Constitutive modeling of hot deformation behavior of X20Cr13 martensitic stainless steel with strain effect

Hot deformation behavior ofX20Cr13 martensitic stainless steel was investigated by conducting hot compression tests on Gleeble-1500D thermo-mechanical simulator at the temperature ranging from 1173 to 1423 K and the strain rate ranging from 0.001 to 10 s^-1. The material constants of a and n, activation energy Q and A were calculated as a function of strain by a fifth-order polynomial fit. Constitutive models incorporating deformation temperature, strain rate and strain were developed to model the hot deformation behavior of X20Cr13 martensitic stainless steel based on the Arrhenius equation. The predictable efficiency of the developed constitutive models of X20Cr13 martensitic stainless steel was analyzed by correlation coefficient and average absolute relative error which are 0.996 and 3.22%, respectively.

Constitutive modeling and springback simulation for 2524 aluminum alloy in creep age forming

The constitutive modeling and springback simulation for AA2524 sheet in creep age forming（CAF） process were presented.A series of creep aging tests were performed on AA2524 at the temperature of 180-200 °C and under the stress of 140-210 MPa for 16 h.Based on these experimental data,material constitutive equations which can well characterize creep aging behaviors of the tested alloy were developed.The effect of interior stress distributed along the sheet thickness on springback was simulated using FE software MSC.MARC by compiling the established constitutive models into the user subroutine.The simulation results showed that the amount of sheet springback was 61.12% when merely considering tensile stress existing along the sheet thickness;while sheet springback was up to 65.93% when taking both tensile and compressive stresses into account.In addition,an AA2524 rectangular sheet was subjected to CAF experiment in resistance furnace.The springback value of the formed rectangular sheet was 68.2%,which was much closer to 65.93%.This confirms that both tensile and compressive stresses across the sheet thickness should be considered in accurately predicting springback of the sheet after forming,which can be more consistent with experimental results.

Effect of pre-deformation on aging creep of Al-Li-S4 alloy and its constitutive modeling

A set of uniaxial tensile creep tests at different pre-deformations, aging temperatures and stress levels were carried out for Al-Li-S4 alloy, and the creep behavior and the effects of pre-deformation on mechanical properties and microstructures were determined under basic thermodynamics conditions of aging forming. The results show that pre-deformation shortens the time of primary creep and raises the second steady-state creep rate. Then, the total creep strain is greater, but in the range of test parameters it is still smaller than that without pre-deformation. In addition, transmission electron microscopy（TEM） observation shows that pre-deformation promotes the formation of T1 phase and θ′ phase and makes them distribute more dispersively, while inhibits the generation of δ′ phase, which leads to the improvement of mechanical properties of the alloy. A unified constitutive model reflecting the effects of aging mechanism, stress levels and different pre-deformations was established. The fitting results agree with the experimental data well.

Constitutive modeling for high temperature flow behavior of a high-strength manganese brass

The hot compressive deformation behaviors of ZHMn34-2-2-1 manganese brass are investigated on Thermecmastor-Z thermal simulator over wide processing domain of temperatures （923–1073 K） and strain rates （0.01–10 s^–1）. The true stress–strain curves exhibit a single peak stress, after which the stress monotonously decreases until a steady state stress occurs, indicating a typical dynamic recrystallization. The analysis of deviation between strain-dependent Arrhenius type constitutive and experimental data revealed that the material parameters （n, A, and Q） for the ZHMn34-2-2-1 manganese brass are not constants but varies as functions of the deformation conditions. A revised strain-independent sine hyperbolic constitutive was proposed, which considered the coupled effects of strain rate temperature and strain on material parameters. The correlation coefficient and the average absolute relative error are used to evaluate the accuracy of the established constitutive model. The quantitative results indicate that the proposed constitutive model can precisely characterize the hot deformation behavior of ZHMn34-2-2-1 manganese brass.

