Study on creep deformation and energy development of underground surrounding rock under four‐dimensional support

There is an urgent need to develop optimal solutions for deformation control of deep high‐stress roadways,one of the critical problems in underground engineering.The previously proposed four‐dimensional support(hereinafter 4D support),as a new support technology,can set the roadway surrounding rock under three‐dimensional pressure in the new balanced structure,and prevent instability of surrounding rock in underground engineering.However,the influence of roadway depth and creep deformation on the surrounding rock supported by 4D support is still unknown.This study investigated the influence of roadway depth and creep deformation time on the instability of surrounding rock by analyzing the energy development.The elastic strain energy was analyzed using the program redeveloped in FLAC3D.The numerical simulation results indicate that the combined support mode of 4D roof supports and conventional side supports is highly applicable to the stability control of surrounding rock with a roadway depth exceeding 520 m.With the increase of roadway depth,4D support can effectively restrain the area and depth of plastic deformation in the surrounding rock.Further,4D support limits the accumulation range and rate of elastic strain energy as the creep deformation time increases.4D support can effectively reduce the plastic deformation of roadway surrounding rock and maintain the stability for a long deformation period of 6 months.As confirmed by in situ monitoring results,4D support is more effective for the long‐term stability control of surrounding rock than conventional support.

Modification of constitutive model and evolution of activation energy on 2219 aluminum alloy during warm deformation process

To investigate the flow behavior of 2219 Al alloy during warm deformation, the thermal compression test was conducted in the temperature range of 483-573 K and the strain rate range of 0.001-5 s^-1 on a Gleeble-3500 thermomechanical simulation unit. The true stress-true strain curves obtained showed that the flow stress increased with the decrease in temperature and/or the increase in strain rate and the softening mechanism primarily proceeded via dynamic recovery. The modification on the conventional Arrhenius-type constitutive model approach was made, the material variables and activation energy were determined to be dependent on the deformation parameters. The modified flow stresses were found to be in close agreement with the experimental values. Furthermore, the activation energy obtained under different deformation conditions showed that it decreased with the rise in temperature and/or strain rate, and was also affected by the coupled effect of strain and strain rate.

Modeling of deformation energy at elevated temperatures and its application in Mg-Li-Al-Y alloy

To control the superplastic flow and fracture and examine the variation in deformation energy,the stress and grain size of Mg-7.28Li-2.19Al-0.091Y alloy were obtained using tensile testing and microstructure quantification,and new high temperature deformation energy models were established.Results show that the grain interior deformation energy increases with increasing the strain rate and decreases with increasing the temperature.The variation in the grain boundary deformation energy is opposite to that in the grain interior deformation energy.At a given temperature,critical cavity nucleation energy decreases with increasing strain rate and cavity nucleation becomes easy,whereas at a given strain rate,critical cavity nucleation energy increases with increasing temperature and cavity nucleation becomes difficult.The newly established models of the critical cavity nucleation radius and energy provide a way for predicting the initiation of microcrack and improving the service life of the forming parts.

Experimental study on the deformation behaviour,energy evolution law and failure mechanism of tectonic coal subjected to cyclic loads

Compared to intact coal,tectonic coal exhibits unique characteristics.The deformation behaviours under cyclic loading with different confining pressures and loading rates are monitored by MTS815 test system,and the mechanical and energy properties are analysed using experimental data.The results show that the stress-strain curve could be divided into four stages in a single cycle.The elastic strain and elastic energy density increase linearly with deviatoric stress and are proportional to the confining pressure and loading rate;irreversible strain and dissipated energy density increase exponentially with deviatoric stress,inversely proportional to the confining pressure and loading rate.The internal structure of tectonic coal is divided into three types,all of which are damaged under different deviatoric stress levels,thereby explaining the segmentation phenomenon of stress-strain curve of tectonic coal in the cyclic loading process.Tectonic coal exhibits nonlinear energy storage characteristics,which verifies why the tectonic coal is prone to coal and gas outburst from the principle of energy dissipation.In addition,the damage mechanism of tectonic coal is described from the point of energy distribution by introducing the concepts of crushing energy and friction energy.

