Model Of Plastic Deformation Research Articles

Modeling of elastic plastic deformation of near-surface layers of materials

According to the results of strain measurements, a kinematically hardening body model is used to describe the process of elastic-plastic deformation of 1X18H9T steel. Special attention is paid to the processes occurring in the surface layers. The model takes into account the increasing tightness of shear deformations deep into the material. The increase in the stress of the plastic flow in depth is described by a second-order polynomial. The main parameters of the surface effect were determined experimentally and by calculations using the method of reduction coefficients in the process of successive approximations: depth, coefficient of hardening of the material, stresses of plastic flow on the surface and inside the material. It is shown that in order to study the near-surface effect by the strain gauge method, it is necessary to give preference to bending tests of samples rather than stretching. The presence of the surface effect explains the following facts: the destruction of the sample during the tensile test does not begin from the surface, but from the inside, the origin of fatigue cracks occurs under the surface, the surface effect practically does not affect the deformed state of the elastic body, but very strongly affects the stress state at the surface.

Plastic deformation and damage modeling of AA7075 synthetic 3D microstructure created using generative AI

3D microstructures provide valuable insight into material behavior which is essential in elucidating microstructural phenomena, such as particle morphology and void damage, and consequent macroscopic material response. However, creating 3D microstructures is extremely laborious and expensive, requiring complex microstructural characterization and imaging techniques such as Focussed-Ion Beam based Scanning Electron Microscopy (FIB-SEM) or X-ray Computed Tomography (XCT). To this end, synthetic 3D microstructures were rapidly generated from orthogonal 2D images using SliceGAN, which proved a practical and cost-effective method. In this study, multiple synthetic microstructures of AA7075-O, a complex microstructure of various strengthening precipitates within a softer aluminum matrix, were post-processed, meshed, and modeled for different damage behavior in FEA using advanced constitutive material models. Subsequently, the synthetic and real microstructures were qualitatively and quantitatively analyzed for their elastoplastic deformation and ductile void damage responses.This study illustrates the viability of an integrated AI-FE methodology in studying microstructural micromechanics, demonstrating that synthetic microstructures exhibited a very similar stress-strain response, especially when using a free boundary condition, and comparable stress distribution and void damage, albeit with some discrepancies. Also, it emphasizes the influence of particle morphology on strength and damage, where highly irregular particles play a dual role in increasing strain hardening by restricting matrix flow at the cost of increased ductile damage induced by decohered particles. Lastly, the more advanced FE models, with multiple voiding mechanisms, reduced the discrepancy between real and synthetic microstructures compared to simpler models

A “poor-man’s” deformation plasticity based approach to topology optimization of elastoplastic structures

This paper presents a topology optimization framework utilizing a deformation plasticity model to approximate the isotropic hardening von-Mises incremental elastoplasticity model under monotone proportional loading. One advantage of the model is that it is based on a yield surface allowing for precise matching to uniaxial elastoplastic isotropic hardening response. The deformation plasticity model and the incremental plasticity model coincides for proportional loading and since the deformation plasticity model is path-independent, the computational cost and implementation complexity reduce significantly compared to the conventional incremental elastoplasticity. To investigate the deformation plasticity model combined with topology optimization, we compare three common elastoplastic optimization objectives: stiffness, strain energy and plastic work. The possibility to limit the peak local plastic work while maximizing the strain energy is also investigated. The consistent analytical sensitivity analysis which only requires the terminal state is derived using adjoint method. Numerical examples demonstrate that the proportionality assumption is reasonable and the deformation plasticity model combined with topology optimization is a competitive alternative to cumbersome incremental elastoplasticity.

