A dynamic damage constitutive model for a rock mass with non-persistent joints under uniaxial compression

Most problems faced by the practicing rock mass engineering involve the evaluation of rock mass dynamic strength and deformability. As part of a rock mass, the mesoscopic flaws such as the microcracks and the macroscopic ones such as the joints both inherently affect the rock mass dynamic strength and deformational behavior. Nearly none of the existing models can handle the co-effect of these two kinds of flaws on the rock mass dynamic mechanical behavior. This study focusses on the rock mass with multi-sets of non-persistent joints and establishes a mathematical model accounting for the anisotropy in dynamic strength and deformability induced by the joints. Accordingly, an approach incorporating the existing models or methods to enable perfect simulation of the dynamic stress-strain relationship of a rock mass is proposed, in which the joint geometrical parameters such as the joint length and dip angle, the strength ones such as the joint internal friction and the deformational ones such as the joint normal and shear stiffness can all be taken into account. In order to investigate the validity of the proposed model, a series of calculation examples have been made and the results fits very well with the theoretical ones.     

单轴压缩下断续节理岩体动态损伤本构模型

断续节理将对工程岩体的强度及变形等力学特性产生显著影响，损伤力学中视节理为岩体的一种宏观损伤，因而采用损伤张量来刻画其对岩体的影响。目前学术界提出了用节理的几何、强度及变形等3类参数来描述节理的物理力学性质，而目前的岩体损伤张量计算方法都只涉及前2类参数，均没有涉及其变形参数即法向及切向刚度。为此，在前人研究的基础上，基于断裂及损伤理论提出了考虑节理法向及切向刚度的单轴压缩下单条断续节理引起的损伤张量计算公式，进而通过考虑节理间相互作用给出了单组单排或多排节理岩体损伤张量计算公式。其次，以岩石细观动态损伤模型为基础，结合宏细观损伤耦合观点提出了一个能够同时考虑节理几何、强度及变形参数的断续节理岩体动态损伤本构模型。最后，利用该模型讨论了节理参数及载荷应变率等对岩体动态力学特性的影响，认为节理长度减小及摩擦角增大将导致岩体动态峰值强度及弹性模量增大；岩体动态峰值强度及弹性模量则随着节理法向及切向刚度的增大分别减小或增大；而当节理法向及切向刚度按照同一比例增大时，岩体动态峰值强度及弹性模量则是增大的。岩体动态峰值强度与载荷应变率呈正相关。     

On flaw size and distribution in lap joints

By using adhesive as the bonding substance between metals or polymeric materials, simple structural joints can be made to bear relatively high loads. Applications have increasingly been made in substituting adhesive joints for conventional mechanical fastenings, especially in the aircraft and aerospace industries where weight is a predominant factor. In order to design a most effective adhesive-bonded joint, an understanding of the stress distribution along the joint is as important as the physical properties of the bonding agent. One of the most common and widely used adhesive joints is the single lap joint.Recent investigations using various analytical models have revealed that the cause of failure in an idealized ‘defect free’ lap joint is primarily due to the localized effect of high stress concentration at the lap ends. With the presence of flaw like defects in the adhesive layer, the load transfer from adherend to adhesive is expected to be different from the idealized joint. In addition, localized stress concentrations induced by irregular adhesive defects that may be found in practical engineering applications can further reduce fracture strength of such an imperfect joint.This paper is intended to describe an investigation into the effect of internal adhesive flaw size and distribution on the fracture behaviour of adhesive-bonded lap joints. The finite element method is used to gain a quantitative understanding of the localized shear stress distributions due to the presence of the internal flaws along the bonding layer. It is observed that the reduction in the fracture strength is relatively small when a flaw is located in the central portion of the bonding length. However, a flaw located near the lap ends of the adhesive joint can cause marked reduction in the fracture strength, due to its interaction with the high stress concentration at the lap ends.     

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.     

海洋平台管节点应力分析研究工作展望

本文在我国目前海洋平台管节点研究工作的基础上,提出今后管节点应力分析研究的几点意见,包括对复杂管节点及组合载荷作用下的研究,管节点静强度应从冲剪强度准则转向极限强度准则的研究,弹-塑性分析的研究,以及管节点局部变形的研究等.对上述研究方向的目的、意义及作法等提出了看法.     

