ANALYTICAL SOLUTIONS TO STRESS CONCENTRATION PROBLEM IN PLATES CONTAINING RECTANGULAR HOLE UNDER BIAXIAL TENSIONS

The stress concentration problem in structures with a circular or elliptic hole can be investigated by analytical methods. For the problem with a rectangular hole, only approximate results are derived. This paper deduces the analytical solutions to the stress concentration problem in plates with a rectangular hole under biaxial tensions. By using the U-transformation technique and the finite element method, the analytical displacement solutions of the finite element equations are derived in the series form. Therefore, the stress concentration can then be discussed easily and conveniently. For plate problem the bilinear rectangular element with four nodes is taken as an example to demonstrate the applicability of the proposed method. The stress concentration factors for various ratios of height to width of the hole are obtained.

Size-dependent effect on biaxial and shear nonlinear buckling analysis of nonlocal isotropic and orthotropic micro-plate based on surface stress and modified couple stress theories using differential quadrature method

The size-dependent effect on the biaxial and shear nonlinear buckling analysis of an isotropic and orthotropic micro-plate based on the surface stress, the modified couple stress theory （MCST）, and the nonlocal elasticity theories using the differential quadrature method （DQM） is presented. Main advantages of the MCST over the classical theory （CT） are the inclusion of the asymmetric couple stress tensor and the consideration of only one material length scale parameter. Based on the nonlinear von Karman assumption, the governing equations of equilibrium for the micro-classical plate consid- ering midplane displacements are derived based on the minimum principle of potential energy. Using the DQM, the biaxial and shear critical buckling loads of the micro-plate for various boundary conditions are obtained. Accuracy of the obtained results is validated by comparing the solutions with those reported in the literature. A parametric study is conducted to show the effects of the aspect ratio, the side-to-thickness ratio, Eringen＇s nonlocal parameter, the material length scale parameter, Young＇s modulus of the surface layer, the surface residual stress, the polymer matrix coefficients, and various boundary conditions on the dimensionless uniaxial, biaxial, and shear critical buckling loads. The results indicate that the critical buckling loads are strongly sensitive to Eringen＇s nonlocal parameter, the material length scale parameter, and the surface residual stress effects, while the effect of Young＇s modulus of the surface layer on the critical buckling load is negligible. Also, considering the size dependent effect causes the increase in the stiffness of the orthotropic micro-plate. The results show that the critical biaxial buckling load increases with an increase in G12/E2 and vice versa for E1/E2. It is shown that the nonlinear biaxial buckling ratio decreases as the aspect ratio increases and vice versa for the buckling amplitude. Because of the most lightweight micro-composite materials with high strength/weight and stiffness/weight ratios, it is anticipated that the results of the present work are useful in experimental characterization of the mechanical properties of micro-composite plates in the aircraft industry and other engineering applications.

Effect of Increasing Speed on Stress of Biaxial Bogie Frames

Increasing the trains’ speed has always been one of the goals of any railway industry and train manufacturers. Also, the influence of the train speed on bogie’s dynamics has an immense importance. Therefore, it is important to analyze the effect of train speed on the stress distribution in different parts of train structure. In this study the result of the increasing speed on the applied stresses of a biaxial bogie frame has been examined. For this purpose, a biaxial bogie frame has been modeled using finite element analysis. Static and dynamic forces applied on the bogie with biaxial frame have been obtained for different speeds and rail roughness. The Von Mises stresses are adopted as equivalent stresses in the strength calculation. The results show that maximum stress always has been induced in the bogie bowl also the increase in bogie’s speed has remarkable effect on the increment of applied stresses in the bogie frame.

Frequency Domain Fatigue Evaluation on SCR Girth-Weld Based on Structural Stress

The Steel Catenary Riser(SCR)is a vital component for transporting oil and gas from the seabed to the floating platform.The harsh environmental conditions and complex platform motion make the SCR’s girth-weld prone to fatigue failure.The structural stress fatigue theory and Master S-N curve method provide accurate predictions for the fatigue damage on the welded joints,which demonstrate significant potential and compatibility in multi-axial and random fatigue evaluation.Here,we propose a new frequency fatigue model subjected to welded joints of SCR under multiaxial stress,which fully integrates the mesh-insensitive structural stress and frequency domain random process and transforms the conventional welding fatigue technique of SCR into a spectrum analysis technique utilizing structural stress.Besides,a full-scale FE model of SCR with welds is established to obtain the modal structural stress of the girth weld and the frequency response function(FRF)of modal coordinate,and a biaxial fatigue evaluation about the girth weld of the SCR can be achieved by taking the effects of multi-load correlation and pipe-soil interaction into account.The research results indicate that the frequency-domain fatigue results are aligned with the time-domain results,meeting the fatigue evaluation requirements of the SCR.