Dynamic Soft Tissue Deformation Estimation Based on Energy Analysis

The needle placement accuracy of millimeters is required in many needle-based surgeries. The tissue deformation, especially that occurring on the surface of organ tissue, affects the needle-targeting accuracy of both manual and robotic needle insertions. It is necessary to understand the mechanism of tissue deformation during needle insertion into soft tissue. In this paper, soft tissue surface deformation is investigated on the basis of continuum mechanics, where a geometry model is presented to quantitatively approximate the volume of tissue deformation. The energy-based method is presented to the dynamic process of needle insertion into soft tissue based on continuum mechanics, and the volume of the cone is exploited to quantitatively approximate the deformation on the surface of soft tissue. The external work is converted into potential, kinetic, dissipated, and strain energies during the dynamic rigid needle-tissue interactive process. The needle insertion experimental setup, consisting of a linear actuator, force sensor, needle, tissue container, and a light, is constructed while an image-based method for measuring the depth and radius of the soft tissue surface deformations is introduced to obtain the experimental data. The relationship between the changed volume of tissue deformation and the insertion parameters is created based on the law of conservation of energy, with the volume of tissue deformation having been obtained using image-based measurements. The experiments are performed on phantom specimens, and an energy-based analytical fitted model is presented to estimate the volume of tissue deformation. The experimental results show that the energy-based analytical fitted model can predict the volume of soft tissue deformation, and the root mean squared errors of the fitting model and experimental data are 0.61 and 0.25 at the velocities 2.50 mm/s and 5.00 mm/s. The estimating parameters of the soft tissue surface deformations are proven to be useful for compensating the needle-targeting error in the rigid needle insertion procedure, especially for percutaneous needle insertion into organs.

Deformation mode and energy absorption of polycrystal-inspired square-cell lattice structures

Lattice structures are widely used in many engineering fields due to their excellent mechanical properties such as high specific strength and high specific energy absorption(SEA)capacity.In this paper,square-cell lattice structures with different lattice orientations are investigated in terms of the deformation modes and the energy absorption(EA)performance.Finite element(FE)simulations of in-plane compression are carried out,and the theoretical models from the energy balance principle are developed for calculating the EA of these lattice structures.Satisfactory agreement is achieved between the FE simulation results and the theoretical results.It indicates that the 30◦oriented lattice has the largest EA capacity.Furthermore,inspired by the polycrystal microstructure of metals,novel structures of bi-crystal lattices and quad-crystal lattices are developed through combining multiple singly oriented lattices together.The results of FE simulations of compression indicate that the EA performances of symmetric lattice bi-crystals and quad-crystals are better than those of the identical lattice polycrystal counterparts.This work confirms the feasibility of designing superior energy absorbers with architected meso-structures from the inspiration of metallurgical concepts and microstructures.

Characterization of deformation transition in the rolled LZ91 magnesium alloy under tensile loading

In this study,the mechanical behavior of crystal group of hexagonal close-packed(hcp;αphase)and body-centered cubic(bcc;βphase)during tensile loading was investigated to elucidate the mechanism from elastic to plastic deformation transition of the rolled LZ91 Mg alloy using transmission-X-ray diffraction(transmission-XRD)measurement,transmission electron microscopy(TEM),scanning transmission electron microscopy(STEM),energy dispersive X-ray spectroscopy(EDS).The approximate proof stress of the LZ91 Mg alloy sample was found that the lattice strain retained the expanded state from 0.6%nominal strain,and the transmission-XRD measurement characterized the crystalline behavior during the transition by the integrated intensity of crystal group hcp(100).The lattice strain of bcc(110)decreased from the 0.6%nominal strain due to dislocation activity,which occurred nearβ/βgrain boundary.In addition,we performed the analyses of electron energy loss spectroscopy(EELS)modes,the Li-K peak disappeared from the segregated Li regions of 10–60 nm nearβ/βgrain boundary at the nominal strain of 0.8%.Understanding this mechanical behavior during the elastic to plastic deformation transition by transmission-XRD is crucial for the development of Mg-Li alloys.

Buoyancy driven Flow of a Second-Grade Nanofluid flow Taking into Account the Arrhenius Activation Energy and Elastic Deformation:Models and Numerical Results

The buoyancy driven flow of a second-grade nanofluid in the presence of a binary chemical reaction is analyzed in the context of a model based on the balance equations for mass,species concentration,momentum and energy.The elastic properties of the considered fluid are taken into account.The two-dimensional slip flow of such non-Newtonian fluid over a porous flat material which is stretched vertically upwards is considered.The role played by the activation energy is accounted for through an exponent form modified Arrhenius function added to the Buongiorno model for the nanofluid concentration.The effects of thermal radiation are also examined.A similarity transformations is used to turn the problem based on partial differential equations into a system of ordinary differential equations.The resulting system is solved using a fourth order RK and shooting methods.The velocity profile,temperature profile,concentration profile,local skin friction,local Nusselt number and local Sherwood number are reported for several circumstances.The influence of the chemical reaction on the properties of the concentration and momentum boundary layers is critically discussed.

