Effect of strain rate and deformation temperature on strain hardening and softening behavior of pure copper

The effects of the deformation temperature and the strain rate on the hot deformation behavior of pure copper were investigated based on compression tests. The expressions of strain hardening rate, dynamic recrystallization critical stress, saturated stress, dynamic recovery volume fraction and dynamic recrystallization volume fraction were determined. According to the processing map, the instability regions occur in regions of 400?450 °C, 0.001?0.05 s?1 and 450?750 °C, 0.05?1 s?1. The deformation mechanism in the stability region is dynamic recrystallization. The flow stress was predicted. The results also show that the true stress–true strain curves predicted by the extracted model are in good agreement with the experimental results.

Elevated temperature strain softening characteristics of 12Cr1MoV steel friction welding pipe joints

The strain softening characteristics analysis of 12Cr1MoV streel friction welding pipe joints.which were removed from heating apparatus pipes ager over 9 and is yearly of service, was undertaken. It is concluded that the evident softening did not occur in the weld metal and HAZ during serice. whereas it did in the base metal 2mm apart from the center of the weld metal. The difference is due to the restriction of the pipe hoop, which is formed on the joint during friction welding. The bainite. microstructure in the weld metal and HA Z, which is harder than the pearlite, pecrostpucture in the base metal, makes contpibution too. ThIS phenomenon is peculiar to the friction weldings pipes.

Influences of strain softening and seepage on elastic and plastic solutions of circular openings in nonlinear rock masses

Considering the influence of strain softening, the solutions of stress, displacement, plastic softening region radius and plastic residual region radius were derived for circular openings in nonlinear rock masses subjected to seepage. The radial stress distribution curve, ground reaction curve, and relation curve between plastic softening region radius and supporting force in three different conditions were drawn respectively. From the comparisons among these results for different conditions, it is found that when the supporting force is the same, the displacement of tunnel wall considering both seepage and strain softening is 85.71% greater than that only considering seepage. The increase values of radial displacement at 0.95 m and plastic softening region radius at 6.6 m show that the seepage and strain softening have the most unfavorable effects on circular opening stability in strain softening rock masses.

Estimation of compaction grouting pressure in strain softening soils

A new method was proposed to predict the limited compaction grouting pressure for the soft soils. Theoretical basis of the method considered the conical shear failure above the grout bulb. Using the Mohr-Coulomb yield criterion as the initial yield function, the limited compaction grouting pressure was determined, according to the softening elastic-plastic model based on the conventional triaxial compression tests to simulate the strain softening soils. The small strain in the elastic zone and large stain in the plastic zone and the rational yield function for the strain softening phase stage, the analytical solutions to the compaction grouting pressure were presented. The results indicate reasonable agreement and show a good potential of the proposed method for rationally optimizing the design of compaction grouting operations.

ELASTO-PLASTIC CONSTITUTIVE MODEL OF SOIL-STRUCTURE INTERFACE IN CONSIDERATION OF STRAIN SOFTENING AND DILATION

The behavior of soil-structure interface plays a major role in the definition of soil-structure interaction. In this paper a bi-potential surface elasto-plastic model for soil-structure interface is proposed in order to describe the interface deformation behavior,including strain softening and normal dilatancy. The model is formulated in the framework of generalized potential theory,in which the soil-structure interface problem is regard as a two-dimensional mathematical problem in stress field,and plastic state equations are used to replace the traditional field surface. The relation curves of shear stress and tangential strain are fitted by a piecewise function composed by hyperbolic functions and hyperbolic secant functions,while the relation curves of normal strain and tangential strain are fitted by another piecewise function composed by quadratic functions and hyperbolic secant functions. The approach proposed has the advantage of deriving an elastoplastic constitutive matrix without postulating the plastic potential functions and yield surface. Moreover,the mathematical principle is clear,and the entire model parameters can be identified by experimental tests. Finally,the predictions of the model have been compared with experimental results obtained from simple shear tests under normal stresses,and results show the model is reasonable and practical.

Damage constitutive model for strain-softening rock based on normal distribution and its parameter determination

Firstly, using the damage model for rock based on Lemaitre hypothesis about strain equivalence, a new technique for measuring strength of rock micro-cells by adopting the Mohr-Coulomb criterion was developed, and a statistical damage evolution equation was established based on the property that strength of micro-cells is consistent with normal distribution function, through discussing the characteristics of random distributions for strength of micro-cells, then a statistical damage constitutive model that can simulate the full process of rock strain softening under specific confining pressure was set up. Secondly, a new method to determine the model parameters which can be applied to the situations under different confining pressures was proposed, by deeply studying the relations between the model parameters and characteristic parameters of the full stress-strain curve under different confining pressures. Therefore, a unified statistical damage constitutive model for rock softening which can reflect the effect of different confining pressures was set up. This model makes the physical property of model parameters explicit, contains only conventional mechanical parameters, and leads its application more convenient. Finally, the rationality of this model and its parameters-determining method were identified via comparative analyses between theoretical and experimental curves.