Continuum Constitutive Modeling for Isotropic Hyperelastic Materials

The partial differential equation for isotropic hyperelastic constitutive models has been postulated and derived from the balance between stored energy and stress work done. The partial differential equation as a function of three invariants has then been solved by Lie group methods. With geometric meanings of deformations, the general solution boils down to a particular three-term solution. The particular solution has been applied for several isotropic hyperelastic materials. For incompressible materials, vulcanized rubber containing 8% sulfur and Entec Enflex S4035A thermoplastic elastomer, three coefficients have been determined from uniaxial tension data and applied to predict the pure shear and equibiaxial tension modes. For a slightly compressible rubber material, the coefficients have also been extracted from the confined volumetric test data.

THE RATE-INDEPENDENT CONSTITUTIVE MODELING FOR POROUS AND MULTI-PHASE NANOCRYSTALLINE MATERIALS

To determine the time-independent constitutive modeling for porous and multi- phase nanocrystalline materials and understand the effects of grain size and porosity on their mechanical behavior, each phase was treated as a mixture of grain interior and grain bound- ary, and pores were taken as a single phase, then Budiansky＇s self-consistent method was used to calculate the Young＇s modulus of porous, possible multi-phase, nanocrystalline materials, the prediction being in good agreement with the results in the literature. Further, the established method is extended to simulate the constitutive relations of porous and possible multi-phase nanocrystalline materials with small plastic deformation in conjunction with the secant-moduli approach and iso-strain assumption. Comparisons between the experimental grain size and porosity dependent mechanical data and the corresponding predictions using the established model show that it appears to be capable of describing the time-independent mechanical behaviors for porous and multi-phase nanocrystalline materials in a small plastic strain range. Further discussion on the modification factor, the advantages and limitations of the model developed were present.

Constitutive Modeling and Dynamic Recrystallization Mechanisms of an Ultralow-carbon Microalloyed Steel During Hot Compression Tests

The hot deformation behavior of an ultralow-carbon microalloyed steel was investigated using an MMS-200 thermal simulation test machine in a temperature range of 1073-1373 K and strain rate range of 0.01-10 s-1.The results show that the flow stress decreases with increasing deformation temperature or decreasing strain rate.The strain-compensated constitutive model based on the Arrhenius equation for this steel was established using the true stress-strain data obtained from a hot compression test.Furthermore,a new constitutive model based on the Z-parameter was proposed for this steel.The predictive ability of two constitutive models was compared with statistical measures.The results indicate the new constitutive model based on the Z-parameter can more accurately predict the flow stress of an ultralow-carbon microalloyed steel during hot deformation.The dynamic recrystallization(DRX)nucleation mechanism at different deformation temperatures was observed and analyzed by transmission electron microscopy(TEM),and strain-induced grain boundary migration was observed at 1373 K/0.01 s^-1.

Constitutive modeling of particle reinforced rubber-like materials

The present study is focused on the constitutive modeling for the mechanical behavior of rubber reinforced with filler particles.A filler-dependent energy density function is proposed with all the continuum mechanics-based necessities of an effective hyperelastic material model.The proposed invariant-based energy function comprises a single set of material parameters for a material subjected to several modes of loading conditions.The model solution agrees well with existing experimental results.Later,the effect of varying concentrations of filler particles in the rubber matrix is also studied.

Constitutive modeling for mechanical behaviors of geomaterials, newdesigns and techniques in geotechnical engineering

This Special Issue of the Journal of Rock Mechanics and GeotechnicalEngineering （JRMGE） contains 13 papers prepared by internationalexperts on various general topics in geomechanics, rockmechanics and geotechnical engineering. It represents a usefulmix of theoretical developments, testing and practical applications.We present in the following brief details in the papers, alphabeticallyin accordance with the last name of the first author.Barla presents a review of tunneling techniques with emphasison the full-face method combining full-face excavation and facereinforcement by means of fiber-glass elements with a yieldcontrolsupport. This method has been used successfully in difficultgeologic conditions, and for a wide spectrum of ground situations.The validation of the method with respect to the Saint Martin LaPorte access adit along the LyoneTurin Base tunnel experiencingseverely squeezing conditions during excavation is also includedin the paper. The numerical modeling with consideration of therock mass time-dependent behavior showed a satisfactory agreementwith monitoring results.