Extracting and analyzing the governing model for plastic deformation of metallic glasses

This paper first detects hidden system from plastic deformation of metallic glasses by sparse identification. The extracted model simulates four types of stress-time curves and displays the prediction of serrated events. This interpretation effectively explains various experimental phenomena of repeated yielding. Further, in terms of parametric sensitivity analysis to the model, two parameters are taken as bifurcation parameter, and the analysis of codimension-one and codimension-two bifurcation are carried out to excavate the causes of dynamic transformation, including saddle–node bifurcation, Hopf bifurcation, Bogdanov–Takens bifurcation and cusp bifurcation. Different bifurcation points correspond different types of stress-time curves. The homologous phase diagrams including periodic orbit, unstable orbit and chaotic behavior are presented to show the dynamics diversity of the model. In addition to dynamic analysis, statistical analysis for plasticity values is also applied to excavate the crossover between periodic and chaotic plastic dynamic transitions. Our results provide a novel perspective on the deformation of metallic glasses from the viewpoint of dynamic model and are also important for evaluating the plastic deformation properties of metallic glasses in practical applications.

A damage constitutive model for consistent description of static and fatigue behaviors of ultra-high performance concrete containing coarse aggregate

A suitable constitutive model for describing the mechanical behaviors of ultra-high performance concrete (UHPC) under various loading histories plays a vital role in analyzing its structural performance. In this work, a consistent elastoplastic damage model is developed for UHPC containing coarse aggregate (UHPC-CA) subjected to static and fatigue loads, in which the driving and alleviating effects induced by the inclusions of coarse aggregate and steel fiber are considered. For damage evolution, based on the acting mechanism of the non-uniformity of stress wave propagation determined by the loading rate on the mechanical responses of UHPC-CA, the loading rate is skillfully integrated into the damage evolution rule to achieve the consistent description of mechanical behaviors of UHPC-CA under static and fatigue loading conditions. Regarding plasticity growth, an empirical plastic deformation model is adopted to improve the computational efficiency of structural nonlinear analysis. To verify the applicability of the proposed model, a user-defined UMAT subroutine is further developed for the subsequent numerical implementation. The comprehensive comparisons between the numerical predictions and independent experimental results at both the material level and structural level solidly demonstrate the capacity of the consistent model to capture the main features concerning the mechanical performance of UHPC-CA subjected to different loading paths.

A crystal plasticity model for multiaxial cyclic deformation of U75V rail steel

The theoretical investigations of cyclic deformation behavior and deformation mechanism of the rail steels under multiaxial loadings are of great significance to the study of rolling contact fatigue. Based on the classical crystal plasticity framework, a new nonproportional parameter at the mesoscale is proposed, and the isotropic and kinematic hardening models are modified. A series of finite element simulations of U75V rail steel under uniaxial and multiaxial cyclic loading are carried out using the proposed model. The simulation results show that the proposed model can reasonably reflect the cyclic softening under strain-controlled uniaxial cyclic loading, cyclic hardening under strain-controlled multiaxial cyclic loadings, and ratcheting behavior under stress-controlled uniaxial and multiaxial cyclic loadings of U75V rail steel. Moreover, the influence of multiaxial loading paths on the plastic strain is explained from a mesoscopic perspective. The values of nonproportional parameters of different slip systems under uniaxial and multiaxial paths are compared, and the difference of nonproportional parameters at the macroscale and mesoscale are discussed. Finally, the simulation results of the proposed model and the existing model with modified kinematic hardening rules are compared. The results show that the proposed model has better predictions on the evolution of ratcheting strain and nonproportionally additional hardening effect caused by nonproportionally multiaxial loadings.

Plastic deformation mechanisms and constitutive modeling of WE43 magnesium alloy at various strain rates and temperatures

In this study, we investigated the mechanical behavior and deformation mechanisms of as-cast and as-rolled WE43 at various strain rates and temperatures. Compression tests were carried out at ambient temperature under 900/s, 1400/s, and 2000/s, and at temperatures of 100 °C, 200 °C, 250 °C, and 300 °C under 1400/s, respectively. The results showed that, with the rise of strain rate, the deformation mechanism of as-cast and as-rolled WE43 both changed from twinning dominant combined with slipping to slipping dominant. As the temperature increased, the deformation mechanism of WE43 changed from twinning to slipping, controlled by non-basal slips at various strain rates and temperatures. As for as-rolled WE43, it was observed that intense dynamic recrystallization and adiabatic shear bands (ASBs) occurred under high strain rate and high temperature conditions. Moreover, this study employed the Johnson-Cook (JC) model to formulate the plastic deformation model of the WE43 alloy under conditions of elevated temperatures and high strain rates. And a dynamic mechanical analyzer (DMA) was successfully employed to refine the accuracy of elastic modulus.

