Equivalent Plastic Strain Rate Research Articles

Heat Mapping and Plastic Strain Radius Modeling of Dual-Tool Friction Stir Welds 6061 Aluminum Alloy Plate Using FEM

This study investigates the effects of Dual-Tool Friction Stir Welding (DT-FSW) parameters on the weld quality of 8 mm thick 6061 aluminum alloy plates, specifically focusing on the elimination or minimization of the "pass-overlap zone" that’s a gap typically observed at the mid-section of the weld cross-section resembling characteristics of the Heat-Affected Zone (HAZ). To address ongoing debates regarding the optimal joint performance concerning this overlap, symmetric increases in the dimensions of both FSW tools were implemented to analyze resultant temperature fields and plastic strain adaptations at the weld interfaces. Simulation visualizations were conducted with tool density variations at intervals of 0.2 mm and 0.4 mm. Results indicate that increasing tool density, thereby reducing the distance between tool surfaces, leads to a decrease in peak temperatures generated during welding. This reduction in temperature correlates with a more uniform distribution of plastic strain rates across all layers of the material—upper, middle, and lower—with the leading edge exhibiting the most significant improvement in strain uniformity. Conversely, during the stabilization phase, a decrease in tool density (S) results in a reduction of the maximum equivalent plastic strain rate. These findings suggest that careful adjustment of tool density in DT-FSW processes can enhance weld quality by promoting more uniform mechanical and thermal properties across the joint.

Theoretical and numerical modeling of the effect of damage and dynamic strain aging on the plastic response of C45 steel alloys

A constitutive model for C45 steel alloys is proposed in this work by integrating the effect of damage and a specific phenomenon, so-called dynamic strain aging. For damage modeling, an energy-based isotropic damage model is implemented within a frame of continuum damage mechanics. The total stress is decomposed into athermal and thermal elements. The former includes the additional term for dynamic strain aging. This term is conceptually inspired by the probabilistic nature of dynamic strain aging, and its derivation is micromechanics-based. Both athermal and thermal components are defined as a function of temperature, equivalent plastic strain, and equivalent plastic strain rate because the occurrence and characteristics of dynamic strain aging are dependent on these factors. A finite element solution for the developed model is addressed additionally to further investigate the characteristics of plastic-damage behaviors and dynamic strain aging. The numerical results are compared to the experiments and theoretical predictions for its validation. The modified model developed in this work has largely reduced the number of fitting parameters compared to the previous model originally developed by the authors in 2019. Nevertheless, predictions from the proposed model still capture the experimental data accurately.

Rate sensitive plasticity-based damage model for concrete under dynamic loading

In this manuscript, a rate-sensitive plasticity-based damage model for concrete subjected to dynamic loads is presented. The developed rate-sensitive damage model incorporates the key experimental evidence related to strain rate and damage rate. With increasing strain rates, the model is able to predict a decrease in the rate of damage evolution due to artificial stiffening effects together with a final higher level of damage. The major contribution of the work is to include the effect of damage rate, strain rate and also to consider all the physical mechanisms of damage. This is achieved by using a power law model to relate the rate of damage to the equivalent plastic strain rate. The damage parameter considers hydrostatic, tension and compression damage. Such a damage definition helps in the prediction of pulverized damage due to a loss in cohesive strength at increased hydrostatic stress, shear-induced compressive damage and tensile microcracking. Strong volumetric deformation of the material that includes hydrostatic and compaction damage is also considered in the model. Because hydrostatic damage accounts for the reduction in stiffness and compaction damage accounts for the increase in stiffness under pure compressive loading. A strain rate-dependent failure surface is considered and with increasing strain rate there is an increase in the size of the failure surface which is capped at an upper limiting value. The incremental effective stress-strain relationship is defined in terms of rate of damage, accumulated damage and viscosity parameters reflecting the inherent inertial, thermal and viscous mechanisms respectively. The stress-strain relationship in the model also accounts for stress reversals that occur due to interference of an incident and reflected wave, by including a Heaviside function. The developed model is implemented in LS-DYNA using vectorized UMAT. Verification, validation and parameterization of the developed model have been made through several numerical analyses.

