Viscoplastic Constitutive Model Research Articles

A non-unified viscoplastic constitutive model based on irreversible thermodynamics and creep-fatigue life prediction for Type 316 stainless

In this work, to describe the cycle behavior considering fatigue-creep interaction, a non-unified viscoplastic constitutive model for 316 stainless steel is derived within the irreversible thermodynamic framework. The internal variables considering kinematic and isotropic hardening properties are selected to construct the evolution equation of visco-plastic and creep terms. The proposed constitutive model was validated by the comparison with the existing literature. It was manifested that this constitutive model could successfully predict the hardening behavior and stress relaxation process under the cyclic loading. During the dwell period, the increment of the inelastic strain is decomposed into the viscoplastic and creep term. The viscoplastic deformation dominates first stage of the stress relaxation, while the stable stage is controlled by the creep term. Finally, the predicted values of mean stress are taken into the Manson-Coffin law, the low cycle fatigue life prediction are carried out based on the numerical model, which showed robust correlation with experimental results.

Application of unified constitutive model of 34CrNiMo6 alloy steel and microstructure simulation for flexible skew rolling hollow shafts

Flexible skew rolling (FSR) is a novel rolling process for shaft parts, which is capable of rolling the hollow shafts. The microstructure of shaft parts is very important to its service performance, and the application of finite element (FE) method has been widely used to simulate microstructure evolution. Firstly, hot compression tests were performed to obtain the flow curves and corresponding microstructure states of the steel under the conditions of 950–1100 °C and 0.1–10 s−1. Secondly, the average grain size (AGS) under different conditions was recorded. A unified viscoplastic constitutive model considering recrystallization is established to characterize the high-temperature deformation and microstructure evolution of 34CrNiMo6 alloy steel. A genetic algorithm (GA) is used to solve the material constants of the constitutive model. The error of the predicted flow stress is 3.632%, and the error of the predicted grain size is less than 10%, which indicates that the established constitutive model can precisely predict the flow stress and grain size variation of 34CrNiMo6 alloy steel. The constitutive model was coded and embedded into the FE software Simufact via a user-defined subroutine interface to simulate the grain evolution during a uniaxial hot compression test and microstructure evolution of alloy steel in the FSR process. The FSR trials of hollow shafts were conducted and the microstructure at different positions of rolled-part was observed to validate the correctness of the model. The FE simulation results of grain size are compared with the experimental results, and the results are in good agreement. The internal variable constitutive model established in this paper can predict and reveal the microstructure evolution of FSR hollow shafts very well, and the AGS of shaft parts rolled by FSR are distinctly refined.

Studying the strengthening mechanism and thickness effect of elastomer coating on the ballistic-resistance of the polyurea-coated steel plate

Experiments have shown that the ballistic performance of the steel plate improves significantly after coating polyurea at the impact face. However, the strengthening mechanism of the elastomer coating on the ballistic-resistance is not understood well until now. In this paper, the strengthening mechanism and thickness effect of the coating under fragment simulating projectiles (FSP) impact are studied through numerical and experimental analysis. Firstly, a viscoplastic constitutive model of polyurea is developed based on experimental characterization and thermodynamic equation of state. It can capture strongly nonlinear volumetric behavior and impact-induced shearing stiffening and strengthening considering the coupling of high pressure, high temperature, and high strain rate under ballistic impact. Then, by applying this newly developed viscoplastic model of polyurea, the underlying ballistic-resistant mechanism of the polyurea-coated steel plate is numerically studied. The analysis shows that the dynamic behavior of polyurea under ballistic impact and propagating regulation of impact wave jointly play the key role. One side, the impact-induced stiffening and strengthening of the polyurea change the failure modes of the steel plate and considerably improve the ballistic-resistance of the structure. The other side, increasing coating thickness can only provide the limited benefit for improving the ballistic-resistance of the structure, as obtained in experiments. For the impact-face-coated steel plate, the low-thickness polyurea coating suffering from FSP impact can increase the frequency of the compressive wave reflection-superposition on the high-impedance polyurea/steel interface before the energy transfer from the impacted location. This helps to improve the pressure level and enhance the instantaneous energy storage and dissipation of the polyurea per volume significantly. However, increasing coating thickness can make the pressure level and the specific energy density of polyurea decrease gradually during penetration. It is also found that the energy dissipation of FSP during penetration is reduced after increasing the coating thickness because of the erosion mitigation from the structure. The new insight on the strengthening mechanism of elastomer coating will be helpful for the light armor design.

