A thermo-mechanical damage constitutive model for deep rock considering brittleness-ductility transition characteristics

This paper developed a statistical damage constitutive model for deep rock by considering the effects of external load and thermal treatment temperature based on the distortion energy.The model parameters were determined through the extremum features of stress−strain curve.Subsequently,the model predictions were compared with experimental results of marble samples.It is found that when the treatment temperature rises,the coupling damage evolution curve shows an S-shape and the slope of ascending branch gradually decreases during the coupling damage evolution process.At a constant temperature,confining pressure can suppress the expansion of micro-fractures.As the confining pressure increases the rock exhibits ductility characteristics,and the shape of coupling damage curve changes from an S-shape into a quasi-parabolic shape.This model can well characterize the influence of high temperature on the mechanical properties of deep rock and its brittleness-ductility transition characteristics under confining pressure.Also,it is suitable for sandstone and granite,especially in predicting the pre-peak stage and peak stress of stress−strain curve under the coupling action of confining pressure and high temperature.The relevant results can provide a reference for further research on the constitutive relationship of rock-like materials and their engineering applications.

Thermo-mechanical coupled particle model for rock

A thermo-mechanical coupled particle model for simulation of thermally-induced rock damage based on the particle simulation method was proposed.The simulation results of three verification examples,for which the analytical solutions are available,demonstrate the correctness and usefulness of the thermo-mechanical coupled particle model.This model is applied to simulating an application example with two cases：one is temperature-independent elastic modulus and strength,while the other is temperature-dependent elastic modulus and strength.The related simulation results demonstrate that microscopic crack initiation and propagation process with consideration of temperature-independent and temperature-dependent elastic modulus and strength are different and therefore,the corresponding macroscopic failure patterns of rock are also different.On the contrary,considering the temperature-dependent elastic modulus and strength has no or little effect on the heating conduction behavior.Numerical results,which are obtained by using the proposed model with temperature-dependent elastic modulus and strength,agree well with the experimental results.This also reveals that the rock subjected to heating experiences much more cracking than the rock subjected to cooling.

Numerical modeling of coupled thermo-mechanical response of a rock pillar

Understanding the rock mass response to excavation and thermal loading and improving the capability of the numerical models for simulating the progressive failure process of brittle rocks are important for safety assessment and optimization design of nuclear waste repositories.The international cooperative DECOVALEX-2011 project provides a platform for development,validation and comparison of numerical models,in which the sp pillar stability experiment（APSE） was selected as the modeling target for Task B.This paper presents the modeling results of Wuhan University（WHU） team for stages 1 and 2 of Task B by using a coupled thermo-mechanical model within the framework of continuum mechanics.The rock mass response to excavation is modeled with linear elastic,elastoplastic and brittle-plastic models,while the response to heating is modeled with a coupled thermo-elastic model.The capabilities and limitations of the model for representation of the thermo-mechanical responses of the rock pillar are discussed by comparing the modeling results with experimental observations.The results may provide a helpful reference for the stability and safety assessment of the hard granite host rock in China＇s Beishan preselected area for high-level radioactive waste disposal.

Shear behavior of intact granite under thermo-mechanical coupling and three-dimensional morphology of shear-formed fractures

The shear failure of intact rock under thermo-mechanical(TM)coupling conditions is common,such as in enhanced geothermal mining and deep mine construction.Under the effect of a continuous engineering disturbance,shear-formed fractures are prone to secondary instability,posing a severe threat to deep engineering.Although numerous studies regarding three-dimensional(3D)morphologies of fracture surfaces have been conducted,the understanding of shear-formed fractures under TM coupling conditions is limited.In this study,direct shear tests of intact granite under various TM coupling conditions were conducted,followed by 3D laser scanning tests of shear-formed fractures.Test results demonstrated that the peak shear strength of intact granite is positively correlated with the normal stress,whereas it is negatively correlated with the temperature.The internal friction angle and cohesion of intact granite significantly decrease with an increase in the temperature.The anisotropy,roughness value,and height of the asperities on the fracture surfaces are reduced as the normal stress increases,whereas their variation trends are the opposite as the temperature increases.The macroscopic failure mode of intact granite under TM coupling conditions is dominated by mixed tensileeshear and shear failures.As the normal stress increases,intragranular fractures are developed ranging from a local to a global distribution,and the macroscopic failure mode of intact granite changes from mixed tensileeshear to shear failure.Finally,3D morphological characteristics of the asperities on the shear-formed fracture surfaces were analyzed,and a quadrangular pyramid conceptual model representing these asperities was proposed and sufficiently verified.

