An improved strain-softening constitutive model of granite considering the effect of crack deformation

This paper presents an improved strain-softening constitutive model considering the effect of crack deformation based on the triaxial cyclic loading and unloading test results.The improved model assumes that total strain is a combination of plastic,elastic,and crack strains.The constitutive relationship between the crack strain and the stress was further derived.The evolutions of mechanical parameters,i.e.strength parameters,dilation angle,unloading elastic modulus,and deformation parameters of crack,with the plastic strain and confining pressure were studied.With the increase in plastic strain,the cohesion,friction angle,dilation angle,and crack Poisson's ratio initially increase and subsequently decrease,and the unloading elastic modulus and the crack elastic modulus nonlinearly decrease.The increasing confining pressure enhances the strength and unloading elastic modulus,and decreases the dilation angle and Poisson's ratio of the crack.The theoretical triaxial compressive stress-strain curves were compared with the experimental results,and they present a good agreement with each other.The improved constitutive model can well reflect the nonlinear mechanical behavior of granite.

Nonlinear coupling modeling and dynamics analysis of rotating flexible beams with stretching deformation effect

Dynamic coupling modeling and analysis of rotating beams based on the nonlinear Green-Lagrangian strain are introduced in this work.With the reservation of the axial nonlinear strain,there are more coupling terms for axial and transverse deformations.The discretized dynamic governing equations are obtained by using the finite element method and Lagrange’s equations of the second kind.Time responses are conducted to compare the proposed model with other previous models.The stretching deformation due to rotating motion is observed and calculated by special formulations under dynamic equilibrium.The stretching deformation and the change of the associated equilibrium position are taken into account to analyze the free vibration and frequency response of the rotating beams.Analytical and numerical comparisons show that the proposed model can provide reliable results,while the previous models may lead to imprecise results,especially in high-speed conditions.

Size effects on plastic deformation behavior in micro radial compression of pure copper

Micro radial compression tests were carried out on cylindrical specimens of pure copper polycrystals with different grain sizes. Experimental results indicated that phenomena of decreasing forming force, increasing scatter of forming force and more irregular surface topography occurred with the increase of grain size. A modified surface model based on dislocations pile-up in surface layer grains, and a flow stress scattering formulation based on standard deviation and grain size distribution were proposed to analyze size effects on forming force in micro compression. The inhomogeneous deformation of surface layer grains was discussed by the main deformation manner of rotation. A good agreement with the experimental results was achieved.

Size effects on deformation behavior of C5210 phosphor bronze thin sheet

To investigate the effects of thickness and grain size on mechanical and deformation properties of C5210 phosphor bronze thin sheets, samples with different grain sizes were obtained through annealing heat treatment at different temperatures; and then tensile tests of samples with different thicknesses and grain sizes were conducted at room temperature. The results show that yield strength increases with decreasing thickness from 800 to 50 μm, but work hardening exponent and total elongation decrease, and a modified model was proposed to describe the relation between yield strength and thickness; yield strength decreases as the grain size increases, but work hardening exponent shows an increasing trend, total elongation increases to a peak and then decreases. Fracture morphology of tensile specimens was observed by SEM, which indicates that all tensile specimens are ductile fracture. The dimple intensity increases as the specimen thickness increases but reduces with the specimen grain size increasing.

Effects of ultrasonic vibration on plastic deformation of AZ31 during the tensile process

An investigation on the plastic behavior of AZ31 magnesium alloy under ultrasonic vibration（with a frequency of 15 kHz and a maximum output of 2 kW） during the process of tension at room temperature was conducted to reveal the volume effect of the vibrated plastic deformation of AZ31.The characteristics of mechanical properties and microstructures of AZ31 under routine and vibrated tensile processes with different amplitudes were compared.It is found that ultrasonic vibration has a remarkable influence on the plastic behavior of AZ31 which can be summarized into two opposite aspects：the softening effect which reduces the flow resistance and improves the plasticity,and the hardening effect which decreases the formability.When a lower amplitude or vibration energy is applied to the tensile sample,the softening effect dominates,leading to a decrease of AZ31 deformation resistance with an increase of formability.Under the application of a high-vibrating amplitude,the hardening effect dominates,resulting in the decline of plasticity and brittle fracture of the samples.

