Elastoplastic Stress Fields Research Articles

Shedding new light on the dislocation-mediated plasticity in wurtzite ZnO single crystals by photoindentation

Dislocation-mediated plasticity in inorganic semiconductors and oxides has attracted increasing research interest because of the promising mechanical and functional properties tuned by dislocations. In this study, we investigated the effects of light illumination on the dislocation-mediated plasticity in hexagonal wurtzite ZnO, a representative third-generation semiconductor material. A (0001) 45o off sample was specially designed to preferentially activate the basal slip on (0001) plane. Three types of nanoindentation tests were performed under four different light conditions (550 nm, 334 nm, 405 nm, and darkness), including low-load (60 μN) pop-in tests, high-load (500 μN) nanoindentation tests, and nanoindentation creep tests. The maximum shear stresses at pop-in were found to approximate the theoretical shear strength regardless of the light conditions. The activation volume at pop-ins was calculated to be larger in light than in darkness. Cross-sectional transmission electron microscope images taken from beneath the indentation imprints showed that all indentation-induced dislocations were located beneath the indentation imprint in a thin-plate shape along one basal slip plane. These indentation-induced dislocations could spread much deeper in darkness than in light, revealing the suppressive effect of light on dislocation behavior. An analytical model was adopted to estimate the elastoplastic stress field beneath the indenter. It was found that dislocation glide ceased at a higher stress level in light, indicating the increase in the Peierls barrier under light illumination. Furthermore, nanoindentation creep tests showed the suppression of both indentation depth and creep rate by light. Nanoindentation creep also yielded a larger activation volume in light than in darkness.

A magneto-mechanical model for the magnetic non-destructive evaluation of ferromagnetic materials

In this paper, a new magneto-mechanical constitutive model is established based on the macro-thermodynamic relationship, the micro-magnetic domain theory and Jiles–Atherton–Sablic (J–A–S) theory. The fitting expression of magnetostriction newly describes the nonlinear stress dependence, which is extended to six-order magnetization terms. In particular, the new expressions of nonlinear functions related to the maximum point of magnetostriction (MPM) are introduced into the magnetostriction expression. In addition, the improved expressions of the plastic stress equivalent field and the three parameters (i.e., the inter-domain coupling parameter, the field relaxation factor and the loss coefficient) considering the nonlinear stress dependence are introduced into the magnetization expressions. Compared to the various experimental results and the theoretical results by the existing models, it is clearly perceived that the new model has an excellent prediction ability of the magnetostrictive and magnetic behaviors in ferromagnetic materials under the elasto-plastic stress and magnetic field. Furthermore, the prediction accuracy of the magnetic parameters related to the magnetic non-destructive evaluation (MNDE) is greatly improved. The integrative analysis of the magnetostrictive and magnetic behaviors in various ferromagnetic materials demonstrates that the presented model can be widely used in the quantitative study of the MNDE as well as in the research of the magneto-mechanical behavior and the application of ferromagnetic materials.

Artificial neural networks-based [formula omitted]-integral prediction for cracked bodies under elasto-plastic deformation state –monotonic loading

Artificial neural networks (ANNs) integrated with a finite element (FE)-based equivalent domain integral method are developed to compute J-integral at the vicinity of crack tips through a time-efficient approach. Robust ANN models are trained to establish nonlinear relationships between FE predicted elastic and elasto-plastic stress, strain, and displacement fields of stainless steel (SS304). Subsequently, elastic–plastic J-integral can be determined by using only elastic FE analysis solution rather than computationally expensive elasto-plastic FE analysis solution. The results show that well-trained ANN models can efficiently and accurately determine J-integral around the crack tips on the basis of numerical elastic FE analysis solution.

