Stress-strain state and durability of mechanically inhomogeneous welds under low-cycle loading

Relations are proposed for the determination of the stress-strain state, strength, and life of butt welds with mild and hard interlayers under cyclic elastoplastic tension-compression. The accumulation of cyclic and quasistatic damages is determined with allowance for the redistribution of the cyclic elastoplastic strains and hardness of the stress state due to changes in the cyclic properties of separate regions of welds. The theoretical distribution of cyclic strains and the durability of welds under cyclic elastoplastic loading are supported by experimental data __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 2, pp. 29–38, February 2008.     

Singular stress field near the edge of interface of bonded dissimilar materials with an interlayer

For bonded dissimilar materials, the free-edge stress singularity usually prevails near the intersection of the free-surface and the interface. When two materials are bonded by using an adhesive, an interlayer develops between the two bonded materials. When a ceramic and a metal are bonded, the residual stress develops because of difference in the coefficient of thermal expansion. An interlayer may be inserted between the two materials to defuse the residual stress. Stress field near the intersection of the interface and free-surface in the presence of the interlayer is then very important for evaluating the strength of bonded dissimilar materials.In this study, stress distributions on the interface of bonded dissimilar materials with an interlayer were calculated by using the boundary element method to investigate the effect of the interlayer on the stress distribution. The relation between the free-edge singular stress fields of bonded dissimilar materials with and without an interlayer was investigated numerically. It was found that the influence of the interlayer on the stress distributions was confined within a small area of the order of interlayer thickness around the intersection of the interface and the free-surface when the interlayer was very thin. The stress distribution near the intersection of the interface and the free-surface was controlled by the free-edge stress singularity of the bonded dissimilar materials without the interlayer. In this case, the interlayer can be called free-edge singularity-controlled interlayer. If a stress distribution on the interface is known for one thickness of an interlayer h, stress distributions on the interface for other values of h can be estimated.     

拉压性能不同材料厚壁圆筒和厚壁球壳的极限压力分析

本文用广义双剪应力强度理论对拉压性能不同的材料制成的厚壁圆筒和厚壁球壳进行了弹塑性应力分析，得出与拉压比有关的弹性极限内压力、塑性极限内压力、弹塑性区的应力以及弹塑性内压力与弹塑性半径之间的关系式．     

Characterization of crack tip stresses in plane-strain fracture specimens having weld center crack

Fracture toughness of metals depends strongly on the state of stress near the crack tip. The existing standards (like R-6, SINTAP) are being modified to account for the influence of stress triaxiality in the flaw assessment procedures. These modifications are based on the ability of so-called ‘constraint parameters’ to describe near tip stresses. Crack tip stresses in homogeneous fracture specimens are successfully described in terms of two parameters like J–Q or J–T. For fracture specimens having a weld center crack, strength mismatch ratio between base and weld material and weld width are the additional variables, along with the magnitude of applied loading, type of loading, and geometry of specimen that affect the crack tip stresses. In this work, a novel three-parameter scheme was proposed to estimate the crack tip opening stress accounting for the above-mentioned variables. The first and second parameters represent the crack tip opening stress in a homogeneous fracture specimen under small-scale yielding and are well known. The third parameter accounts for the effect of constraint developed due to weld strength mismatch. It comprises of weld strength mismatch ratio (M, i.e. ratio of yield strength of weld material to that of base material), and a plastic interaction factor (I_p) that scales the size of the plastic zone with the width of the weld material. The plastic interaction factor represents the degree of influence of weld strength mismatch on crack tip constraint for a given mismatch ratio. The proposed scheme was validated with detailed FE analysis using the Modified Boundary Layer formulation.     

基于数字散斑相关实验测量的材料构型力的计算方法

材料构型力学主要研究材料中的缺陷(夹杂、空穴、位错、裂纹、塑性区等)的构型(形状、尺寸和位置)改变时,所引起的系统自由能的变化。本研究将基于数字散斑相关技术,实验测量材料试件的位移场分布,随后通过材料构型力的定义式,计算求得弹塑性材料中缺陷构型力的分布。其方法概括如下:位移场通过数字图像相关技术测得;应变及位移梯度场利用三次样条拟合获得;线弹性材料应力通过简单线弹性本构方程获取,而塑性材料的表面应力场通过Ramberg-Osgood本构方程计算求得;弹塑性应变能密度分布则由应力-应变曲线数值积分获得。该方法对普通弹性材料或者弹塑性材料均适用,可以用于各种不同的缺陷及缺陷群的材料构型力测量。     