Static deformation of a multilayered one-dimensional hexagonal quasicrystal plate with piezoelectric effect

Quasicrystals （QCs） are sensitive to the piezoelectric （PE） effect. This paper studies static deformation of a multilayered one-dimensional （1D） hexagonal QC plate with the PE effect. The exact closed-form solutions of the extended displacement and traction for a homogeneous piezoelectric quasicrystal （PQC）plate are derived from an eigensystem. The general solutions for multilayered PQC plates are then obtained using the propagator matrix method when mechanical and electrical loads are applied on the top surface of the plate. Numerical examples for several sandwich plates made up of PQC, PE, and QC materials are provided to show the effect of stacking sequence on phonon, phason, and electric fields under mechanical and electrical loads, which is useful in designing new composites for engineering structures.

Closed-form solution to thin-walled box girders considering effects of shear deformation and shear lag

Considering three longitudinal displacement functions and uniform axial displacement functions for shear lag effect and uniform axial deformation of thin-walled box girder with varying depths,a simple and efficient method with high precision to analyze the shear lag effect of thin-walled box girders was proposed.The governing differential equations and boundary conditions of the box girder under lateral loading were derived based on the energy-variational method,and closed-form solutions to stress and deflection corresponding to lateral loading were obtained.Analysis and calculations were carried out with respect to a trapezoidal box girder under concentrated loading or uniform loading and a rectangular box girder under concentrated loading.The analytical results were compared with numerical solutions derived according to the high order finite strip element method and the experimental results.The investigation shows that the closed-form solution is in good agreement with the numerical solutions derived according to the high order finite strip method and the experimental results,and has good stability.Because of the shear lag effect,the stress in cross-section centroid is no longer zero,thus it is not reasonable enough to assume that the strain in cross-section centroid is zero without considering uniform axial deformation.

Anchoring effect and energy-absorbing support mechanism of large deformation bolt

To research the anchoring effect of large deformation bolt,tensile and drawing models are established.Then,the evolution laws of drawing force,bolt axial force and interfacial shear stress are analyzed.Additionally,the influence of structure element position on the anchoring effect of large deformation bolt is discussed.At last,the energy-absorbing support mechanism is discussed.Results show that during the drawing process of normal bolt,drawing force,bolt axial force and interfacial shear stress all gradually increase as increasing the drawing displacement,but when the large deformation bolt enters the structural deformation stage,these three values will keep stable;when the structure element of large deformation bolt approaches the drawing end,the fluctuation range of drawing force decreases,the distributions of bolt axial force and interfacial shear stress of anchorage section are steady and the increasing rate of interfacial shear stress decreases,which are advantageous for keeping the stress stability of the anchorage body.During the working process of large deformation bolt,the strain of bolt body is small,the working resistance is stable and the distributions of bolt axial force and interfacial shear stress are steady.When a rock burst event occurs,the bolt and bonding interface cannot easily break,which weakens the dynamic disaster degree.

Closed-form solution for shear lag effects of steel-concrete composite box beams considering shear deformation and slip

Based on the consideration of longitudinal warp caused by shear lag effects on concrete slabs and bottom plates of steel beams,shear deformation of steel beams and interface slip between steel beams and concrete slabs,the governing differential equations and boundary conditions of the steel-concrete composite box beams under lateral loading were derived using energy-variational method.The closed-form solutions for stress,deflection and slip of box beams under lateral loading were obtained,and the comparison of the analytical results and the experimental results for steel-concrete composite box beams under concentrated loading or uniform loading verifies the closed-form solution.The investigation of the parameters of load effects on composite box beams shows that:1) Slip stiffness has considerable impact on mid-span deflection and end slip when it is comparatively small;the mid-span deflection and end slip decrease significantly with the increase of slip stiffness,but when the slip stiffness reaches a certain value,its impact on mid-span deflection and end slip decreases to be negligible.2) The shear deformation has certain influence on mid-span deflection,and the larger the load is,the greater the influence is.3) The impact of shear deformation on end slip can be neglected.4) The strain of bottom plate of steel beam decreases with the increase of slip stiffness,while the shear lag effect becomes more significant.