Phase-field study on the formation of α variant clusters induced by elastoplastic stress field around the void in titanium alloys

The formation of α variant clusters during β to α transformation under the elastoplastic stress field around a void was investigated using J2 plasticity theory and phase field simulation. Compared with elastic materials, taking an elastic–plastic phase field model in the present work, the stress fields around the void can be partially relaxed by plastic deformation, and the maximum amplitude of the stress reduces. With the increase of the void size, the selection effect on α variant clusters in titanium alloys is gradually enhanced. The variant selection is asymmetric under the conditions of applied tensile and compressive stresses, and the influence of the stress fields around the void under external shear stress is stronger. These could be predicted and confirmed by the interaction energy calculations between the stress fields around the void and α variants. Some interesting variant clusters appear, such as “windmill”, “butterfly”, and “wing” types under external tensile, compressive and shear stresses respectively. The “equilateral triangle”, “nearly parallel” and “quasi equilateral triangle” type variant clusters can form through sympathetic nucleation, given the particular α/α orientation relationship corresponding to lower energy. The ultimate microstructures of α variant clusters around a void are determined by both inter-variant and variant-external stress field interactions. The high-throughput calculations under different applied stress states would provide support for the generation and optimization of the microstructures of titanium alloys in follow-up work.

A computational framework based on FEA, ML and GA for estimation of welding residual stresses

The present work describes a computational framework based on finite element (FE) analysis and machine learning (ML) and genetic algorithm (GA) to accurately estimate and minimize the residual stresses in welding. The FE analysis comprises of sequentially coupled thermal and mechanical analyses that are nonlinear due to temperature-dependent thermal/mechanical properties. In the FE analysis, the effective stress function (ESF) algorithm is used for accurate computation of the temperature-induced elasto-plastic stress field during welding. The ESF algorithm accounts for the large variation of yield curves due to temperature changes in welding. To improve the accuracy of the thermal and mechanical analyses, an optimization process combining supervised machine learning and binary coded genetic algorithm is utilized. This optimization technique is implemented to derive an accurate phase-change model for the thermal FE analysis of SS304, which is otherwise a burdensome and costly task to obtain from calorimetric experiments. The results obtained through the derived phase-change model are validated through welding time-temperature distribution reported for a welding experiment in literature. The same optimization process is further used to obtain a set of weld operating conditions (such as weld voltage, current, welding speed, and the gap between plates) for SS304 that reduce the tensile residual stresses. It is found that the accurate estimation and reduction of welding residual stresses can be realized by using the present computational framework. • A detailed FE analysis is presented for the estimation of residual stresses in welding. • ESF algorithm implemented in the FE analysis is found very useful. • An optimization methodology is proposed based on machine learning and genetic algorithm. • Proposed optimization scheme is used to estimate the phase-change model and weld parameters. • Accuracy in estimation of welding temperature field is improved and tensile residual stress is minimized to a certain extent.

The introduction of critical distance in the description of dynamic experiments based on simulation mesodefect evolution

The Theory of Critical Distances is a group of phenomenological methods for fracture prediction of materials subjected different loading conditions with accounting effect of stress concentration features. When estimating strength of components under dynamic loading by directly postprocessing the elastoplastic stress fields acting on the material in the notch tip the critical distance is a material parameter. Based on research of physical processes taking place at a micro/mesoscopic level near the notch tip the physical meaning of the parameters of theory of critical distances was investigated. The modeling of solids with defects behavior based on self-similar solutions for stress and defect density fields in one- and three-dimensional cases was carried out. Established link between critical distance and fundamental length of dissipative structure growing in a blow-up regime.

Fatigue Crack Growth under Non-Proportional Mixed Mode Loading in Rail and Wheel Steel Part 1: Sequential Mode I and Mode II Loading

Fatigue tests were performed to estimate the coplanar and branch crack growth rates on rail and wheel steel under non-proportional mixed mode I/II loading cycles simulating the load on rolling contact fatigue cracks; sequential and overlapping mode I and II loadings were applied to single cracks in the specimens. Long coplanar cracks were produced under certain loading conditions. The fracture surfaces observed by scanning electron microscopy and the finite element analysis results suggested that the growth was driven mainly by in-plane shear mode (i.e., mode II) loading. Crack branching likely occurred when the degree of overlap between these mode cycles increased, indicating that such degree enhancement leads to a relative increase of the maximum tangential stress range, based on an elasto–plastic stress field along the branch direction, compared to the maximum shear stress. Moreover, the crack growth rate decreased when the material strength increased because this made the crack tip displacements smaller. The branch crack growth rates could not be represented by a single crack growth law since the plastic zone size ahead of the crack tip increased with the shear part of the loading due to the T-stress, resulting in higher growth rates.