拉压异性材料含受压圆孔大平板的极限分析

探讨了广义双剪应力强度理论在平面应力状态下的屈服轨迹及其方程式,并用于拉压异性材料圆孔受内压的极限分析,得到了与拉压比有关的弹性极限内压力,弹塑性区的应力、塑性内压力与弹塑性分界半径之间的关系、塑性区的最大半径和最大内压力,所得极值均高于用莫尔强度理论分析的结果。     

Hoek–Brown criterion applied to circular tunnel using elastoplasticity and in situ axial stress

Based on the nonlinear Hoek–Brown failure criterion, elastoplastic analytical solutions are developed for the elastoplastic stresses, strains and plastic zones around a circular tunnel subjected to different value of the axial in situ stress. Effects of the transverse in situ stress, the axial in situ stress and the strength parameters of rock masses on the elastoplastic stresses, strains and plastic zones in the surrounding rock masses are investigated. It is found from the numerical results that the stresses, strains, and plastic zones in the surrounding rock depend not only on the transverse in situ stress but also on the axial in situ stress as well as the mechanical parameters of rock masses.     

Progressive failure constitutive model of fracture plane in geomaterial based on strain strength distribution

Progressive failure constitutive model of fracture plane in geomaterial based on strain strength distribution is proposed. The basic assumption is that strain strength of geomaterial comply with a certain distribution law in space. Failure of tensile fracture plane and shear fracture plane in representative volume element (RVE) with iso-strain are discussed, and generalized failure constitutive model of fracture plane in RVE is established considering combined effect of tension and shear. Fracture plane consists of elastic microplanes and fractured microplanes. Elastic microplanes are intact parts of the fracture plane, and fractured microplanes are the rest parts of the fracture plane whose strain have ever exceeded their strain strength. Interaction mode on elastic microplanes maintains linear elasticity, while on fractured microplanes it turns into contact and complies with Coulomb’s friction law. Intact factor and fracture factor are defined to describe damage state of the fracture plane which can be easily expressed with cumulative integration of distribution density function of strain strength. Strong nonlinear macroscopic behavior such as yielding and strain softening can be naturally obtained through statistical microstructural damage of fracture plane due to distribution of strain strength. Elastic–brittle fracture model and ideal elastoplastic model are special cases of this model when upper and lower limit of distribution interval are equal.     

A novel semi-inverse solution method for elastoplastic torsion of heat treated rods

Torsion rods are a primary component of many power transmission and other mechanical systems. The behavior of these rods under elastoplastic torsion is of major concern for designers. Different methods have so far been proposed which deal with the elastoplastic torsion of rods, most of which assume constant yield stress. This assumption produces rough and inaccurate results when the rods are heat treated, since in the process of heat treatment the form of yield stress distribution across the rod cross section changes. We propose a new method for calculating elastoplastic torsion of rods of simply connected cross section which is based on heat treatment observations. In our method the full plastic stress function is obtained by using the semi-inverse method. Elastoplastic stress function is obtained by generalizing the idea of the membrane analogy and using a piecewise continuous stress function. Since the proposed form of yield stress distribution can not be handled by the current Finite Element packages, we produce a computer package with a 3D graphical interface capable of calculating and displaying the 3D elastoplastic stress function, shear stress contours, and torque-angle of rotation per unit length. We show that our method produces excellent agreement for several known cross sections in comparison to methods which assume constant yield stress.     

多层氧化石墨烯的三维弹性常数及氧化度对力学性能的影响

宏观氧化石墨烯膜由多层石墨烯组成,其法向拉伸和层间剪切性能远比面内性能低。本文视多层氧化石墨烯为一种特殊的三维正交各向异性材料——横观各向同性材料,通过建立羟基和环氧基在石墨烯表面随机分布的多层氧化石墨烯三维模型,采用分子动力学方法模拟多层氧化石墨烯的面内拉伸、法向拉伸和层间剪切行为,分别得到了多层氧化石墨烯材料的全部五个独立弹性常数E2、E3、μ12、μ32和G23,进而确定了三维弹性矩阵（柔度矩阵和刚度矩阵）,并进一步分析了氧化度对弹性常数和强度的影响规律。结果表明：随着氧化度R逐步增大,多层氧化石墨烯面内杨氏模量E2和拉伸强度σ2max逐步降低,法向杨氏模量E3和拉伸强度σ3max、层间剪切模量G23和剪切强度τ23max均逐步增大,而对泊松比的影响较小;拉伸和剪切断裂破坏位置由氧化基团(羟基和羧基)与碳原子结合键能大小所决定。     

