J. KRALJ et al.: FATIGUE BEHAVIOUR OF COPPER-BRAZED 316L STAINLESS STEEL
433–440
FATIGUE BEHAVIOUR OF COPPER-BRAZED 316L STAINLESS
STEEL
UTRUJANJE BAKRENEGA LOTNEGA SPOJA Z NERJAVNIM
JEKLOM 316L
Jernej Kralj
1
, Bla` Han`eli~
1
, Sre~ko Glode`
1*
, Janez Kramberger
1
, Roman
Sato{ek
2
, Branko Ne~emer
1
1
University of Maribor, Faculty of Mechanical Engineering, Smetanova 17, 2000 Maribor, Slovenia
2
Danfoss Trata d.o.o, Korenova 5, SI-1241 Kamnik, Slovenia
Prejem rokopisa – received: 2023-11-02; sprejem za objavo – accepted for publication: 2024-04-24
doi:10.17222/mit.2023.1036
The plate heat exchanger (PHE) is a component that provides heat to be transferred from hot water to domestic cold water with-
out mixing them with high efficiency. Over the lifetime of the PHE, cyclic pressure acts on the brazing points and the plates, and
this can lead to fatigue failure. The fatigue behaviour of the PHE, designed by using copper-brazed 316L (also known as 1.4404)
stainless steel, was investigated by performing fatigue tests to obtain the S-N curve of the analysed brazed joint. The fatigue
tests were performed on a Vibrophore 100 testing machine under the load ratio R = 0.1 for different values of calculated ampli-
tude stress. Based on the obtained experimental results, an appropriate material model of the analysed brazed joint was created,
which was validated with a numerical calculation in the framework of a program code Ansys. A validated material model can
then be used for the subsequent numerical analysis of the PHE.
Keywords: plate heat exchanger, brazed joint, fatigue, experimental testing
Plo{~ni toplotni izmenjevalec je naprava, ki se uporablja za prenos toplote iz vro~ega na hladni medij, pri tem pa je prenos
toplote izveden brez me{anja medijev. Tekom dobe trajanja toplotnega izmenjevalca le-ta prena{a cikli~ne tla~ne obremenitve,
ki so vzrok za poru{itev lotnih spojev med dvema plo~evinama toplotnega izmenjevalca iz materiala 316L (poznano tudi kot
nerjavno jeklo 1.4404). V tem delu je opisana {tudija obna{anja lotnih spojev pod dinami~no obremenitvijo. Na
visokofrekven~nem pulzatorju Vibrophore 100 so bili izvedeni utrujenostnih testi lotnih spojev pri razli~nih amplitudah in
obremenitvenemu razmerju R = 0,1. Na podlagi dobljenih rezultatov je bil definiral materialni model lotnega spoja, ki je bil
naknadno validiran z numeri~nimi simulacijami znotraj programskega paketa Ansys. Razviti materialni model bo tako uporaben
za bodo~e trdnostne analize plo{~nega toplotnega izmenjevalca.
Klju~ne besede: toplotni izmenjevalec, lotni spoj, utrujanje, eksperimentalno testiranje
1 INTRODUCTION
In different engineering applications we can find a lot
of machines that are capable of transferring heat from
hot to cold water. Because of many factors (the needs of
industry, world population growth, etc.), the total number
of those machines increases every year, which results in
intensive technical progress. Machines that transfer heat
are called heat exchangers and are used in many areas of
everyday life. Heat exchangers can be used for the cen-
tral heating of houses, the heating of domestic water, and
many other purposes, including provision for different
industries, e.g., the food industry, the pharmaceutical in-
dustry, and others.
1,2
Due to high applicability, there are many different
types of heat exchangers. Even though they all do the
same tasks (transferring heat), they use different methods
to execute the task. On a base level we can divide all the
heat exchangers into two separate groups, which are re-
cuperators and regenerators. In the first case, the heat is
transferred from hot to cold water simultaneously, while
in the second case, a time delay due to the heat-transfer
method is used.
3
According to the aggregate state of the
heat transferring medium, we also know single-phase
and multi-phase heat exchangers. In this study, a sin-
gle-phase heat recuperator will be analysed. In the case
of this type of heat exchanger, both media have the same
chemical composition (water), and they do not mix with
each other.
3,4
When it comes to different types of heat exchangers,
we also know many geometrical designs, depending on
the heat-transfer method and many other factors, includ-
ing the type of medium, the intensity of the heat transfer,
etc.
4
In this study, a plate heat exchanger (PHE) will be
used. The PHE’s geometrical design and mode of opera-
tion are shown in Figure 1.
This type of PHE consists of many parallel plates
separating the hot and cold channels of the PHE. The
number of plates and the plate thickness greatly depend
on the power of different PHEs, which are needed for a
certain scope of application.
4
In this study, the stainless
steel 1.4404 (copper-brazed 316L) is used as a plate ma-
terial. As connecting elements, which connect plates to-
gether inside the heat exchanger, brazed joints are being
used.
Materiali in tehnologije / Materials and technology 58 (2024) 3, 433–440 433
UDK ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 58(3)433(2024)
*Corresponding author's e-mail:
srecko.glodez@um.si (Sre~ko Glode`)