A study of the pore size effect on the formation of hot spot in a 1,3,5,7-tetranitro-1,3,5,7-tetrazocane crystal under a low-to-medium shock velocity

ABSTRACT It is rather difficult to observe, record and analyze the pore-collapse-induced initiation of a 1,3,5,7-tetranitro-1,3,5,7-tetrazocane or HMX crystal via experiment because it is an extreme phenomenon involving multiphysics (such as shock, phase change of HMX) and chemical reactions (thermal decomposition of HMX) occurring in microseconds or even nanoseconds. Herein, a mechanical-thermal-chemical coupled finite element model is proposed to simulate the pore collapse in a HMX crystal under a shock loading at velocities under 500 m/s. A viscoplastic constitutive model and a Birch-Murnaghan equation of state (EoS) are employed to predict the mechanical response of the HMX crystal. The melting of the HMX crystal is also considered. A multi-step thermal-decomposition model is employed to simulate the chemical reaction of the HMX. Firstly, numerical simulations were implemented for a few plane shock experiments and it is demonstrated that the material model of HMX have reasonable accuracy. Then, the pore collapse in a HMX crystal under a shock at 500 m/s was simulated. It is shown that severe plastic deformation and high-velocity impact of HMX jet both contribute to the temperature rise of local materials. Finally, the influence of pore size on the calculated maximum temperature of the HMX crystal was simulated under various shock velocities ranging from 100 m/s to 500 m/s. It seems that there exists an “optimal” pore size for the HMX crystal to obtain the highest temperature under a shock, which is explained with simulation results.

STRAIN RATE–DEPENDENT BEHAVIOR OF UNCURED RUBBER: EXPERIMENTAL INVESTIGATION AND CONSTITUTIVE MODELING

ABSTRACT The strain rate dependence of uncured rubber is investigated through a series of tensile tests (monotonic, multistep relaxation, cyclic creep tests) at different strain rates. In addition, loading/unloading tests in which the strain rate is varied every cycle are carried out to observe their dependence on the deformation history. A strain rate–dependent viscoelastic–viscoplastic constitutive model is proposed with the nonlinear viscosity and process-dependent recovery properties observed in the test results. Those properties are implemented by introducing evolution equations for additional internal variables. The identified material parameters capture the experiments qualitatively well. The proposed model is also evaluated by finite element simulations of the building process of a tire, followed by the in-molding.

Experimental And Numerical Modelling of Cyclic Softening and Damage Behaviors for a Turbine Rotor Material at Elevated Temperature

In order to better understand the physical process of deformation and cyclic softening a 12% Cr martensitic stainless steel FV566 has been cyclically tested at high temperature in strain control. Increase in temperature was found to increase the cyclic life, softening rate and viscous stress magnitude. An increase in the dwell time led to the acceleration of the material degradation. The microstructure changes and dominating deformation mechanisms were investigated by means of scanning electron microscopy, electron backscatter diffraction and transmission electron microscopy. The results have revealed a gradual sub-grain coarsening, transformation of lath structure into fine equiaxed sub-grains, and misorientation angle development in blocks and packets until material failure. Further, a unified viscoplastic constitutive model coupled with a physically-based damage variable, is proposed to capture the cyclic mechanical behavior and microstructural evolution of the material at elevated temperature. The mechanical strength can be reduced by the decrease in the dislocation density, the coarsening of the martensitic lath and the loss of the martensitic structure under cyclic loading. The proposed physically-based damage variable is driven by the evolutions of dislocation density and martensitic lath width. The good comparisons with test results mean that the proposed model can reasonably model the cyclic elastic-viscoplastic constitutive behavior of the material at high temperature.

Modelling lead-rubber seismic isolation bearings using the unified mechanics theory

Lead-rubber seismic isolation bearings (LRB) have been installed in a number of essential and critical structures, like hospitals, universities and bridges, in order to provide them with period lengthening and the capacity of dissipating a considerable amount of energy to mitigate the effects of strong ground motions. Therefore, studying the damage mechanics of this kind of devices is fundamental to understand and accurately describe their thermo-mechanical behavior, so that seismically isolated structures can be designed more safely. Hitherto, the hysteretic behavior of LRB has been modeled using 1) Newtonian mechanics and empirical curve fitting degradation functions, or 2) heat conduction theories and idealized bilinear curves which include degradation effects. The reason for using models that are essentially phenomenological or that contain some adjusted parameters is the fact that Newton’s universal laws of motion lack the term to account for degradation and energy loss of a system. In this paper, the Unified Mechanics Theory – which integrates laws of Thermodynamics and Newtonian mechanics – is used to model the force-displacement response of LRB. Indeed, there is no need for curve fitting techniques to describe their damage behavior because degradation is calculated at every point using entropy generation along the Thermodynamics State Index (TSI) axis. A finite element model of a lead-rubber bearing was constructed in ABAQUS, where a user material subroutine UMAT was implemented to define the Unified Mechanics Theory equations and the viscoplastic constitutive model for lead. Finite element analysis results were compared with experimental test data.