Constitutive modeling of flow behavior of precipitation-hardened AA7022-T6 aluminum alloy at elevated temperature

The thermomechanical behavior of precipitation-hardened aluminum alloy AA7022-T6 was studied using isothermal compression at temperatures of 623−773 K and strain rates of 0.01−1 s^−1.The experimental results indicated that dynamic recrystallization(DRX)is a predominant hot deformation mechanism,especially at elevated temperatures and low strain rates.The modified Johnson−Cook(J−C)and the strain compensated Arrhenius-type models were developed to predict the hot flow behavior under different deformation conditions.The correlation coefficients of modified J−C model and the strain compensated Arrhenius-type models were 0.9914 and 0.9972,respectively,their average relative errors(ARE)were 6.074%and 4.465%,respectively,and their root mean square errors(RMSE)were 10.611 and 1.665 MPa,respectively,indicating that the strain compensated Arrhenius-type model can predict the hot flow stress of AA7022-T6 aluminum alloy with an appropriate accuracy.

Hot deformation behavior and constitutive modeling of Q345E alloy steel under hot compression

Q345E as one of typical low alloy steels is widely used in manufacturing basic components in many fields because of its eminent formability under elevated temperature. In this work, the deformation behavior of Q345E steel was investigated by hot compression experiments on Gleeble-3500 thermo-mechanical simulator with the temperature ranging from 850 ℃ to 1150 ℃ and strain rate ranging from 0.01 s-1 to 10 s-1. The experimental results indicate that dynamic softening of Q345E benefits from increasing deformation temperature and decreasing strain rate. The mathematical relationship between dynamic softening degree and deformation conditions is established to predict the dynamic softening degree quantitatively, which is further proved by some optical microstructures of Q345E. In addition, the experimental results also reveal that the stress level decreases with increasing deformation temperature and decreasing strain rate. The constitutive equation for flow stress of Q345E is formulated by Arrihenius equation and the modified Zener-Hollomon parameter considering the compensation of both strain and strain rate. The flow stress values predicted by the constitutive equation agree well with the experimental values, realizing the accurate prediction of the flow stress of Q345E steel under hot deformation.

Constitutive Modeling for Ti-6Al-4V Alloy Machining Based on the SHPB Tests and Simulation

A constitutive model is critical for the prediction accuracy of a metal cutting simulation. The highest strain rate involved in the cutting process can be in the range of 104-106 s 1. Flow stresses at high strain rates are close to that of cutting are difficult to test via experiments. Split Hopkinson compression bar （SHPB） technology is used to study the deformation behavior of Ti-6Al-4V alloy at strain rates of 10 -4-10 4s- 1. The Johnson Cook （JC） model was applied to characterize the flow stresses of the SHPB tests at various conditions. The parameters of the JC model are optimized by using a genetic algorithm technology. The JC plastic model and the energy density-based ductile failure criteria are adopted in the proposed SHPB finite element simulation model. The simulated flow stresses and the failure characteristics, such as the cracks along the adiabatic shear bands agree well with the experimental results. Afterwards, the SHPB simulation is used to simulate higher strain rate（approximately 3 × 10 4 s -1） conditions by minimizing the size of the specimen. The JC model parameters covering higher strain rate conditions which are close to the deformation condition in cutting were calculated based on the flow stresses obtained by using the SHPB tests （10 -4 - 10 4 s- 1） and simulation （up to 3 × 10 4 s - 1）. The cutting simulation using the constitutive parameters is validated by the measured forces and chip morphology. The constitutive model and parameters for high strain rate conditions that are identical to those of cutting were obtained based on the SHPB tests and simulation.

