考虑应变梯度效应的三点弯梁模型解析研究--第一部分:局部化带的传播

为分析应变软化和由此带来的应变局部化问题,将梯度塑性理论引入裂纹带模型。以拉应变局部化区域代替裂纹带,在三点弯梁裂纹带(具有一定尺寸的带宽由特征长度确定)内部存在着不均匀分布的拉应变,这与实验结果相符。对拉应变进行积分,得到了拉应变局部化区域的张拉位移的理论表达式,结果表明:该位移与拉应力成线性规律,拉应变局部化区域的宽度越大,弹性模量越小或降模量越小,则该位移越大。此外,采用应力平衡条件、应变软化的本构关系及平截面假定,还得到了拉应变局部化区域的扩展规律,结果表明:下降模量越大、三点弯梁高度越小及弹性模量越小,则在相同的拉应力的情况下,拉应变局部化区扩展的长度越小;抗拉强度对拉应变局部化区扩展长度的最大值没有影响。此外,还研究了梁中部横截面内中性轴到具有最大承载能力的点的距离的变化规律。     

考虑应变梯度及刚度劣化的剪切带局部变形分析

基于梯度塑性理论,研究了应变软化阶段的刚度劣化对剪切带内部的局部应变及相对剪切位移的影响。剪切带被看作一维剪切问题,本构关系为线弹性及线性应变软化。考虑刚度劣化后,剪切带的弹性应变由弹性剪切模量、损伤变量及残余剪切模量确定。剪切带的非局部总应变由双线性的本构关系确定。将非局部总应变减去弹性应变,可得剪切带的非局部塑性应变。剪切带非局部塑性应变与流动应力及损伤变量等参数有关,此关系即为在经典弹塑性理论框架之内的考虑刚度劣化的屈服函数。将二阶应变梯度项引入该函数,可得剪切带内部的局部塑性剪切应变及局部总剪切应变的分布规律。对局部塑性剪切应变积分,得到了局部塑性剪切位移。结果表明:考虑了刚度劣化后,剪切带内部的弹性剪切应变及位移增加,而局部塑性剪切应变及位移降低。若不考虑刚度劣化,理论结果可蜕化为以前的结果。理论结果与岩石局部变形的观测结果在定性是一致的。     

岩样单轴压缩峰后泊松比理论研究

研究了单轴压缩岩样应变软化阶段侧向应变与轴向应变的比值(峰后泊松比)的变化规律。岩样的塑性变形假设根源于塑性应变局部化。岩样的轴向及侧向变形被分别分为两部分:弹性变形(由虎克定律描述)及由局部化引起的塑性变形(由梯度塑性理论及几何关系确定)。应变软化阶段的轴向应变-侧向应变曲线、轴向应力-轴向应变曲线及轴向应力-侧向应变曲线都得到了实验验证。在峰值强度时,峰后泊松比等于峰前泊松比。当压缩应力降至零时,峰后泊松比达到临界值。该临界值可能比峰前泊松比大,也可能比它小。峰后泊松比还和试件尺寸有关,这与峰前泊松不同。峰后泊松比与轴向压应力之间的关系可能是一条直线,也可能是上凸的,或上凹的。这取决于岩石的本构参数(弹性模量、剪切及软化模量、剪切带宽度及峰前泊松比)、试件的结构尺寸(试件宽度及高度)及剪切带倾角之间的关系。     

考虑材料的拉压模量不同及应变软化特性的柱形孔扩张问题

建立了拉压模量不同及应变软化特性材料的柱形孔扩张理论。对于岩土类材料,提出用a及b分别作为拉压模量不同和软化特征的控制参数,运用不同模量弹性理论及应力跌落软化模型推导了Tresca和Mohr-Coulomb材料柱形圆孔扩张问题的应力及位移解。分析了不同模量及软化特性材料对柱形孔扩张的影响,结果表明:圆孔极限扩张压力,塑性区的发展规律,应力场,位移场等均随着模量参数a和软化系数b的变化而变化,因此若采用经典的弹性理论及传统的不考虑应变软化来对岩土类的工程材料进行设计计算,必会带来较大的误差。     

