Cyclic Elastoplastic Deformation Research Articles

Microstructure and residual stress evolution during cyclic elastoplastic deformation of AISI316L fabricated via laser powder bed fusion

In metal additive manufacturing (MAM), microstructural properties such as texture, residual stresses, and dislocation density have emerged as key factors ruling the resulting mechanical performances. In this study, cylindrical AISI 316L specimens, fabricated with laser powder bed fusion (LPBF), were tested under cyclic elastoplastic (EP) deformation using a constant strain amplitude to highlight the evolution of residual stresses (RS), dislocation density and texture with increasing number of EP cycles, N, across the hardening-softening (H–S) transition stage, in the attempt to find correlations between relevant microstructural parameters and macroscopic properties. The structural and microstructural analysis is carried out through whole powder pattern modeling (WPPM) of neutron diffraction (ND) data and Electron Back-Scattering Diffraction (EBSD) analysis. The H–S transition is found to occur within 7–9 cycles, with RS fading out already after 5 cycles. Across the H–S transition, the trend of the maximum tensile stress correlates closely with the trend of WPPM-calculated total dislocation density, suggesting a major role of dislocations’ characteristics in the evolution of macroscopic mechanical properties. EBSD analysis reveals the rearrangement of geometrically necessary dislocations (GND) into cellular structures, and moderate grain refinement, which are deemed to be responsible for the quick fading of RS in the very early stage of EP loading. ND-based texture analysis reveals a (220) preferential orientation retained throughout the EP tests but with orientation density functions (ODFs) changing non-monotonically with N, suggesting preliminary partial randomization of grains around the deformation axis followed by the recovery of crystallographic anisotropy and more localized ODFs.

LOW-CYCLE FATIGUE OF STRUCTURES WITH STRESS CONCENTRATORS

The results of experimental and theoretical studies of structures with stress concentrators under cyclic loads are presented. The studies were carried out on cylindrical samples with a V-shaped annular recess under mild cyclic loading. The tests were carried out on samples of the BrH08-Sh alloy with a cyclic change in the tensile load from 0 to 10.8 kN. Under such loading, the material in the recess area undergoes cyclic elastoplastic deformation, which leads to destruction as a result of low-cycle fatigue. For mathematical modeling of the elastic-plastic behavior and destruction of structures with stress concentrators, a variant of the theory of plasticity based on the theory of flow under combined hardening is used. In the chosen plasticity model, a memory surface is introduced that separates the processes of monotonous and cyclic loading. This separation makes it possible to take into account various features of isotropic and anisotropic hardening of the material. Anisotropic hardening is represented as a sum of microstresses of three different types, which make it possible to describe the effects of landing and stepping of the elastic-plastic hysteresis loop. The plasticity model makes it possible to assess the damaged state of a material based on the kinetic equation of damage accumulation based on the energy principle (the operation of microstresses in the field of plastic deformations). The material behavior model is embedded in the finite element software package SIMULIA Abaqus. The results of calculations and experiments on the magnitude of axial deformation, the average axial deformation on the surface of the recess and the number of cycles to failure are compared. It is found that in a design with a recess with a radius of 1 mm, a soft asymmetric loading with a unilateral accumulation of deformation (ratcheting) is realized in the concentration zone.

Modeling on magnetization behavior of ferromagnetic material during cyclic deformation

In this paper, a nonlinear magneto-mechanical coupling constitutive model is established to describe the magnetization behavior of ferromagnetic materials under cyclic elastoplastic deformation. The critical state is introduced into the hysteretic magneto-mechanical model. In the critical state, the magnetization rates of loading and unloading are different. A new nonlinear plastic effective magnetic field is proposed by considering the effect of pinning sites caused by cross slip dislocation to describe the magnetization behavior under asymmetric cyclic loading. The softening factor and activation condition of plastic modulus parameter are introduced based on the cyclic plastic constitutive model to describe the decrease of plastic modulus. A new magnetization model for ferromagnetic materials under cyclic plastic deformation is established by combining the magneto-mechanical coupling model with the cyclic plastic constitutive model. Compared with the experiments and existing models, it is shown that the proposed model can capture the deformation and magnetization behavior well under cyclic loading.

