Prediction and Verifcation of Forming Limit Diagrams Based on a Modifed Shear Failure Criterion

The forming limit diagram plays an important role in predicting the forming limit of sheet metals.Previous studies have shown that,the method to construct the forming limit diagram based on instability theory of the original shear failure criterion is efective and simple.The original shear instability criterion can accurately predict the left area of the forming limit diagram but not the right area.In this study,in order to improve the accuracy of the original shear failure criterion,a modifed shear failure criterion was proposed based on in-depth analysis of the original shear failure criterion.The detailed improvement strategies of the shear failure criterion and the complete calculation process are given.Based on the modifed shear failure criterion and diferent constitutive equations,the theoretical forming limit of TRIP780 steel and 5754O aluminum alloy sheet metals are calculated.By comparing the theoretical and experimental results,it is shown that proposed modifed shear failure criterion can predict the right area of forming limit more reasonably than the original shear failure criterion.The efect of the pre-strain and constitutive equation on the forming limits are also analyzed in depth.The modifed shear failure criterion proposed in this study provides an alternative and reliable method to predict forming limit of sheet metals.

Shear Failure Criterion and Constant Volume Ring Shear Testing Method for Clayey Soil

This paper discusses the shortcomings of the traditional Coulomb shear criterion and the direct shear-box testing method used for clayey soil and presents a modified shear criterion that considers the elasto-plastic behavior of cohesive soil. This modified approach involves direct shear testing under constant volume, a method that has been developed by the author. A modified ring shear apparatus and the theory behind the shear criterion and its implication for slope stability analysis are then discussed and the results of investigated tuffitic clayey sediments are presented. The results show that the presented new shear criterion does not consider the cohesion as material constant, but rather it depends on the void ratio. In this case, the stress state and the consolidation status and thus the elasto-plastic behavior of the clayey soil are considered.

Three-Dimensional Analysis of Rolling by Twin Shear Stress Yield Criterion

Using the twin shear stress yield criterion, the surface integral of the co-line vectors, and the integration depending on upper limit, Kobayashi＇s three-dimensional velocity field of rolling was analyzed and an analytical expression of rolling torque and single force was obtained. Through redoing the same experiment of rolling pure lead as Sims, the calculated results by the above expression were compared with those of Kobayashi and Sims formulae. The results show that the twin shear stress yield criterion is available for rolling analysis and the calculated results by the new formula are a little higher than those by Kobayashi and Sims ones if the reduction ratio is less than 30%.

Cracking Patterns of Shear Walls in Reinforced Concrete Structure due to Strong Earthquake Based on Mohr-Coulomb Criterion

A primary goal of seismic design of buildings is to protect people's life safety during strong earthquakes. Fundamentally,to predict the survived space and estimate people escape intervals during structural collapse are very important,which requires to describe the failure process more detailedly not only for structural joints but also for slabs and shear walls. In the present paper,the details of Mohr-Coulomb failure criterion with tension-cutoff together with its expression in failure surface and local coordinate system of reinforced concrete( RC) shear wall are given firstly,and then several typical cracking patterns of RC shear wall,such as tension shear crack and compression shear crack, are analyzed based on Mohr-Coulomb failure criterion with tension-cutoff.

考虑T应力及裂隙参数的岩体压剪断裂准则

针对压剪作用下裂隙面将发生闭合及摩擦滑移的特点,首先基于Muskhelishvili复变函数理论,建立了压剪作用下裂隙岩体的Kolossoff-Muskhelishvilli应力函数,并求得考虑裂隙3类参数(即几何参数、摩擦强度参数和变形参数)的裂隙尖端应力强度因子K和3个T应力分量的计算公式;其次,将其代入经典的最大周向应力准则,得到考虑裂隙尖端T应力及裂隙3类参数的修正最大周向应力准则;同时该准则认为裂隙法向及切向刚度与裂隙面受力特征密切相关,而非定值,并给出了不同裂隙倾角时的裂隙变形参数.最后,基于压剪作用下翼裂纹起裂角试验结果对该准则的合理性进行了初步验证,结果说明考虑裂隙变形参数是有必要的.

