Physically-based Constitutive Model Research Articles

Modelling of fracture-involved large strain behaviors of amorphous glassy polymers via a unified physically-based constitutive model coupled with phase field method

To promote the application of amorphous glassy polymers in structural components, a reliable prediction of the deformation and the potential fracturing behaviors is in demand. This work aims to provide a simple and feasible computational method to analyze the large strain behaviors, including elasticity, viscoplasticity, and the subsequent fracture, of amorphous glassy polymers. This is achieved by incorporating a physically-based constitutive model coupled with the fracture phase field method into the commercial finite element software Abaqus/Explicit. Inside the constitutive model, shear-yielding, crazing, and disentangling are considered as the underlying mechanisms for viscoplastic deformation and damage initiation. It is noteworthy that a unified craze-initiation criterion with a clear physical meaning is proposed, distinguishing this work from the previous in the literature. Moreover, a relatively user-friendly numerical implementation is suggested by exploiting the built-in features of Abaqus/Explicit. Taking the typical amorphous glassy polymers for example, i.e., polycarbonate (PC) and poly-methyl-methacrylate (PMMA), various experiments from the literature have been simulated. The proposed approach has been validated, since an acceptable agreement between the simulated and experimental results is realized.

Microstructure-Based Flow Stress Model to Predict Machinability of Inconel 718.

Due to its exceptional mechanical and chemical properties at high temperatures, Inconel 718 is extensively utilized in industries such as aerospace, aviation, and marine. Investigating the flow behavior of Inconel 718 under high strain rates and high temperatures is vital for comprehending the dynamic characteristics of the material in manufacturing processes. This paper introduces a physics-based constitutive model that accounts for dislocation motion and its density evolution, capable of simulating the plastic behavior of Inconel 718 during large strain deformations caused by machining processes. Utilizing a microstructure-based flow stress model, the machinability of Inconel 718 in terms of cutting forces and temperatures is quantitatively predicted and compared with results from orthogonal cutting experiments. The model's predictive precision, with a margin of error between 5 and 8%, ensures reliable consistency and enhances our comprehension of the high-speed machining dynamics of Inconel 718 components.

Study on the influence of κ-carbide on the high temperature flow behavior of the medium-Mn lightweight steel: Modeling and characterization

Isothermal compression tests were carried out on the Fe-11Mn-10Al-0.9C medium-Mn lightweight steel in the temperature range from 800 °C to 1100 °C and strain rate range from 0.001 s−1 to 10 s−1 to investigate the influence of κ-carbide on the hot flow behavior. The true stress-true strain curves were analyzed to evaluate the role of κ-carbide on the softening phenomena during straining. It's found flow stress drops more remarkably from the peak point to the end of deformation at low temperature and low strain rate, that condition is favorable for the precipitation of κ-carbide instead of the occurrence of DRX. The activation energy of hot deformation based on the peak stress was calculated as 454.517 kJ mol−1, but this typical strain-compensated Arrhenius-type constitutive equation was found inappropriate to model the flow behavior of the present steel, especially at the low temperature regime. By comparison, a physically-based constitutive model consisting of Bergström's equation (ε<εp) and Kolmogorov-Johnson-Mehl-Avrami's equation (ε>εp) was developed and could predict the flow behavior of the steel accurately. Electron backscattered diffraction (EBSD) analysis revealed the formation of necklace structure at high strain rate and the dynamic recrystallization (DRX) proceeded more adequately with the decrease in strain rate and increase in the deformation temperature. The precipitation of κ-carbides in both austenite grain interior and boundaries (GI and GBs) were enhanced at relatively low deformation temperature (e.g., 800 °C) and greatly improved the peak stress by hindering the dislocation motion. With the increase of deformation, the GB κ-carbide gradually coarsened and induced the decomposition of deformed austenite via the eutectoid reaction (γ→α+κ) at lower strain rate (e.g., 0.001 s−1) due to the sufficient transformation time, consequently leading to the remarkable flow stress softening. The microstructure characterization result was in agreement with variations of parameters (i.e., U, Ω, ρp and nA) with different deformation condition.

