J^＊ INTEGRAL OF THE SPECIFIC DEVIATOR STRAIN ENERGY AND ITS APPLICATION

First the deviator strain energy is introduced, then the problem of plane-crack critical growth was discussed, a path independent line integral J* was defined, furthermore its conservation was proved strictly. As application examples, Mode-I stress intensity factors of cracked beams were obtained with present approach. The results are shown to agree well with those available in the open literature.

Strength characteristics and energy dissipation evolution of thawing silty clay during cyclic triaxial loading

Cyclic triaxial tests are conducted to analyze the evolution of strength parameters and energy dissipation of thawing silty clay under different stress paths.The effects of freezing temperature,thawing temperature and confining pressures on the stress-strain and strength characteristics of soil samples are studied through monotonic loading and cyclic loading tests by using high-and low-temperature triaxial apparatus.The variation of the total work,elastic deformation energy,dissipated energy,energy dissipation rate,residual strain,and damage variable during loading and unloading are discussed.The experimental results show that the samples have higher strain tolerance under high confining pressure,low freezing temperature,and low thawing temperature,and the same other conditions.The soil sample state and failure pattern can be judged by using the energy parameters measured in the experiment.

Novel Ring Compression Test Method to Determine the Stress-Strain Relations and Mechanical Properties of Metallic Materials

Although there are methods for testing the stress-strain relation and strength,which are the most fundamental and important properties of metallic materials,their application to small-volume materials and tube components is lim-ited.In this study,based on energy density equivalence,a new dimensionless elastoplastic load-displacement model for compressed metal rings with isotropy and constitutive power law is proposed to describe the relations among the geometric dimensions,Hollomon law parameters,load,and displacement.Furthermore,a novel test method was developed to determine the elastic modulus,stress-strain relation,yield and tensile strength via ring compression test.The universality and accuracy of the method were verified within a wide range of imaginary materials using finite element analysis(FEA),and the results show that the stress-strain curves obtained by this method are consistent with those inputted in the FEA program.Additionally,a series of ring compression tests were performed for seven metallic materials.It was found that the stress-strain curves and mechanical properties predicted by the method agreed with the uniaxial tensile results.With its low material consumption,the ring compression test has the potential to be as an alternative to traditional tensile test when direct tension method is limited.

A new mixed-mode phase-field model for crack propagation of brittle rock

Study on crack propagation process of brittle rock is of most significance for cracking-arrest design and cracking-network optimization in rock engineering.Phase-field model(PFM)has advantages of simplicity and high convergence over the common numerical methods(e.g.finite element method,discrete element method,and particle manifold method)in dealing with three-dimensional and multicrack problems.However,current PFMs are mainly used to simulate mode-I(tensile)crack propagation but difficult to effectively simulate mode-II(shear)crack propagation.In this paper,a new mixed-mode PFM is established to simulate both mode-I and mode-II crack propagation of brittle rock by distinguishing the volumetric elastic strain energy and deviatoric elastic strain energy in the total elastic strain energy and considering the effect of compressive stress on mode-II crack propagation.Numerical solution method of the new mixed-mode PFM is proposed based on the staggered solution method with self-programmed subroutines UMAT and HETVAL of ABAQUS software.Three examples calculated using different PFMs as well as test results are presented for comparison.The results show that compared with the conventional PFM(which only simulates the tensile wing crack but not mode-II crack propagation)and the modified mixed-mode PFM(which has difficulty in simulating the shear anti-wing crack),the new mixed-mode PFM can successfully simulate the whole trajectories of mixed-mode crack propagation(including the tensile wing crack,shear secondary crack,and shear anti-wing crack)and mode-II crack propagation,which are close to the test results.It can be further extended to simulate multicrack propagation of anisotropic rock under multi-field coupling loads.

Assessment of cyclic deformation and critical stress amplitude of jointed rocks via cyclic triaxial testing

Jointed rock specimens with a natural replicated joint surface oriented at a mean dip angle of 60were prepared,and a series of cyclic triaxial tests was performed at different confining pressures and cyclic deviatoric stress amplitudes.The samples were subjected to 10,000 loading-unloading cycles with a frequency of 8 Hz.At each level of confining pressure,the applied cyclic deviatoric stress amplitude was increased incrementally until excessive deformation of the jointed rock specimen was observed.Analysis of the test results indicated that there existed a critical cyclic deviatoric stress amplitude(i.e.critical dynamic deviatoric stress)beyond which the jointed rock specimens yielded.The measured critical dynamic deviatoric stress was less than the corresponding static deviatoric stress.At cyclic deviatoric stress amplitudes less than the critical dynamic deviatoric stress,minor cumulative residual axial strains were observed,resulting in hysteretic damping.However,for cyclic deviatoric stresses beyond the critical dynamic deviatoric stress,the plastic strains increased promptly,and the resilient moduli degraded rapidly during the initial loading cycles.Cyclic triaxial test results showed that at higher confining pressures,the ultimate residual axial strain attained by the jointed rock specimen decreased,the steadystate dissipated energy density and steady-state damping ratio per load cycle decreased,while steadystate resilient moduli increased.

