Time to Creep Failure of Thin-Walled Cylindrical Pipes under Torsion

The time to creep failure is calculated for rectilinear thin-wall pipes subjected to pure torsion, torsion with uniaxial tension, and torsion with internal pressure. The problem is solved using the concept of equivalent stress. The equivalent stresses are found from the generalized mixed failure criterion whose form depends on the signs of the principal stresses. The criterion relates the maximum normal stress and the intensity of shear stress if the signs coincide, and the maximal shear stress and the octahedral shear stress if the signs are opposite. A technique for determining the material constants is developed. The calculated and experimental data are compared and found to be in satisfactory agreement     

Numerical Modeling of Elastic Spherical Contact for Mohr-Coulomb Type Failures in Micro-Geomaterials

The contact behavior for geological materials, such as reservoir shale rock, is simulated using the finite element method by considering a nano-indenter tip indenting into a geomaterial obeying the Mohr-Coulomb failure criterion. The deformation and slip at the micro-scale along the shear direction in grain-to-grain contact follows the Coulomb frictional/sliding failure criterion, while the linear elastic force-displacement law is enforced in the direction normal to the contact surface. A series of simulations are performed to study the effect of cohesion, friction angle, and tensile strength on the contact response. For a material with very high cohesion and frictionless contact, the indented geomaterial behaves almost purely as an elastic medium. In this case, the indentation process converges to the classic Hertz grain-to-grain spherical contact model. For a material with extremely low cohesion, the geomaterial behaves like cohesionless granular material at the micro-scale. For materials with finite cohesion values, such as shales, the force-displacement responses are analyzed and reported. This simulation is compared to micro-indentation tests using a spherical indenter tip conducted on preserved samples of Woodford shale.     

Stability of boreholes in a geologic medium including the effects of anisotropy

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饱和超固结黏性土的三剪弹塑性本构模型研究

针对饱和超固结黏性土现有下加载面修正剑桥模型中破坏应力比为定值、土体黏聚力为零,以及不能准确反映不同应力状态下土的强度差异这些问题,基于三剪统一强度准则以及应力坐标平移法得到了扩展破坏应力比,其特点是能更好地反映应力状态变化以及土体黏聚力的影响。在此基础上提出了饱和超固结黏性土的三剪弹塑性本构模型,该模型的特点是能描述土体受力时的中间主应力效应,应力区间效应和拉压差影响,同时也能更好地考虑土体黏聚力的影响。基于该模型对ABAQUS软件进行了二次开发,并利用其模拟了饱和超固结黏性土在排水和不排水条件下的真三轴和常规三轴压缩试验特性。对常规三轴压缩条件下土体力学特性作了模拟和试验结果对比。结果表明所提模型能很好地反映不同超固结比下土体的变形、剪胀、孔隙水压力变化特性。     

The role of a realistic volume constraint in modelling a two dimensional granular assembly

This paper presents a deceptively simple mathematical model for the deformation of granular materials composed of rigid particles. The model captures many of the diverse features of the behaviour of such a material and emphasises the importance of volume constraints in situations where the deformation is mainly by particle rearrangement. It is constructed using a simple dissipation function and a rather more complicated dilatancy rule containing an updateable reference strain. This allows the solid-like and fluid-like properties of granular materials to be reconciled in a single model.The model has been used to simulate experiments that use an analogue of an ideal granular material [Joer, H.A., Lanier, J., Fahey, M., 1998. Deformation of granular materials due to rotation of principal axes. Geotechnique 48 (5), 605-619] consisting of a two dimensional assembly of thin PVC rods. These experiments clearly illustrate: partially reversible dilatancy in direct shear tests; cyclic shearing leading to liquefaction in constant volume shear tests; and non-coaxiality of the principal axes of stress and strain increment in circular loading tests. These radically different modes of deformation provide a challenging data set that allows the model's potential to be clearly demonstrated.The authors believe that the comparison of these experimental results and our simulations give strong support to the assertion that volume changes associated with shear deformation are responsible for the rotational kinematic hardening seen in granular materials, and hence, the non-coaxiality of the stress and strain-rate tensors.     