Numerical simulation of microstructural failure of natural fibre–hydrogel composites

In this article, we conduct a numerical simulation to investigate the failure mechanism of natural fibre–hydrogel composites under tensile deformation and swelling. Firstly, a physical-based constitutive model is chosen to describe the deformation of the hydrogel matrix. Concurrently, a macroscopic phenomenological hyperelastic constitutive model, incorporated into the material database of Abaqus, is employed to describe the mechanical responses of natural fibres. Then, we implement the model for a numerical analysis. The material parameters of the model for the hydrogel matrix and fibres are determined by a trial-and-error method from the experimental curves of pure hydrogel and fibres; the numerically simulated stress–strain curve of the composites is compared with the experimental one to verify the effectiveness of the simulation. Subsequently, several numerical analyses are performed to discuss the failure mechanism of hydrogel composites caused by the microstructural features of fibres. The findings revealed that fibre protrusion, fibre orientation deviation, and interface strength significantly affect the local failure of the composites during tensile deformation and swelling; the composites’ strength and toughness mainly depend on the cooperation of various microstructural features. These results provide valuable insights into the design of fibre–hydrogel composites.

A novel physics-based modeling approach for tangential fretting contact behavior of jointed interface considering multi-scale effects

A novel physics-based constitutive model has been developed to map the tangential fretting behavior of joint surfaces. The model integrates the fractal normal contact model, which considers multi-scale effects, and the Iwan model through the Coulomb friction law. In this model, a new distribution of yield force is proposed for Jenkins elements, which is determined by fractal topography and material parameters and related to the scale of asperity. The effects of fractal topography, material parameters, and the normal load applied to the joint surface on the tangential responses such as tangential force, tangential stiffness, energy dissipation, and the distribution of yield force have been discussed. It has been found that the fractal parameters D and G have opposite effects on the tangential responses and yield force distribution.

The Constitutive Equation-Based Recrystallization Mechanism of Ti-6Al-4V Alloy during Superplastic Forming

The present paper is concerned with the dynamic recrystallization of the Ti-6Al-4V alloy. Electron Backscatter Diffraction (EBSD) observations are performed after high-temperatures tensile tests, with the temperature ranging from 700 to ~950 °C, and the strain rates varying between 10−4 and 10−2/s. Based on the analysis of flow behavior, the dominant mechanism is identified, and a mechanism map is proposed. In particular, the conditions of 890 °C and strain rates ranging from 10−3 to ~10−2/s serve as the delineating boundary of dynamic recovery (DRV) and dynamic recrystallization (DRX). For superplastic deformation, the dominant softening mechanism is DRV. Consequently, the occurrence of continuous dynamic recrystallization (CDRX) can naturally be ascribed to the process of grain refinement. Then, a multi-scales physical-based constitutive model of CDRX is developed, demonstrating a good agreement is obtained between the experimental and calculated grain sizes, so the above model could be used to describe the grain growth for superplastic deformation. In conclusion, DRV and DRX in the superplastic forming of Ti-6Al-4V are studied in this study, the condition boundaries of their occurrence are distinguished, and a constitutive equation-based CDRX recrystallization mechanism is given, which might be employed in the fracture mechanism research.

Stress softening of nanoparticle-crosslinked hydrogels described using a physics-based damage model

Despite the promising applications of hydrogels, their poor mechanical properties still greatly limit their further applications. To improve the mechanical properties of hydrogels, various strategies have been proposed. Hydrogels with nanoparticle-crosslinked polymer networks show excellent toughness, self-recovery, and other advantages, and thus have great prospects for use in tissue engineering, artificial muscles, flexible electronics, and other fields. There have been experimental and theoretical studies of its damage. However, the underlying microscale physical mechanisms have not been fully elucidated. Herein, we established a physics-based constitutive model to describe the mechanical behavior of nanoparticle-crosslinked hydrogels under cyclic loading. The deformation-induced damage and the rate-dependent damage were explained by the network alteration and kinetics of chain dissociation/association, respectively. The kinetics dissociation/association theory was modified considering the polymer chains that wind around nanoparticles. The Mullins stress softening and recovery during cyclic loading were described. Cyclic loading tests on nanoparticle-crosslinked hydrogels were carried out to verify the proposed constitutive model. It is demonstrated that the model can well describe the mechanical behavior of nanoparticle-crosslinked hydrogels during cyclic loading.