隧洞式内衬储气库极限储存压力解析解

隧洞式内衬储气库是一种新型能源储存方法,有助于平衡供需,推动国家由化石能源向绿色能源的持续过渡,有利于国家“碳中和、碳达峰”目标的实现.本文采用极限平衡方法和弹塑性分析方法推导隧洞式内衬储气库极限储存压力的解析解.在极限平衡方法中,考虑上覆围岩自重、破裂面受力和极限储存压力,选用刚性锥模型,推导了上限压力表达式;在弹塑性分析方法中,根据围岩中应力分布规律和剪切、抗拉强度,推导获得了弹塑性条件下上限与下限压力表达式.最终综合考虑两方法求得的结果,确定极限储存压力解析解.结果表明:极限平衡方法求得上限压力与埋深呈二次函数关系,且随着侧压力系数的增大而增大;弹塑性分析方法确定的上限压力和下限压力与埋深呈线性关系,下限压力随着侧压力系数的增大而减小,且Ⅰ级围岩条件下的内衬储气库不用考虑下限压力.在侧压力系数λ=1.2时上限压力最大,因此应尽量在侧压力系数为1.2的围岩条件下修建隧洞式储气库.最后根据典型工况下上限和下限压力曲线给出内衬洞室推荐压力范围.     

Sensitivity analysis for 3-D elastoplastic structural reliability

By taking the elastoplastic effect of structural material into account and based on 3-D elastoplastic stochastic finite element method, methods for sensitivity analysis with respect to both the distribution parameters of random variables and parameters in the limit state function are suggested. In the incremental iterative calculation, the sub-increment changingK, method and the corresponding formulas for accelerating convergence are used. The sensitivity of 3-D structural system reliability with respect to random variables is also studied.     

Influence of layer orientation and interlayer bonding force on the mechanical behavior of shale under Brazilian test conditions

The mechanical behavior of inherently anisotropic shale rocks under Brazilian test conditions are investigated in this study based on experimental studies and numerical simulations. The effects of the weak lamination planes and interlayer bonding force of these layers on the failure strength and fracture patterns are studied systematically. Numerical simulations using particle flow code in two dimensions based on the discrete element method showed a good agreement with the experimental results in the failure strength and fracture patterns. The shale revealed strong anisotropic behavior with the failure strength perpendicular to the lamination plane greater than failure strength parallel to lamination plane. The failure strength of the different interlayer bonding force against the layer orientations changed significantly. Four types of fracture patterns were observed: curved fracture, broken-linear fracture, layer-activated fracture, and central-linear fracture. The observed fracture patterns are either or a combination of tensile and/or shear fractures. Increase in interlayer bonding strength decreased the quantity of micro cracks and this directly led to reduction in the anisotropic behavior. Overall the layer orientation and interlayer bonding force of the shale thus play a very important role in the anisotropic behavior of the shale.     

Triaxial stress state of cylindrical openings for rocks modeled by elastoplasticity and strength criterion

An analytical solution for calculating the triaxial stress state around a cylindrical opening in an elastoplastic cohesive medium is developed. Magnitude of the slip zones around a cylindrical opening in crack-weakened rock masses is considered by modifying the existing strength criterion for rocks of different types. The disturbance coefficient, the geological strength index and the other strength parameters are also investigated.     

考虑微裂纹相互作用的的岩石微观力学弹塑性损伤模型研究

本文建立基于微裂纹扩展的岩石弹塑性损伤微观力学模型。用自洽方法考虑裂隙间相互影响,压缩载荷下微裂纹尖端翼裂纹稳定扩展表征岩石的微观损伤,基于应变能密度准则用Newton迭代法求复合型断裂的翼裂纹扩展长度,并采用微裂隙统计的二参数Weibull函数模型反映绝对体积应变对微裂纹分布数目影响,进而用翼裂纹扩展所表征的应力释放体积和微裂纹数目来表示含有微裂隙的岩石损伤演化变量;宏观塑性屈服函数采用Voyiadjis等的等效塑性应变的硬化函数,反映塑性内变量对硬化函数的影响;建立岩石的弹塑性损伤本构关系及其数值算法,并用回映隐式积分算法编制了弹塑性损伤模型的程序。从围压和微裂隙长度等因素分析弹塑性损伤模型的岩石的损伤和宏观塑性特性。     

Dissimilar ultrasonic spot welding of Mg-Al and Mg-high strength low alloy steel

Sound dissimilar lap joints were achieved via ultrasonic spot welding (USW), which is a solid-state joining technique. The addition of Sn interlayer during USW effectively blocked the formation of brittle al₁₂Mg₁₇ intermetallic compound in the Mg-Al dissimilar joints without interlayer, and led to the presence of a distinctive composite-like Sn and Mg₂Sn eutectic structure in both Mg-Al and Mg-high strength low alloy (HSLA) steel joints. The lap shear strength of both types of dissimilar joints with a Sn interlayer was significantly higher than that of the corresponding dissimilar joints without interlayer. Failure during the tensile lap shear tests occurred mainly in the mode of cohesive failure in the Mg-Al dissimilar joints and in the mode of partial cohesive failure and partial nugget pull-out in the Mg-HSLA steel dissimilar joints.     

