拉压强度不等材料的厚壁圆筒的统一极限解

采用俞茂鋐统一强度理论分析了厚壁圆筒的极限荷载,得出统一解形式,它既可以适用于拉压强度相等的材料,也可以适用于拉压强度不相等的材料．     

一个弹-粘塑性问题的统一解析解

采用统一强度理论对平面应变轴对称问题在弹－粘塑性状态下的解析解进行了分析,由此得到的统一解可以蜕化成一系列从Ｍｏｈｒ－Ｃｏｕｌｏｍｂ单剪强度理论到双剪强度理论的平面应变轴对称问题解析式。献中已有的关于弹－粘塑性问题的单剪解为本的特例,统一强度理论可以给出更符合各种不同材料特性的合理解。     

强度理论百年总结

自从1900年著名的Mohr-Coulomb强度理论建立以来,已有100年的历史.在20世纪,关于材料在复杂应力状态下的强度理论进行了大量的理论研究和实验研究工作.本文对材料(包括金属材料、岩石、土、混凝土、冰、铁、聚合物、含能材料等)在复杂应力状态下强度理论(屈服准则、破坏准则等)的百年发展进行了总结,讨论了各种准则之间的关系,为研究和工程应用中的合理选择破坏准则提供了一种方法.文中还总结了三大系列强度理论、统一屈服准则、统一强度理论和其他各种强度理论,并简述了强度理论的计算机实施,以及多轴疲劳等问题.     

弹塑性材料的平面应力非连续分岔

基于平面应力非连续分岔特性的一般描述,运用统一强度理论,得出了非相关流动情形的弹塑性材料平面应力非连续分岔的起始方位角以及相应的最大硬化模量的统一解析解,并且分析了材料拉压异性以及不同程度的中间应力对结果的影响,进而发现所得的结果一强度准则的选取有关,揭示了在分岔研究中正确选取符合材料特性的强度准则的重要性。最后,同特线理论比较发现平面应力剪切带型非连续分岔同平面应力特征线重合。     

Effect of intermediate principal stress on flat-ended punch problems

The intermediate principal stress has certain effects on the yield strength of metallic materials under complex stress states. The flat-ended punch problem is a classical and fundamental problem in plasticity theory and mechanical engineering in which the metal beneath a flat-ended punch is under complex stress states. Using the finite difference codes, fast Lagrangian analysis of continua and Unified Strength Theory, the effect of the intermediate principal stress on the flat-ended punch problem is analyzed in this paper. First, the limit pressures of strip and circular punches pressed into an elastoplastic and homogeneous metallic medium are calculated by the two-dimensional finite difference method. The problems of square and rectangular punches are analyzed by the three-dimensional finite difference method. Finally, the effect of the intermediate principal stress on flat-ended punch problems with different punch geometries is analyzed.     

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.     

基于统一强度理论的钢管混凝土柱承载力计算

从Von Mises屈服准则和双剪统一强度理论出发,对钢管和核心混凝土的受力性能进行分析．从核心区混凝土所受侧向压应力的角度出发,基于大量实验数据,得到核心区混凝土约束系数计算公式．从而完善了钢管混凝土柱的轴心受压承载力计算公式,使公式的精确性和适用性有所提高．所得计算结果与试验结果吻合良好,并与目前公式的计算结果进行对比,说明所提出公式的合理性．从尺寸大小和材料强度两个方面,对钢管混凝土柱承载力的影响因素进行探讨．     

STUDY OF THREE-SHEAR STRESS UNIFIED STRENGTH THEORY

材料强度理论研究是高等材料力学的一个重要研究领域,200多年来,各国学者提出了许多强度理论及试验研究结果.这些理论都是从不同的假设和力学模型出发,推导出不同的数学表达式,但一般只适用于某一类特定的材料.各种强度理论之间是否有联系?是否可能建立一个广泛适用的统一强度理论?自19世纪末以来,世界各国学者都在努力寻求建立统一强度理论,但一直没有成功.本文应用理论研究和试验验证相结合的方法,提出并验证了三剪应力统一强度理论。认为当作用于菱形十二面单元体上的三个主剪应力及其作用面上的三个正应力的函数达到某一极限值时,材料发生破坏.三剪应力统一强度理论是全应力理论,它用一个统一的线性表达式包含或逼近了现有的和其他新的各种单一和统一、线性和非线性、外凸和非凸的强度理论,形成了以单剪强度理论为下限、而以三剪应力强度理论为上限的一系列强度理论的新体系,实现了外凸强度理论和非凸强度理论的高度统一,使强度理论从适用于某一类材料、某种应力状态的单一强度理论发展为可以适用于各种材料及不同应力状态的统一强度理论,并能更大程度地发挥材料的强度潜力.通过与大量试验结果的对比分析表明：三剪应力统一强度理论可以广泛适用于各种材料及其不同的应力状态.     