Influence of deformation path on the forming effect in a multistep flexible rolling process

The flexible rolling process(FRP) is a novel three-dimensional(3 D) forming process that combines the multipoint and traditional rolling forming. The principle of FRP is based on thickness thinning, so the deformation path significantly impacts the forming effect. In this study, the multistep forming process with different deformation paths was introduced to improve the forming effect of FRP. For instance, with the convex surface part, three finite element models of multistep FRP(MSFRP) were established. The corresponding numerical simulations and forming experiments performed among different deformation paths showed the surface part with a longer effective forming region was obtained and the forming regions with more steps in MSFRP were smoother. Thus, the sheet-metal utilization rate was greatly improved. Moreover, the MSFRP can improve the longitudinal bending effect dramatically and thereby endowing the forming part with a better forming effect. Therefore, MSFRP is a prospective method for broad applications.

Grain size effect on cyclic deformation behavior and springback prediction of Ni-based superalloy foil

In order to clarify the influence of grain size on cyclic deformation response of superalloy sheets and springback behavior,cyclic loading-unloading and shearing tests were performed on the superalloy foils with 0.2 mm in thickness and diverse grain sizes.The results show that,the decline ratio of elastic modulus is weakened with increasing grain size,and the Bauschinger effect becomes evident with decreasing grain size.Meanwhile,U-bending test results determine that the springback is diminished with increasing grain size.The Chaboche,Anisotropic Nonlinear Kinematic(ANK)and Yoshida-Uemori(Y-U)models were utilized to fit the shear stress-strain curves of specimens.It is found that Y-U model is sufficient of predicting the springback.However,the prediction accuracy is degraded with increasing grain size.

ELECTRO-THERMAL EFFECTS AND DEFORMATION RESPONSE OF CARBON FIBER MAT CEMENT BEAMS

A carbon fiber mat is a sheet composed of intercrossing short carbon fibers,which has more stable and lower electrical resistivity compared with dispersed short carbon fiber mixed in cement.Thereby carbon fiber mat cement could exhibit obvious electro-thermal effect.When electrified,the temperature of composite structures made up of cement mortar and carbon fiber mat will rise rapidly.If the temperature field is not uniform,temperature difference will cause structures to deform,which can be used to adjust the deformation of structures.The temperature field and deformation response driven by the electro-thermal effects of a type of carbon fiber mat cement beams are studied.Firstly,the temperature and deformation responses are studied using theories of thermal conduction and elasticity.Secondly,experimental results are given to verify the theoretical solution.These two parts lay the foundation for temperature and deformation adjustment.

Effects of microrolling parameters on the microstructure and deformation behavior of pure copper

Microrolling experiments and uniaxial tensile tests of pure copper under different annealing conditions were carried out in this paper. The effects of grain size and reduction on non-uniform deformation, edge cracking, and microstructure were studied. The experimen- tal results showed that the side deformation became more non-uniform, resulting in substantial edge bulge, and the uneven spread increased with increasing grain size and reduction level. When the reduction level reached 80% and the grain size was 65 μm, slight edge cracks occurred. When the grain size was 200 μm, the edge cracks became wider and deeper. No edge cracks occurred when the grain size was 200 μm and the reduction level was less than 60%; edge cracks occurred when the reduction level was increased to 80%. As the reduction level increased, the grains were gradually elongated and appeared as a sheet-like structure along the rolling direction; a fine lamellar structure was obtained when the grain size was 20 lam and the reduction level was less than 60%.

EXPERIMENTAL PLASTIC DEFORMATION ANALYSIS BY MEANS OF THERMOPLASTIC EFFECT

This paper proposes a new experimental method of quantitative plastic deformation analysis by means of the thermoplastic effect. The incremental plastic strain distribution for a single shear specimen was obtained by using this method.

