MODELING THE STRESS-STRAIN CURVES UNDER DYNAMIC RECRYSTALLIZATION

An analytical model for dynamic recrystallization (DRX) is studied based on the relative grain size model proposed by Sakai and Jonas, and the characteristic flow behaviors under DRX are analyzed and simulated. Introducing the variation of dynamic grain size and the heterogeneous distribution of disolo- cation densities densities under DRX,a simple method for modeling and simulating DRX processes is developed by using Laplace transformation theory. The results derived from the present model agree well with the experimental results in literatures. This simulation can reproduce a number of features in DRX flow behaviors, for example,single and multiple peak flow behaviors followed by a steady state flow, the transition between them, and so on.

ISOCHRONOUS STRESS-STRAIN CURVES OF LOW ALLOY STEEL CROSS-WELD-SPECIMEN AT HIGH TEMPERATURE

In this work, a parametric approach is presented and utilized to determine the creep properties of weldments; then the model of creep strain for cross weld specimen is given. On the basis of the experimental results, attempt has been made to establish equations of the isochronous stress-strain for weld joint that can predict the function of loading and service time in use of the creep data of base metal and weld metal.

Numerical simulation of the stress-strain curve and the stress and strain distributions of the titanium-duplex alloy

The stress-strain curve of an α-β Ti-8Mn alloy was measured and then it was calculated with finite element method （FEM） based on the stress-strain curves of the single α and β phase alloys. By comparing the calculated stress-strain curve with the measured one, it can be seen that they fit each other very well. Thus, the FE model built in this work is effective. According to the above mentioned model, the distributions of stress and strain in the α and β phases were simulated. The results show that the stress gradients exist in both α and β phases, and the distributions of stress are inhomogeneous. The stress inside the phase is generally higher than that near the interface. Meanwhile, the stress in the α phase is lower than that in the β phase, whereas the strain in the α phase is higher than that in the β phase.

The Complete Stress-strain Curve of Recycled Aggregate Concrete under Uniaxial Compression Loading

The mechanical performance of recycled aggregate concrete （RAC） is investigated. An experiment on the complete stress-strain curve under uniaxial compression loading of RAC is carried out. The experimental results indicate that the peak stress, peak strain, secant modulus of the peak point and original point increase with the strength grade of RAC enhanced. On the contrary, the residual stress of RAC decreases with the strength grade enhancing, and the failure of RAC is often broken at the interface between the recycled aggregate and the mortar matrix. Finally, the constitutive model of stress-strain model of RAC has been constituted, and the results from the constitutive model of stress-strain meet the experiment results very well.

Charactersitics of Stress-strain Curve of High Strength Steel Fiber Reinforced Concrete under Uniaxial Tension

A whole of 110 specimens divided into 22 groups were tested with varying the volume fraction of steel fibers and the matrix strength of these specimens. The stress-strain behaviors of four types of steel fiber reinforced concrete （SFRC） under uniaxial tension were studied experimentally. When the matrix strength and the fiber content increase, the tensile stress and tensile strain vary differently according to the fiber type. The mechanisms of reinforcing effect for different types of fiber were analyzed and the stress-strain curves of the specimens were plotted. Some experimental factors for stress or strain of SFRC were given. A tensile toughness modulus Re0.5 was introduced to evaluate the toughness characters of SFRC under uniaxial tension. Moreover, the formula of the tensile stress-strain curve of SFRC was regressed. The theoretical curve and the experimental ones fit well, which can be used for references in construction.

Relations of complete creep processes and triaxial stress-strain curves of rock

Based on the results of triaxial compressive creep tests for five kinds of rock under the different stress loading,unloading and cycle-loading-unloading conditions,the creep deformation is not only a function of stress and time,but also it has the corresponding relations to the triaxial stress-strain curves of rock.The deformation properties of soften-strain,harden-strain and ideal plasticity presented by conventional triaxial compressive test curves under the different stress states were utilized,and the creep characteristics,the creep starting stress and the different entire creep process curves of rock were studied systematically according to creep experiment results,and the relations of the triaxial stress-strain curves to the creeping starting stress,the terminating curve,the different creep processes,and the different creep fracture properties were established.The relations presented in this paper were verified partially by the creep experiment results of five types of rock.