Maximum twin shear stress factor criterion for sliding mode fracture initiation

Previous researches on the mixed mode fracture initiation criteria were mostly focused on opening mode fracture. In this study, the authors proposed a new criterion for mixed mode sliding fracture initiation, which is the maximum twin shear stress factor criterion. The authors studied a finite width plate with central slant crack, subject to a far field uniform uniaxial tensile or compressive stress.

非饱和黏性土的广义有效应力三剪弹塑性本构模型

将非饱和土广义有效应力原理与三剪强度准则相结合,提出了非饱和土广义有效应力三剪强度准则。将所提准则作为破坏准则,分别采用等量代换法和坐标平移法推导出新的破坏应力比,并将其与非饱和土修正剑桥模型相结合得到了新的屈服函数。相比于原来修正剑桥模型中的破坏应力比为定值,新的屈服函数可以更好地反应土体全应力状态、中间主应力效应和拉压不等效应。在弹塑性理论的框架下,建立了非饱和土的广义有效应力三剪弹塑性本构模型。以江西正常固结非饱和重塑红黏土作为试验研究对象,进行室内土工试验、土水特征曲线试验、压缩回弹试验、非饱和土常规三轴固结排水试验。将该本构模型计算结果与非饱和土三轴固结排水试验结果进行对比验证。结果表明:数值模拟结果与试验结果吻合较好,验证了该本构模型的正确性。在轴向应变较小时,等量代换法和坐标平移法模拟结果比较接近,随着轴向应变增大直至偏应力达到平稳状态的过程中,等量代换法计算结果要大于坐标平移法计算结果,且更接近于试验值。真三轴计算预测结果表明:在固结排水条件下,初始压实度、净围压、基质吸力相同,中间主应力影响系数越大,则剪应力和体应变越大。b值相同的情况下,轴向应变较小时,等量代换法计算结果和坐标平移法计算结果比较接近,随着轴向应变的增大,二者之间的差值也越来越大。

四川盆地涪陵南地区奥陶系五峰组—志留系龙马溪组页岩古构造应力场及裂缝特征

通过岩石力学实验、声发射实验和地震资料综合解释,利用有限元数值模拟方法,对涪陵南地区奥陶系五峰组—志留系龙马溪组海相页岩古构造应力场进行了数值模拟,并结合岩心实测结果,预测了构造裂缝的发育特征。研究结果表明:①涪陵南地区裂缝主要形成期(燕山晚期)构造应力和裂缝的分布受断层、岩石力学性质和构造应力的影响,断层广泛发育的区域容易出现应力集中,并引起较大的应力梯度。②利用库伦-莫尔破裂准则预测了研究区构造裂缝的发育,同时引入剪切破裂指数R定量表征裂缝发育的强度,其值越大反映裂缝发育程度越高。窄陡断背斜和断层附近裂缝发育,以高角度剪切裂缝为主,而在宽缓向斜部位裂缝发育程度最弱,研究区五峰组—龙马溪组底部硅质页岩应力集中,裂缝最发育。③涪陵南地区海相页岩气保存有利区主要为3个区带:远离大断层的凤来向斜内部,主要构造变形期未遭受大的破坏作用,其位于应力低值区,具有良好的保存条件,为Ⅰ类有利区;白马向斜内部小断层发育,应力值位于中等水平,保存条件中等,为Ⅱ类较有利区;石门—金坪断背斜遭受到强烈改造作用,容易产生大规模剪切裂缝,破坏了保存条件,为Ⅲ类不利区。

重塑黄土直剪试验误差分析及对边坡可靠性影响评价

为通过室内快剪试验误差来源分析强度参数的随机特性,比较了击实法和压样法对抗剪强度离散性的影响,并在两种制样方式的基础上,进行再现性试验,通过对抗剪强度及正应力修正,采用Grubbs准则检验可疑值,求得了能反映强度参数随机特性的概率分布,并使用K-L级数展开法离散强度参数正态随机场,分析了两种制样方式对边坡可靠性的影响.研究表明:压样法制样比击实法获得数据离散性更小,使用再现性法能够体现强度参数的随机特性;两种制样方法在边坡稳定性分析时安全系数接近,由于击实法统计数据的离散性更大,可靠性分析时比压样法产生更大的失效概率.

