Effect of annealing temperature on microstructure and mechanical properties of Mg-Zn-Zr-Nd alloy with large final rolling deformation

In this study,the Mg-3Zn-0.5Zr-χNd(χ=0,0.6)alloys were subjected to final rolling treatment with large deformation of 50%.The impact of annealing temperatures on the microstructure and mechanical properties was investigated.The rolled Mg-3Zn-0.5Zr-0.6Nd alloy exhibited an ultimate tensile strength of 386 MPa,a yield strength of 361 MPa,and an elongation of 7.1%.Annealing at different temperatures resulted in reduced strength and obviously increased elongation for both alloys.Optimal mechanical properties for the Mg-3Zn-0.5Zr-0.6Nd alloy were achieved after annealing at 200℃,with an ultimate tensile strength of 287 MPa,a yield strength of 235 MPa,and an elongation of 26.1%.The numerous deformed microstructures,twins,and precipitated phases in the rolled alloy could impede the deformation at room temperature and increase the work hardening rate.After annealing,a decrease in the work hardening effect and an increase in the dynamic recovery effect were obtained due to the formation of fine equiaxed grains,and the increased volume fraction of precipitated phases,which significantly improved the elongation of the alloy.Additionally,the addition of Nd element could enhance the annealing recrystallization rate,reduce the Schmid factor difference between basal and prismatic slip systems,facilitate multi-system slip initiation and improve the alloy plasticity.

Case study on the mechanics of NPR anchor cable compensation for large deformation tunnel in soft rock in the Transverse Mountain area,China

A study was conducted to analyze the deformation mechanism of strongly weathered quartz schist in the Daliangshan Tunnel,located in the western Transverse Mountain area.A large deformation problem was experienced during the tunnel construction.To mitigate this problem,a support system was designed incorporating negative Poisson ratio(NPR)anchor cables with negative Poisson ratio effect.Physical model experiments,field experiments,and numerical simulation experiments were conducted to investigate the compensation mechanical behavior of NPR anchor cables.The large deformations of soft rocks in the Daliangshan Tunnel are caused by a high ground stress,a high degree of joint fracture development,and a high degree of surrounding rock fragmentation.A compensation mechanics support system combining long and short NPR anchor cables was suggested to provide sufficient counter-support force(approximately 350 kN)for the surrounding rock inside the tunnel.Comparing the NPR anchor cable support system with the original support system used in the Daliangshan tunnel showed that an NPR anchor cable support system,combining cables of 6.3 m and 10.3 m in length,effectively prevented convergence of surrounding rock deformation,and the integrated settlement convergence value remained below 300 mm.This study provides an effective scientific basis for resolving large deformation problems in deeply buried soft rocks in western transverse mountain areas.

Topology Optimization of Metamaterial Microstructures for Negative Poisson’s Ratio under Large Deformation Using a Gradient-Free Method

Negative Poisson’s ratio(NPR)metamaterials are attractive for their unique mechanical behaviors and potential applications in deformation control and energy absorption.However,when subjected to significant stretching,NPR metamaterials designed under small strain assumption may experience a rapid degradation in NPR performance.To address this issue,this study aims to design metamaterials maintaining a targeted NPR under large deformation by taking advantage of the geometry nonlinearity mechanism.A representative periodic unit cell is modeled considering geometry nonlinearity,and its topology is designed using a gradient-free method.The unit cell microstructural topologies are described with the material-field series-expansion(MFSE)method.The MFSE method assumes spatial correlation of the material distribution,which greatly reduces the number of required design variables.To conveniently design metamaterials with desired NPR under large deformation,we propose a two-stage gradient-free metamaterial topology optimization method,which fully takes advantage of the dimension reduction benefits of the MFSE method and the Kriging surrogate model technique.Initially,we use homogenization to find a preliminary NPR design under a small deformation assumption.In the second stage,we begin with this preliminary design and minimize deviations in NPR from a targeted value under large deformation.Using this strategy and solution technique,we successfully obtain a group of NPR metamaterials that can sustain different desired NPRs in the range of[−0.8,−0.1]under uniaxial stretching up to 20% strain.Furthermore,typical microstructure designs are fabricated and tested through experiments.The experimental results show good consistency with our numerical results,demonstrating the effectiveness of the present gradientfree NPR metamaterial design strategy.