巷道开挖围岩能量释放与偏应力应变能生成的分析计算

巷道开挖,围岩能量释放,同时在围岩中产生偏应力。围岩应力是原岩应力与偏应力的叠加,偏应力或偏应力能控制岩体破坏。在静水压力p0和岩体体积应变为0的条件下,利用文[1]在弹性、非线性软化本构模型导得的巷道围岩应力分布表达式,用重积分计算了围岩弹性区和软化区中的偏应力应变能Ud,证明了Ud可以简捷地用地应力p0关于巷壁位移ua做一次积分再乘巷壁周长的途径来得到,阐述了该计算途径的原理。巷道开挖过程围岩释放的能量等于围岩压力pa关于ua的积分乘巷壁周长。由此,可通过p0～ua曲线、pa～ua曲线所围面积的几何形式,表示围岩偏应力能、围岩弹性能释放量随ua变化的情况。所得研究结果可以深化围岩由于开挖产生的力学响应及挖成后围岩工况规律的认识。

非静水压力条件下巷道围岩偏应力场分布特征与围岩破坏规律

通过理论分析对受三向应力非静水压力条件下的巷道围岩偏应力场与应变能密度分布规律进行了深入研究,以此来探究巷道围岩破坏规律,巷道塑性区数值模拟结果与现场工程实例验证了理论结果的正确性。研究结果表明:①非静水压力条件下,不同的主导型应力场中,巷道围岩偏应力场分布规律差异较为明显。σ_(x)主导型应力场中,巷道顶底板偏应力大于两帮;σ_(y)主导型应力场中,巷道顶底板与两帮偏应力大小差别不大;σ_(z)主导型应力场中,巷道两帮处的偏应力大于顶底板。主导应力值的变化会引起巷道围岩偏应力分布数值上的变化,不引起偏应力分布形态的改变。②等p、等q时,在σ_(x)与σ_(y)主导型应力场中,巷道顶底板应变能密度大于两帮,而在σ_(z)主导型应力场中,巷道两帮应变能密度大于顶底板。等p、不等q情况下,3种主导型应力场中,巷道顶底板与两帮应变能密度均随偏应力比M的增大而增大;等q、不等p情况下,巷道顶底板与两帮应变能密度均随偏应力比M的减小而增大。③三向应力状态下,巷道围岩应变能密度分布规律可以反映塑性区形态。M<1时,任意主导型应力场中,巷道围岩应变能密度呈椭圆形分布,M>1时,巷道围岩应变能密度呈“8”字形或“X”形分布。处于σ_(x)主导型应力场中的巷道需注重巷道顶底板的支护;对于σ_(y)主导型应力场,巷道在围岩条件较差时,应注重全断面支护;对于σ_(z)主导型应力场,需注意围岩塑性区出现“X”形扩展。④回坡底1021巷围岩偏应力场与应变能密度均呈倾斜的“8”字形分布,工程现场与巷道围岩偏应力场及应变能密度分布规律相互验证。基于理论分析结果,对回坡底1021巷提出非对称性支护技术,现场应用效果良好。

巷道围岩状态的等效应力等效应变表述

在体积应变为零的条件下,根据巷道围岩属简单加载的特性得到围岩中同时关联三向应力σθ,σz,σr和三向应变εθ,εz,εr的,用等效应力σi和等效应变εi表示的对围岩加载-形变关系式。严格地论证了巷道围岩的弹性、硬化、软化和流动区的应力应变状态分别与围岩的等效应力-等效应变曲线各阶段的应力应变状态相对应。以等效应力、等效应变为中间变量可以简化围岩弹性分析,简捷地写出巷道围岩偏应力应变能的计算公式。等效剪应力τi是围岩中的最大剪应力τmax,等效剪应力单元受正应力和剪应力作用,但其上只有剪切应变,这突出了巷道围岩形变破坏是由于最大剪应力和偏应力应变能所致的实质。根据等效剪应力概念确定的滑移线,可适用于材料应变硬化和软化阶段,不要求刚塑性假定条件。

Static Recrystallization Behavior of SCM435 Steel

The static recrystallization behaviors in SCM435 steel were investigated by two-pass hot compression tests on MMS-200 thermosimulation machine. Effects of deformation temperature, strain rate,deformation degree and the initial austenite grain size on static softening were analyzed. The stress compensation method was used to calculate the static recrystallization. The kinetics model of the static recrystallization of SCM435 steel was established and the obtained activation energy for static recrystallization was 182. 8 kJ /mol. Results showed that within a certain time interval( 1-100 s),the static recrystallization fraction X of SCM435 steel increased as the deformation temperature,the deformation rate and the amount of deformation increased,and it decreased as the initial grain size increased and increased as the time interval increased.