Study on the Flow Behavior of 5052 Aluminum Alloy over a Wide Strain-Rate Range with a Constitutive Model Based on the Arrhenius Model Extension

The formability at room temperature and low speed limits the application of aluminum alloy, while high strain rates positively improve the formability of materials. The constitutive behaviors of materials under high strain rates or impact loadings are significantly different from those under quasi-static conditions, while few constitutive models consider the effect of the mobile dislocation and forest dislocation evolution on the dynamic strain aging (DSA) over a wide strain-rate range. The 5052 aluminum alloy, of which the primary source of strain-hardening is dislocation–dislocation interaction, is widely used in manufacturing automotive covering parts and is considered one of the most promising alloys. Therefore, this study conducts uniaxial tensile tests on AA5052-O under conditions of temperatures ranging from 293 K to 473 K and strain rates ranging from 0.001 s−1 to 3000 s−1, and compares the stress–strain relationships of AA5052-O under different conditions to illustrate the constitutive relationship affected by the dislocation evolution over a wide strain-rate range. The Arrhenius model based on the thermal activation mechanism is modified and extended by considering the effects of dynamic strain aging (DSA), drag stress, and the evolution of mobile dislocation and forest dislocation. Thus, a new physics-based constitutive model for AA5052-O is proposed, which can well reflect the change in strain-rate sensitivity with the strain rate increasing. The mobile dislocation density and total dislocation density are predicted with a modified Kubin–Estrin (KE) model, and the influences of variable mobile dislocation on DSA and dislocation drag are discussed as well. In order to verify the reliability of the new constitutive model, the dislocation densities of the specimens before and after deformation are obtained with TEM and XRD, which are in good agreement with the predicted values. This study also compares the newly proposed model with classic constitutive models using multiple statistical evaluation methods, which shows that the new physics-based constitutive model has not only more clear physical meanings for its parameters but also has a higher prediction accuracy.

Hot workability behaviour of two P92 creep resistant steels: Constitutive analysis

This article reports the flow stress behaviour of two P92 steels at a temperature range of 850–1000°C and a strain rate of 0.1–10 s−1 using the Gleeble® 3500 thermomechanical simulator. A physically-based constitutive model was used to analyse the effects of deformation conditions on the flow stress behaviour during deformation. This model incorporates the influence in the variation of Young’s modulus and the self-diffusion coefficient as affected by temperature. The study developed constitutive equations that predict the flow stress behaviour of the two steels investigated. From the constitutive analysis of the results, the stress exponent n was: 9.8 (steel A) and 10.3 (steel B). The model used the self-diffusion activation energy of steel. The statistical parameters: correlation coefficient of 0.99 (for steel A and B), the absolute average relative error of 2.18% (steel A) and 2.20% (steel B) quantified the applicability of the model. The quantification results show that the constitutive equations developed have high accuracy in predicting the workability of the two P92 steels. The study has shown that this method is applicable in predicting the metal flow pattern of two P92 steels in the metalworking processes.

Hot Deformation Behavior of Hastelloy C276 Alloy: Microstructural Variation and Constitutive Models.

