Evaluation of cyclic instability by mechanical characteristics for structural materials/Konstrukciniu medziagu ciklinio nestabilumo ivertinimas pagal mechanines charakteristikas.
Daunys, M. ; Sniuolis, R. ; Stulpinaite, A. 等
1. Introduction
Working conditions and material properties of machines must be
analyzed in order to improve their quality, reliability and lifetime.
Strain and stress change during the exploitation depend on material type
(cyclically hardening, softening or stable), therefore we must know the
material type that is chosen for the structures under low cycle loading.
The application of particular structural material on certain
exploitation conditions is determined by its type.
Hardened steels cyclically soften, tempered or normalized steels
are cyclically stable or harden under low cycle loading [1]. Regulation
of the temperature and determining of the stress strain curves, in
particular at elevated temperature, make the experiments of low cycle
loading complicated and expensive. Therefore it is very important that
the parameter of cyclic instability (hardening or softening intensity)
could be obtained from monotonous tension curves without cyclic loading.
Over 300 structural materials that are used in nuclear power
engineering were tested under monotonous tension and symmetric low cycle
tension-compression in Kaunas University of Technology together with St.
Peterburg Central Research Institute of Structural Materials. The main
mechanical, low cycle loading and fracture characteristics of alloyed
structural steels, stainless steels and metals of their welded joints
with different types of thermal treatment at room and elevated
(200-350[degrees]C) temperatures were determined during these
experiments.
Cyclic instability of welded joint materials, obtained by the same
methods and testing equipment, was evaluated according to mechanical
properties in this work for 227 structural materials. Various methods of
evaluation of cyclic instability have been used in many scientific
works, but to the lesser number of materials.
2. Evaluation of cyclic instability of materials according to
mechanical properties
Monotonous tension and low cyclic loading are similar by
accumulation of plastic strain, therefore the mechanical characteristics
can be used for quantitative evaluation of materials. This method was
used in the early works of R. Landgraf and A. Romanov.
R. Landgraf [2] determined that at [[sigma].sub.u]/[[sigma].sub.y]
> 1.4 structural materials cyclically harden, at
[[sigma].sub.u]/[[sigma].sub.y] < 1.2 they cyclically soften and at
1.2 < [[sigma].sub.u]/[[sigma].sub.y] < 1.4 they are cyclically
stable (Table 1), where [[sigma].sub.y] is yield strength and
[[sigma].sub.u] is ultimate strength of structural materials.
In A. Romanov's and A. Gusenkov's works [3], after
testing of 48 structural materials, it was shown, that the relation
[[sigma].sub.u]/[[sigma].sub.y] is not the main factor for the
evaluation of cyclic properties. Their proposal was, that the main
factor is the relation [e.sub.u]/[e.sub.f]. Here [e.sub.u] is the strain
of uniform reduction of area (before necking of specimen) and [e.sub.f]
is the fracture strain under monotonous tension. A. Romanov determined,
that at [e.sub.u]/[e.sub.f] < 0.45 materials cyclically soften, at
[e.sub.u]/[e.sub.f] > 0.6 cyclically harden and at 0.45 <
[e.sub.u]/[e.sub.f] < 0.6 are cyclically stable (Table 1). A.
Romanov's premise is valuable, because strain, but not stress
characteristics more precisely describe the behaviour of materials under
low cycle loading. The main drawback of this premise is complicated
determination of the strain of uniform reduction of area [e.sub.u].
Furthermore, [e.sub.u] is not given in technical manuals, because it is
not a standard characteristic of a material.