Flattening aluminum plates with tuning asymmetric rolling parameters

The asymmetric rolling (ASR) process can introduce shear strains inside the plate, resulting in the improvements of microstructures and mechanical properties. Its industrial application for rolling the (mid-)thick plates is impeded by the uncontrollable bending behavior. In this study, the influences of rolling parameters on the bending behavior of the rolled AA 7050 aluminum alloy plates were investigated. It is found that the plate will bend towards the slower roll with larger speed ratios and initial plate thickness as well as lower thickness reduction. A flat plate can be obtained by choosing appropriate rolling parameters. The equivalent plastic strain rate distribution is considered to be critical to the plate bending, the downward bending (towards faster roll) would be associated with an obvious increase of the equivalent plastic strain rate at the top surface of the plate near the end of the deformation zone. Multi-pass asymmetric rolling routes considering bending optimization were proposed and verified through rolling trials. As the speed ratio increased from 1.1 to 1.2, the through-thickness plastic strain became more homogeneous and the total rolling pass numbers decreased by 33 % (from 9 passes to 6 passes).

High strain rate constitutive and fracture characterization of AA7075-T6 sheet under various stress states

The stress state and strain rate dependent fracture behavior of high strength aluminum sheet, AA7075-T6, is characterized experimentally and numerically. Experiments were performed using shear, hole tension, notch tension, and groove tension specimen geometries at strain rates in the regime 10−2 – 500 s−1. The temperature change on the specimen surface was measured utilizing high speed thermal imaging, while strains were acquired using DIC-based optical measurements. Mild positive rate sensitivity was observed in the flow response for equivalent strains up to approximately 20%, while the flow stress decreased at higher (500 s−1) strain rates as the strain levels increased. An increase in temperature was observed within the gauge region of the specimens during elevated strain rate (500 s−1) tests leading to thermal softening. Positive strain rate sensitivity was observed in the measured axial force response for the hole tension and notch tension specimens. The fracture limits of the AA7075-T6 in the shear, hole tension, and notch specimens decreased between strain rates of 0.01 and 10 s−1, then increased at strain rates between 10 and 500 s−1. A strain rate and temperature dependent Hockett–Sherby (HS-SRT) constitutive model was proposed to capture the dependency of the flow stress on the equivalent plastic strain, strain rate, and temperature. The generalized Drucker-Prager (GDP) fracture model was extended to capture the effect of strain rate on fracture initiation. Numerical simulations of the coupon experiments were then performed to extract the local stress and strain states to calibrate the GDP fracture model across the range of strains considered.

Two novel alternative integration schemes for multi-invariants dependent isotropic finite deformation plasticity

Multi-invariants dependent isotropic yield function in terms of first invariant I1 of stress tensor, second J2 and third J3 invariants of deviatoric stress tensor is required for accurate description of plasticity of polycrystalline solids. In the context of multi-invariants dependent multiplicative hyperelasto-plasticity, two integration schemes (IS-1 and IS-2) are formulated and their computational costs are compared for the first time in this paper. IS-1 is fully-implicit in which backward Euler difference approximation of equivalent plastic strain rate is coupled with the exponential approximation of return mapping in principal Kirchhoff stress space and accordingly principal Kirchhoff stresses, equivalent plastic strain and plastic Lagrange multiplier need to be updated iteratively. IS-2 is semi-implicit in which plastic Lagrange multiplier evaluated at current time step and semi-implicit forward Euler difference approximation of equivalent plastic strain rate is coupled with logarithmic approximation of return mapping in Kirchhoff stress space and accordingly only plastic Lagrange multiplier needs to be updated iteratively. For J2 dependent plasticity, computation time involved in numerical simulations for both the integration schemes is nearly the same for same accuracy. For IS-1, computation time involved in simulation for multi-invariants dependent plasticity is significantly greater than that for J2 dependent plasticity due to the computation of the Jacobian matrix in return mapping involving lengthy terms of second order partial derivatives of multi-invariants dependent yield function. For IS-2, computation time involved in simulation for multi-invariants dependent plasticity is nearly the same as that for J2 dependent plasticity. This is due to the fact that the computation of the Jacobian matrix in IS-2 is not required and return mapping involves only first partial derivatives of yield function. Thus, IS-2 is computationally cost effective than IS-1.

Influence of temperature and plastic deformation on AA2024 T3 friction stir welded joint microstructure

This paper deals with analysis and comparison of the equivalent plastic strain and temperature fields in the aluminium alloy 2024 T3 (AA2024 T3) joint, with macro/microstructure appearance and hardness profile. In the alloys hardened by heat treatment, grain size and particle size of the precipitate are functions of equivalent plastic strain, strain rate and temperature. By analysing the equivalent plastic strain fields and temperature fields it is possible, to some extent, to capture the effect of welding parameters and thermo-mechanical conditions on grain structure, and therefore hardness and strength in the welded joint. A coupled thermo-mechanical model is applied to study the material behaviour during the linear welding stage of friction stir welding. The 3-D finite element model has been created in ABAQUS/EXPLICIT software using the Johnson-Cook material law. The values of thermo-mechanical quantities during the welding stage are obtained from the numerical model and shown as distributions across the joint. The obtained values of these quantities are related to the microstructure of the joint zones and hardness distribution, and this relation is discussed.