Calculating real-time surface deformation for large active surface radio antennas using a graph neural network

This paper presents an innovative surrogate modeling method using a graph neural network to compensate for gravitational and thermal deformation in large radio telescopes.Traditionally,rapid compensation is feasible for gravitational deformation but not for temperature-induced deformation.The introduction of this method facilitates real-time calculation of deformation caused both by gravity and temperature.Constructing the surrogate model involves two key steps.First,the gravitational and thermal loads are encoded,which facilitates more efficient learning for the neural network.This is followed by employing a graph neural network as an end-to-end model.This model effectively maps external loads to deformation while preserving the spatial correlations between nodes.Simulation results affirm that the proposed method can successfully estimate the surface deformation of the main reflector in real-time and can deliver results that are practically indistinguishable from those obtained using finite element analysis.We also compare the proposed surrogate model method with the out-of-focus holography method and yield similar results.

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.

Excavation compensation theory and supplementary technology system for large deformation disasters

Given the challenges in managing large deformation disasters in energy engineering,traffic tunnel engineering,and slope engineering,the excavation compensation theory has been proposed for large deformation disasters and the supplementary technology system is developed accordingly.This theory is based on the concept that“all destructive behaviors in tunnel engineering originate from excavation.”This paper summarizes the development of the excavation compensation theory in five aspects:the“theory,”“equipment,”“technology,”the design method with large deformation mechanics,and engineering applications.First,the calculation method for compensation force has been developed based on this theory,and a comprehensive large deformation disaster control theory system is formed.Second,a negative Poisson's ratio anchor cable with high preload,large deformation,and super energy absorption characteristics has been independently developed and applied to large deformation disaster control.An intelligent tunnel monitoring and early warning cloud platform system are established for remote monitoring and early warning system of Newton force in landslide geological hazards.Third,the double gradient advance grouting technology,the two-dimensional blasting technology,and the integrated Newton force monitoring--early warning--control technology are developed for different engineering environments.Finally,some applications of this theory in China's energy,traffic tunnels,landslide,and other field projects have been analyzed,which successfully demonstrates the capability of this theory in large deformation disaster control.

Numerical simulation of rockburst disaster and control strategy of constant resistance and large deformation anchor cable in Gaoloushan tunnel

The Gaoloushan Tunnel in Longnan City,Gansu Province,China,frequently experiences rockburst disasters due to high in-situ stress.Managing rockburst in deep-buried tunnels remains a challenging issue.This paper employs RFPA(Rock Failure Process Analysis)software to establish a calculation model of constant resistance and large deformation(CRLD)anchorages and analyzes the effects of different support methods and pre-stress levels on rockburst.We simulate the process of tunnel rockburst disasters and find that ordinary anchor support incurs rockburst on the right arch waist and arch top,forming a V-shaped explosion pit.CRLD anchor support has several advantages in rockburst control,such as more uniform stress distribution in the surrounding rock,a uniform distribution of plastic zones,less noticeable damage to the tunnel,and effective control of the arch top displacement.The effectiveness of the CRLD anchor support under varying pre-stress conditions shows that a higher prestress results in a smaller plastic zone of the surrounding rock and arch top displacement and a lower number of acoustic emission signals,which better explains the excavation compensation effect.Moreover,adding long anchorages in the deep surrounding rock area can better control rockburst and reduce surrounding rock deformation.Based on these findings,we propose a comprehensive control system that combines long and short anchorages and provides the optimal scheme based on calculations.Therefore,by using high-prestress CRLD anchor support and the combination of long and short anchorages at critical positions,we can enhance the integrity of the surrounding rock,effectively absorb the energy released by the surrounding rock deformation,and reduce the incidence of rockburst disasters.

A dynamic large-deformation particle finite element method for geotechnical applications based on Abaqus

In this paper,the application of Abaqus-based particle finite element method(PFEM)is extended from static to dynamic large deformation.The PFEM is based on periodic mesh regeneration with Delaunay triangulation to avoid mesh distortion.Additional mesh smoothing and boundary node smoothing techniques are incorporated to improve the mesh quality and solution accuracy.The field variables are mapped from the old to the new mesh using the closest point projection method to minimize the mapping error.The procedures of the proposed Abaqus-based dynamic PFEM(Abaqus-DPFEM)analysis and its implementation in Abaqus are detailed.The accuracy and robustness of the proposed approach are examined via four illustrative numerical examples.The numerical results show a satisfactory agreement with published results and further confirm the applicability of the Abaqus-DPFEM to solving dynamic large-deformation problems in geotechnical engineering.

LARGE DEFORMATION OF CIRCULAR MEMBRANE UNDER THE CONCENTRATED FORCE

Making use of basic equation of large deformation of circular membrane under the concentrated force and its boundary conditions and Hencky transformation, the problems of nonlinear boundary condition were solved. The Hencky transformation was extended and a exact solution of large deformation of circular membrane under the concentrated force has been obtained.

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.

