Determination of local constitutive behavior and simulation on tensile test of 2219-T87 aluminum alloy GTAW joints

The local and global mechanical responses of gas tungsten arc welds（GTAW） of a 2219-T87 aluminum alloy were investigated with experiment and numerical simulation.Digital image correlation（DIC） was used to access the local strain fields in transversely loaded welds and to determine the local stress-strain curves of various regions in the joint.The results show that the DIC method is efficient to acquire the local stress-strain curves but the curves of harder regions are incomplete because the stress and strain ranges are limited by the weakest region.With appropriate extrapolation,the complete local stress-strain curves were acquired and proved to be effective to predict the tensile behavior of the welded joint.During the tensile process,the fracture initiates from the weld toes owing to their plastic strain concentrations and then propagates along the fusion line,finally propagates into the partially melted zone（PMZ）.

Constitutive behavior, microstructural evolution and processing map of extruded Al-1.1Mn-0.3Mg-0.25RE alloy during hot compression

Hot compression tests of an extruded Al-1.1Mn-0.3Mg-0.25RE alloy were performed on Gleeble-1500 system in the temperature range of 300-500 ℃ and strain rate range of 0.01-10 s-l. The associated microstructural evolutions were studied by observation of optical and transmission electron microscopes. The results show that the peak stress level decreases with increasing deformation temperature and decreasing strain rate, which can be represented by a Zener-Hollomon parameter in the hyperbolic-sine equation with the hot deformation activation energy of 186.48 kJ/mol. The steady flow behavior results from dynamic recovery whereas flow softening is associated with dynamic recrystallization and dynamic transformation of constituent particles. The main constituent particles are enriched rare earth phases. Positive purifying effects on impurity elements of Fe and Si are shown in the Al-l.lMn-0.3Mg-0.25RE alloy, which increases the workability at high temperature. Processing map was calculated and an optimum processing was determined with deformation temperature of 440-450 ℃ and strain rate of 0.01 s-1.

Constitutive behavior of Ni-Ti shape memory alloy under hot compression

Constitutive behavior of nickel-titanium shape memory alloy （Ni-Ti SMA） under hot deformation was investigated by means of the compression tests and the linear fitting method. Based on the true stres-strain curves of Ni-Ti SMA under compression at the strain rates of 0.001-1 s land at the temperatures ranging from 600 to 1 000 ℃, the constitutive equation of Ni-Ti SMA with respect to the Zener-Hollomon parameter was established according to the high stress level and the low stress level at various temperatures so as to more accurately describe the deformation behavior of Ni-Ti SMA during hot working. Dynamic recovery and dynamic recrystallization of Ni-Ti SMA occur under hot compression, which lays the theoretical foundation for understanding the constitutive behavior of Ni-Ti SMA.

Constitutive behavior and processing maps of a new wrought magnesium alloy ZE20 (Mg-2Zn-0.2Ce)

ZE20(Mg-2Zn-0.2Ce)^2 is a new wrought magnesium alloy with improved extrudability and mechanical properties[1].To understand the constitutive behavior and workability of this new alloy,Gleeble thermomechanical testing has been carried out in this study.The flow stress behavior of ZE20 was investigated between 250℃–450℃ and 10^–3 s^–1–1.0 s^–1 in isothermal compression.Constitutive descriptions of the flow stress are provided.A new general approach at application of the extended Ludwik equation is demonstrated and was found to be more accurate than the hyperbolic sine Arrhenius model while having a similar number of model constants.Processing maps were developed based on the experimental results and are verified with microstructural investigation.A region of safe processing with non-basal texture and high activity of dynamic recrystallization(DRX)was found between 375℃ and 450℃,from 10^–1 s^–1 to 10^–2.5 s^–1.A region of potentially safe processing with annealing that is associated with shear band nucleation of non-basal grains was identified for temperatures as low as 300℃ and rates as high as 10^–1 s^–1.