一种碳纤维织物增强复合材料应变率相关的各向异性强度准则

为了获得一种碳纤维二维正交平纹机织布增强树脂基复合材料在一维应变状态下的强度准则,在已完成的准静态和动态压缩实验的基础上,拟合出了单轴压缩下三个主方向上的计及应变率的应力-应变关系式,进而得到初始屈服应力和压缩破坏强度与应变率相关性表达式。依据该表达式,得到了该复合材料在一维应变下考虑应变率效应的Tsai-Hill屈服强度和破坏强度准则方程。通过计算,考察了Tsai-Hill屈服强度和破坏强度准则随应变率的变化规律。结果表明,本文中研究的复合材料的强度性能,不但存在应变率效应,而且这种效应是各向异性的。     

确定复合材料宏观屈服准则的细观力学方法

运用细观力学中的均匀化方法，分析了含周期性微结构复合材料的宏观屈服准则，并对Hill-Tsai准则进行了修正。从基于复合材料细观结构的代表性胞元入手，运用塑性极限理论中的机动分析以及有限元方法，计算了细观结构的极限载荷域。通过宏细观尺度对应关系，得到复合材料的宏观屈服准则。     

Investigation on critical triaxiality along unified yield loci at crack tip under mixed mode (I + II) fracture

Metallic components used in industries and day to day appliances often contain micro-cracks. In general, cracks occur in various orientations to the loading axis. The present paper discusses the criticality of stress triaxiality, a well-known ductile fracture parameter, on the yield loci at the crack tip. In the process, an old model of stress triaxiality has been generalized using unified strength theory to incorporate various convex and nonconvex failure criteria, including single shear, twin shear, etc. The new triaxiality model also reveals about the effect of intermediate principal stress at the crack tip for materials with and without strength difference. The crack initiation angles at the crack tip, obtained through the proposed model have been found to be in unison with those obtained through other fracture criteria.     

基于新弹塑性模型全程模拟金属疲劳失效

金属材料疲劳失效问题是工程中一类主要问题,选择合理的材料本构关系对于准确确定疲劳失效强度至关重要．本文提出一个简单形式的自由光滑新弹塑性模型,该模型在不涉及通常的屈服条件以及加卸载条件的意义上完全自由,避免了模量间断问题,且比经典模型更简单、更符合实际．结果表明,该模型可直接模拟金属材料在循环加载下直至疲劳破坏的全过程,不涉及任何损伤变量以及人为假设的失效判据,特别地,可直接模拟金属材料的高周、低周疲劳直至最终失效破坏行为．应用P92钢的相关实验数据,给出了循环加载下的数值模拟结果,结果表明,在各种加载-卸载循环情形下,随着应力幅值的增大,疲劳失效循环数减少,这与实际材料行为相一致．     

冲击荷载作用下简支圆板的塑性动力响应统一解

采用统一强度理论求解了简支圆板在中等脉冲荷载作用下的动力响应问题,得出了统一的动力塑性极限荷载、内力场和速度场,并给出了上限解和下限解。讨论了静力许可条件和运动许可条件。利用本文的解还得出了简支圆板在静力荷载作用下的极限荷载、内力场和速度场。根据选择不同的拉压比参数,本文所给出的解可以适用于各种拉压异性和拉压同性材料。Tresca解、Mohr Coulomb解和双剪统一屈服准则解是本文的特例,Mises解是本文当=1和b=0.5时的线性逼近。研究结果表明,拉压比和强度理论参数b对动力解的影响要大于对静力解的影响,所以,根据材料的不同选择合适的强度理论,对于更好的发挥材料的强度潜力,减轻结构的重量具有重要的意义。     

基于指数准则在莫尔空间对岩石剪切强度的研究

岩石是多种矿物颗粒构成的天然材料,内部存在不同尺度的孔隙、裂隙等损伤;岩体工程设计及灾害防治所使用的强度准则仍在研究之中.材料的黏结和摩擦在局部不能同时存在,线性的Coulomb准则仅在小范围内近似描述圆柱试样的常规三轴强度,众多非线性强度准则只是经验公式而缺乏物理背景. 作者提出的指数准则可描述岩石剪切破坏时强度与围压的关系;基于对11组试验数据的拟合结果在莫尔应力空间分析黏结力和摩擦力的变化特征:岩石承载的剪切力存在上限即材料的真实黏结力c₀;在试验范围内莫尔概念的内摩擦力达到约为0.38 c₀的峰值,且黏结力在其附近相交. 材料真实黏结力与正应力无关,因而名义黏结力表征了完好材料剪切破裂的面积;基于裂隙面积计算的等效摩擦因子随正应力降低,意味着裂隙滑移的爬坡角减小,而后者取决于正应力与真实黏结力的比值. 等效摩擦因子与指数准则的材料参数具有确定关系,体现了岩石在压应力作用下剪切破裂的物理背景.      

现代土力学的基本问题

现代土力学可望在今后３０年内建成基本框架，其主要内容将包括新一代的本构模型及一个变形理论和两个破坏理论．本文介绍了作者对这些问题的今后研究重点及发展方向的一些看法．     

托马斯-杨之力学贡献

托马斯--杨是一位多才多艺的学者, 在光学、声学、流体动力学、医学、材料力学、 考古学、语言学、保险学等众多领域做出了突出贡献, 但由于种种原因使他在力学方面的贡 献未曾得到学术界的足够重视. 杨在力学方面的研究涉及到材料力学、血液流动力学、能量、 冲击动力学、表面浸润力学、工程结构分析等方面. 他是一位纯粹的自然哲学家, 同时他能 够将理论与实验和工程实际相结合, 实现了后辈力学家所提倡的``技术科学'的理念.     

