Kinematic Hardening Research Articles

SANISAND-MSf: a sand plasticity model with memory surface and semifluidised state

A new constitutive model for sand is formulated by incorporating two new constitutive ingredients into the platform of a reference critical state compatible bounding surface plasticity model with kinematic hardening, in order to address primarily the undrained cyclic response. The first ingredient is a memory surface for more precisely controlling stiffness affecting the plastic deviatoric and volumetric strains and ensuing excess pore pressure development in the pre-liquefaction stage. The second ingredient is the concept of a semifluidised state and the related formulation of stiffness and dilatancy degradation, aiming at modelling large shear strain development in the post-liquefaction stage. In parallel, a modified flow rule aimed at providing a better description of non-proportional monotonic and cyclic loading is introduced. With a single set of constants, for which a detailed calibration procedure is provided, this new model successfully simulates undrained cyclic torsional and triaxial tests with different cyclic stress ratios, separately for the pre- and post-liquefaction stages, as well as liquefaction strength curves based on [Formula: see text] and shear strain criteria for initial liquefaction. The successful reproduction of the sand element response under undrained cyclic shearing contributes to future applications in realistic and thorough seismic site response analysis.

Analytical Modeling of Residual Stress in Laser Powder Bed Fusion Considering Volume Conservation in Plastic Deformation

Residual stress (RS) is the most challenging problem in metal additive manufacturing (AM) since the build-up of high tensile RS may influence the fatigue life, corrosion resistance, crack initiation, and failure of the additively manufactured components. While tensile RS is inherent in all the AM processes, fast and accurate prediction of the stress state within the part is extremely valuable and results in optimization of the process parameters to achieve a desired RS and control of the build process. This paper proposes a physics-based analytical model to rapidly and accurately predict the RS within the additively manufactured part. In this model, a transient moving point heat source (HS) is utilized to determine the temperature field. Due to the high temperature gradient within the proximity of the melt pool area, the material experiences high thermal stress. Thermal stress is calculated by combining three sources of stresses known as stresses due to the body forces, normal tension, and hydrostatic stress in a homogeneous semi-infinite medium. The thermal stress determines the RS state within the part. Consequently, by taking the thermal stress history as an input, both the in-plane and out of plane RS distributions are found from the incremental plasticity and kinematic hardening behavior of the metal by considering volume conservation in plastic deformation in coupling with the equilibrium and compatibility conditions. In this modeling, material properties are temperature-sensitive since the steep temperature gradient varies the properties significantly. Moreover, the energy needed for the solid-state phase transition is reflected by modifying the specific heat employing the latent heat of fusion. Furthermore, the multi-layer and multi-scan aspects of metal AM are considered by including the temperature history from previous layers and scans. Results from the analytical RS model presented excellent agreement with XRD measurements employed to determine the RS in the Ti-6Al-4V specimens.

Cyclic response of electrodeposited copper films. Experiments and elastic–viscoplastic mean-field modeling

The goal of the present work is to identify and model the elastic–viscoplastic behavior of electrodeposited copper films under tension–compression loadings. From the experimental point of view, as proposed in the literature, a film of copper is electrodeposited on both sides of an elastic compliant substrate. The overall specimen is next subjected to tensile loading–unloadings. As the substrate remains elastic, the elastic–plastic response of copper under cyclic loading is experimentally determined. A clear kinematic hardening behavior is captured. To model the mechanical response, a new elastic–viscoplastic self-consistent scheme for polycrystalline materials is proposed. The core of the model is the tangent additive interaction law proposed in Molinari (2002). The behavior of the single grain is rate dependent where kinematic hardening is accounted for in the model at the level of the slip system. The model parameters are optimized via an evolutionary algorithm by comparing the predictions to the experimental cyclic response. As a result, the overall response is predicted. In addition, the heterogeneity in plastic strain activity is estimated by the model during cyclic loading.

