Intelligent method to develop constitutive relationship of Ti-6Al-2Zr-1Mo-1V alloy

The isothermal compression tests were carried out in the Thermecmastor-Z thermo-simulator at temperatures of 800, 850, 900, 950, 1000 and 1050 ℃ and the strain rates of 0.01, 0.1, 1 and 10 s-1. The influence of deformation temperature and strain rate on the flow stress of Ti-6Al-2Zr-IMo-IV alloy was studied. Based on the experimental data sets, the high temperature deformation behavior of Ti-6A1-2Zr-IMo-IV alloy was presented using the intelligent method of artificial neural network （ANN）. The results indicate that the predicted flow stress values by ANN model is quite consistent with the experimental results, which implies that the artificial neural network is an effective tool for studying the hot deformation behavior of the present alloy. In addition, the development of graphical user interface is implemented using Visual Basic programming language.

Numerical Method for Modeling the Constitutive Relationship of Sand under Different Stress Paths

A numerical method was used in order to establish the constitutive relationship of sands under different stress paths, Firstly, based on the numerical method modeling the constitutive law of sands, the elastoplastic constitutive relationship of sand was established for three paths： the constant proportion of principle stress path, the conventional triaxial compression （CTC） path, and the p=constant （TC） path. The yield lines of plastic volumetric strain and plastic generalized shear strain were given. Through visualization, the three dimensional surface of the stress-strain relationship in the whole stress field （p, q） obtained under the three paths was plotted. Also, by comparing the stress-strain surfaces and yield locus of the three stress paths, the differences were found to be obvious, which demonstrates that the influence of the stress paths on constitutive law was not neglected. The numerical modeling method overcame the difficulty of finding an analytical expression for plastic potential. The results simulated the experimental data with an accuracy of 90% on average, so the constitutive model established in this paper provides an effective constitutive equation for this kind of engineering, reflecting the effect of practical stress paths that occur in sands.

Mechanical Properties and Constitutive Relationship of the High-Durable Parallel Strand Bamboo

Engineered bamboo has recently received lots of attention of civil engineers and professional researchers due to its better mechanical performance than that of softwood timber.Parallel strand bamboo is one important part of engineered bamboo for its excellent durable performance compared to the laminated veneer bamboo.The required curing temperature in hot-pressing process is usually higher than 120°C to reduce the content of nutri-tional ingredients and hemy cellulose,and to avoid the decay from the environment and insects.Nonetheless,the appearance of engineered bamboo gets darker with the increase of temperature during the hot-pressing process.In order to minimize the color deepening while maintaining the durability,a high-durable parallel strand bamboo(HPSB)with relative high hot-pressing temperature(140°C)was produced and tested.The present study inves-tigates the mechanical performance through tension,compression,shear and bending tests.The experimental behavior of the specimens was identified,including the failure mode and load-displacement relationship.It was demonstrated that the HPSB material had better mechanical performance parallel to grain,making it as a considerable structural material.The average elastic modulus parallel to grain was 14.1 GPa,and the tensile and compressive strengths were 120.7 MPa and 121.0 MPa,respectively.The tension perpendicular to grain should be avoided in the practical application due to the lower strength and elastic modulus.Two stress-strain relationships of tension and compression parallel to grain,including three-linear and quadratic function models,were proposed and compared with the experimental results.The three-linear model was then applied to the finite element model.The finite element analysis using ANSYS software was conducted to validate the feasibility of the constitutive relationship.The quadratic function model showed better agreement with the experimental results,but the three-linear relationship was also precise enough to analyze the bending tests of HPSB material,whereas being less accurate to describe the elastic-plastic compression behavior.