An instrumented fastener for shear force measurements in joints

A preliminary investigation has been conducted on instrumented fasteners for use as sensors to measure the shear loads transmitted by individual fasteners installed in double-splice joints. Calibration and load verification tests were conducted for instrumented fasteners installed at three fastener torque levels. Results from calibration tests show that the shear strains obtained from the instrumented fasteners vary linearly with the applied load and that the instrumented fasteners can be effectively used to measure shear loads transmitted by individual fasteners installed in double-splice joints. Tests were also conducted with three instrumented fasteners installed in a typical double-splice joint. The test results showed that the load distribution between individual fasteners is dependent on the location of the fastener in the joint and the fastener torque level. The fastener located near the end of the joint with the single plate carried more load than the fasteners located near the end of the joint with the two plates. Installing the fasteners with a torque greater than finger tight results in a significant amount of the load being carried by friction between the faying surfaces of the plates even if the faying surfaces are polished and lubricated. Increasing the fastener torque increases the load being carried by friction between the faying surfaces of the joint. Increasing friction between the faying surfaces of the joint. Increasing the fastener torque also results in a more uniform distribution of the loads between the individual fasteners for joints in aluminum plates with two fasteners, but does not have a significant effect for joints in steel plates with three fasteners. Paper was presented at the 1992 SEM Spring Conference on Experimental Mechanics held in Las Vegas, NV on June 8–11.     

甘肃北山地质处置库围岩节理抗剪强度经验估算

节理抗剪强度参数是地质处置库预选地段工程地质对比和围岩稳定性分析的重要指标。本文在旧井地段英云闪长岩节理分组的基础上,运用定向统计测量方法估测节理粗糙度系数,通过评价节理粗糙度系数的尺寸效应,确定节理抗剪强度经验估算有效长度,由JRC-JCS模型求得各组节理4个方向的抗剪强度参数,并评价了地质处置库围岩节理抗剪强度的各向异性特征。     

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.     

Experimental investigations of the joint-mortar behaviour

An important failure mode of the masonry walls is the shearing process in joint mortar. In order to understand better this phenomenon, an experimental study is carried out on half brick couplet specimen. Load/Unload shear tests are performed to assess the type of the shear behaviour of the joint mortar. The cohesion and the internal friction angle are then derived from linear regression while assuming Mohr–Coulomb criterion. In particular, the influence of holes on the joint behaviour is studied by comparing results obtained with both solid and hollow bricks. In both cases, the experimental results show that there is not any stiffness degradation even in the softening regime. Actually, the shear modulus remains constant. Hence, the joint behaviour is considered to be elastoplastic, independently on the brick type. However, it seems that the presence of holes increases the stiffness but does not affect the internal friction angle of the joint mortar.     

用于RC框架-轻钢增层混合结构的新型外箍式节点抗震性能试验研究

RC框架-轻钢增层混合结构是一种上轻下重、刚度突变明显的复杂结构,为了保证结构整体协同工作,本文提出了一种能够有效减缓刚度突变和增强对上部结构约束的新型外箍式连接节点。通过对新型外箍式节点与传统植筋节点的1∶2缩尺模型拟静力试验研究,得到了试件破坏模式和荷载-位移滞回曲线,对比分析了其滞回特性、梁端塑性铰、骨架曲线、强度退化、刚度退化和耗能能力等抗震性能。结果表明:新型外箍式节点可以使梁端塑性铰远离梁根部,有效保护了节点核心区;新型节点通过外箍钢板的构造措施提高了试件的初始刚度、承载力和耗能能力,减缓了刚度与强度退化速度,表明新型节点的抗震性能大幅度优于传统植筋节点,研究成果可为RC框架-轻钢增层混合结构的节点设计提供一定参考。     

Dynamic tensile strength of composite laminate joints fastened mechanically

The tensile strength of composite joints is determined under dynamic loading conditions. The composites are laminates made from hybrid fiber reinforced plastic (HFRP) and carbon fiber reinforced plastic (CFRP). Three different mechanically fastened joint configurations are considered: they are the pin-connected, single-lap and double-lap type. The joint strength under dynamic load is found to be lower than that under quasi-static load. The pin-connected joint was the weakest. Investigated also are the influence of geometric parameters for pin-connected HFRP laminate joints. The results shed light on how to improve the bearing strength of mechanical joints when encountering dynamic loads.     

