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.

Pressure generation under deformation in a large-volume press

Deformation can change the transition pathway of materials under high pressure,thus significantly affects physical and chemical properties of matters.However,accurate pressure calibration under deformation is challenging and thereby causes relatively large pressure uncertainties in deformation experiments,resulting in the synthesis of complex multiphase materials.Here,pressure generations of three types of deformation assemblies were well calibrated in a Walker-type largevolume press(LVP)by electrical resistance measurements combined with finite element simulations(FESs).Hard Al_(2)O_(3) or diamond pistons in shear and uniaxial deformation assemblies significantly increase the efficiency of pressure generation compared with the conventional quasi-hydrostatic assembly.The uniaxial deformation assembly using flat diamond pistons possesses the highest efficiency in these deformation assemblies.This finding is further confirmed by stress distribution analysis based on FESs.With this deformation assembly,we found shear can effectively promote the transformation of C60 into diamond under high pressure and realized the synthesis of phase-pure diamond at relatively moderate pressure and temperature conditions.The present developed techniques will help improve pressure efficiencies in LVP and explore the new physical and chemical properties of materials under deformation in both science and technology.

Size-dependent thermomechanical vibration characteristics of rotating pre-twisted functionally graded shear deformable microbeams

A three-dimensional(3D)thermomechanical vibration model is developed for rotating pre-twisted functionally graded(FG)microbeams according to the refined shear deformation theory(RSDT)and the modified couple stress theory(MCST).The material properties are assumed to follow a power-law distribution along the chordwise direction.The model introduces one axial stretching variable and four transverse deflection variables including two pure bending components and two pure shear ones.The complex modal analysis and assumed mode methods are used to solve the governing equations of motion under different boundary conditions(BCs).Several examples are presented to verify the effectiveness of the developed model.By coupling the slenderness ratio,gradient index,rotation speed,and size effect with the pre-twisted angle,the effects of these factors on the thermomechanical vibration of the microbeam with different BCs are investigated.It is found that with the increase in the pre-twisted angle,the critical slenderness ratio and gradient index corresponding to the thermal instability of the microbeam increase,while the critical material length scale parameter(MLSP)and rotation speed decrease.The sensitivity of the fundamental frequency to temperature increases with the increasing slenderness ratio and gradient index,and decreases with the other increasing parameters.Moreover,the size effect can suppress the dynamic stiffening effect and enhance the Coriolis effect.Finally,the mode transition is quantitatively demonstrated by a modal assurance criterion(MAC).

Shear deformation and plate shape control of hot-rolled aluminium alloy thick plate prepared by asymmetric rolling process

Asymmetric rolling （ASR）, as one of severe plastic deformation （SPD） methods to make ultra-fine materials with enhanced performance is mainly used to prepare foil and thin strip. The asymmetrical rolling was achieved by adjusting the diameters of the upper roll and the bottom roll and was used to prepare hot-rolled thick plate of 5182 aluminium alloy. The shear deformation and plate shape control were experimentally studied. The experimental results show that asymmetrical rolling has a significant effect on metal deformation stream and can somehow refine microstructure and improve the uniformity of microstructure and properties. The asymmetrical rolling process can also reduce the rolling force. However, bending of rolling plate often happens during asymmetrical rolling process. The factors affecting the bending were discussed.

基于Deform 3D的AZ31镁合金不对称挤压变形工艺模拟

通过Deform 3D软件模拟了AZ31镁合金不对称挤压变形工艺过程。结果表明,设置不同水平长度流动距离促使材料不对称地流入挤压通道,进而形成不对称剪切变形,出现应变及应力集中分布的不对称性,促使材料晶粒沿着剪切面偏转,获得细晶、弱织构的高性能镁合金坯料。

Anchorage performance of large-diameter FRP bolts and their application in large deformation roadway