FATIGUE CRACK PROPAGATION FOR BIAXIAL STRESS CYCLING

Based on the experimental study of complex biaxial mode Ⅰ fatigue crack growth and the discussion on Von Mises'theory,a new approach is proposed for correlating crack propaga- tion rate under both in-phase and out-of-phase biaxial stress cycling.The results emphasize the contribution of plasticity to fatigue crack growth.

Mechanism of biaxial pre-stress method on welding residual stress and hot cracks controlling

Based on the conventional uniaxial pre-tensile stress method during welding, this study presents a new method of welding with biaxial pre-stress. With the help of numerical simulation, experiments were carried out on the self-designed device. Except for the control on residual stress and distortion us-welded, the experimental results also show its effect on the prevention of hot cracks, thus this method can make up for the disadvantage of the conventional pre-stress method. Hot cracks disappear when the value of pre-stress surpasses 0. 2 σs（yield limit）. Welded thin plates with low-level residual stress, little distortion and no hot cracks are obtained with longitudinal pre-tensile stress level between 0. 6σsand 0. 7σs and precompressive stress between 0. 2 σs and 0. 3 σs in transverse direction.

Electronic and magnetic properties of single-layer and double-layer VX_(2)(X=Cl,Br)under biaxial stress

First-principles calculations and Monte Carlo simulations reveal that single-layer and double-layer VX_(2)(X=Cl,Br)can be tuned from antiferromagnetic(AFM)semiconductors to ferromagnetic(FM)state when biaxial tensile stress is applied.Their ground states are all T phase.The biaxial tensile stress at the phase transition point of the double-layer VX_(2) is larger than that of the single-layer VX_(2).The direct band gaps can be also manipulated by biaxial tensile stress as they increases with increasing tensile stress to a critical point and then decreases.The Neel temperature(´TN)of double-layer VX_(2) are higher than that of single-layer.As the stress increases,the TN of all materials tend to increase.The magnetic moment increases with the increase of biaxial tensile stress,and which become insensitive to stress after the phase transition points.Our research provides a method to control the electronic and magnetic properties of VX_(2) by stress,and the single-layer and double-layer VX_(2) may have potential applications in nano spintronic devices.

Evaluation of stress intensity factors of thin AZ31B magnesium alloy plate under biaxial tensile loading

Stress intensity factors of thin AZ31B magnesium alloy sheet under biaxial tension loading were analyzed by modified Dugdale model. K-values with crack angle of 90° obviously show that there is no influence of the loading condition in Mode-I. In the 45° case, K1 values are obtained within 10% errors when they are calculated by modified Dugdale model under biaxial loading. It is concluded that the modified Dugdale model is one of effective ways to evaluate stress intensity factor of AZ31 magnesium alloy sheet appropriately.

Undrained semi-analytical solution for cylindrical cavity expansion in anisotropic soils under biaxial stress conditions

This paper presents an undrained semi-analytical elastoplastic solution for cylindrical cavity expansion in anisotropic soil under the biaxial stress conditions.The advanced simplified SANICLAY model is used to simulate the elastoplastic behavior of soil.The cavity expansion is treated as an initial value problem and solved as a system of eight first-order ordinary differential equations including four stress components and four anisotropic parameters.The results are validated by comparing the new solutions with existing ones.The distributions of stress components and anisotropic parameters around the cavity wall,the expansion process,the stress yield trajectory of a soil element and the shape and size of elastoplastic boundary are further investigated to explore the cavity expansion response of soils under biaxial in situ stresses.The results of extensive parameters analysis demonstrate that the circumferential position of the soil element and the anisotropy of the soils have noticeable impacts on the expansion response under biaxial in situ stresses.Since the present solution not only considers the anisotropy and anisotropy evolution of natural soil,but also eliminates the conventional assumption of uniform radial pressure,the solution is better than other theoretical solutions to explain the pressure test and pile installation effect of shallow saturated soil.