Isothermal deformation experiments of the Hastelloy C276 alloy were executed using the Gleeble-3500 hot simulator at a temperature range of 1000-1150 °C and a strain rate range of 0.01-10 s-1. Microstructural evolution mechanisms were analyzed via transmission electron microscope (TEM) and electron backscatter diffraction (EBSD). Results reveal that the influences of hot compression parameters on the microstructure variation features and flow behaviors of the Hastelloy C276 alloy were significant. The intense strain hardening (SH) effects caused by the accumulation of substructures were promoted when the strain rates were increased, and true stresses exhibited a notable increasing tendency. However, the apparent DRV effects caused by the annihilation of substructures and the increasingly dynamic recrystallization (DRX) behaviors occurred at high compressed temperature, inducing the reduction in true stresses. In addition, a physical-based (PB) constitutive model and a long short-term memory (LSTM) model optimized using the particle swarm optimization (PSO) algorithm were established to predict the flow behavior of Hastelloy C276 alloy. The smaller average absolute relative error and greater relation coefficient suggest that the LSTM model possesses a higher forecasting accuracy than the PB model.

Microstructure evolution mechanisms and a physically-based constitutive model for an Al–Zn–Mg–Cu–Zr aluminum alloy during hot deformation

High-temperature flow features of the Al−Zn−Mg−Cu−Zr aluminum alloy was revealed by hot compression tests. The evolution mechanisms of dislocation clusters, subgrain, and dynamic recrystallization (DRX) grains, are thoroughly explored by EBSD and TEM analysis. Experimental results suggest that the high strain rate can exacerbate dislocation clusters formation, as well as subgrain nucleation/accumulation, inducing the increasing of flow stress. Nevertheless, the noticeable annihilation of substructures, as well as the growth of DRX grains, emerge at the higher temperature, causing the descending of flow stress. Three types of DRX nucleating mechanisms, i.e., discontinuous DRX (DDRX), geometric DRX (GDRX) and continuous DRX (CDRX) are activated in the Al−Zn−Mg−Cu−Zr aluminum alloy during hot compression. Simultaneously, the GDRX often appears at a high compressed temperature or a low strain rate. A physically-based (PB) model is proposed to collaboratively reconstruct true stresses and microstructure evolution features. The estimated values of true stress, DRX fractions and average grain size preferably fit the experimental data, indicating the proposed PB model can precisely catch the thermal compression behaviors and microstructure evolution characteristics of the Al−Zn−Mg−Cu−Zr aluminum alloy.

Large deformation mechanical behavior and constitutive modeling of oriented PMMA

Compared with the unoriented polymethyl methacrylate (PMMA), oriented PMMA has much better mechanical properties, hence widely used in engineering structures. To establish a new constitutive model that is suitable for oriented PMMA at different strain rates and investigate the large deformation mechanical behavior of oriented PMMA, compression experiments of oriented PMMA were conducted at low (0.001 s−1, 0.01 s−1) and high (2000 s−1, 3000 s−1) strain rates. The effects of orientation degree (ϕ) on the mechanical behavior were clarified by making a quantitative comparison of unoriented PMMA (ϕ=0) with the PMMA of various orientation degrees (ϕ=65%, 72%, and 85%). The experimental results demonstrated that orientation degree has different effects on the mechanical behavior of PMMA at different strain rates. Particularly, it was found that the strain hardening behavior after yielding can be significantly enhanced with the increase of orientation degree. According to the experimental results, the influence mechanism of orientation degree on the microscopic deformation of PMMA was revealed, and the theoretical relationship between orientation degree and the entropic resistance was established by introducing an initial deformation gradient. On this basis, a modified physically-based constitutive model of oriented PMMA was proposed. Numerical simulations and analysis of PMMA with different orientation degrees were conducted using the proposed model. The stress–strain curves predicted by the present model were in good agreement with the experimental results, which indicates the proposed constitutive model can well describe the large deformation mechanical behavior of oriented PMMA under different strain rates.

