Plastic Deformation Of Materials Research Articles

Investigating Grain-Resolved Evolution of Lattice Strains during Plasticity and Creep Using 3DXRD and Crystal Plasticity Modelling

Microstructure-informed crystal plasticity finite element models have shown great promise in predicting plastic and creep deformation in polycrystalline materials. These models can provide substantial insight into the design, fabrication and lifetime assessment of critical metallic components during operation, for instance, in thermal power plants. However, to correctly incorporate damage prediction into models, the microstructural strain simulated at the grain level must be accurately predicted with suitable validation. For this reason, a 3D X-ray Diffraction (3DXRD) experiment was carried out on 316H stainless steel, a material commonly used in thermal power plants, to obtain the per-grain strain response during plastic and creep deformation at 550°C. Several hundred grains within a probed X-ray volume were tracked and measured whilst loading in-situ, obtaining per-grain centre-of-mass positions, crystallographic orientations, and average lattice strain over individual grains. These data were used to calibrate a crystal plasticity model to study the plastic and creep deformation using macroscopic stress-strain and stress-relaxation data. Subsequently, the model was used to predict the average elastic strain in different grains during the cyclic creep experiment, which was validated by 3DXRD datasets. The model results reveal that {100} or {311} grain families are strongly sensitive to microstructure, thereby a polycrystal model that describes specific orientation and neighbourhood characteristics is essential to predict the local response of these grain families. Whereas, self-consistent models are suitable for {110} and {111} grain families. This study shows that only with a suitable calibration of subsurface grain behaviour, crystal plasticity models reveal grain characteristic-dependent micromechanical behaviour.

Microstructural and fatigue characterization of 316L stainless steel subjected to flow drilling and tapping: comparison with machined threads

Despite extensive research on the plastic deformation of materials to enhance their fatigue resistance, the influence of the flow tapping process on the fatigue resistance of drilled and tapped bars remains poorly understood. Herein, the fatigue performance of flow-drilled (friction-drilled) and flow-tapped 316L stainless steel bars was experimentally analyzed and compared with that of conventional material-shearing-based drilling and tapping operations. The effect of flow processes on the material properties was evaluated via microhardness tests and microstructural analyses. The results indicated that the hardness near the holes produced via flow forming was 62 % higher than that of the base metal. Moreover, grain refinement and plastic deformation were observed beneath the thread surfaces. Metallographic observations revealed the occurrence of craters and folds at the crest of the flow-formed threads. Following the ASTM F382-17 standard, four-point bending fatigue tests were performed at three stress amplitudes with a stress ratio of 0.1. No noteworthy differences were observed when the maximum bending moments applied were at 75 % and 60 % of the bending moment at yield. However, when the maximum bending moment applied was limited to 50 % of the bending moment at yield, the average fatigue life of the specimens with machined threads was longer than that of their flow-formed counterparts. Fractographic observations were used to identify the crack initiation regions and elucidate the underlying fracture mechanisms. For both types of specimens, failure originated at the crest of the first thread, beneath the surface of the maximum tensile stress. The flow-processed specimens exhibited secondary cracks at the root of the threads, where grain refinement also occurred. This study provides robust empirical evidence that using flow-forming processes to thread 316L stainless steel does not systematically improve the fatigue resistance of the material surrounding the holes. Furthermore, by optimizing the flow process and eliminating discontinuities, the threading process proposed herein could help improve the fatigue resistance of orthopedic implants.

Surface Interaction and Wear Due to Sliding Electrical Contact of Materials

This article reports a research study on sliding electrical contacts of copper–diamond materials, involving modeling and validation, contact status simulations, and parametric studies. The simulation model includes the analyses of both mechanical and electrical heat sources, evaluations of heat partition and temperature, and the capture of material thermal softening, plastic deformation, and material removal. The simulation model is validated through result comparison with experimental average temperature and measured wear. With this model, temperature variation and surface wear accumulation were numerically predicted under the influences of material property variations. Factors influencing wear of the copper surfaces were explored, and parameter sensitivity was investigated by means of the Taguchi L18 matrix. The results reveal that thermally related parameters of the contact interface strongly affect the wear of the copper pin, and thermal conductivity of its mating surface material is of critical importance. The research also suggests that the electromagnetic field change due to switching the polarity of the power supply does not affect the friction and wear results; however, the polarity change influences material electrochemistry, which results in a difference in friction and wear.