Global and local constitutive behaviors of friction stir welded AA2024 joints

In this study, the global and local tensile properties of friction stir welded AA2024 joints were measured with the aid of digital image correlation(DIC) method. A novel model was proposed to describe the global and local constitutive behavior of the joints based on DIC data. Different from conventional division of the zones across the joints, a new reasonable division was proposed, i.e. four zones including central low hardness zone(CLHZ), first heat affected zone(HAZ-I) close to TMAZ, second heat affected zone(HAZ-II)close to base metal(BM) and BM in term of the characteristic distribution of hardness. Results reveal that local true stress-true strain curves are different in each zone of interest. Plastic deformation of the joints is concentrated in CLHZ, where the lowest yield stress and the largest strain appear. Therefore, strain localization and necking occur here in a sequence. In addition, the global true stress-true strain curves and yield stresses at various ratios of the width of CLHZ zone to the gauge length are accurately predicted using the proposed constitutive model of the joints.

Probing the constitutive behavior of microcrystals by analyzing the dynamics of the micromechanical testing system

The constitutive behavior of microcrystals remains mysterious since very little,or no information regarding plastic deformation in the measured stress-strain curve is available due to plastic instability.Furthermore,the measured stress-strain curves vary greatly under different control modes,while constitutive behavior should remain unaffected by test methods.Beyond these reasons,probing the real constitutive behavior of microcrystals has long been a challenge because the nonlinear dynamical behaviors of micromechanical testing systems are unclear.Here,we perform and carefully analyze the experiments on singlecrystal aluminum micropillars under displacement control and load control.To interpret these experimental results,a lumpedparameter physical model based on the principle of micromechanical testing is developed,which can directly relate nonlinear dynamics of the micromechanical testing system to the constitutive behavior of microcrystals.This reveals that some stages of the measured stress-strain curve attributed to the control algorithm are not related to constitutive behavior.By solving the nonlinear dynamics of the micromechanical testing system,intense plastic instability(large strain burst)starting from the equilibrium state is attributed to the strain-softening stage of microcrystals.Parametric studies are also performed to reduce the influence of plastic instability on the measured responses.This study provides critical insights for developing various constitutive models and designing a reliable micromechanical testing system.

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.

ON PLASTIC ANISOTROPY OF CONSTITUTIVE MODELFOR RATE-DEPENDENT SINGLE CRYSTAL

An algorithm for single crystals was developed and implemented to simulate plastic anisotropy using a rate-dependent slip model. The proposed procedure was a slightly modified form of single crystal constitutive model of Sarma and Zacharia. Modified Euler method, together with Newton-Raphson method was used to integrate this equation which was stable and efficient. The model together with the developed algorithm was used to study three problems. First, plastic anisotropy was examined by simulating the crystal deformation in tension and plane strain compression, respectively. Secondly, the orientation effect of some material parameters in the model and applied strain rate on plastic anisotropy for single crystal also is investigated. Thirdly, the influence of loading direction on the active slip system was discussed.

A Comprehensive Review of Experience with the Application of the Mechanical Threshold Stress Model

Accurate prediction of stress-strain behavior of metals as a function of arbitrary temperature and strain rate paths has remained a challenge. The Mechanical Threshold Stress constitutive model is one formalism that has emerged following several decades of research. Vast experience has accumulated with the application of the Mechanical Threshold Stress model over a wide variety of pure metals and alloys. Out of this has arisen common trends across metal systems. The magnitude of activation energies presents one example of this, where these variables consistently increase in magnitude as the obstacle to dislocation motion transitions from short range to long range. Trends in strain hardening are also observed. In Face-Centered Cubic metals the magnitude of strain hardening scales with the stacking fault energy;trends in Body-Centered Cubic metals are less clear. Model parameters derived for over twenty metals and alloys are tabulated. Common trends should guide future application of the MTS model and further model development.

A temperature/strain-rate-dependent finite deformation constitutive and failure model for solid propellants

The stress-strain response under progressive damage and the ultimate failure of solid propellants are two key issues affecting the integrity of solid rocket motors.Previous research primarily focused on the progressive damage in solid propellants during production and storage.However,they failed to take the temperature/strain-rate-dependent ultimate failures into consideration.The failure strains of solid propellants are experimentally observed to show strong temperature/strain-rate dependence and exhibit an abnormal evolution at low and high temperatures,respectively.With increasing loading strain rate,the failure strains decrease at low temperatures near the glass transition temperature(T_g)but increase at high temperatures far above T_(g).In this study,we introduce the glassy and rubbery failure criteria based on strain energy densities at ultralow and ultrahigh temperatures,respectively,into a viscoelastic constitutive model and build a unified model for the progressive damage and the ultimate failure of solid propellants.With the introduction of these two additional criterion parameters,the developed model can effectively predict the yield-type stress-strain responses,microscopic damage-induced volume dilatations,and temperature/strain-ratedependent ultimate failures of the solid propellants by comparing the model predictions with the experimental results.The competition between the glassy failure and the rubbery failure results in the propellants exhibiting a maximum break strain near the glass transition temperature.Consequently,when the strain rate is increased,the propellants exhibit a predominantly glassy response,which shifts the failure envelope toward a higher temperature.This induces an abnormal evolution of failure strains by making the propellants stretchable at high temperatures and brittle at low temperatures.