Strength regularity and failure criterion of plain HSHPC under biaxial compression after exposure to high temperatures

Biaxial compression tests are performed on 100 mm × 100 mm × 100 mm cubic specimens of plain high-strength highperformance concrete （HSHPC） at seven kinds of stress ratios, σ2：σ3 =0 ： - 1, -0.20 ： - 1, -0.30 ： - 1, -0.40 ： - 1, -0.50 ： -1, -0. 75 ： - 1, and - 1.00 ： - 1 after exposure to normal and high temperatures of 20, 200, 300, 400, 500 and 600 ℃, using a large static-dynamic true triaxial machine. Frictionreducing pads are three layers of plastic membranes with glycerine in-between for the compressive loading plane. Failure modes of the specimens are described. The two principally static compressive strengths are measured. The influences of the temperatures and stress ratios on the biaxial strengths of HSHPC after exposure to high temperatures are also analyzed. The experimental results show that the uniaxial compressive strength of plain HSHPC after exposure to high temperatures does not decrease completely with the increase in temperature; the ratios of the biaxial to its uniaxial compressive strengths depend on the stress ratios and brittleness-stiffness of HSHPC after exposure to different high temperatures. The formula of the Kupfer-Gerstle failure criterion modified with the temperature and stress ratio parameters for plain HSHPC is proposed.

Simulation on Residual Stress of Shot Peening Based on a Symmetrical Cell Model

The symmetrical cell model is widely used to study the residual stress induced by shot peening. However, the correlation between the predicted residual stresses and the shot peening coverage, which is a big challenge for the researchers of the symmetrical cell model, is still not established. Based on the dynamic stresses and the residual stresses outputted from the symmetrical cell model, the residual stresses corresponding to full coverage are evalu- ated by normal distribution analysis. The predicted nodal dynamic stresses with respect to four corner points indicate that the equi-biaxial stress state exists only for the first shot impact. Along with the increase of shot number, the interactions of multiple shot impacts make the fluctuation of the nodal dynamic stresses about an almost identical value more and more obvious. The mean values and standard deviations of the residual stresses gradually tend to be stable with the increase of the number of shot peening series. The mean values at each corner point are almost the same after the third peening series, which means that an equi-biaxial stress state corresponding to the full coverage of shot peening is achieved. Therefore, the mean values of the nodal residual stresses with respect to a specific transverse cross-section below the peened surface can be used to correlate the measured data by X-ray. The predicted residual stress profile agrees with the experimental results very well under 200% peening coverage. An effective correlation method is proposed for the nodal residual stresses predicted by the symmetrical cell model and the shot peening coverage.

Experimental investigations on mechanical performance of rocks under fatigue loads and biaxial confinements

In this research,a series of biaxial compression and biaxial fatigue tests were conducted to investigate the mechanical behaviors of marble and sandstone under biaxial confinements.Experimental results demonstrate that the biaxial compressive strength of rocks under biaxial compression increases firstly,and subsequently decreases with increase of the intermediate principal stress.The fatigue failure characteristics of the rocks in biaxial fatigue tests are functions of the peak value of fatigue loads,the intermediate principal stress and the rock lithology.With the increase of the peak values of fatigue loads,the fatigue lives of rocks decrease.The intermediate principal stress strengthens the resistance ability of rocks to fatigue loads except considering the strength increasing under biaxial confinements.The fatigue lives of rocks increase with the increase of the intermediate principal stress under the same ratio of the fatigue load and their biaxial compressive strength.The acoustic emission(AE)and fragments studies showed that the sandstone has higher ability to resist the fatigue loads compared to the marble,and the marble generated a greater number of smaller fragments after fatigue failure compared to the sandstone.So,it can be inferred that the rock breaking efficiency and rock burst is higher or severer induced by fatigue loading than that induced by monotonous quasi-static loading,especially for hard rocks.