Study on inhomogeneous cooling behavior of extruded profile with unequal and large thicknesses during quenching using thermo-mechanical coupling model

The interfacial heat transfer coefficient between hot profile surface and cooling water was determined by using inverse heat conduction model combined with end quenching experiment. Then, a Deform-3 D thermo-mechanical coupling model for simulating the on-line water quenching of extruded profile with unequal and large thicknesses was developed. The temperature field, residual stress field and distortion of profile during quenching were investigated systematically. The results show that heat transfer coefficient increases as water flow rate increases. The peak heat transfer coefficient with higher water flow rates appears at lower interface temperatures. The temperature distribution across the cross-section of profile during quenching is severe nonuniform and the maximum temperature difference is 300 ℃ at quenching time of 3.49 s. The temperature difference through the thickness of different parts of profile first increases sharply to a maximum value, and then gradually decreases. The temperature gradient increases obviously with the increase of thickness of parts. After quenching, there exist large residual stresses on the inner side of joints of profile and the two ends of part with thickness of 10 mm. The profile presents a twisting-type distortion across the cross-section under non-uniform cooling and the maximum twisting angle during quenching is 2.78°.

Thermo-mechanical coupled analysis of hot ring rolling process

A 3D rigid-plastic and coupled thermo-mechanical FE model for hot ring rolling(HRR) was developed based on DEFORM 3D software,then coupled heat transferring,material flow and temperature distribution of the ring in HRR were simulated and the effects of process parameters on them were analyzed.The results show that the deformation nonuniformity of ring blank increases with the increase of the rotational speed of driver roll and friction factor or the decrease of the feed rate of idle roll and initial temperature of ring blank.The temperature nonuniformity of ring blank decreases with the increase of the feed rate of idle roll or the decrease of initial temperature of ring blank and friction factor.There is an optimum rotational speed of driver roll under which the temperature distribution of ring blank is the most uniform.The results obtained can provide a guide for forming parameters optimization and quality control.

An Innovative Finite Element Geometric Modeling of Single-Layer Multi-Bead WAAMed Part

Finite element (FE) coupled thermal-mechanical analysis is widely used to predict the deformation and residualstress of wire arc additive manufacturing (WAAM) parts. In this study, an innovative single-layermulti-bead profilegeometric modeling method through the isosceles trapezoid function is proposed to build the FE model of theWAAMprocess. Firstly, a straight-line model for overlapping beads based on the parabola function was establishedto calculate the optimal center distance. Then, the isosceles trapezoid-based profile was employed to replace theparabola profiles of the parabola-based overlapping model to establish an innovative isosceles trapezoid-basedmulti-bead overlapping geometric model. The rationality of the isosceles trapezoid-based overlapping model wasconfirmed by comparing the geometric deviation and the heat dissipation performance index of the two overlappingmodels. In addition, the FE-coupled thermal-mechanical analysis, as well as a comparative experiment of thesingle-layer eight-bead deposition process show that the simulation results of the above two models agree with theexperimental results. At the same time, the proposed isosceles trapezoid-based overlappingmodels are all straightlineprofiles, which can be divided into high-quality FE elements. It can improve the modeling efficiency andshorten the simulation calculation time. The innovative modeling method proposed in this study can provide anefficient and high-precision geometricmodelingmethod forWAAMpart FE coupled thermal-mechanical analysis.