Study of the generalized curves of the static and cyclic deformation, damage and fracture

Individual deformation diagrams of all materials on metal, non-metal, or composite base under static and cyclic load link stresses and strains. These diagrams are obtained in standard tensile, compression, torsion or bending tests of laboratory samples with the registration of forces and deformations of their working parts upon loading. The diagram for a single static deformation in the stress-strain coordinates in this case covers both the region of elastic deformations and the region of elastic-plastic deformation, when deformations are localized in the neck of the loaded sample up to the moment of its destruction at a critical stress level. It is shown that linear, fractional-linear and power approximation of the obtained deformation curve are widely used in the description of the obtained deformation diagrams. Direct experiments, the theory of dislocations and the statistical theory of strength confirm the priority of power approximation of considered diagrams. At the same time for all construction materials the generalized deformation diagram in relative coordinates is described by a single power equation with the individual hardening parameter which is determined experimentally or theoretically using the dependences linking data on the module of elasticity, yield stresses, strength, and ultimate plasticity of the material. Diagrams of a cyclic elastoplastic deformation in the form of loops of plastic hysteresis are recorded by analogy with static tension diagrams with «stress – strain» axes of in conditional and true relative values. The generalized deformation diagrams for a single static and cyclic loading form a scientific basis for construction of the generalized fatigue curve on the basis of deformation fracture criterion for a wide range of cycles to failure. An effective solution to the problems of strength and service life for the most complex engineering objects such as nuclear reactors, aircraft, rocket and space systems can be achieved through introduction of generalized deformation and fracture diagrams into consideration and corresponding calculations. Their significance will especially increase in the design and implementation of new unique science-intensive facilities.

Intragranular thermal fatigue of Cu thin films: Near-grain boundary hardening, strain localization and voiding

In order to obtain a fundamental understanding of the phenomena accompanying thermomechanical fatigue of Cu metallization used in power electronics, as well as the resulting deterioration of electric properties, there is a need to assess intragranular microstructure and strain evolution within individual Cu grains and near grain boundaries. Here, synchrotron dark field X-ray microscopy (DFXM) is used to characterize as-deposited and 5 × 104 times thermally-cycled 20 µm thick Cu films. The cycling was performed using a dedicated test chip in the range of 100–400 °C applying a heating rate of 106 K/s. The thermomechanical treatment results in severe shear deformation of Cu grains, film surface roughening, gradual grain microstructural refinement, the emergence of microscopic voids preferably at high angle grain boundaries (HAGBs) and finally in the voids' percolation, as revealed by in-situ and ex-situ scanning electron microscopy. DFXM provides experimental evidence that mosaicity of Cu grains, residual tensile and compressive elastic strain concentrations and full width at half maximum of Cu 111 reflections increase simultaneously in the vicinity of the HAGBs. The latter is interpreted as resulting from vacancy condensation in front of the HAGBs, after dislocations have moved across cycled grains and partly annihilated. Moreover, the observed HAGB decohesion and gradual void formation are correlated with the supposed hardening of regions near HAGBs, which thus lose their ductility during cyclic elasto-plastic deformation. The results are complemented with the ex-situ X-ray nanotomography data, which document the voids' percolation across the film's thickness with a “crack” width of up to ∼2 µm. In general, the study identifies the inhomogeneous intragranular microstructural refinement and a gradual condensation of structural defects near HAGBs as driving forces for void formation in thick Cu metallizations during fast thermo-mechanical fatigue.