Influence of niobium and yttrium on plastic deformation energy and plasticity of Ti-based amorphous alloys

Many amorphous alloys have been developed to date,but the low plasticity has limited their application.To achieve an amorphous alloy with high plasticity,a series of(Ti_(40)Zr_(25)Cu_(9)Ni_(8) Be_(18))_(100-x)TM_(x)(x=0,1,2,3,4 at.%,TM=Nb,Y)alloys were designed to study the influence of Nb and Y addition on the plasticity.The amorphous samples were prepared using the vacuum melting and copper mold casting process.The microstructures,glass forming ability and mechanical properties of the alloys were investigated by X-ray diffractometry(XRD),scanning electron microscopy(SEM),high-resolution transmission electron microscopy(HRTEM),depth-sensitive nanoindentation,and uniaxial compressive test.The plasticity of different bulk amorphous alloys was investigated by measuring the plastic deformation energy(PDE)during loading.The relationship between the PDE value and plasticity in bulk amorphous alloys was explored.Results show that Nb addition decreases the PDE value and promotes the generation of multiple shear bands,which significantly increases the fracture strength and plasticity,while the addition of Y element reduces the fracture strength and plastic strain of the alloy.

Orthogonal basic deformation mode method for zero-energy mode suppression of hybrid stress elements

A set of basic deformation modes for hybrid stress finite elements are directly derived from the element displacement field. Subsequently, by employing the so-called united orthogonal conditions, a new orthogonalization method is proposed. The result- ing orthogonal basic deformation modes exhibit simple and clear physical meanings. In addition, they do not involve any material parameters, and thus can be efficiently used to examine the element performance and serve as a unified tool to assess different hybrid elements. Thereafter, a convenient approach for the identification of spurious zero-energy modes is presented using the positive definiteness property of a flexibility matrix. More- over, based on the orthogonality relationship between the given initial stress modes and the orthogonal basic deformation modes, an alternative method of assumed stress modes to formulate a hybrid element free of spurious modes is discussed. It is found that the orthogonality of the basic deformation modes is the sufficient and necessary condition for the suppression of spurious zero-energy modes. Numerical examples of 2D 4-node quadrilateral elements and 3D 8-node hexahedral elements are illustrated in detail to demonstrate the efficiency of the proposed orthogonal basic deformation mode method.

The Continuum Stored Energy for Constitutive Modeling Finite Deformations of Polymeric Materials

With symmetries measured by the Lie group and curvatures revealed by differential geometry, the continuum stored energy function possesses a translational deformation component, a rotational deformation component, and an ellipsoidal volumetric deformation component. The function, originally developed for elastomeric polymers, has been extended to model brittle and ductile polymers. The function fits uniaxial tension testing data for brittle, ductile, and elastomeric polymers, and elucidates deformation mechanisms. A clear distinction in damage modes between brittle and ductile deformations has been captured. The von Mises equivalent stress has been evaluated by the function and the newly discovered break-even stretch. Common practices of constitutive modeling, relevant features of existing models and testing methods, and a new perspective on the finite elasticity-plasticity theory have also been offered.

Analytical solution to mapping rail deformation under bridge transverse deformation using energy variational principle

The track geometry is a critical factor that affects the running safety and riding comfort of trains moving on a high-speed railway bridge.This study addresses the mapping relationship between the track deformation and lateral deformations of bridges.Equilibrium equations and natural boundary conditions of the track-bridge system are established based on the energy variational principle,and an analytical solution is derived for the track deformation accounting for lateral bridge deformations.A five-span simply-supported bridge with continuous welded rail has been selected as the case study.The mapping rail deformations are compared to the finite element results,and both results agree well with each other,validating the analytical method proposed in this paper.The influence factors on the mapping rail deformation are further evaluated.Results show that the mapping rail deformation is consistent with the girder displacement at the area that is away from the girder ends when the flexural stiffness ratio between the track and the bridge girder is low.The interlayer stiffness has a significant effect on the mapping rail deformation when the track flexural stiffness is of a high value.