CONSTITUTIVE RELATIONSHIP OF IN718 ALLOY FOR THERMOVISCOPLASTIC AND MICROSTRUCTURE EVOLUTION COUPLED ANALYSIS

The interaction between thermomechanical parameters and microstructure evolution is so intense that it must be considered during the finite element method （FEM） simulation of the hot plastic working process, for materials that are difficult to deform. Taking the microstructure evolution into account, a novel type of constitutive relationship has been put forward for the IN718 alloy. The microstructure evolution model was first established for the dominant microstructure evolution processes. Then the microstructure evolution models and the method to determine the local flow stress of the corresponding microstructure for current thermomechanical parameters and deformation history were presented. Once the local flow stresses of different structures and their volume contributions were defined, the apparent flow stress of the material could be determined as the weighted sum of the local flow stresses and volume contributions. To validate the proposed method, a thermoviscoplastics and microstructure evolution coupled analysis for a forging process of a critical IN718 disk forging was performed. The predicting results were in close agreement with the experimental data.

Constitutive relationship of ionic polymer-metal composite and static response character of its cantilever setup to voltage

As a new ionic polymer-metal composite(IPMC) for artificial muscle,the mechanical performance parameters and the relationship between the deformation and the electrical parameters of the IPMC were studied. With the digital speckle correlation method,the constitutive relationship of the IPMC was confirmed. With non-contact photography measurement,a cantilever setup was designed to confirm the relationship between the deformation of the IPMC film and the applied voltage. The relationship curve of tip displacement of the IPMC cantilever setup vs the voltage was achieved. The results indicate that the IPMC is isotropic,its elastic modulus is 232 MPa and Poisson ratio is 0.163. The curve achieved from the test of the tip displacement of the IPMC cantilever setup shows that the tip displacement reaches the maximum when the stimulated voltage is 5 V. And the tip displacement descends largely when the frequency of the applied voltage is between 30 mHz and 100 mHz.

ARTIFICIAL NEURAL NETWORK MODEL OF CONSTITUTIVE RELATIONSHIP FOR 2A70 ALUMINUM ALLOY

The hat deformation behavior of 2A70 aluminum alloy was investigated by means of isothermal compression tests performed on a Gleeble-1500 thermal simulator over a wide range of temperatures 360-480℃ with strain rates of 0.01-1s^-1 and the largest deformation of 60%, and the true stress of the material was obtained under the above-mentioned conditions. The experimental results shows that 2A70 aluminum alloy is a kind of aluminum alloy with the property of dynamic recovery; its flow stress declines with the increase of temperature, while its flow stress increases with the increase of strain rates. On the basis of experiments, the constitutive relationship of the 2A70 aluminum alloy was constructed using a BP artificial neural network. Comparison of the predicted values with the experimental data shows that the relative error of the trained model is less than ±3% for the sampled data while it is less than ±6% for the nonsampled data. It is evident that the model constructed by BP ANN can accurately predict the flow stress of the 2A70 alloy.

bStudy on constitutive relationship of coal based on conventional triaxial compression test

Constitutive relationship of coal under triaxial compression must be determined during solving the theoretical calculation and numerical simulation about coal body failure. This paper carried out conventional triaxial compression test on No.3 coal of Baodian Colliery using MTS815.03 servo-controlled rock mechanical test system. The results indicate that the failure process of coal can be divided into 5 stages： densification stage, apparent linear elastic deformation stage, accelerated inelastic deformation stage, fracture and developing stage and plasticity flow stage. Combined with the test results, the constitutive relationship model of coal can be simplified as the four segments of straight line model of elastic-plastic hardening-plastic softening-residual perfectly plastic. Through fitting calculation of test data, the segmented constitutive equation of coal can be obtained.

CONSTITUTIVE RELATIONSHIP OF SUPERALLOY IN718

Isothermal constant speed compression tests of superalloy IN718 were conducted using a computer-controlled MTS machine at temperatures from 960 to 1040℃, with initial strain rates from 0.001 s￣(1) to 1.0 s￣(1) and engineering strain from 0.1 to 0. 7.The variations of flow stress with deformation temperature, initial strain rate and engineering strain were analyzed in the paper. It was found that there was an obvious power-law relationship between flow stress and initial strain rate, which showed the behavior of strain rate hardening of superalloy IN718 at elevated temperatures.The relationship between flow stress and temperature could be described by an inverse trigonometric function.And the turning point on the curve may be related to the behavior of δ phase at 1000℃. Meanwhile, it was found that there was a complicated relationship between flow stress and strain,which was indicative of the comprehensive effect of work hardening and dynamic softening on flow stress during hot deformation. From the results of these tests, a constitutive equation of superalloy IN718 was developed.