A brazed joint is a type of connection that is formed
when two points of material are pressed together while
exposed to non-stationary temperature in a good vacuum.
This process is also known as vacuum brazing and is
commonly used in the PHE industry. Vacuum brazing is
a jointing process that is accomplished at high tempera-
tures, usually between 930 °C and 1230 °C, using a pure
copper or nickel base alloy as the filler material.
6,7
In this
production technology, a lower residual oxygen level in-
side the vacuum is achieved, and the contamination of
parts is prevented. Here, the naturally formed oxide lay-
ers on the base metals can be decomposed in a vacuum at
high temperatures, and it provide better joint properties
such as high strength and less porosity through enhanced
wetting. Additionally, vacuum brazing is favourable for
lean and agile manufacturing due to the repeatability and
reliability of brazed joints. In order to have a high-qual-
ity brazed joint, the parts must be closely fitted, and the
base metal surfaces must be well cleaned. Here, the suit-
able clearance between braising parts should be a maxi-
mum of 0.1 mm in order to reach a good capillary effect.
Brazing-surface cleanliness is very important since the
contaminations on the surface can lead to insufficient
wetting.
8
Due to possible defects resulting from the manufac-
turing process, the brazed joint itself represents a possi-
ble weak spot where failure may occur. The failure oc-
curs as a consequence of pressure inside the liquid
medium and the presence of manufacturing defects. As a
result of pressure changes in a liquid medium (water), a
dynamic tensile force is applied to a brazed joint. When
failure occurs in one of the PHE’s brazed joints, the ten-
sile stress on the remaining brazed joins in the surround-
ing area increases, which leads to a higher possibility of
failure in those joints. With the increasing number of
failures in brazed joints, the lifetime of the PHE de-
creases.
9
In addition to the material’s mechanical properties,
the strength of brazed joints is also greatly influenced by
the dynamic character of the tensile load, which also var-
ies with different applications of use and types of PHEs.
To define the dynamic character of the tensile force act-
ing on a brazed joint, the appropriate loading ratio R
should be applied. Furthermore, the amplitude stress
level must also be considered because it has a significant
impact on the fatigue behaviour of the analysed brazed
joint.
10
There are also many other factors that can have,
in some cases, a great impact on the lifetime of a PHE:
surface roughness, loading frequency, notch effects, tem-
perature, etc.
11
In this study we focused on the constant
loading frequency, constant temperature (all tests were
performed at room temperature) and constant surface
roughness. In that respect, a special specimen has been
constructed to analyse the mechanical and fatigue prop-
erties of brazed joints for subsequent use in different ap-
plications of PHE. Furthermore, a material model of the
analysed brazed joint has been developed, which enables
further computational simulations of the PHEs made
with brazing joint technology.
2 EXPERIMENTAL TESTING
2.1 Specimen preparation
The test specimen shown in Figure 2 was prepared
using the same manufacturing process (vacuum brazing)
as normally used when making brazed joints in PHEs
(see also Section 1). Here, two bars made of stainless
steel 1.4404 (see Table 1) were vacuum brazed using a
copper foil with a thickness of 0.1 mm.
2.2 Quasi-static tests
Quasi-static tests were made on a Zwich/Roel
Vibrophore 100 testing machine. Four quasi-static tensile
tests were made to obtain the engineering – diagram of
J. KRALJ et al.: FATIGUE BEHAVIOUR OF COPPER-BRAZED 316L STAINLESS STEEL
434 Materiali in tehnologije / Materials and technology 58 (2024) 3, 433–440
Figure 1: Geometry of PHE under consideration
5
Table 1: Chemical composition of the steel 1.4404 in w/% according to the EN 10088-3
C Si Mn P S Cr Mo Ni N
 0.03  1.0  2.0  0.045  0.015 16.5-18.5 2.0-2.5 10.0-13.0  0.11

