Isotropic Plasticity Research Articles

Formulation and implementation of an isotropic plasticity model enriched with shift stress and fractional flow rule

Formulation and implementation of an isotropic plasticity model enriched with shift stress and fractional flow rule

On anisotropic local bifurcation based on hypoplastic model

The incipience of shear band in homogeneous granular materials is well captured by the bifurcation analysis. Most bifurcation analyses are based on isotropic plastic constitutive models. In this paper, a hypoplastic constitutive model is presented by considering a fabric tensor for inherent anisotropy. Based on this model, we carry out bifurcation analysis for the plane strain case, and then extend the analysis to consider general three-dimensional stress state. The theoretical results are compared with experiments on sand conducted using a plane strain device and a true triaxial device. It's indicated the salient features of stress-strain behaviour and shear band formation are well captured by our analyses.

Application of single surface isotropic damage plasticity model in nonlinear dynamic analysis of the Koyna Dam

PurposeIn the present study, the application of a recent damage plasticity model is presented for nonlinear dynamic analysis of the Koyna gravity dam. This is a single surface isotropic damage plasticity concrete model, which is based on the decomposition of stresses and was proposed in a previous study. The theoretical aspects of the model are initially reviewed, and a few preliminary verification examples are illustrated. Thereafter, the HHT-α (i.e. Hilber–Hughes–Taylor) algorithm is presented for nonlinear dynamic analysis of concrete gravity dams.Design/methodology/approachBased on the prepared tools, nonlinear behavior of the Koyna Dam is studied by applying the invoked damage plasticity model. For this purpose, three cases are considered for the present study. Case A, which is based on the linear model, is mainly used for comparative purposes. The other two cases (B and C) correspond to the nonlinear (i.e. damage plasticity) model. The basic data for these two cases are similar. However, the employed damping algorithms are different and correspond to constant and variable damping algorithms, respectively. This means that the damping matrix is either kept constant or updated for all iterations of different time increments through the course of analysis.FindingsThe time histories of horizontal displacement at the dam crest were initially compared for the three cases: the linear Case A, and two nonlinear Cases B and C. It was observed that nonlinear cases’ responses begin to deviate from the corresponding linear case after the time of about 4.3 s. However, the amount of change for Case C (i.e. variable damping) was much greater than for Case B (i.e. constant damping). This was manifested initially in the peaks of response. It was also noticed that the period of response changed slightly for Case B in comparison with the linear Case A, while this change was significant for Case C. The obtained tensile and compressive damages were subsequently compared for the two nonlinear cases. For constant damping Case B, it was noticed that tensile damage occurred in the D/S face kink and on the U/S face slightly at a lower elevation. Moreover, it had a scattered nature. However, in variable damping Case C, it was noticed that tensile damage was much more localized and acted similar to a discrete crack. Of course, both cases also show tensile damages at the dam’s heel. In regard to compressive damages, it is observed that low values are occurring for both nonlinear cases as expected.Originality/valueThe application of a recent single surface isotropic damage plasticity concrete model is presented for nonlinear dynamic analysis of the Koyna gravity dam. The nonlinear response of the dam is investigated for two different damping algorithms. Moreover, the influence of variable characteristic length is also investigated in the latter part of this study.

Johnson–Cook yield functions for cyclotetramethylene-tetranitramine (HMX) and cyclotrimethylene-trinitramine (RDX) derived from single crystal plasticity models