An empirical statistical constitutive relationship for rock joint shearing considering scale effect

The scale effect of rock joint shearing is of great significance in rock engineering. Most existing shear constitutive models could describe the pre- and post-peak deformation of rock joints, but only in one particular scale, that is, those existing models will fail to depict the rock joint shearing in different length scales. Therefore, this study aims to establish a constitutive relationship for rock joints with considering the scale effect. Based on the assumption of a random statistical distribution of rock material strength and statistical mesoscopic damage theory, damage variables are defined as the ratio of the number of damaged elements to the total number in the shear process. Together with the nonlinear relationship between the microelement failure and the joint scale, an empirical statistical constitutive relationship for joint is established. And then, the determination method of constitutive relationship parameters and the variation laws with the scale are discussed. Results show that the predicted results of the proposed empirical relationship not only agree well with the experimental results but also fully describe nonlinear deformation, pre-peak softening, post-peak softening, residual stage, and other mechanical properties of the shear deformation of joint with different dimensions, thereby demonstrating the rationality of the constitutive relationship. The physical meaning of the constitutive relationship parameters is clear, and the expressions of the constitutive relationship parameters can be deduced from the experimental results. In addition, the influence of scale effect on the shear deformation of rock joints can be quantified using parameters, which help accurately describe the action form of scale effect.     

共面闭合断续节理岩体直剪强度特性研究

介绍了节理面和岩桥各自的抗剪强度机制,引入法向变形协调条件,基于Mohr-Coulomb理论,推导了共面闭合断续节理岩体的直剪强度公式。模型试验发现,剪切破坏面以拉剪复合破坏为主,同时岩块中伴随大量的拉张微裂隙。试样的强度和变形具有明显的阶段性,全应力应变曲线主要经历了线弹性增长、节理面错动、次生裂纹起裂稳态扩展、节理面贯通破坏和残余强度5个阶段。对比发现,理论计算结果与试验值吻合较好。     

Finite Fracture Mechanics model for mixed mode fracture in adhesive joints

Up to now the failure load assessment of bonded joints is still not fully understood. This work provides a new approach for assessing the crack initiation load of bonded joints. A failure model for single lap joints is proposed that is based on Finite Fracture Mechanics. Only two basic fracture parameters are required: the tensile strength and the fracture toughness of the adhesive. A coupled stress and energy criterion proposed in 2002 by Leguillon is used to model crack initiation in the adhesive layer. The theory of this criterion is outlined in detail, its relationship to other failure criteria is discussed and an overview of applications found in literature is given. An enhanced weak interface model that predicts a linear variation of the shear stresses in the adhesive layer is utilized to model the single lap joint. To compare joint designs and to reveal the limitations of the given approach a dimensionless brittleness number for mixed-mode loading is proposed. Along with a detailed discussion of the results for exemplary joint designs a comparison to experimental results from literature is performed. The two necessary fracture parameters are each taken from standard test results published in literature. A good agreement of the failure load predictions with the experimental results is observed. A remarkable outcome is that the presented failure model renders the adhesive thickness effect correctly. The paper concludes with a discussion of the limitations of the approach and the effect of material parameters.     

节理抗剪强度综合评价的试验研究

选取不同吻合度自然节理试样,进行干燥状态和饱和状态的JRC-JCS模型和JRC-JMS模型试验研究。结果表明,在节理粗糙度系数的定向统计测量和尺寸效应分析,以及剪切过程衰减折减的基础上,运用JRC-JCS模型综合评价节理抗剪强度可靠性较好,考虑吻合度系数的JRC-JMC模型比JRC-JCS模型具更好的预测能力。     

Fatigue strength of welded joints based on local, semi-local and nominal approaches

Analysis based on the so-called “local approach” is made to estimate the fatigue strength of welded joints. Numerical analyses or strain gauges are employed for finding the stress and/or strain state in the vicinity of the weld toe. The notch stress intensity factor (NSIF) approach applied to fillet welded joints, as far as the opening angle between the weld and the main plate surface is constant (e.g. 135°, typical for many fillet welds), is able to rationalise the fatigue strength data both for different joint geometries and absolute dimensions. The NSIF approach has been previously developed as an extension of the Linear Elastic Fracture Mechanics (LEFM) to open V-notches and is based on the exponential local stress field around the V-notch tip. Several different “local approaches”, although simpler and more practical than the NSIF, are based on the stress (or strain) values determined beyond the exponential local one. To distinguish such approaches from the NSIF based one, we define the former as semi-local or nominal approaches while the latter is a local approach. The paper underlines that the local approaches, differently from the other ones, are able to unify in a single scatter band the fatigue strength data obtained from welded joints having different geometry and absolute dimensions.     