Finite Element Analysis of Plastic Deformation in Ultrasonic Vibration Superimposed Face Milling of Steel X46Cr13.

Ultrasonic vibration superimposed face milling enables the generation of predefined surface microstructures by an appropriate setting of the process parameters. The geometrical reproducibility of the surface characteristics depends strongly on the plastic material deformation. Thus, the precise prediction of the emerging surface microstructures using kinematic simulation models is limited, because they ignore the influence of material flow. Consequently, the effects of plastic as well as elastic deformation are investigated in depth by finite element analysis. Microstructured surfaces resulting from these numerical models are characterized quantitatively by areal surface parameters and compared to those from a kinematical simulation and a real machined surface. A high degree of conformity between the values of the simulated surfaces and the measured values is achieved, particularly with regard to material distribution. Deficits in predictability exist primarily due to deviations in plastic deformation. Future research can address this, either by implementing a temperature consideration or adapting specific modeling aspects like an adjusted depth of cut or experimental validated material parameters.

Effect of Al Content on Microstructure and Properties of AlxCr0.2NbTiV Refractory High-Entropy Alloys.

High-temperature creep refers to the slow and continuous plastic deformation of materials under the effects of high temperatures and mechanical stress over extended periods, which can lead to the degradation or even failure of the components' functionality. AlxCr0.2NbTiV (x = 0.2, 0.5, or 0.8) refractory high-entropy alloys were fabricated by arc melting. The effects of Al content on the microstructure of AlxCr0.2NbTiV alloys were studied using X-ray diffraction, scanning electron microscopy, and electron backscatter diffraction. The microhardness, compression properties, and nanoindentation creep properties of AlxCr0.2NbTiV alloys were also tested. The results show that the AlxCr0.2NbTiV series exhibits a BCC single-phase structure. As the Al content increases, the lattice constant of the alloys gradually decreases, and the intensity of the (110) crystal plane diffraction peak increases. Adding aluminum enhances the effect of solution strengthening; however, due to grain coarsening, the microhardness and room temperature compressive strength of the alloy are only slightly improved. Additionally, because the effect of solution strengthening is diminished at high temperatures, the compressive strength of the alloy at 1000 °C is significantly reduced. The creep mechanism of the alloys is predominantly governed by dislocation creep. Moreover, increasing the Al content helps to reduce the sensitivity of the alloy to the loading rate during the creep process. At a loading rate of 2.5 mN/s, the Al0.8Cr0.2NbTiV alloy exhibits the lowest creep strain rate sensitivity index (m), which is 0.0758.

Nanoscale speckle patterning for combined high‐resolution strain and orientation mapping of environmentally sensitive materials

AbstractScanning electron microscopy‐based high‐resolution digital image correlation (HRDIC) is now an established technique, providing full‐field strain and displacement measurement at the microscale. Techniques for generating speckle patterns for sub‐micron strain mapping can often be either substrate dependent or rely on applying aggressive conditions which may alter the microstructure of interest or damage the substrate in highly sensitive materials. We detail a modification of a methodology successfully applied in the literature to allow its use with metallic materials that are particularly sensitive to the corrosive media, such as copper‐base alloys. Nanometre‐thick silver films, applied with physical vapour deposition, are remodelled using NaBr in non‐aqueous isopropanol, replacing the aqueous solution of NaCl in the original method, forming a uniform dispersion of silver islands highly suitable for digital image correlation (DIC) measurement. The entire procedure is performed at ambient temperature. We find that the DIC pattern is suitably electron transparent to allow electron backscatter diffraction (EBSD) measurements without pattern removal, producing diffraction patterns of sufficient quality for cross‐correlation based high‐angular resolution EBSD. This property facilitates simultaneous EBSD and DIC mapping experiments, providing deeper insights into the kinematics of plastic deformation in crystalline materials. Sub‐100 nm islands are achieved through control of the sputter coating parameters, resulting in DIC cross‐correlation subwindows of 140 nm with a 50% overlap. This resolution is sufficient to capture the fine detail of strain localisation phenomena during plastic deformation, demonstrated here with a case study in CuCrZr, a precipitation‐hardened heat sink material for application in nuclear fusion components. Here, we extract full‐field displacement data with DIC and corresponding orientation information using EBSD without the need for pattern removal.