直接剪切下页岩的各向异性破坏特征和强度预测模型

了解页岩剪切破坏特性对页岩气储层改造和井壁稳定性控制具有重要意义。然而,由于页岩本身的各向异性属性,页岩的剪切破坏行为复杂。本文对6种不同层理倾角(0°、30°、60°、90°、120°和150°)的立方体页岩进行了系统的直接剪切破坏测试,详细分析了在层理弱面影响下页岩的剪切应力–剪切位移、抗剪强度、剪切模量和破坏模式的各向异性特征。结果表明:页岩的剪切破坏表现为典型的非线性渐进破坏特征;页岩平均抗剪强度和剪切模量随层理倾角的增加均呈现“M”型变化趋势;在90°~180°的层理倾角区间,平均抗剪强度的极值差明显大于0°~90°区间,而剪切模量近似关于90°呈对称变化;当层理倾角从0°变化到180°时,页岩剪切各向异性行为呈现非对称演化规律。在层理倾角和直接剪切荷载作用下,页岩的破坏模式有3类:层理倾角为0°时,沿层理面剪切滑移破坏;层理倾角为30°、60°和90°时,表现为穿透层理和基质的剪切滑移破坏;其他倾角下呈现穿透层理和基质的剪切滑移与沿层理的拉伸劈裂相结合的复合破坏。基于试验结果和组构张量,构建了一个可考虑页岩本征各向异性和剪应力诱导各向异性影响的直接剪切破坏准则,其理论预测值与试验结果的平均偏差率低于3%,能够定量表征黏聚力和摩擦系数的各向异性程度,合理评估页岩直接剪切强度对外加法向应力的敏感性,可推广应用于理论表征所有层状岩土材料的直接剪切强度。

基于三剪能量屈服准则的岩石弹塑性耦合模型

为建立能够准确描述岩石变形过程中能量演化规律的力学模型,提出利用三剪能量屈服准则和弹性剪应变能获取岩石黏聚力与内摩擦角,以及基于三剪能量塑性势函数获取剪胀角的方法,依据所提方法和岩石循环加卸载试验数据,得到了各级围压下不同塑性累积阶段岩石的弹性模量、黏聚力、内摩擦角及剪胀角等参数,发现随着塑性变形的增大,弹性模量呈负指数关系减小,黏聚力峰前线性增大而峰后呈负指数减小,内摩擦角满足比例参数为1、形状参数为1.5的Weibull函数,剪胀角线性减小;随着围压的增大,弹性模量和黏聚力均呈线性关系增大而剪胀角呈线性减小。建立岩石三剪能量弹塑性耦合力学模型,实现了模型在有限差分软件中的二次开发并编写了能量演化监测程序。模拟岩石室内试验,结果表明所建模型能较准确地描述岩石后继屈服过程中的硬化软化、剪胀、围压效应以及能量演化等力学行为。研究成果可为从能量角度研究岩体失稳提供理论支撑和现实手段。

Theoretical and experimental study on multiscale coupled Mohr-Coulomb shear strength criterion of fibre-reinforced sand

Fibre-reinforced sand(FRS)is a multiphase and multiscale geo-material,which is widely used in geotechnical engineering as supporting structure of excavation of underground space and reinforcement of foundation of underground structures,and its strength is determined by the properties of the heterogeneous substances of the FRS and their coupling mechanical responses.In order to investigate the influence of fibre characteristics and mechanical properties on the shear strength of the FRS,according to the microscopic interface slip effect generated by the interaction between sand particles and the interaction between these particles and fibre,the material phase of the FRS is divided to conceptualize a micro cell element of the FRS that is capable of reflecting the internal material characteristic information of the FRS.Moreover,based on the coordinated deformation condition between fibres and sand particles at the microscale and the couple stress theory that is capable of effectively describing the discontinuous mechanical responses at the sand-fibre interface,a mesomechanism-based multiscale Mohr–Coulomb shear strength criterion of the FRS is derived,and the yield locus of the FRS is also drawn on the p plane.Furthermore,a series of FRS samples with different fibre content and fibre length were prepared by adopting the freezing method,and consolidated and drained triaxial compression tests were conducted on these samples to validate the proposed multiscale coupled Mohr–Coulomb shear strength criterion.Results show that the multiscale coupled Mohr–Coulomb shear strength criterion is capable of effectively reproducing and predicting the yield strength of the FRS.The yield locus of the FRS extends outwards as fibre content and fibre length increase.The yield stress of the FRS predicted by the proposed multiscale coupled Mohr–Coulomb shear strength criterion is in good agreement with that of the test result.

