Physically-based Constitutive Model Research Articles

A physically-based model considering dislocation–solute atom dynamic interactions for a nickel-based superalloy at intermediate temperatures

The uniaxial tensile tests are performed to study flow behavior of a nickel-based superalloy with different initial microstructures at an intermediate temperature range (473–973K). The experimental results show that the obvious serrated flow characteristics can be observed from the flow stress curves. Meanwhile, it is concluded that the occurrence of serrated flow features not only associate with deformation parameters, but also are prominently influenced by different initial microstructures. Furthermore, based on the plastic deformation mechanism of the investigated superalloy and dislocation-solute atoms dynamic interactions, a physically-based constitutive model is developed. The dynamic characteristics of the developed model are discussed, i.e., the evolution of moving dislocation, solute atoms concentration, and the strain rate dependent stress are analyzed. Additionally, various types of serrations are numerically simulated by appropriate parameters. Also, the predicted results show a good coincident with the observed data, suggesting that the established model can accurately describe the intermediate-temperature flow behaviors involving the serrated flow features of the investigated nickel-based superalloy.

A multi-mechanism constitutive model for the dynamic failure of quasi-brittle materials. Part II: Integrative model

In Part I, we established a model for amorphization during the failure of quasi-brittle materials. In this Part II, we present a multi-mechanism physics-based constitutive model which incorporates amorphization, microcracking and granular flow as basic deformation mechanisms. With this new integrative model, we investigate the interaction and competition of the different mechanisms. In the amorphization model we considered the initiation and evolution of amorphization bands. Microcracking is described with the micromechanics-based damage model developed in Tonge and Ramesh (2016a). Both amorphization and microcracking may introduce damage to the material, and granular flow is activated when the accumulated damage reaches some threshold value. Using boron carbide (BC) as the model material, we examine the response of a representative volume element (RVE) under different loading conditions and loading rates. We apply the full model to full simulations of plate impact and dynamic Vickers indentation into the material. Next, we simulate the sphere-on-cylinder impact experiments as an application of the integrative model. By comparing the simulation results with experiments and studying the influence of the various material parameters, we demonstrate the ability of the integrative model to capture the effects of multiple mechanisms and suggest some promising directions for material-design.

Physics-Based Constitutive Model of Porous Materials for Die/Isostatic Compaction of Metallic Powders

A physics-based constitutive model of porous materials is proposed to enhance the accuracy of numerical analysis in die/isostatic compaction. The correlation between the yield function and equivalent work equation was derived, and the numerical integration method was modified with the correlation. It is found that the apparent work of porous materials is lower than the product of relative density and equivalent work of solid materials at the beginning of compaction, implying the kinematic motion of powders and the resultant particle rearrangement. For verification of the proposed model, finite element analyses were performed for the die/isostatic compaction of three metal powders: Ti, SUS316L, and Al6061 powders. Compared with two conventional constitutive models, the proposed model improves the accuracy of the densification behaviors in all the stage during die/isostatic compaction. Furthermore, this study is a groundwork to link the densification behavior of porous materials at bulk scale to the particulate behavior of powders at microscale.

Flow stress characteristics and microstructure evolution during hot compression of Nb-47Ti alloy

The thermal-deformation allows fast and efficient grain refinement and microstructure modification in medical Ti-Nb based alloys. To design compatible process parameters, a study was carried out to investigate the softening mechanism and microstructure evolution behavior in Nb-47Ti alloy at 660–910 °C with a strain rate range of 0.01-1s−1. And then, based on the dislocation density evolution and kinetics of dynamic recrystallization, a physically-based constitutive model was established to predict the flow stress of the alloy. We showed that dynamic recovery is more active than dynamic recrystallization when the alloy is deformed below 810 °C. Meanwhile, recrystallized grains were observed over this temperature at low strain rate, i.e. lower than 0.1s−1. The presented model was incorporated into Deform 3D to provide an effective means to verify the reliability of the hot deformation behavior. Results confirmed that the model provides high accuracy and the simulation work well by running in a view to DRX.