Study of the mechanism of the strength-ductility synergy of α-Ti at cryogenic temperature via experiment and atomistic simulation

Alpha titanium (α-Ti) is a promising material for making high-performance components for applications in aerospace, marine, energy and healthcare fields. The excellent strength-ductility synergy has been observed for α-Ti at cryogenic temperature. Twinning is generally considered a key mechanism of outstanding cryogenic ductility. The dislocation-grain boundaries (GBs) interaction and void nucleation usually play crucial roles in the plastic deformation of polycrystalline materials, but their effects on the cryogenic ductility of α-Ti are rarely considered. To eliminate this confusion and gain an in-depth insight into the mechanism of the cryogenic strength-ductility synergy of α-Ti, in this work, a series of characterization experiments and molecular dynamics (MD) simulations were designed and carried out. 1) From uniaxial tension tests of the coarse-grained α-Ti sheets at the temperature from 25 to -180 °C, the uniform elongation and post-necking elongation were increased by 92 % and 20 %, respectively. The material maintained a larger strain hardening rate within a greater range of strain at cryogenic temperature compared with room temperature. 2) Via microstructure and fractography observations and the analysis of slip and geometrically necessary dislocation (GND) activities, the uniform plastic deformation was mainly accomplished by prismatic slip, whether at room temperature or at cryogenic temperature. The significantly increased uniform elongation is mainly attributed to the more uniform distribution of GND pile-ups at cryogenic temperature. 3) The MD simulations revealed that cryogenic temperatures made the GBs present a stronger barrier effect on dislocation transmission compared with that at room temperature, contributing to the more uniform distribution of GNDs and lower densities of GND pile-ups. The GBs at cryogenic temperature show a greater ability to resist void nucleation due to the decreased accumulation rate of excess potential energy and increased energy required to void nucleation. The larger strains were thus required to increase the densities of GND pile-ups to induce large stress concentrations for driving void nucleation. This made the uniform elongation of α-Ti increase significantly at cryogenic temperature. This study revealed that the enhanced barrier effect of GBs on dislocation transmission and the improved ability of GBs to resist void nucleation are key mechanisms besides twinning governing the cryogenic strength-ductility synergy of α-Ti. The understanding developed in this work can be useful for the development of new high-performance materials and the precise forming of complex components with high quality.

МАТЕМАТИЧНА МОДЕЛЬ ВПЛИВУ ПОВОРОТУ ВИДОВЖЕНИХ ЗЕРЕН НА ПРОЦЕС ВИСОКОТЕМПЕРАТУРНОГО ДЕФОРМУВАННЯ КЕРАМІКИ НА ОСНОВІ НІТРИДУ КРЕМНІЮ

The speed of direct high-temperature extrusion of ceramics based on silicon nitride was analyzed. The influence of rotation of elongated grains on mass transfer processes and deformation rate is established. The influence of the parameters of the high-temperature deformation process on the deformation rate is shown. An equation is proposed that describes the effect of rotation of elongated grains on the strain rate. The described equation of strain rate can be used to create technological processes of plastic deformation of ceramic materials.

МАТЕМАТИЧНА МОДЕЛЬ ВПЛИВУ ЗЕРНОГРАНИЧНОГО КОВЗАННЯ НА ПРОЦЕС ВИСОКОТЕМПЕРАТУРНОГО ДЕФОРМУВАННЯ КЕРАМІКИ НА ОСНОВІ НІТРИДУ КРЕМНІЮ

The speed of direct high-temperature extrusion of ceramics based on silicon nitride was analyzed. The influence of grain boundary slip and viscous flow of the intergrain phase on mass transfer processes and deformation rate is established. The influence of the parameters of the high-temperature deformation process on the deformation rate is shown. An equation is proposed that describes the effect of grain boundary slip and viscous flow of the intergranular phase on the strain rate. The described equation of strain rate can be used to create technological processes of plastic deformation of ceramic materials.