Atomistic modeling of plastic deformation in BCC niobium nanowire under bending

Design of high-performance nanodevices require nanowires with optimized bending properties, which relies on a thorough understanding of the mechanical behavior of nanowires. To explore the mechanism underlying bending plasticity of the nanowire, we adopted a 〈110〉-oriented body-centered cubic (BCC) Nb nanowire as the model system and performed bending tests at various temperatures by means of molecular dynamics simulation. Our results reveal that the BCC Nb nanowire bends plastically and homogeneously into a smoothed arc shape with significant curvature by slip of perfect dislocations, showing excellent bending plasticity and toughness. The generated dislocations are identified as geometrically necessary dislocation for accommodating the strain gradient related to bending, and they accumulate linearly with the bending angle to a value of an order of 1017 m−2. Temperature dependence was found in both elastic modulus and yield strength of the nanowire. In particular, we find that a completely dislocation-mediated plasticity at high temperature changes into a deformation mechanism involving predominant dislocation slip plus additional anti-twinning as temperature is reduced. Both development of high dislocation density and reduced mobility of dislocation at low temperature contribute to the initiation of anti-twinning. Our findings not only enrich the current understanding of deformation behavior of BCC nanomaterials under non-uniaxial load, but also provide valuable information for design of flexible and stretchable nanodevices based on metallic nanowires.

Mechanisms of formation and accumulation of misorientations in deformable metals and alloys

The formation of misoriented substructures in plastically deformable metal materials has been theoretically studied. Expressions are obtained for the intensity of accumulation of low-angle and high-angle misorientation boundaries. Within the framework of a mathematical model of shear plastic deformation and hardening, numerical calculations of the dependences of the average characteristics of a defective medium on the degree of deformation under conditions of uniaxial compression with a constant strain rate at room temperature are performed. It is shown that the intensity of generation of low-angle tilt walls depends significantly on the scenario of changes in the density of jogs on the screw segments of dislocation loops emitted by dislocation sources. The main mechanism for the formation of low-angle walls is the rearrangement of clusters of edge segments of dislocation loops into tilt dislocation walls under the influence of flows of interstitial atoms generated by moving screw segments. It is assumed that low-angle walls merge into one until the total misorientation angle of the merged walls reaches a critical value of about 10°, after which the distance between dislocations in the wall decreases to the corresponding critical value and further penetration of individual dislocations into the wall becomes impossible. The expression for the intensity of the formation of high-angle boundaries was obtained as a consequence of the continuation of the work of dislocation sources and the formation of clusters of low-angle walls, the total energy of which is higher than the energy of an equilibrium high-angle boundary at the same misorientation.

Low-velocity impact experiments of porous ice balls simulating Saturn's ring particles: Porosity dependence of restitution coefficients and the mechanism of inelastic collision

We investigated the porosity dependence of the restitution coefficient (ε) of porous ice balls with porosities of 49.6%, 53.8%, and 60.8% colliding with granite, ice and porous ice plates at a low impact velocity (vi = 0.93–96.9 cm s−1) and temperature of −13.8 °C. The relationship between the impact velocity and the restitution coefficient was divided into two regions by the critical velocity vc: In the quasi-elastic region (vi≤vc), the restitution coefficient had a constant value of εqe regardless of the impact velocity and could be explained by using Dilley's viscous dissipation model. In the inelastic region (vi≥vc), the restitution coefficient decreased with the impact velocity and could be explained by using the improved Andrews' plastic deformation model. We then determined the porosity dependence of the εqe and vc empirically for collisions between the porous ice ball and the porous ice plate from our results. Then we extrapolated the porosity dependence of the restitution coefficient by substituting the calculated εqe and vc for the porosity of 10 to 70%. The restitution coefficient was found to decrease with increasing porosity of the porous ice, and to be strongly dependent on the porosity of the porous ice. Considering the energy budget in the steady-state dense ring system which is controlled by the restitution coefficient of the ring particles, the velocity dispersion of the ring particles was estimated to be ∼10−2 mm s−1 to cm s−1 for the ring particles with the porosity from 45% to 70% and < 10–90 cm s−1 for those with the porosity <45%.