Investigation on surface integrity in laser-assisted machining of Inconel 718 based on in-situ observation

Inconel 718, a nickel-based superalloy, is widely used in the key parts of aero-engine owing to its high performance at elevated temperatures. Meanwhile, Inconel 718 is a typical difficult-to-cut material which is hard to obtain ideal surface integrity by conventional machining (CM). Laser-assisted machining (LAM) has a good potential to improve the machinability. In order to study the processing mechanism in the LAM of Inconel 718, the in-situ and ex-situ studies were presented in this paper. In the in-situ analysis, LAM and CM experiments were carried out based on in-situ observation and digital image correlation (DIC) technology. The Von Mises strain and equivalent plastic strain rate in the primary shear zone (PSZ) and cutting force were measured. According to the DIC results, under the experimental conditions of this paper, the average Von Mises strain and average equivalent plastic strain rate of PSZ in LAM increase by about 10% and 20% respectively due to the softening of Inconel 718 by laser heating, compared with CM. In-situ analysis shows that Inconel 718 in LAM is more prone to plastic flow, resulting in lower cutting forces. As for the ex-situ characterization, the surface roughness, residual stress and tool wear were measured. The measured results show that LAM can significantly reduce surface roughness and tool wear, and cause compressive residual stress on the machined surface.

Dynamic Strain Aging in AA5182 Alloys at a Wide Range of Temperatures

The dynamic strain aging (DSA) on the mechanical behavior of AA5182 aluminum alloys is investigated through theoretical and numerical methods at a wide range of temperatures. This study proposes a physically-based constitutive model to explain the DSA-induced hardening of AA5182 aluminum alloys. This proposed constitutive model consists of two main components, athermal and thermal components. Between two main components, an athermal component contains an extra hardening caused by the DSA. To describe this hardening, a probability density function is introduced as a function of equivalent plastic strain, equivalent plastic strain rate, and temperature. The results show that this function can precisely describe characteristics of the DSA hardening. Experimental data obtained in the literature are utilized to examine the validity of the proposed model. Lastly, finite element (FE) solution for the proposed model is presented and validated by comparing with experimental data.

Effect of localized defects on mechanical and creep properties for pyramidal lattice truss panel structure by analytical, experimental and finite element methods

The localized defects, including the ruptured truss and debonding joint, have been severely threatening the structural integrity of the pyramidal lattice truss panel structure (PLTPS). In this paper, a series of analytical models, i.e., equivalent elastic modulus, plastic and creep strain rate models, were developed to study the effects of localized defects on the mechanical properties and creep performance of the PLTPS, which have been verified by the experiments and finite element (FE) simulation. Based on the experimental data, the equivalent elastic modulus model was modified when the defect fraction exceeds the threshold value. The complete stress–strain curve was plotted by the proposed analytical models. At elevated temperature, both the analytical model and finite element results indicate that the equivalent creep rate increases exponentially with the increase of the defect fraction. In addition, for the long-term service, the total equivalent strain is the superposition of the steady-state creep strain and the saltatorial strain stimulated by the inconsecutive stress once the truss or joint fails, which is more susceptible to the effective stress comparing with the servicing time. The proposed analytical model which considering the effect of localized defects of the PLTPS provides an efficient criterion to justify whether the structure with certain defects satisfies the engineering requirements.

Experimental and numerical investigations of dynamic strain ageing behaviour in solid solution treated Inconel 718 superalloy

PurposeThe purpose of this paper is to systematically investigate the dynamic strain aging (DSA) effect in solid solution treated IN718 at different temperatures through experiments and simulations to gain an understanding of the inelastic deformation mechanisms.Design/methodology/approachIn the present work, uniaxial tensile tests have been carried out in conjunction with finite element (FE) simulations to investigate the behaviour of the solid solution treated Inconel 718 superalloy at different temperatures and strain rates. Dynamic strain aging (DSA) effects, which manifested during the tests in the form of a negative strain rate sensitivity and stress serrations, are investigated. The most significant DSA effect occurs at 500°C and at a strain rate of 10–4 s-1. In a newly proposed rate-dependent constitutive formulation, the DSA model, proposed by McCormick, Kubin and Estrin, was introduced into slip-assisted solute hardening, and an activation energy-dependent exponential flow rule was adopted.FindingsThe observed negative strain rate sensitivity and stress serrations are well predicted by a 3 D FE. The FE results indicate that the equivalent plastic strain rate distribution in the specimen gauge length is as highly inhomogeneous as in the other materials exhibiting DSA effects such as aluminium and titanium alloy. During inelastic deformation, propagating high strain rate bands can be closely correlated to the stress serrations.Originality/valueFor the DSA effect in solid solution treated IN718, the existing researching mainly focuses on the mechanical properties experiment and microstructure observation. In this study, a constitutive formulation, combined with the DSA model, has been proposed, and the mechanical behaviors, including the DSA effect, have been well predicted by a finite element model.