Failure of brittle micro-spherical shells embedded in elastomer matrix under indentation

Silicone elastomer filled with glass micro balloons (GMB) is an elastomeric syntactic foam used in electronics and component packaging for encapsulation, potting, stress-relief layer, and electrical insulation purposes. Under mechanical loading, the reinforcing phase, namely the GMBs embedded in the elastomer matrix, may break or delaminate, leading to internal damage and macroscale stiffness degradation, which can alter the material's protective capacity against mechanical shock and vibration. The degree of damage is controlled by the loading history, delamination, and failure behavior of the GMBs. We investigate the GMB failure behavior in this work wherein we present an indentation experiment to measure the force required to fail individual GMBs that are either embedded in the elastomer matrix or adhered to the surface of an elastomer layer. The indentation apparatus is augmented with an inverted optical microscope to enable in situ imaging of the GMB. Failure modes for the embedded or non-embedded GMBs are discussed based on the morphology of the broken GMBs and the measured failure forces. We also measure the adhesion energy between the glass balloon and the elastomer, based on which the possibility of delamination between the GMB and the surrounding elastomer matrix during the failure process is evaluated. Our results can facilitate the development of a failure criterion of GMBs which is necessary for establishing a physics-based constitutive model to describe the macroscopic damage mechanics of elastomeric syntactic foams.

High-temperature deformation mechanisms and physical-based constitutive modeling of ultra-supercritical rotor steel

This study presents an investigation that characterizes the evolution of the dynamically recrystallized structure and flow behavior of FB2 rotor steel during hot deformation in the temperature range from 900 °C to 1200 °C at strain rates from 0.001s−1 to 0.1s−1 using Gleeble-3500 thermo-simulation machine. Dynamic recrystallization (DRX) plays a key role in softening mechanism for hot deformed FB2 rotor steel. The fraction of LABs greatly increases with the decrease of deformation temperature. Low angle boundaries (LABs) always have higher local misorientation angle, which means the lower deformation temperature is capable of providing not enough driven force for the migration of LABs and thereby decelerates the DRX process to consume the dislocations. Furthermore, the critical stress and critical strain for initiation of DRX are calculated by setting the second derivative of the third order polynomial. Based on the classical stress–dislocation relation and the kinetics of dynamic recrystallization, a two-stage constitutive model is developed to predict the flow stress of FB2 steel. Comparisons between the predicted and measured flow stress indicate that the established physically-based constitutive model can accurately characterize the hot deformations for the studied steel.

Physical-based constitutive model considering the microstructure evolution during hot working of AZ80 magnesium alloy

A physical-based constitutive model was developed to model the viscoplastic flow behavior and microstructure evolution of AZ80 magnesium alloy during the hot working process. The competing deformation mechanisms, including work hardening, dynamic recovery, and dynamic recrystallization, in an isothermal compression environment were considered in the model. The internal state variables, including the normalized dislocation density and recrystallized volume fraction, were incorporated into the model to articulate the microstructure evolution during hot deformation. The kinetic condition critical for dynamic recrystallization, considering the effects of the deformation temperature and strain rate, was obtained by employing both the Poliak-Jonas criterion and Zener-Hollomon parameter. Microstructure observations indicate that the recrystallized volume fraction increases with decreasing Z parameter at constant strain, which is consistent with the predicted kinetics model. Based on the developed model, a good correlation was also obtained between the predicted and experimental flow stress. The results indicate a good predictability of the model in describing the hot deformation behavior and microstructure evolution of AZ80 magnesium alloy.

Ultrasonic vibration-assisted metal forming: Constitutive modelling of acoustoplasticity and applications

This paper presents a new physics-based constitutive model to accurately describe the deformation behaviour of metals during ultrasonic vibration assisted (UVA) forming. Dislocation dynamics and acoustic energy transformation mechanisms in materials under ultrasonic vibration were considered in the modelling. A user defined subroutine was also developed for modelling the UVA forming processes using the finite element method. To assess the proposed model, upsetting forming, press forming, and incremental forming were simulated separately, and the predicted results were compared with their corresponding experiments. It was found that the application of the ultrasonic vibration can significantly decrease the material flow stress, making the material softer in forming. A large vibration amplitude results in a large reduction in flow stress. Relevant experimental measurements showed that the model has captured the material behaviour and the major mechanics in UVA forming. Different forming processes, due to their difference in tool-workpiece contact condition, would have different acoustic energy and stress transformation efficiency.