High-fidelity constitutive models are critical for accurate meso-scale continuum modeling and prediction of shock initiation of crystalline energetic materials (EMs). While empirically calibrated or atomistic-guided anisotropic elastoplastic models of EM such as cyclotetramethylene-tetranitramine (HMX) and cyclotrimethylene-trinitramine (RDX) capture important micromechanical phenomena (such as dislocation evolution, slip-resistance, and anisotropic elasticity), the computational cost of using anisotropic single-crystal plasticity models can become prohibitive for meso-scale computations of void-collapse and hotspot formation in microstructures. Thermo-mechanically representative, isotropic, pressure, temperature, and rate-dependent material constitutive models are practical alternatives for meso-scale simulations of the shock response of microstructures. To this end, this work constructs physically consistent isotropic plasticity from anisotropic single-crystal plasticity models for HMX and RDX. State-of-the-art crystal plasticity models for HMX and RDX are used to compute the stress states in single crystals oriented in three different directions relative to shocks generated by impact at velocities ranging from 100 to 1000 m/s. Post-shock von Mises stress fields for the three orientations are then used to calibrate the strain-rate hardening coefficient and the reference strain rate for a rate-dependent Johnson–Cook (JC) yield surface model. We compare the pressures and the post-shock von Mises stresses between the JC and the anisotropic models to show that the isotropic computations closely approximate the averaged deformation response of the three different crystal orientations. We then model the interaction of a shock generated by a 500 m/s impact with a 0.5 μm void and show that the pressures and the deviatoric stresses obtained using the isotropic model closely match those computed from anisotropic models for both HMX and RDX. The resulting isotropic J2 plastic flow model for HMX and RDX can be employed to perform meso-scale simulations for energy localization due to shear bands and void collapse in the two materials.

Elastic-Gap Free Formulation in Strain Gradient Plasticity Theory

AbstractThis article presents an elastic-gap free isotropic higher-order strain gradient plasticity theory that effectively captures dissipation associated to plastic strain gradients. Unlike conventional methods that divide the higher-order stress, this theory focuses on dividing the plastic strain gradient into energetic and dissipative components. The moment stress that arises from minimizing a dissipating potential demonstrates a nonlinear evolution over time, resembling the Armstrong–Frederick nonlinear kinematic hardening rule in classical plasticity. The thermodynamically consistent framework establishes additional dissipation in the dissipation inequality. The energetic moment stress saturates as the effective plastic strain increases during plastic flow. In contrast to the Gurtin-type nonincremental model, the proposed model smoothly captures the apparent strengthening at saturation without causing a stress jump. A passivated shear layer is analytically assessed to demonstrate that the proposed theory exhibits the same amount of dissipation as the existing Gurtin-type model when they show similar shear responses at saturation. It is also shown that the plastic flow remains continuous under nonproportional loading conditions using an intermediately passivated shear layer problem. Finally, the proposed theory is validated against a recent experiment involving combined bending torsion of an L-shaped beam using a 3D finite element solution. Overall, the proposed model provides an alternative approach to evaluating the size effect within the nonincremental isotropic strain gradient plasticity theory without introducing any stress jump.

A novel geometric predictive algorithm for assessing compressive elastic modulus in MEX additive processes, based on part nonlinearities and layers stiffness, validated with PETG and PLA materials

MEX (Material Extrusion) is an intrusive technological process that inherently induces alterations in the elastic and mechanical parameters of plastic materials. Manufacturers provide initial mechanical parameters for plastic filaments, which undergo modifications during MEX manufacturing, influenced by intrinsic manufacturing factors such as temperature and pressure changes, as well as geometric and technological parameters of the 3D additive process. These factors, compounded by the inherent geometric nonlinearities in plastic components, directly impact the post-manufacture mechanical and elastic properties of the material. Presently, material characterization in MEX manufacturing relies on manual experimental testing, necessitating new tests for any variation in manufacturing parameters. In this scenario of mechanical uncertainty, rigorously validating component behavior involves costly experimental trials. Intending to solve the problems of MEX components manufacturing, the paper presents an innovative methodology based on the use of a new predictive algorithm created by the researchers capable of obtaining the elastic modulus of a plastic material manufactured with MEX and its mechanical behavior in the elastic zone under compressive loads. The predictive algorithm only needs as input the compressive elastic modulus of the isotropic plastic material filament and the manufacturing parameters of the MEX process. The smart developed algorithm calculates the stiffness of each layer considering the number of holes in the projected area. The innovative predictive algorithm has been experimentally and numerically validated using PETG (Polyethylene Terephthalate Glycol) material and PLA (Polylactic Acid) on test specimens and on a case study of variable topology. The results show deviations from [0.2%–4.3%] for PETG and [0.4%] for PLA concerning the experimental tests and [1.1%–13.5%], to the numerical analyses. In this line, the presented algorithm greatly improves the results obtained by the simulation software since this software currently can not consider the geometric and technological parameters associated with the 3D manufacturing process of the component. The predictive algorithm is valid for each print pattern and manufacturing direction. The new algorithm improves the existing state of the art significantly since this algorithm extends its utility to most plastic polymer materials suitable for MEX 3D printing, provided that the mechanical and elastic properties of the filament are known. Its versatility extends to complex component geometries subjected to uniaxial compression loads, eliminating the need for mechanical analysis software or expensive experimental validations.