Phase-field modeling for anisotropic ductile damage of magnesium alloys at finite deformations

The damage anisotropy of an extruded ZK60 Mg alloy is characterized using tensile tests and scanning electronic microscopy.The accumulation of anisotropic deformations leads to the great differences of the dimple evolution and strains at fracture along different loading directions.To introduce the anisotropic deformation information into the damage constitutive relationship,a thermodynamically consistent phase-field model of ductile damage fully coupled with elastoplastic finite deformations is developed in this study.Using the user-defined constitutive relationship and displacement-temperature coupling element,the finite element simulations are conducted.The results show that:(1)ZK60 Mg alloys presents clear R-value difference in 0°,45°,and 90°tests of intact specimens.The 45°test possesses the greatest R-value(1.50)and the greatest strain at fracture,however,the R-value for 0°is less than 1,indicating the thinning is preferential.(2)The higher ultimate stress leads to a larger average dimension of the dimples,whereas the higher density correlates with a larger elongation ratio at the fracture.The disappearance of the stress-bearing area indicates that the phase-field assumption on stress degradation is completely compatible with the dimple analysis on fractography.(3)The simulation results of the stress-strain relationships and damage paths correlate well with the experimental ductile damage of magnesium alloys at 200◦C.Slight errors are basically attributed to the modeling parameters and finite element iteration algorithm.The proposed model presents fine applicability and reliability for the predictions of plastic deformations,ductile damage,and fracture of anisotropic Mg alloys.

Stochastic response of an axially moving viscoelastic beam with fractional order constitutive relation and random excitations

A convenient and universal residue calculus method is proposed to study the stochastic response behaviors of an axially moving viscoelastic beam with random noise excitations and fractional order constitutive relationship, where the random excitation can be decomposed as a nonstationary stochastic process, Mittag-Leffler internal noise, and external stationary noise excitation. Then, based on the Laplace transform approach, we derived the mean value function, variance function and covariance function through the Green＇s function technique and the residue calculus method, and obtained theoretical results. In some special case of fractional order derivative α , the Monte Carlo approach and error function results were applied to check the effectiveness of the analytical results, and good agreement was found. Finally in a general-purpose case, we also confirmed the analytical conclusion via the direct Monte Carlo simulation.

Constitutive analysis of AZ31 magnesium alloy plate

The plastic deformation simulation of AZ31 magnesium alloy at different elevated temperatures （from 473 to 723 K） was performed on Gleeble-1500 thermal mechanical simulator at the strain rates of 0.01, 0.1, 1, 5 and 10 s-t and the maximum deformation degree of 80%. The relationship between the flow stress and deformation temperature as well as strain rate was analyzed. The materials parameters and the apparent activation energy were calculated. The constitutive relationship was established with a Zener-Hollomon （Z） parameter. The results show that the flow stress increases with the increase of strain rate at a constant temperature, but it decreases with the increase of deformation temperature at a constant strain rate. The apparent activation energy is estimated to be 129-153 kJ/mol, which is close to that for self-diffusion of magnesium. The established constitutive relationship can reflect the change of flow stress during hot deformation.

TEST AND STUDY ON THE CONSTITUTIV ERELATIONSHIP OF DESERT SAND UNDER MOVING VEHICLE

The mechanical properties of the sand of Takelamagan desert in Xinjiang under moving vehicle are studied by soil dynamic triaxial test apparatus. The nonlinear elastic constitutive model of the sand under moving vehicle is established first. These results lay the foundations for studying the interaction between vehicle running gear and the sand of Takelamagan desert in Xinjiang. and developing sand vehicle.