A study of the strength characteristics of marine sediments utilizing a submersible: A. L. Inderbitzen and F. SimpsonASTM Spec. Techn. Publ. No. STP 501, 204–215 (1972)

One of the tasks of the Lockheed Missiles and Space Company's submersible Deep Quest has been to obtain detailed information on the strength characteristics of the sea floor. Continuing projects, carried out with a corer and a vane shear machine mounted on the submersible, are a comparison of in-place and laboratory vane shear strength values and an investigation of the lateral and vertical variability of in-place shear strength. The area being investigated for these projects is approximately 13 nautical miles southwest of San Diego, Calif., on the floor of the San Diego Trough at a depth of 4050 ft. Because the projects are still incomplete, no definitive conclusions can be made. However, initial results indicate inconsistencies in the difference between in-place and laboratory vane shear strength values. Lateral variability between in-place vane shear strength measurements does not appear to be related to distance test locations. Vertical variability in in-place vane shear strength values appears to decrease with depth into the sediment.     

应用三维有限元法探讨RC梁柱节点的破坏机理

为了探究节点加强后RC梁柱节点的抗剪承载力、延性提高以及节点破坏模式由剪切破坏转变为梁弯曲破坏的实质,本文在RC节点的三维有限元分析的基础上探讨RC梁柱节点加强后的破坏机理。通过详细考察加固前后节点内部不同位置混凝土的应力-应变发展规律,探讨加强前后节点混凝土的宏观损伤发展过程;同时,通过考察核心混凝土的应力-应变关系及发展过程定量探讨加强钢板、梁柱主筋及箍筋对核心混凝土的约束作用。基于上述混凝土损伤过程的宏观分析,可以得出由于梁主筋的粘结加强、加强钢板以及箍筋对混凝土约束作用,使节点核心混凝土的实际强度增大、损伤延迟,RC节点由加强前的节点剪切破坏模式转变成梁端的弯曲破坏模式,从而提高RC梁柱节点的抗剪承载力和延性。     

Design and validation of a new fixture for the shear testing of cellular solids

The design and validation of a new fixture for the shear testing of cellular solids are presented. The fixture is an extended version of a picture-frame shear fixture (EPF) and is suited for comparatively thick rectangular block specimens. The stress state in the specimen is analyzed using a detailed finite element model. The finite element model is based on a 3D CAD model and incorporates friction in the revolute joints. Using specimens with low stiffness, a nearly pure and uniform shear stress state is induced in the specimen. A correction factor for the shear stress is derived which takes into account the friction in the joints and the nonuniformity of the shear stress distribution in the gauge section. The shear response of the polymer foam Rohacell^® 200 WF is determined in order to demonstrate the capabilities of the EPF. The strain state is analyzed by means of digital image correlation and is detected to be very pure and uniform on the specimen’s surface, as predicted by the numerical analysis. The shear modulus obtained with the EPF is in good agreement with the calculated shear modulus derived from tensile tests on the same material. In addition, there is only little scatter of the strength values over the tested specimens which further confirms the accuracy of the new fixture.     

Modification of the fracture criterion for V-shaped notches (plane problem). Relationship between toughness and strength and structural parameters

A fracture criterion of the type of the Neuber-Novozhilov criterion is proposed to describe the fracture in the vicinity of the tip of a V-shaped notch under tensile and shear loading. In the proposed criterion, the limits of averaging of the stresses along the notch axis depend on the presence, location, and size of the initial defects in the material. The crystal lattice parameter of the initial material is chosen for the characteristic linear size. For a V-shaped notch subjected to tension and shear, simple equations are obtained that relate the stress intensity factors for the modified singularity coefficients, the singularity coefficients themselves, and the theoretical tensile and shear strengths of a single crystal of the material taking into account the damage to the material in the vicinity of the notch tip. The equations obtained allow a passage to the limit from a notch to a crack. It is shown that the classical critical stress intensity factor used in the strength analysis of cracked solids is not a material constant.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 1, pp. 106–115, January–February, 2005.