Low-cycle fatigue of V-notched cylindrical samples of bronze alloy

The article presents the results of experiments on cyclic loading of samples with an annular V-shaped notch and their mathematical modeling. The tests were carried out on specimens of the BrKh08-Sh alloy with a cyclic change in the tensile load from 0 to a given value. Under such loading, the material in the groove area is subjected to cyclic elastoplastic deformation, which leads to failure due to low-cycle fatigue. When testing samples using the digital image correlation method, the deformation of the material on the surface of the undercut was measured, which made it possible to determine the nature of the change in its range from cycle to cycle. Mathematical modeling of experiments is carried out according to the finite element method. For this purpose, models of elastic-plastic deformation and accumulation of material damages are introduced into the SIMULIA Abaqus software package. The plasticity model is based on the theory of flow under combined hardening. The damage accumulation model is based on the energy strength criterion. The article presents the basic equations used to calculate the models. The material parameters are determined and verified based on the results of a basic experiment on cyclic tension-compression of a smooth cylindrical sample under asymmetric rigid loading. Based on the results of the calculation, cartograms of stresses, deformations, and accumulated damages were constructed. It is shown that when the sample is unloaded, in the area of stress concentration close to the annular groove, compressive stresses arise, the values of which are close to the values of tensile stresses at the moment of application of the maximum load. The results of mathematical modeling are compared with the experiment. A comparison of the results was carried out in terms of the range of axial deformation of the material on the surface of the undercut and the number of cycles before failure.

Statistical Characterization of Strain-Controlled Low-Cycle Fatigue Behavior of Structural Steels and Aluminium Material.

Probabilistic evaluation of the resistance to low-cycle deformation and failure of the critical components in the equipment used in the energy, engineering, metallurgy, chemical, shipbuilding, and other industries is of primary importance with the view towards their secure operation, in particular, given the high level of cyclic loading acting on the equipment during its operation. Until recently, systematic probabilistic evaluation has been generally applied to the results of statistical and fatigue investigations. Very few investigations applying this approach to the low-cycle domain. The present study aims to substantiate the use of probabilistic calculation in the low-cycle domain by systematic probabilistic evaluation of the diagrams of cyclic elastoplastic deformation and durability of the materials representing the major types of cyclic properties (hardening, softening, stabilization) and investigation of the correlation relationships between mechanical properties and cyclic deformation and failure parameters. The experimental methodology that includes the calculated design of the probabilistic fatigue curves is also developed and the curves are compared to the results of the experiment. Probabilistic values of mechanical characteristics were determined and calculated low-cycle fatigue curves corresponding to different failure probabilities, to assess them from the probabilistic perspective. A comparison of low-cycle fatigue curves has shown that the durability curves generated for some materials using analytical expressions are not accurate. According to the analysis of the relative values of experimental probabilities of low-cycle fatigue curves, the use of analytical expressions to build the curves can lead to a significant error. The results obtained allow for the revision of the load bearing capacity and life of the structural elements subjected to cyclic elastoplastic loading in view of the potential scattering of mechanical properties and resistance parameters to low-cycle deformation and failure. In addition, the results enable determination of the scatter tolerances, depending on the criticality of the part or structure.

Computation and experimental analysis of the resistance of superalloys to low cycle deformations

Diagrams of cyclic elastoplastic deformation in a general case characterize the resistance of a material to a low cycle loading and display a relation between current values of stresses and strains during deformation process. Those diagrams in the mechanics of deformation and fracture are described by rather complicated state equations with a nonlinear dependence on conditions and modes of loading including temperature, deformation rate, cycle form, type of the stress state, absolute size of sections, working medium, type of constructional material, etc. The entity of aforementioned factors affects a shape of the deformation curve (diagram) of the material and key parameters of the corresponding state equations, including basic characteristics of the mechanical properties, i.e., the elasticity module, yield point and ultimate stress, indicators of static and cyclic hardening. Experimental data on the kinetics of cyclic and one-way accumulated plastic strains in each loading half-cycle (cycle) obtained in static and low cycle tests of nickel superalloy specimens revealed that change in deformation characteristics exhibit a drastically nonlinear character in conditions of cyclic elastoplastic strain which is described on the basis of power equations and corresponding parameters of cyclic deformation diagrams. The parameters of those equations depend on the type of cyclically hardening/softening or stable material under deformation of the material in elastoplastic region. It is noted that resistance of materials to cyclic elastic-plastic strain can be described by a set of analytical expressions containing a kinetic function (which changes with number of loading half-cycles) in the form of power or exponential expressions depending on the cyclic properties and characteristics of the mechanical properties of the specific structural material. The obtained calculated and experimental data on the kinetics of strain of the alloy under study in conditions of cyclic elastoplastic loading, as well as on the parameters of the strain diagram (which are basic characteristics for the corresponding state equations) provide the possibility to take full advantage of using the deformation-kinetic criteria of damage accumulation under considered loading conditions to calculate the fatigue life of the structural elements manufactured from the alloy and operated, as a rule, under severe temperature and heavy-loaded conditions. The results of the experiments and calculations are given in the form of diagrams of cycle-by-cycle kinetics of the cyclic and accumulated plastic strains of the material for the soft and hard modes of loading in a wide range of test temperatures.

