Plastic Strain Distribution Research Articles

Computational and Experimental Studies on the Effect Back Pressure on Twist Extrusion Process

In the current study, aluminium 6063 alloy (AA6063) was successfully gain refined by twist extrusion (TE) technique. TE is a representative severe plastic deformation process to fabricate ultrafine-grained in bulk materials by repetitive passes. In order to investigate the influence of back pressure, a direct extrusion (DE) channel was embedded after the twist zone and the behavior of AA6063 was investigated and compared with and without this channel. Analyzing microstructural evolutions by scanning electron microscope and Vickers microhardness evaluations showed that, adding the DE channel increased the hardness distribution and a more homogenous structure was obtained. Finite element analysis was utilized to study the distribution of the equivalent plastic strain (PEEQ) numerically. According to the obtained results, with applying the TE process, strain increase was observed all over the sample surface, whereas modeling the DE channel after the twist zone caused a better homogeneity in the PEEQ distribution of the transverse cross-section. The PEEQ distribution during TE process can be correlated to the extent of grain refinement and the uniformity of ultrafine grains. This method seems to be very interesting and very promising for the future industrial application.

The residual plastic strain distribution over elastic–viscous–plastic cylindrical shell length upon longitudinal impact on the face

This work is devoted to the study of the distribution of residual plastic strains on outer and inner surface over the length of a cylindrical shell in the process of dynamic deformation generated by a longitudinal impact on its end face. As a mathematical model, the Timoschenko’s model was used to describe the dynamic deformation of elastic thin shells, modified for the case of plastic deformations using the Bingham’s model. As the boundary conditions, we selected a longitudinal impact applied at the end face of the shell with longitudinal strains constant in time. As a method for solving the resulting system of differential equations in partial derivatives of a hyperbolic type, the third–order ray method was implemented. The paper represents options for the numerical calculation of the distribution of residual plastic strains for various thicknesses, as well as the corresponding shell shape after unloading.

Development of a new integrated severe plastic deformation method

ABSTRACT A novel one-pass integrated severe plastic deformation method, entitled extrusion compression angular pressing forward extrusion (ECAP-FE), was designed and used for fabricating a fine-grained as-cast AZ31 Mg alloy. Subsequently, mechanical (room temperature compression, tensile and microhardness) and microstructural properties of the processed sample were investigated in detail. In addition, a finite element simulation of the proposed method was carried out for evaluating the equivalent plastic strain and strain rate distribution. The results showed that the ECAP-FE method is a powerful method for processing the ultrafine-grained as-cast AZ31 Mg alloy in a single pass to achieve a uniform and fine microstructure with enhanced mechanical properties. Therefore, it appears that the proposed method has a great potential to a wide range of industrial applications.

Effect of Transmitting Boundary on Soil – Slope - Foundation Interaction

In recent years, extensive research has been performed when the foundation is placed on the crest of slope. Besides of so many researches less number of researches has been done for foundation is placed on slope considering Soil-Structure Interaction (SSI) effect. Construction on slopes poses more challenges especially under seismic load due to an earthquake in addition to the forces of sliding slope itself. The failure of slope not only affects any structure but also has damaging consequences on the environment in general. Therefore, transmitting boundaries should be adequate to absorb the seismic energy at the boundaries. In this paper, effect of transmitting boundary on soil-slope-foundation interaction (SSFI) is studied. Two cases have analysed for SSFI when foundation is placed at various position on the crest and slope itself. El-Centro earthquake (1940) with three different PGA viz. 0.25g, 0.5g and 1g is applied as input motion for both the cases. It is observed that the foundation placed near the slope is more susceptible to damage. Responses of slope (acceleration and displacement) have also been observed at three different nodal points on slope. Results show that the amplification in soil mass leads to settlement of foundation. Shear stress and equivalent plastic strain distribution for SSFI is discussed for different load conditions. It is found that the slope-foundation system shows the local and global failure. Further Post earthquake peak settlement for foundation is plotted and it shows the true behavior of soil.

