Experimental and numerical study on dynamic mechanical behaviors of shale under true triaxial compression at high strain rate

High-energy gas fracturing of shale is a novel,high efficacy and eco-friendly mining technique,which is a typical dynamic perturbing behavior.To effectively extract shale gas,it is important to understand the dynamic mechanical properties of shale.Dynamic experiments on shale subjected to true triaxial compression at different strain rates are first conducted in this research.The dynamic stress-strain curves,peak strain,peak stress and failure modes of shale are investigated.The results of the study indicate that the intermediate principal stress and the minor principal stress have the significant influence on the dynamic mechanical behaviors,although this effect decreases as the strain rate increases.The characteristics of compression-shear failure primarily occur in shale subjected to triaxial compression at high strain rates,which distinguishes it from the fragmentation characteristics observed in shale under dynamic uniaxial compression.Additionally,a numerical three-dimensional Split Hopkinson Pressure Bar(3D-SHPB),which is established by coupling PFC3D and FLAC3D methods,is validated to replicate the laboratory characteristics of shale.The dynamic mechanical characteristics of shale subjected to different confining stresses are systematically investigated by the coupling PFC3D and FLAC3D method.The numerical results are in good agreement with the experimental data.

Calculation of Valence Subband Structures for Strained Quantum-Wells by Plane Wave Expansion Method Within 6×6 Luttinger-Kohn Model

The valence subband energies and wave functions of a tensile strained quantum well are calculated by the plane wave expansion method within the 6×6 Luttinger Kohn model.The effect of the number and period of plane waves used for expansion on the stability of energy eigenvalues is examined.For practical calculation,it should choose the period large sufficiently to ensure the envelope functions vanish at the boundary and the number of plane waves large enough to ensure the energy eigenvalues keep unchanged within a prescribed range.

Topology Optimal Design of Material Microstructures Using Strain Energy-based Method

Sensitivity analysis and topology optimization of microstructures using strain energy-based method is presented. Compared with homogenization method, the strain energy-based method has advantages of higher computing efficiency and simplified programming. Both the dual convex programming method and perimeter constraint scheme are used to optimize the 2D and 3D microstructures. Numerical results indicate that the strain energy-based method has the same effectiveness as that of homogenization method for orthotropic materials.

Comparison of Strain Ellipsoid Shape in the South of Ardabil Range (NW), Based on the Results of the Magnetic Susceptibility Anisotropy and Paleostress Methods

In recent years, the method of magnetic survey as one of the new techniques in geological and geophysical studies is known. In this study to determine the shape of the stress field of the two methods, Anisotropy of Magnetic Susceptibility (AMS) and paleostress?have been used. Paleomagnetism is the characteristics of magnetic rocks. Some issues in associated with the past places of continental and oceanic plates can be solved. AMS is one of the paleomagnetism methods that pay to measurement of parameters (which are reflector of the magnetic fabrics rocks). It is presenting an ellipsoid with three-axis perpendicular to each other that defines magnetic ellipsoid. In this regard, the number of 12 stations in different rocks (Jurassic to Quaternary) in the southern region of Ardebil sampling was conducted. In this connection, the study of magnetic fabrics has shown an elliptical magnetic susceptibility with the prolate shape. For the separation of paleostress phases in the Khalkhal area using the analysis of the paleostress based on the study of heterogeneous fault-slip data and sliding lineaments. Firstly, data were picked from 10 stations, and after their analysis, the elliptical shape (prolate) has been determinated. The shape of the ellipsoid, based on AMS and paleostress methods and their results show that in both methods the shape of the stress field is prolate.

Uncertainty analysis of strain modal parameters by Bayesian method using frequency response function

Structural strain modes are able to detect changes in local structural performance, but errors are inevitably intermixed in the measured data. In this paper, strain modal parameters are considered as random variables, and their uncertainty is analyzed by a Bayesian method based on the structural frequency response function （FRF）. The estimates of strain modal parameters with maximal posterior probability are determined. Several independent measurements of the FRF of a four-story reinforced concrete flame structural model were performed in the laboratory. The ability to identify the stiffness change in a concrete column using the strain mode was verified. It is shown that the uncertainty of the natural frequency is very small. Compared with the displacement mode shape, the variations of strain mode shapes at each point are quite different. The damping ratios are more affected by the types of test systems. Except for the case where a high order strain mode does not identify local damage, the first order strain mode can provide an exact indication of the damage location.

