Mixed Hardening Research Articles

Application of a modified mixed hardening model to cyclic degradation of saturated clay

Application of a modified mixed hardening model to cyclic degradation of saturated clay

A homogenized anisotropic constitutive model of perforated sheets for numerical simulation of stamping

Perforated sheets exhibit strong anisotropy related to the arrangement of holes during plastic deformation, which poses significant challenges for accurate prediction of the macroscopic plastic behavior in stamping. Addressing this, unit cell simulations were conducted to determine the homogenized yielding and hardening behaviors of perforated sheets with hexagonal or square arrays of circular holes under in-plane loading conditions. The local deformation mode, which determines the macroscopic anistropy, is unveiled. A mechanism-motivated homogenized yield criterion was proposed based on the local deformation modes, which provides a concise yet unified approach to modeling complex material anisotropic behavior with high accuracy. Additionally, a mixed hardening strategy was developed to capture the evolution of yield loci in term of size and shape. The proposed constitutive model demonstrates precise predictions of flow stress variations and the apparent r-value with loading angles during uniaxial tension. Furthermore, it successfully forecasts two distinct types of earing profiles in the deep drawing of perforated sheets with square arrays of circular holes at different hole fractions. This modeling approach provides a feasible way for predicting the deformation behavior of perforated sheets during stamping with high computational efficiency.

Low-cycle fatigue simulation of ductile materials using elasto-plastic gradient damage approach

This work presents a novel computational strategy based on gradient enhanced damage and cyclic yielding with nonlinear mixed hardening behaviour for simulating low-cycle fatigue of ductile materials. A new yield function is introduced which accommodates the cyclically evolving state variables during mixed hardening and the damage induced during the application of repetitive loads. The resulting constitutive relations are derived in an incremental form. The non-local strains facilitate the computation of incremental damage in the material. A finite element scheme is developed from the governing physics through full coupling between damage and cyclic-elastoplastic deformations. In order to obtain an accurate computational response, a stress-return mapping scheme is formulated for the damage-dependent yield function. The developed numerical strategy is investigated for specimens made of various ductile materials exhibiting elasto-plastic behaviour under low-cycle fatigue loads. The stress-strain hysteresis and cyclic softening computed by the present numerical framework agree well with experimental data available in literature. The low-cycle fatigue crack-growth results are also accurately captured for various fatigue loading conditions.

Experimental analysis and modeling of mixed hardening of Steel Matrix Composites under monotonic and reverse simple shear loading: Application to SPIF process

This study explores the distinctive characteristics of Steel Matrix Composites (SMCs) reinforced with TiB2, concentrating on their hardening behavior during simple shear tests. The analysis considers an elastoplastic model with Isotropic and Mixed hardening. Emphasizing the necessity of kinematic hardening, experimental characterizations using EBSD and XRD highlight effects of matrix grain size and reinforcement impact on mechanical properties. Validation of the numerical model through Stress-Strain curves reveals a strong correlation, particularly with the mixed hardening model under reverse shear loading. Comprehending SMC strain hardening is crucial for optimizing parameters and numerically designing forming processes, enhancing manufacturing efficiency.

Research on welding simulation for vacuum chamber test specimens

The vacuum chamber is an important component of nuclear fusion devices, and the deformation control of the welding process is relatively strict. In this paper, the isothermal multi-level cyclic loading tests have been conducted to explore a nonlinear mixed hardening mode, which can be used as the material input for the welding simulation. Then, welding simulation has been performed for test specimens of the vacuum chamber, and the deformation of test specimens has been obtained under different welding paths. After the first welding simulation is completed, the clamp and limiting plates have been designed based on the deformation of the test specimens. The welding simulation has been performed again with the clamp and limiting plates, in order to evaluate the rationality of the welding process and the design for the clamp and limiting plates. Finally, according to the determined welding process and design for the clamp and limiting plates, welding tests have been conducted, and the welding deformation has been measured. It is found that the difference between the measurement values of the tests and the simulation results is small, which implies that the welding simulation is reasonable.