Experimental and numerical analysis of cyclic deformation and fatigue behavior of a Mg-RE alloy

Strain-controlled fatigue of Mg–1Mn-0.5Nd (wt.%) alloy were studied by experiment and simulation. The microstructure was made up of a dispersion of strongly texture grains (13%) embedded in a matrix of grains with a random texture. The cyclic stress-strain curves showed limited tension-compression anisotropy because of the limited texture. Cyclic hardening under compression and cyclic softening under tension occurred due to the presence of twinning. Moreover, the twin volume fraction of the broken samples depended on whether the sample was broken in tension or compression, indicating that twining-detwinning occurs during the whole fatigue life. The mechanical response of the polycrystalline alloy was simulated by means of computational homogenization. The behavior of the Mg grains was modeled using a phenomenological crystal plasticity model that accounted for basal, prismatic and pyramidal slip (including isotropic and kinematic hardening) as well as twining and detwinning. The model parameters were calibrated from the cyclic stress-strain curves at different cyclic strain amplitudes. Numerical simulations were used to understand the dominant deformation mechanisms and to predict the fatigue life by means of a fatigue indicator parameter based on the accumulated plastic shear strain in each fatigue cycle.

Fukae bridge collapse (Kobe 1995) revisited: New insights

The paper revisits the notorious collapse of 18 spans of the elevated Route No. 3 of Hanshin Expressway during the 1995 Kobe earthquake. The overturned deck was monolithically connected to 3.1 m diameter piers, which failed dramatically. In stark contrast, the massive 17–pile groups survived the earthquake and are still in use, supporting the new bridge. The scope of the study is dual. Initially, the actual pile group–bridge–soil system is investigated employing the finite element (FE) method, accounting for material and geometric nonlinearities. Reinforced concrete (RC) members (pier and piles) are modelled using the Concrete Damaged Plasticity (CDP) model, while a kinematic hardening model is employed for the soil. The numerical simulation reproduces the observed shear-dominated failure at the region of reinforcement cut-off. The analysis reveals that the pile group sustains non-negligible rocking during shaking (despite being over-designed), leading to alternating tension and compression of the edge piles, combined with shear-moment loading. The resulting stiffness reduction of the cracked under tension piles leads to load redistribution towards the stiffer compressed piles, preventing plastic hinging of the weaker piles (under tension). These findings are consistent with post-earthquake in-situ testing, qualitatively verifying the numerical analysis technique. Subsequently, alternative foundation concepts are explored, starting with the pilecap of the original configuration acting as a shallow footing, provoking nonlinear rocking response. It is shown that soil yielding acts as a “fuse”, preventing collapse at the cost of increased settlements and limited residual foundation rotation. The benefits and limitations of such a shift towards nonlinear soil–foundation response are further explored, studying four intermediate foundation schemes.

The effects of kinematic hardening on thermal ratcheting and Bree diagram boundaries

Elastoplastic design of process equipment in petrochemical and power generation industries requires the consideration of thermal ratcheting. Classical Bree diagrams assuming no strain hardening have been the basis in most of today's design Codes and Standards, which can be excessively conservative. In this study, three major kinematic hardening models by Pager, Armstrong and Frederick, and Chaboche are considered for modeling detailed thermal ratcheting behaviors and establishing Bree diagrams. It is found that the linear hardening model by Prager provides a reasonable upper bound ratcheting strain estimation while the perfect plastic assumption by Bree is adequate for the design diagram construction.

On the ratcheting of the VT6 alloy in a range of loading scenarios

A set of experimental results concerning the accumulation of inelastic strain in the VT6 titanium alloy is presented. The considered tests include cyclic stress-controlled loading with monotonically increasing stress amplitude and constant mean stress. The focus of the study is on the accurate phenomenological modelling of the complex material behaviour. Four different material models are employed to capture the phenomena of ratcheting and nonlinear kinematic hardening. Two models are of the Armstrong-Frederick type and the remaining two models are of the Ohno-Wang type. Since all the considered models contain a big number of material parameters, a sophisticated nested procedure is used for the parameter identification; the obtained material parameters are validated by additional experiments. It is shown that all the models yield nearly the same accuracy; the limitations of the phenomenological approach are highlighted and discussed.