Machine learning of evolving physics-based material models for multiscale solid mechanics

In this work we present a hybrid physics-based and data-driven learning approach to construct surrogate models for concurrent multiscale simulations of complex material behavior. We start from robust but inflexible physics-based constitutive models and increase their expressivity by allowing a subset of their material parameters to change in time according to an evolution operator learned from data. This leads to a flexible hybrid model combining a data-driven encoder and a physics-based decoder. Apart from introducing physics-motivated bias to the resulting surrogate, the internal variables of the decoder act as a memory mechanism that allows path dependency to arise naturally. We demonstrate the capabilities of the approach by combining an FNN encoder with several plasticity decoders and training the model to reproduce the macroscopic behavior of fiber-reinforced composites. The hybrid models are able to provide reasonable predictions of unloading/reloading behavior while being trained exclusively on monotonic data. Furthermore, in contrast to traditional surrogates mapping strains to stresses, the specific architecture of the hybrid model allows for lossless dimensionality reduction and straightforward enforcement of frame invariance by using strain invariants as the feature space of the encoder.

A physically-based constitutive model for amorphous glassy polymers in large deformations

A physically-based constitutive model for predicting the mechanical response of amorphous glassy polymers at room temperature and low strain rates was established within the frame of thermodynamics and kinematics. In our previous work (Lan et al., 2022b), the concepts of permanent entanglement (PE) and dynamic entanglement (DE) were utilized to reproduce the complicated behavior of amorphous glassy polymers from quasi-static to dynamic loading at temperatures from below to near the glass transition temperature. PE formed by the coiling of macromolecular chains is relatively stable and contributes to the yield and unloading behavior. DE formed by the weak interaction between monomers of adjacent segments is unstable and contributes to the macroscopic yield peak and strain hardening. However, due to including many parameters, the model is not easy to apply in practice. In this work, by ignoring the influence of temperature, the previous model (Lan et al., 2022b) was simplified. Taking polycarbonate (PC) and polystyrene (PS) as examples, the simplified model focused on the macroscopic mechanical behavior under simple compression and cyclic simple compression, analyzed the effects of mesh and specimen size on the evolution of shear bands under plane strain compression, and compared the obvious differences in localized deformation of these two types of amorphous polymers under plane strain compression. In addition, the forging process of PC at room temperature was simulated. By comparing the predictions with the experiments, it is demonstrated that the simplified model can reproduce the macroscopic mechanical response of amorphous polymers under simple compression, cyclic simple compression, plane strain compression and forging.

A physically-based constitutive model for a novel heat resistant martensitic steel under different cyclic loading modes: Microstructural strengthening mechanisms

Cyclic responses of a novel heat resistant martensitic steel, 9Cr3Co3W1CuVNbB steel, under different loading modes were studied to reveal its complex strengthening mechanisms at high temperature. Based on the experimental observations, dislocation strengthening, precipitation strengthening by M23C6 phase, MX phase, and Cu-rich phase, and subgrain boundary strengthening were the main mechanisms for its excellent fatigue and creep-fatigue properties. In particular, the dynamic process of interaction between phase and dislocation were studied with the help of molecular dynamics method, and the different contributions of hard and soft phases in the studied steel were determined in fatigue and creep-fatigue loading. Based on these phenomena, a physically-based constitutive model was proposed for both fatigue and creep-fatigue (dwell fatigue at elevated temperature) tests considering various micromechanical mechanisms. Three ways for dislocation annihilation were proposed to simulate the dislocation evolution under different loadings. In addition, the effect of Cu-rich phase was modeled by critical breaking angle and dislocation line tension. The capability of the proposed model under different loading modes was verified by comparing cyclic responses, hysteresis loops, stress relaxation, and dislocation density evolution. The proposed model provides an alternative perspective on understanding fatigue and creep-fatigue behaviors of heat resistant martensitic steels owning the similar strengthening mechanisms.