青藏高原东北缘重力势能与水平偏应力研究

偏应力场的定量研究结果对于揭示区域构造运动具有重要意义.本文使用重力与GPS联合观测数据计算青藏高原东北缘的重力势能,估计其产生的水平偏应力,并与全球应变率图(GSRM)进行对比分析,发现研究区域的重力势能分布形态总体具有青藏高原高、鄂尔多斯块体低的特点.重力势能最高值位于青藏高原北部,量值为1.53×10^(14) N/m,最低值位于秦岭南部,量值为1.45×10^(14) N/m.由重力势能差异引起的偏应力在青藏高原北部、鄂尔多斯块体南部和秦岭东段较大,最大值达14 MPa左右,位于青藏高原与阿拉善块体交界处.

Property of Corroded Concrete under Compressive Uniaxial Loads

In order to study the compressive property of corroded concrete, accelerated corrosion test were performed on concrete C30.6 corrosive solutions, including hydraulic acid solution （pH=2）, hydraulic acid solution （pH=3） were applied as the corrosive medium. 6 series of corrosion tests, including 111 specimens, were carried out. Mechanical properties of all the corroded specimens were tested respectively. Compressive properties of the corroded specimens （e.g. compressive strength, stress-strain relation, elastic modulus etc.） were achieved. Taking the strength degradation ratio and strain energy loss as damage index, effects of the corrosion solution on the compressive property of corroded concrete were discussed in detail. Relationship between the damage index and corrosion state of specimens were achieved.

Application of the Mechanical Threshold Stress Model to Large Strain Processing

Large-strain deformations introduce several confounding factors that affect the application of the Mechanical Threshold Stress model. These include the decrease with the increasing stress of the normalized activation energy characterizing deformation kinetics, the tendency toward Stage IV hardening at high strains, and the influence of crystallographic texture. Minor additions to the Mechanical Threshold Stress model are introduced to account for variations of the activation energy and the addition of Stage IV hardening. Crystallographic texture cannot be modeled using an isotropic formulation, but some common trends when analyzing predominantly shear deformation followed by uniaxial deformation are described. Comparisons of model predictions with measurements in copper processed using Equal Channel Angular Pressing are described.

Characteristics and geological significance of the stress state of the lithosphere in the Qinghai-Tibetan Plateau and its neighboring areas

The present-day lithospheric stress state of the Qinghai-Tibetan Plateau and neighboring areas is controlled by both the lithosphere itself and the underlying mantle.In other words,the stress is affected by the gravitational potential energy(GPE)difference caused by the change in the density distribution within the lithosphere and the drag force on the base of the lithosphere caused by mantle convection.The study of the lithospheric stress state plays an important role in further understanding the dynamic background and mechanism for the evolution of the Qinghai-Tibetan Plateau.In this study,the Crust1.0 crustal density model combined with the S40RTS mantle shear wave velocity variation model was used to calculate the GPE.The EGM2008gravity field model was used to calculate the drag force from mantle convection at the base of the lithosphere.The lithospheric and joint stress fields of the two sources were obtained by solving the force balance under the thin sheet approximation.This way,we could comprehensively analyze the characteristics of the stress state within the Plateau.Six regions were classified according to the GPE stress field,mantle drag force stress field,the relative magnitude of the two stress fields,and correlation between the two stress fields and surface deformation.The lithospheric stress fields of the Tarim Basin and other stable blocks are mainly controlled by the GPE difference.The lithospheric stress field in the collision zone between the Indian Plate and the QinghaiTibetan Plateau is predominantly controlled by the deep mantle drag force.The lithospheric stress field in the interior of the Plateau is controlled by both GPE and mantle drag.The correlation between the lithospheric stress field and surface deformation at the southeast margin of the Qinghai-Tibetan Plateau is poor.It is hypothesized that the presence of lower crustal flow with lower effective viscosity leads to crust-mantle decoupling,and the mantle drag force has a weaker influence on the shallow crust,resulting in the inconsistency between the average lithospheric stress field and surface deformation.