On Considering the Influence of Kinematic Hardening in Finite Element Simulation of Hot Levelling of Structural Steel Heavy Plates

Flatness is an important quality parameter of heavy plates and it is generally achieved through cyclic elastoplastic deformation of the plate in a hot roller leveller following the rolling and cooling processes. To investigate and optimize the hot plate levelling (straightening) process, Finite Element (FE) simulations are widely used. Generally, flow curves with isotropic hardening are used for hot plate levelling simulations. However, the plate material might exhibit kinematic hardening, due to the load reversal that is seldom considered due to laborious high temperature cyclic material characterization. The current work aims at understanding the implications of considering kinematic hardening within hot heavy plate levelling simulations. Hot uniaxial and cyclic material characterization of S355 steel at 1000 °C is performed and the corresponding stress-strain curves are extracted. Using an inverse modelling technique, the associated isotropic and kinematic hardening models are calibrated. The cyclic data showed that the S355 steel exhibits kinematic hardening and the Chaboche kinematic hardening model is suitable to model this behaviour. Hot levelling simulations of plates with isotropic and kinematic hardening models showed a noticeable difference in the roll reaction forces and local curvature of the plate during the process while the resulting flatness of the final plate is not very sensitive to the material model for the investigated scenarios.

Mechanical properties of materials in calculations of low cycle deformation of structures

It is noted that calculations of the rated strength for bearing elements of extremely loaded structures, including nuclear power plants allow inelastic deformation of the materials of these elements. At the same time calculations of the low cycle fatigue require taking into account factors that are not observed under single loading including, i.e., kinetics of cyclic strains, cyclic creep, change of the mode of inelastic cyclic deformation upon normal operation. Moreover, the materials can be of different types: cyclically hardening, softened or stable. For the first type of materials at a soft loading with constant amplitude of stresses in cycles, the range of strains decreases with an increase in the number of cycles, but increases for the second one. Under a hard mode of loading with constant amplitude of strains the maximum stresses in a cycle for the hardening material increase, and, on the contrary, decrease for softened material. Moreover, the soft loading of softened material results in one-sided accumulation of plastic strains as the number of loading cycles increases. These circumstances must be taken into account both in the analytical description of the kinetics of deformation diagrams and in the corresponding calculation equations used in the strength standards. It is noted that at early stages of forming computation methods developed for these conditions, calculation of stresses was carried out in the assumption of ideal elasticity of the material. The use of such approach was attributed to the lack of available methods for addressing the problem of an inelastic cyclic deformation, complicated on the statement. The subsequent evolution of the theory of cyclic elastoplastic deformation, analytical and numerical solutions of cyclic boundary-value problems, developing of numerical methods of computation and powerful computer packages fundamentally changed the situation providing the possibility of analysis and modeling of physically and geometrically nonlinear deformation processes. It is shown that transition from the elastic adaptability (with an elastic deformation of the structure in a stable cycle) to a sign-variable flow is smooth and continuous, similar to the transition from the elastic to plastic deformation under a single loading. Such a mechanism is similar to conditional boundary of the transition from low cycle to high-cycle fatigue under a cyclic strain. At the same time, we offer to use in calculations the existing rather simple models and experimentally determined parameters of cyclic deformation diagrams of materials. In the modern statement of the problems under consideration, taking into account both the kinetics of cyclic and unilaterally accumulated deformations, with allowance for the manifestation of creep effects in cycles is of fundamental importance. This approach also makes it possible to take into account the acceleration of unsteady cyclic creep due to previous plastic deformation of a different sign, which can be rather significant.