Microstructural Changes During Static Recrystallization of Austenitic Stainless Steel 304L: Cellular Automata Simulation

Static recrystallization and microstructural changes in austenitic stainless steel 304L were studied. The rolling experiments at 200 °C were carried out, and then, annealing treatment was made at temperatures ranging between 500 and 830 °C. A model was also developed to simulate the kinetics of non-isothermal recrystallization within the rolled steel. The distribution of plastic strains during rolling was predicted utilizing an elastic–plastic finite element formulation performed in ABAQUS/Explicit, while the predicted results were used to generate the as-rolled microstructure and to estimate the stored energy. Finally, microstructural–thermal model based on cellular automata was developed to evaluate the rate of static recrystallization within the rolled steel. The comparison between experimental and simulations showed a good consistency. The predictions illustrated that inhomogeneous distribution of plastic strain was produced during multi-pass rolling leading to different rates of recrystallization in the center and the surface regions of the rolled plate. The onset temperature of recrystallization was found about 700 °C, and the activation energies for nucleation and growth for recrystallization were determined as 180 kJ/mol and 240 kJ/mol, respectively. It was found that homogenous nucleation mechanism can be operative in recrystallization of multi-pass rolled steel, i.e., for reduction of 40% or higher.

Plastic strain localization induced by microstructural gradient in laser cladding repaired structures

Laser Cladding is an additive manufacturing technology well suited for the repair of complex metallic components. The repair is a two-step process: first, one removes the worn region and then, the initial geometry is reconstructed locally. The aim of this work is to study the influence of the microstructural gradient on the strain localization in repaired structures. More precisely, we perform in-situ SEM tensile tests completed by EBSD observations of the microstructure in the interface neighborhood between the base material and the repaired region. Furthermore, we monitor the evolution of the local plastic strain distribution at the grain level until failure. This is performed by Digital Image Correlation methods and superposition of grains contours and strain maps. The observations of grain size and plasticity are compared with predictions provided by a Hall-Petch model. The study emphasizes the importance of the microstructural gradient in the vicinity of reparation interface, more precisely it reveals that this gradient induce multiaxial strains and that the strain localization phenomenon is governed mainly by a grain size effect.

Exact reconstruction formulas for plastic strain distribution in the surface-treated plate and their applications

Surface-treated bodies are considered under the assumption that the plastic strain distribution is uniform along the surface and changes only with depth. The elastic problem of the surface-treated plate is solved. The obtained solution is used to derive the explicit exact reconstruction formulas for distributions of main tangential components of the plastic strain tensor. It has been proved that the deflection of the surface-treated strip does not depend on the width of the strip. These results are intended for use in destructive testing methods and for numerical prediction of strength. The following initial data were used: (a) the dependence of the deflection on the thickness of the removed material layer obtained by the Davidenkov method, (b) the dependence of the tangential residual stress components on the depth, and (c) the dependence of the surface tangential stress components or elastic strain tangential components on the thickness of the removed material layer obtained by the X-ray diffraction method. The obtained formulas were analyzed and approved for all types of initial data, wherefore two experiments were conducted. A way to incorporate the plastic strain distribution into a model of a machine part of complex geometry to take into account the residual stress field in fatigue, wear, cracking, the and corrosion strength predictions is presented.