UPPER BOUND METHOD FOR SINTERED POWDER MATERIALS IN PLANE STRAIN

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DEPENDENCE OF PREDICTION MODEL OF FORMING LIMIT STRAINS ON FORMING METHOD AND MECHANICAL PROPERTIES OF SHEET METALS

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Influence of radial forging process on strain inhomogeneity of hollow gear shaft using finite element method and orthogonal design

Due to the current trend towards lightweight design in automotive industry,hollow stepped gear shafts for automobile and its radial forging process are widely investigated.Utilizing coupled finite element thermo-mechanical model,radial forging process of a hollow stepped gear shaft for automobile was simulated.The optimal combination of three process parameters including initial temperature,rotation rate and radial reduction was also selected using orthogonal design method.To examine the strain inhomogeneity of the forging workpiece,the strain inhomogeneity factor was introduced.The results reveal that the maximum effective strain and the minimum effective strain appeared in the outermost and innermost zones of different cross sections for the hollow stepped gear shaft,respectively.Optimal forging parameters are determined as a combination of initial temperature of 780°C,rotation rate of 21°/stroke and radial reduction of 3 mm.

Displacement fields denoising and strains extraction by finite element method

Optical full-field measurement methods are now widely applied in various domains. In general,the displacement fields can be directly obtained from the measurement,however in mechanical analysis strain fields are preferred.To extract strain fields from noisy displacement fields is always a challenging topic.In this study,a finite element method for smoothing displacement fields and calculating strain fields is proposed.An experimental test case on a holed aluminum specimen under tension is applied to validate this method.The heterogeneous displacement fields are measured by digital image correlation(DIC).By this proposed method,the result shows that the measuring noise on experimental displacement fields can be successfully removed,and strain fields can be reconstructed in the arbitrary area.

C^1 natural element method for strain gradient linear elasticity and its application to microstructures

C^1 natural element method （C^1 NEM） is applied to strain gradient linear elasticity, and size effects on mi crostructures are analyzed. The shape functions in C^1 NEM are built upon the natural neighbor interpolation （NNI）, with interpolation realized to nodal function and nodal gradient values, so that the essential boundary conditions （EBCs） can be imposed directly in a Galerkin scheme for partial differential equations （PDEs）. In the present paper, C^1 NEM for strain gradient linear elasticity is constructed, and sev- eral typical examples which have analytical solutions are presented to illustrate the effectiveness of the constructed method. In its application to microstructures, the size effects of bending stiffness and stress concentration factor （SCF） are studied for microspeciem and microgripper, respectively. It is observed that the size effects become rather strong when the width of spring for microgripper, the radius of circular perforation and the long axis of elliptical perforation for microspeciem come close to the material characteristic length scales. For the U-shaped notch, the size effects decline obviously with increasing notch radius, and decline mildly with increasing length of notch.

A new method of characterizing equivalent strain for equal channel angular processing

In order to establish the quantitative relationship between equivalent strain and the performance index of the deformed material within the range of certain passes for equal channel angular processing （ECAP）, a new approach to characterize the equivalent strain was proposed. The results show that there exists better accordance between mechanical property （such as hardness or strength） and equivalent strain after rolling and ECAP in a certain range of deformation amount, and Gauss equation can be satisfied among the equivalent strain and the mechanical properties for ECAP. Through regression analysis on the data of hardness and strength after the deformation, a more generalized expression of equivalent strain for ECAP is proposed as：ε=k0exp[-（k1M-k2）^2], where M is the strength or hardness of the material, k1 is the modified coefficient （k1∈ （0, 1））, ko and k2 are two parameters dependent on the critical strain and mechanical property that reaches saturation state for the material, respectively. In this expression the equivalent strain for ECAP is characterized novelly through the mechanical parameter relating to material property rather than the classical geometry equation.

A new method--the inverse strain method(ISM)for preventing welding hot cracking of high strength aluminium alloy LY12CZ

In this paper a new method for preventing welding hot cracking—the inverse strain method(ISM)is developed on the principle of welding mechan- ics.Effectiveness and feasiblity of method in preventing welding hot cracking of high strength aluminum alloy LY12CZ by synchronous rolling during welding (SRDW)along both sides of the weld at a suitable distance behind the welding arc are examined.Experimental resulte indicate that welding hot cracking of LY12CY can be effectively prevented and the mechanical properties of welded joint can also be improved by the method.It is an important new solution for preventing hot cracking in welding of sheet metal.