岩石卸荷的Mogi-Coulomb强度准则适用性研究

大量工程实践表明:岩石在卸荷条件下的强度特性与加载条件下相比,存在本质上的不同。结合岩石卸荷的破坏特征和强度特性,建立了岩桥贯通力计算模型,并基于应力强度因子叠加减原理,推导了岩石卸荷条件下的岩桥贯通力计算公式,从而探究Mogi-Coulomb强度准则对于岩石卸荷强度的适用性。将岩桥贯通力作为表征岩石卸荷破坏的强度参数,并与Mogi-Coulomb强度准则的核心参数——八面体剪应力进行对比,发现二者的量值具有极高相似性,这一发现可以间接证明Mogi-Coulomb强度准则适用于岩石卸荷强度方面的相关研究。本文揭示了岩石卸荷破坏时其岩桥贯通与八面体剪应力之间存在的紧密联系,可为岩石卸荷破坏的研究提供借鉴与参考。

南昌地铁含泥饱和砂土的三剪次加载面模型

以三剪强度准则作为破坏准则,推导出饱和土的三剪破坏应力比。考虑到砂土的剪胀特性,引入剪胀状态参量对三剪破坏应力比进行修正得到相变应力比。用相变应力比对修正剑桥模型中为定值的破坏应力比进行替换,得到新的屈服函数。将其与次加载面理论相结合,提出含泥饱和砂土三剪次加载面模型。取用南昌地铁某路线路段地下砂土和黏土作为试验土样,砂土中掺入粒径小于0.075 mm的黏土作为含泥砂土,并设定密实度为70%的试样含泥量为0、5%和10%,通过相关土工试验确定模型参数。将本构模型计算结果与常规静三轴试验结果和循环常规动三轴试验结果进行对比验证。静三轴试验验证结果表明,本构模型计算结果与试验结果变化规律基本一致,验证了该本构模型的正确性。其他条件相同情况下,随着含泥量增大,土体抗剪强度增大,体积剪缩阶段变长,剪胀现象越不明显。动三轴试验验证结果表明,本构模型数值计算曲线与试验结果吻合较好,在加载初期土体塑性应变发展较快,随着加载和卸载的不断交替以及循环次数的不断增加,滞洄圈变得越来越密集。

水压作用下岩体裂隙压剪起裂准则

为深入研究裂隙闭合与非闭合2种情况下裂隙水导致岩体压剪断裂机理,建立相应的压剪起裂准则。首先,研究初始地应力及裂隙水压作用下的非闭合裂隙尖端应力强度因子及起裂准则,并讨论压剪系数和水压对裂隙压剪起裂应力的影响;其次,研究闭合裂隙压剪破坏机理,并讨论裂隙尖端相对临界尺寸和裂隙面摩擦因数对临界水压(裂隙起裂时的水压)的影响;最后,采用室内试验及现场测试结果对上述两类准则的合理性进行验证。研究结果表明:非闭合裂隙尖端应力强度因子KⅠ应为裂隙面上法向压应力引起的KⅠ(N)及平行于裂隙面的横向压应力引起的KⅠ(T)之和,且其起裂模式多为压剪起裂;基于周群力等提出的经验压剪断裂准则,提出相应的非闭合裂隙压剪起裂准则;随着压剪系数增加,起裂应力分别呈非线性增加;随着水压增加,起裂应力呈非线性减小。在水压作用下,闭合裂隙压剪起裂模式往往为拉伸起裂,且裂隙尖端的KⅠ≡0,由此提出了考虑裂隙尖端T应力的修正最大周向应力准则;随着裂隙尖端相对临界尺寸增加,临界水压呈线性减小;随着裂隙面摩擦因数增加,临界水压呈非线性增加。

A Linearized and Unified Yield Criterion of Metals and Its Application

In this paper a linearized and unified yield crierion of metals is presented, which is in a form of a set of linear functions with two pararneters. The parameters are ex- pressed in terms of tension yield stress and so-called “shear-stretch ratio” and can bereadily determined from experimental data. It is shown that in stress space the set of yield functions is a set of polygons with twelve edges located between the Tresca’s hexagon and twin-shear-stress hexagon￣[1]. In this paper the present yield function isused to analyse the prestressiap loose running fit cylinders.

