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.

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.

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.

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.

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.

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.

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.

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.

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.

Evaluation of Physical and Mechanical Properties of Glued Bamboo:A Review

The use of glued bamboo(GB)in structural engineering is growing interest in the construction industry,as it is a kind of natural material with strong regenerative ability.In addition,the utilizing of GB can reduce the demand for concrete,a possible way to decrease the destruction to natural environment and the consumption of fossil energy.This paper presents a comprehensive analysis on the properties of GB based on the experimental data available in the published researches.Some important physical,mechanical,and chemical properties of GB are discussed.It can be concluded that,at present,more emphasis has been given to study the mechanical property and gluing performance of GB.By analyzing existing research results,this paper provides some recommendations for future research.

Constitutive modeling and analysis on high-temperature flow behavior of 25 steel

The constitutive relationship is the basis for studying the material processing technology and controlling the quality of products.Data and models of the plastic flow behavior of materials are often required during the manufacturing process.Therefore,establishing constitutive models with high precision and generalization and enriching material database is of great significance for optimizing processing technology and product quality of the material.Based on the Gleeble thermal compression test results,the essential relationship of 25 steel between the flow stress and thermal–mechanical state variables,such as temperature,strain rate,and strain,is quantitatively discussed for the first time.Combined with the Zener–Hollomon parameter and considering the influence of strain compensation,the constitutive model of 25 steel is built by the hyperbolic-sine equation over the full strain range.In the modeling process,the influence of strain on material constants is characterized by polynomial fitting.The selection basis of polynomial order is discussed in-depth,and the inconsistency between calculation accuracy and fitting effect is clarified.Finally,the accuracy of the model is analyzed,and the generalization and applicability are discussed.It is proved that the developed model can accurately predict the flow behavior of materials in the full strain range.

Variation in Chromosome Constitution of the Xiaoyan Series Partial Amphiploids and Its Relationship to Stripe Rust and Stem Rust Resistance

The wild relatives of wheat （Triticum aestivum L.） contain tremendous amounts of potentially useful genes and represent a promising source of genetic diversity for wheat improvement （Bommineni and Jauhar, 1997）. Thinopyrum ponticum （Popd.） Barkworth and D. R. Dewey [syn. Agropyron elongatum （Host） P. Beauv., Elytrigia pontica （Podp.） Holub, Lophopy- rum ponticum （Podp.） A. L6ve] （2n = 10x = 70）, has high crossability with various Triticum species. Numerous studies have shown that Th. ponticum carries many potentially valu- able resistance genes against biotic and abiotic stresses （Shannon, 1978; Cox, 1991; Zheng et al., 2014a,b）. Transferring the useful genes from Th. ponticum to common wheat through chromosome engineering had been a successful way to enhance the resistance of wheat to pests and diseases （Sharma et al., 1989; McIntosh, 1991）.

On hot deformation behavior and workability characteristic of 42CrMo4 steel based on microstructure and processing map

In order to determine the safe region of 42CrMo4 steel during hot working and obtain excellent workability,the hot deformation behavior at the temperatures of 850-1150℃and the strain rates of 0.01-10 s^(-1)was investigated through single-pass compression test of thermo-simulation.Through observing and analyzing the true stress-strain curves,the conclusion may be drawn that the flow stress value increases with the decrease in deformation temperature and the increase in strain rate.Raising temperature and reducing strain rate are conductive to dynamic recrystallization(DRX)nucleating and growing,but adiabatic heating caused by higher strain rate can also promote it.Since the Zener-Hollomon(Z)value and dynamic recrystallized grain size(D_(DRX))have completely opposite trends with deformation condition parameters,the expression of Z value and DDRX can be determined as:D_(DRx)=15,567.645Z^(-02174).The processing map and instability map constructed at a strain of 0.9 show that the suitable window for hot working with a true strain of 0.9 is in the temperature range of 970-1150℃and strain rate range of 0.01-0.25 s^(-1),as well as at the temperature of 1150℃ and strain rate range of 0.25-10 s^(-1).The instability phenomenon appears in the process interval of 850-1096℃ and 0.22-10 s^(-1).

FINITE ELEMENT NUMERICAL SIMULATION OF LAND SUBSIDENCE AND GROUNDWATER EXPLOITATION BASED ON VISCO-ELASTICPLASTIC BIOT'S CONSOLIDATION THEORY

The land subsidence due to groundwater exploitation has an obvious hysteretic nature with respect to the decrease of the under groundwater level, and the uneven settlement often causes ground fissures. To study these important features, a visco-elasticplastic constitutive relationship with consideration of the coupling of seepage and soil deformation is proposed, and a finite element model with variable coefficients based on the Biot＇s consolidation theory is built. With the groundwater exploitation and the land subsidence control in Cangzhou City, Hebei Province as an example, the variations of the under groundwater level and the deve- lopment of the land subsidence due to the groundwater exploitation are simulated and ground fissures are predicted by the horizontal displacement calculation. The results show that the lag time between the land subsidence and the under groundwater level descent is about a month, and the simulated results of fissures agree well with the observed data. The model can well reveal the characterization of the interaction between the land subsidence and the groundwater exploitation.

Numerical model establishment and verification of cold pilgering on cycle feed rate

A numerical model was established to calculate the cycle feed rate through studying the case of a cold pilger mill with the 304 stainless steel pipe. Firstly, the precise constitutive equation of 304 stainless steel was obtained through nonlinearly fitting the true stress-strain data from unidirectional tensile test. Then, the numerical method to calculate the equivalent deformation was determined according to the plastic deformation feature of the steel tube during cold rolling and the incremental theory. Finally, the cycle feed rate of cold roiled 304 stainless steel pipe was extracted when formulating springback through utilizing above results comprehensively and unloading law. Stress state, metal flow, finished pipe size and distribution of residual stress were obtained by finite element method to calculate the whole rolling process when the cycle feed rate was 10 mm, and the optimized model was verified through finished pipe size.

Hot deformation behavior and finite element simulation of Mg-8.3Gd-4.4Y-1.5Zn-0.8Mn alloy

To study the hot deformation behavior of Mg-8.3 Gd-4.4 Y-1.5 Zn-0.8 Mn(wt%) alloy,hot compression tests were conducted using a Gleeble-3500 thermal simulator at temperatures ranging from 653 to773 K,true strain rates of 0.001-1 s^(-1),and a deformation degree of 60%.Results of hot compression experiments show that the flow stress of the alloy increases with the strain rate.The true stress-true strain curves are corrected by correcting the effect of temperature rise in the deformation process.Activation energy,Q,equal to 287380 J/mol and material constant,n,equal to 4.59 were calculated by fitting the true stress-true strain curves.Then,the constitutive equation was established and verified via finite element simulation.Results of the hot processing map show that the probability of material instability increases with the degree of deformation,which indicates that the material is not suitable for large deformation in a single pass.On the whole,the alloy is appropriate for multipass processing with small deformation and a suitable processing temperature and strain rate are 733 K and 0.01 s-1,respectively.