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Evaluation of cyclic instability by mechanical characteristics for structural materials/Konstrukciniu medziagu ciklinio nestabilumo ivertinimas pagal mechanines charakteristikas.

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
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Author:Daunys, M.; Sniuolis, R.; Stulpinaite, A.
Publication:Mechanika
Article Type:Report
Geographic Code:4EXLT
Date:May 1, 2012
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