TRANSFORMATION OF CARBIDЕ PHASE IN RAILS AT LONG-TERM OPERATION

Evolution of carbide phase in surface layers of volume (passed gross tonnage 500 and 100 million tons) and differentially hardened rails (passed tonnage – 691.8 million tons) to a depth of 10 mm along the central axis and along the rail head fillet was studied by means of transmission electron diffraction microscopy. The grains of lamellar perlite, ferrite-carbide mixture, structurally free ferrite are analyzed. The flow of two complementary mechanisms of transformation of carbide phase of steel in the surface layers during the rails operation was identified: mechanism of cutting cementite particles and their subsequent­ transfer into the ferrite grains or plates volume (in perlite structure); mechanism of cutting and following dissolution of cementite particles, transition of carbon atoms to dislocations (into the Cottrell­ clouds and the dislocation centers), transfer of carbon atoms within dislocations to the volume of grains (or plates) of ferrite, with the following repeated formation of nanoscale cementite particles. A fragmented dislocation substructure is formed instead of former plates. Fragments boundaries decorate places where cementite-α phase interphase boundaries used to be. The main reason for dissolution of cementite is that it is energetically more preferable for carbon atoms to be on dislocation centers and on subboundaries than in cementite lattice. Binding energy of carbon atom-dislocation is 0.6 eV, for carbon atom-subboundary bond it is 0.8 eV, while in cementite it is held by 0.4 eV. Formation of elastoplastic stress fields is detected, concentrators of which are intra and interphase boundaries between grains of ferrite and perlite, cementite and ferrite plates of perlite colonies, particles of globular cementite and ferrite. The main sources of curvaturetorsion of metal lattice of rails metal are intraand interphase bounda­ries­ of grain separation of ferrite and perlite, cementite and ferrite plates of perlite colonies, particles of globular cementite and ferrite. Approaching to the rolling surface, number of stress concentrators and amplitude of internal fields of longrange stress are increasing.

Transformation of Carbides in Prolonged Rail Operation

The evolution of the carbide phase in the surface layers of bulk-quenched rails (after the passage of 500 and 1000 million t of traffic) and differentially quenched rails (after the passage of 691.8 million t) to a depth of 10 mm at the central axis of the rail cross section and at the nearby rounded section is studied by transmission electron-diffraction microscopy. The grains of plate pearlite, ferrite–carbide mixture, and structure-free ferrite are analyzed. The carbide phase in the surface layers of the steel changes in two mutually complementary processes during rail operation: (1) cleavage of cementite particles with subsequent entrainment in ferrite grains or plates (in the pearlite structure); (2) cleavage and dissolution of cementite particles, with transfer of carbon atoms to dislocations (in Cottrell atmospheres and in dislocational cores), which transport them to the ferrite grains (or plates), where cementite nanoparticles are formed again. In the previous location of the plates, fragmented dislocational substructure appears. The boundaries of the fragments are found at the positions previously occupied by cementite α-phase boundaries. The solution of cementite is mainly due to the energy of carbon atoms at dislocation cores and subboundaries in comparison with the cementite lattice. The binding energy of the carbon atom and the dislocations is 0.6 eV and the binding energy of the carbon atom and the subboundary is 0.8 eV, as against 0.4 eV for the carbon atom in cementite. Elastoplastic stress fields are formed; their stress concentrators are intra- and interphase boundaries of ferrite and pearlite grains, cementite plates and ferrite of the pearlite colonies, and globular cementite and ferrite particles. Those are also the basic sources of curvature and torsion in the crystal lattice of the rail steel. On approaching the contact surface, the number of stress concentrators increases, and the internal long-range stress fields are of greater amplitude.