In underground coal mines, fibre reinforced polymer(FRP) bolt is ideal for mined rib reinforcements as it can prevent gas explosions caused by shearer frictional spark. With increasing mining depth, small diameter FRP bolts used in shallow underground mining cannot fulfil the rib support requirements. Under the engineering background of deep underground shortwall mining in Wudong coal mine, this paper systematically studies Φ27 mm FRP bolt support for large deformation coal rib. Specimens with a fan-shaped cross-section were used to enable the tensile testing of the bolt rod, the measured average tensile strength of the studied FRP bolt was(486.1 ± 9.6) MPa with a maximum elongation of 5.7%±0.6%.The shear strength of the bolt was measured as approximately 258 MPa using a self-made double shear testing apparatus. Based on the equivalent radial stiffness principle, a laboratory short encapsulation pullout test(SEPT) method for rib bolting has been developed undertaken consideration of the mechanical properties of the coal seam. Results showed that the average peak anchorage forces of the Φ27 mm FRP bolt and Φ20 mm steel rebar bolt were 108.4 and 66.4 k N, respectively, which were agreed with the theoretical calculations and field measurements. Based on theoretical analysis of the loading states of the bolt under site conditions, bolting method of full-length resin grouting was adopted to offset the weaknesses of the FRP bolt. Numerical method was employed to compare the bolting effect using Φ27 mm FRP bolts and steel rebar bolts. Large diameter FRP bolting was determined as the optimum rib support scheme to increase the productivity of the coal mine and to enhance the ground control capability for+425 level mining roadways. This study provides the laboratory testing design and theoretical prediction of large diameter FRP bolts used for rib support in large deformation roadways.

Structural and Geochronological Evidence for Multiple Episodes of Tertiary Deformation along the Ailaoshan-Red River Shear Zone, Southeastern Asia, Since the Paleocene

Structural analyses show that the Ailaoshan-Red River shear zone （ASRRSZ） in Ailao Mountain is composed of three different deformational domains. These domains may represent three episodes of left-lateral slip experienced by the ASRRSZ. The first episode of such deformation occurred throughout the eastern high-grade belt of the ASRRSZ under a transtensional regime and produced L- type tectonites of amphibolite grade. The second episode of left-lateral slip formed high strain zones overprinting the high-grade belt. Its deformational mechanism is similar to simple shear and the deformed rocks are L-S mylonites of greenschist grade. The third episode of left-lateral slip took place chiefly in a western low-grade belt of the ASRRSZ. This deformation occurred in a transpressional regime, formed an overall structure pattern of a sinistral thrust system and produced phyllonites of low-greenschist grade. Geochronological data indicated that the three episodes of left-lateral slip happened before ～58-56 Ma, at least from ～27 Ma to 22 Ma and at ～13-12 Ma respectively. The first episode of slip in the ASRRSZ appeared to correspond to the initial collision of India and Asia at ～60 Ma. The second episode took place almost at the same time as the most intensive compression and uplift in Tibet. The latest event might represent a further eastward material flow in Tibet after ～16-13 Ma. Thus, the ASRRSZ of southeastern Asia probably experienced three main episodes of Tertiary left- lateral slip in the course of intracontinental convergence since the India-Asia collision.

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.

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.

A new higher-order shear deformation theory and refined beam element of composite laminates

A new higher-order shear deformation theory based on global-local superposition technique is developed. The theory satisfies the free surface conditions and the geometric and stress continuity conditions at interfaces. The global displacement components are of the Reddy theory and local components are of the internal first to third-order terms in each layer. A two-node beam element based on this theory is proposed. The solutions are compared with 3D-elasticity solutions. Numerical results show that present beam element has higher computational efficiency and higher accuracy.

Deformation behaviour and microstructure evolution of AlMg6Mn alloy during shear spinning

Deformation behavior and microstructure of AlMg6Mn alloy subjected to shear spinning were studied by means of mechanical characterization, optical and SEM＋EDS microscopy. Specimens were shear spun on an industrial spinning machine using different mandrels, providing reductions of wall thickness of 30%, 50% and 68%. The grain structure developed during shear spinning refines gradually. The grains elongate in axial direction with increase of reduction, and also stretches along circumferencial direction. Optimal combination of strength and elongation is observed. This is attributed to grain refinement and dislocation reactions with particles and atoms of Mg and Mn in solid solution.