Thermo-mechanical constitutive modeling of unsaturated clays based on the critical state concepts

A thermo-mechanical constitutive model for unsaturated clays is constructed based on the existingmodel for saturated clays originally proposed by the authors. The saturated clays model was formulatedin the framework of critical state soil mechanics and modified Cam-clay model. The existing model hasbeen generalized to simulate the experimentally observed behavior of unsaturated clays by introducingBishop＇s stress and suction as independent stress parameters and modifying the hardening rule and yieldcriterion to take into account the role of suction. Also, according to previous studies, an increase intemperature causes a reduction in specific volume. A reduction in suction （wetting） for a given confiningstress may induce an irreversible volumetric compression （collapse）. Thus an increase in suction （drying）raises a specific volume i.e. the movement of normal consolidation line （NCL） to higher values of voidratio. However, some experimental data confirm the assumption that this reduction is dependent on thestress level of soil element. A generalized approach considering the effect of stress level on themagnitude of clays thermal dependency in compression plane is proposed in this study. The number ofmodeling parameters is kept to a minimum, and they all have clear physical interpretations, to facilitatethe usefulness of model for practical applications. A step-by-step procedure used for parameter calibrationis also described. The model is finally evaluated using a comprehensive set of experimental datafor the thermo-mechanical behavior of unsaturated soils.2015 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

Constitutive modeling and springback prediction of stress relaxation age forming of pre-deformed 2219 aluminum alloy

Stress relaxation ageing behavior of pre-deformed AA2219 is studied through stress relaxation age experiments and finite element(FE) simulation. The results show that the stress can promote the process of ageing precipitation, and shorten the time to reach the peak strength. Meanwhile,the residual stress and yield strength increase along with the increase in the initial stress. Based on microstructure evolution and ageing strengthening theory,a unified constitutive model is established and incorporated into the FE simulation model through a user subroutine. It is found that the relative error of the radius is 3.6% compared with the experimental result and the springback is 16.8%. This indicates that the proposed stress relaxation ageing constitutive model provides a good prediction on the springback of such stiffened panel during its ageing process.

Comparative Study on Constitutive Modeling of Tantalum and Tantalum Tungsten Alloy

As a model bee metal, tantalum and its alloys have wide applications in defense-related fields. The KHL （Khan, Huang, Liang, 1999） model and the constitutive model proposed by Nemat-Nasser et al （Nemat-Nasser and Kapoor, 2001） for tantalum and its alloys were analyzed and compared with each other. A set of published data recorded during elastic-plastic deformations of tantalum, tantalum alloy containing tungsten of 2.5% （Ta-2.5W）, over a wide range of strains, strain rates, and temperatures were used to correlate the two models. Overall, it can be concluded that KHL model correlates much better with the data than the model used by Nemat-Nasser et al.

Flow stress behavior and constitutive modeling of 20MnNiMo low carbon alloy

The hot deformation behavior of 20 Mn Ni Mo low carbon alloy was investigated by isothermal compression tests over wide ranges of temperature(1223-1523 K) and strain rate(0.01-10 s^(-1)). According to the experimental true stress-true strain data, the constitutive relationships were comparatively studied based on the Arrhenius-type model, Johnson-Cook(JC) model and artificial neural network(ANN), respectively. Furthermore, the predictability of the developed models was evaluated by calculating the correlation coefficient(R) and mean absolute relative error(AARE). The results indicate that the flow stress behavior of 20 Mn NiM o low carbon alloy is significantly influenced by the strain rate and deformation temperature. Compared with the Arrhenius-type model and Johnson-Cook(JC) model, the ANN model is more efficient and has much higher accuracy in describing the flow stress behavior during hot compressing deformation for 20 Mn Ni Mo low carbon alloy.

