On the experimental analysis of dissipative processes under cyclic loading of metals

The article is devoted to the experimental study of dissipative material properties tested under homogeneous stress-strain conditions, which realized on the gage part of a smooth sample subjected to cyclic loading with increasing amplitude. A new method to estimate inelastic material properties under strain lower than the nominal strength is proposed. At the initial stages of loading, the method makes it possible to find out irreversible changes in sample characteristics and define material elastic limit under cyclic loading. Strain, longitudinal and lateral stress, as well as temperature of the gage part of a sample are the sample characteristics measured simultaneously. They make it possible to distinguish the components connected with reversible and irreversible strain processes associated with fatigue damage of material.


Introduction
Data on inelastic stress of metals obtained at stresses in the range between the proportional elastic limit and yield strength of the material are often applied in the preliminary estimation of fatigue damage resistance characteristics. In particular, Coffin's formula [1] is widely used to describe the fatigue stress accumulation process. The formula includes inelastic stress characteristics which is a width of hysteresis loop. There are several methods in which damage accumulation is connected with the change of various integral parameters of metal energy dissipation, based on measurement of the absorption coefficient, logarithmic decrement of oscillation and temperature inside damage nucleus [2 -4]. The phenomenon of elasto-plastic loosening of the material and the material model describing the formation of micropores are used in some approaches [5,6].
There is a necessity in experimentally derived dependencies from general inelasticity concepts, for example, to identify equations describing the real inelastic strain process, which follows degradation of the material under cyclic loadings.
Modern concepts of reversible processes deal with the term "hysteresis loop", which is widely used to describe inelastic strain cycle.
Indeed, the sigma-epsilon diagrams in Figure 1 are not closed loops (and the stress process is not cyclic) because the "loops" are broken, and the presented trajectories are closed (coincide) only at one point. From the point of view of thermodynamics such a cycle is irreversible.
The hysteresis loop for plastic materials is known to be open at stresses below the endurance limit [8]. Then a question arises: "Why does the irreversible stress not lead to destruction?" The research which takes into account the kinetics of phase transformations in stress of metastable austenitic steels [9] shows the correlation between the density of microcracks and the amount of martensite. The research presents methods to define the characteristics of materials describing dissipative processes. The approach is based on the concepts of reversible and irreversible processes [10]. The main goal of the research is to show the possibility of experimental determination of the material's characteristics describing its fatigue damage from the point of physics of strength.
In the research it is required to obtain the following effects under periodic loading: nonlinear stress when loaded beyond the limit of proportionality; changes in volume or shape, deterministic change of material microstructure; dissipative heating of the material.
For the research, the metastable steel 08Х18Н10Т of austenitic class with the following chemical composition was chosen [11]: C not more than 0.08%, Si not more than 0.8%, Mn not more than 2%, Cr 17-19%, Ni 9-11%, Ti not more than 0.7%, S not more than 0.02%, P not more than 0.035%, Cu not more than 0.3%, the basic element is -Fe. The mechanical characteristics were obtained under quasistatic soft loading at a speed of 150 N/s. Modulus of elasticity is 200700 MPa, proportional elastic limit is 280 MPa, conventional yield strength is 302 MPa, temporary stress resistance is 586 MPa. Choosing austenitic steel we relied on the ability of austenite to transform isothermally into strain-induced martensite under mechanical stresses.

Samples, equipment and methods
For the research, samples of rectangular cross section of 6 x 10 mm 2 with a gage length of 50 mm were used which allowed fixing two extensometers for measuring axial and transverse strains.
The sample surface, intended to measure the temperature with the help of a thermal imagery camera, was preliminary blackened covering with a thin layer of soot, thus ensuring a blackness coefficient of the surface close to 1. To eliminate the influence of external thermal fields on the measurements radiant temperature screens were used.
The samples were deformed by zero-to-compression stress cycle with a stress amplitude increasing in proportion to time. The selected zero-to-compression stress cycle made it possible to obtain the stressed state characteristics and the sample surface temperature in the part of maximum stresses of a cycle and after unloading at the end of each loading cycle. Thus, the beginning of a spontaneous irreversible dissipation process was identified by the change in characteristics and was characterized by the maximum limit stress in the cycle.
The loading frequency is permanent and equal to 0.5, 1, 2, 4 Hz. The test duration is 680 seconds. During testing, the maximum stress in the cycle is 276 MPa.
During testing, the loading, axial and transverse stress, radiation temperature of the gage part of a sample are measured synchronously. The samples are loaded and the stress is recorded using the INSTRON equipment, and temperature is measured by thermal camera TKVr-IFP SVIT. The experiments are made at a room temperature.