Hot shear deformation constitutive analysis of fine-grained ZK60 Mg alloy sheet fabricated via dual equal channel lateral extrusion and sheet extrusion

Dual equal channel lateral extrusion(DECLE)process with various passes followed by sheet extrusion process was performed to produce fine-grained ZK60 alloy sheets.The coarse grain structure of the annealed sample after applying sheet extrusion(size:68μm)changed to fine grains of 6.0 and 5.2μm after 3 and 5 passes of DECLE and following extrusion.The hot shear deformation behavior of samples was studied by developing constitutive equations based on shear punch test(SPT)results.SPT was carried out in the temperature range of 200−300℃ and strain rate range of 0.003−0.33 s^(–1).The activation energy of 125−139 kJ/mol and the stress exponent of 3.5−4.2 were calculated for all conditions,which indicated that dislocation creep,controlled by dislocation climb and solute drag mechanism,acted as the main hot deformation mechanism.It was concluded that material constants of n and Q are dependent on the microstructural factors such as grain size and second phase particle fraction,and the relationship of which was anticipated using a 3D surface curve.Moreover,the similar strong basal texture of extruded sheets gave rise to the same deformation mechanisms during SPT and similar n and Q values for ZK60 alloy.

Deformation Localization and Shear Fracture of a Rapidly Solidified Al-Fe-V-Si Alloy at Elevated Temperature

The tensile and fatigue behavior of a dispersoid strengthened, powder metallurgy Al-Fe-V-Si alloy at ambient and elevated temperatures was investigated. The results show that the strength and ductility of the alloy decrease significantly with increasing temperature and decreasing strain rate. Micro-structural examinations reveal that this change in mechanical behavior with increasing temperature is related to the mode of deformation of the alloy. Further observations show that localized shear deformation is responsible for the losses in both strength and ductility of the alloy at elevated temperature.

Experimental Study of Drop Deformation and Breakup in Simple Shear Flows

The experimental results of the deformation and breakup of a single drop immersed in a Newtonian liq-uid and subjected to a constant shear rate which generated by counter rotating Couette apparatus were presented in this paper. From experimental observations, the breakup occurred by three mechanisms, namely, necking, end pinching, and capillary instability. Quantitative results for the deformation and breakup of drop are presented. The maximum diameter and Sauter mean diameter of daughter drops and capillary thread radius are linearly related to the inverse shear rate and independent of the initial drop size, the dimensionless wavelength which is the wave-length divided by the thread width at breakup is independent of the shear rate and initial drop size, and the deforma-tion of threads follows a pseudo-affine deformation for Cai/Cac larger than 2.

DIFFERENTIAL QUADRATURE METHOD FOR BENDING OF ORTHOTROPIC PLATES WITH FINITE DEFORMATION AND TRANSVERSE SHEAR EFFECTS

Based on the Reddy's theory of plates with the effect of higher-order shear deformations, the governing equations for bending of orthotropic plates with finite deformations were established. The differential quadrature (DQ) method of nonlinear analysis to the problem was presented. New DQ approach, presented by Wang and Bert (DQWB), is extended to handle the multiple boundary conditions of plates. The techniques were also further extended to simplify nonlinear computations. The numerical convergence and comparison of solutions were studied. The results show that the DQ method presented is very reliable and valid. Moreover, the influences of geometric and material parameters as well as the transverse shear deformations on nonlinear bending were investigated. Numerical results show the influence of the shear deformation on the static bending of orthotropic moderately thick plate is significant.

Assessment of Deformation of Shear Localized Chip in High Speed Machining

As the cutting speed goes higher, the mechanism of chip deformation will be changed significantly, i.e., continuous chip in low cutting speed will shift to serrated chip with shear localization. For the shear localized chip, the parameters used to assess the chip deformation for continuous chip, such as shorten coefficient ξ, shear angle φ and shear strain ε, can not describe the chip deformation correctly or comprehensively. This paper deals with the assessment of chip deformation of shear localization. There are two deformation regions in shear localized chip, one is the chip segment body with relative smaller plastic deformation, another one is the boundary between segments with shear localization, so called shear band. Considering the two distinct deformation regions, two parameters are used to define their deformation respectively. According to the analysis of chip formation process, the equations have been deduced to calculate the shear strains of shear band ε, shear strain of chip segment ε 1 and shear rate so that the shear localized chip deformation can be assessed correctly and comprehensively. By use of this assessment, the chip deformation in machining selenium treated stainless steel (STSS) and common stainless steel at various cutting conditions is investigated. The experiment results obtained by the machining of stainless steel prove that: (1) the shear strain and strain rate increase with the increasing of cutting speed; (2) the shear strain in shear band can be over 10 when cutting speed exceeding 200 m/min for both types of stainless steel, and it is much higher than the strain of chip segment. The difference will be enlarged as the cutting speed increasing; (3) As the comparison, the shear strain for the STSS is a little lower than that for JIS304; (4) The stain rate is extremely high (= 2.5×10 5 1/s ). In range of cutting speed less than 180 m/min, the strain rate for STSS is lower than that for JIS304. However, when the cutting speed is higher than 180 m/min, the strain rate for STSS is higher than that for JIS304.