Finte element modeling of the behavior of polymethyl-methacrylate (PMMA) during high pressure torsion process.

High Pressure Torsion (HPT) is a highly effective super-plastic deformation process for obtaining nano-materials with high performance mechanical properties. In view of its optimization, it is of paramount importance to evaluate the relations between the behavior of the material under the effects of different processing parameters. In this context, this work aims to highlight the plastic strain distribution in the deformed material as a function of the hydrostatic pressure, the torsion angle and the temperature of the material applied during the process. A typical amorphous polymer (Polymethyl-Methacrylate: PMMA) has been tested. Firstly, in order to identify the material parameters of a phenomenological elasto-viscoplastic model compression tests at different temperatures and strain rates have been carried out. Then, the distributions of the effective plastic strain, the equivalent plastic strain rate and the hydrostatic stress were analyzed using finite elements method. Recommendations on process conditions were proclaimed at the end of this work according to the obtained numerical results.

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.

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.

Anisotropic plasticity characterization of 6000- and 7000-series aluminum sheet alloys at various strain rates

This study aims to characterize the high strain rate constitutive behavior and the anisotropic plasticity of three high strength aluminum sheet alloys, AA6013-T6, AA7075-T6 and a developmental AA7xxx-T76 alloy. A comprehensive series of mechanical characterization tests were performed under uniaxial tension, simple shear and through-thickness compression (representing equal-biaxial tension) at room temperature and various strain rates ranging from 10−3 to 103 s−1. It was observed that all three alloys exhibited appreciable plastic anisotropy in terms of the measured r-values along various sheet orientations, although they exhibited minimal anisotropy in the stress response. For all three alloys, the flow stress slightly increases with increasing strain rate, which indicates mild positive strain rate sensitivity. However, the flow stress ratios and r-values do not show any explicit relation with respect to strain rate suggesting a negligible effect of strain rate on in-plane plastic anisotropy. Measurement of the constitutive response to large strains (beyond onset of diffuse necking) was achieved using shear specimens that are not subject to onset of necking. To model the flow stress dependence on equivalent plastic strain and strain rate, an extended Hockett–Sherby constitutive model is proposed and shown to fit accurately the experimental data over the studied range of strain and strain rates. The yield behavior of the sheet alloys was predicted using the Barlat YLD2000-2D plane stress yield function (Barlat et al., 2003) assuming both associative and non-associative (NA) flow rules, as well as for general stress states employing two 3D anisotropic models, Barlat YLD2004 (Aretz and Barlat, 2004) and modified–Yoshida (Lou and Yoon, 2018). An associative flow rule was assumed for both of the higher order 3D yield functions considered herein. The measured flow stress ratios and r-values from the uniaxial tension and equal-biaxial tension experiments, along with the stress ratios from the shear tests, were used to determine the coefficients of the yield functions. The calibrated yield functions exhibited good agreement with the experimental data for most loading conditions considered. The higher order Barlat YLD2004 and modified–Yoshida yield functions provided the better predictive accuracy. The non-associative Barlat YLD2000 yield function also performed reasonably well, while the associative Barlat YLD2000 yield function had the lowest accuracy. The constitutive models were implemented into the FE simulation, in order to evaluate the accuracy of the model parameters calibrated in this work.