Preparation of AZ91D magnesium alloy semi-solid billet by new strain induced melt activated method

New strain induced melt activated (new SIMA) method for preparing AZ91D magnesium alloy semi-solid billet is introduced by applying equal channel angular extrusion into strain induced step in SIMA method, by which semi-solid billet with fine spheroidal grains and average grain size of 18 μm can be prepared. Furthermore, average grain size of semi-solid billet is reduced with increasing extrusion pass of AZ91D magnesium alloy obtained in ECAE process. By using semi-solid billet prepared by new SIMA, thixoforged magazine plates component with high mechanical properties such as yield strength of 201.4 MPa, ultimate tensile strength of 321.8 MPa and elongation of 15.3%, can be obtained.

Process parameter effects on microstructure and mechanical properties of tubes processed via friction assisted tube straining method

This paper investigates process parameter effects on microstructure and mechanical properties of the tubes processed via recently developed friction assisted tube straining(FATS)method.For this purpose,design of experiment was used to arrange finite element analyses and experimental tests.Numerical and experimental tests were executed by changing rotary speed,feed rate and die angle.Taguchi design results show that increasing feed rate and decreasing rotary speed enhance Zener-Hollomon(Z)parameter and decrease average grain size,while die angle has no considerable effect.Increasing Z value reduces grain size and enhances flow stress of the processed samples,while the experiment with the highest Z value refines initial microstructure from 40 to 8μm and increases flow stress by 5 times.

Dynamic stability analysis of porous functionally graded beams under hygro-thermal loading using nonlocal strain gradient integral model

We present a study on the dynamic stability of porous functionally graded(PFG)beams under hygro-thermal loading.The variations of the properties of the beams across the beam thicknesses are described by the power-law model.Unlike most studies on this topic,we consider both the bending deformation of the beams and the hygro-thermal load as size-dependent,simultaneously,by adopting the equivalent differential forms of the well-posed nonlocal strain gradient integral theory(NSGIT)which are strictly equipped with a set of constitutive boundary conditions(CBCs),and through which both the stiffness-hardening and stiffness-softening effects of the structures can be observed with the length-scale parameters changed.All the variables presented in the differential problem formulation are discretized.The numerical solution of the dynamic instability region(DIR)of various bounded beams is then developed via the generalized differential quadrature method(GDQM).After verifying the present formulation and results,we examine the effects of different parameters such as the nonlocal/gradient length-scale parameters,the static force factor,the functionally graded(FG)parameter,and the porosity parameter on the DIR.Furthermore,the influence of considering the size-dependent hygro-thermal load is also presented.

A FINITE ELEMENT METHOD FOR STRESS ANALYSIS OR ELASTOPLASTIC BODY WITH POLYGONAL LINE STRAIN——HARDENING

In this paper, the stress-strain curve of material is fitted by polygonal line composed of three lines. According to the theory of proportional loading in elastoplasticity, we simplify the complete stress-strain relations, which are given by the increment theory of elastoplasticity. Thus, the finite element equation with the solution of displacement is derived. The assemblage elastoplastic stiffness matrix can be obtained by adding something to the elastic matrix, hence it will shorten the computing time. The determination of every loading increment follows the von Mises yield criteria. The iterative method is used in computation. It omits the redecomposition of the assemblage stiffness matrix and it will step further to shorten the computing time. Illustrations are given to the high-order element application departure from proportional loading, the computation of unloading fitting to the curve and the problem of load estimation.

Fatigue Safety Assessment of Concrete Continuous Rigid Frame Bridge Based on Rain Flow Counting Method and Health Monitoring Data

The fatigue of concrete structures will gradually appear after being subjected to alternating loads for a long time,and the accidents caused by fatigue failure of bridge structures also appear from time to time.Aiming at the problem of degradation of long-span continuous rigid frame bridges due to fatigue and environmental effects,this paper suggests a method to analyze the fatigue degradation mechanism of this type of bridge,which combines long-term in-site monitoring data collected by the health monitoring system(HMS)and fatigue theory.In the paper,the authors mainly carry out the research work in the following aspects:First of all,a long-span continuous rigid frame bridge installed with HMS is used as an example,and a large amount of health monitoring data have been acquired,which can provide efficient information for fatigue in terms of equivalent stress range and cumulative number of stress cycles;next,for calculating the cumulative fatigue damage of the bridge structure,fatigue stress spectrum got by rain flow counting method,S-N curves and damage criteria are used for fatigue damage analysis.Moreover,it was considered a linear accumulation damage through the Palmgren-Miner rule for the counting of stress cycles.The health monitoring data are adopted to obtain fatigue stress data and the rain flow counting method is used to count the amplitude varying fatigue stress.The proposed fatigue reliability approach in the paper can estimate the fatigue damage degree and its evolution law of bridge structures well,and also can help bridge engineers do the assessment of future service duration.