Effect of Temperature on Strength and Hardness in Multi-pass Equal Channel Angular Pressing (ECAP) of Aluminum Alloys

In the Equal channel angular pressing (ECAP) process, the sample passes through the channel and the shear stress applied to the sample leads to grain refinement and consequently, the mechanical properties of the sample will be increased. In this article, the effect of implementing the ECAP process at elevated temperature on the strength and hardness of the samples will be studied. Commercially pure (99.0% Al) and AA6063 aluminum round bars are prepared and ECAPed in a die with channel angle of $$\phi$$ = 120° and a corner angle of $$\varphi$$ = 20°. The tensile strength and hardness are compared for 1–8 pass ECAPed samples at 150 °C and room temperature. Also, the ECAP process is modeled in a finite element software to predict the plastic strain distribution in repetitive passes of ECAP. The results show that performing ECAP at elevated temperature decreases the tensile strength by about 5% and 12% in the AA6063 and commercially pure aluminum alloy samples, respectively. Also, at 150 °C, the percent of the increase in the tensile strength decreases in pass #1 but at pass #8 of ECAP, the percent of increase in the tensile strength is equal. So, decrease in the tensile strength in initial passes cannot be compensated by repetition of the ECAP process and at higher passes the strain saturation does not allow to recompense the decrease in the strength at initial passes. The finite element results show that the plastic strain heterogeneity and the value of equivalent plastic strain obtained from FEM are comparable with analytical formulations proposed by other researchers with acceptable error.

Finite-Element Modeling of Magnetic Properties Degradation Due to Plastic Deformation

In this article, the anhysteretic Sablik model is identified from measurements and implemented in a finite-element (FE) code. The model takes into account the effect of the plastic deformation through the dislocation density, and thus, enables to account for the degradation of the magnetic properties. A new model for magnetostriction is proposed and implemented in the Sablik model. Experimental data are used to identify the parameters of both Sablik model and proposed magnetostriction. Furthermore, the mechanical punching process of an electrical steel sheet is simulated in view of evaluating the plastic strain distribution near the punched edge. Based on the Sablik model and the simulated plastic strain, FE simulations are carried out on a steel sheet and a cage induction machine. The effect of the punching process on the distribution of magnetic-flux density and the magnetization current is analyzed.

Modelling and numerical simulation of steel sheet fine blanking process

The steel sheet metal blanking is widely used for the manufacture of mechanical parts for automotive industry. The general concept of blanking seems a simple one but governing parameters are many and have a complex relation-ship, which directly affects the quality of the produced parts. The latter is assessed using three main criterions: the burr amount, the appearance of the cut edge and dimensional accuracy. However, the optimization of these parts depends on full understanding of the shearing process. The paper presents results of the investigations on numerical computations and experimental verification concerning the influence of selected parameter of the cutting process on the stress state of cold-rolled steel sheets being cut.The commercial code Lsdyna® has been chosen to simulate this process. The material testing and the characterization are carried out in order to fit the constitutive model parameters to the experimental data and to establish the sheet metal constitutive law. The identified model is, then, used for numerical simulations which are performed using LsDyna/Explicit software of various fine blanking tests.The aim of this paper is to predict the shear stress and plastic strain distribution in shearing zone during blanking versus punch-die clearance. The assumption of a deformable punch or not has also been considered. The finite elements predictions have been compared with experimental results. The numerical results of the validation simulations were in agreement with the experimental data with an approximate error margin of 31%, since the springback phenomena after unloading and tools warming up during the cutting procedure have not been considered.

Finite Element Study on Chain-Die Forming of an AHSS Channel with Variable Depth

A novel manufacturing technology called chain-die forming was in recent years proposed by Dr. Ding as an alternative to conventional roll forming. Mainly applied in the automotive industry, its prolonged deformation range enables the forming of advanced high strength steels (AHSS) with considerably reduced residual strain, which enables an adequate response to the increasing market requirements of this industry. In this paper, the finite element simulation of chain-die forming an AHSS channel with variable depth is performed. For more accurate predictions, the Bauschinger effect is well considered through the Chaboche hardening model implemented. The residual plastic strain and thickness distributions of the U shaped variable-depth profile are numerically evaluated. The forming limit at a critical zone is analyzed and the predicted magnitude of springback after forming is also calculated. The results portray the forming feasibility and strength of the chain-die forming technology as a valid alternative solution to stamping and roll forming, which are commonly used methods to manufacture such products. In one pass, a complete profile is achieved as opposed to roll forming, with no product defect such as wrinkling or cracking with limited springback development.