FE thermo-mechanical simulation of welding residual stresses and distortion in Ti-containing TWIP steel through GTAW process

Abstract The effect of residual stresses can be beneficial or harmful depending on their magnitude, type and distribution. This research work applied the isotropic and kinematic hardening models with different strain rates (0.001-100 s−1) to simulate the non-linear mechanical behavior of Twinning Induced Plasticity (TWIP) steel microalloyed with titanium. A finite element (FE) thermo-mechanical model was employed to analyze the welding thermal cycle in the TWIP-Ti steel. The numerical prediction of residual stress was validated by X-ray diffraction (XRD) measurements in welding critical regions. Furthermore, a residual stress critical zone (SCZ) was defined as a function of the maximum tensile residual stress and hardness in the fusion zone (FZ) and heat affected zone (HAZ). The magnitude of residual stresses estimated in the SCZ was lower than the TWIP-Ti steel yield strength. The weld joint preparation and the mechanical constraint provided a control to mitigate both residual stress and distortion. Quantitatively, the results provided good weldability of the TWIP-Ti steel in higher plate thickness through the Gas Tungsten Arc Welding (GTAW) process at low heat input.

Experimental characterization of rolled annealed copper film used in flexible printed circuit boards: Identification of the elastic-plastic and low-cycle fatigue behaviors

The elastic-plastic and low-cycle fatigue behaviors of copper films are studied experimentally and identified for further simulation works. A rolled annealed copper grade is considered here, as it is often used in flexible printed circuit boards for its mechanical resistance to high elongations. During operation, the printed circuit board (PCB) will undergo various loadings, whether purely mechanical or environmental. These loadings can lead to the fracture of copper and thus to the disconnection of the electrical signal in the PCB. Copper has a low yield stress, so it undergoes easily plastic deformation. In the present work, a predominant kinematic hardening has been observed experimentally and modeled with the combined hardening model of Lemaitre-Chaboche. The fatigue behavior has been identified on cyclic loadings at different strain amplitudes. A Coffin-Manson model has been adopted to reproduce experimental data. Identified behaviors have been introduced in a numerical simulation of a flexible PCB under cyclic bending/reverse bending, in order to estimate its mechanical reliability.

Comparative assessment of backstress models using high-energy X-ray diffraction microscopy experiments and crystal plasticity finite element simulations

Crystal plasticity (CP) models have been evolving since their inception. Advanced experimental characterization methods have contributed significantly to assess the performance and subsequent improvement of many empirical relations in CP, which were directly adopted from classical plasticity theories of solids at the macro-scale. In this research, high energy X-ray diffraction microscopy (HEDM) has been used to track the stress-state of individual grains within a polycrystalline aggregate of a Nickel-base superalloy subjected to cyclic loading. Using path-dependent, mesoscopic stress-states from the HEDM experiment, the performance of two kinematic hardening models, in the context of CP, has been assessed. One of the models is an empirical Armstrong-Frederick equation, and the other is a geometrically necessary dislocation (GND)-based phenomenological model. The results suggest that the GND-based model is capable of capturing the cyclic crystal plasticity response. The present validation efforts are expected to take CP models one step closer towards their implementation in modern engineering workflow.

Extending the effective temperature model to the large strain hardening behavior of glassy polymers

Amorphous polymers exhibit a viscoplastic strain hardening behavior at large strains. To describe this hardening behavior, we have developed an effective temperature model for the nonequilibrium behavior of amorphous polymers that incorporate the effects of network orientation and relaxation at large plastic deformation. The development of network orientation is introduced as a backstress that produces kinematic hardening in the stress response, while network relaxation describes the effects of temperature and strain rate on the hardening response. The model was applied to simulate the thermomechanical behavior of polycarbonate (PC) to determine the model parameters from standard dynamic frequency sweep and differential scanning calorimetry tests. The simulation results showed that the model can quantitatively capture the dependence of the hardening modulus on strain, strain rate, and temperature, as well as the unloading and reloading behavior measured in uniaxial compression tests. We applied the model to investigate the effect of plastic dissipation on the peeling of a polymer filament from a rigid substrate to guide the design of peel tests to measure the intrinsic fracture toughness of polymers fabricated by melt extrusion additive manufacturing processes.