A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel

In this study, we employ a physics-based crystal plasticity finite element method (CPFEM) approach to study the microstructural response of DP600 steel to various loading types. With the pursued approach, it is possible link microstructural changes in the dual phase (DP) steel to its macroscopic response in a convenient and efficient manner. Microstructural data were acquired first from experimental work via the electron backscattered diffraction (EBSD) method. DP crystallographic features were then fed to a numerical hybrid calculation subroutine combining a comprehensive physics-based crystal plasticity scheme for ferrite along with an isotropic plasticity scheme for martensite defined on a single-layer representative volume element (RVE). The developed single-layer 3D mode, while allowing for high computational efficiency, can capture the stress/strain distribution, revealing the microscopic features of the deformation process including the physical evolution of the dislocation density, retexturing, and morphology. The single-layer RVE physics-based method employed herein establishes the strong correlation between morphology, dislocation density and deformation response of the material under various loading types. Specifically, findings reveal that the tendency of the ferrite phase neighboring the martensite regions in the DP steel to retexture is much more profound than pure ferrite when subjected to the same loading conditions, pointing out to the steep strain gradients in the former component. Martensite phase facilitates considerable heterogeneity in the stress and strain distribution, increases the misorientation polarization as well as leading to local strain hardening in the neighboring ferrite volume that stem from profound increase in spatial dislocation density. Stress-strain curves under various loading schemes are simulated and discussed in the light of the experimental findings in literature, revealing the dependence of the microstructural evolution on the loading type.

A coupled phase‐field method (PFM) and thermo‐hydro‐mechanics (THM) based framework for analyzing saturated ice‐rich porous materials

AbstractThis study proposes a novel framework for ice‐rich saturated porous media using the phase‐field method (PFM) coupled with a thermo‐hydro‐mechanical (THM) formulation. By incorporating the PFM and THM approaches based on the continuum theory, we focus on the mechanical responses of fully saturated porous media under freeze‐thaw conditions. The phase transition between liquid water and crystalline ice can be explicitly expressed as captured by evaluating the internal energy and implementing thermal, mechanical, and hydraulic couplings at a diffused interface using PFM. Accurately modeling the coupled mechanical behaviors of ice and soil presents significant challenges. Therefore, in previous numerical frameworks, ad hoc constitutive models were adopted to phenomenologically estimate the overall behavior of frozen soil. To address this, we employ a method that differentiates between the kinematics of the solid and ice constituents, enabling our framework to accommodate distinct constitutive models for each constituent. Within this framework, we naturally introduce anisotropy of frozen soil as it undergoes the freezing process by integrating a transversely isotropic plastic constitutive model for ice. We illustrate the capabilities of our proposed approach through numerical examples, demonstrating its effectiveness in modeling the phase transition process and revealing the overall anisotropic responses of frozen soil.