Hot deformation behavior of novel high-strength Mg-0.6Mn-0.5Al-0.5Zn-0.4Ca alloy

The hot compression behavior of as-extruded Mg-0.6Mn-0.5Al-0.5Zn-0.4Ca alloy was studied on a Gleeble-3500 thermal simulation machine.Experiments were conducted at temperatures ranging from 523 to 673 K and strain rates ranging from 0.001 to 1 s^(-1).Results showed that an increase in the strain rate or a decrease in deformation temperature led to an increase in true stress.The constitutive equation and processing maps of the alloy were obtained and analyzed.The influence of deformation temperatures and strain rates on microstructural evolution and texture was studied with the assistance of electron backscatter diffraction(EBSD).The as-extruded alloy exhibited a bimodal structure that consisted of deformed coarse grains and fine equiaxed recrystallized structures(approximately 1.57μm).The EBSD results of deformed alloy samples revealed that the recrystallization degree and average grain size increased as the deformation temperature increased.By contrast,dislocation density and texture intensity decreased.Compressive texture weakened with the increase in the deformation temperature at the strain rate of 0.01 s-1.Most grains with{0001}planes tilted away from the compression direction(CD)gradually.In addition,when the strain rate decreased,the recrystallization degree and average grain size increased.Meanwhile,the dislocation density decreased.Texture appeared to be insensitive to the strain rate.These findings provide valuable insights into the hot compression behavior,microstructural evolution,and texture changes in the Mg-0.6Mn-0.5Al-0.5Zn-0.4Ca alloy,contributing to the understanding of its processing-microstructure-property relationships.

Hot compressive behavior of Ti-3.0Al-3.7Cr-2.0Fe-0.1B titanium alloy

The hot deformation behavior of Ti-3.0Al-3.7Cr-2.0Fe-0.1B (TACFB) titanium alloy was investigated using a Gleeble-1500D thermal simulator in the temperature range of 800-950 °C, at constant strain rate from 0.01 s-1 to 10 s-1 and with height reduction of 70%. Flow stress and microstructure evolution during hot compression of TACFB alloy were investigated. The processing map of TACFB alloy was obtained. The results indicate that the hot deformation behavior of TACFB alloy is sensitive to the deformation temperature and strain rate. The peak flow stress decreases with increasing the test temperature and decreasing the strain rate. The constitutive relationship of TACFB alloy was obtained on the base of Arrhenius equations. When the strain rates are higher than 1.0 s-1, the dynamic recrystallization occurs, and the higher the strain rates are, the more the recrystallization is.

A review of experimental and theoretical research on the deformation and failure behavior of rocks subjected to cyclic loading

Rock engineering is highly susceptible to cyclic loads resulting from earthquakes,quarrying or rockbursts.Acquiring the fatigue properties and failure mechanism of rocks is pivotal for long-term stability assessment of rock engineering structures.So far,significant progress has been gained on the mechanical characteristics of rocks subjected to cyclic loading.For providing a global insight of typical results and main features of rocks under cyclic loading conditions,this study comprehensively reviews the state-ofthe-art of deformation and failure mechanism and fatigue constitutive relationship of rocks subjected to cyclic loading in the past 60 years.Firstly,cyclic tests on rocks are classified into different types based on loading paths,loading parameters,loading types and environment conditions.Secondly,representative results are summarized and highlighted in terms of the fatigue response of rocks,including the deformation degradation,energy dissipation,damage evolution and failure characteristics;both laboratory testing and numerical results are presented,and various measurement techniques such as X-ray microcomputed tomography(micro-CT)and digital image correlation(DIC)are considered.Thirdly,the influences of cyclic loads on the mechanical characteristics of rocks are discussed,including the cyclic stress,frequency,amplitude and waveform.Subsequently,constitutive relationships for rocks subjected to cyclic loading are outlined,in which typical fatigue constitutive models are compared and analyzed,regarding the elastoplastic model,the internal variable model,the energy-based damage model and the discrete element-based model.Finally,some ambiguous questions and prospective research are interpreted and discussed.