Features of the Kinetics of Cyclic Elastoplastic Deformation Diagrams at Dwells in Cycles and Superimposition of Variable Stresses on Them

Features of the Kinetics of Cyclic Elastoplastic Deformation Diagrams at Dwells in Cycles and Superimposition of Variable Stresses on Them

Study of the regularities of resistance to deformation and damage accumulation under irregular low cycle loading

The results of computation and experimental studies of changes in the regularities of the strain resistance and damage accumulation in conditions of the irregular low cycle loading are presented and compared with similar data for a regular cyclic elastoplastic deformation at the same loading. The irregular mode of low cycle loading implemented in the study is adopted in the form of an equiprobable distribution of changes in the stress amplitudes within a given range between maximum and minimum levels at the symmetric form of the cycles. This mode was reproduced on test equipment through introduction of the corresponding functional dependence of changes in the stress amplitude in the cycles into the control program. The data on a cycle-by-cycle kinetics of both cyclic and unilaterally accumulated strains obtained under irregular mode of loading were recorded in a databank and then compared with the data for a regular loading. This provided the possibility of their analytical description by the corresponding equations of state with the correction of the parameters of the diagrams of cyclic elastoplastic deformation taking into account the conditions of irregularity of loading modes. The results of the experiments are presented in the form of diagrams of the tests modes, curves of a low cycle fatigue of the studied material at the soft and hard loading modes, diagrams of a cycle-by-cycle kinetics of the cyclic and accumulated strains at the regular and irregular modes, and also as kinetic diagrams of damages accumulation for these conditions. Using the summation criteria expressed through the deformation characteristics of accumulated damage, it is shown that taking into account change in the character of the strain development under irregular low-cycle loading, the criterion dependences can be used to assess the durability and compare it with the similar data under regular modes when accepting the condition of attaining the limiting state.

Method for studying the kinetics of plastic deformation and energy dissipation during fatigue of structural materials

The evolution of mechanical properties of Russian steel St3 subjected to cyclic elasto-plastic deformation is analyzed under a broad spectrum of loading conditions. This particular material is chosen due to its wide use in industrial facilities operating in Arctic and Russian North. Basic state parameters are determined, including the true strains, secant and tangent moduli, heat generation due to plastic dissipation, thus characterizing the evolution of the thermo-mechanical state. The temporal evolution of kinetic parameters during each loading block provides insights into the hardening and damage accumulation. These data form an experimental basis for development, calibration, and validation of new material models. The main effects are identified and discussed, and the modelling approaches are assessed.

FTMP-based Simulation and Evaluation of Apparent Reduction in Elastic Modulus

This study attempts to quantitatively evaluate the apparent reduction in elastic moduli, generally observed in metallic materials during unloading and/or cyclic elasto-plastic deformation, based on Field Theory of Multiscale Plasticity (FTMP). Two typical arrangements of bowing-out dislocation segments that yield mutually-distinct trends are examined by utilizing the FTMP-based duality diagram representation scheme. It is demonstrated that not only the scheme allows us to visualize the associated energy flow but also to correlate the resultant apparent shear modulus reduction rate in a unified manner by the duality coefficient measured on the duality diagrams. The scheme is demonstrated to be effective also for more complex cases accompanied by pinning/unpinning and the following relaxation processes.

Features of the kinetics of cyclic elastoplastic deformation diagrams at dwells in cycles and superimposition of variable stresses on them