Shear band analysis and shear moduli calibration

Strain localization is a well known phenomenon, generally associated with plastic deformation and rupture in solids, especially in geomaterials. In this process, deformation is observed to concentrate in narrow zones called shear bands. This phenomenon has been studied extensively in the last 20 years by different researchers, experimentally, theoretically and numerically. A criterion for the onset of localization can be predicted solely on the basis of the constitutive law of the material, using the so-called shear band analysis. This criterion gives the critical orientation, and the critical stress state and strain for a given loading history. An important point, already stressed by Vardoulakis in 1980, is that in particular, out-of-axes shear moduli play a central role in the criterion. These are the moduli involved in the response to a deviatoric stress increment with principal axes oriented at 45° from total stress principal axes. Out-of-axes shear moduli are difficult parameters to calibrate; common tests, with fixed principal stress and strain directions, do not provide any information on these moduli, as long as they remain homogeneous. Still, real civil engineering and environmental problems are definitely not simple axisymmetric triaxial tests; practical modeling involves complex stress paths, and need complex parameters to be calibrated. Only special tests, like compression–torsion on hollow cylinder tests, or even more complex tests can be used for shear moduli calibration. However, shear band initiation in homogeneous, fixed-axes tests does activate out-of-axes shear. Hence, it is natural that shear band analysis makes shear moduli enter into the analysis.Then, a typical inverse analysis approach can be used here: experimental observation of strain localization in triaxial tests can be used together with a proper shear band analysis for the model considered, in order to determine out-of-axes shear moduli.This approach has been used for a stiff marl in the framework of a calibration study on a set of triaxial tests. The steps of the method are presented, and the bifurcation surface in the stress space is exhibited.     

超弹性橡胶材料的改进Rivlin模型

讨论了不可压缩橡胶材料的超弹性唯象本构模型。针对典型实验,给出选择应变能函数的原则。从物理机理上,分析了Neo-Hookean模型、Mooney模型、三阶Rivlin模型及Ogden模型的优缺点。在此基础上,将Rivlin模型改进成为 ,这种新形式具有三个优点：①若取前三项（N=1）,则其结果与不可压缩线弹性的应变能相等,能够近似满足剪切的线性关系,但拉伸及压缩的线性关系是精确满足的。②当N≥2时,简单剪切中的应变能及剪应力τxy在小应变情况下是以剪应变γxy为等比的多项式展开;而Rivlin模型只能保证简单剪切实验中的应变能及剪应力τxy是以(γxy)2为等比的级数展开的形式,当取前两项的情况下,Rivlin模型只能精确保证常剪切,拉伸及压缩的线性关系无法得到保证。针对典型实验数据,若取同阶次多项式,本文模型的同类实验数据预测及不同类实验数据间相互预测的精度都比Rivlin模型的高。     

A new three-dimensional Hoek-Brown strength criterion

The Hoek-Brown(HB) strength criterion has been widely applied to the estimation of strength of intact rock and rock mass,while evolving ever since.However,negligence of the effect of the intermediate principal stress still remains in the criterion’s latest version.At the same time,several three-dimensional(3D) HB strength,which can takes into account the influence of the intermediate principal stress,have already been proposed,among which the 3D HB criterion proposed by Zhang and Zhu seems to be the most reasonable one.However,the Zhang 3D HB criterion may have problems with some stress path close to triaxial extension state because of the non-convexity characteristic of its failure surface.In this paper,a new 3D HB strength criterion is presented based on a generalized form of the HB criterion,which also considers the effect of the intermediate principal stress and inherits all the merits of the original version of the HB criterion.In addition,this new criterion can remedy to some extent the shortcomings observed in the Zhang 3D HB criterion.Polyaxial tests for five different rocks from published literatures are used for evaluating this new criterion and comparing it with the Zhang 3D HB criterion.The results show that this new criterion may over-predict or underpredict the polyaxial strength of rocks but the errors are relatively small,and similar results are also found for the Zhang 3D HB criterion,which one is better depends on the type of the rock under estimation.     

Failure criteria for transtropic,pressure dependent materials

A convenient criterion in the 3D-principal stress space for describing the yielding and failure behaviour of transversely isotropic (transtropic) materials, presenting also the strength differential effect (SDE) along the three principal stress axes, is the elliptic-paraboloid failure criterion (EPFC). The general properties of the EPFC were examined previously for the general anisotropic material with SDE and its validity was established by comparing it with other criteria and the real behaviour of various anisotropic materials. In this paper the particular properties of materials showing a transverse isotropy were studied and important results were established which simplify considerably the complicated expressions established in the case of total anisotropy. The particular properties of the EPFC for transtropic materials were also compared with experimental evidence and were found to be in agreement with it.     