Support principles of NPR bolt/cable and control techniques of large-deformation disasters

Deep mining has been paid much more attention because of the depletion of shallow mining resources.Traditional bolts could be invalid to accommodate large displacement and deformation in geomaterials.Consequently, alternative support and reinforcement bolts need to be studied and their constitutive models also need to be developed to help understanding for the complex stress-strain responses of rock masses under loadings. The effect of Negative Poisson's Ratio(NPR) that is attributed to the swelling phenomenon along the lateral direction may appear in metal materials under tensional loadings. Thence NPR materials often have an advantage over NPR ones in mechanical behavior such as impact resistance, antishearing, and energy absorbed. From the characteristics of NPR materials, a series of bolt and cable supports with the effect of NPR and constant-resistance have been recently developed. We here firstly introduce the structural features of NPR support. Then the constitutive model of NPR support is presented and its corresponding equation of energy equilibrium. Its basic principle interacted on rock masses is further discussed. Finally, NPR cables are employed to support the slope of an open-pit mine. The applications show that NPR cables can ease failure within the slope and play an important role in predicting and providing early warning of slope failure, together with a monitoring system of slope stability.

Plastic Flow Modeling of Ti-5 Al-2 Sn-2 Zr-4 Mo-4 Cr Alloy at Elevated Temperatures and High Strain Rates

The true stress-sWain relationships of Ti-5A1-2Sn-2Zr-4Mo-4Cr（TC17） alloy with a wide range of strain rates were investigated by tmiaxial quasi-static and dynamic compression tests, respectively. Quasi- static compression tests were carried out with Instron 8874 test machine, while dynamic compression tests were performed with the split Hopkinson pressure bar （SHPB） which was installed with heating device and synchro- assembly system. The dynamic mechanical behaviors tests of TC17 were carded out from room temperature to 800 ℃ at intervals of 200 ℃ and at high sWain rates （5 500-1 9200 s-l）. The stress-strain curves considering temperature-sWain rate coupling actions were obtained. The Johnson-Cook constitutive model was developed through data fitting of the stress-sWain curves. The material constants in the developed constitutive model can be determined using isothermal and adiabatic stress-strain curves at different strain rates. The Johnson-Cook constitutive model provided satisfied prediction of the plastic flow stress for TC17 alloy.

Study on the Dynamic Behavior of Tungsten Alloy at Strain Rates up to 5 000 s^(-1)

The dynamic stress-strain curves of 93% tungsten (W) alloy in the forged state at strain rates up to (5 000 s^(-1)) and in the temperature range from 223 K to 473 K were measured with the split Hopkinson pressure bar (SHPB) technique. Based on the above experimental data a dynamic constitutive equation considering the effects of strain rate, temperature and the special microstructure of such a kind of W-alloy was proposed. The numerical simulation for the experimental process with this constitutive equation was also carried out, the results show that the constitutive relationship constructed in this paper is very satisfactory for representing the dynamic responsive behavior of material..

A MULTI-DIMENSIONAL COMPOSITE MODEL FOR PLASTIC CONTINUA UNDER POLYAXIAL LOADING CONDITION

By replacing a medium with reinforcing components oriented and distributed uniformly in a mul- ti-dimensional space,a constitutive model is constructed.The components are extended/compressed compatibly with the strain and the resultant of load exerted on them to balance the stress.Their load-elongation relation can be determined from a conventional material test.Each component undergoes different elongation history depending on its own orientation during deformation,so that the model can simulate elasto-plastic behavior of materials un- der polyaxial loading conditions.The incremental constitutive matrix bas been derived for application in numeri- cal analysis and a yield criterion is also introduced.A few subsequent yield surfaces have been predicted and com- pared with experiments.

Forging process modeling of cone-shaped posts

Using the rigid visco-plastic Finite Element Method (FEM), the process offorging for long cone-shaped posts made of aluminum alloys was modeled and the correspondingdistributions of the field variables were obtained based on considering aberrance of grids, dynamicboundary conditions, non-stable process, coupled thermo-mechanical behavior and other specialproblems. The difficulties in equipment selection and die analysis caused by the long cone shape ofpost, as well as by pressure calculation were solved.