Atom-continuum coupled model for thermo-mechanical behavior of materials in micro-nano scales

In this paper,an atom-continuum coupled model for thermo-mechanical behaviors in micro-nano scales is presented.A representative volume element consisting of atom clusters is used to represent the microstructure of materials.The atom motions in the RVE are divided into two phases,structural deformations and thermal vibrations.For the structural deformations,nonlinear and nonlocal deformation at atomic scales is considered.The atomistic-continuum equations are constructed based on momentum and energy conservation law.The non-locality and nonlinearity of atomistic interactions are built into the thermo-mechanical constitutive equations.The coupled atomistic-continuum thermal-mechanical simulation process is also suggested in this work.

Mathematical model of coupled thermo-mechanical behavior during plane strain compression of 06Cr19Ni9NbN steel

The process of plane strain compression of 06Cr19Ni9NbN steel was carried out in the temperature range of 1000-1200℃ and the reduction ratio range of 10-50%.Combining the finite element numerical simulation,a new constitutive model of thermal deformation was established, which provides the theoretical basis to optimize the plarie strain compression process of the steel.The temperature and grain size at different regions were achieved by experiment and simulation,respectively.According to the results,the mathematical models of stress and temperature during the plane strain compression were established by mathematical analysis method.The new temperature models were established in three regions,respectively,and the stress models took account of the variation of temperature and'st^rain rate.Finally,by comparing the results of calculation,numerical simulation and experiment,the accuracy and validity of these mathematical models were verified.

Numerical studies of effect of tool sizes and pin shapes on friction stir welding of AA2024-T3 alloy

Coupled thermo-mechanical model was used to investigate the effects of the pin diameter, the shoulder diameter and the in conical angle on the heat generations, the material deformations and the energy histories in friction stir welding（FSW） of AA2024-T3 alloy. Results indicate that the shoulder-plate contact area takes more important contribution to the heat generation than the pin-plate contact area. The increase of the shoulder diameter or the decrease of the pin diameter can lead to the increase of the welding temperature in FSW, but the change of shoulder size is more important. Compared to the cases in FSW of AA6061-T6, the input power is obviously increased in FSW of AA2024-T3 and the ratio of the plastic dissipation to the friction dissipation becomes decreased.

一种高效的FE-PSBFE耦合方法及在岩土工程弹塑性分析中的应用

针对复杂岩土工程结构建模困难、耗时费力的难题,结合八叉树网格离散技术,对网格中的六面体采用等参单元,对于非六面体采用多面体比例边界有限单元(PSBFE),建立了一种快速、高效的FE-PSBFE弹塑性耦合数值分析方法。采用实现的PSBFE对标准土石坝进行数值模拟,验证了其正确性和计算精度;通过典型复杂心墙坝对提出FE-PSBFE耦合方法的灵活性、通用性和高效性进行了研究,研究结果表明:与传统FEM相比,该耦合方法可大幅加速模型前处理进程,解决了复杂三维空间河谷形状、水平分层填筑和材料分区导致的网格剖分难题,几十万单元的网格划分一般仅需几分钟;与PSBFE相比,显著提高了岩土结构弹塑性分析的效率,FE-PSBFE可减少超过80%的求解时间。FE-PSBFE耦合方法对其他复杂几何条件的工程问题也具有良好的实用性,为快速精细化抗震分析提供了技术手段。

Fe-Ga合金发音振子换能器的多场耦合模型

建立了Fe-Ga合金弓张结构发音振子换能器电场、磁场和固体力学场的多场耦合模型,研究了发音振子换能器磁场强度、磁感应强度和应变分布情况,并进行了换能器在不同频率下的磁场强度分析和模态分析。分析发现,随着频率的增高,Fe-Ga合金发音振子换能器的磁场强度逐渐减小,计算得到换能器的共振频率为984 Hz。测试了Fe-Ga合金换能器中的核心元件Fe-Ga合金的磁场强度与应变的关系,当磁场强度饱和值为40 k A·m-1时,应变为70×10-6。搭建了磁致伸缩材料磁特性测试系统,测试了Fe-Ga合金磁场频率为5、20、50 Hz的磁滞曲线,并测试了Fe-Ga合金的应变随频率的变化曲线,实验结果与换能器中Fe-Ga合金的应变仿真结果一致。