RPC应力-应变曲线系数与塑性损伤因子无量纲化计算模型研究

为了方便活性粉末混凝土(Reactive Powder Concrete,RPC)等效矩形应力图系数与塑性损伤因子的计算与取值,对RPC应力-应变曲线系数与塑性损伤因子的计算模型进行了理论研究。通过对现有的计算方法进行无量纲化转化,推导了决定计算模型的四个原函数条件;对一个实际的应力-应变关系进行了计算,将得到的结果进行了分析;并对受弯矩形梁非极限状态下截面内力和力矩的推定计算进行了演示。针对应力-应变关系式含有非整次有理分式的情况提出了曲线拟合方法;研究了拟合次数、拟合区间和拟合函数类型对拟合精度与稳定性的影响。比较了4种典型的RPC本构模型在同种材料下的应力-应变曲线系数与损伤因子取值模型曲线,结果显示:拟合曲线得到的取值模型与其他原始曲线得到的取值模型在曲线上具有较高的相似度,证明了曲线拟合方法的准确可靠性;最后给出了一种RPC受压应力-应变曲线系数与塑性损伤因子无量纲化取值模型。

利用远震面波估计凉山州地震综合观测钻孔应变仪的耦合系数

分量钻孔应变观测中的耦合系数(A、B)对于定标应变观测量具有重要意义,本文通过中国地震科学实验场深井地震综合观测项目积累的地震仪与应变仪共点观测地震波资料,验证了钻孔应变观测面波标定方法的可行性.利用三个观测台站的多个远震记录,开展了多频点面波标定实验,所获取的耦合系数对比理论固体潮标定结果具有更好的稳定行和合理性.本文的研究结果表明,提高现有钻孔应变观测台站的采样率至不少于1 Hz,深入开展远震应变地震波和共点(或近场)地震仪的面波记录对比研究,有利于获取全频段的耦合系数结果,对于提高应变观测数据的准确度及其深入应用具有重要意义.

川滇主要断裂带应力应变积累速率的三维有限元模拟:初步结果

川滇地区构造活动强烈,活动断裂众多,强震活动频繁.了解主要活动断裂的应力应变积累速率对于评估该区的长期地震危险性具有重要参考作用.本文新建立川滇地区及其主要活动断裂的三维黏弹性有限元模型,其中考虑了该区的岩石圈结构分层以及介质在水平和深度方向的不均匀性;采用1996—2018年的平均GPS水平速度场约束模型的侧边界,同时考虑川滇地块深部介质的拖曳力过程,模拟计算了构造加载作用下模型的动力学响应——区域变形特征和断裂的应力积累速率.模拟的位移场能很好拟合GPS观测的速度场,模拟的水平主应力方向在川滇块体和华南块体西缘与地震震源主应力方向相符,反映所建模型与模拟结果有较好的可信度.尝试将模拟的应力积累速率与基于GPS/GNSS观测的应变速率相结合,计算能反映区域地壳应变积累程度的弹性应变能密度分布;讨论了主要断裂带的背景应力、弹性应变能密度和库仑应力积累速率与M≥6.0地震发生的关系.结果显示除了模型边界附近的应力奇异地带外,川滇其余地区1996年以来M≥6.0地震大多数发生在模拟应力积累速率高或次高的断裂带(段),以及弹性应变能密度积累速率中偏高的断裂带(段).在模拟的背景应力速率高而且库仑应力增长快的龙门山断裂带南段和鲜水河断裂带最南段,分别在本文写作和定稿阶段发生2022年6月1日四川芦山M6.1地震和2022年9月5日四川泸定M6.8地震.认为研究区具有类似高或者次高的模拟应力和弹性应变能密度积累速率、但至今无强震发生和记录的断裂带(段),潜在的地震危险性需要关注.