A Generalized Non-Linear Flow Law Based on Modified Zerilli-Armstrong Model and Its Implementation into Abaqus/Explicit FEM Code

Non-linear numerical modeling, widely used in research and development to understand many complex processes such as forming or machining, does not guarantee the success of a study to be performed. Indeed, the numerical simulation uses finite element codes where the models already integrated are not based on shapes adjustable to any type of study. In this study, a new form of non-linear constitutive flow law based on the Modified Zerilli-Armstrong model, which can answer the above problem, has been developed to apply it to the numerical simulation of two different tests (a quasi-static compression test, the necking of a circular bar). This flow law is based on the modified Zerilli-Armstrong model, which, together with the new modified Johnson-Cook model, has been compared to appreciate the relevance of the proposal. For that, an implementation of this new law via the VUHARD subroutine into the Abaqus/Explicit finite element code was made to model the two tests. The comparison of the results obtained (from identification) by our proposed law with those obtained using the NMJC shows that this new law better approaches the experiments than the other one. This is also shown through the numerical results using the Abaqus software. It can be said that this way of formulating a flow law allows highlighting the great performance of the proposed approach. Although this law has been only used for quasi-static tests, we can say that it can also be used in dynamic tests.

Constitutive modeling of compression behavior of TC4 tube based on modified Arrhenius and artificial neural network models

Warm rotary draw bending provides a feasible method to form the large-diameter thin-walled（LDTW）TC4 bent tubes, which are widely used in the pneumatic system of aircrafts. An accurate prediction of flow behavior of TC4 tubes considering the couple effects of temperature,strain rate and strain is critical for understanding the deformation behavior of metals and optimizing the processing parameters in warm rotary draw bending of TC4 tubes. In this study, isothermal compression tests of TC4 tube alloy were performed from 573 to 873 K with an interval of 100 K and strain rates of 0.001, 0.010 and0.100 s^（-1）. The prediction of flow behavior was done using two constitutive models, namely modified Arrhenius model and artificial neural network（ANN） model. The predictions of these constitutive models were compared using statistical measures like correlation coefficient（R）, average absolute relative error（AARE） and its variation with the deformation parameters（temperature, strain rate and strain）. Analysis of statistical measures reveals that the two models show high predicted accuracy in terms of R and AARE. Comparatively speaking, the ANN model presents higher predicted accuracy than the modified Arrhenius model. In addition, the predicted accuracy of ANN model presents high stability at the whole deformation parameter ranges, whereas the predictability of the modified Arrhenius model has some fluctuation at different deformation conditions. It presents higher predicted accuracy at temperatures of 573-773 K, strain rates of 0.010-0.100 s^（-1）and strain of 0.04-0.32, while low accuracy at temperature of 873 K, strain rates of 0.001 s^（-1）and strain of 0.36-0.48.Thus, the application of modified Arrhenius model is limited by its relatively low predicted accuracy at some deformation conditions, while the ANN model presents very high predicted accuracy at all deformation conditions,which can be used to study the compression behavior of TC4 tube at the temperature range of 573-873 K and the strain rate of 0.001-0.100 s^（-1）. It can provide guideline for the design of processing parameters in warm rotary draw bending of LDTW TC4 tubes.