the analysed brazed joint. The quasi-static tests were dis-
placement-controlled using a mechanical extensometer
with a constant displacement rate of 0.5 mm/min up to
the final fracture of the specimen. The results for all four
tests are presented in Figure 3 and summarised in Ta-
ble 2.
The axial deformation of the test specimen is a com-
bination of the axial deformation of the steel pieces and
the copper part in the middle of the test specimen. How-
ever, the volume of the copper part in the middle of the
test specimen is practically negligible if compared to the
volume of the steel pieces. It is, therefore, reasonable
that the majority of the total axial deformation is due to
the elongation of the steel part of the test specimen. For
the same reason it is also reasonable to expect the value
of the modulus of elasticity to be approximately equal to
that of the base material of the test specimen (200 GPa
for the selected stainless steel). The same is also valid for
the yield stress and tensile strength of the analysed
brazed joint.
Based on the average values of the mechanical prop-
erties presented in Table 2, the average engineering
stress–strain curve ( eng
– eng
) was obtained. However, the
true stress–strain curve ( true
– true
) should be applied
when creating the material model of the analysed brazed
joint (see Section 4). Therefore, the following equations
should be used to make this transformation:
12

true eng
=+ ln( ) 1 (1)

true eng eng
=+ () 1 (2)
When creating the material model of the analysed
brazed joint, the elastic part of the true stress–strain
curve can be given by the Youngs’ modulus E (see Ta-
ble 2). Therefore, only the plastic part should be defined
as a data pair ( true
– true
).
2.3 Fatigue tests
Fatigue tests were made on the same machine as the
quasi-static tests (Zwich/Roel Vibrophore-100) using the
same specimens (see Figure 2). The fatigue tests were
performed at a temperature of 20 °C under a loading ra-
tio R = 0.1 and a loading frequency of approximately 98
Hz. All the tests were performed in the high-cycle fa-
tigue regime (HCF), which means that the maximum
stress in each loading cycle did not exceed the yield
stress of the analysed braised joint (i.e., R
e
= 237 MPa,
see Table 2). Following this limitation, the maximum
tensile stress of (0.6–0.8)⋅R
e
was selected. Figure 4
shows the S−N plot of fatigue tests where the amplitude
stress a
is given on the ordinate axis.
As already explained above, the fatigue tests were
performed under a loading ratio R = 0.1. It means that
J. KRALJ et al.: FATIGUE BEHAVIOUR OF COPPER-BRAZED 316L STAINLESS STEEL
Materiali in tehnologije / Materials and technology 58 (2024) 3, 433–440 435
Figure 2: Geometry of test specimens
Figure 3. Engineering diagram – of quasi-static tests
5
Table 2: Mechanical properties of the analysed brazed joint
Youngs modulus Poissons ratio Yield stress Ultimate tensile stress Elongation
Specimen No. E (MPa) v (–) Re
(MPa) R
m
(MPa) EL (%)
#1 200,049 0.28 240 469 13.5
#2 197,472 0.28 234,5 387 7.4
#3 196,078 0.28 238 420 9.1
#4 199,951 0.28 235,5 473 14.4
Average 198,387 0.28 237 437 11.1

for each amplitude stress  a
, the belonging mean stress
 m
can be obtained as follows:
  m
a
=
+
−
() 1
1
R
R
(3)
However, the standardised fatigue tests of different
engineering materials are usually performed with zero
mean stress (i.e.,  m
=0;R = –1). With that respect, the
fatigue material parameters of engineering materials
taken from the literature are usually related to the zero
mean stress. For that reason, the S-N curve for R = 0.1
presented in Figure 4 could be transformed into the S–N
curve for R = –1 using the Goodman equation:
13,14

 a D
m
m
(. ) R
R
==−
⎡ ⎣ ⎢ ⎤ ⎦ ⎥ 01 1 (4)
where D
is the fatigue strength for R=–1andR
m
is the
ultimate tensile stress of the analysed braised joint. Con-
sidering the average ultimate tensile strength of the ana-
lysed brazed joint R
m
≈ 437 MPa (see Table 2), the fol-
lowing data pairs for zero mean stress can be defined:
N
1
= 171269  a1
=90MPa  D1
= 120.3 MPa
N
2
= 6822251  a2
=60MPa  D2
= 72.1 MPa
When analysing the fatigue problems of engineering
components and structures, the Basquine equation is nor-
mally used to describe the S–N curve:

true eng eng
=+ () 1 (5)
where  f
’ is the fatigue-strength coefficient and b is the
fatigue-stress exponent. Considering the data pairs (N
1
,
 D1
) and (N
2
,  D2
) as described above, the material pa-
rameters  f
’andb for zero mean stress (i.e.,  m
=0 ;
R = –1) result in f
’= 706.1 MPa and b = – 0.139. These
parameters will then be considered when creating the fa-
tigue material model of the analysed brazed joint (see
Section 3).
3 NUMERICAL MODELLING
The numerical modelling of the analysed brazed
joints was performed using Ansys software, where the
simplified geometry of the brazed joint specimen was
applied for that purpose. In this case, the numerical
model was built as a solid homogeneous piece of the ma-
terial with the same cross-section area as already used in
the experimental testing (see Figure 2). However, only
the measuring length of the specimen (i.e., 50 mm) was
considered for the subsequent numerical computations.
In the material section of the Ansys database, the new
material was defined. It had the same mechanical proper-
ties as obtained in the framework of the experimental
testing. Here, it should be pointed out that all the me-
chanical properties were applied at room temperature
 0
= 20 °C. In the next step, all the boundary conditions
of the numerical model were obtained in order to per-
form the proper numerical simulation. In that respect,
certain degrees of freedom in the numerical model were
limited by setting some displacement values to zero. Fur-
thermore, external loading was applied indirectly by the
non-zero values of the displacement on the front surface
of the numerical model (see Figure 5). These values of
the displacement should be large enough to reach an en-
gineering stress that is higher than the yield strength of
the material (i.e., analysed braised joint), resulting in
plastic strain. The described loading procedure was only
used to perform static numerical simulations to confirm
the experimental results obtained previously with tensile
tests (see Section 2.2).
In the case of the numerical simulation of the fatigue
loading, different values of the tensile force were pre-
scribed on the same surface, as explained above for the
quasi-static numerical simulation. Here, the maximum
tensile force and, consequently, different levels of ampli-
tude stress were defined for each simulation considering
J. KRALJ et al.: FATIGUE BEHAVIOUR OF COPPER-BRAZED 316L STAINLESS STEEL
436 Materiali in tehnologije / Materials and technology 58 (2024) 3, 433–440
Figure 4: S–N plot of the analysed brazed joints
5

the loading ratio R = 0.1 and Goodmann’s model to eval-
uate the mean stress effect. In computational modelling,
a standard Ansys finite element type SOLID 186 was se-
lected. This is a 3D quadratic finite element that has a
cuboid shape.
15,16
After the comprehensive mesh-conver-
gence analysis, a FE mesh with a FE size of 1 mm was
used.
The numerical model, as described above, was then
used for the subsequent numerical simulations. In the
first step, the quasi-static numerical simulation was per-
formed to obtain the engineering  − diagram (see Fig-
ure 6). Here, the reaction forces acting in the opposite
direction with regard to the external loading were ob-
tained in each loading step and then divided by the
cross-section area of the specimen.
When creating the fatigue material model of the ana-
lysed brazed joint, the characteristic data pairs ( a
, N)
taken from the trendline of the S–N plot in Figure 4 (see
Table 3) were considered. For this purpose, we con-
verted the values of amplitude stress  a
from Table 3 to
values of maximum stress  max
and then calculated the
number of cycles N for the load ratio R = 0.1 using
Goodman’s equation to consider the mean stress effect.
Figure 7 shows the S–N plot of the fatigue numerical
simulation as described above.
Table 3: Calculated data pairs ( a
, N) taken from the trendline of the
S–N plot in Figure 4
Amplitude stress a
(MPa) Number of loading cycles N (–)
90 171269
85 287917
80 499498
75 897941
70 1680899
65 3296275
60 6822251
4 RESULTS AND DISCUSSION
Figure 8 shows the comparison between the experi-
mental and computational results for the engineering dia-
gram – . It is evident that for all the considered experi-
mental tests the yield stress was around 237 MPa, which
corresponds to the numerical simulations. In the elastic
area (below the yield stress) a very good match between
the experimental and numerical results was observed.
However, in the plastic area (above the yield stress),
more mismatches appeared, especially in the case of the
ultimate tensile strength. It is clear that the ultimate
strength determined by the numerical simulation was
around 437 MPa, which corresponds to the average value
J. KRALJ et al.: FATIGUE BEHAVIOUR OF COPPER-BRAZED 316L STAINLESS STEEL
Materiali in tehnologije / Materials and technology 58 (2024) 3, 433–440 437
Figure 5: Applied load case for the static numerical simulation
Figure 7: S−N plot of the fatigue numerical simulation Figure 6: Numerical determination of the engineering diagram –