A physically-based mixed hardening model for the prediction of the ductility limits of thin metal sheets using a CPFE approach

An advanced Crystal Plasticity Finite Element (CPFE) approach is developed to accurately predict the ductility limit strains of thin metal sheets. This method uses polycrystalline unit cells to represent the metal sheets at the macroscopic level. The macroscopic behavior of these unit cells is determined based on that of the constituent single crystals using the periodic homogenization multiscale scheme. At the single crystal scale, the constitutive framework follows a finite strain rate-independent formulation, with the flow rule governed by the Schmid law. The evolution of the single crystal yield surface is described through a physically-based mixed hardening model, where isotropic hardening is characterized by a dislocation density-based formulation, while kinematic hardening is described by the nonlinear Armstrong–Frederick model. The unit cell ductility limit strains are predicted by the Rice bifurcation criterion. The reliability of the mixed hardening model in accurately reproducing mechanical behavior is confirmed through simulations of uniaxial tension/compression loading. Then, the developed computational strategy is used to investigate the impact of key microstructural hardening parameters on the initiation of localized necking under linear strain paths. The numerical predictions reveal the significant influence of these parameters on the formability of thin metal sheets. Additionally, the analysis of ductility limits under non-linear strain paths demonstrates a strong dependency of the numerical predictions on strain path changes. The numerical predictions obtained by the developed CPFE multiscale strategy are compared with experimental results from the literature. In summary, the proposed approach provides a reliable tool for accurately predicting the ductility limits of thin metal sheets, offering valuable insights for engineering applications.

Elastoplastic peridynamic formulation for materials with isotropic and kinematic hardening

We present an ordinary state-based peridynamic model in 2D and 3D consistent with rate-independent J2 plasticity with associated flow rule. The new contribution is the capability of the elastoplastic law to describe isotropic, kinematic and mixed hardening. The hardening formulations follow those available in the literature for classical elastoplasticity. The comparison between the results obtained with the peridynamic model and those obtained with a commercial FEM software shows that the two approaches are in good agreement. The extent of the plastic regions and von Mises stress computed with the new model for 2D and 3D examples match well those obtained with FEM-based solutions using ANSYS.

Research on the 2A11 Aluminum Alloy Sheet Cyclic Tension–Compression Test and Its Application in a Mixed Hardening Model

The increasing application of aluminum alloy, in combination with the growth in the complexity of components, provides new challenges for the numerical modeling of sheet materials. The material elastic–plasticity constitutive model is the most important factor affecting the accuracy of finite element simulation. The mixed hardening constitutive model can more accurately represent the real hardening characteristics of the material plastic deformation process, and the accuracy of the material property-related parameters in the constitutive model directly affects the accuracy of finite element simulation. Based on the Hill48 anisotropic yield criterion, combined with the Voce isotropic hardening model and the Armstrong–Frederic nonlinear kinematic hardening model, a mixed hardening constitutive model that considers material anisotropy and the Bauschinger effect was established. Analysis of the tension–compression experiment on the sheet using finite element method. Using the finite element model, the optimum geometry of the tension–compression experiment sample was determined. The cyclic deformation stress–strain curve of the 2A11 aluminum alloy sheet was obtained by a cyclic tensile–compression test, and the material characteristic parameters in the mixed hardening model were accurately determined. The reliability and accuracy of the established constitutive model of anisotropic mixed hardening materials were verified by the finite element simulation and by testing the cyclic tensile–compression problem, the springback problem, and the sheet in bending, unloading, and reverse bending problems. The tensile–compression experiment is an effective method to directly and accurately obtain the characteristic parameters of constitutive model materials.

New double surface constitutive model of intermittent plastic flow applied to near 0 K adiabatic shear bands