The main results
According to the data of [12][13][14], the volume fraction of the magnetic α' phase in the process of cyclic loading of steel 08Х18Н10Т increases in the course of material degradation that leads to a change of the elastic characteristics in fatigue. If the sample is deformed, for example, by a zero-to-compression stress cycle with a frequency of 4 Hz, recording the characteristics at the moment of unloading, then it is possible to define not only some limited critical stress, but also the property of a material when loaded above this stress. Figure 1 shows the patterns of a smooth sample stress. Let us remark here, that the represented diagrams are not smooth curves, which are usually obtained when constructing sigma-epsilon diagrams, but a collection of points placed nearby. Figure 2. Dependencies of the sample stress with a zero-to-compression stress cycle.  Dependence of the temperature change in the cycle is represented in Figure 3. The amplitude of the temperature a T grows linearly as well as the stress and the stress amplitude in the cycle (Figure. 3 a) and does not depend on the loading frequency.
The nonlinear dependence of the average component of the temperature cycle m T on stress, (Figure 3 b), is an indicator of irreversible energy dissipation in the sample and is observed in the same stress area as inelastic stress. Division of the characteristics describing material deformation process into amplitude (linear) and average (nonlinear dependence) components allows presenting the material thermomechanical properties in the form of a surface (Figure 4).
Received reactions can be considered as a slow change in the sample stressed state under conditions of the asymmetric stress cycle and resembles the creep of a material under the periodic loading.

Discussion
The results are obtained under homogeneous conditions; they characterize the behaviour of the material at a point and do not contradict the known practice of tests for the material strength and structural elements.
The small inelastic components of the total stress (microplastic stress -irreversible motion of separate dislocations) during periodic stress are different from the residual stresses observed in creep where the corporate movement of the elements of the material's structure is observed (plastic stress in the whole volume of the material -an increase in the dislocation density by more than two orders and interaction among them) [15]. In contrast to the creep observed under quasistatic loading, small inelastic stresses during periodic loading are followed by local structural changes [16], which in the literature are referred to as martensitic transformations of materials [17]. Despite the local nature of the transformations, they are unidirectional and, for a considerable number of stress cycles, can change the initial properties of the material throughout the entire gage part of the sample's surface. Fatigue damage -formation of a microcrack -occurs in the place where the coherence of the lattice of the material self-organized structure is disturbed. A crack can develop if under the action of mechanical stresses the next evolution of the material takes place on its top and conditions for martensitic transformations and destruction of the material on its top will be created. The martensitic structure is brittle and breaks delicately, which is observed on the surface of fatigue fractures. These arguments are confirmed by the established facts of martensitic transformations in the sample surface and data from factographic studies of the samples in which the traces of transformations phases of the material known as fish-eye and bird's-eye are observed at the site of failure [18], as well as data on the change in the transverse strain coefficient of the samples [16].
In the authors' opinion, the results of the presented material tests can be claimed to characterize the material not only for identification of material model parameters, in which the material properties must vary from cycle to load cycle, but also for practical applications where it is necessary to measure the material's ability to deform without irreversible processes.

Conclusion
It has been shown experimentally that the phenomenon of dissipation under cyclic soft loading is caused by a process of monotonous accumulation of the average component of the strain cycle, ratchetting, and leads to heating of the material at stresses much lower than the yield strength of the material. Despite this, the linear dependence of the stress cycle amplitude from the stress amplitude remains in the researched area.