地震波斜入射地下隧道地震响应:2.5维FE-BE耦合模拟

针对地震波斜入射导致的非一致地震激励结构地震响应问题,提出了地下隧道三维地震响应分析的一个2.5维有限元–边界元(FE-BE)耦合分析方法,该耦合方法具有分析效率高和计算精度高的优势。利用有限元模拟隧道结构,并引入弹簧单元考虑衬砌管片接头的影响;半无限土域利用基于场地三维动力刚度矩阵和移动斜线荷载格林函数的边界元方法模拟。通过与文献结果比较验证了耦合方法的正确性。利用该2.5维FE-BE方法,以某盾构隧道为例,研究了斜入射地震波作用下隧道结构的三维地震响应,着重分析了管片接头对隧道衬砌地震变形和内力的影响,并讨论了通过对隧道衬砌整体刚度进行折减(等效均质圆环模型)来考虑管片接头影响的方法的适用性。研究表明,管片接头对隧道地震响应有重要影响,随接头刚度减小隧道衬砌变形呈增大趋势,但衬砌内力显著减小;而且,对于管片接头刚度较大的情况,等效均质圆环模型可以在一定程度上反映管片接头对隧道结构地震响应的影响,但可能导致隧道纵向弯矩的低估。

Effect of Traverse/Rotational Speed on Material Deformations and Temperature Distributions in Friction Stir Welding

A fully coupled thermo-mechanical model was developed to study the temperature fields and the plastic deformations of alloy AL6061-T6 under different process parameters during the friction stir welding （FSW） process. Three-dimensional results under different process parameters were presented. Results indicate that the maximum temperature is lower than the melting point of the welding material. The higher temperature gradient occurs in the leading side of the workpiece. The calculated temperature field can be fitted well with the one from the experimental test. A lower plastic strain region can be found near the welding tool in the trailing side on the bottom surface, which is formed by the specific material flow patterns in FSW. The maximum temperature can be increased with increasing the welding speed and the angular velocity in the current numerical modelling.

A new method for modeling thermo-mechanical behaviors of polycrystalline aggregates

We present in this paper a numerical algorithm that couples the atomistic and continuum models for the thermal-mechanical coupled problem of polycrystalline aggregates.The key point is that the conservation laws should be satisfied for both the atomistic and continuum models at the microscale.Compared with the traditional methods which construct the constitutive equations of the grain interiors and grain boundaries by continuum mechanics,our model calculates the continuum fluxes through molecular dynamics simulations,provided that the atomistic simulations are consistent with the local microstate of the system.For the grain interiors without defects,central schemes are available for solving the conservation laws and the constitutive parameters can be obtained via molecular dynamics simulations.For the grain boundary structures,the front tracking method is employed because the solutions of the conservation equations are discontinuous near the defects.Firstly,appropriate control volumes are chosen at both sides of the interface,then the finite volume method is applied to solve the continuum equations in each control volume.Fluxes near both sides of the interface are calculated via atomistic simulations.Therefore,all thermo-mechanical information can be obtained.

地铁振动预测的周期性有限元-边界元耦合模型

针对地铁列车运行引起的隧道结构和自由场中的振动响应问题,提出了一个在频率-波数域内的三维周期性有限元-边界元耦合的数值模型,此模型中隧道结构采用有限元法计算,自由场采用边界元法模拟。此模型采用Floquet变换,利用隧道和自由场在隧道轴线方向上的周期性,把无限长的隧道及自由场的网格划分限制在一个基本元内,这样使动力学数值计算的效率大大提高。利用此模型计算了在隧道底板上施加固定单位谐振荷载情况下隧道-自由场相互作用系统的动力响应,结果表明此模型可应用于地铁列车运行引起的隧道和自由场中的动力响应预测。