The goal of the study is determination of the regularities of changes in cyclic strains and related deformation diagrams attributed to the existence of time dwells in the loading modes and imposition of additional variable stresses on them. Analysis of the obtained experimental data on the kinetics of cyclic elastoplastic deformation diagrams and their parameters revealed that in contrast to regular cyclic loading (equal in stresses), additional deformations of static and dynamic creep are developed. The results of the studys are especially relevant for assessing the cyclic strength of unique extremely loaded objects of technology, including nuclear power equipment, units of aviation and space systems, etc. The experiments were carried out on the samples of austenitic stainless steel under low-cycle loading and high temperatures of testing. Static and dynamic creep deformations arising under those loading conditions promote an increase in the range of cyclic plastic strain in each loading cycle and also stimulate an increase in the range of elastoplastic strain due to active cyclic deformation. At the same time the existence of dwells on extrema of stresses in cycles without imposition of additional variable stresses on them most strongly affects the growth of plastic strain ranges in cycles. Imposition of additional variable stresses on dwells also results in the development of creep strains, but their growth turns out to be somewhat less than in the presence of dwells without stresses imposed. The diagrams of cyclic deformation obtained in the experiments are approximated by power dependences, their kinetics being described in terms of the number of loading cycles using corresponding temperature-time functions. At the same time, it is shown that increase in the cyclic plastic deformation for cycles with dwells and imposition of additional variable stresses on them decreases low cycle fatigue life compared to regular loading without dwells at the same stress amplitudes, moreover, the higher the values of static and dynamic creep, the greater decrease in low-cycle fatigue life. This conclusion results from experimental data and analysis of conditions of damage accumulation for the considered forms of the loading cycle using the deformation criterion of reaching the limit state leading to fracture.

СТРУКТУРА И СВОЙСТВА ДЕТАЛЕЙ, ПОЛУЧЕННЫХ СЕЛЕКТИВНЫМ ЛАЗЕРНЫМ СПЛАВЛЕНИЕМ ПОСЛЕ ИСПЫТАНИЯ НА МАЛОЦИКЛОВУЮ УСТАЛОСТЬ

Results of low cycle fatigue (LCF) testing, investigation of microstructure, and fractures of specimens, which was, obtain by selective laser melting process (SLM) of the powders from Inconel 718 alloy have been carried out in the present article. Chemical composition of the considered specimens, microstructure before and after testing, results at room and elevated temperatures, which were built in XY direction (horizontal), were carrying-out. The specimens in the as-build state were exposed by hot isostatic pressing (HIP) with subsequent inherent Inconel 718 heat treatment. It was established that in specimens in as-built state observe accurately expressed zones of layer-by-layer smelting with 100 μm height. After HIP with subsequent heat treatment strengthening of the considered alloy provides by intermetallic γ'' – Ni3Nb phase, γ'-phase and carbides, also was identified lamellar δ-phase in the microstructure. LCF-testing was conducted in a so-called «soft» cycle of loading with a predetermined interval of the strain for providing of fatigue life in 103, 5х103, 104 cycles. The obtained data was built logarithmic curve in coordinates «Strain σ – Number of cycles N», that allows, with sufficient reliability, determine a rational strain level at LCF-testing for providing a predetermined number of cycles. The following ratios of σ – N were established (Rσ=0, υ=1 Hz): for providing N=103, σ≤1020 МPа, N=5х103, σ=931…961 МPа, N= 104, σ≤941 МPа. Results of the fractures investigation after LCF-testing at 20°С and 550°С shows that during the cyclic elastoplastic deformation at room temperature multicentricity of crack initiations zones observes. Mainly fixed a viscous pattern of fracture with a fatigue grooves presence, which size increases in the process of crack advance to the zone of fracture area. At elevated temperature in the zones of fatigue crack initiation and spreading quasi-brittle character of destruction observes, and turns in viscous in the zone of fracture area. Authors should be pointed out that the application of additive technologies in the manufacture of aerospace parts requires extensive R&D works, and testing efforts to confirm the repeatability of alloy characteristics.

Deformation Resistance and Damage Accumulation of Unstable Structural Material under Cyclic Elastoplastic Deformation

The peculiarities of deformation propagation and damage accumulation in a structurally unstable material, like bronze, are considered, and a way to increase the cyclic plasticity of solid (cold-worked) bronze is revealed. It is noted that in estimation of the levels of accumulated damages and in the extreme case of crack formation in unstable structural materials it is necessary to determine the degree of “softening” of material under the action of alternating-sign amplitudes of elastoplastic deformation.