MODELLING OF TENSILE STRESS-STRAIN CURVE OF WOVEN FABRICS

A general shape of tensile stress-strain curves of woven fabrics is first recognised by puttingtested and predicted results together.An exponential function with two parameters is then selectedfor the prediction of tensile stress-strain relationship.The predicted results by using the proposedfunction show excellent agreement with experimental data.

Stress—strain curves for different loading paths and yield loci of aluminum alloy sheets

To carry out biaxial tensile test in sheet metal, the biaxial tensile testing system was established. True stress—true strain curves of three kinds of aluminum alloy sheets for loading ratios of 4:1, 4:2, 4:3, 4:4, 3:4, 2:4 and 1:4 were obtained by conducting biaxial tensile test in the established testing systems. It shows that the loading path has a significant influence on the stress—strain curves and as the loading ratio increases from 4:1 to 4:4, the stress—strain curve becomes higher and n-value becomes larger. Experimental yield points for three aluminum alloy sheets from 0.2% to 2% plastic strain were determined based on the equivalent plastic work. And the geometry of the experimental yield loci were compared with the yield loci calculated from several existing yield criteria. The analytical result shows that the Barlat89 and Hosford yield criterion describe the general trends of the experimental yield loci of aluminum alloy sheets well, whereas the Mises yield criterion overestimates the yield stress in all the contours.

Finite Element Modeling of Stress Strain Curve and Micro Stress and Micro Strain Distributions of Titanium Alloys— A Review

Most of the alloys like titanium, steel, brass, copper, etc., are used in engineering applications like automobile, aero- space, marine etc., consist of two or more phases. If a material consists of two or more phases or components it is very difficult to predict the properties like mechanical and other properties based on simple laws such as rule of mixtures. Titanium alloys are capable of producing different microstructures when it subjected to heat treatments, so much of money and time are squandering to study the effect of microstructure on mechanical properties of titanium alloys. This squandering can be reduced with the help of modeling and optimization techniques. There are many modeling tech- niques like Finite element method, Mat lab, Mathematical modeling etc. are available. But Finite element method is widely used for prediction because of capable of producing distributions of stresses and strains at any different loads. From the literature it is observed that there is a good agreement between the calculated and measured stress strain curves. This review paper describes the effect of volume fraction and grain size of alpha phase on the stress strain curve of the titanium alloys. It also can predict the effect of strength ratio on stress strain curve by using FEM. This informa- tion will be of great use in designing and selecting the titanium alloys for various engineering applications.

Investigation into the stress-strain curves of deformation-induced ferrite transformation in a low carbon steel

A series of tests of deformation-induced ferrite transformation （DIP-T） in a low carbon steel were carried out by the Gleeble-3500 hot simulation machine at a temperature range of Ae3-Ar3. The overall stress-strain curves during DIFT can be divided into three typical types： ＂double-humped＂,＂ single-humped＂ and ＂transitional＂. The peaks exhibited in the curve are involved with deformation-induced transformation which happened in grains or at the grain boundaries. According to the stress-time curve and strain-time curve, strain capacity dramatically postponed the strain-induced transformation, which leads to the start of the transformation right ahead of the finish of deformation and the majority of the ferrite transformation process mainly happened after the deformation. Deformation-induced transformation is a metadynamic transformation process with dynamic nucleation.

Use of Plastic Correction Formula to Improve Accuracy of Welding Residual Stress Test with Blind-Hole Method

The blind-hole method is the most widely used approach to experimentally determine the distribution of residual stress. This paper aims to improve test accuracy of welding residual stress and conducts an experimental study on the strain release factors involved when using the blind-hole method for Q235 and Q345, two steels commonly used in building structures. The ranges of strain release factors A and B in the elastic stage, the effects of strain release factors on residual stress calculated values, and the plastic corrected strain release factors are analyzed considering of the effect of plastic deformation around the blind hole on measurement accuracy. Finally, a simplified calculation formula to determine strain release factors is proposed for use with the blind-hole method. Results show that in the elastic stage, strain release factor A for Q235 and Q345 ranges from-0.399 to-0.525 and strain release factor B from-0.791 to-0.960. Changing the strain release factors A and B shows that calculated residual tensile stress varies in relation to a decrease in both factor values. However, there is a increase in calculated residual compressive stress with a decrease in the strain release factor A value, but there is an decrease with a decrease in strain release factor B value. Calculated residual stress applied to elastic strain release factors is compared with that applied to amended plastic strain release factors for Q235 steel. The maximum deviation between calculated residual stress and test stress is reduced from 21.1 to 1.0%,and for Q345 steel from 26.5 to 1.2%. It is thus evident that the plastic correction formula proposed in this paper can be used in calculations when conducting a residual stress test.