波浪与新型双排开孔圆筒防波堤相互作用三维数值模拟

双排开孔圆筒防波堤是基于圆筒、板式结构的一种复合式新型结构型式;基于不可压缩两相流模型建立三维数值波浪水槽,通过RNG k-ε湍流模型进行湍流封闭,并采用TruVOF方法捕捉自由液面,开展波浪与双排开孔圆筒防波堤相互作用数值模拟,探究相对排间距、开孔率对新型双排开孔圆筒防波堤消浪性能的影响,分析了后排开孔圆筒防波堤附近的复杂水动力现象和流动特性.结果表明,在本文研究工况范围内,沿程平均波高随相对排间距的增大先增大后减小,随开孔率的增大而增大,周期对沿程平均波高的影响没有明显规律;当B/D=9,e=23.11%时,新型双排开孔圆筒防波堤消浪效果最优,反射系数在0.4~0.46之间,透射系数在0.3~0.35之间,耗散系数在0.8~0.85之间;自由液面破碎、水气掺混、环状涡运动演化是新型双排开孔圆筒防波堤紊动耗能消波的主要原因;相对排间距会引起后排防波堤附近涡量分布以及剪切层形态的变化,从而导致不同的紊动特性,影响双排开孔圆筒防波堤消浪特性.研究结果可以为新型双排开孔圆筒防波堤工程设计与消浪机理研究提供理论支撑.

The effect of two-dimensional shear flow on the stability of a crystal interface in a supercooled melt

A model is developed based on the time-related thermal diffusion equations to investigate the effects of twodimensional shear flow on the stability of a crystal interface in the supercooled melt of a pure substance. Similar to the three-dimensional shear flow as described in our previous paper, the two-dimensional shear flow can also be found to reduce the growth rate of perturbation amplitude. However, compared with the case of the Laplace equation for a steady-state thermal diffusion field, due to the existence of time partial derivatives of the temperature fields in the diffusion equation the absolute value of the gradients of the temperature fields increases, therefore destabilizing the interface. The circular interface is more unstable than in the case of Laplace equation without time partial derivatives. The critical stability radius of the crystal interface increases with shearing rate increasing. The stability effect of shear flow decreases remarkably with the increase of melt undercooling.

Nonlinear earthquake response analysis and energy calculation for seismic slit shear wall structures

Based on the concept of structural passive control,a new type of slit shear wall,with improved seismic performance when compared to an ordinary solid shear wall,was proposed by the authors in 1996.The idea has been verified by a series of pseudo-static and dynamic tests.In this paper a macro numerical model is developed for the wall element and the energy dissipation device.Then,nonlinear time history analysis is carried out for a 10-story slit shear wall model tested on a shaking table.Furthermore,the seismic input energy and the individual energy dissipated by the components are calculated by a method based on Newmark-β assumptions for this shear wall model,and the advantages of this shear wall are further demonstrated by the calculation results from the viewpoint of energy.Finally,according to the seismic damage criterion on the basis of plastic accumulative energy and maximum response,the optimal analysis is carried out to select design parameters for the energy dissipation device.

Formulation of cross-anisotropic failure criterion for soils

Inherently anisotropic soil fabric has a considerable influence on soil strength. To model this kind of inherent anisotropy, a three-dimensional anisotropic failure criterion was proposed, employing a scalar-valued anisotropic variable and a modified general three- dimensional isotropic failure criterion. The scalar-valued anisotropic variable in all sectors of the deviatoric plane was defined by correlating a normalized stress tensor with a normalized fabric tensor. Detailed comparison between the available experimental data and the corresponding model predictions in the deviatoric plane was conducted. The proposed failure criterion was shown to well predict the failure behavior in all sectors, especially in sector II with the Lode angle ranging between 60° and 120°, where the prediction was almost in accordance with test data. However, it was also observed that the proposed criterion overestimated the strength of dense Santa Monica Beach sand in sector III where the intermediate principal stress ratio b varied from approximately 0.2 to 0.8, and slightly underestimated the strength when b was between approximately 0.8 and 1. The difference between the model predictions and experimental data was due to the occurrence of shear bending, which might reduce the measured strength. Therefore, the proposed anisotropic failure criterion has a strong ability to characterize the failure behavior of various soils and potentially allows a better description of the influence of the loading direction with respect to the soil fabric.