Numerical Theoretical Study on Mechanical Properties of New Reinforced Tenon Precast Shear Walls

Precast construction technologies have several advantages in industrialized production, such as quality control and energy conservation. However, the joint interface slippage between the precast components causes detrimental effect on the mechanical properties, such as dowel shear stress on the connecting steel bars, which strictly restricts the development of assembly technology in aseismic structure. In order to eliminate the horizontal slippage along the assemble joint and optimize the mechanical performance of horizontal joint connections, a new reinforced tenon joint precast shear wall is proposed in this paper. Finite element numerical simulations are conducted on three reinforced tenon joint specimens and a reference specimen to understand the mechanical properties of the reinforced tenon and boundary confinement components of shear wall. The load‐displacement curves, the equivalent plastic strain distribution diagram, and the concrete damage distribution diagram are obtained. It is found that the boundary components provide bending strength and the reinforced tenon can reduce the harmful influence of dowel‐action shear stress on longitudinal connecting reinforcements. Therefore, the bending and shearing forces are separated at the joint interface. Based on the numerical simulation results and the calculation theory of normal section bearing capacity, the theoretical calculation bending capacity formula of reinforced tenon precast shear wall is established. The obtained calculation results are in good agreement with the simulation results and can accurately reflect the bending capacity of the jointed interface.

Effect of hardening law and process parameters on finite element simulation of single point incremental forming (SPIF) of 7075 aluminum alloy sheet

In the last two decades, the advances of using computers in sheet metal forming processes have introduced a novel adjustable process known as incremental sheet forming (ISF) as an optimal method for fast prototyping and low numbers of production. Formability and deformation behavior of ISF process are highly affected by the selected process parameters, such as the toolpath, step size, tool diameter, feed rate, and lubrication. The purpose of this work was to study the effect of these process parameters as well as hardening law on single point incremental forming (SPIF) process. For this work, a truncated-cone geometry was considered as a target shape with 7075-O aluminum alloy sheets. The simulations were conducted with different process parameters, i.e., toolpath type, step size, tool size, feed rate, friction coefficient, and wall angle with respect to the tool force and moment, effective plastic strain distribution and thickness of the part. In addition, three types of hardening laws i.e., isotropic extended Voce type hardening law, combined isotropic-kinematic Chaboche type hardening laws with single and double back-stress terms were applied in the finite element simulation of SPIF process. A detailed comparison of these hardening laws' predictions was made with respect to the tool force and moment, effective plastic strain distribution and thickness of the part.

Modeling mechanical properties and plastic strain for hot forming-quenching AA6061 aluminum alloy parts

The hot forming-quenching integrated process (HFQ) has proved to be an effective forming method, achieving good formability and excellent mechanical properties simultaneously for aluminum alloys parts. However, the relationship between the mechanical properties and plastic deformation in the part formed by the HFQ process remains unclear. An analytical model of mechanical properties and plastic strain for an HFQ-formed 6061 aluminum alloys part was established by curve fitting of experimental data. The mechanical properties were evaluated by tensile and micro-hardness tests, and the plastic strain distribution in the HFQ process was analyzed by an automatic strain measuring system. The tensile strength and Vickers hardness showed a linear function for the HFQ-formed 6061 aluminum alloys part, and the relationship between Vickers hardness and plastic strain also presented a linear mathematical function model. The proposed analytical model reveals the mechanical properties of the HFQ-formed 6061 aluminum alloys part quickly and accurately in a non-destructive way. Furthermore, the microstructural characteristics of the HFQ-formed aluminum alloys parts were observed by scanning electron microscopy and transmission electron microscopy to clarify the strengthening mechanism. Disperse and dense Mg2Si precipitates significantly increased with increasing plastic strain during hot forming. The results showed that the improvement in strength was mainly attributable to the increase in precipitates caused by dislocation tangle and lattice distortion after HFQ forming.