A computational framework for modeling distortion during sintering of binder jet printed parts

Sintering of binder jet 3D printed (BJ3DP) parts results in significant nonlinear distortion with typical shrinkage value of 5–20%, which makes design for BJ3DP and post-machining difficult. In this work, a computational modeling framework with calibration and validation procedure is developed to simulate distortion during sintering of BJ3DP parts accurately for the first time. The computational model employs the finite element analysis with a viscoplastic constitutive model that accounts for effects of gravity and friction. A calibration procedure is proposed to obtain values of different model parameters systematically through dilatometric, gravity bending, and grain growth experiments. For model validation, four bridges with different spans and a second part with a circular hole and two free overhangs are designed. The calibration procedure is applied to develop a computational model for sintered 316L stainless steel BJ3DP parts. The displacements at various locations on the sintered parts are simulated using the calibrated model and are found to have errors less than 3.5% compared to those obtained by experiment.

Elastic–viscoplastic constitutive theory of dense granular flow and its three-dimensional numerical realization

The problem of the movement of dense granular media is common in industrial processes. Dense granular media cannot only show solid-like properties when stacked but can also flow like a liquid, exhibiting properties of fluids. Simultaneous modeling and description of these two states remain a challenge. In this study, a new constitutive model describing the motion of dense granular media is established. A linear elastic model is used to describe the solid phase. After reaching the plastic yield criterion, a viscoplastic constitutive model based on rheology is used to describe the liquid phase. The transitional relationship between these two models is deduced in detail, and the elastic–viscoplastic constitutive theory that describes the movement of dense granular media is more in line with physical reality. Smoothed particle hydrodynamic method is used to discretely solve the new model, and the relationship between smoothed particles and actual particles is illustrated. A series of basic calculation tests is used to verify the theoretical model and numerical method. Through a comparison with experiments and other numerical results, it is shown that the theoretical model and numerical method are suitable for the analysis of the movement of dense granular media and have important practical value for the preparation and processing of similar materials, three-dimensional printing, and mineral mining.

A bayesian optimisation methodology for the inverse derivation of viscoplasticity model constants in high strain-rate simulations

We present an inverse methodology for deriving viscoplasticity constitutive model parameters for use in explicit finite element simulations of dynamic processes using functional experiments, i.e., those which provide value beyond that of constitutive model development. The developed methodology utilises Bayesian optimisation to minimise the error between experimental measurements and numerical simulations performed in LS-DYNA. We demonstrate the optimisation methodology using high hardness armour steels across three types of experiments that induce a wide range of loading conditions: ballistic penetration, rod-on-anvil, and near-field blast deformation. By utilising such a broad range of conditions for the optimisation, the resulting constitutive model parameters are generalised, i.e., applicable across the range of loading conditions encompassed the by those experiments (e.g., stress states, plastic strain magnitudes, strain rates, etc.). Model constants identified using this methodology are demonstrated to provide a generalisable model with superior predictive accuracy than those derived from conventional mechanical characterisation experiments or optimised from a single experimental condition.

High-Temperature Viscoplastic Constitutive Model and Rheological Behavior Analysis for Axle Steel

High-Temperature Viscoplastic Constitutive Model and Rheological Behavior Analysis for Axle Steel

A novel fatigue-oxidation-creep life prediction method under non-proportional loading

In this paper, a new life assessment framework is proposed based on the elastic-viscoplastic modeling and the damage behavior for the structural component under multiaxial non-proportional loading at high temperature. The viscoplastic constitutive model with the ability to capture the non-proportional hardening effect is used to obtain the stress–strain fields, in which a new method based on the rotation of strain axis is proposed to evaluate the notch rotation factor. The damage model, which can comprehensively capture the multiaxial fatigue-oxidation-creep behaviors, is used to assess the failure life. In addition, the proposed framework is evaluated by the life results under proportional and non-proportional fatigue loadings at 650 °C, and the errors are found to be within a factor of 2.