Plastic strip model of cracked weld joint with residual stresses

The effect of residual stresses on the fracture behavior of a cracked weld joint is studied by making use of the continuous dislocation formulation. Considered are the plastic zone length of the strip model zone and the opening displacement of a crack that is normal to both weld line and base metal boundary; they depend on the character of the yield stresses for the base metal (BM), weld material (WM), and heat affected zone (HAZ). The crack driving force is found to increase with the tensile residual stress while crack initiation and growth are suppressed if the residual stress is compressive. Moreover, the plastic zone and crack opening displacement are found to decrease linearly with the HAZ yield strength as the HAZ width is increased for HAZ yield strength greater than that of BM.     

Enhanced SCC resistance of AA7005 welds with appropriate filler metal and post-welding heat treatment

Stress corrosion cracking (SCC) resistance for weldment of Al-Zn-Mg alloys is enhanced with appropriate filler metal and post-welding heat treatment while maintaining the weld strength integrity. Tungsten insert gas (TIG) arc welding is used to join the AA7005-T4 plates with three high-Mg fillers, ER5183, ER5556 and ER5356. Four heat treatments, NA (natural ageing), T6, T73, and RRA, were applied to the welded plates. Micro-hardness test, tensile test and stress corrosion test were conducted on the heat-treated specimens. Differential scanning calorimetry (DSC) analyses and transmission electron microscopy (TEM) observations were also performed on the specimens cut from the fusion zone. For the three high-Mg filler metals, only the ER5356 filler with low Mn content showed improvement in the tensile property after different post-welding heat treatments. Weld strength improvement were ideal for the T7 post-welding heat treatment. No improvements were observed for the ER5183 and ER5556 filler wires. The ultimate tensile strength of ER5183, ER5556 and ER5356 weld were found to fall within the, respective, ranges of 250-280, 270-300, and 280-360 MPa corresponding to the different heat treatments.Post-welding heat treatment improves the SCC resistance of welds made with ER5356 and specimens with T7 and RRA heat treatments. DSC analyses showed that only the specimen fabricated from the weld made with ER5356 has an endothermic dissolution reaction peaked at 141 °C. The TEM images from the fusion zone (FZ) of T7 and RRA welds with ER5356 filler wire showed similar micro-structure and distribution of precipitates. They both have relatively large and non-continuous precipitates at the grain boundary. The size of precipitates differed in the matrix. The combination of ER5356 filler metal and post-welding T7 treatment can offer the AA7005 weld with better SCC resistance and high tensile strength.     

Numerical study of the plastic behaviour in tension of welds in high strength steels

The influence of the mismatch between material properties and constraint on the plastic deformation behaviour of the heat affected zone of welds in high strength steels is investigated in this study, using finite element simulations. An elastoplastic implicit three-dimensional finite element code (EPIM3D) was used in the analysis. The paper presents the mechanical model of the code and the methodology used for the numerical simulation of the tensile test of welded joints. Numerical results of the tensile test of welded samples with different hypothetical widths for the Heat Affected Zone and various material mismatch levels are shown. The analysis concerns the overall strength and ductility of the joint and in relation to the plastic behaviour of the heat affected zone. The influence of the yield stress, tensile strength and constraint on the stress and plastic strain distribution in the soft heat affected zone is also discussed.     

基于统一强度理论的岩石弹塑性本构模型及其数值实现

基于弹塑性力学理论,以统一强度准则为屈服准则,建立了考虑硬化/软化行为和应变率效应的岩石弹塑性本构模型;采用Fortran语言通过LS-DYNA的用户自定义材料接口(Umat)对该弹塑性本构模型进行编程,并把该程序生成求解器以达到对该模型进行应用的目的;通过岩石的单轴压缩实验和SHPB实验对所建的弹塑性本构模型进行验证,结果表明,该弹塑性本构模型能够反映岩石在准静态和动态下的力学行为。