Phase Field Fracture Modelling of Crack Initiation and Propagation in Dual-Phase Microstructures

Dual-phase (DP) steel's spread in the industry has been fueled by its highly desirable qualities, which include a unique balance of strength and ductility, making it a valuable material for applications ranging from automotive manufacturing to construction. Despite the continued progress in the research of DP steels, the complex failure mechanisms at the microscale, resulting from the coexistence of brittle martensite phases within the ductile ferrite phase, remain an area of ongoing exploration. This study aims to investigate the micro structural evolution, as well as crack initiation and propagation, in DP steels at the microscale. In this context, to accurately capture the microstructural evolution of DP steels, a rate-dependent crystal plasticity formulation is utilized for the ferrite phase alongside a phenomenological isotropic J2 plasticity model for the martensite phase. A novel ductile phase-field fracture framework has been implemented to predict crack initiation and propagation, integrating both crystal plasticity and J2 plasticity constitutive models with the phase field fracture model. Generic 3D polycrystalline Representative Volume Elements (RVEs) are created and simulated to analyze the trends influencing the failure behavior of DP steels. The numerical study includes examples with two different martensite volume fractions (15% and 37%), each characterized by varying random crystallographic orientation sets and morphologies. The obtained results suggest that despite the similarity in stress concentration regions within two different random orientation sets in a simulation with fixed volume fraction and morphology, the resulting crack paths exhibit significant differences. Additionally, it is inferred that damage appears to accumulate at the junction points of the martensite islands. Moreover, an increase in the martensite volume fraction is found to diminish the influence of crystallographic orientation on the resultant crack path. Therefore, given the aforementioned findings, it is essential to analyze the microstructural evolution, as well as crack initiation and propagation in DP steels, utilizing appropriate material and fracture modeling frameworks at the microscale.

A simple spectral representation of a second-order symmetric tensor and its variation

The spectral decomposition of a second-order, symmetric tensor is widely adopted in many fields of Computational Mechanics. As an example, in elasto-plasticity under large strain and rotations, given the Cauchy deformation tensor, it is a fundamental step to compute the logarithmic strain tensor.Recently, this approach has also been adopted in small-strain isotropic plasticity to reconstruct the stress tensor as a function of its eigenvalues, allowing the formulation of predictor–corrector return algorithms in the invariants space. These algorithms not only reduce the number of unknowns at the constitutive level, but also allow the correct handling of stress states in which the plastic normals are undefined, thus ensuring a better convergence with respect to the standard approach.While the eigenvalues of a symmetric, second-order tensor can be simply computed as a function of the tensor invariants, the computation of its eigenbasis can be more difficult, especially when two or more eigenvalues are coincident. Moreover, when a Newton–Raphson algorithm is adopted to solve nonlinear problems in Computational Mechanics, also the tensorial derivatives of the eigenbasis, whose computation is still more complicated, are required to assemble the tangent matrix.A simple and comprehensive method is presented, which can be adopted to compute a closed form representation of a second-order tensor, as well as their derivatives with respect to the tensor itself, allowing a simpler and numerically accurate implementation of spectral decomposition of a tensor in Computational Mechanics applications.

COMPARISON BETWEEN JOHNSON COOK’S PLASTICITY WITH DAMAGE MODEL AND ISOTROPIC HARDENING PLASTICITY WITH DUCTILE DAMAGE MODEL ON ALUMINIUM ALLOY SHEET 2024 T3 TENSILE TEST IN CORRELATING THE FINITE ELEMENT METHOD (FEM) TO THE EXPERIMENT TEST RESULT

Sometimes students and/or researchers are faced with a limited sample and data issue and need to choose carefully which approaches to be used, especially in performing analysis with numerical analysis. As there are a lot of numerical analysis approaches that are having similar purposes and the approaches can be used depending on the analysis cases and objectives. For example, Johnson Cook’s plasticity model and isotropic plasticity hardening model are the common approaches available and used in ABAQUS software to determine the metal and metal alloy plasticity or inelastic mechanical properties. Therefore, in this paper, two approaches – Johnson Cook’s plasticity with damage model and isotropic plasticity hardening with ductile damage model which is used to define the metal and metal alloy mechanical properties and performance are studied using ABAQUS Computer Aided Engineering (CAE) software and compared accordingly. In this study, the experimental result of the tensile test was used to determine the mechanical properties of the Aluminium alloy 2024 T3 sheet with 0.29mm thickness. Then the experiment test data are used to correlate the finite element method (FEM) model and the experimental test result by using Johnson Cook’s plasticity hardening with damage model approach and the isotropic hardening plasticity with ductile damage model approach. Based on the comparison with the experiment failure sample mode, both FEM model failure mode is closely identical to the experiment failure sample. From the mechanical properties comparison, Johnson Cook’s model shows a bigger deviation compared to the isotropic plasticity with ductile damage model in comparison to the experiment value. From this paper, it can be concluded that the ductile damage model is more appropriate to be used when the sample and data are limited.