40t轴重重载铁路扣件刚度研究

研究目的：针对大轴重重载铁路扣件刚度的合理取值问题,基于车辆-轨道耦合动力学理论,以美国五级轨道谱作为激励输入,分析扣件刚度对低频振动响应的影响;利用三维轮轨瞬态滚动接触显式有限元模型,分析钢轨波磨、焊接接头和车轮擦伤等短波长几何不平顺激励下扣件刚度对轨道高频动态响应的影响规律。研究结论：（1）大轴重重载铁路扣件刚度主要取决于钢轨位移和轨枕承载能力,钢轨位移决定了扣件刚度的下限,轨枕承载能力决定了扣件刚度的上限;（2）扣件刚度对于低频动态响应（小于50 Hz）的影响可以忽略;随着扣件刚度的增加,短波不平顺所激起的最大轮轨力呈现出逐渐变小的趋势,最大枕上压力和道床应力却逐渐变大,轮轨力和道床应力在扣件刚度大于200 MN/m以后减小幅度变缓,趋于稳定,相对于轮轨力和道床应力,枕上压力对扣件刚度的变化更为敏感;（3）综合考虑轮轨力、钢轨位移和轨枕承载能力,对于设计轴重40 t、最高行车速度90 km/h的重载有砟轨道结构,若钢轨的最大容许垂向位移为3.30 mm,最大容许枕上压力为150 kN,则最优扣件动态刚度范围为200-250 MN/m;若最大容许枕上压力为180 kN,则最优扣件动态刚度范围为200-600 MN/m;（4）本研究结果可供大轴重重载铁路轨道结构设计参考。

裂隙岩体渗流溶质运移耦合离散裂隙模型数值计算方法

研究裂隙岩体渗流溶质运移问题对于岩土工程地下水污染物预测控制具有重要意义。基于离散裂隙网络模型,采用实体单元模拟基质岩块、无厚度单元模拟复杂裂隙网络,提出了裂隙岩体渗流溶质运移耦合的三维数值计算方法。针对无反应项和含反应项两种情况,通过算例分析了单裂隙中溶质迁移行为,并与精细模拟方法、解析方法的结果进行对比验证;进一步将该法应用于预测大规模裂隙岩体溶质浓度分布规律及发展趋势,并评价了主要影响因素。结果表明,该法可有效模拟裂隙网络、基质岩块中水分溶质传输行为;由于贯通裂隙网络的优势流影响,溶质羽主要受控于裂隙水的对流作用,出现了高度非均匀分布现象;通过参数敏感性分析发现,相较于岩块基质的扩散作用,裂隙开度产生的对流作用是影响浓度场分布的主控因素。在保证精度的前提下,该法可大幅减小计算量和计算时长,对于解决含复杂裂隙网络岩体渗流传质的三维数值模拟问题具有明显优势。

基于刚柔耦合模型的汽车排气系统运动包络面仿真方法

将经过自由模态试验验证的排气系统有限元模型导入ADAMS虚拟样机平台,建立了更接近实际结构的动力总成-排气系统刚柔耦合仿真模型。在汽车极限载荷工况下计算了排气系统上4个关注点的位移,将刚柔耦合仿真方法与传统有限元方法的仿真结果相比较,结果显示,两种方法的预测一致性较好,间接验证了刚柔耦合仿真方法的准确性。

潜艇受撞数值仿真的附加质量模型

潜艇受撞有限元数值仿真计算时需要考虑流—固耦合作用的影响,可以直接采用流-固耦合模型计算,但需要花费巨大的计算时间,也可以采用附加质量模型,在不影响计算精度的前提下,可以大大减小计算时间,提高计算效率。文中分别采用增加密度和增加质量点单元质量的方法建立了两种潜艇受撞的附加质量模型,并进行了有限元数值仿真计算,通过与流—固耦合模型计算结果对比、分析,表明采用后一种方法建立的附加质量模型与流—固耦合模型的仿真计算结果比较接近,可作为潜艇受撞有限元数值仿真的计算模型。