FAILURE MODE AND CONSTITUTIVE MODEL OF PLAIN HIGH-STRENGTH HIGH-PERFORMANCE CONCRETE UNDER BIAXIAL COMPRESSION AFTER EXPOSURE TO HIGH TEMPERATURES

An orthotropic constitutive relationship with temperature parameters for plain highstrength high-performance concrete （HSHPC） under biaxial compression is developed. It is based on the experiments performed for characterizing the strength and deformation behavior at two strength levels of HSHPC at 7 different stress ratios including a=σs ： σ3=0.00：-1,-0.20：-1,-0.30 ： -1,-0.40：-1,-0.50：-1,-0.75：-1,-1.00：-1, after the exposure to normal and high temperatures of 20, 200, 300, 400, 500 and 600℃, and using a large static-dynamic true triaxial machine. The biaxial tests were performed on 100 mm×100 mm×100 mm cubic specimens, and friction-reducing pads were used consisting of three layers of plastic membrane with glycerine in-between for the compressive loading plane. Based on the experimental results, failure modes of HSHPC specimens were described. The principal static compressive strengths, strains at the peak stress and stress-strain curves were measured; and the influence of the temperature and stress ratios on them was also analyzed. The experimental results showed that the uniaxial compressive strength of plain HSHPC after exposure to high temperatures does not decrease dramatically with the increase of temperature. The ratio of the biaxial to its uniaxial compressive strength depends on the stress ratios and brittleness-stiffness of HSHPC after exposure to different temperature levels. Comparison of the stress-strain results obtained from the theoretical model and the experimental data indicates good agreement.

Stress-induced butterfly and square-like magnetostriction loops transition

The stress-induced magnetic domain switching in FeGa thin films is studied using phase-field method. In particular, the magnetic field is applied along the [110] direction and biaxial stresses are applied along [ 100] and [010]. A compressive pre-stress corresponds to a smaller coercive magnetic field while a tensile pre-stress corresponded to a larger coercive field. At the same time, it is also found that the transition between butterfly and square-like magnetostriction loops occurs at the critical opposite biaxial stress state. The two different evolutions correspond to two different mechanisms： one is that the single domain swings across a fan area back and forth; the other is that the single domain turns a clockwise circle. The results can be explained bv the stress tuned anisotronv energy well.

Stress—strain curves for different loading paths and yield loci of aluminum alloy sheets

To carry out biaxial tensile test in sheet metal, the biaxial tensile testing system was established. True stress—true strain curves of three kinds of aluminum alloy sheets for loading ratios of 4:1, 4:2, 4:3, 4:4, 3:4, 2:4 and 1:4 were obtained by conducting biaxial tensile test in the established testing systems. It shows that the loading path has a significant influence on the stress—strain curves and as the loading ratio increases from 4:1 to 4:4, the stress—strain curve becomes higher and n-value becomes larger. Experimental yield points for three aluminum alloy sheets from 0.2% to 2% plastic strain were determined based on the equivalent plastic work. And the geometry of the experimental yield loci were compared with the yield loci calculated from several existing yield criteria. The analytical result shows that the Barlat89 and Hosford yield criterion describe the general trends of the experimental yield loci of aluminum alloy sheets well, whereas the Mises yield criterion overestimates the yield stress in all the contours.

Anisotropic Damage Mechanics Modeling of Concrete under Biaxial Fatigue Loading

An anisotropic damage mechanics model is presented to describe the behavior and failure of concrete under biaxial fatigue loading. Utilizing the approach of bounding surfaces, the limit surface becomes a special case when the number of loading cycles is set to one. By increasing the number of loading cycles, the strength of concrete gradually decreases and the limit surface is allowed to contract and form new curves representing residual strengths. The magnitude of loading, load range, and the load path are known to influence the fatigue life and hence are addressed in this formulation. In this paper, a strength softening function is proposed in order to address the reduction in the strength of concrete due to fatigue. Separate softening functions are also proposed to account for the deformation characteristics in concrete under cyclic loading. Numerical simulations predicted by the model in both uniaxial and biaxial stress paths show a good correlation with the experimental data available in the literature.