MicroROM: A Physics-Based Constitutive Model for Ni-Based Superalloys

In this article, a physics-based constitutive model is developed for representing the stress–plastic strain response of Ni-based superalloys by considering the hardening mechanisms that contribute to the macroscopic yield stress and the subsequent strain-hardening response in order to derive the entire tensile stress–strain curve. It is demonstrated that the log stress vs log plastic strain curves of Ni-based superalloys such as 702 Li and ME3 exhibit a bilinear behavior with a lower strain-hardening exponent in the low plastic strain regime and a much higher strain-hardening exponent in the high plastic strain regime. These two hardening regimes can be modeled on the basis of self-hardening of individual slip planes and latent hardening of five operative independent slip systems due to cross-slip from {111} planes to {001} planes, leading to the formation of incomplete and complete Kear-Wilsdorf locks. The proposed physics-based constitutive model, dubbed as MicroROM, exhibits a form that is similar to the Ramberg–Osgood (RO) constitutive model, which is widely used in structural analyses of engineering designs and components. MicroROM is applied to predict the tensile stress–strain curves of 720 Li and ME3 with either a subsolvus or supersolvus microstructure for temperatures ranging from 24 °C to 815 °C. The agreement is good between model predictions and experiment data from the literature. The sensitivity of the predicted stress–strain response to individual microstructural parameters is highlighted and the relation to individual hardening mechanisms is elucidated.

Physics-based Constitutive Model for the Hot Deformation of 2Cr11Mo1VNbN Martensitic Stainless Steel

The hot deformation behavior of 2Cr11Mo1VNbN martensitic stainless steel is investigated through isothermal compression tests between 1173 and 1423 K with strain rates of 0.005-5 s−1. Based on experimental results, the work hardening–dynamic recovery stage and dynamic softening stage are evaluated, and a couple-stage constitutive model is developed to describe the work hardening–dynamic recovery and dynamic softening behaviors. Phenomenological constitutive models, which consider temperature, strain and strain rate, are established. A comparison between the predicted and experimental flow stress values indicates that the established models accurately describe the hot deformation behaviors for the studied supercritical steel.

Multi-holes configurations of woven fabric kenaf composite plates: experimental works and 2-D modelling

A study on structures response in multi-holes plates is important to understand the effect of neighbouring hole on stress concentration as subjected to tensile loading prior to bearing failure in multi-bolted joints. Current work implemented experimental framework on staggered and non-staggered multi-holes configurations to include various lay-up types, plate thickness and hole configurations as specified in the testing series. Experimental observations found that all configurations failed in net-section path suggesting that fracture initiates and propagates from the notch tip perpendicular to loading direction in self-similar fashion through the plate thickness. Non-staggered hole configurations demonstrated peak load compared to staggered counterparts due to more congested holes in staggered configurations. Two-dimensional Extended Finite Element Method (XFEM) modelling framework was carried out in all configurations investigated by sufficient meshing refinements, damage stabilization value and boundary conditions. XFEM was extended from classical finite element expression which has enriched function to enable the crack be tracked visually. A physically-based constitutive model from traction-separation relationship was applied and independently measured material properties and in-plane elastic properties were implemented in current work. Strength prediction results showed that good agreement was found in all testing series and showed discrepancies of less than 15%, the best prediction in combination of PX4 lay-ups and staggered multi-holes configurations series.

Physically-based constitutive model for flow behavior of a Ti-22Al-25Nb alloy at high strain rates

The objective of the study is to understand the dynamic flow behavior of Ti–22Al–25Nb alloy at high temperatures using a modified Zerilli–Armstrong (Z-A) model. To investigate the dynamic mechanical behavior of titanium alloy, the material was subjected to quasi static and dynamic compression testing. It is found out that the modified Z-A models possess better predictability in evaluating the flow behavior of the Ti–22Al–25Nb alloy at elevated strain rates and temperatures. The model well established the quasi-static and dynamic behavior of the titanium alloy, mainly the effects of strain hardening and thermal softening. The regimes of high strain rate deformation behavior represented by dynamic recrystallization (DRX), lamellar globularization and the instability flow have been discussed. Using transmission electron microscopy (TEM) studies, it is found that the dislocation density is directly associated with strain rate.