J. KRALJ et al.: FATIGUE BEHAVIOUR OF COPPER-BRAZED 316L STAINLESS STEEL
438 Materiali in tehnologije / Materials and technology 58 (2024) 3, 433–440
Figure 9: Experimentally and computationally obtained S–N plot for R = 0.1
Figure 8: Experimentally and computationally obtained engineering diagram – Figure 10: Computationally obtained S–N plot for R = –1 (i.e., m
=0)

of the ultimate tensile strength obtained experimentally.
Considering this fact, the material model for the
quasi-static loading of the analysed braised joint was val-
idated.
Figure 9 shows a comparison between the experi-
mental and computational results for the fatigue load-
ing(S–N plot) of the analysed brazed joint. In both cases,
the fatigue life (i.e., the number of cycles N until failure)
increased with a decrease in the amplitude stress  a
.
However, the scatter of the experimental results is much
wider if compared to the quasi-static loading. This is
probably due to a greater impact of the manufacturing er-
rors on the fatigue strength occurring during the manu-
facturing process of the specimens. On the other hand,
the computational results are still a good representation
of the experimental results, which validate the material
model for the fatigue evaluation.
In the case of the loading ratio R = 0.1, the mean
stress level is not constant for all levels of the amplitude
stress. The constant value of the mean stress can be
achieved by adjusting the loading ratio R to the value –1
(i.e., zero mean stress). As the amplitude stress  a
changes, the mean stress remains zero; therefore, it is
possible to determine the number of loading cycles at
different values of  a
and zero mean stress. The S–N
curve of the analysed brazed joint for zero mean stress is
presented in Figure 10.
5 CONCLUSION
For the purpose of this study, tensile experimental
testing of brazed joint specimens was conducted. In the
first phase, quasi-static testing was performed to define
the engineering  – curve. Furthermore, comprehensive
fatigue tests under a pulsating loading (load ratio
R = 0.1) were performed to obtain the S–N curve of the
analysed brazed joints. Based on the theoretical study,
experimental testing, and comprehensive numerical anal-
yses, the following conclusions can be drawn:
In the case of quasi-static testing, the yield stress var-
ied between 235 MPa and 240 MPa for all the tested
specimens. Therefore, the average value R
e
= 237 MPa
was obtained as the yield stress of the analysed brazed
joint. On the other hand, different values of the ultimate
tensile stress R
m
ranging between 387 MPa and 473 MPa
were obtained for the individual specimens.
Based on the obtained experimental results, an aver-
age engineering  – curve was created and then divided
into individual linear segments. For the purpose of the
subsequent computational analyses, the amount of elastic
strain was subtracted from the total strain in the true – diagram.
In the second phase, the fatigue testing under load ra-
tio R = 0.1 at a temperature of 20 °C was performed to
obtain the S–N plot of the analysed brazed joint. Further-
more, the Goodman mean stress correction was applied
to express the obtained experimental results for the load
ratio R = –1 (i.e., for the zero mean stress), which usu-
ally appears when presenting the fatigue properties of
engineering materials in the literature.
The material model was validated with a numerical
analysis using the Ansys software. A validated material
model can then be used for the subsequent numerical
analysis of PHE in different engineering applications.
Acknowledgements
The authors acknowledge the financial support of the
Research Core Funding (No. P2-0063) and the Basic
Postdoc Research Project (No. Z2-50082) from the
Slovenian Research Agency. The authors also acknowl-
edge for the use of research equipment High-Frequency
Pulsator, procured within the project “Upgrading na-
tional research infrastructures – RIUM”, which was
co-financed by the Republic of Slovenia, the Ministry of
Education, Science and Sport and the European Union
from the European Regional Development.
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440 Materiali in tehnologije / Materials and technology 58 (2024) 3, 433–440