Phase-field modeling of fatigue coupled to cyclic plasticity in an energetic formulation

This paper presents a modeling framework to describe the driving mechanisms of cyclic failure in brittle and ductile materials, including cyclic plasticity and fatigue crack growth. A variational model is devised using the energetic formulation for rate-independent systems, coupling a phase-field description of fatigue fracture to a cyclic plasticity model that includes multi-surface kinematic hardening, gradient-enhanced isotropic hardening/softening and ratcheting. The coupled model embeds two distinctive fatigue effects. The first captures the characteristic features of low-cycle fatigue, driven by the accumulation of plastic strains, while the second accounts for high-cycle fatigue, driven by free energy accumulation. The interplay between these mechanisms allows to describe a wide range of cyclic responses under both force loading and displacement loading, as shown in several numerical simulations. Moreover, the phase-field approach to fracture accounts for the initiation and propagation of fatigue-induced cracks.

Experimental and numerical prediction and comprehensive compensation of springback in cold roll forming of UHSS

Ultra-high-strength steels (UHSS), for instance, dual phase (DP) and martensitic steels, get growing challenges in strip metal forming processes of car industry manufacturing to achieve lightweight and improve passenger security. Predict and compensate for springback is still a major problems to be solved in cold roll forming (CRF) for complex section materials. In this study, the springback performance UHSS in cold roll forming is discussed by simulation and experimental methods. At the same time, one 3D FEA model was established to analyze the CRF process by COPPA RF and MSC MARC, in which planar swift’s model, anisotropic Hill’s 48 model, and Yid2000-2d model in the company with Yoshida-Uemori kinematic hardening pattern were investigated. Automobile threshold section CRF experiment and springback evaluation carried out through the comparison of numerical results. Considering Yoshida-Uemori kinematic hardening, the anisotropic Yid2000-2d model improves the springback prediction accuracy in CRF car threshold section in comparison with other models. The improved model is used to compensate the springback of product. A new method is proposed, which takes into account angle overbending compensation (AOC), small radius compensation (SRC), and revere-bending compensation (RBC) based on roll shape design. The method, which we call “USTB-Durable Integration of Springback Control (UDI),” is general for it considers the fact radius and angle would occur during springback. Compared with the AOC, SRC, and RBC method, the new method has higher precision especially for the springback compensation of ultra-high-strength complex section in CRF. The researchers are expected to conduct design engineer to calculate and compensate the springback trend before applying roller design to actual production.

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.

Effect of soil models on the prediction of tunnelling-induced deformations of structures

Computational modelling of the effect of underground excavations on adjacent structures has shown great potential to aid the assessment of tunnelling-induced damage to structures. However, the complexity of the mechanisms involved and the uncertainties connected to the use of sophisticated constitutive laws still limit the application of numerical modelling in civil engineering practice. This paper evaluates the effectiveness of soil models with different levels of complexity when predicting tunnelling-induced displacements of the soil surface, and consequently the assessment of building deformations. The performance of a non-linear elastic, a linear elastic–perfectly plastic and a critical-state-based kinematic hardening soil model were compared with the results of centrifuge testing of a tunnel excavation in sand. Results demonstrated that both the non-linear elastic and the kinematic hardening models are suitable to reproduce the effect of soil–structure interaction on the soil surface displacements and the building deformations, while also demonstrating the limitations of these methods in predicting local soil strains around the tunnel itself.

Nanoscale modelling of combined isotropic and kinematic hardening of 6000 series aluminium alloys

Kinematic hardening is incorporated into a nanoscale model for 6000 series aluminium alloys consisting of three sub-models describing in turn precipitation of hardening particles, yield strength and work hardening. The kinematic hardening model assumes that the backstress is caused by an unrelaxed plastic strain around non-shearable particles which is defined by an evolution equation. Compression-tension tests are performed on a cast and homogenized AA6063 aluminium alloy in tempers T6 (peak strength), T7 (overaged) and O (annealed). These tempers have different amounts of non-shearable hardening precipitates and thus exhibit various levels of kinematic hardening. The pre-compression is varied between 0.5% and 6% strain, after which the specimen is stretched to fracture. The grain structure, the constituent particles and the precipitate structure of the three tempers of the alloy are characterized by means of optical microscopy and scanning and transmission electron microscopy. The alloy displays marked kinematic hardening in all three tempers, whereas hardening stagnation is observed for tempers T7 and O. The proposed model captures the stress-strain response during strain reversal by means of the backstress and the storage and annihilation of geometrically necessary dislocations at the non-shearable particles.