Finite element investigation of steel built-up shear links subjected to inelastic deformations

Non-linear finite element models accounting for large displacements have been used to investigate the behavior of steel built-up shear links that had previously been tested using large-scale experiments. The links were designed using steel grades with yield points ranging from high to low strengths. The objectives of the numerical analyses were to further investigate the non-linear behavior and to correlate the numerical results with experimental observations. Elasto-plastic as well as cyclic stress-strain material properties were incorporated to study the influence of material behavior on the overall shear link response. Non-linear monotonie analyses of the shear links incorporating the cyclic stress-strain steel properties resulted in similar trends in the response as the backbone curves recorded from the physical experiments. The numerical models of built-up shear links utilizing structural grade steels closely correlated to the experimentally recorded shear strength. Models utilizing low yield point steels overestimated the shear strength, which was caused by the characteristics of cyclic behavior of those steels. The detailed numerical models also allowed for investigation of the plastic strain demands on the different components of the link. It was shown that finite element models combined with appropriate stress-strain relationship may be used with confidence to check the design of shear links of different steel grades and sectional geometries.

THIRD ORDER SHEAR DEFORMATION MODEL FOR LAMINATED SHELLS WITH FINITE ROTATIONS:FORMULATION AND CONSISTENT LINEARIZATION

The paper presents an approach for the formulation of general laminated shells based on a third order shear deformation theory. These shells undergo finite (unlimited in size) rotations and large overall motions but with small strains. A singularity-free parametrization of the rotation field is adopted. The constitutive equations, derived with respect to laminate curvilinear coordinates, are applicable to shell elements with an arbitrary number of orthotropic layers and where the material principal axes can vary from layer to layer. A careful consideration of the consistent linearization procedure pertinent to the proposed parametrization of finite rotations leads to symmetric tangent stiffness matrices. The matrix formulation adopted here makes it possible to implement the present formulation within the framework of the finite element method as a straightforward task.

DEFORMATION LOCALIZATION AND SHEAR BAND FRACTURE IN STRONG ANISOTROPY SHEET TENSION

The tensile deformation localization and the shear band fracture behaviors of sheet metals with strong anisotropy are numerically simulated by using Updating Lagrange finite element method, Quasi-how plastic constitutive theory([1]) and B-L planar anisotropy yield criterion([2]). Simulated results are compared with experimental ones. Very good consistence is obtained between numerical and experimental results. The relationship between the anisotropy coefficient R and the shear band angle theta is found.

Thermoelastic Analysis of Non-uniform Pressurized Functionally Graded Cylinder with Variable Thickness Using First Order Shear Deformation Theory(FSDT) and Perturbation Method

Recently application of functionally graded materials（FGMs） have attracted a great deal of interest. These materials are composed of various materials with different micro-structures which can vary spatially in FGMs. Such composites with varying thickness and non-uniform pressure can be used in the aerospace engineering. Therefore, analysis of such composite is of high importance in engineering problems. Thermoelastic analysis of functionally graded cylinder with variable thickness under non-uniform pressure is considered. First order shear deformation theory and total potential energy approach is applied to obtain the governing equations of non-homogeneous cylinder. Considering the inner and outer solutions, perturbation series are applied to solve the governing equations. Outer solution for out of boundaries and more sensitive variable in inner solution at the boundaries are considered. Combining of inner and outer solution for near and far points from boundaries leads to high accurate displacement field distribution. The main aim of this paper is to show the capability of matched asymptotic solution for different non-homogeneous cylinders with different shapes and different non-uniform pressures. The results can be used to design the optimum thickness of the cylinder and also some properties such as high temperature residence by applying non-homogeneous material.