Identification of creep parameters from multi‐step relaxation tests on miniaturised specimen

AbstractThe small punch test (SPT) is a miniaturised method for thermo‐mechanical materials testing. The combination of simple specimen geometry and low required specimen volume is ideal for minimally invasive characterisation and monitoring of the current material condition in technological systems, including nuclear plants.The aim of the present study is to identify creep material properties of the chromium steel P91 (X10CrMoVNb9‐1) via small punch testing. It is examined to which extent a single relaxation test is suitable to replace several creep tests at different force levels. The inverse parameter identification method utilises a non‐linear optimisation approach in order to match the results of simulation and experiment. The simulation is performed using finite element analysis (FEA) and the considered material law aims to represent the high‐temperature behaviour of steels. To this end, a modified Liu–Murakami model is specifically used along with linear elasticity and non‐linear isotropic plasticity. We propose a strategy, that can be used to separately identify the Norton‐parameters from multi‐step relaxation tests performed on one specimen. Thereby, the applied strain (displacement, if utilising SPT) is kept constant after initial loading, which enables stress relaxation within the specimen. In case of the SPT, this behaviour yields a decreasing reaction force which approximately approaches a constant value. During the repeated loading phases, specimen failure may occur, due to further plastification of the specimen. Loading and relaxation cycles are repeated until specimen failure.The identified parameters are validated via small punch creep experiments at different force levels. It will be shown that good agreement is observed when comparing the sets of identified parameters.

Constitutive modeling of orthotropic nonlinear mechanical behavior of hardened 3D printed concrete

3D printing of concrete is a promising construction technology, offering the potential to build geometrically complex structures without the use of cost-intensive formwork. The layer-wise deposit of filaments during the 3D printing process results in an intrinsic orthotropic mechanical behavior in the hardened state. Beyond that, the material behavior of 3D printed concrete (3DPC) is governed by a highly nonlinear behavior, characterized by irreversible deformations, strain hardening, strain softening and a degradation of the material stiffness. In this contribution, a new constitutive model for describing the orthotropic and highly nonlinear material behavior of 3DPC will be presented. It is formulated by the extension of a well-established isotropic damage plasticity model for concrete to orthotropic material behavior by linear mapping of the stress tensor into a fictitious isotropic configuration. The performance of the new model will be evaluated by finite element simulations of three-point bending tests of 3DPC samples, performed for different orientations of the loading direction relative to the printing direction and comparison with experimental results. In addition, the applicability of the model to replicate the mechanical behavior of 3DPC, manufactured by the alternative 3D printing process of binder jetting of cementitious powders, will be demonstrated by 3D finite element simulations of an arch structure with varying orientations of the loading direction relative to the layering. Overall, the proposed model provides a computationally efficient modeling approach for large-scale finite element simulations of 3DPC structures, being a promising alternative to complex and computationally expensive finite element models considering distinct interfacial planes.

“Implicit” vs “Explicit” gradient plasticity models: Do they always remove mesh dependence in softening materials?