剪切带内部应变(率)分析及基于能量准则的失稳判据

应用应变梯度塑性理论对局部化剪切带内部(塑性)剪应变(率)规律进行了理论分析。研究了剪切降模量及岩石材料内部长度等参数对剪切带内部应变(率)的影响。推导了剪应力(率)与剪切带相对错距(速度)的本构关系。研究了剪切降模量和岩石材料内部长度对剪切带稳定性的影响。将岩石试件直剪试验试验机简化为钢块,采用能量准则对岩石试件(剪切带)及钢块系统的稳定性进行了理论研究,提出了系统失稳判据。研究表明:岩石材料的剪切降模量越大,岩石材料的内部长度越小,试验机的剪切刚度越小及试验机的等效高度越大剪切带--钢块系统越容易失稳。     

一种计算功能梯度材料杆与轴弹性模量的方法

介绍一种功能梯度材料杆和轴的弹性模量E和剪切模量G的测定方法,考虑弹性模量E和剪切模量G为杆和轴长度方向的函数,将杆和轴离散化。在保证离散化后的单元满足平衡方程的条件下,分别建立单元节点处的弹性摸量E和位移、剪切模量G和转角的关系。此关系表明,当单元节点处的位移和转角被分别测定后,可得到离散分布的弹性摸量E和剪切模量G。数字仿真时假设弹性模量E和剪切模量G为沿长度方向的指数函数,用有限元软件计算了单元节点处的位移和转角。用这些位移和转角反过来计算得出的离散弹性摸量和剪切模量和假设的指数函数值的误差是可以控制在一定范围的。     

基于能量原理的岩样单轴压缩剪切破坏失稳判据

利用能量原理对倾斜的剪切带-带外弹性岩石构成的系统的稳定性进行了研究。单轴压缩岩样沿轴向的变形被分解为两部分,带外弹性岩石压缩引起的变形和剪切带错动引起的变形。后者与剪切带的相对剪切变形具有简单的几何关系。系统的总势能由剪切带的弹性及耗散势能和带外弹性岩石对剪切带所作的外力功构成。剪切带的弹性及耗散势能与剪切带的体积有关系。剪切带的尺寸由梯度塑性理论确定。将系统的总势能对相对剪切变形求一阶导数(等于零),得到了弹性岩石的平衡条件。将总势能对相对剪切变形求二阶导数(小于零),得到了系统的失稳判据。它综合反映了岩石材料弹性及应变软化阶段本构参数(弹性模量及软化模量)、剪切带之外弹性岩石的尺寸、剪切带的尺寸及系统的结构形式(剪切带倾角)对系统稳定性的影响。失稳判据比以往所得到的失稳判据更严格,更精确,更具有广泛意义。     

悬臂弯曲加载表面裂纹长度与施力点位移的相关性研究

在悬臂弯曲加载方式下,采用五件带缺口光滑板状试样,通过循环载荷控制模式,研究了表面裂纹长度2c与试样施力点位移的相关性,结果表明:表面裂纹长度与施力点位移的谷值无相关性,但与施力点位移的峰值DP具有明显的相关性,即在表面裂纹扩展初期,DP几乎不发生变化,但随着表面裂纹的进一步扩展,DP开始增加,在表面裂纹扩展的后期,DP显著增加;在表面裂纹扩展的中后期,2c与DP满足递增多项式关系。根据2c与DP的函数关系,可为实现复杂环境条件下表面裂纹长度的自动化测量提供依据。     