Analytical network-averaging of the tube model: Strain-induced crystallization in natural rubber

In this contribution, we extend the analytical network-averaging concept (Khiêm and Itskov, 2016) to phase transition during strain-induced crystallization of natural rubber. To this end, a physically-based constitutive model describing the nonisothermal strain-induced crystallization is proposed. Accordingly, the spatial arrangement of polymer subnetworks is driven by crystallization nucleation and consequently alters the mesoscopic deformation measures. The crystallization growth is elucidated by diffusion of chain segments into crystal nuclei. The crystallization results in a change of temperature and an evolution of heat source. By this means, not only the crystallization kinetics but also the Gough–Joule effect are thoroughly described. The predictive capability of the constitutive model is illustrated by comparison with experimental data for natural rubbers undergoing strain-induced crystallization. All measurable values such as stress, crystallinity and heat source are utilized for the comparison.

A physically-based constitutive modelling of a high strength aluminum alloy at hot working conditions

The hot deformation behavior of a high strength aluminum alloy (Al-Zn-Mg-Cu) was studied by isothermal hot compression tests performed over a range of temperatures (350–490 °C) and strain rates (0.001–1 s−1). A constitutive equation was established using experimental results to predict the flow stress of the alloy under elevated temperature. In the work hardening-dynamic recovery regime, a physically-based constitutive equation for the flow stress was obtained from the stress-dislocation relation. In the subsequent dynamic recrystallization region, the flow stress after the peak was predicted by employing the kinematics of the dynamic recrystallization in the constitutive model. The stress-strain curves of the alloy predicted by the established models were in good agreement with experimental results. The results indicate that the proposed physically-based constitutive equation can accurately predict the flow behavior of the Al-Zn-Mg-Cu alloy.

Through-process modelling of welding and service of 9Cr steel power plant components under load-following conditions

This paper is concerned with the development of a through-process model to predict the in-service performance of high-temperature, 9Cr steel, power plant components. A multi-pass welding simulation is conducted using the finite element software Abaqus. A user-material subroutine, including microstructure evolution and a physically-based constitutive model, is employed to predict the mechanical response of the material during welding and to predict welding residual stresses. Points are sampled from the FE geometry and their microstructure parameters and residual stress values are used in a uniaxial code to predict the relative in-service lives of the different weld regions under load-following power plant operating conditions. It is shown that post-weld heat treatment significantly improves predicted life and that there is a strong correlation between predicted microstructure before service and the predicted in-service life.

Relaxation oscillation of borosilicate glasses in supercooled liquid region

Most supercooled non-polymeric glass-forming melts exhibit a shear thinning phenomenon, i.e., viscosity decreases with increasing the strain rate. On compressing borosilicate glasses at high temperature, however, we discovered an interesting oscillatory viscous flow and identified it as a typical relaxation oscillation caused by the peculiar structure of borosilicate glass. Specifically, the micro-structure of borosilicate glass can be divided into borate network and silicate network. Under loading, deformation is mainly localized in the borate network via a transformation from the three coordinated planar boron to trigonal boron that could serve as a precursor for the subsequent formation of a BO4 tetrahedron, while the surrounding silicate network is acting as a stabilization/relaxation agent. The formation of stress oscillation was further described and explained by a new physics-based constitutive model.

Elucidating the atomistic mechanisms underpinning plasticity in Li-Si nanostructures