Finite element quasi-static solutions of rate-independent softening plasticity models are known to depend on the mesh size (i.e., are unreliable) due to loss of ellipticity of the governing partial differential equations, which allows for the development of non-smooth solutions, such as shear bands of zero thickness. A “regularization” scheme that has been proposed is the use of “non-local” (Bažant et al., 1984) or “strain-gradient” theories (Aifantis, 1984). We examine in detail the families of “explicit” and “implicit” gradient plasticity models and show that use of such theories does not always eliminate mesh dependence of finite element solutions in rate-independent softening materials. Depending on the value of the non-local hardening modulus, the mathematical problem may still lose ellipticity and allow for the development of solutions with discontinuous spatial velocity gradients, which are responsible for the mesh dependence of numerical solutions. As an example, a rate-independent “implicit” gradient version of the von Mises yield condition with the associated flow rule is implemented in ABAQUS, and the formation of shear bands in plane strain tension is analyzed numerically; it is shown that, unless the material parameters in the non-local model are such that ellipticity is retained, the finite element solutions depend on the mesh size. The example of isotropic porous metal plasticity with a hardening matrix material is considered (e.g., the Gurson (1977) model); it is shown that regularization is achieved if an implicit non-local model is used, in which the local porosity f is replaced by its non-local (neighborhood average) counterpart f̄ in the yield condition. In all non-local plasticity models, dimensional consistency requires the introduction of one or more “material lengths” ℓi, which multiply the additional terms with the higher-order spatial derivatives introduced by the non-local models. The boundary layers associated with the singular perturbation problem when the material lengths ℓi→0 are examined. A linear stability analysis is carried out to study the stability of homogeneous problems under small harmonic perturbations; it is shown that the stability range of the non-local models is always larger than that of the corresponding local models.

Particle-matrix debonding with Strength-Differential effects

In this work the onset of failure caused by particle-matrix debonding in aluminum alloy 2090-T3 and magnesium alloy AZ31 under either overall uniaxial plane strain tension or compression load is studied numerically using a unit cell model. Especially for magnesium AZ31, experiments show a significant difference in the tensile-compressive yield stresses, the so-called Strength-Differential-effect (SD-effect). This SD-effect cannot be captured by any isotropic yield function and only by recent anisotropic yield functions. To accurately model AA 2090-T3 and magnesium AZ31 the general yield function by Yoon et al. (2014) is adopted in addition to the isotropic von Mises plasticity yield function and the anisotropic yield function of Hill (1948). The numerically predicted strain at which void nucleation initiates is generally found to be larger for magnesium AZ31 than for AA 2090-T3. However, depending on the orientation of the principal axes of plastic anisotropy this void nucleation strain varies significantly. This holds true for both materials, but the void nucleation strain of AA 2090-T3 in compression is numerically predicted to be practically identical whether or not isotropic or anisotropic plasticity is considered. In tension the void nucleation strain of AA 2090-T3 based on anisotropic plasticity is found to be more than double the strain obtained by von Mises plasticity. The numerically predicted void nucleation strain of magnesium AZ31 is significantly affected by the yield function adopted. For the von Mises yield function the value of the void nucleation strain is in between the predictions based on the anisotropic yield functions. For both tension and compression, the yield function of Yoon et al. (2014) results in the largest void nucleation strain, whereas the yield function of Hill results in the smallest strain value. This holds true for all five orientations of the principal axes of plastic anisotropy investigated.

Dynamic Phase Transition Leading to Extraordinary Plastic Deformability of Thermoelectric SnSe2 Single Crystal

AbstractPlastic/ductile inorganic van der Waals (vdW) thermoelectric semiconductors offer transformative advantages for high‐performance flexible thermoelectric devices, which can displace the self‐charge system of wearable electronics. However, the chemical origin of their plasticity remains unclear. Here, it is reported that the exceptionally large plastic strain of the bulk SnSe2 crystal results from its polytype conversion under an external force. The SnSe2 single crystal consists of a large‐period polytype with 18R low‐symmetry structure rather than the trigonal and hexagonal‐phase that are frequently observed in the polycrystalline specimen. In situ applied pressure to the specimen drives a phase transition from low to high‐symmetry, that is, from 18R to 4H, and finally to 2H‐SnSe2. First principle calculations corroborate that the dynamic phase transition is a pressure‐activated process and only 15 MPa pressure erases their energy gaps, consistent with experimentally measured strain–stress curves. This dynamic phase transition results in superior and near isotropic plasticity along the direction parallel and perpendicular to the cleavage plane.

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.

On the Springback and Load in Three-Point Air Bending of the AW-2024 Aluminium Alloy Sheet with AW-1050A Aluminium Cladding.