Analytical solutions of stress and displacement in strain softening rock mass around a newly formed cavity

The closed form solutions of the stress and displacement in strain softening rock mass around a newly formed cavity are derived with a three step-wise elasto-plastic model. Hoek-Brown criterion is adopted as the yielding criterion of rock mass. Damage factors are proposed to account for degradation of the material parameters to reflect the degree of strain softening. The surrounding rock mass around the cavity is divided into three regions: elastic region, strain softening region and residual state region. The analytical solutions of stress, strain, displacement and radius of each region are obtained. The effects of the strain softening and shear dilatancy behavior on the results are investigated with parametric studies. The results show that the radii of the residual state region and strain softening region in the surrounding rock mass with higher damage degree are larger. The radii of the residual state region and strain softening region are 1-2 times and 1.5-3 times of the cavity radius, respectively. The radial and tangential stresses decrease with the increase of the damage factor. The displacement of the cavity wall for the case with maximum plastic bulk strain is nearly twice than that with no dilation. Rock mass moves more toward the center for the case with larger damage factor and shear dilation. The area of the plastic region is larger when the damage factors are considered. The displacements in the surrounding rock mass increase with the increase of the damage factors and shear dilation factors. The solutions can be applied to the stability analysis and support design of the underground excavation.

Effect of strain hardening and strain softening on welding distortion and residual stress of A7N01-T4 aluminum alloy by simulation analysis

The effect of strain hardening and strain softening behavior of flow stress changing with temperature on welding residual stress, plastic strain and welding distortion of ATN0 1-T4 aluminum alloy was studied by finite simulation method. The simulation results show that the weld seam undergoes strain hardening in the temperature range of 180-250 ℃, however, it exhibits strain softening at temperature above 250 ℃ during welding heating and cooling process. As a result, the strain hardening and strain softening effects counteract each other, introducing slightly influence on the welding residual stress, residual plastic strain and distortion. The welding longitudinal residual stress was determined by ultrasonic stress measurement method for the flat plates of A7N01-T4 aluminum alloy. The simulation results are well accordant with test ones.

Strain Softening and Hardening Behavior in AZ61 Magnesium Alloy

The deformation behavior of AZ61 Mg alloy during hot deformation has been investigated in wide temperature and strain rate range by a Gleeble simulator. Specimens are deformed in compression in the temperature range of 523-673 K and at strain rates of 0.001-1 s-1. It is found that the flow curves exhibit a peak and then decrease towards steady-state of classical DRX, which decrease with rising temperature and decreasing strain rate. The deformation behavior of the specimens can be attributed to the occurrence of strain hardening and softening. As stress decreases, the strain hardening rate declines at a fast rate when temperature rises or strain rate decreases. The shapes of θ-σ curves indicate some important features such as subgrain formation, the criticai stress, the peak stress and steady stress. The onset of DRX can be determined by the point of inflection on θ-σ or Inθ-σ curves.

MICROMECHANICAL MODELLING OF STRAIN SOFTENING IN MICROCRACK-WEAKENED QUASI-BRITTLE MATERIALS

By using the concept of domain of microcrack growth(DMG),the micromechanisms of damage in quasi-brittle materials subjected to triaxial either tensile or compressive loading are investigated and the complete strew-strain relation including four stages is obtained from micromechanical analysis.The regime of pre-peak nonlinear hardening corresponds to the distributed damage,i.e.the stable propagation of microcracks.After the attainment of the ultimate strength of load-bearing capacity, some microcracks experience the second unstable growth and the distributed damage is transmitted to the localization of damage.These analyses improve our understanding of the hardening and softening behaviors of quasi-brittle materials.

THE ASYMPTOTIC SOLUTION TO THE ANTIPLANE SHEAR DYNAMICCRACK-TIP FIELD IN AN ELASTIC STRAIN-SOFTENING VISCOPLASTIC MATERIAL

The elastic strain softening-viscoplastic model is given in this paper. Using this model, the asymptotic stress and strain equations surrounding the tip of a propagating crock are given and numerical results ale obtained under antiplane shear. The analysis and calculation show that at the crack tip the strain possesses logarithmic singularity (ln(R/r))(1/(n+1)) while the stress is like (ln(R/r))(-n/(n+1)), therefore the asymptotic behaviour of the elastic strain-softening viscoplastic field is revealed under the antiplane shear.