An efficient 2D discrete dislocation Dynamics-XFEM coupling framework and its application to polycrystal plasticity

A new efficient framework coupling the two dimensional (2D) discrete dislocation dynamics (DDD) and the extended finite element method (XFEM) is developed for modeling the dynamic evolution of multiple dislocations in crystalline materials with abundant interfaces/surfaces. By a specially introduced stress calculation scheme with cut-off radius and virtual elements, the present algorithm can capture interaction between neighboring dislocations accurately although no time-consuming dislocation-core enrichment is employed. Since it is not sensitive to the FE mesh size and large XFEM time step can be used, its efficiency is evidently improved compared with other DDD frameworks. Due to the merits of XFEM itself, the present DDD-XFEM scheme can treat intractable surface/interface problems conveniently, with no additional image stress calculation as in the DDD-FEM superposition framework and special plastic-strain distribution near the surfaces/interfaces as in the discrete-continuous method (DCM) needed. For these, it can be used to model plastic behaviors of crystals with abundant interfaces/surfaces (i.e. grain/phase boundaries and crack/void surfaces). To show the ability of present DDD-XFEM scheme, it is used to simulate the mechanical responses of polycrystalline aluminum with assumed rigid and penetrable grain boundaries. A three-stage model for dislocation penetrating through grain boundary (DPTGB) is suggested. The results show that the present DDD-XFEM scheme can capture the formation of dislocation pile-ups and thus the Hall-Petch effect successfully. The DPTGB can decrease the flow stress and hardening rate evidently; moreover, it can weaken the grain size effect and may enhance the cyclic stress relaxation of polycrystals greatly.

Prediction of welding-induced distortions in large weld structure through improved equivalent load method based on average plastic strains

Prediction and minimisation of weld-induced distortion at the design stage incites pre and in-process mitigation techniques to improve the weld structure. As a result, it inhibits the need for post welding processes like line heating, straightening etc. In this work, to get more accurate results for distortion prediction, an effort has been made to improve the existing equivalent load method. In this method, the transient behaviour of plastic strain distribution was considered to analyse the large welded structure. Here, the actual transient phenomenon of a weld was considered, i.e. the effect of start, end and middle quasi-steady-state was considered. The separate average loads were applied at the start, middle and end regions of the welding line instead of the same average load throughout the weld length. This proposed method was validated with experimentally obtained results, which showed a perfect agreement and hence, confirmed its efficacy. This method was also validated for published results for different welding joints to assure its effectiveness. At last, a large weld structure was analysed for distortion prediction by using the proposed equivalent load-based technique.

Expanding Cavity Model Combined With Johnson–Cook Constitutive Equation for the Dynamic Indentation Problem

Abstract The indentation formed on a metallic component by the high-velocity impingement of a small object can fracture the component, and this is known as foreign object damage. In this type of dynamic indentation, it is necessary to consider the effects of work hardening, strain rate hardening, and thermal softening in the impinged material. In this study, in order to consider these effects, the expanding cavity model based on a spherical formulation is modified via the Johnson–Cook constitutive equation for the dynamic indentation problem. Additionally, an equation is developed based on energy conservation and the modified expanding cavity model to predict the size of the indentation formed by an impingement of a solid sphere (EPIS). The distributions of equivalent plastic strain, equivalent plastic strain rate, temperature, and equivalent von Mises stress obtained via the expanding cavity model were in good agreement with the data obtained from the finite element analysis (FEA). Furthermore, it was demonstrated that EPIS accurately predicted the indentation size formed on various metallic materials at several impingement velocities in the range of 50–300 m/s. Consequently, EPIS can be effectively applied to an impingement problem of a hard sphere onto a sufficiently thick ductile material within 300 m/s without any help of FEA.