Measurement of the Energy Absorbed during Nanoscale Deformation of Human Peritubular and Intertubular Dentin

Mineralized tissues are usually constructed of nanosized materials with ordered hierarchical structures. The main reason for their high load-bearing ability is the multi-scale hierarchy. It is important to have a method for measuring the energy absorbed during the nanoscale deformation of mineralized tissues. The objective of this study was to use a combination of nanoindentation and elastic-plastic mechanics techniques to measure the damage resistance of peritubular and intertubular dentin, based on the energy consumed in the plastic deformation regime and the volume created by the indents. The control materials were soda-lime glass, gold, and poly-methyl methacrylate (PMMA). Plastic deformation energy was calculated from the plastic part of load-displacement curves. The mean values of peritubular dentin and intertubular dentin were 3.8 × 109, and 5.2 × 109 J/m3, respectively, compared to glass, PMMA, and gold which were 3.3 × 107, 1.3 × 109, and 3.1 × 109 J/m3, respectively. This method can be applied to study the resistance of mineralized tissues or organic/inorganic hybrid materials to deformation at the nanoscale.

Hot deformation behavior of TC11/Ti-22Al-25Nb dual-alloy in isothermal compression

The high-temperature flow behavior of TCll/Ti-22Al-25 Nb electron beam（EB） weldments was investigated by the isothermal compression tests at the temperature of 900-1060℃ and the strain rate of 0.001-10 s-（-1）.Based on the experimental data,the constitutive equation that describes the flow stress as a function of strain rate and deformation temperature is obtained.The apparent activation energy of deformation is calculated,which decreases with increasing the strain and the value is 334 kJ/mol at strain of 0.90.The efficiency of power dissipation η changes obviously with the variation of deformation conditions.Under the strain rates of 0.01,0.1 and 1 s-（-1）,the value of η increases with increasing the true strain for different deformation temperatures.While the value of η decreases with increasing the strain under the strain rates of 0.001 and 10 s-（-1）.The optimum processing condition is（t（opi）=1060℃,ε（opi）=0.1 s-（-1）） with the peak efficiency of 0.51.Under this deformation,dynamic recrystallization（DRX） is observed obviously in the microstructure of welding zone.Under the condition of 1060℃ and 0.001 s-（-1）,the deformation mechanism is dominated by dynamic recovery（DRV） and the value of η decreases sharply（η=0.02）.The flow instability is predicted to occur since the instability parameter ξ（ε）becomes negative.The hot working process can be carried out safely in the domain with the strain rate of 0.001-0.6 s-（-1） and the temperature of 900-1060℃.

Deformation mechanism and softening effect of extruded AZ31 magnesium alloy sheet at moderate temperatures

The flow stress behavior of extruded AZ31 magnesium alloy sheet was investigated by means of compression tests at temperatures between 473 and 523 K and strain rates ranging from 0.001 to 1.0 s-1. The deformation activation energy of the sheet in extrusion direction （ED） was calculated, and the relationship between the softening effect and deformation mechanism was elucidated by optical microscopy and transmission electron microscopy. The results show that when the extruded AZ31 magnesium alloy samples were compressed at moderate temperatures in ED direction, the deformation activation energy is 174.18 kJ/mol, which means that dynamic recrystallization （DRX） is the main softening effect and is controlled by cross slip of thermal active dislocation. Dislocation slip is the main deformation mechanism in moderate-temperature deformation process except twinning. The main DRX effect at moderate temperatures can be considered to be continuous dynamic recrystallization accommodated with twinning DRX.

Hot deformation behavior of Mg-7.22Gd-4.84Y-1.26Nd-0.58Zr magnesium alloy

The behavior evolvement of Mg-7.22Gd-4.84Y-1.26Nd-0.58Zr（GWN751K） magnesium alloy during the hot deformation process was discussed.The flow stress behavior of the magnesium alloy over the strain rate range of 0.002 to 2.000 s^-1 and in the temperature range of 623 to 773 K was studied on a Gleeble-1500D hot simulator under the maximum deformation degree of 60%.The experimental results showed that the relationship between stress and strain was obviously affected by strain rate and deformation temperature.The flow stress of GWN751K magnesium alloy during high temperature deformation could be represented by the Zener-Hollomon parameter in the hyperbolic Arrhenius-type equation.The stress exponent n and deformation activation energy Q were evaluated by linear regression analysis.The stress exponent n was fitted to be 3.16.The hot deformation activation energy of the alloy during hot deformation was 230.03 kJ/mol.The microstructures of hot deformation were also influenced by strain rate and compression temperature strongly.It was found that the alloy could be extruded at 723 K with the mechanical properties of σ0.2 = 260 MPa,σb = 320 MPa,and δ = 18%.