Disturbed state concept as unified constitutive modeling approach

A unified constitutive modeling approach is highly desirable to characterize a wide range of engineeringmaterials subjected simultaneously to the effect of a number of factors such as elastic, plastic and creepdeformations, stress path, volume change, microcracking leading to fracture, failure and softening,stiffening, and mechanical and environmental forces. There are hardly available such unified models. Thedisturbed state concept （DSC） is considered to be a unified approach and is able to provide materialcharacterization for almost all of the above factors. This paper presents a description of the DSC, andstatements for determination of parameters based on triaxial, multiaxial and interface tests. Statementsof DSC and validation at the specimen level and at the boundary value problem levels are also presented.An extensive list of publications by the author and others is provided at the end. The DSC is considered tobe a unique and versatile procedure for modeling behaviors of engineering materials and interfaces. 2016 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. This is an open access article under the CC BY-NC-ND license

Modeling constitutive relationship of 6013 aluminum alloy during hot plane strain compression based on Kriging method

Hot plane strain compression tests of 6013 aluminum alloy were conducted within the temperature range of 613?773 K and the strain rate range of 0.001?10 s?1. Based on the corrected experimental data with temperature compensation, Kriging method is selected to model the constitutive relationship among flow stress, temperature, strain rate and strain. The predictability and reliability of the constructed Kriging model are evaluated by statistical measures, comparative analysis and leave-one-out cross-validation (LOO-CV). The accuracy of Kriging model is validated by the R-value of 0.999 and the AARE of 0.478%. Meanwhile, its superiority has been demonstrated while comparing with the improved Arrhenius-type model. Furthermore, the generalization capability of Kriging model is identified by LOO-CV with 25 times of testing. It is indicated that Kriging method is competent to develop accurate model for describing the hot deformation behavior and predicting the flow stress even beyond the experimental conditions in hot compression tests.

Constitutive Modeling for Flow Behaviors of Superaustenitic Stainless Steel S32654 during Hot Deformation

Hot deformation behavior of superaustenitic stainless steel S32654 was investigated with hot compression tests at temperatures of 950-1250 C and strain rates of 0. 001-10 s-1. Above 1150 ℃, with strain rate lower than 0.1 s -1 , the flow curves exhibit nearly steady state behavior, while at higher strain rate, continuous flow softening occurs. To provide a precise prediction of flow behavior for the alloy, the constitutive modeling considering effect of strain was derived on the basis of the obtained experimental data and constitutive relationship which incorporated Ar- rhenius term and hyperbolic sine type equation. The material constants α, n, Q and lnA are found to be functions of the strain and can be fitted employing eighth-order polynomial. The developed constitutive model can be employed to describe the deformation behavior of superaustenitic stainless steel S32654.

Microstructure Evolution and Strain-Dependent Constitutive Modeling to Predict the Flow Behavior of 20Cr–24Ni–6Mo Super-Austenitic Stainless Steel During Hot Deformation

Hot compression tests were carried out with specimens of 20Cr-24Ni-6Mo super-austenitic stainless steel at strain rate from 0.01 to 10 s^-1 in the temperature range from 950 to 1150 ℃,and flow behavior was analyzed.Microstructure analysis indicated that dynamic recrystallization（DRX）behavior was more sensitive to the temperature than strain rate,and full DRX was obtained when the specimen deformed at 1150℃.When the temperature reduced to 1050 ℃,full DRX was completed at the highest strain rate 10 s-l rather than at the lowest strain rate 0.01 s-1 because the adiabatic heating was pronounced at higher strain rate.In addition,flow behavior reflected in flow curves was inconsistent with the actual microstructural evolution during hot deformation,especially at higher strain rates and lower temperatures.Therefore,flow curves were revised in consideration of the effects of adiabatic heating and friction during hot deformation.The results showed that adiabatic heating became greater with the increase of strain level,strain rate and the decrease of temperature,while the frictional effect cannot be neglected at high strain level.Moreover,based on the revised flow curves,strain-dependent constitutive modeling was developed and verified by comparing the predicted data with the experimental data and the modified data.The result suggested that the developed constitutive modeling can more adequately predict the flow behavior reflected by corrected flow curves than that reflected by experimental flow curves,even though some difference existed at 950℃ and 0.01 s^-1.The main reason was that plenty of precipitates generated at this deformation condition and affected the DRX behavior and deformation behavior,eventually resulted in dramatic increase of deformation resistance.