Structural Stress-Fatigue Life Curve Improvement of Spot Welding Based on Quasi‑Newton Method

ΔF-N curves are usually used to predict the fatigue life of spot welding in engineering,but they are time-consuming and laborious and not universal.For the purpose of predicting the fatigue life of spot welding accurately and efficiently,tensile-shear fatigue tests were conducted to obtain the fatigue life of spot-welded specimens with different sheet thicknesses combinations.These specimens were simulated by using the finite element method,and the structural stress was theoretically calculated.In the double logarithmic coordinate system,the structural stress-fatigue life(S-N)curve of spot welding was fitted by the least-squares method,based on the quasi-Newton method.The square of the correlation coefficient of the S-N curve was taken as the optimization objective,with the correction coefficients of force,bending moment,spot welding diameter,and sheet thickness as the variables.During the optimization process,three different ways were utilized to get three optimized spot welding S-N curves,which are suitable for different situations.The results show that the fitting effect of the S-N curve is improved,the data points are more compact,and the optimization effect is significant.These S-N curves can be used to predict the fatigue life,which provide the basis for practical engineering application.

Stress-strain Model of Corroded Concrete under Uniaxial Compressive Loading

The prism specimens of corroded concrete were subjected to uniaxial compressive load to develop the stress-strain model. Compared to the un-corroded concrete, the mechanical prop- erties of corroded concrete, such as peak strength, Young＇s modulus, and residual deformation, et al are degraded. The concrete, which were subjected to the aggressive media in the environment, were resulted in randomly distributed pre-loading flaws and defects. The propagation of these corrosion flaws during the procedure of loading was the main reason of degradation of corroded concrete properties. By the application of the statistic theory of continuum damage, the compressive stress-strain curve of corroded concrete was simulated. The initial damage factor was introduced to represent the corrosive effects of different media. The present damage constitutive model agreed well with the test results.

Application of the Mechanical Threshold Stress Model to Large Strain Processing

Large-strain deformations introduce several confounding factors that affect the application of the Mechanical Threshold Stress model. These include the decrease with the increasing stress of the normalized activation energy characterizing deformation kinetics, the tendency toward Stage IV hardening at high strains, and the influence of crystallographic texture. Minor additions to the Mechanical Threshold Stress model are introduced to account for variations of the activation energy and the addition of Stage IV hardening. Crystallographic texture cannot be modeled using an isotropic formulation, but some common trends when analyzing predominantly shear deformation followed by uniaxial deformation are described. Comparisons of model predictions with measurements in copper processed using Equal Channel Angular Pressing are described.

Effect of tempering temperature on strain hardening exponent and flow stress curve of 1000MPa grade steel for construction machinery

To study the effect of tempering temperature on strain hardening exponent and flow stress curve,one kind of 1000 MPa grade low carbon bainitic steel for construction machinery was designed,and the standard uniaxial tensile tests were conducted at room temperature.A new flow stress model,which could predict the flow behavior of the tested steels at different tempering temperatures more efficiently,was established.The relationship between mobile dislocation density and strain hardening exponent was discussed based on the dislocation-stress relation.Arrhenius equation and an inverse proportional function were adopted to describe the mobile dislocation,and two mathematical models were established to describe the relationship between tempering temperature and strain hardening exponent.Nonlinear regression analysis was applied to the Arrhenius type model,hence,the activation energy was determined to be 37.6kJ/mol.Moreover,the square of correlation coefficient was 0.985,which indicated a high reliability between the fitted curve and experimental data.By comparison with the Arrhenius type curve,the general trend of the inverse proportional fitting curve was coincided with the experimental data points except of some fitting errors.Thus,the Arrhenius type model can be adopted to predict the strain hardening exponent at different tempering temperatures.