Investigating micro-cutting mechanism of glow discharge polymer based on material properties and removal behaviors analysis

Glow discharge polymer (GDP) is the unique artificial material for the target balls in Inertial Confinement Fusion tests, while its practical micromachining such as the fabrication of microstructure on material surfaces keeps challenging due to its unclear micro-cutting mechanism. Hence, this paper seeks to investigate the micro-cutting mechanism of GDP from the perspective of the material flow and cutting energy. To achieve it, the energy conservation equation of three cutting modes triggered by different ratios of uncut chip thickness to the tool cutting edge radius (RTS) was established based on cutting deformation behaviors. Meanwhile, the diamond cutting tests and the FEM simulation at different RTS were developed. The experimental observation of cutting forces and specific cutting forces verified the evolution of three cutting modes, including shearing, shearing-ploughing and ploughing in the micro-cutting of GDP with the decrease of RTS. Next, from the change of the node displacement vector observed from the simulated results, it can be seen that the real-time material flow behavior during micro-cutting of GDP varies obviously with the evolution of cutting modes. Besides, the fracture toughness Gc, and the energy dissipation of different cutting modes were analyzed. The proportion of the energy spent on material fracture (Gc=9.95 N/mm) is the largest one in shearing and shearing-ploughing modes, while in ploughing mode, the material plastic deformation consumed the most energy. The above results reveal the specific material properties and removal behaviors of GDP and contribute to optimizing the machining strategies for the practical micromachining of microstructures on material surfaces.

Enhancing the Structural and Mechanical Properties of Ti-Zr Alloy through Boron Doping

This study aims to improve the structural strength of the commonly used Ti-15Zr alloy in dental applications by investigating the effects of low boron additions. Ti-15Zr alloys containing 1-4% boron have been produced by vacuum arc melting. The phase ratios in the microstructure of the produced alloys vary according to the boron content. With increasing boron content, the ratio of TiB compound in the phase structure increases. The hardness of Ti-Zr-B alloys exhibited a notable increase in correlation with rising boron content. Measured hardness values of 36.31, 39.50, 44.14, and 53.40 displayed a clear upward trend with higher boron percentages. The tensile strength of the Ti-Zr-B alloys exhibits a trend of initially increasing with boron content, reaching its highest value of 888 MPa at 1% boron. The yield strength follows a similar with tensile strengh, with an initial rise from 449 MPa at 0% boron to a peak of 562 MPa at 1% boron content. Beyond this point, the yield strength slightly decreases to 469 MPa at 2% boron but sharply drops to 186 MPa at 4% boron content. As boron content increases in the Ti-Zr-B alloys, the percentage elongation, indicating the material's plastic deformation capacity before fracture, consistently decreases from 17.03% at 0% boron to 0.70% at 4% boron content.

Modeling of shock wave propagation in porous magnesium based on artificial neural network

Data transfer from the level of atomistic simulations to the level of continuum modeling is one of the urgent problems in the mechanics of materials. In this work, we perform multiple molecular dynamics (MD) simulations of the uniaxial (along different crystallographic directions) and volumetric (isotropic) compression of porous HCP magnesium single crystals in order to study the atomistic processes of the plastic deformation of anisotropic porous material and to create a reference dataset (strain dependencies of stresses, porosity and dislocation density at different temperatures and initial porosities). The MD data are used to train two artificial neural networks (ANNs): the first ANN is a surrogate of the constitutive equation of porous magnesium, while the second ANN describes the dislocation nucleation/emission as the onset of plastic flow. In contrast to the previously considered case of porous FCC aluminum, the present approach takes into account the anisotropy of the matrix material. The ANN-based constitutive equation is successfully used within the continuum mechanics model for numerical study on the shock wave structure in porous magnesium in comparison with direct MD simulation of the shock wave problem.

Effects of moisture content and soil suction on the permanent deformation of tropical subgrade soils: experimental investigations and modelling

This study presents the effects of moisture variation and the influence of matric suction on the permanent deformation (PD) of three tropical soils with different geological-geotechnical characteristics used in road subgrades in southern Brazil. The experimental programme consisted in determining the soil-water characteristic curves and in dynamic triaxial tests to obtain the PD in different compaction and post-compaction moisture contents. The variation of compaction moisture content caused microstructural changes, influencing the plastic behaviour of soils: the higher the initial moisture content, the greater their accumulated permanent deformations. As expected, the post-compaction moisture variation (wetting process) tended to increase the plastic deformation of materials, evidencing the influence of the suction variation on the performance of the soils studied. In addition, matric suction proved to be the best variable to represent the effects of moisture variation on the plastic behaviour of soils subjected to cyclic loading. Thus, a PD prediction model for tropical soils with the inclusion of this parameter was proposed. The model proved to be highly predictive and may become an important tool to be incorporated into current mechanistic-empirical design methods.