Application of MLPG in large deformation analysis

Two-dimensional large deformation analysis of hyperelastic and elasto-plastic solids based on the Meshless Local Petrov-Galerkin method （MLPG） is presented. A material configuration based the nonlinear MLPG formulation is introduced for the large deformation analysis of both path-dependent and path-independent materials. The supports of the MLS approximation functions cover the same sets of nodes during material deformation, thus the shape function needs to be computed only in the initial stage. The multiplicative hyperelasto-plastic constitutive model is adopted to avoid objective time integration for stress update in large rota- tion. With this constitutive model, the computational formulations for path-dependent and path-independent materials become identical. Computational efficiency of the nonlinear MLPG method is discussed and optimized in several aspects to make the MLPG an O（N） algorithm. The numerical examples indicate that the MLPG method can solve large deformation problems accurately. Moreover, the MLPG computations enjoy better convergence rate than the FEM under very large particle distortion.

Nonlinear formulation for flexible multibody system with large deformation

In this paper, nonlinear modeling for flexible multibody system with large deformation is investigated. Absolute nodal coordinates are employed to describe the displacement, and variational motion equations of a flexible body are derived on the basis of the geometric nonlinear theory, in which both the shear strain and the transverse normal strain are taken into account. By separating the inner and the boundary nodal coordinates, the motion equations of a flexible multibody system are assembled. The advantage of such formulation is that the constraint equations and the forward recursive equations become linear because the absolute nodal coordinates are used. A spatial double pendulum connected to the ground with a spherical joint is simulated to investigate the dynamic performance of flexible beams with large deformation. Finally, the resultant constant total energy validates the present formulation.

Two-Dimensional Large Deformation Finite Element Analysisfor the Pulling-up of Plate Anchor

Based on mesh regeneration and stress interpolation from an old mesh to a new one, a large deformation finite element model is developed for the study of the behaviour of circular plate anchors subjected to uplift loading. For the deterruination of the distributions of stress components across a clay foundation, the Recovery by Equilibrium in Patches is extended to plastic analyses. ABAQUS, a commercial finite element package, is customized and linked into our program so as to keep automatic and efficient running of large deformation calculation. The quality of stress interpolation is testified by evaluations of Tresca stress and nodal reaction forces. The complete pulling-up processes of plate anchors buried in homogeneous clay arc simulated, and typical pulling force-displacement responses of a deep anchor and a shallow anchor are compared. Different from the results of previous studies, large deformation analysis is of the capability of estimating the breakaway between the anchor bottom and soils. For deep anchors, the variation of mobilized uplift resistance with anchor settlement is composed of three stages, and the initial buried depths of anchors affect the separation embedment slightly. The uplift bearing capacity of deep anchors is usually higher than that of shallow anchors.

Compensation excavation method control for large deformation disaster of mountain soft rock tunnel

In recent years,the mine tunneling method and the new Austrian tunneling method have been considered the main theories of tunneling approaches in China.It is difficult for the traditional technique to overcome the large deformation problems imposed by complex geological conditions of mountain soft rock tunneling.Hence,the compensation excavation method has been proposed to solve this issue under the consideration that all damage in tunneling originates from the excavation.It uses supportive strategies to counteract the excavation effects successfully.This paper provides an overview of the fundamental ideas of the compensation excavation method,methodologies,and field applications.The scientific validity and feasibility of the compensation excavation method were investigated through the practical engineering study of the Muzhailing and Changning tunnels.

Isogeometric analysis of free-form Timoshenko curved beams including the nonlinear effects of large deformations

In the present paper, the isogeometric analysis（IGA） of free-form planar curved beams is formulated based on the nonlinear Timoshenko beam theory to investigate the large deformation of beams with variable curvature. Based on the isoparametric concept, the shape functions of the field variables（displacement and rotation） in a finite element analysis are considered to be the same as the non-uniform rational basis spline（NURBS） basis functions defining the geometry. The validity of the presented formulation is tested in five case studies covering a wide range of engineering curved structures including from straight and constant curvature to variable curvature beams. The nonlinear deformation results obtained by the presented method are compared to well-established benchmark examples and also compared to the results of linear and nonlinear finite element analyses. As the nonlinear load-deflection behavior of Timoshenko beams is the main topic of this article, the results strongly show the applicability of the IGA method to the large deformation analysis of free-form curved beams. Finally, it is interesting to notice that, until very recently, the large deformations analysis of free-form Timoshenko curved beams has not been considered in IGA by researchers.

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.

