar, J. F. 1976.
Grain size effects in hydrogen-assisted cracking. Metallurgical Transactions 7A: 953-960.
2. W o o d , W. E., Das, K. B „ and Parrish, P.
A. 1977. The influence of microstructure on
hydrogen embrittlement in high-strength steel.
Proc. of 2nd International
Congress on Hydrogen in Metals, Vol. 3.
3. Esterling, K. 1983. Introduction to the
Physical Metallurgy of Welding, pp. 182-193,
London, Butterworths.
4. Christian, J. W. 1965. The Theory of
Transformations
in Metals and Alloys, p p .
4 1 5 - 4 2 7 and 9 1 5 - 9 2 3 , O x f o r d , Pergamon
Press.
5. Deng, Y. 1985. A theory for thermoelastic martensitic transformation in Cu-Zn-AI alloys. Ph.D. dissertation, Rensselaer Polytechnic Institute, Troy, N.Y.
6. Savage, W. F., Nippes, E. R, and Husa,
E. I. 1982. Hydrogen-assisted cracking in HY130 weldments. Welding Journal 61(8): 233-s
to 242-s.
7. Fujita, F. E. 1977. Theory of hydrogeninduced delayed fracture of steel. Proc. of 2nd
International Congress on Hydrogen in Metals, Vol. 3, Oxford, U.K. Pergamon Press.
8. Coe, F. R. 1973. Welding Steels without
Hydrogen Cracking, pp. 6 4 - 6 6 , The Welding
Institute, Abington, Cambridge, U.K.
9. Beachem, C. D. 1972. A new model for
hydrogen-assisted cracking.
Metallurgical
Transactions 3(2): 259-273.
DAMPING AND RESONANCE
IN HEAT EXCHANGER TUBE BUNDLES
WRC Bulletin 389 presents the results of two studies on vibration
in heat exchanger tube bundles:
VIBRATION DAMPING OF HEAT EXCHANGER TUBE BUNDLES
IN TWO-PHASE FLOW
by M. J. Pettigrew, C. E. Taylor and A. Yasuo
ACOUSTIC RESONANCE IN HEAT EXCHANGER TUBE BUNDLES
by R. D. Blevins
The objective of the first project was to develop a model to formulate damping in two-phase crossflow. The model is based on information available in the literature and particularly on the results of a recently
completed comprehensive experimental program. The report outlines the compilation ol the data base, the
development of a semi-empirical model, and the formulation of design guidelines for the calculation of tube
damping due to two-phase flow.
The second report presents the results of basic experimental work involving acoustic resonance and
how that work produced practical design methods for heat exchangers. The report covers laboratory
experimental results for single tubes, tube rows, and full tube arrays and presents an acoustic resonance heat
exchanger design guide as well as an example which includes field measurements from a large resonating
petrochemical heat exchanger.
The publication of this Bulletin was sponsored by the Committee on Dynamic Analysis and Testing of
the WRC Pressure Vessel Research Council.
The price of WRC Bulletin 389 (February 1994) is $65.00 per copy, plus $5.00 for U.S. and
Canada, or $10.00 for overseas, postage and handling. Orders should be sent with payment to the Welding
Research Council, Inc., 345 E. 47th St., Room 1301, New York, NY 10017, (212) 705-7956; FAX (212) 371-9622.
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