Investigation of the Flow Stress Model for Cr4Mo4V Bearing Steel under Ultrasonic Vibration Conditions

To investigate the mechanisms behind the effect of ultrasonic vibration on the plastic deformation of materials, the flow stress model of Cr4Mo4V was established according to the dislocation dynamics and thermal activation theory, which considers the effect of dislocation density evolution on plastic deformation under ultrasonic vibration conditions. The effect of amplitude and strain rate on the flow stress was analyzed by fitting the stress-strain data obtained from an ultrasonic vibration-assisted tensile (UVAT) single-factor test. To investigate the influence of strain rate and vibration duration on the acoustic effect, comparative tests with and without vibration were performed for various strain rates. The results showed that the flow stress decreased significantly in the tensile test with ultrasound compared to the test without ultrasound, and the degree of reduction increased with increasing amplitude. In addition, the nonlinear relationship between the acoustic softening effect and the strain rate was analyzed. The result demonstrates that the dislocation density absorbs the ultrasonic vibration energy, which results in slip and proliferation. Macroscopically, due to a greater susceptibility to plastic deformation, the dislocation density shows residual hardening at the end of the ultrasound. Finally, the average absolute relative error (AARE) between predicted flow stresses and experimental results under three ultrasonic conditions using the developed model were 4.49%, 1.27%, and 5.64%, which proved the validity of the model.

Enhancing friction stir welding efficiency through rotational speed adjustment: a microstructural and mechanical analysis of Al-Cu alloy

Friction stir welding (FSW) has gained prominence in the aerospace and automotive industries due to its ability to produce high-strength and defect-free welds in aluminum alloys. The present investigation focuses on the impact of different tool rotational speeds (such as 700 rpm, 900 rpm, 1100 rpm and 1300 rpm), on the microstructure and mechanical characteristics of friction stir welded Al-Cu alloys. With the use of optical microscopy, scanning electron microscopy (SEM), x-ray diffraction (XRD), and evaluations of hardness, tensile characteristics, and fracture behavior, a thorough analysis was carried out. The weld nugget zone contained significant changes in grain size and shape as a function of rotational speed, as shown by microstructural analysis. The grain structure gradually became more refined when the rotating speed was raised from 900 to 1500 rpm. According to SEM observations, at faster speeds, the weld zone showed fewer defects per unit area and better bonding properties, which might be attributed to better material flow and plastic deformation. The effect was further clarified by XRD analysis, which showed differences in phase composition with varying rotating speeds. Evaluations of the mechanical properties showed a significant relationship between rotating speed and the mechanical performance of the welds. Hardness measurements showed that as rotating speed increased, hardness levels gradually increased. Welds made at faster rotational speeds had better elongation and tensile qualities, according to tensile tests. Additionally, fracture behavior study revealed that higher rotational speed welds displayed a more ductile fracture mode, indicating increased toughness.

Refined model of leather

The structure of finished leather and semi-finished products differ in physical and mechanical parameters. To obtain the properties of elasticity, pliability, and viscosity required in leather production, it is necessary to ensure their values that guarantee the high quality of the resulting product. In this article, a model for finished leather is obtained based on combining the viscoelastic Kelvin model with the deformationinert Khusanov model and the Bingham–Shvedov viscoplastic model. This model makes it possible to improve the elastic-viscous plastic deformation of a fibrous material (leather). The possibility of clarifying the pattern of change in the deformation curve depending on the time the fibrous material is loaded by a certain force was explored. The aim of refining the deformation curve is that in known models, at the initial moment of loading, deformation occurs instantly up to a certain value, which does not fully describe the real physical process of deformation of the material. Consequently, in the proposed refined model, the deformation is fixedat zero value, which provides a real physical pattern of deformation of the fibrous material. The refined model will serve designers of technological machines to develop parameters of deformation during the mechanical processing of elastic-viscous plastic materials.