Flow Behavior and Constitutive Modeling of Delta-processed Inconel 718 alloy

The flow behavior of delta-processed Inconel 718 was studied in temperature range of 900-1 060℃ and strain rate range of 0.001-0.5s-1.The effects of friction and temperature on the compressive deformation behavior were investigated,and the flow stress-strain error caused by friction was revised.The results showed that the effect of the friction was obvious with increasing strain rate and decreasing deformation temperature.The revised flow stress is decreased by increasing temperature and decreasing strain rate and exhibits a typical dynamic recrystallization behavior.The constitutive model has been developed through a hyperbolic-sine Arrhenius type equation to relate the flow stress,strain rate and temperature.The influence of strain has also been incorporated by considering the variation of material constants as a function of strain.The prediction accuracy of developed constitutive model has been assessed using standard statistical formulae.According to the analysis results,the proposed deformation constitutive equation gives an accurate and precise estimate of flow stress of delta-processed Inconel 718 alloy.

Time- and temperature-dependence of compressive and tensile behaviors of polypropylene fiber-reinforced cemented paste backfill

The understanding of compressive and tensile behaviors of polypropylene fiber-reinforced cemented paste backfill(FR-CPB)play crucial roles in the successful implementation of reinforcement technique in underground mine backfilling operations.However,very limited studies have been performed to gain insight into the evolution of compressive and tensile behaviors and associated mechanical properties of FR-CPB under various curing temperatures from early to advanced ages.Thus,this study aims to investigate the time(7,28,and 90 d)-and temperature(20°C,35°C,and 45°C)-dependence of constitutive behavior and mechanical properties of FR-CPB.The obtained results show that pre-and post-failure behaviors of FR-CPB demonstrate strongly curing temperature-dependence from early to advanced ages.Moreover,the pseudo-hardening behavior is sensitive to curing temperature,especially at early ages.Furthermore,the mechanical properties including elastic modulus,material stiffness,strengths,brittleness,cohesion,and internal friction angle of FR-CPB show increasing trends with curing temperature as curing time elapses.Additionally,a predictive model is developed to capture the strong correlation between compressive and tensile strength of FR-CPB.The findings of this study will contribute to the successful implementation of FR-CPB technology.

A unified plasticity methodology for rate-and temperature-sensitive alloys exhibiting a non-linear kinematic hardening behavior

In this paper, a novel unified plasticity methodology is proposed to allow the coupling of rate-and temperature-sensitivity of engineering alloys as well as the non-linear kinematic hardening behavior often observed during cyclic loading. The proposed methodology is general in the sense that an arbitrary constitutive model may be chosen for the viscoplastic part, as well as the cyclic part. We adapt our model with a physically-motivated viscoplasticity flow rule and a nonlinear kinematic hardening model. In contrast with other unified plasticity models, the simplified theory involves few material parameters that can be readily calibrated from standard mechanical tests. The capabilities of the proposed theory are demonstrated for a hot rolled annealed 304 L stainless steel supplied by Vimetal Peckover. The model is tested with stress–strain curves obtained from standard tensile and cyclic uniaxial tests at various strain amplitudes and strain-rates, and good accuracy of the response is obtained for strains up to 15%, within a temperature range of 293–673 K. We note that the cyclic plasticity model in our adapted theory can be readily enhanced with ratchetting, mean stress relaxation, strain amplitude history, Masing effects or other complex capabilities.

Hot deformation behavior of an antibacterial Co–29Cr–6Mo–1.8Cu alloy and its effect on mechanical property and corrosion resistance

In order to optimize the deformation processing, the hot deformation behavior of Co-Cr-Mo-Cu （here- after named as Co-Cu） alloy was studied in this paper at a deformation temperature range of 950-1150 ℃ and a strain rate range of 0.008-5 s^-1. Based on the true stress-true strain curves, a constitutive equation in hyperbolic sin function was established and a hot processing map was drawn. It was found that the flow stress of the Co-Cu alloy increased with the increase of the strain rate and decreased with the increase of the deforming temperature. The hot processing map indicated that there were two unstable regions and one well-processing region. The microstructure, the hardness distribution and the electro- chemical properties of the hot deformed sample were investigated in order to reveal the influence of the hot deformation. Microstructure observation indicated that the grain size increased with the increase of the deformation temperature but decreased with the increase of the strain rate. High temperature and low strain rate promoted the crystallization process but increased the grain size, which results in a reduction in the hardness. The hot deformation at high temperature （1100-1150 ℃） would reduce the corrosion resistance slightly. The final optimized deformation process was： a deformation temperature from 1050to 1100 ℃, and a strain rate from 0.008 to 0.2 s^-1, where a completely recrystallized and homogeneously distributed microstructure would be obtained.