Amorphous lithium-silicon (a-Li-Si), especially in nanostructure form, is an attractive high-capacity anode material for next-generation Li-ion batteries. During cycles of charging and discharging, a-Li-Si undergoes substantive inelastic deformation and exhibits microcracking. The mechanical response to repeated lithiation-delithiation eventually results in the loss of electrical contact and consequent decrease of capacity, thus underscoring the importance of studying the plasticity of a-Li-Si nanostructures. In recent years, a variety of phenomenological continuum theories have been introduced that purport to model plasticity and the electro-chemo-mechanical behavior of a-Li-Si. Unfortunately, the micromechanisms and atomistic considerations underlying plasticity in Li-Si material are not yet fully understood and this impedes the development of physics-based constitutive models. Conventional molecular dynamics, although extensively used to study this material, is grossly inadequate to resolve this matter. As is well known, conventional molecular dynamics simulations can only address phenomena with characteristic time scales of (at most) a microsecond. Accordingly, in such simulations, the mechanical behavior is deduced under conditions of very high strain rates (usually, ${10}^{8}\phantom{\rule{4.pt}{0ex}}{\text{s}}^{\ensuremath{-}1}$ or even higher). This limitation severely impacts a realistic assessment of rate-dependent effects. In this work, we attempt to circumvent the time-scale bottleneck of conventional molecular dynamics and provide novel insights into the mechanisms underpinning plastic deformation of Li-Si nanostructures. We utilize an approach that allows imposition of slow strain rates and involves the employment of a new and recently developed potential energy surface sampling method---the so-called autonomous basin climbing---to identify the local minima in the potential energy surface. Combined with other techniques, such as nudged elastic band, kinetic Monte Carlo and transition state theory, we assess the behavior of a-Li-Si nanostructures under tensile strain rates ranging from ${10}^{3}$ to ${10}^{8}\phantom{\rule{4.pt}{0ex}}{\text{s}}^{\ensuremath{-}1}$. We find significant differences in the deformation behavior across the strain rates and discover that the well-known shear transformation zones (widely discussed in the context of amorphous materials) are formed by a ``diffusionlike'' process. We identify the rotation of the shear transformation zone as a key dissipation mechanism.

An effective constitutive model for polycrystalline ferroelectric ceramics: Theoretical framework and numerical examples

We present an efficient, physics-based constitutive model for bulk polycrystalline ferroelectric ceramics, which links domain switching mechanisms and phase transitions at the microscale to the observed electro-thermo-mechanically coupled material response at the macroscale. In particular, a convexified energy density is formulated based on domain volume fractions and extended to polycrystals via the common Taylor assumption of uniform strains (alternative descriptions are discussed as well). The chosen kinetic relations admit to account for differences in 90°- and 180°-domain wall motion and rate effects. The model is applied to tetragonal barium titanate (BaTiO3) and we present results for both material point calculations and finite element simulations, which demonstrate good qualitative agreement with experiments. We deliberately target bulk polycrystalline ferroelectrics in contrast to thin films that have been studied extensively.

A physical-based constitutive model for surface integrity prediction in machining of OFHC copper

Due to the rising interest in predicting machined surface integrity and sustainability, various models for metal cutting simulation have been developed. However, their accuracy depends deeply on the physical description of the machining process. This study aims to develop an orthogonal cutting model for surface integrity prediction, which includes a physical-based constitutive model of Oxygen Free High Conductivity (OFHC) copper. This constitutive model incorporates the effects of the state of stress and microstructure on the work material behavior, as well as a dislocation density-based model for surface integrity prediction. The coefficients of the constitutive model were identified through a hybrid experimental/numerical approach, consisting in mechanical tests, numerical simulations and an optimization-based algorithm. The orthogonal cutting model was simulated by FEM, using ALE formulation, and was validated by comparing predicted and measured results, including residual stresses, dislocation density and grain size. The model is then used to analyze the influence of the cutting parameters and cutting geometry on surface integrity, and its results are compared to those obtained by the Johnson-Cook model.

A physical-based constitutive model to describe the strain-hardening and dynamic recovery behaviors of 5754 aluminum alloy

Plane strain hot compression tests of 5754 aluminum alloy were conducted on a Gleeble-3500 thermo-mechanical simulator under various conditions. These tests simulated flat rolling to investigate how hardening and softening behaviors respond to controlled parameters, such as the deformation temperature and strain rate. This data allowed the parameters for the hot rolling process to be optimized. The restoration mechanism primarily proceeds via dynamic recovery, as shown by the deformed microstructure analysis and strain-stress curves. The dislocation density was used as internal state variable to develop a physical constitutive model, which characterized the evolution of the dislocation density caused by strain-hardening and dynamic recovery behaviors. The relationship between the flow stress and the dislocation density could be quantified with this model. The strain-hardening and softening behavior was analyzed in detail by Kocks-Mecking type plots. Furthermore, the relevant material coefficients were expressed as functions related to the temperature and the strain rate. The experimental flow stress was found to be in close agreement with the calculated, which confirms that the model developed herein can represent the flow behaviors of the 5754 aluminum alloy effectively.