Evaluation of cyclic instability by mechanical characteristics for structural materials

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°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.


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°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.

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]  between stable and softening zones appears for weld materials (Table 1).

Mechanical and cyclic characteristics and their relationship
Relationship between stress and strain for the cyclic stress strain curve is described by the equation [1] where k  and k S are cyclic strain and stress range for k semicycle respectively; k  is the width of hysteresis loop; k is the number of cemicycle.welded metal 106 materials (steels and welded metal of alloyed structural steels and 4 aluminium alloys) were tested In Eq. ( 1) stress and strain are normalized to the stress and strain of proportionality limit, i.e. ;; According to the test conditions under low cycle loading with limited strain, const k   .Therefore cyclic stress range k S 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.
or the width of hysteresis loop for cyclically softening materials (Fig. 2) The width of hysteresis loop for cyclically hardening materials (Fig. 3)
The values of k  were rejected (marked "x") for semicycles 9 1  k due to unsettled change of cyclic stress strain curves for these semicycles (Figs. 2 and 3).
In previous works [4][5][6][7]  The comparison of experimental and calculated (Table 2) parameter α 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.

Conclusions
1. Parameter α 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 α 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 α 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.After the investigation of 227 structural materials at low cycle straining, the cycle properties of structural materials by mechanical characteristics were evaluated.After a thorough analysis of the graphical results, the cyclic stress-strain curves parameter α, which characterizes intensity of cyclic hardening or softening of structural materials at room and elevated temperature rather precisely, was determined.Dependences for the evaluation of cyclic instability according to modified plasticity  

Fig. 1 Fig. 2
Dependence of cyclic stress on the number of semicycles for steel 15Ch2MFA under cyclic loading with limited strain At cyclic straining the behavior of a material is determined by the dependence of cyclic stress k S and the width of hysteresis loop k  on the number of cemicycles k.It is shown in the work [4], that the dependence of width of hysteresis loop  k on the number of cemicycles k in double logarithmic coordinate makes straight line at cycle straining.Dependence of hysteresis loop width on the number of semicycles for softening material (steel 15Ch2MFA), when 19 k  are rejected According to graphical interpretation of linear regression, the width of hysteresis loop of k-th semicycle

Table 1 )
[3]here 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 y is yield strength and u 

Table 1
Evaluation of cyclic instability of structural materials according to mechanical properties

Table 3
Comparison of experimental and calculated parameter α at room and elevated temperature