A nonlinear viscoelastic–viscoplastic constitutive model for adhesives under creep

In this study, we consider the nonlinear viscoelastic–viscoplastic behavior of adhesive films in scarf joints. We develop a three-dimensional nonlinear model, which combines a nonlinear viscoelastic model with a viscoplastic model using the von Mises yield criterion and nonlinear kinematic hardening. We implement an iterative scheme for the viscoplastic solution and a numerical algorithm with stress correction for the combined viscoelastic–viscoplastic model into finite element analysis. The viscoelastic component of the model is calibrated using creep-recovery data from adhesive films in scarf joints. The viscoplastic parameters are calibrated from the residual strains of recovered creep tests with varying load durations. A two-dimensional form of the model shows good agreement with the three-dimensional model for the scarf joint considered in this work and is compared with experiment. The numerical results show favorable agreement with the experimental creep and recovery responses of two epoxy adhesive systems. We also discuss the contribution of nonlinear viscoelasticity and viscoplasticity to the stress/strain distribution along the adhesive center lines. Viscoplasticity tends to lower the stress concentration.

A particle‐continuum coupling method for multiscale simulations of viscoelastic–viscoplastic amorphous glassy polymers

AbstractIn this contribution, we present a partitioned‐domain method coupling a particle domain and a continuum domain for multiscale simulations of inelastic amorphous polymers under isothermal conditions. In the continuum domain, a viscoelastic–viscoplastic constitutive model calibrated from previous molecular dynamics (MD) simulations is employed to capture the inelastic properties of the polymer. Due to the material's rate‐dependence, a temporal coupling scheme is introduced. The influence of the time‐related parameters on the computational cost and accuracy is discussed. With appropriate parameters, multiscale simulations of glassy polystyrene under various loading conditions are implemented to showcase the method's capabilities to capture the mechanical behavior of polymers with different strain rates and with non‐affine deformations of the MD domain.

Revealing ductile/quasi-cleavage fracture and DRX-affected grain size evolution of AA7075 alloy during hot stamping process

The microstructural evolution, including ductile fracture modes and grain size at elevated temperature, exhibited significant effects on the macroscopic rheological behaviour and restricted the formability of the high-strength AA7075 alloy employed in the hot stamping process. In this study, AA7075 alloy was subjected to uniaxial hot tensile tests at deformation temperatures of 350–450 ℃ and strain rates of 0.01–1 s−1 to analyse the thermal rheological behaviour, damage and grain size evolution, in tandem with the preferred grain orientations affected by intergranular and intracrystalline evolution. A set of improved viscoplastic damage constitutive models was established, which consider the combined interactions of dislocation density and grain size as well as the ductile and quasi-cleavage fracture modes, to elaborate and reveal the fracture modes and grain size evolution of AA7075 alloy during the hot stamping process. Particularly, the evolution of dislocations accumulation was established incorporated with DRX-affected grain refinement. Subsequently, the material parameters were determined and calibrated based on a genetic algorithm, and the feasibility of the constitutive model was verified by simulations of uniaxial tension experiments. Finally, a finite element (FE) simulation of a hot formed T-shaped specimen was carried out. The mesoscopic and macroscopic deformation behaviours, including the evolution of grain size, damage and thickness distribution, were predicted, and the influences of grain size and damage on the formability were explained. Especially it was found that the grain size of the T-shaped components at the punch fillet was the largest, while the grain size at the bottom of the T-parts was the smallest. In addition, severe thinning region of T-shaped parts possess the largest normalized grain size. This study provides theoretical guidance and a scientific basis for the application and forming control of AA7075 alloy in hot stamping processes.

Study of the Mechanical Behavior of Municipal Solid Waste Landfill Using a Viscoplastic Constitutive Model

As long as there is the need for disposal of household waste there will be the need to understand the phenomena taking place in storage facilities for nonhazardous waste (municipal solid waste landfill). The understanding of landfill technology is of great importance because of its ever-changing state, whether mechanical, chemical or hydrological. In this context, there is a need to better understand the stress-strain behavior evolution with time of the landfilled waste. Based on triaxial and oedometric compression tests of municipal solid waste samples ranging from fresh to degraded waste, a viscoplastic constitutive model (Burgers creep-viscoplastic model) is used to describe the behavior of the municipal solid waste under loading. This model is able to adequately capture the stress-strain and pore water pressure response of the municipal solid waste at different ages. To illustrate its applicability, settlements due to the incremental loading of waste with time are predicted for a typical municipal solid waste landfill. The proposed model predicts the total settlement of a storage facilityin a range similar to results published in the literature. An extension of the studied municipal solid waste landfill was also investigated.