H形钢构件双向压弯下全过程弯矩计算模型

为探究可发展全截面塑性的H形钢构件在双向压弯加载全过程中塑性应力及两主轴弯矩的发展机制,基于经由已有实验数据校核过的建模方法,采用ABAQUS建立了不同轴压比、腹板和翼缘宽厚比的H形截面构件在不同加载角度下的参数分析模型。结合有限元分析结果,考察了双向压弯下H形截面钢构件的塑性应力发展规律,引入平截面假定,对其应力分布形式进行一定的简化处理。进一步,通过最小二乘法拟合得到相关参数,建立加载位移、塑性发展程度和宏观承载能力三者之间内在联系,构建H形钢构件双向弯矩的理论计算模型。该模型充分考虑了截面尺寸、位移加载方向角、轴压比和加载位移的影响。通过对模型计算结果的分析,验证了该模型可得到构件在加载任意时刻的应力分布形式,并为考虑一定截面塑性发展的双向抗弯设计提供更为简便的设计方法。

正交异性钢桥面板双轴疲劳性能评估

为精确评估正交异性钢桥面板在双轴应力状态下的疲劳性能,以东营胜利黄河大桥为背景,建立该桥正交异性钢桥面板顶板、U肋、横隔板交叉连接部位焊缝的节段三维有限元模型,采用等效结构应力法对正交异性钢桥面板体系的双轴疲劳问题进行研究;通过模型试验验证正交异性钢桥面板体系的双轴疲劳特性,并进行其构造细节疲劳寿命评估。结果表明:弧形切口起焊点的疲劳裂纹萌生位置在横隔板下方焊趾处,经历裂纹萌生、裂纹稳定扩展和裂纹失效3个阶段,最终失效阶段裂纹形式为Ⅱ型裂纹主导的Ⅰ-Ⅱ型复合裂纹,此为该桥正交异性钢桥面板结构体系的主导疲劳失效模式;顶板焊缝焊趾及弧形切口起焊点焊趾处于双轴应力状态,面内剪切结构应力幅对疲劳应力的影响显著,按单轴疲劳应力进行寿命预测误差较大,按单轴疲劳应力状态对结构进行疲劳寿命设计偏于不安全;基于组合等效结构应力法的计算值与试验值吻合较好,各焊接细节计算得到的最大值下的疲劳裂纹起裂位置均与试验结果一致,按双轴疲劳应力预测疲劳寿命与试验值吻合较好,疲劳寿命评价精确度较高。

中间主应力对花岗岩双轴压缩破坏过程的声发射演化特征影响

为了探究中间主应力对花岗岩双轴压缩破坏过程的声发射演化特征影响,对花岗岩于不同中间主应力下双轴压缩破坏过程的声发射信号开展了时域及频域多角度综合分析。试验结果表明:中间主应力对花岗岩双轴压缩破坏的声发射前兆有显著影响,即随着中间主应力增大,声发射累计振铃计数达到连续性急剧突变增长阶段的应力水平减小,b值的连续下降速率减小,优势频段(125~250 kHz)占比发生明显转变时的应力水平降低,但低频高幅值信号所占比例增加。得到了花岗岩双轴压缩破坏的多种声发射前兆特征,即在岩石失稳破坏前夕,声发射累计振铃计数呈现连续性急剧突变增长以及b值持续性显著下降,低频高幅值信号出现,优势频段(125~250 kHz)占比展现增加趋势。

考虑损伤效应的二向不等压深埋圆形隧道弹塑性统一解

为了研究二向不等压地应力环境下深埋圆形隧道损伤后的力学响应问题,通过考虑深部围岩的损伤效应,基于统一强度理论建立二向不等压深埋圆形隧道弹塑性解,依托华丽高速东马场隧道验证解的准确性和适用性;研究损伤效应和中间主应力对围岩应力分布和变形的影响,并探讨不同侧压力系数、剪胀系数和支护反力下深埋圆形隧道围岩的损伤程度。研究结果表明:二向不等压深埋圆形隧道开挖后,围岩峰后的损伤效应会加剧隧道的挤压变形,考虑损伤效应的变形计算结果与现场实测结果更接近;中间主应力能提高围岩的承载能力,抑制隧道的挤压变形,不考虑中间主应力会高估隧道的变形潜势;侧压力系数决定围岩损伤区的形状和大小,施工时应根据围岩不同位置的损伤程度对关键变形部位进行注浆加固;剪胀系数越大,围岩的损伤程度越大,损伤区的范围越大;支护反力能抑制围岩的损伤效应,在实际工程中需及时施作支护约束围岩变形,以改善围岩的受力情况。