Long-term operation surface changes in differentially quenched 100-m rails

By optical microscopy and transmission electron diffraction microscopy, the evolution of the structural and phase states in the surface layers over a depth of 10 mm in the head of differentially quenched rail (category DT350) is studied, as the rail is subjected to passed tonnage of 691.8 million t at the experimental loop of AO VNIIZhT. In the initial state, the following structural components are present in the rail head: plate-pearlite grains (relative content 0.7); mixed ferrite–carbide grains (0.25); and grains of structure-free ferrite. After experiencing a passed tonnage of 691.8 million t, this state only remains beyond a depth of 10 mm. At that depth, a large quantity of bend extinction contours is observed. That indicates elastoplastic distortion of the material’s crystal lattice. The stress concentrators in the steel are intraphase and interphase boundaries of the ferrite and pearlite grains, cementite and ferrite plates in pearlite colonies, and globular cementite and ferrite particles. Structural transformations are observed at the macro level: microcracks appear, running at acute angles from the surface to a depth of 140 μm; and a decarburized layer is formed. At the micro level, elastoplastic stress fields are formed, and the cementite plates in the pearlite colonies break down. The stress concentrators in that case are intraphase and interphase boundaries of the ferrite and pearlite grains, cementite and ferrite plates in pearlite colonies, and globular cementite and ferrite particles. In structure-free ferrite grains, cementite nanoparticles are formed. The results are compared with the evolution of the structural and phase states at the surface of a recess in bulk-quenched rail as the rail is subjected to gross loads of 500 million t: the transformation of the structural and phase states in the surface layers is more pronounced. Plate pearlite is characterized by solution of the cementite plates. That leads to the formation of chains of globular carbide particles at the sites of the cementite plates. This may be associated with transfer of the carbon atoms from the cementite lattice to dislocations.

Refined Analysis of Fatigue Crack Initiation Life of Beam-to-Column Welded Connections of Steel Frame under Strong Earthquake

This paper presents a refined analysis for evaluating low-cycle fatigue crack initiation life of welded beam-to-column connections of steel frame structures under strong earthquake excitation. To consider different length scales between typical beam and column components as well as a few crucial beam-to-column welded connections, a multiscale finite element (FE) model having three different length scales is formulated. The model can accurately analyze the inelastic seismic response of a steel frame and then obtain in detail elastoplastic stress and strain field near the welded zone of the connections. It is found that the welded zone is subjected to multiaxial nonproportional loading during strong ground motion and the elastoplastic stress-strain field of the welded zone is three-dimensional. Then, using the correlation of the Fatemi-Socie (FS) parameter versus fatigue life obtained by the experimental crack initiation fatigue data of the structural steel weldment subjected to multiaxial loading, the refined evaluation approach of fatigue crack initiation life is developed based on the equivalent plastic strain at fatigue critical position of beam end seams of crucial welded connections when the steel frame is subjected to the strong earthquake excitation.

CHANGES IN STRUCTURE AND PHASE COMPOSITION OF THE SURFACE OF DIFFERENTIALLY HARDENED 100-METER RAILS IN OPERATION

By the methods of optical and transmission electron diffraction microscopy the evolution of structural-phase states of the surface layers in the head of differentially hardened rails of category DT350 was studied to the depth up to 10 mm in the fillet after the passed tonnage of 691.8 million gross tones on the experimental ring of JSC “VNIIZhT”. It is shown that in the initial state the following structural constituents present in the rail head: grains of lamellar perlite (relative content is 0.7), grains of ferrite-carbide mixture (0.25) and grains of structurally free ferrite. After the passed tonnage of 691.8 million gross tones this state is preserved only at a depth of more than 10 mm. A distinctive feature of the structure at this distance is a large number of bending extinction contours, which reveals elastoplastic distortions of the crystal lattice in the material. Stress concentrators of the steel under study are intra- and interphase interfaces of grains of ferrite and perlite, cementite plates and ferrite of perlite colonies, globular cementite particles and ferrite. The transformation of the structure is manifested at the macro level in the formation of microcracks at an acute angle to the surface to a depth up to 140 μm, and in the formation of the decarburized layer. At the micro level, the formation of elastoplastic stress fields and the destruction of cementite plates of perlite colonies have been revealed. It is shown that stress concentrators are intra- and interphase interfaces of ferrite and perlite grains, cementite and ferrite plates of ferrite colonies, globular cementite particles and ferrite. In the grains of structurally free ferrite, the formation of nano-sized particles of cementite was observed. The comparison is made with the results of the evolution of structural-phase states in the fillet of volume-hardened rails after the passed tonnage of 500 million gross tones: the most significant transformations of structural-phase states are observed in the surface layers. The evolution of the structural-phase state of perlite of lamellar morphology consists in the dissolution of cementite plates, which leads to the formation of a chain of particles of the carbide phase with globular shape in place of the cementite plate. This is possible due to the transfer of carbon atoms from the crystalline lattice of cementite to dislocations.