After the investigation of test results of structural materials
(about 300 steels and their weld metals), such zones of cyclic
properties were determined in coordinate
Z-[[sigma].sub.u]/[[sigma].sub.y] (here Z is reduction of the area at
fracture) [1]: 1) when [[sigma].sub.u]/[[sigma].sub.y] > 1.8
materials cyclically harden; 2) when [[sigma].sub.u]/[[sigma].sub.y]
< 1.4 and Z < 0.7 cyclically soften; 3) when
[[sigma].sub.u]/[[sigma].sub.y] < 1.4 and Z > 0.7 are cyclically
stable; 4) when 1.4 < [[sigma].sub.u]/[[sigma].sub.y] < 1.8 there
is the transition zone, where, independently of Z, weak hardening,
softening or stable materials are revealed. An additional transition
area 0.5 < Z < 0.7 between stable and softening zones appears for
weld materials (Table 1).
3. Mechanical and cyclic characteristics and their relationship
Relationship between stress and strain for the cyclic stress strain
curve is described by the equation [1]
[[bar.[epsilon]].sub.k] = [[bar.S].sub.k] + [[bar.[delta]].sub.k]
(1)
where [[bar.[epsilon]].sub.k] and [[bar.S].sub.k] are cyclic strain
and stress range for k semicycle respectively; [[bar.[delta]].sub.k] is
the width of hysteresis loop; k is the number of cemicycle.
In Eq. (1) stress and strain are normalized to the stress and
strain of proportionality limit, i.e.
[[bar.S].sub.k] = [[S.sub.k]/[[sigma].sub.pl]]; [bar.[epsilon]] =
[epsilon]/[e.sub.pl]; [bar.[delta]] = [delta]/[e.sub.pl] (2)
According to the test conditions under low cycle loading with
limited strain, [[bar.[epsilon]].sub.k] = const. Therefore cyclic stress
range [[bar.S].sub.k] is variable under loading with limited strain
(Fig. 1). The same materials can harden, soften or be stable in
dependence on the number of cycles and loading level.
[FIGURE 1 OMITTED]
At cyclic straining the behavior of a material is determined by the
dependence of cyclic stress [[bar.S].sub.k] and the width of hysteresis
loop [[bar.[delta]].sub.k] on the number of cemicycles k. It is shown in
the work [4], that the dependence of width of hysteresis loop
[[bar.[delta]].sub.k] on the number of cemicycles k in double
logarithmic coordinate makes straight line at cycle straining.
[FIGURE 2 OMITTED]
According to graphical interpretation of linear regression, the
width of hysteresis loop of k-th semicycle
lg[[bar.[delta]].sub.k] = lg[[bar.[delta]].sub.1] + [alpha]lg k (3)
or the width of hysteresis loop for cyclically softening materials
(Fig. 2)
[[bar.[delta]].sub.k] = [[bar.[delta]].sub.1][k.sup.a] (4)
The width of hysteresis loop for cyclically hardening materials
(Fig. 3)
[[bar.[delta]].sub.k] = [[bar.[delta]].sub.1][k.sup.-[alpha]] (5)
[FIGURE 3 OMITTED]
For cyclically stable materials parameter [alpha] = 0 and the width
of hysteresis loop
[[bar.[delta]].sub.k] = [[bar.[delta]].sub.1] (6)
When the widths of hysteresis loop for semicycles
[[bar.[delta]].sub.1] and [[bar.[delta]].sub.k] are determined in
coordinate lg[[bar.[delta]].sub.k] - lgk, the parameter for the
evaluation of cyclic instability (hardening or softening intensity) is
determined by the equation
[alpha] = lg[[bar.[delta]].sub.k] - lg[[bar.[delta]].sub.1]/lg k
(7)
[FIGURE 4 OMITTED]
Parameter [alpha] was determined from experimental results of all
materials tested at low cycle straining. These materials have been
divided into three groups in such manner: if -0.01 [less than or equal
to] [alpha] [less than or equal to] 0.01 the material was nominated as
cyclically stable, if [alpha] > 0.01--as cyclically softened and if
[alpha] < -0.01--as cyclically hardened [4, 5].
The values of [[bar.[delta]].sub.k] were rejected (marked
"x") for semicycles k = 1 - 9 due to unsettled change of
cyclic stress strain curves for these semicycles (Figs. 2 and 3).