一种适用于岩土的扩展强度及屈服准则

土壤材料是一种典型的摩擦型材料,然而天然岩石却具有一定的凝聚力,而金属材料则完全是凝聚型材料. 在分析三种典型的材料强度准则表达式基础上,即SMP,Lade-Duncan以及广义Von-Mises准则,通过利用应力张量的不变量表达形式,提出了一种扩展准则即VML准则,该准则能够分别退化为上述3种典型准则. 在偏平面上,新准则能够描述从曲边三角形到圆形在内的多种开口形态;在子午面上,采用幂函数作为破坏准则公式,能够描述静水压力对于强度特性影响的非线性性质. 而对于土壤的屈服性质,岩土材料具有典型的压剪耦合特性,因此,为了描述剪切与等方向压缩两种路径下的体积耦合现象,采用水滴型屈服面作为屈服准则. 对于偏平面上的截面形状,讨论了给定球应力下偏应力强度值的分布形式及特点,讨论了应力罗德角对于偏平面上强度曲线的凹凸性的影响. 最后,通过多种材料的破坏与屈服试验成果,用所提新准则进行了验证. 通过强度以及屈服特性测试对比,验证了所提VML准则的合理性.      

岩土材料的非线性统一强度模型

将材料的破坏归结为剪切破坏,每种材料对应于特定的剪切滑动面,抗剪强度为滑动面上正应力的函数,基于不同材料的强度特性将一系列的剪切滑动面统一起来,建立了岩土材料的非线性统一强度模型.非线性统一强度模型的滑动面为β应力空间内的等倾面,在β应力空间内的强度面为圆锥面;在普通应力空间内的强度面为一系列连续光滑、外凸的锥面,在偏平面上强度曲线涵盖了从下限Matsuoka-Nakai曲线到上限Drucker-Prager圆之间的所有区域,子午面上强度线为直线.非线性统一强度模型只有3个材料参数,参数都具有明确的物理意义,通过与国内外学者已取得的岩土类材料真三轴强度试验结果的比较,表明模型可适用于多种类型的材料,并合理描述其非线性强度特性.      

A failure criterion for fiber reinforced polymer composites under combined compression–torsion loading

A fracture mechanics based failure criterion for unidirectional composites under combined loading has been developed. The predictions from this criterion have been compared with experimental data obtained from combined compression–torsion loading of glass and carbon fiber reinforced polymer composites of 50% fiber volume fraction. The specimens were loaded under rotation control and displacement control in a proportional manner. Comparison of the Budiansky–Fleck kinking model, specialized to a solid circular cylinder, and the new failure model against experimental data suggests that the Budiansky–Fleck model predictions do not capture the variation of compressive strength as a function of shear stress for glass fiber composites. This is because these composites fail predominantly by compressive splitting. The Budiansky–Fleck model predictions are appropriate for composites that fail by compressive kinking. The new model predictions capture the experimental results for glass composites where the compression strength is initially unaffected by shear stress but undergoes a drastic reduction when a critical value of shear stress is reached.     

The elliptic paraboloid failure surface for transversely isotropic materials off-axis loaded

The elliptic paraboloid failure surface has been well established as a potential criterion for yielding and failure of transversely isotropic materials, presenting also the strength differential effect [1]. This was done by extending well established criteria for isotropic materials presenting the strength differential effect (SDE), through an introduction process which maintained basic physical principles for the anisotropic materials. All previous literature concerned the special case where the principal axes of the external loading coincided with the principal strength axes of the material. In this paper the most general case where the two systems of frames are arbitrarily oriented relatively to each other is considered. In this situation the simplifications derived from the coincidence of the external principal stress and material principal strength axes are lost and the material should be considered as a general orthotropic one. The general properties for such types of loading of the transversely isotropic material are established by maintaining the general features of the failure locus invariant. Then, this study completes the investigation of yielding and failure mode of such materials considering the most general case of their loading.     

一种非线性强度准则及转换应力法

岩土材料在二维破坏模式下具有较强烈的曲线形态,在一般剪应力与正应力空间中提出用幂参数曲线来表达上述曲线,该曲线与摩尔圆的外切点即对应为破坏应力点,则利用该点的外切直线斜率的反正切值来得到有效滑移角.对于三维单元体,共存在三个有效滑移角,利用三个有效滑移角确定出空间有效滑移面.基于岩土材料为摩擦型材料这一基本特性,利用空间有效滑移面上的应力比为一定值作为衡量材料破坏与否的判断准则,基于上述思路推导得到了t强度准则,在偏平面上,t准则开口形状为介于Von-Mises圆形曲线到SMP曲边三角形形态.在子午面上,引入开口的幂函数作为反映静水压力效应以及剪切破坏的曲线,而闭口的水滴型屈服面函数作为反映体积压缩屈服曲线,反映了岩土材料的压剪耦合特性.基于所提出的t强度准则, 推导了变换应力公式,可将以$p,q$为应力量的二维模型简单方便的转换为三维应力状态本构模型.通过强度以及多种应力路径的测试对比,验证了所提t准则及基于该准则的变换应力公式的合理性.      