Research Progress on Prediction Models of Plastic Deformation and Ductile Fracture of Titanium Alloy

Research Progress on Prediction Models of Plastic Deformation and Ductile Fracture of Titanium Alloy

Моделювання процесів виготовлення тонкостінних втулок з поруватих заготовок з використанням прямого видавлювання та радіального ущільнення

The deformation process of powder materials thin-walled bushings manufacture was investigated by computer modeling. Two shape formation bushings schemeswere considered (direct extrusion and radial compaction).A continuum approach was used to create a modeling method. The method is based on rheological models of porous body plastic deformation and the finite element method. The accepted material rheological model allows describing the deformation of both powder and porous blanks. It takes into account the different resistance of these materials in tension and compression. Modeling of the deformation process was carried out in stages, using the method of successive loads. The elastic stresses were determined, the plastic potential was calculated and, if it was necessary, the stresses and material parameters of the model were corrected at each load step. The porosity value is reach maximum in blank and area, that is free from the loads, and the accumulated deformation is reachminimum in direct extrusion. The effect of back pressure leads to a more uniform distribution of these parameters, a decrease in porosity and an increase in the accumulated deformation of the solid phase. During radial compaction of thin-walled bushings, deformation of the material occurs locally. Porosity in the product section increases with increasing radius. Increasing the number of technological transitions with a gradual increase in the forming tool diameter reduces the uneven distribution of residual porosity and its value. However, the unevenness of the porosity distribution over the radius remains. In the process of radial compaction, a burr is formed on the ends of the product. The burr can be reduced by changing the initial shape of the blank. The process of direct extrusion allows obtaining more uniform distribution of residual porosity and accumulated plastic deformation of product material. However, this technological process requires the higher loads application, which leads to less stability of the tool. The radial compaction method (which characterized by local deformation) requires not high loads and allows not powerful equipment using. However, the distribution of residual porosity over the radius of the bushing is uneven. Keywords: plasticity theory, powder materials, computer modeling, finite element method, stress-strain state, porosity distribution.

Numerical Study on Metal Transverse Flow Law and Model of Rolled Strip under Variable Specification in Hot Rolling

The research on metal transverse flow under variable specification is of great significance for shape calculation and control in hot strip rolling. The finite element software ABAQUS 2016 is used to establish the elastic–plastic deformation model of a hot rolled strip to study the metal transverse flow. The edge transverse strain εe and center transverse strain εc are introduced to characterize metal transverse flow and calculate the strip flatness. The effect on εe, εc and the flatness increment of similarity of profile under different widths, thicknesses and reduction rates is simulated and calculated. The results show that the change in similarity of profile has a linear influence on εe and εc. The strip has the ability of flatness self-correction due to the metal transverse flow. The ksc of the strip with B = 700 mm is 0.87, which is significantly greater than the 0.45 ksc value of the strip with B = 2100 mm. Priority can be given to ensure the crown requirements during narrow strip rolling. The ksc of the strip with H = 50 mm is 0.45, which is higher than the 0.22 ksc value of the strip with H = 6 mm, and the ksc of the strip with ε = 50% is 0.52, which is higher than 0.30 ksc value of the strip with ε = 10%. It is more reasonable to adjust the crown to a greater extent in the upstream stand to meet the requirement of both flatness and crown for the large entry thickness reduction rate and self-correction ability. A metal transverse flow prediction model based on the full test simulation results is established, which can meet the requirement of crown setting at the exit of each stand and the rapid calculation of online flatness control, and can further make the crown and flatness reach the target values at the finishing exit.