In previous works [4-7] the accomplished statistical analysis
confirmed that parameter [alpha] and modified plasticity
([[sigma].sub.u]/[[sigma].sub.y])Z at room and elevated temperatures
were distributed according to the normal law and describe test results
in the best way.
After the investigation of 227 test results, the dependences of
parameter [alpha] on modified plasticity
([[sigma].sub.u]/[[sigma].sub.y])z for structural steels and their weld
metal at room and elevated temperature and 95% confidence intervals
(dotted line) for the theoretical regression line are represented in
Figs. 4-10. The analytical dependences of parameter [alpha] on modified
plasticity ([[sigma].sub.u]/[[sigma].sub.y])Z for all investigated
materials at room and elevated temperature are given in Table 2.
For the comparison of experimental and calculated results the
intervals: [bar.x] [+ or -] 0.675s (probable deviation) with the
probability P [approximately equal to] 0.50; [bar.x] [+ or -] s with the
probability P [approximately equal to] 0.68 and [bar.x] [+ or -] 1.96s
with the probability P [approximately equal to] 0.95 (95% area of normal
curve) [6] were determined. Here [bar.x] is the mean value of
experimental cyclic instability a of structural materials and s is
standard deviation.
[FIGURE 5 OMITTED]
[FIGURE 6 OMITTED]
[FIGURE 7 OMITTED]
[FIGURE 8 OMITTED]
[FIGURE 9 OMITTED]
[FIGURE 10 OMITTED]
[FIGURE 11 OMITTED]
The comparison of experimental and calculated (Table 2) parameter
[alpha] for alloyed structural steels at room temperature is shown in
Fig. 11, for all investigated materials at low cycle straining are shown
in Table 3.
4. Conclusions
1. Parameter [alpha] characterizes intensity of cyclic hardening or
softening rather precisely and can be used for all investigated
structural materials at room and elevated temperature.
2. Cyclic instability parameter [alpha] for all materials and
testing temperatures may be evaluated according to modified plasticity.
3. According to scatter of the results of linear relationship
between the parameter [alpha] and modified plasticity, it is likely that
it would be more precise when all investigated structural materials were
subgrouped according to chemical composition or heat treatment.
References
[1.] Daunys, M. 1989. Strength and Fatigue Life under Low Cycle
Non-Stationary Loading. Vilnius: Mokslas. 256p (in Russian).
[2.] Landgraf, R.W. 1970. The Resistance of Metals to Cyclic
Deformation, Achievement of High Fatigue Resistance in Metals and
Alloys. Philadelphia, 3-36.
[3.] Gusenkov, A.P; Romanov, A.N. 1971. Characteristics of
resistance to low cycle loading and fracture of structural materials.
Kaunas: KPI. 45p (in Russian).
[4.] Sniuolis, R. 1999. Dependence of Low Cycle Fatigue Parameters
on Mechanical Characteristics of Structural Materials, Doctoral Thesis,
117p (in Lithuanian).
[5.] Sniuolis, R.; Daunys, M. 1999. Determination of low cycle
loading curves parameters for structural materials by mechanical
characteristics, Mechanika 2(16): 16-23.
[6.] Sniuolis, R.; Daunys, M. 2001. Methods for determination of
low cycle loading curves parameters for structural materials, Mechanika
3(29): 11-16.
[7.] Daunys, M.; Sniuolis, R. 2006. Statistical evaluation of low
cycle loading curves parameters for structural materials by mechanical
characteristics, Nuclear Engineering and Design 236(13): 1352-1361.
http://dx.doi.org/10.1016/j.nucengdes.2006.01.008.