A vector sum analysis method for stability evolution of expansive soil slope considering shear zone damage softening

Slope stability analysis is a classical mechanical problem in geotechnical engineering and engineering geology.It is of great significance to study the stability evolution of expansive soil slopes for engineering construction in expansive soil areas.Most of the existing studies evaluate the slope stability by analyzing the limit equilibrium state of the slope,and the analysis method for the stability evolution considering the damage softening of the shear zone is lacking.In this study,the large deformation shear mechanical behavior of expansive soil was investigated by ring shear test.The damage softening characteristic of expansive soil in the shear zone was analyzed,and a shear damage model reflecting the damage softening behavior of expansive soil was derived based on the damage theory.Finally,by skillfully combining the vector sum method and the shear damage model,an analysis method for the stability evolution of the expansive soil slope considering the shear zone damage softening was proposed.The results show that the shear zone subjected to large displacement shear deformation exhibits an obvious damage softening phenomenon.The damage variable equation based on the logistic function can be well used to describe the shear damage characteristics of expansive soil,and the proposed shear damage model is in good agreement with the ring shear test results.The vector sum method considering the damage softening behavior of the shear zone can be well applied to analyze the stability evolution characteristics of the expansive soil slope.The stability factor of the expansive soil slope decreases with the increase of shear displacement,showing an obvious progressive failure behavior.

A COMBINED PARAMETRIC QUADRATIC PROGRAMMING AND PRECISE INTEGRATION METHOD BASED DYNAMIC ANALYSIS OF ELASTIC-PLASTIC HARDENING/SOFTENING PROBLEMS

The objective of the paper is to develop a new algorithm for numerical solution of dynamic elastic-plastic strain hardening/softening problems. The gradient dependent model is adopted in the numerical model to overcome the result mesh-sensitivity problem in the dynamic strain softening or strain localization analysis. The equations for the dynamic elastic-plastic problems are derived in terms of the parametric variational principle, which is valid for associated, non-associated and strain softening plastic constitutive models in the finite element analysis. The precise integration method, which has been widely used for discretization in time domain of the linear problems, is introduced for the solution of dynamic nonlinear equations. The new algorithm proposed is based on the combination of the parametric quadratic programming method and the precise integration method and has all the advantages in both of the algorithms. Results of numerical examples demonstrate not only the validity, but also the advantages of the algorithm proposed for the numerical solution of nonlinear dynamic problems.

A WORK SOFTENING JOINT ELEMENT USED IN DYNAMIC ANALYSIS OF SOIL-STRUCTURE

This paper introduces an elasto-plastic joint element characterised by strain hardening and softening in the analysis of dynamic soil-structure interaction, the phenomena of sep- aration and sliding on the contact surface between soil and structure can be better simulated and the process can also be described. The interaction problems in a typical soil-structure system are analyzed in terms of elasto-plastic joint element as well as elastic ones. The results show that the elasto-plastic joint element is much better than the elastic one in modelling, especially in that the relative displace- ments accross the joint element can be much greater than that of the elastic case. Separation and slid- ing are not only related to the coefficient of friction and cohesion but also to their changes with plastic volumetric strain.

Numerical modelling of post-failure behaviors of coal specimens

A modelling approach consisting of best-fit relations to estimate the post-yield strength parameters is presented for simulating post-peak behavior beyond the point of residual strength of coal pillars having different w/h ratios.The model was developed based on back-analysis of the complete stress-strain behavior of specimens belonging to six different Indian coal seams with different w/h ratios of 0.5 e13.5.It was found that the simultaneous degradation of the cohesion and friction angle of the Mohr-Coulomb rock material characterizes the post-peak strength behavior of the rock.The resulting expressions are simplistic as they require parameters that can be easily determined using uniaxial and triaxial compression results.Eventually,the developed model was validated by simulating the triaxial tests of coal specimens with different sizes under varying confining stresses and comparing its findings with the published test results.The study showed that its implementation in the numerical model could reproduce laboratory-observed mechanical response,deformation behavior,and failure mechanism very closely.

Theoretical solution for displacement and stress in strain-softening surrounding rock under hydraulic-mechanical coupling

This study focuses on the stress and displacement of a circular opening that is excavated in a strain-softening rock mass under hydraulic-mechanical coupling.It follows the generalized Hoek-Brown(H-B) failure criterion.Moreover,an improved numerical method and stepwise procedure are proposed.This method considers the deterioration of the strength,deformation,and dilation angle.It also incorporates the hydraulic-mechanical coupling and the variation of elastic strain in the plastic region.Several examples are conducted to demonstrate the validity and accuracy of the proposed solution through MATLAB programming and FLAC software.Parametric studies are also conducted to highlight the influence of hydraulic–mechanical coupling on stress and displacement.Results show that in this case,stress confinement is lower and tunnel convergences are higher than the corresponding stresses and displacements obtained when those factors are not considered.The displacement and plastic radius are also larger than those obtained when hydraulic-mechanical coupling is not considered.