Elastic-Plastic Constraints Analysis for Hole-Edge Crack

This paper mainly conducts an elastic-plastic constraint analysis on rectangular plate specimens with hole-edge crack under remote uniaxial uniformly distributed load by using J-A2 elastic-plastic fracture theory. In order to analyze the effect of orifice on elastoplastic stress field of hole-edge crack tip, this paper calculates a series of round hole-edge crack, diamond hole-edge crack and corresponding pure crack models. The interference effects of the orifice shape on elastic-plastic J integral and crack constraint parameter A2 are discussed. The results show that: the orifice has an amplification effect on the fracture driving force (J-integral), and this amplification effect in elastic-plastic is smaller than that in elastic; the orifice has a shielding effect on the crack tip constraint (A2 parameter), and this shielding effect gradually weaken with the crack increasing.

Elasto-Plastic Stresses in a Functionally Graded Rotating Disk

A numerical method based on the extension of the variable material property method was developed to obtain the elasto-plastic stress field in a functionally graded (FG) rotating disk. The method was applied to estimate the stress field in a metal–ceramic functionally graded solid disk. To establish the validity of the proposed method, results were compared with finite element results. Unlike uniform rotating disks, where yielding starts from the disk center, plasticity in FG disks can originate at any point. The effect of different metal–ceramic grading patterns as well as the relative elastic moduli and densities of the ceramic and metallic constituents on the developed stresses were studied. Reinforcement of a metal disk with ceramic particles, in both elastic and plastic regimes, can significantly influence the mechanical response of the disk such as the stress distribution and the critical angular velocities corresponding to the onset of plasticity in the disk and plastic disk. Disks with increasing ceramic content from inner to outer radius showed a more uniform von Mises stress distribution for a fixed value of total ceramic content. In contrast, disks with decreasing ceramic content from inner to outer radius had the lowest outer edge displacement for a fixed value of total ceramic content.

The influence of thermomechanical loading history on the stress level in WWER NPP reactor pressure vessels under thermal shock

We present the results of calculations of the kinetics of stress-strain state and stress intensity factors for surface and under-the-cladding circumferential cracks in modeling the emergency core cooldown conditions for the WWER-1000 reactor. The calculation procedure is based on a mixed finite-element method statement which provides stability of numerical solution and a high accuracy of results for both the displacements as well as stresses and strains. The authors analyze the influence of the density of the finite-element discretization of the crack-tip area for the surface and under-the-cladding circumferential cracks on the accuracy and convergence of computation of fracture-mechanics parameters in the modeling of thermal shock conditions. The results of calculation of kinetics of stress intensity factors allowing for the thermomechanical loading history and residual process-induced stress fields are reported. It is demonstrated that if the elastoplastic deformation history and residual process-induced stress fields are disregarded in the calculations of stress intensity factors for under-the-cladding cracks the reactor pressure vessel strength and lifetime may turn out to be overestimated.

Zonal disintegration phenomenon in enclosing rock mass surrounding deep tunnels—Elasto-plastic analysis of stress field of enclosing rock mass

The zonal disintegration phenomenon (ZDP) is a typical phenomenon in deep block rock masses. In order to investigate the mechanism of ZDP, an improved non-linear Hoek-Brown strength criterion and a bi-linear constitutive model of rock mass were used to analyze the elasto-plastic stress field of the enclosing rock mass around a deep round tunnel. The radius of the plastic region and stress of the enclosing rock mass were obtained by introducing dimensionless parameters of radial distance. The results show that tunneling in deep rock mass causes a maximum stress zone to appear in the vicinity of the boundary of the elastic and the plastic zone in the surrounding rock mass. Under the compression of a large tangential force and a small radial force, the rock mass in the maximum stress zone was in an approximate uniaxial loading state, which could lead to a split failure in the rock mass.