冲击载荷下不同尺寸煤岩动力学分析及损伤特性研究

为探究冲击载荷作用下不同尺寸煤岩的动态力学及损伤特性，利用分离式霍普金森压杆系统对直径50 mm长度分别为15 mm, 20 mm, 25 mm, 30 mm, 35 mm, 40 mm, 45 mm和50 mm的煤岩开展了冲击压缩试验，通过分析应力-应变曲线特征得出应变率、峰值应力和动态弹模随尺寸变化的关系，并基于能量耗散规律提出煤岩受载全过程动态损伤指标K,同时与Weibull分布结合D-P准则得出的损伤变量D_w进行对比，探究不同尺寸煤岩的动态损伤特性。结果表明：不同尺寸煤岩的动态应力-应变曲线包含弹性、塑性和塑性软化3个阶段。随煤岩尺寸的增加，应变率和峰值应力呈减小趋势，动态模量为线性增加；动态损伤指标K是煤岩弹性阶段结束后的瞬时破碎耗能与完全破坏时对应总破碎耗能的比值；动态损伤指标与损伤变量的曲线形态具有相似性，变化趋势具有一致性，表明了K的合理性。指标K的最大损伤值更稳定、更符合破坏状态假设，说明了其具有一定的适用性。     

较大塑性变形下纳晶镍剪切带的演化模型

较大塑性变形下,采用TEM原位拉伸实验揭示了纳晶镍内剪切带演化的微观机制,优化了微观力学模型。结果表明:在纳米尺度范围内,随着晶粒尺寸的增加,应变软化的趋势越来越明显,剪切带宽度也随着增加;晶粒尺寸降低将导致纳晶材料中剪切带的产生提前;内部特征长度的值随着晶粒尺寸的增加呈现先增加后下降的特点;剪切带内的塑性应变分布为:在剪切带两个边界处应变为零,在剪切带中央剪切塑性应变达到最大值。     

Dynamic fracture of a beam or plate under tensile loading

The dynamic fracture response of a long beam of brittle elastic material under tensile loading is studied. If the magnitude of the applied loading is increased to a critical value, a crack is assumed to propagate across the beam cross section. In a parallel analysis to [t] the crack length and applied loading at the fracture face are determined as functions of time measured from fracture initiation. The results of the analysis are shown in graphs of crack length, crack tip speed and fracturing section tensile loading vs time. As found in [1], the crack tip accelerates very quickly to a speed near the characteristic terminal speed for the material, travels at this speed through most of the beam thickness, and then decelerates rapidly in the final stage of the process. Finally, by appropriate change of the elastic modulus, the results may be applied to plane strain fracture of a plate under pure tensile loading.     

梯度复合材料裂纹扩展路径和起裂载荷的有限元分析

为了模拟功能梯度材料(FGM)在工程应用中可能会出现的断裂问题并计算相应的开裂载荷,通过编写用户自定义UEL子程序将梯度扩展单元嵌入到ABAQUS软件中模拟功能梯度材料的物理场,并编写交互能量积分后处理子程序计算裂纹尖端的混合模式应力强度因子(SIF),采用最大周向应力准则编写子程序计算裂纹的偏转角,并模拟了裂纹扩展路径,计算了裂纹的起裂载荷。讨论了材料梯度参数对裂纹扩展路径以及起裂载荷的影响规律。通过与均匀材料的对比,验证了功能梯度材料断裂性能的优越性。研究表明:外载平行于梯度方向时,垂直梯度方向的初始裂纹朝着等效弹性模量小的方向扩展,且偏转角在梯度指数线性时出现峰值,并随着组分弹性模量比的增加而变大;当外载和初始裂纹均平行于梯度方向时,材料等效弹性模量和断裂韧性的增加或者梯度指数的减小都导致起裂载荷变大。     

Effects of fiber orientation and anisotropy on tensile strength and elastic modulus of short fiber reinforced polymer composites

An experimental study was conducted to investigate anisotropy effects on tensile properties of two short glass fiber reinforced thermoplastics. Tensile tests were performed in various mold flow directions and with two thicknesses. A shell–core morphology resulting from orientation distribution of fibers influenced the degree of anisotropy. Tensile strength and elastic modulus nonlinearly decreased with specimen angle and Tsai–Hill criterion was found to correlate variation of these properties with the fiber orientation. Variation of tensile toughness with fiber orientation and strain rate was evaluated and mechanisms of failure were identified based on fracture surface microscopic analysis and crack propagation paths. Fiber length, diameter, and orientation distribution mathematical models were also used along with analytical approaches to predict tensile strength and elastic modulus form tensile properties of constituent materials. Laminate analogy and modified Tsai–Hill criteria provided satisfactory predictions of elastic modulus and tensile strength, respectively.     