One of the most interesting phenomena that occur in ductile materials strained in the proximity of absolute zero are the adiabatic shear bands. In the stainless steels, massively used to construct superconducting magnets, their occurrence can be detected by various techniques, including magnetometric methods (feritscope). Formation of adiabatic shear bands is strictly correlated to the occurrence of the intermittent plastic flow (IPF), characteristic of stainless steels strained in liquid or superfluid helium. Evidence for the occurrence of the phase transformation during nucleation and formation of the shear bands in the proximity of absolute zero is for the first time given. The rate of shear bands propagation along the sample as well as the amount of secondary phase is measured. In order to describe the intermittent plastic flow, novel double surface model has been developed. It includes type Huber-Mises-Hencky yield surface, and new recovery surface reflecting the lower bound for the stress oscillations. The yield surface can move and expand due to nonlinear mixed (kinematic and isotropic) hardening, resulting from the phase transformation, whereas, the recovery surface remains constant. The serrations occur between the yield surface and the recovery surface, with the yield surface coming back to its initial position after each serration. Each serration corresponds to formation of single shear band there, where the easy slip planes are available, and the mechanism of anchoring the shear bands by the secondary phase is explained. New double surface model has been correlated to the experimental data and applied to explain stress oscillations during the regular stage of the intermittent plastic flow, when the shear bands gradually cover the gauge length of the sample.

3D thermoelastoplastic study of FML structure under the action of a moving Gaussian-distributed laser heat source

Fiber metal laminated (FML) structures are used widely, however, studies on the three-dimensional thermoelastoplastic behaviors of FML structure subjected to a moving Gaussian-distributed laser heat source have not yet been developed. In present work, the semi-analytical solution of three-dimensional transient heat transfer equation for FML structure under the action of a moving Gaussian-distributed laser heat source is obtained through the separate variable method (SVM) and the Newton Cotes method (NCM). A yield criterion related to spherical tensor of stress is proposed to describe the mixed hardening of the orthotropic FML structure. Based on classical nonlinear laminated plate theory, the incremental nonlinear governing equations are obtained, and the equations are solved by the combination of finite difference method, Newmark method and iterative method. Numerical results show that the temperature field, moving velocity of laser, number of FML layers, thickness ratio and boundary condition have great influences on thermoelastoplastic behaviors of the FML structure.

Characterization and modeling of the hardening and softening behaviors for 7XXX aluminum alloy subjected to welding thermal cycle

The evolution of thermo-elasto-plastic stress-strain during welding process plays a key role in determining the welding residual stresses and mechanical properties of welded joints for age-hardening 7XXX aluminum alloy, which is influenced by the softening and hardening behaviors. In this study, a Gleeble 3800 thermo-mechanical testing machine was employed to simulate the welding thermal cycle process of 7XXX aluminum alloy, and dynamic yield strengths under different temperatures were measured to elucidate the softening behavior. An isothermal multi-level cyclic loading tests at various temperatures were conducted to characterize the cyclic hardening feature. The calculation formulas for the proportion of kinematic and isotropic hardening model were deduced, and the cyclic hardening behavior was quantitatively described. A softening model and a nonlinear mixed hardening model were explored to simulate the evolution of dynamic yield strength and the cyclic hardening behavior, and excellent agreements were obtained between predicted and measured dynamic yield strengths and cyclic stress-strain curves.

A large strain one-dimensional ductile damage model for space truss analysis considering Gurson’s porous plasticity, thermal effects and mixed hardening

A large strain one-dimensional ductile damage model for space truss analysis considering Gurson’s porous plasticity, thermal effects and mixed hardening

Springback prediction of multiple reciprocating bending based on different hardening models

The metal forming process often involves multiple reciprocating bending springback problems. The springback prediction of reciprocating bending is more difficult than that of single bending. Based on the isotropic hardening model, the kinematic hardening model, the mixed hardening model and the YU model, the effects of different hardening models, variable elastic modulus and bending times on the springback are studied. An experimental method for measuring the springback of multiple reciprocating bending is adopted. The multiple reciprocating pure bending is realized by arc-shaped punch and die. The results show that different hardening models have good predictions for the springback of the first bending. However, as the number of bending increases, compared with the increasing error value of other hardening models, only the YU model that considers the variable elastic modulus can realize the accurate prediction of springback, and the error of springback results is within 5% for each bending. The research work is a basic research on the springback problem of multiple reciprocating bending, which can improve the simulation accuracy of metal forming processes involved in this problem, especially for the roller straightening and setting round process with more reciprocating bending.