A physically-based method for predicting high temperature fatigue crack initiation in P91 welded steel

A methodology is presented for physically-based prediction of high temperature fatigue crack initiation in 9Cr steels, with a focus on material inhomogeneity due to welding-induced metallurgical transformations. A modified form of the Tanaka-Mura model for slip band formation under cyclically-softening conditions is implemented in conjunction with a physically-based unified cyclic viscoplasticity constitutive model. The physically-based constitutive model accounts for the key strengthening mechanisms, including precipitate hardening and hierarchical grain boundary strengthening, successfully predicting cyclic softening in 9Cr steels. A five-material, finite element model of a P91 cross-weld test specimen, calibrated using the physically-based yield strength and constitutive models, successfully predicts the measured detrimental effect of welding on high temperature low-cycle fatigue crack initiation for P91 cross weld tests, via the modified Tanaka-Mura model. A key finding of the current work is the requirement to adopt an energy-based Tanaka-Mura method to account for cyclic softening in 9Cr steels, with packet size as the critical length-scale for slip band formation. The work demonstrates the significant effect of highly flexible operation on the service life of welded connections.

Multiphase theory of granular media and particle simulation method for projectile penetration in sand beds

Studying projectile penetration in sand beds is of great significance for solving practical problems in the fields of weapon damage, consolidation of foundations, and mine explosions. In this study, a coupled model using the elastic-viscoplastic-kinetic constitutive relation and discrete particle dynamics was established to describe the multiple phases of sand-like materials, namely, the solid-like, liquid-like, gas-like, and inertial discrete phases. A linear elastic model was used to describe the solid-like phase; however, after the plastic yield point was reached, a viscoplastic constitutive model based on rheology was used to describe this liquid-like phase. When the volume fraction of the particles reduced to a certain value, the gas-like phase was described using the kinetic theory of granular flow; however, when the assumption of binary collisions was no longer satisfied, discrete particle dynamics was used to describe this inertial discrete phase. Smoothed discrete particle hydrodynamics coupled with the discrete element method was used to discretize our model based on established multiphase models of sand-like materials. Our new theoretical model and numerical method were used to simulate the high-speed penetration of spherical and slender projectiles in dry sand accumulation. A comparison with the results from experiments and other numerical methods shows that the new numerical method is suitable for describing the different motion states of sand-like materials owing to different projectile penetration velocities. Finally, the ricochet phenomenon of a conical projectile penetrating a sand bed was captured, which further verifies the applicability of our model for solving engineering problems.

A new simplified method for calculating short-term and long-term consolidation settlements of multi-layered soils considering creep limit

The long-term consolidation settlement of soft soils under infrastructures is seriously concerned in coastal areas. In practice, soft soil ground is usually composed of multiple layers with different properties, and the effect of soil creep is nonnegligible. However, in conventional consolidation analysis, creep is seldom included during the “primary” consolidation. With conventional creep model, creep strain will reach infinity with time, which is unreasonable in the long-term view. In this study, a new simplified method based on Hypothesis B is presented to calculate both short-term and long-term consolidation settlements of multi-layered soils exhibiting non-linear creep. There are three main characteristics for this new simplified method: (a) the consolidation analysis for multi-layered soil is conducted using spectral method; (b) a nonlinear creep function with creep limit is incorporated to calculate both short-term and long-term creep settlements; (c) the “primary” consolidation and creep are calculated independently and combined with an empirical parameter α together with the consolidation degree U for correcting the creep settlement. Finite element analysis with a self-developed Elastic Visco-Plastic (EVP) constitutive model considering creep limit was also carried out. Verifications by field cases and finite element simulation demonstrate the efficiency and accuracy of the new simplified method in calculating the long-term settlements of soft soil ground under varied engineering conditions. Influences of major parameters selection in the calculation of the new simplified method are also discussed.

Characterization and modeling of the ratcheting behavior of unidirectional off-axis composites

The ratcheting behavior of unidirectional carbon/epoxy composites under cyclic off-axis loading with non-zero average stress was investigated, with a focus on the influence of peak stress (stress ratio R = 0) and fiber orientation. The experimental results show that nonlinear hysteresis and ratcheting behaviors heavily depend on fiber orientation and loading stress. Herein, the evolutionary features of the nonlinear hysteresis behavior and ratcheting deformation of the material are discussed. Furthermore, a creep damage-coupled viscoplastic cyclic constitutive model based on the nonlinear hysteresis behavior and cyclic creep is proposed to simulate the ratcheting behavior of carbon fiber composites under different stress levels and with various fiber orientations. The proposed model can adequately predict the nonlinear response during loading, hysteresis behavior during unloading and reloading, and ratcheting phenomena after a large number of cycles.