Effects of high order deformations on the strength of planar lattice materials

Lattice materials have been attractive over the last decade for use as load-carrying structures, energy absorbing elements and heat exchanging structures because of their excellent mechanical properties and multifunctional characters. However, the quantitative analysis accounting for high order deformations upon the collapse of lattice materials, which is important for their applications, has not been reported. An analytical investigation of yield surfaces with respect to the high order deformations was carried out for two typical planar lattice materials： triangular and Kagome lattices separately. The analytical results were validated by the finite element method （FEM） simulations. It was found that the effect of high order deformation on the yield strength increases with the relative density. The bending effect of the Kagome lattice is more obvious than that of the triangular one with the same relative density and stress state. The yield strength of the Kagome lattice calculated by neglecting the bending effect overestimates the result by more than 10% when the relative density is higher than about 11.1%, which may not be ignored in engineering applications. The yielding surfaces of the two lattice materials demonstrated in the paper also confirm the analytical results.     

Multi-mechanism anisotropic model for granular materials

By representing the assembly by a simplified column model, a constitutive theory, referred to as sliding–rolling theory, was recently developed for a two-dimensional assembly of rods subjected to biaxial loading, and then extended to a three-dimensional assembly of spheres subjected to triaxial (equibiaxial) loading. The sliding–rolling theory provides a framework for developing a phenomenological constitutive law for granular materials, which is the objective of the present work. The sliding–rolling theory provides information concerning yield and flow directions during radial and non-radial loading. In addition, the theory provides information on the role of fabric anisotropy on the stress–strain behavior and critical state shear strength. In the present paper, a multi-axial phenomenological model is developed within the sliding–rolling framework by utilizing the concepts of critical state, classical elasto-plasticity and bounding surface. The resulting theory involves two yield surfaces and falls within the definition of the multi-mechanism models. Computational issues concerning the solution uniqueness for stress states at the corner of yield surfaces are addressed. The effect of initial and induced fabric anisotropy on the constitutive behavior is incorporated. It is shown that the model is capable of simulating the effect of anisotropy, and the behavior of loose and dense sands under drained and undrained loading.     

Unified nano-mechanics based probabilistic theory of quasibrittle and brittle structures: I. Strength, static crack growth, lifetime and scaling

Engineering structures must be designed for an extremely low failure probability such as 10⁻⁶, which is beyond the means of direct verification by histogram testing. This is not a problem for brittle or ductile materials because the type of probability distribution of structural strength is fixed and known, making it possible to predict the tail probabilities from the mean and variance. It is a problem, though, for quasibrittle materials for which the type of strength distribution transitions from Gaussian to Weibullian as the structure size increases. These are heterogeneous materials with brittle constituents, characterized by material inhomogeneities that are not negligible compared to the structure size. Examples include concrete, fiber composites, coarse-grained or toughened ceramics, rocks, sea ice, rigid foams and bone, as well as many materials used in nano- and microscale devices.This study presents a unified theory of strength and lifetime for such materials, based on activation energy controlled random jumps of the nano-crack front, and on the nano-macro multiscale transition of tail probabilities. Part I of this study deals with the case of monotonic and sustained (or creep) loading, and Part II with fatigue (or cyclic) loading. On the scale of the representative volume element of material, the probability distribution of strength has a Gaussian core onto which a remote Weibull tail is grafted at failure probability of the order of 10⁻³. With increasing structure size, the Weibull tail penetrates into the Gaussian core. The probability distribution of static (creep) lifetime is related to the strength distribution by the power law for the static crack growth rate, for which a physical justification is given. The present theory yields a simple relation between the exponent of this law and the Weibull moduli for strength and lifetime. The benefit is that the lifetime distribution can be predicted from short-time tests of the mean size effect on strength and tests of the power law for the crack growth rate. The theory is shown to match closely numerous test data on strength and static lifetime of ceramics and concrete, and explains why their histograms deviate systematically from the straight line in Weibull scale.Although the present unified theory is built on several previous advances, new contributions are here made to address: (i) a crack in a disordered nano-structure (such as that of hydrated Portland cement), (ii) tail probability of a fiber bundle (or parallel coupling) model with softening elements, (iii) convergence of this model to the Gaussian distribution, (iv) the stress-life curve under constant load, and (v) a detailed random walk analysis of crack front jumps in an atomic lattice. The nonlocal behavior is captured in the present theory through the finiteness of the number of links in the weakest-link model, which explains why the mean size effect coincides with that of the previously formulated nonlocal Weibull theory. Brittle structures correspond to the large-size limit of the present theory. An important practical conclusion is that the safety factors for strength and tolerable minimum lifetime for large quasibrittle structures (e.g., concrete structures and composite airframes or ship hulls, as well as various micro-devices) should be calculated as a function of structure size and geometry.