The Parameter Identification of Physical-Based Constitutive Model by Inverse Analysis Method for Application in Near-Net Shape Forging of Aluminum Wheels

A reliable constitutive model is a prerequisite to simulate a new complex forming technique, which is represented by the near-net shape forging process of aluminum wheels in this study. The aim of the present work was to identify the physical-based constitutive model parameters of Al-Zn-Mg alloy via the inverse analysis method based on experimental data and numerical analysis: the stress–strain curves at different temperatures and strain rates were obtained based on hot compression tests. On the basis of the shape of the compressed specimens and experimental force–displacement data, the friction coefficients and the optimized physical-based constitutive model were determined by using two-times inverse analysis techniques. Results showed that the global average error between the predicted and experimental force–displacement curves was only 3.8%. Then, thermo-mechanical finite element models were built in the Deform-3D software to simulate the two-stage forging processes of the near-net shape forging of aluminum alloy wheels, and the results showed that the predicted load–stroke curves were in good agreement with the experimental ones in all forging stages, which verified the prediction accuracy of the optimized physical-based constitutive model. In addition, the identification of the physical-based constitutive model parameters by the inverse analysis method provides a theoretical basis for formulating and optimizing the near-net shape forging process parameters of aluminum alloy wheels.

Characterization of fibronectin properties by integrated micro-fluidic experiments and fluid-structure interaction simulations

Fibronectin (Fn) has been observed to assemble in the extracellular matrix (ECM) of cell culture and stretch in response to the external force. The alteration of molecule domain functions generally follows the extension of Fn. Several researchers have investigated fibronectin extensively in molecular architecture and conformation structure. However, the bulk material behavior of the Fn in the ECM has not been fully depicted at the cell scale, and many studies have ignored physiological conditions. Conversely, microfluidic techniques that explore cellular properties based on cell deformation and adhesion have emerged as a powerful and effective platform to study cell rheological transformation in a physiological environment. However, directly quantifying properties from microfluidic measurements remains a challenge. Therefore, it is an efficient way to combine experimental measurements with a robust and reliable numerical framework to calibrate the mechanical stress distribution in the test sample. In this paper, we present a monolithic Lagrangian fluid–structure interaction (FSI) approach within the Optimal Transportation Meshfree (OTM) framework that enables the investigation of the adherent Red Blood Cell (RBC) interacting with fluid and overcomes the drawbacks of the traditional computational tools such as the mesh entanglement and interface tracking, etc. This study aims to assess the material properties of the RBC and Fn fiber by calibrating the numerical predictions to experimental measurements. Moreover, a physical-based constitutive model will be proposed to describe the bulk behavior of the Fn fiber inflow, and the rate-dependent deformation and separation of the Fn fiber will be discussed.

A simple physics-based constitutive model to describe strain hardening in a wide strain range

A simple physics-based constitutive model to describe strain hardening in a wide strain range

A visco-hyperelastic model for hydrogels with tunable water content

Hydrogels without special treatment would lose water dramatically, which significantly alters their properties. No physically-based constitutive models have been developed so far to quantify the evolution of visco-hyperelastic responses with water content of hydrogels. In this work, systematical experiments are performed on polyacrylamide (PAAm) hydrogels with varied water content. The results reveal that the increase of modulus caused by deswelling is much more pronounced than the decrease of modulus caused by swelling. A more significant strain-softening phenomenon and a transition from almost pure hyperelastic behaviors to apparent viscoelastic behaviors are observed as the water content decreases. To fully capture the experimental observations, a micromechanical model is developed. In this model, the rate-independent hyperelastic response comes from the contributions of both cross-linked networks and entanglements, while the rate-dependent viscoelastic response arises from the reptation of free chains. The relations between model parameters (e.g., cross-linked shear modulus, entangled shear modulus, and relaxation time) and water content are further derived using the scaling law in polymer physics. The developed visco-hyperelastic model exhibits remarkable prediction ability for PAAm hydrogels with a wide water content distribution. The finite element analysis also verifies that the model can describe the mechanical responses of hydrogels in complex loading conditions. The current work deepens our fundamental understanding on the effect of water content on mechanical behaviors of hydrogels. It also provides an efficient theoretical framework to predict the performance of hydrogels in practical applications.

A physically-based constitutive model for the prediction of yield strength in the precipitate-hardened high-entropy alloys

A physically-based constitutive model for the prediction of yield strength in the precipitate-hardened high-entropy alloys