Elasto-Plastic Analysis of 3-D Inner Cracks Using the Finite Element Alternating Method

The finite element alternating method (FEAM) was extended to obtain fracture mechanics parameters and elasto-plastic stress fields for 3-D inner cracks. For solving a problem of a 3-D finite body with cracks, the FEAM alternates independently the finite element method (FEM) solution for the uncracked body and the solution for the crack in an infinite body. As the required solution for a crack in an infinite body, the symmetric Galerkin boundary element method formulated by Li and Mear was used. For elasto-plastic numerical analysis, the initial stress method proposed by Zienkiewicz and co-workers and the iteration procedure proposed by Nikishkov and Atluri were used after modification. The extended FEAM was examined through comparing with the results of commercial FEM program for several example 3-D crack problems.

Two-Dimensional Adaptive-Surface Elasto-Plastic Asperity Contact Model

When contact problems are solved by numerical approaches, a surface profile is usually described by a series of discrete nodes with the same intervals along a coordinate axis. Contact computation based on roughness datum mesh may be time consuming. An adaptive-surface elasto-plastic asperity contact model is presented in this paper. Such a model is developed in order to reduce the computing time by removing the surface nodes that have little influence on the contact behavior of rough surfaces. The nodes to be removed are determined by a prescribed threshold. The adaptive-surface asperity contact model is solved by means of the element-free Galerkin-finite element coupling method because of its flexibility in domain discretization and versatility in node arrangements. The effects of different thresholds on contact pressure distribution, real contact area, and elasto-plastic stress fields in contacting bodies are investigated and discussed. The results show that this model can help reduce about 48% computational time when the relative errors are about 5%.

Dislocation simulation of brittle-ductile transition in ferritic steels

Two-dimensional discrete dislocation simulations of the crack-tip plasticity of a macrocrack-micro-crack system representing the fracture behavior in ferritic steels are presented. The crack-tip plastic zones are represented as arrays of discrete dislocations emitted from crack-tip sources and equilibrated against the friction stress. The dislocation arrays modify the elastic field of the crack; the resulting field describes the elastoplastic crack field. The simulated crack system involves a microcrack in the plastic zone of the macrocrack (elastoplastic stress field). The effects of the crack-tip blunting of the macrocrack are included in the simulations; as dislocations are emitted, the microcrack is kept at a constant distance from the blunted tip of the macrocrack. The brittle-ductile transition (BDT) curve is obtained by simulating the fracture toughness at various temperatures. A consideration of the effects of blunting is found to be critical in predicting the sharp upturn of the BDT curve. The obtained results are compared with existing experimental data and are found to be in reasonable agreement.

An approximate, analytical approach to the `HRR'-solution for sharp V-notches

The well-known so-called `HRR-solution' (Hutchinson, 1968 and Rice and Rosengren, 1968) considers the elasto-plastic stress field in a power-law strain hardening material near a sharp crack. It provides a closed form explicit expression for the stress singularity as a function of the power-law exponent `n' of the material, but the stress angular variation functions are not found in closed form. More recently, similar formulations have appeared in the literature for sharp V-notches under mode I and II loading conditions. In such cases not only is the angular variation of the stress fields obtained numerically, but so is the singularity exponent of the stress field. In the present paper, approximate but accurate closed form solutions are first reported for sharp V-notches with an included angle greater than π/6 radians. Such solutions, limited here to Mode I loading conditions, allow a very satisfactory estimate of the angular stress components in the neighbourhood of the notch tip, in the entire range of notch angles and for the most significant values of n (i.e. from 1 to 15). When the notch opening angle tends towards zero, and the notch approaches the crack case, the solution becomes much more complex and a precise evaluation of the parameters involved requires a best-fitting procedure which, however, can be carried out in an automatic way. This solution is also reported in the paper and its degree of accuracy is discussed in detail.