3D deformation effect and optimal excavated design of surface mine

The three-dimensional （3D） deformation effect of the slope engineering under the step-by-step excavation for the Antaibao surface mine was analyzed using the FLAC^3D technique. An optimal excavated scheme with a relatively steeper slope angle of 47° instead of 30° was successfully implemented at the west wall in the geological section 73200 of the mine area, where the 3D effect of the nonlinear large deformation of the slope was taken into account. Based on the above research conclusion, put forward the countermeasures of shortening mining length, excavating by different regions, timely foot backfilling to protect the excavated slope, and monitoring and feedback adjustment by studying the nonlinear effect. The results show that these countermeasures are effective in controlling maximum deformation and increasing the stability of the slope.

Effect of Hot Deformation on Microstructure and Hardness of In-situ TiB_2/7075 Composite

Hardness of the TiB2/7075 composite increased with increasing deformation temperature. In the annealed TiB2/7075 composite, a great amount of fiber-like MgZn2 phases (about 1 mum in length) and small MgZn2 phases (about 100 nm in size) were precipitated nearby the grain boundaries where the TiB2 particles exist. After deformation at 300 degreesC, some of the large precipitates and all the small precipitates in these area dissolved into the matrix, meanwhile, fine precipitates were formed in grains. After deformation at 450 degreesC, all the precipitates in the annealed composite dissolved into the matrix, and new phases were precipitated in grains. The dissolution of the large fiber-like precipitate makes the saturation level of the matrix increased and leads to an increased solution hardening and natural aging, which contribute much to the hardening effect.

Effects of Plastic Deformation and Stresses on Dilatation duringthe Martensitic Transformation in a B-bearing Steel

To provide data for improved modelling of the behaviour of steel components in a simultaneous forming and quenching process, the effects of plastic deformation and stresses on dilatation during the martensitic transformation in a B-bearing steel were investigated. It was found that plastic deformation of austenite at high temperatures enhances ferrite formation significantly, and consequently, the dilatation decreases markedly even at a cooling rate of 280'C/s. The created ferritic-martensitic microstructure possesses clearly lower hardness and strength than the martensitic structure. Elastic stresses cause the preferred orientation in martensite to be formed so that diametric dilatation can increase by nearly 200% under axial compression.

Kaiser Effect of EME During Deformation and Fracture of Coal and Rock

The Kaiser effect of electromagnetic emission (EME) during the deformation and fracture of coal and rock is studied experimentally and theoretically. The results show that the electromagnetic emission can be produced during these processes and has the Kaiser effect. The Kaiser effect of electromagnetic emission (EME) is produced because of the inconvertibility of energy dissipation and the memorability of structures of coal and rock.

EFFECTIVE STRESS AND STRAIN IN FINITE DEFORMATION

Whether the concept of effective stress and strain in elastic-plastic theory is still valid under the condition of finite deformation was mainly discussed. The uni-axial compression experiments in plane stress and plane strain states were chosen for study. In the two kinds of stress states, the stress-strain curve described by logarithm strain and rotated Kirchhoff stress matches the experiments data better than the curves defined by other stress-strain description.

BAUSCHINGER EFFECT AND DISLOCATION STRUCTURE IN STAINLESS STEEL DURING CYCLIC DEFORMATION

Cyclic deformation in symmetrical push-pull mode was carried out at room temperature in air using a Schenck hydropuls machine.The total strain amplitude which was kept constant dur- ing the test ranged from ±0.004 to±0.012.The 0.2% offset yield stress σ_(0.2f) in tension and σ_(0.2r) in compression and peak stress σ were measured from the stress-strain hysteresis loop at various cycles.The Bauschinger strenghth differential factor(BSDF)was then calcu- lated from σ_(0.2f) and σ_(0.2r).The energy loss △E of each cycle was determined from hysteresis loop areas.These parameters,BSDF,σ and △E,appear to have two distinctively different stages. The dislocation structures were observed using TEM in specimens deformed cyclically,for various cycles.The observation shows that the dislocations pile-up mainly against grain boundaries and there exist large amount of deformation twins.The addition of 0.25 wt-% ni- trogen reduced the stacking fault energy of the alloy significantly.Cross-slip and climb are therefore rather difficult to occur during the cyclic deformation at room temperature,and well-defined dislocation cells and walls can only be seen at the final stage of fatigue.