Prediction of Indentation Size Formed by a High-Velocity Impingement of a Solid Sphere Based on an Expanding Cavity Model

The fan blades and turbine blades in a jet engine are seriously damaged by high velocity impingements of various foreign objects. In this study, a prediction method of indentation size formed by a high-velocity impingement of a solid sphere (PMIS) was developed from a theoretical model based on an expanding cavity model and energy conservation before and after impingement. The Johnson-Cook constitutive equation was employed to introduce effects of work hardening, strain rate hardening and thermal softening into the cavity model. As a result, the distribution of equivalent plastic strain, equivalent plastic strain rate, temperature and equivalent von Mises stress estimated using the expanding cavity model was in good agreement with the data obtained from the finite element analysis. In addition, it has been demonstrated that PMIS can accurately predict the radius of indentation formed on various metallic materials subjected to the impingement of a solid sphere with the radii of 0.75, 1.5 and 3 mm at several impact velocities from 50 to 300 m/s.

Plastic Behavior of Ferrite–Pearlite, Ferrite–Bainite and Ferrite–Martensite Steels: Experiments and Micromechanical Modelling

In this work, low carbon low alloy steel specimens were subjected to suitable heat treatment schedules to develop ferrite–pearlite (FP), ferrite–bainite (FB) and ferrite–martensite (FM) microstructures with nearly equal volume fraction of hard second phase or phase mixture. The role of pearlite, bainite and martensite on mechanical properties and flow behaviour were investigated through experiments and finite element simulations considering representative volume elements (RVE) based on real microstructures. For micromechanical simulation, dislocation based model was implemented to formulate the flow behaviour of individual phases. The optimum RVE size was identified for accurate estimation of stress–strain characteristics of all three duplex microstructures. Both experimental and simulation results established that FM structure exhibited superior strength and FP structure demonstrated better elongation while FB structure yielded moderate strength and ductility. The von Mises stress and plastic strain distribution of the individual phase was predicted at different stages of deformation and subsequent statistical analyses indicated that hard phases experienced maximum stress whereas, maximum straining occurred in soft ferrite phase for all three structures. Micromechanical simulation further revealed that strain accumulation occurred at the F–P and F–B interfaces while the same was observed within the martensite particles apart from the F–M interfaces for FM. These observations were further substantiated through the identification of void and crack initiation sites via subsurface examinations of failed tensile specimens.

Strain gradient crystal plasticity model based on generalized non-quadratic defect energy and uncoupled dissipation

The present paper proposes a flexible Gurtin-type strain gradient crystal plasticity (SGCP) model based on generalized non-quadratic defect energy and uncoupled constitutive assumption for dissipative processes. A power-law defect energy, with adjustable order-controlling index n, is proposed to provide a comprehensive investigation into the energetic length scale effects under proportional and non-proportional loading conditions. Results of this investigation reveal quite different effects of the energetic length scale, depending on the value of n and the type of loading. For n ≥ 2, regardless of the loading type, the energetic length scale has only influence on the rate of the classical kinematic hardening, as reported in several SGCP works. However, in the range of n < 2, this parameter leads to unusual nonlinear kinematic hardening effects with inflection points in the macroscopic mechanical response, resulting in an apparent increase of the yield strength under monotonic loading. More complex effects, with additional inflection points, are obtained under non-proportional loading conditions, revealing new loading history memory-like effects of the energetic length scale. Concerning dissipation, to make the dissipative effects more easily controllable, dissipative processes due to plastic strains and their gradients are assumed to be uncoupled. Separate formulations, expressed using different effective plastic strain measures, are proposed to describe such processes. Results obtained using these formulations show the great flexibility of the proposed model in controlling some major dissipative effects, such as elastic gaps. A simple way to remove these gaps under certain non-proportional loading conditions is provided. Application of the proposed uncoupled formulations to simulate the mechanical response of a sheared strip has led to accurate prediction of the plastic strain distributions, which compare very favorably with those predicted using discrete dislocation mechanics.