Dynamic analysis of fault rockburst based on gradient-dependent plasticity and energy criterion

Fault rockburst is treated as a strain localization problem under dynamicloading condition considering strain gradient and strain rate. As a kind of dynamic fracturephenomena, rockburst has characteristics of strain localization, which is considered as aone-dimensional shear problem subjected to normal compressive stress and tangential shear stress.The constitutive relation of rock material is bilinear (elastic and strain softening) and sensitiveto shear strain rate. The solutions proposed based on gradient-dependent plasticity show thatintense plastic strain is concentrated in fault band and the thickness of the band depends on thecharacteristic length of rock material. The post-peak stiffness of the fault band was determinedaccording to the constitutive parameters of rock material and shear strain rate. Fault bandundergoing strain softening and elastic rock mass outside the band constitute a system and theinstability criterion of the system was proposed based on energy theory. The criterion depends onthe constitutive relation of rock material, the structural size and the strain rate. The staticresult regardless of the strain rate is the special case of the present analytical solution. Highstrain rate can lead to instability of the system.

Effect of heterogeneity on mechanical and acoustic emission characteristics of rock specimen

The influence of heterogeneity on mechanical and acoustic emission characteristics of rock specimen under uniaxial compress was studied with numerical simulation methods.Weibull distribution function was adopted to describe the mesoscopic heterogeneity of rocks.The failure process of heterogeneous rock specimen under uniaxial loading was simulated using FLAC 3D software.Five schemes were adopted to investigate the influence of heterogeneity.The results demonstrate that as the homogeneity increases,the peak strength and brittleness of rocks increase,and the macro elastic modulus improves as well.Heterogeneity has great influence on macro elastic modulus and strength when the homogeneity coefficient is less than 20.0.The volume expansion is not so obvious when the homogeneity increases.As the homogeneity coefficient increases the acoustic emissions modes change from swarm shock to main shock.When the homogeneity coefficient is high,the cumulative acoustic emission events-axial strain curve is gentle before the rock failure.The numerical results agree with the previously numerical results and earlier experimental measurements.

Analysis of progressive failure of pillar and instabilitycriterion based on gradient-dependent plasticity

A mechanical model for strain softening pillar is proposed considering the characteristics of progressive shear failure and strain localization. The pillar undergoes elastic, strain softening and slabbing stages. In the elastic stage, vertical compressive stress and deformation at upper end of pillar are uniform, while in the strain softening stage there appears nonuniform due to occurrence of shear bands, leading to the decrease of load-carrying capacity. In addition, the size of failure zone increases in the strain softening stage and reaches its maximum value when slabbing begins. In the latter two stages, the size of elastic core always decreases. In the slabbing stage, the size of failure zone remains a constant and the pillar becomes thinner. Total deformation of the pillar is derived by linearly elastic Hookes law and gradient-dependent plasticity where thickness of localization band is determined according to the characteristic length. Post-peak stiffness is proposed according to analytical solution of averaged compressive stress-average deformation curve. Instability criterion of the pillar and roof strata system is proposed analytically (using) instability condition given by Salamon. It is found that the constitutive parameters of material of pillar, the geometrical size of pillar and the number of shear bands influence the stability of the system; stress gradient controls the starting time of slabbing, however it has no influence on the post-peak stiffness of the pillar.

Dilation angle variations in plastic zone around tunnels in rocks-constant or variable dilation parameter

Dilation angle is a significant parameter needed for numerical simulation of tunnels.Even though dilation parameter is physically variable and dependent on confinement and experienced shear plastic strain based on the existing dilation models,numerical simulations of tunnels and underground openings with constant dilation parameter usually lead to satisfactory results in practical use.This study aims to find out why constant dilation angle is enough under practical conditions to simulate numerically tunnels and underground excavations in spite of the fact that dilation angle is variable in laboratory and experimental scale.With this aim,this work studies how mobilized dilation angle varies in a plastic zone surrounding a tunnel.For the circular tunnel under uniform in situ stress field,the stepwise finite difference approximation analytical solution considering strain softening rock mass behavior with mobilized dilation angle was used to study how mobilized dilation angle varies in plastic zone around tunnel under very different conditions.In practical conditions determined in this study,dilative behavior of all over the plastic zone around the tunnel can be approximated to constant dilation angle in the middle region of the plastic zone.Moreover,the plastic zone displacements for mobilized and constant dilation angle models are compared with each other.Further investigation under more general non-uniform in situ stress conditions and non-circular tunnels is performed by using the commercial finite difference software to numerically simulate the Mine-by experimental tunnel of AECL(Atomic Energy of Canada Limited)and the arched tunnel.Although the Mine-by and arched tunnels were numerically simulated based on the mobilized dilation angle model,the variability associated with dilation angle around the simulated Mine-by and arched tunnels is insignificant,and dilation angle is approximately constant in the plastic zone.