Effect of strain rate on the compressive deformation behaviors of lotus-type porous copper

Lotus-type porous copper was fabricated by unidirectional solidification, and compressive experiments were subsequently conducted in the strain rate range of 10-3-2400 s-1 with the compressive direction parallel to the pores. A GLEEBLE-1500 thermal-mechanical simulation system and a split Hopkinson pressure bar （SHPB） were used to investigate the effect of strain rate on the compressive deforma-tion behaviors of lotus-type porous copper. The influence mechanism of strain rate was also analyzed by the strain-controlling method and by high-speed photography. The results indicated that the stress-strain curves of lotus-typed porous copper consist of a linear elastic stage, a plateau stage, and a densification stage at various strain rates. At low strain rate （〈1.0 s^-1）, the strain rate had little influence on the stress-strain curves; but when the strain rate exceeded 1.0 s^-1, it was observed to strongly affect the plateau stage, showing obvious strain-rate-hardening characteristics. Strain rate also influenced the densification initial strain. The densification initial strain at high strain rate was less than that at low strain rate. No visible inhomogeneous deformation caused by shockwaves was observed in lotus-type porous copper during high-strain-rate deformation. However, at high strain rate, the bending deformation characteristics of the pore walls obviously differed from those at low strain rate, which was the main mechanism by which the plateau stress exhibited strain-rate sensitivity when the strain rate exceeded a certain value and exhibited less densification initial strain at high strain rate.

Effect of deformation temperature and strain rate on semi-solid deformation behavior of spray-formed Al-70%Si alloys

Spray-formed Al-70%Si(mass fraction) alloys were deformed by compression in the semi-solid state. The effects of the deformation temperature, strain rate and the microstructure were studied. Two strain rates(1s -1and 0.1s -1) and six deformation temperatures (600℃, 720℃ , 780℃, 900℃, 1000℃ and 1100℃) were chosen. The stress—strain curve exhibits a peak at low strain and then decreases to a plateau before it starts to increase again as the strain increases. The stress required for deformation at lower strain rate and at higher deformation temperatures is less than those at higher strain rate and at lower deformation temperatures. Four mechanisms of semi-solid deformation can be used to explain the different behaviors of the stress—strain curves under different conditions.

Orientation dependency of shear stress-strain curves in B2-ordered Fe_3Al single crystals deformed in tension at room temperature

B2-ordered Fe3Al single crystals with various orientations were deformed in tension at room temperature in vacuum. The shape of shear stress-strain curves and work hardening rates were found to be strongly dependent on the orientation. The formation of the five different work hardening stages were considered to be related to the number of operative slip systems, the effect of secondary slip systems and the dissociation of the twofold superdislocation. Stage I is an easy glide stage corresponding to single slip. Stage II, with high hardening rate, often corresponds to the existence of conjugate slip systems. Stage III, with relatively low hardening rate, corresponds to the weaker hardening of secondary slip systems. Stage IV, with the highest hardening rate, is not only related to multiple slip but also the dissociation of twofold superdislocations and the moving of superpartials with an antiphase boundary (APB) trap. Stages V, with a negative hardening rate, may be caused by the cross slip of single dissociated superdislocation. The number of stages and the work hardening rate of the same stage were also found to change significantly, when the tensile orientation lies in different orientation regions.

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.

Full-Range Compressive Stress-Strain Curves for Cold-Formed 304 Stainless Steel Circular Hollow Sections After Exposure to Vacuum Brazing

With the rapid development of microscale cellular structures, the small-diameter cold-formed welded stainless steel tubes have recently been used for creating the metallic lat- tice topologies with high mechanical properties. In this paper, to obtain the accurate material properties of the circular hollow section （CHS） under pure compression, a series of concentric compression tests are conducted on the millimeter-scale cold-formed 304 stainless steel circu- lar tubular stub columns after exposure to a vacuum brazing process. The tests cover a total of 18 small-diameter stub tubes with measured thickness-to-diameter ratios （t/D） from 0.023 to 0.201. A generalized three-stage nominal stress-strain model is developed for describing the compressive behavior of the post-brazing CHSs over the full strain range. This mechanical model is especially applicable to computer code implementation. Hence, an interactive computer pro- gram is developed to simultaneously optimize three strain hardening exponents （n1, n2, n3） in the expression of the model to produce the stress-strain curve capable of accurately replicating the test data. To further reduce the number of the model and material parameters on which this model depends, this paper also develops five expressions for determining the 2.5% proof stress （ap2）, n2, the ultimate compressive strength （σp3）, n3, and the ultimate plastic strain （p3%） for given experimental values of three basic material parameters （E0, σ0.01, σ0.2）. These expressions are validated to he effective for the CHSs with t/D 〉_ 0.027. The analytically predicted full-range stress-strain curves have generally shown close agreement with the ones obtained experimentally.