Hot compression deformation behavior of the Mg-Al-Y-Zn magnesium alloy

The hot deformation behavior of a Mg-Al-Y-Zn magnesium alloy was investigated by hot compressive testing on a Gleeble-1500 thermal simulator at the temperature ranging from 523 to 673 K with the strain rate varying from 0.001 to 1 s^-1. The relationships among flow stress, strain rate, and deformation temperature were analyzed, and the deformation activation energy and stress exponent were calculated. Microstructure evolution of the alloy under different conditions was examined. The results indicated that the maximum value of the flow stress increased with the decrease of deformation temperature or the increase of strain rate. Under the present deformation conditions, dynamic recrystallization （DRX） occurred in the alloy, which was the main softening mechanism during deformation at elevated temperature. The deformation temperature and strain had significant effects on the microstructure of the alloy.

Hot compression deformation behavior of AISI 321 austenitic stainless steel

The hot compression behavior of AISI 321 ll00~C and the strain rates of 0.01-1 s-1 using a Baehr austenitic stainless steel was studied at the temperatures of 950- DIL-805 deformation dilatometer. The hot deformation equations and the relationship between hot deformation parameters were obtained. It is found that strain rate and deformation temperature significantly influence the flow stress behavior of the steel. The work hardening rate and the peak value of flow stress increase with the decrease of deformation temperature and the increase of strain rate. In addition, the activation energy of deformation （Q） is calculated as 433.343 kJ/mol. The microstructural evolution during deformation indicates that, at the temperature of 950~C and the strain rate of 0.01 s-1, small circle-like precipitates form along grain boundaries; but at the temperatures above 950~C, the dissolution of such precipitates occurs. Energy-dispersive X-ray analyses indicate that the precipitates are complex carbides of Cr, Fe, Mn, Ni, and Ti.

Simple physically-based constitutive equations for hot deformation of 2024 and 7075 aluminum alloys

The hot working behaviors of 2024 and 7075 aluminum alloys were studied through constitutive analysis based on a physically-based approach which accounts for the dependence of the elastic modulus and the self-diffusion coefficient of aluminum on temperature. It was demonstrated that the lattice self-diffusion activation energy of aluminum（142 k J/mol） can be used in the Zener-Hollomon parameter＇s formula as the deformation activation energy and the theoretical exponent of 5 can be set in the modified hyperbolic sine law to describe the peak flow stresses. By consideration of physically-based material＇s parameters, it was possible to conduct a comparative study on the hot flow stress of 2024 and 7075 aluminum alloys. It was concluded that the used approach in the current work can be considered as a versatile tool in future comparative hot working studies, especially in studies dedicated to alloy development.

High-temperature mechanical properties and deformation behavior of high Nb containing TiAl alloys fabricated by spark plasma sintering

A high Nb containing TiA1 alloy was prepared from the pre-alloyed powder of Ti-45Al-8.5Nb-0.2B-0.2W-0.02Y （at%） by spark plasma sintering （SPS）. Its high-temperature mechanical properties and compressive deformation behavior were investigated in a temperature range of 700 to 1050℃ and a strain rate range of 0.002 to 0.2 s 1. The results show that the high-temperature mechanical properties of the high Nb containing TiA1 alloy are sensitive to deformation temperature and strain rate, and the sensitivity to strain rate tends to rise with the deformation temperature increasing. The hot workability of the alloy is good at temperatures higher than 900℃, while fracture occurs at lower temperatures. The flow curves of the samples compressed at or above 900℃ exhibit obvious flow softening after the peak stress. Un- der the deformation condition of 900-1050℃ and 0.002-0.2 s 1, the interrelations of peak flow stress, strain rate, and deformation tempera- ture follow the Arrhenius＇ equation modified by a hyperbolic sine function with a stress exponent of 5.99 and an apparent activation energy of 441.2 kJ.mol-1.