Size scaling of hypervelocity-impact ejecta mass and momentum enhancement: Experiments and a nonlocal-shear-band-motivated strain-rate-dependent failure model

Impact tests were performed from 4 to 5.77 km/s of 3.0-cm-diameter aluminum spheres impacting 2024-T351 aluminum targets. This data was compared to previously published data for smaller scale impactors (0.1588 cm to 1.27 cm). It was seen that there are no size-scaling effects for the crater depth. The slight size-scaling effect in the crater diameter directly correlated with the nonlinear size-scaling effect in the ejecta mass. There is a qualitative change in the ejecta mass somewhere in the vicinity of 1.27-cm-diameter impactors, in that impactors with diameters less than this have ejecta mass showing a strong diameter dependence while for impactors larger than this diameter there is little size dependence and the ejecta mass scales only with impact velocity squared. A strain-rate-dependent failure model is developed based on a mechanical model of shear-band slip over a characteristic finite length. The underlying mechanical model is nonlocal, but, through certain assumptions, leads to a failure strain expression that depends on the equivalent plastic strain rate to the 2/3rds power. This failure model was implemented in the hydrocode CTH and showed excellent agreement with experimental ejecta mass data. It can explain the origin of the size scale dependence in the ejecta mass as well as the observed saturation. The saturation in the ejecta mass is due to the static failure properties of the material. The new data also shows that the 0.45 power dependence on the projectile diameter for the momentum enhancement β continues up through the 3.0-cm-diameter sphere impactors. This size scaling behavior of the momentum enhancement is surprising in that there is not a change in the momentum enhancement scaling behavior even though there is a qualitative and quantitative change in the ejecta mass scaling behavior. The new damage model does not predict the experimentally-observed momentum enhancement size-scaling behavior, even though it does predict the ejecta mass behavior.

Full-stage prediction of discontinuous dynamic recrystallization of a titanium alloy through a sub-mesh internal state variables method

A sub-mesh internal state variables (ISVs) based cellular automata-crystal plasticity finite element model (CACPFEM) is proposed for the full-stage prediction of discontinuous dynamic recrystallization (DDRX) of a titanium alloy during deformation. The idea of the sub-mesh scale is proposed to break through the mesh size limit in a finite element analysis by considering the typical physical characteristics of a new DDRX nucleus and the computational availability. Physical characteristics of a new DDRX nucleus including extremely small size, new grain orientation, low level dislocation density and strain-free deformation state, can be fully considered in the sub-mesh scale. The subsequent growth of the nucleus during deformation can be well described by introducing an important ISV, the volume fraction of the DDRX grain in the sub-mesh scale. The microstructure evolution of DDRX will be calculated by the previously developed CACPFEM when the DDRX grain reaches the mesh size. By doing this, the full stage of the DDRX evolution during hot deformation can be well predicted. With a titanium alloy (Ti-6Al-2Zr-1Mo-1V) being applied, it can be found that the size of the nucleus plays an important role in slip resistance at early stage. The grain growth velocity of the DDRX grain in sub-mesh scale first increases and then decreases with the dislocation density increasing from a low level. The stress of the DDRX grain increases from zero to a high level that is relevant to its grain orientation. The equivalent plastic strain rate of DDRX during early stage keeps an ‘S-type’ increasing trend during deformation.

Analytical expression of mechanical fields for Gurson type porous models

In this work, analytical expressions of mechanical fields are provided for strain hardening thermo-viscoplastic porous materials containing spheroidal voids subjected to homogeneous strain rate loading. Explicit relationships are provided for the macroscopic stress, the plastic multiplier, the effective equivalent plastic strain rate in the matrix when the constitutive behavior of the porous medium is of Gurson type model. Axisymmetric and non-axisymmetric loadings are considered. The behavior of the porous material is governed by the model developed by Gologanu et al. (Gologanu, M., Leblond, J.-B., Perrin, G., Devaux, J., 1997, CISM Courses and lectures,377, 61–130). The particular case of the Gurson model (Gurson, A. L., 1977, ASME Journal of Engineering Materials and Technology 99, 2–15) is also investigated since it is widely adopted in the literature for analytical modeling or finite elements calculations. Various matrix behaviors are considered. The matrix is first considered as rigid perfectly plastic. Interestingly, the approach is also valid for nonlinear viscoplastic material with work hardening and temperature dependency. Extensions are also considered when the matrix material is orthotropic. Finally, the numerical implementation is discussed and it is shown that by adopting the proposed approach, the efficiency of the radial return algorithm can be improved.

Biaxial deformation and martensitic transformation behaviour observation on type 304 stainless sheet by biaxial bulge test

Metallurgical characteristic phenomenon on type 304 stainless steel is the deformation induced martensitic transformation. To clarify the stress-strain curves and martensitic transformation behaviour, biaxial bulge test apparatus was developed. It enables to control the stress ratio of axial and circumference directions and equivalent plastic strain rate simultaneously. Biaxial bulge tests for uniaxial, equi-biaxial and plane strain cases were conducted at the constant temperature 20°C. The obtained martensite volume fraction vs. equivalent stress curves for all the tests were well agreed, so that it can be said that the martensite volume fraction was predictable by the maximum austenie stress.