循环荷载作用下超高性能混凝土的轴拉力学性能及本构关系模型

对具有不同拉伸应变特性(应变强化和应变软化)的超高性能混凝土(Ultra high performance concrete, UHPC)进行了单调和循环荷载作用下的直接拉伸试验。试验结果表明:应变强化UHPC基体开裂后进入多点微裂纹分布的应变强化段,达到极限抗拉强度后进入单缝开裂的应变软化段;应变软化UHPC基体开裂后直接进入单缝开裂的应变软化段;循环荷载下两种类型UHPC的轴拉应力-应变曲线包络线与单调荷载下的应力-应变曲线基本一致;基于刚度退化过程建立了两种类型UHPC的轴拉损伤演化方程,根据实测应力-应变曲线和试件的裂缝分布形态建立了两种类型UHPC的轴拉本构关系模型,与试验结果基本吻合;采用能量法研究了应变强化UHPC两阶段轴拉本构关系在数值计算时的等效方法。最后,通过无筋应变强化UHPC抗弯试验梁的数值模拟对本文建立的应变强化UHPC轴拉本构关系模型和损伤演化方程及相关假定进行了验证,结果表明本文建立的应变强化UHPC轴拉本构模型能较好地预测UHPC弯拉构件的极限承载力,轴拉损伤变量能在宏观层面上较好地反应试件的裂缝分布状态。      

An analytical approach for fracture and fatigue in functionally graded materials

The problem of brittle crack propagation and fatigue crack growth in functionally graded materials (FGMs) is addressed. The proposed analytical approach can be used to estimate the variation of the stress-intensity factor as a function of the crack length in FGMs. Furthermore, according to the Paris’ law, the fatigue life and the crack-tip velocity of crack propagation can be predicted in the case of fatigue crack growth. A comparison with numerical results obtained according to the Finite Element method will show the effectiveness of the proposed approach. Detailed examples are provided in the case of three-point bending beam problems with either a FGM interlayer, or a FGM external coating. A comparison is presented between two types of grading in the elastic modulus: a continuous linear variation in the FGM layer and a discrete approximation with a multi-layered beam and a constant Young’s modulus in each layer.     

An analysis of mode I interlaminar deformation ahead of crack front in composite DCB specimens

An analytical model was employed to study mode I interlaminar deformation in double cantilever beam specimens of unidirectional carbon fiber/epoxy laminates. The crack opening displacements experimentally determined by moiré interferometry were compared with the model to evaluate the interlaminar tensile modulus and strain distribution ahead of the crack front. The findings showed that the modulus makes an important contribution to increasing the value of crack opening displacement, and that the strain distribution was dependent on both the modulus and thickness of the specimen. Also, a specific correlation was recognized between the modulus and the maximum strain evaluated at the crack tip.     

A cohesive edge crack

The nucleation and growth of a cohesive edge crack is studied. This topic is germane to the initiation and early stage of crack growth during unnotched beam testing, the growth of short edge cracks in finite test pieces, and the formation of tension cracks of geological origin. This paper focuses on an edge crack in a semi-infinite plane, under a uniform far-field tensile stress acting parallel to the plane boundary. Expressions for the Mode I stress-intensity-factor and crack-opening-displacement for an edge crack subjected to arbitrary crack face loading are determined via the weight function method. All of the constants needed to define the weight function and associated integrals are themselves explicit functions of just two constants: f_r and ψ. Two types of softening behavior in the cohesive zone are examined: rectangular softening, and linear softening. In each case the process zone size, energy-release-rate, crack-opening displacement and load-ratio are examined. The different test behavior exhibited under load-control versus fixed-grip displacement control is explored. The test control conditions alter the fracture behavior significantly. For a linear softening cohesive edge crack, it is found out that under fixed-grip control (load-control), the process zone size decreases (increases) steadily with increasing traction-free crack length, approaching the semi-infinite crack asymptote from above (below). The differences between load-control versus fixed-grip control decrease rapidly with increasing traction-free crack length.