Crystal plasticity model for creep and relaxation deformation of OFP copper

ABSTRACT We demonstrate a dislocation density-based crystal plasticity (CP) model approach for simulating mesoscale deformation and damage. The existing CP framework is extended to be compatible with the oxygen-free phosphorous copper microstructure that is the focus of this study. The key aim is to introduce relevant plastic deformation mechanisms and to develop a failure model capable of depicting creep damage in the material. The effect of local variations in material is evaluated, and the model response is compared with experiments and characterisation. The basis of this work is CP material modelling, including grain orientation and size, obtained using electron backscatter diffraction and experimental test data of real relaxation test specimens. This will yield a realistic description of texture and grain shape and, ultimately, accurate stress–strain response at the microstructural level for further evaluation of performance with respect to material creep(−fatigue) damage.

Constitutive Modeling of Annealed OFHC with Wide Strain-Rate and Temperature Effects: Incorporating Dislocation Dynamics and Normalized Microstructural Size Evolution.

The flow stress of face-centered cubic (FCC) metals exhibits a rapid increase near a strain rate of 104 s-1 under fixed-strain conditions. However, many existing constitutive models either fail to capture the mechanical characteristics of this plastic deformation or use piecewise strain-rate hardening models to describe this phenomenon. Unfortunately, these piecewise models may suffer from issues such as discontinuity of physical quantities and difficulties in determining segment markers, and struggle to reflect the underlying physical mechanisms that give rise to this mutation phenomenon. In light of this, this paper proposes that the abrupt change in flow stress sensitivity to strain rate in FCC metals can be attributed to microstructural evolution characteristics. To address this, a continuous semiempirical physical constitutive model for FCC metals is established based on the microstructural size evolution proposed by Molinari and Ravichandran and the dislocation motion slip mechanism. This model effectively describes the mutation behavior of strain-rate sensitivity under fixed strain, particularly evident in an annealed OFHC. The predicted results of the model across a wide range of strain rates (10-4-106 s-1) and temperatures (77-1096 K) demonstrate relative errors generally within ±10% of the experimental values. Furthermore, the model is compared with five other models, including the mechanical threshold stress (MTS), Nemat-Nasser-Li (NNL), Preston-Tonks-Wallace (PTW), Johnson-Cook (JC), and Molinari-Ravichandran (MR) models. A comprehensive illustration of errors reveals that the proposed model outperforms the other five models in describing the plastic deformation behavior of OFHC. The error results offer valuable insights for selecting appropriate models for engineering applications and provide significant contributions to the field.

Molecular dynamics modeling of hydrogen-induced plastic deformation and cracking of ɑ-iron

In this work, molecular dynamics modeling was conducted to study hydrogen (H)-induced plastic deformation and cracking of polycrystal α-Fe. Under cyclic loading, the number of vacancies and the stress intensity increase with H atom concentration and the number of loading cycles. However, the effect of cyclic loading on cracking is not as significant as the increment of H concentration. As the H concentration increases, the dislocation generation and emission are enhanced in the {110}<111> slip system, but are inhibited in other slip systems. There is a critical H atom concentration, below which the plastic deformation of α-Fe is facilitated by H atoms. When the critical H concentration is exceeded, the dislocation emission is inhibited by H atoms at grain boundaries, where the H atoms can pin dislocations, causing piling-up of the dislocations to generate a stress concentration.

Development of Cold‐Rolling Edge‐Drop Control Technology for Electrical Steel: A Review

As an emerging technology in the production of electrical steel, edge‐drop control (EDC) caters to the increasing requirements for the overall shape quality of strips. Herein this review, the development of EDC theory, method, and control system used in the cold‐rolling process is summarized. Also, in this review, research on EDC theory is found to be based on the 3D plastic deformation model of the strip, considering the lateral metal flow. Further, an analytical model and a numerical calculation method are employed to establish an edge‐drop calculation model with high accuracy and speed. Next, taper‐work‐roll shifting (T‐WRS), a conventional EDC technology, is found to have been greatly improved in actual production. However, T‐WRS technology involves coupling problems in terms of edge drop and crown and flatness control. Finally, the closed‐loop EDC is found to depend on the online WRS of multiple stands. Particularly, the genetic law of strip thickness in the continuous rolling process and the edge‐drop regulation characteristics of each stand in the continuous rolling mill are significant aspects; thus, a reasonable roll‐shifting control strategy must be formulated. Based on the reviewed research, the development prospect of EDC is characterized.