Determination of the Uniaxial Stress-Strain Relations of Ductile Materials by Small Disk Specimens

In this work,the small lateral-compression testing based on energy equivalent(SLTEE)method is put forward to determine the stress-strain curves of materials utilizing small disk specimens.Numerical simulations of small lateral-compression testing with imaginary materials are conducted to examine the validity of the SLT-EE method.The results demonstrate that the stress-strain curves determined by the SLT-EE method coincide with the curves input by finite element analysis.In order to predict the stress-strain curves of materials with different dimensions,a modified SLT-EE method is successfully proposed by introducing a correction factor/.Finally,the small disk compression experiments of Q345B,304,7075 and 6061 are performed.The stress-strain curves of the four materials predicted by the SLT-EE method show agreement with the tension results.Furthermore,the mechanical properties of in-service hollow components are also determined utilizing the same method successfully.

基于偏应力分布特征的综放区段煤柱宽度研究

针对王家岭煤矿20 m宽煤柱条件下回采巷道大变形控制难题,运用数值模拟方法,研究了顶板煤岩体偏应力第二不变量分布及迁移演化规律,得出203盘区相邻综放区段间煤柱合理宽度为4~8 m,且回采巷道煤柱侧顶板需要进行强化支护的结论。现场试验8 m宽煤柱,采用槽钢桁架锚索与单体锚索平行布置非对称支护技术支护20321综放工作面回风巷,顶板最大下沉量为102 mm,煤柱宽度留设合理。

Stress-strain relationship for reactive powder concrete with recycled powder under uniaxial compression

The recycled powder(RP)from construction wastes can be used to partially replace cement in the preparation of reactive powder concrete.In this paper,reactive powder concrete mixtures with RP partially replacing cement,and natural sand instead of quartz,are developed.Standard curing is used,instead of steam curing that is normally requested by standard for reactive powder concrete.The influences of RP replacement ratio(0%,10%,20%,30%),silica fume proportion(10%,15%,20%),and steel fiber proportion(0%,1%,2%)are investigated.The effects of RP,silica fume,and steel fiber proportion on compressive strength,elastic modulus,and relative absorption energy are analyzed,and theoretical models for compressive strength,elastic modulus,and relative absorption energy are established.A constitutive model for the uniaxial compressive stress-strain relationship of reactive powder concrete with RP is developed.With the increase of RP replacement ratio from 0% to 30%,the compressive strength decreases by 42% and elastic modulus decreases by 24%.

Experimental study of dynamic mechanical properties of reactive powder concrete under high-strain-rate impacts

The dynamic mechanical properties of reactive powder concrete subjected to compressive impacts with high strain rates ranging from 10 to 1.1×102 s-1 were investigated by means of SHPB (split-Hopkinson-pressure-bar) tests of the cylindrical specimens with five different steel fiber volumetric fractions.The properties of wave stress transmission,failure,strength,and energy consumption of RPC with varied fiber volumes and impact strain rates were analyzed.The influences of impact strain rates and fiber volumes on those properties were characterized as well.The general forms of the dynamic stress-strain relationships of RPC were modeled based on the experimental data.The investigations indicate that for the plain RPC the stress response is greater than the strain response,showing strong brittle performance.The RPC with a certain volume of fibers sustains higher strain rate impact and exhibits better deformability as compared with the plain RPC.With a constant fiber fraction,the peak compressive strength,corresponding peak strain and the residual strain of the fiber-reinforced RPC rise by varying amounts when the impact strain rate increases,with the residual strain demonstrating the greatest increment.Elevating the fiber content makes trivial contribution to improving the residual deformability of RPC when the impact strain rate is constant.The tests also show that the fiber content affects the peak compressive strength and the peak deformability of RPC in a different manner.With a constant impact strain rate and the fiber fraction less than 1.75%,the peak compressive strength rises with an increasing fiber volume.The peak compressive strength tends to decrease as the fiber volume exceeds 1.75%.The corresponding peak strain,however,incessantly rises with the increasing fiber volume.The total energy Edisp that RPC consumed during the period from the beginning of impacts to the time of residual strains elevates with the fiber volume increment as long as the fiber fraction is not larger than 2%.It turns to decrease if the fiber volume exceeds 2%.The added fibers make various contributions to enhancing the capability of RPC to consume energy at different loading stages.If the fiber fraction is not larger than 2%,the added fibers make more contribution to enhancing the energy consumption ability of RPC in the period before the peak strain than in the period after the peak strain.The impact strain rate,however,distinctively affects the total energy that RPC consumed and the energy consumed in the different loading periods.The higher the impact strain rate,the more the energy consumed in the stages and therefore the higher the dynamic impact toughness.The empirical relationships of the peak compressive strength,corresponding peak strain,residual strain,total consumed energy and the energy consumed in the varied periods with the impact strain rate and the fiber fraction are derived.Four generalized forms of the dynamic impact stress-strain responses of RPC are formulated by normalizing stresses and strains as the generalized coordinates and by taking account of the influences of impact strain rates and fiber volumetric fractions.