STRUCTURAL FEATURES OF DAMAGES ACCUMULATION IN CONDITIONS OF COMBINED CYCLIC LOADING

A significant part of the elements of machines and structures along with stationary fatigue is subjected to combined impacts of low-cycle and multi-cycle fatigue loading in operation. The physical nature of their fracture in these conditions depends on the ratio of the mode parameters and entails the necessity of advanced research. The predominance of this or that process determines the nature of the damage accumulation which leads to the destruction. Under such conditions, i.e., preliminary cyclic elastoplastic deformation followed by subsequent fatigue loading, the material subjected to preliminary loading at the first stage can be considered the "new material" with the new properties acquired upon cyclic elastoplastic loading which then undergoes further fatigue loading at the second stage. Hence, at the second stage, the new properties of the material are determined by the level of structural changes and damages earlier accumulated in the material. In this case, the damage to the material is considered on the basis of the well-known statement about the staging character of plastic flow, two main processes, i.e., shear, caused by the interaction of dislocations, and destructuring, attributed to violation of the continuity or integrity of the metal. Experimental studies of changes in the durability of cyclically hardened and cyclically softened steel specimens at different levels of preliminary elastoplastic deformation with varying number of cycles and amplitudes of preliminary elastoplastic strain showed the occurrence of an additional damage to the material when combination of loading modes leads to change in the fatigue durability at the subsequent stage of the basic multi-cycle loading. It is shown that correlation between changes in the fatigue durability and structural state of the material, caused by accumulated damage upon preliminary overloads, and, moreover, those changes can be characterized by the ratio of plastic and destructive strains as a Q-factor of the material.

Modeling of Cyclic Elastoplastic Deformation During Material Testing for Bending

В прочностных расчетах элементов конструкций для характеристики напряженного состояния в опасных зонах концентрации (участки резьб, различного назначения выточки, переходы диаметров валов, отверстия, шпоночные пазы, трещины) используются номинальные напряжения, определяемые без учета влияния концентратора, или местные условные напряжения, вычисляемые в предположении упругого деформирования как произведение номинальных напряжений и теоретического коэффициента концентрации. В действительности при перегрузках конструкций, а нередко и в штатных режимах переменного нагружения, в зонах концентрации возникают трехмерные неоднородные поля главных местных напряжений и упругопластических деформаций, которые в результате циклической нестабильности материалов изменяются с ростом числа нагружений. Для определения напряжений и упругопластических деформаций несущих элементов конструкций при простом (пропорциональном или близком к нему) однократном нагружении широко используется сравнительно хорошо разработанная теория малых упругопластических деформаций в формулировке А. А. Ильюшина. Применительно к переменному пропорциональному нагружению деформационная теория пластичности разработана и экспериментально обоснована не в полной мере во многом из-за недостатка современного испытательного оборудования, доступных экспериментальных методик и ограниченности экспериментальных результатов, характеризующих закономерности циклического упругопластического деформирования широкого круга конструкционных материалов в характерном для несущих элементов конструкций широком диапазоне числа нагружений. В связи с этим представленная в данной работе сравнительно простая методика, доступное оборудование и полученные результаты экспериментального и аналитического моделирования закономерностей циклического упругопластического деформирования при испытаниях материала на изгиб имеют научное и практическое значение для совершенствования методов оценки усталостной прочности и долговечности несущих элементов конструкций.

Micro-deformation evolutions of the constituent phases in duplex stainless steel during cyclic nanoindentation

Cyclic elastoplastic deformation behaviors of austenite phase and ferrite phase in a duplex stainless steel were investigate by load-controlled cyclic nanoindentation with a Berkovich indenter. During the tests, the maximum penetration depth per cycle increased rapidly with cycle number at transient state, and reached stable at quasi-steady state. Plastic dissipated energy was quantitatively proved to be the driving force for the propagation of deformation zones during cyclic nanoindentation tests. Transmission electron microscopy combined with FIB was used to reveal the deformation mechanisms of both phases underneath indents with cycles. After quasi-static single loading, nucleation and concentration of dislocations were observed in both austenite phase and ferrite phase under the indenter. After cyclic loading, dislocations propagated to further regions in both phases. Besides, slip bands were generated within single nanoindentation and propagated during the subsequent cyclic nanoindentation. The sizes of the deformation regions for both phases under the indents after cyclic indentation observed by TEM were consistent with those calculated by the expansion model of spherical cavity.