This article presents the results of an analysis of the bending load characteristics and the springback phenomenon occurring during three-point bending of 1.0 and 2.0 mm thick AW-2024 aluminium alloy sheets with rolled AW-1050A cladding. A new proprietary equation was proposed for determining the bending angle as a function of deflection, which takes into account the influence of the tool radius and the sheet thickness. The experimentally determined springback and bending load characteristics were compared with the results of numerical modelling using different models: Model I, a 2D model for a plane deformation state, disregarding the material properties of the clad layers; Model II, a 2D model for a plane deformation state, taking into account the material properties of the cladding layers; Model III, a 3D shell model with the Huber-von Mises isotropic plasticity condition; Model IV, a 3D shell model with the Hill anisotropic plasticity condition; and Model V, a 3D shell model with the Barlat anisotropic plasticity condition. The effectiveness of these five tested FEM models in predicting the bending load and springback characteristics was demonstrated. Model II was the most effective in predicting bending load, while Model III was the most effective in predicting the amount of springback after bending.

Multiscale nanoindentation modelling of concentrated solid solutions: A continuum plasticity model

Recently developed single-phase concentrated solid-solution alloys (CSAs) contain multiple elemental species in high concentrations with different elements randomly arranged on a crystalline lattice. These chemically disordered materials present excellent physical properties, including high-temperature thermal stability and hardness, with promising applications to industries at extreme operating environments. The aim of this paper is to present a continuum plasticity model accounting for the first time for the behaviour of a equiatomic five-element CSA, that forms a face-centred cubic lattice. The inherent disorder associated with the lattice distortions caused by an almost equiatomic distribution of atoms, is captured by a single parameter α that quantifies the relative importance of an isotropic plastic contribution to the model. This results in multiple plasticity mechanisms that go beyond crystallographic symmetry-based ones, common in the case of conventional single element metals. We perform molecular dynamics simulations of equiatomic CSAs: NiFe, NiFeCr, NiFeCrCo, and Cantor alloys to validate the proposed continuum model which is implemented in the finite element method and applied to model nanoindentation tests for three different crystallographic orientations. We obtain the representative volume element model by tracking the combined model yield surface.

Simulation and dimensional analysis of instrumented dynamic spherical indentation of ductile metals

Finite element (FE) modeling of instrumented dynamic indentation experiments in a miniature Kolsky bar is undertaken. Geometry, including an output bar with machined spherical indenter tip, and velocity history boundary conditions are extracted directly from experimental diagnostics. The test material (i.e., substrate) is polycrystalline aluminum alloy Al 6061-T6. The constitutive model used in simulations accounts for isotropic elasticity and isotropic plasticity with strain hardening, strain-rate hardening, and thermal softening under adiabatic conditions. The FE model, with representative material parameters culled from the literature, accurately reproduces the curvature of the experimental load versus depth data for three different experimental indentation velocity histories. A framework for dimensional analysis of instrumented dynamic spherical indentation is set forth, improving upon prior work. Parametric FE simulations reveal sensitivity, or lack thereof, of the predicted response to variations in the proposed independent dimensionless variables encompassing material properties. For the indenter size, maximum depth, and maximum strain rate imposed experimentally on the order of 103/s, force-depth predictions are nearly unaffected by realistic variations in mass density, melting temperature, and thermal softening parameters when the sample is initially at room temperature. Predictions are affected by elastic constants (the elastic modulus and to a lesser extent, Poisson’s ratio), initial yield strength, two strain hardening parameters, and strain rate sensitivity. Predictions are also notably affected by initial temperature, with thermal softening prominent at high enough initial temperature or much higher loading rates. Based on the dimensional analysis, static indentation and elevated temperature indentation experiments are proposed for extraction of quasi-static and thermal material properties from previously uncharacterized metals, and dynamic indentation is proposed for extraction of rate sensitivity that cannot be obtained from static tests. Rate sensitivity obtained in this way from the novel instrumented dynamic spherical indentation experiments and FE simulations produces a parameterized stress–strain response for Al 6061-T6 reasonably validated by external studies for strain rates up to the order of 103/s.