Isotropic and kinematic hardening of a high entropy alloy

The contribution of kinematic hardening to the overall strain hardening of a high entropy alloy (HEA) was investigated for the first time ever. It was assessed for a single-phase equiatomic CoCrFeMnNi alloy based on a study of the Bauschinger effect. The observed occurrence of high back stresses signifies substantial kinematic hardening. We attribute it to the low probability of cross-slip in this HEA which, however, rises in the process of straining. A model that captures the mentioned effects was proposed and validated.

Thermodynamic analysis on two plasticity models considering the time-dependency of metal materials

Time-dependency and kinematic hardening are two important features of metal materials, and the corresponding behaviors are the emphases of numerical modeling for the safety evaluation of engineering structures. The robust models should not only capture the deformation characteristics, but also satisfy the fundamental thermodynamic laws. This paper aims at discussing the thermodynamic consistency of a unified viscoplasticity (UVP) model and a non-unified viscoplasticity (NUV) model that possess many characteristics in common. Within the thermodynamic framework, the analytical form of a dissipation potential function is defined, and thus the constitutive equations are derived with the introduction of Helmohltz energy function. Finally, a series experimental data of a Nickel based supper alloy is employed to verify the utility of the models. Different from the UVP model, the contribution of creep in a dissipation potential is considered in NUV model, which significantly improves the accuracy of modeling results in the creep and stress relaxation.

A modified kinematic hardening model considering hetero-deformation induced hardening for bimodal structure based on crystal plasticity

Heterogeneous structures (HS) have been reported to overcome the longstanding challenge of the trade-off between strength and ductility in metallic materials. The deformation incompatibility between the fine grains (FG) and coarse grains (CG), producing hetero-deformation induced (HDI) hardening, is the primary mechanism for superior mechanical properties of HS. In this paper, a kinematic hardening law within the framework of crystal plasticity is modified to quantify the HDI hardening of HS in which a new parameter is established to consider the strength mismatch between FG and CG. Taking bimodal structure (BS) as an example of HS, the good agreement between the experimental and numerical results show that the proposed model can successively predict the mechanical properties, including the evolution of back stress, yield strength and strain hardening of BS with various grain size distributions. Furthermore, the underlying strengthening mechanisms are revealed by switching the HDI hardening term and analyzing the partitioning of the strain and stress in different components of BS. By manipulating the grain size ratio of BS, it is found that the effect of HDI hardening is more sensitive to the size of FG than that of CG. The proposed hardening law can provide a significant guide for heterogeneous material design.

Quasistatic mechanical behavior of HMX- and TATB-based plastic-bonded explosives

Data on the macroscopic quasistatic mechanical behavior of pressed HMX- and TATB-based plastic-bonded explosives (PBXs) are listed in this paper. This review shows that (1) few characterizations are available for TATB-based PBXs. This gap is filled in this paper. An extensive database is detailed for the CEA M2 explosive composition. The HMX and TATB database then enables selection of the deformation mechanisms to be considered: viscoelasticity, damage-induced anisotropy and its effectivity (i.e.: whether or not the damage is influenced by the loading direction), plasticity with kinematic and isotropic hardenings, pressure and temperature dependencies and asymmetric failure threshold. The review also shows that (2) HMX- and TATB-based materials share close elastic and ultimate properties when the compositions (binders, solid volume fractions) and the mechanical behavior of the two crystals differ. The constitutive laws proposed in the literature are reiterated. In our opinion, a universal law could be proposed in the near future, each material being considered by its own set of parameters. The objective of this paper is to draw up the guidelines for model improvement.