Numerical modeling of large deformation and nonlinear frictional contact of excavation boundary of deep soft rock tunnel

Roadways excavated in soft rocks at great depth are difficult to be maintained due to large deformation of surrounding rocks, which greatly influences the safety and efficiency of deep resources exploitation. During the excavation process of a deep soft rock tunnel, the rock wall may be compacted due to large deformation. In this paper, the technique to address this problem by a two-dimensional (2D) finite element software, large deformation engineering analyses software (LDEAS 1.0), is provided. By using the Lagrange multiplier method, the kinematic constraint of non-penetrating condition and static constraint of Coulomb friction are introduced to the governing equations in the form of incremental displacement. The numerical example demonstrates the efficiency of this technology. Deformations of a transportation tunnel in inclined soft rock strata at the depth of 1 000 m in Qishan coal mine and a tunnel excavated to three different depths are analyzed by two models, i.e. the additive decomposition model and polar decomposition model. It can be found that the deformation of the transportation tunnel is asymmetrical due to the inclination of rock strata. For extremely soft rock, large deformation can converge only for the additive decomposition model. The deformation of surrounding rocks increases with the increase in the tunnel depth for both models. At the same depth, the deformation calculated by the additive decomposition model is smaller than that by the polar decomposition model.

Characteristics of microseismic b-value associated with rock mass large deformation in underground powerhouse caverns at different stress levels

Rock mass large deformation in underground powerhouse caverns has been a severe hazard in hydropower engineering in Southwest China.During the development of rock mass large deformation,a sequence of fractures was generated that can be monitored using microseismic(MS)monitoring techniques.Two MS monitoring systems were established in two typical underground powerhouse caverns featuring distinct geostress levels.The MS b-values associated with rock mass large deformation and their temporal variation are analysed.The results showed that the MS bvalue in course of rock mass deformation was less than 1.0 in the underground powerhouse caverns at a high stress level while larger than 1.5 at a low stress level.Prior to the rock mass deformation,the MS b-values derived from both the high-stress and low-stress underground powerhouse caverns show an incremental decrease over 10%within 10 d.The results contribute to understanding the fracturing characteristics of MS sources associated with rock mass large deformation and provide a reference for early warning of rock mass large deformation in underground powerhouse caverns.

Similar simulation study on the deformation and failure of surrounding rock of a large section chamber group under dynamic loading

Large and super-large section chamber groups in coal mines are frequently affected by dynamic loads resulting from production activities such as roadway driving and blasting.The stability of the surrounding rock is poor,and it is difficult to control.In this paper,a similar simulation test was used to study the deformation and evolution laws of the surrounding rock of a triangle-shaped chamber group under different dynamic loads.The results showed that under dynamic loading,the vertical stress of the surrounding rock of the chamber group increased in an oscillatory form.The maximum stress concentration coefficient reached 4.09.The damage degree of the roof was greater than that of the two sides.The deformation of the roof was approximately 1.2 times that of the two sides.For the chamber closer to the power source,the stress oscillation amplitude of the surrounding rock was larger,and the failure was more serious.The force of the anchorage structure showed a phased increasing characteristic;additionally,the force of the anchorage structure on the adjacent side of the chambers was greater than that on the other side.This study reveals the deformation and failure evolution laws of the surrounding rock of large section chamber groups under dynamic loading.

Time-dependent squeezing deformation mechanism of tunnels in layered soft-rock stratum under high geo-stress

Large squeezing deformation of layered soft rock tunnel under high geo-stress has a significant time-dependent deformation behavior.In this paper,we studied the deformation mechanism during the construction period of deep-buried softrock tunnel by means of a combination of field observations and a numerical method.First,a new classification criterion for large deformations based on the power exponent variation law between the deformation and the strength-stress ratio is proposed.Then,the initial damage tensor reflecting the bedding plane(joint)distribution and an equivalent damage evolution equation derived from the viscoplastic strain are introduced based on the geometric research method,i.e.,a new rheological damage model(RDL model)of layered soft rock is established consisting of elastic,viscous,viscoelastic,viscoplastic and plastic elements.A field test was conducted on the Maoxian tunnel in Sichuan province,southwestern China,which is in broken phyllite(layered soft rock)under high geo-stress.The tunnel has experienced large deformation due to serious squeezing pressure,thus we adopted double primary support method to overcome the supporting structure failure problems.The rheological parameters of phyllite in the Maoxian tunnel were recognized by using SA-PSO optimization,and the RDL model does a good job in describing the time-dependent deformation behavior of a layered soft-rock tunnel under high geo-stress.Thus,the RDL model was used to investigate the supporting effect and bearing mechanism of the double primary support method.Compared with the single primary support method,the surrounding rock pressure,secondary lining force,surrounding rock deformation,and the depth of the damage to the rock mass was reduced by 40%-60%after the double primary support method was used.