From yield to fracture,failure initiation captured by molecular simulation

While failure of cracked bodies with strong stress concentrations is described by an energy criterion (fracture mechanics), failure of flawless bodies with uniform stresses is captured by a criterion on stress (yielding). In-between those two cases, the problem of failure initiation from flaws that moderately concentrate stresses is debated. In this paper, we propose an investigation of the process of failure initiation at the atomic scale by means of molecular simulations. We first discuss the appropriate scaling conditions to capture initiation, since system sizes that can be simulated by molecular mechanics are strongly limited. Then, we perform a series of molecular simulations of failure of a 2D model material, which exhibits strength and toughness properties that are suitable to capture initiation with systems of reasonable sizes. Transition from fracture failure to yield failure is well characterized. Interestingly, in some specific cases, failure exceeds yield failure which is in contradiction with most initiation theories. This occurs when stress are highly concentrated while little mechanical energy is stored in the material. This observation calls for a theory of initiation which requires that both stress and energy are necessary conditions of failure. Such an approach was proposed by Leguillon (2002). We show that the predictions of this theory are consistent with the molecular simulation results.     

NONLINEAR UNIFIED STRENGTH MODEL OF GEOMATERIALS

将材料的破坏归结为剪切破坏,每种材料对应于特定的剪切滑动面,抗剪强度为滑动面上正应力的函数,基于不同材料的强度特性将一系列的剪切滑动面统一起来,建立了岩土材料的非线性统一强度模型.非线性统一强度模型的滑动面为β应力空间内的等倾面,在β应力空间内的强度面为圆锥面;在普通应力空间内的强度面为一系列连续光滑、外凸的锥面,在偏平面上强度曲线涵盖了从下限Matsuoka-Nakai曲线到上限Drucker-Prager圆之间的所有区域,子午面上强度线为直线.非线性统一强度模型只有3个材料参数,参数都具有明确的物理意义,通过与国内外学者已取得的岩土类材料真三轴强度试验结果的比较,表明模型可适用于多种类型的材料,并合理描述其非线性强度特性.     

Prediction of forming limit diagrams based on shear failure criterion

Maximum shear stress theory, also called the ‘Third Strength Theory’, is a classical theory used to predict the failure of common metal, but it cannot be used directly to predict sheet metal failure due to anisotropy and the loading path. Therefore, this paper proposes a maximum shear stress calculating method, which has been named “shear failure criterion” for the purpose of this paper. In order to validate the shear failure criterion, a general program was developed, and two typical materials, steel, and aluminum alloy, were used to study the new shear failure criterion in this study. The two materials were modeled by advanced constitutive models, including Hill1948 and Yld2000-2d yield functions and several types of isotropic hardening models. Experimental validation has indicated the accuracy of predicted FLD using shear failure criterion, which is able to provide a new alternative method to numerically predict FLD.     

Mixed-mode crack initiation at a v-notch in presence of an adhesive joint

The failure criterion for v-notched specimens developed for mixed-mode loadings by Yosibash et al. [Yosibash, Z., Priel, E., Leguillon, D., 2006. A failure criterion for brittle elastic materials under mixed mode loading. Int. J. Fract. 141(1), 289–310.] is generalised in order to consider the influence of the shear stresses and the mode-dependence of the toughness. This is demonstrated to be important in some cases with adhesive joints under complex loadings for instance. The original criterion assumes that an abrupt onset of a crack with a finite extension occurs when two conditions are fulfilled simultaneously: first the normal traction all along the presupposed crack path reaches a critical value, and second the onset is energetically allowed. The influence of the shear stresses is now considered through a mixed law involving critical shear and tensile stresses as well as the mode-dependent toughness introducing a new equivalent SIF. This extended criterion is applied to the simulation of an Arcan test on v-notched compact tension shear (CTS) specimens made of two parts bonded together along the geometric plane of symmetry of the specimen. The competition between two modes of failure is studied: crack initiation along the weak joint which may constitute a privileged fracture surface and initiation in the homogeneous material at an optimum angle that minimizes the critical load to failure.