Modeling and simulation of ductile damage in forged steel used to encapsulate high-level radioactive waste

Andra, the French national radioactive waste management agency, is in charge of studying the disposal of high-level and long-lived intermediate-level waste (HLW and ILW-LL) in a deep geological repository. According to the reference concept, it is planned to encapsulate high-level waste in non-alloy P285NH steel overpacks before inserting them into horizontal steel cased micro-tunnels. This work is a part of the study about the long-term behavior of a welded steel overpack subjected to external hydrostatic pressure and several localized loading paths. Indeed, the main objective of this work is to develop the most suitable model for non-alloy steel P285NH to be used in the prediction of the long-term overpack behavior. Dealing with a ductile steel, elastoplastic constitutive equations accounting for mixed nonlinear isotropic and kinematic hardening strongly coupled with ductile isotropic damage are adopted. They are formulated based on the classical thermodynamics of irreversible processes framework with state variables at the macroscopic scale, (Germain, 1973) (Lemaitre 1985, Saanouni 2012). In this paper, a new coupling formulation between the scalar isotropic ductile damage and the deviatoric and spherical part of the Cauchy stress and elastic strain tensors is proposed. In order to calibrate the developed model on P285NH steel, multiple tensile tests are performed using classical cylindrical specimens, notched specimens and double notched specimens. In the last part, some experimental fields are measured using digital image correlation. Application is made to a simplified overpack represented by thick walled cylinder subject to compressive loading path. A FEM (Finite Element method) crushing operation of an overpack’s cylindrical part has simulated and analysed.

A low cycle fatigue cracking simulation method of non-ordinary state-based peridynamics

We established a simulation method for low cycle fatigue elastoplastic fracture under the framework of the Non-ordinary State-based peridynamics. It used mixed hardening models and failure criteria based on accumulated plastic strain. Furthermore, the numerical solution method of the elastoplastic constitutive equation was given. In order to verify the simulation method, the simulations of 316L steel strain control symmetric cyclic test and Q235 low cycle fatigue failure test were conducted, which showed good agreement with the experimental results. Our findings demonstrated the suitability of the proposed simulation method for damage fracture analysis with elastoplastic low cycle fatigue.

A new mixed hardening methodology applied to a 28 nm FDSOI 32-bits DSP subjected to gamma radiation

This work presents the performance degradation of a 32-bit DSP fabricated with 28 nm FDSOI technology subjected to different levels of gamma radiation. A new mixed hardening methodology based on electrical compensation and thermal regeneration is applied to the irradiated devices to recover the degraded electrical characteristics induced by the total ionizing dose. The application of this new methodology seeks to extend the lifetime of FDSOI integrated circuits under high radiation conditions while keeping good reliability.

Design on progressive corners of dies and macro textures of blank holders for S stamped parts

The shape dimensions of die corners and surface textures of blank holders are important in the effective control of twist springback. For predicting springback accurately, a mixed hardening model is presented for a thin-walled S beam made from TRIP780. Based on a proposed evaluation index for twist springback, the experiments of stamping and twist springback for TRIP780 are carried out. The twist springback angle is gauged by a three-coordinate measure instrument. A Response Surface Model (RSM) between the parameters of the mixed hardening model and the twist springback angles is established, and the parameters are inversed. The progressive die corners are designed for the twist springback compensation based on the stress distribution of the thin-walled S beam after stamping, and the die corner radius is optimized by the RSM and an Ant Colony Algorithm (ACA). Meanwhile, the macro textures of blank holders including longitudinal texture and transverse texture are designed. Based on the compensation analysis, a comprehensive compensation method which combined the progressive die corners with the longitudinal texture of the blank holder is proposed. The results show that the springback angle is reduced by 33.6%, proving the proposed comprehensive compensation method is effective.

An implicit numerical scheme for cyclic elastoplasticity and ratcheting under plane stress conditions

The paper reports the development of an implicit numerical scheme for plane stress cyclic elasto-plasticity, capable of integrating a wide range of hardening rules, and simulating multi-axial ratcheting in metal structural components. Constitutive relations account for von Mises yielding in combination with mixed hardening. Emphasis is given to the kinematic hardening part, which is described with an advanced multiple back-stress model suitable for multi-axial material ratcheting simulation. The constitutive equations are integrated implicitly, and the accuracy of the algorithm is assessed via iso-error maps. Two main novelties of the algorithm refer to the incremental update of the internal variables through the solution of a single scalar equation, and the explicit formulation of the consistent tangent moduli. The numerical scheme is implemented within the finite element environment as an external material subroutine, and its computational efficiency is demonstrated through the simulation of large-scale experiments on pipe elbows. Using the proposed computational framework, two kinematic hardening rules are employed to simulate the elbow response with emphasis on local strain amplitude and accumulation (“ratcheting”). The good comparison between numerical and experimental results demonstrates the computational efficiency of the numerical scheme and highlights some key issues concerning multi-axial ratcheting simulation.