Patterns of localized deformation at pre-fracture stage in carbon steel – stainless steel bimetal

The work is devoted to the study of strain localization at macroscale level during parabolic mechanical hardening and pre-fracture under quasi-static loading of a carbon steel – stainless steel bimetal. The problem of estimating the scale of the phenomena that determine plasticity is decisive in the development of any theories of plastic deformation, in particular, dislocation theories. The main difficulty in constructing such theories is the reconciling the dislocation scales, characteristic for most deformation and mechanical hardening mechanisms, with macroscopic parameters of deformation processes. In the framework of the autowave model of localized plastic deformation, this problem can be reduced to the possibility of obtaining parameters from the results of macroscale observations of localized plastic flow development. During the experiments, it was confirmed that in a bimetal at any forming stage, a specific pattern of localization centers distribution is spontaneously generated - a pattern of localized plastic flow. The shape of such patterns is determined by the law of mechanical hardening acting in the material. It is shown that the observed localization patterns can be used as an informative feature in predicting the plasticity margin. In the process of uniaxial tension at the stage of parabolic mechanical hardening of the bimetal, the deformation mode is realized with the formation of several potential fracture centers. It was established that at the pre-fracture stage, during the time evolution of the wave pattern of deformation localization, the zone of active plastic deformation narrows, but the number of centers in it either remains the same with a decrease in the distance between them, or even increases. The result of this process is the formation of a macroscopic neck, and then fracture. At the pre-fracture stage, the collapse point indicates the place of future fracture and signals the need to stop the deformation process in order to avoid the fracture of the bimetallic material. Thus, the well-known manifestation of deformation macroscopic localization – formation of a neck – is preceded by complex phenomena of mutually coordinated motion of localized plasticity centers at the pre-fracture stage.

Incorporating dynamic recrystallization into a crystal plasticity model for high-temperature deformation of Ti-6Al-4V

During hot deformation of (α+β) titanium alloys, the simultaneous action of strain and temperature in the (α+β) regime facilitates dynamic recovery, dynamic recrystallization (DRX), and phase transformations via non-equilibrium paths. DRX is manifested in the form of fine recrystallized α or β grains. In the present study, a two-phase crystal plasticity finite element framework (CP-DRX) has been developed which incorporates DRX kinetics into the crystal plasticity (CP) model to predict the flow characteristics of Ti-6Al-4V alloys during thermo-mechanical processing. The CP slip system parameters, as well as elastic properties from both α and β phases of Ti, are calibrated for different strain rate conditions. An EBSD-informed two-phase microstructure representation has been utilized in the CP-DRX framework to explore the time-dependent evolution of DRX microstructure and crystal orientation for different strain rate conditions. The proposed CP-DRX can capture the evolution of crystal orientation and plastic flow stress–strain response of polycrystalline Ti-6Al-4V during the deformation process. Furthermore, the proposed model is able to capture the softening behavior, observed in average stress–strain response from experiments performed using a Gleeble thermomechanical simulator and predict the recrystallization texture.

Microhardness and Microstructural Evolution of Pure Nickel Processed by High-Pressure Torsion

High-purity Ni was processed by high-pressure torsion (HPT) at room temperature under an imposed pressure of 6.0 GPa and a rotation rate of 1 rpm through 1/4 to 10 turns, and samples were then examined using Electron Back-Scattered Diffraction (EBSD) and microhardness measurements. The results show that the grain size and low-angle grain boundaries (LAGBs) gradually decrease with the growth of HPT revolutions while the microhardness values gradually increase. After 10 turns of HPT processing, ultrafine-grained (UFG) pure Ni with a reasonable microhardness value and microstructure homogeneity can be achieved across the disk, thereby giving great potential for applications in micro-forming. A grain refinement model for severe plastic deformation (SPD) of pure Ni is proposed.