Numerical Simulation of the Residual Stress at the Interface between Thermal Barrier Coating and Nickel-Based Single-Crystal Superalloy Based on Crystal Plasticity Theory

Residual stress plays an important role in the formation and growth of cracks in thermal barrier coatings and single-crystal superalloy substrates. In this study, a finite element model for a planar double-layer thermal barrier coating and a crystal plasticity finite element model based on dislocation slip-induced plastic deformation of single-crystal materials were established to analyze the residual stress in the coatings and the substrate, considering the creep and crystal plasticity of the substrate materials. The simulation results show that the thermal barrier coatings bear most of the stress generated by high temperatures, and the residual stress of the substrate is small. By comparing the two material properties to calculate the interface stress when the amplitude of the interface between the substrate and the coating is 30 μm and the thickness of the thermal grown oxide layer is 5 µm, the interfacial stress of the substrate at the macro scale was found to be similar to the interfacial stress at the micro slip system scale. Based on the cumulative shear strain, it was determined that the [001]-, [011]-, and [111]-oriented alloys activated the 12, 8, and 4 groups, respectively, under the combined action of thermal stress and centrifugal force of the coating. Comparing the activation of different initial orientation slip systems and the magnitude of the yield stress provides a theoretical foundation to study the structural integrity of single-crystal alloys.

Temperature effect on the transition between grain boundary migration and sliding

Grain boundary (GB) dynamics plays an important role in the mechanical and physical properties of nanocrystalline metals. In this study, we investigate the temperature effect on GB deformation transition using molecular dynamics simulations of [100] symmetric tilt GBs in Au bicrystals. Different deformation behaviours were revealed in GBs with the same structures at varied temperatures. GB sliding occurs as the predominant deformation mechanism at elevated temperatures, while GB migration dominates at low temperatures. The temperature-dependent critical stresses for GB migration and GB sliding were compared, revealing that temperature alters the critical GB misorientation at which GB migration transitions to GB sliding. Our study provides new insight into GB-mediated plastic deformation in nanocrystalline materials.

Grain-level mechanism of plastic deformation in harmonic structure materials revealed by high resolution X-ray diffraction

Materials with heterogeneous microstructures have been reported to have an attractive combination of strength and ductility. This is attributed to synergistic strengthening effects from the difference in strength of fine- and coarse-grained regions. Understanding the interaction of the regions is crucial for further optimization of the microstructures. In this work, we fabricated nickel of harmonic structure (HS) and a reference with homogenous coarse grains. The HS constitutes of an interconnected fine-grained network that surrounds regions of coarse grains. The interplay of the regions was studied by monitoring Bragg reflections from individual grains in situ during tensile deformation until approximately 2 % strain through synchrotron X-ray diffraction. The technique allows grain-level assessment of the degree of plastic deformation. Two grains were followed in the reference and two small grains (fine-grained region) and two large grains (coarse-grained region) in the HS. Three deformation regimes were identified: elastic deformation, onset of plastic deformation and significant plastic deformation. Our results reveal that the large grains in the harmonic structure onset plastic deformation during the macroscopic elastic stage. With increasing applied stress, the small grains yield plastically also and once a large fraction of the fine-grained network deforms plastically the large grains undergo significant plastic deformation. Notably, the onset of significant plastic deformation of large grains in the HS occurs at approximately 100 MPa higher applied stress than in the grains in the reference. This shows that fine grains constrain the large grains from deforming plastically in the HS.

INVESTIGATION OF STAMPING BY WRAPPING PROCESSES THROUGH MATERIAL DEFORMATION MODELING ANALYSIS

This scientific article addresses the pressing issue of material deformation modeling in the context of stamping by wrapping processes (SWP). The main challenges in the development of these processes include the likelihood of workpiece failure due to insufficient material plasticity and unfavorable stress-strain states, determined by technological process parameters. Thus, effective SWP process development requires the utilization of material deformation modeling. The article indicates that any material deformation model in plastic deformation processes comprises three main elements: Analytical representation of the curve or surface of boundary plastic deformations during stationary deformation: This element describes how the material's plastic deformation changes during stationary deformation with alterations in the invariant stress state indicators. Mathematical model of the deformation path in coordinates of stress state indicators - accumulated plastic deformation. This model determines the path along which material deformation develops with changing stress state indicators and is dependent on accumulated plastic deformation. Damage accumulation model: This element takes into account accumulated damage in the material and can be used to predict workpiece failure. Specifically, the article analyzes the surface of boundary plastic deformations during stationary cold deformation and employs terminology to describe the dependence of accumulated plastic deformation until failure on invariant stress state indicators. The term "stationary deformation" is used to denote material deformation under unchanged values of these indicators.