Evolution of subsequent yield surfaces with plastic deformation along proportional and non-proportional loading paths on annealed AA6061 alloy: Experiments and crystal plasticity finite element modeling

This work presents an experimental and numerical investigation of annealed aluminum alloy AA6061 subjected to proportional and non-proportional loading paths at various finite levels of pre-strain. A careful mechanical characterization program is conducted for subsequent yield surfaces in the σ11−3σ12 stress space using an equivalent 10με offset linearity definition of yield. Electron backscatter diffraction (EBSD) is also used to characterize the microstructure of the material in the annealed condition. Each subsequent surface shows a very well-known shape of being nearly flat in unloading and having a prominent “nose” in the loading direction that deviates substantially from a generalized isotropic behavior. All proportional loading conditions show a rapid evolution of the mixed hardening effect that was characterized by the first load reversal in the first yield surface probe. Differences associated with the path-dependent effect in shifting the non-proportional yield surfaces are also observed in experiments. The experimental program is followed by Taylor-type crystal plasticity finite element (CPFE) simulations of the observed mechanical phenomenon. The Taylor-type CPFE model is calibrated using only the proportional uniaxial tension response and the EBSD imaging to predict all subsequent proportional and non-proportional loading paths. All CPFE show good predictive capabilities in capturing the experimental yield surface measurements for both proportional and non-proportional loading conditions. The CPFE simulations predict both the resulting shape and magnitude of the “nose” in the yield surfaces, as well as the mixed hardening, distortion, and yield surface translations. A systematic study is presented to investigate the effects of latent hardening on the yield surface predictions. This work highlights the promising results of advanced material model developments for larger-scale component simulations of lightweight aluminum alloys.

Mixed Hardening Characteristics of the Anisotropic Coal under Cyclic Loading

Pulse fracturing has been used to increase permeability and weaken the strength of the coal seam, making the coal fracture under cyclic loading. During the cyclic loading, the rock-like materials tend to present mixed hardening (mixed mode of isotropic and kinematic hardening) from initial yielding to failure (critical yielding). At present, understanding of the mixed hardening characteristics in anisotropic coal involving massive cleats remains challenging and crucial. In this paper, the cylinder specimens (diameter: 50 mm; length: 100 mm) of the coal were tested under cyclic uniaxial loading (loading rate: 900 N/s), and acoustic emission (AE) was employed to characterize the hardening process. The samples were drilled at the angle (α) of 0°, 45° and 90° with the coal surface cleat respectively. The upper-stress limit (P max) increases by 2 kN at each loading cycle, and the lower-stress limit (P min) was kept at 1 kN. Several findings were obtained based on the experimental results. (1) Uniaxial compression strength and the cyclic number increase with α, presenting isotropy. (2) The remarkable accumulation of AE energy is the feature of identifying plastic hardening. Both the isotropic and kinematic hardening processes are significant for the specimen with α dip angle (α) of 90°, validated by the dramatically increased isotropic and kinematic hardening indexes. However, the coal presents a slight isotropic and kinematic hardening, with a ranging from 0° to 45°. (3) The remarkably mixed hardening (α=90°) corresponding to a complex fragmentation of the coal, which is supposed to be caused by the continuous weakening of coal matrix (including the butt cleat). In contrast, at α of 0° and 45°, the mixed hardening characteristics are slight. Accordingly, the final fracture surfaces of coal tend to be relatively single, roughly along with the surface cleats. Thus, we can infer that the slightly mixed hardening is due to the weakening of surface cleats. Based on the mixed hardening characteristics of anisotropic coals, conducting pulse fracturing to apply cyclic loading perpendicular to the cleat surface is supposed to be beneficial for generating more complex fractures, to improve coal permeability.