M. Daunys *, R. Sniuolis **, A. Stulpinaite ***
* Kaunas University of Technology, Kestucio str. 27, 44312 Kaunas,
Lithuania, E-mail: Mykolas.Daunys@ktu.lt
** Siauliai University, Vilniaus str. 141, 76353 Siauliai,
Lithuania, E-mail: rsrs@tf.su.lt
*** Siauliai University, Vilniaus str. 141, 76353 Siauliai,
Lithuania, E-mail: agette@gmail.com
doi: 10.5755/j01.mech.18.3.1887
Table 1
Evaluation of cyclic instability of structural materials according to
mechanical properties
R.W. [[sigma].sub.u]/[[sigma].sub.y] materials cyclically
Landgraf > 1.4 harden
[[sigma].sub.u]/[[sigma].sub.y] materials cyclically
< 1.2 soften
1.2 < [[sigma].sub.u]/ materials cyclically
[[sigma].sub.y] < 1.4 stable
35 materials (steels, aluminium and titanium alloys) were tested.
The suggested premise was confirmed for 26 materials
A. Gusenkov, [[sigma].sub.u]/[[sigma].sub.y] is not the main
A. Romanov factor for the
determination of
cyclic properties
of materials
[e.sub.u]/[e.sub.y] > 0.6 materials cyclically
harden
[e.sub.u]/[e.sub.y] < 0.45 materials cyclically
soften
0.45 < [e.sub.u]/[e.sub.y] materials cyclically
< 0.6 stable
[e.sub.u]--strain of uniform
elongation;
[e.sub.f]--fracture strain
48 materials (44 steels and 4 aluminium alloys). This premise was very
well confirmed for 25 steels.
M. Daunys, [[sigma].sub.u]/[[sigma].sub.y] materials cyclically
A. Branas, > 1.8, independent of Z harden
others [[sigma].sub.u]/[[sigma].sub.y] materials cyclically
< 1.4, Z < 0.7 soften
[[sigma].sub.u]/[[sigma].sub.y] materials cyclically
< 1.4, Z > 0.7 stable
1.4 < [[sigma].sub.u]/ transition zone
[[sigma].sub.y]
< 1.8, independent of Z
[[sigma].sub.u]/[[sigma].sub.y] welded metal
< 1.4, 0.5 < Z < 0.7
106 materials (steels and welded metal of alloyed structural steels and
4 aluminium alloys) were tested
Table 2
Relationship of cyclic instability parameter and modified plasticity
for all investigated materials
Materials Room temperature Elevated temperature
Alloyed [alpha] = 0.054 - 0.039 [alpha] = 0.047 - 0.025
structural ([[sigma].sub.u]/ ([[sigma].sub.u]/
steels [[sigma].sub.y])z [[sigma].sub.y])z
Weld metal [alpha] = 0.034 - 0.019 [alpha] = -0.034 + 0.039
of alloyed ([[sigma].sub.u]/ ([[sigma].sub.u]/
structural [[sigma].sub.y])z [[sigma].sub.y])z
steels
Stainless [alpha] = 0.052 - 0.035 [alpha] = 0.036-0.030
steels ([[sigma].sub.u]/ ([[sigma].sub.u]/
[[sigma].sub.y])z [[sigma].sub.y])z
Weld metal [alpha] = 0.036 - 0.018 -
of stainless ([[sigma].sub.u]/
steels [[sigma].sub.y])z
Table 3
Comparison of experimental and calculated parameter a at room and
elevated temperature
Number Materials Number of samples, when the
of dispersion between experimental
samples and calculated parameter [alpha]
is in the interval
[bar.x] [bar.x] [bar.x]
[+ or -] [+ or -] [+ or -]
0,675s s 1,96s
n % n % n %
36 Alloyed structural steels 23 64 24 67 36 100
at room temperature
23 Alloyed structural steels 10 43 17 74 22 96
at elevated temperature
69 Weld metal of alloyed 27 39 50 72 66 96
structural steels at
room temperature
33 Weld metal of alloyed 16 48 24 73 33 100
structural steels at
elevated temperature
28 Stainless steels at room 18 64 24 86 28 100
temperature
13 Stainless steels at 5 38 9 69 13 100
elevated temperature
25 Weld metal of stainless 13 52 19 76 25 100
steels
