危岩主控结构面疲劳断裂寿命计算方法

危岩的破坏机理和安全性受控于危岩主控结构面．通过计算危岩主控结构面在自重、裂隙水压力及地震力作用下的Ⅰ型及Ⅱ型应力强度因子,建立了主控结构面临界长度计算方法;把主控结构面内的裂隙水压力视作交变荷载,通过计算其对主控结构面应力强度因子的贡献,遵循P-M准则运用Paris疲劳方程建立了处于临界状态条件下主控结构面的疲劳断裂寿命计算方法,并通过疲劳断裂试验确定了三峡库区万州地区典型长石石英砂岩的疲劳系数C值和m值．     

考虑地震力方向的倾倒式危岩可靠度分析

侧向卸荷作用导致高陡边坡发育大量危岩体,危岩体在降雨、地震作用下易发生失稳破坏,判断其失稳的概率对危岩防治具有重要意义.该文以倾倒式危岩体为例,建立了考虑地震力作用方向下最危险方向的物理力学模型,利用函数极值理论建立了最危险地震力作用方向的表达式,结合可靠度理论建立了倾倒式危岩体可靠度指标、失稳概率表达式及判断标准.通过对重庆南川金佛山危岩体案例的分析表明:工况1的最危险地震力作用方向与水平方向的偏转角θ在5°范围内,工况2的最危险地震力作用方向与水平方向的偏转角θ在10°左右;危岩体最危险作用方向不是一个固定角,其值与危岩体形态、裂隙水作用力大小、岩腔深度等有关.当主控结构面裂隙长度较小时,最危险地震力作用方向与水平夹角很小,随主控结构面裂隙长度增大,最危险地震力作用方向与水平夹角显著增大;危岩体失稳概率随主控结构面裂隙长度增加而增大,工况2较工况1增大幅度更明显.该研究成果对危岩的防灾减灾具有重要意义.     

危岩主控结构面损伤模型研究

危岩是迄今研究程度极其薄弱的地质灾害类型,而主控结构面受荷损伤是危岩发育机理研究的核心技术．通过定义主控结构面裂端损伤区,运用损伤力学方法建立了裂端损伤区的即时泊松比和即时弹性模量的计算方法,并据此构建了主控结构面裂端损伤本构方程,为主控结构面断裂演化数值模拟奠定了理论基础．     

扁壳压曲的蠕变效应

本文讨论了混凝土扁壳压曲的蠕变效应.基于弹性薄壳的非线性理论,发现椭圆抛物面扁壳,其荷载-挠度曲线的上临界荷载将随时间而降低,而下临界荷载则随时间而上升.至于扁壳的局部失稳问题,其临界荷载仅取决于压曲发生瞬间材料的弹性模量.     

一维六方压电准晶双材料界面共线裂纹问题北大核心CSCD

利用复变函数理论中的解析延拓、奇性主部分析和推广的Liouville定理,求解了一维六方压电准晶双材料在集中载荷作用下界面共线裂纹反平面弹性问题.导出了含有一条和两条有限长界面裂纹的封闭解,同时给出了裂纹尖端场强度因子(包含声子场和相位子场应力强度因子和电位移强度因子)的表达式.数值算例分析了外荷载与耦合系数之比对裂纹尖端场强度因子变化规律的影响.从数值结果中可以看出,当裂纹长度增加时,裂纹尖端场强度因子随之增加;应力强度因子随双材料耦合系数之比的增大而增大,电位移强度因子几乎不变;不同载荷作用下,裂纹尖端场强度因子随着裂纹长度改变时的变化趋势也不尽相同.研究结果可为压电准晶双材料的设计和制备提供一定的理论参考.     

垂直分布荷载g0/cos2θ作用下圆弧双铰拱失稳临界力的解

在计入轴力对拱弯曲的影响后,建立了圆弧双铰拱在垂直分布荷载ｇ０／ｃｏｓ２θ作用下的总势能·按Ｒｉｔｚ法求得在该荷载作用下具有足够工程精度的拱失稳临界力的第４次近似值,并与圆弧双铰拱受径向均布荷载作用的情况作了比较,得到一些可供参考的结果     

裂纹面分布加载裂尖SIFs分析的广义参数Williams单元北大核心CSCD

带裂缝服役是工程结构的常态,由于流体侵入到裂缝内部,裂纹面直接受荷,使得裂缝进一步扩展,甚者影响结构的安全性.广义参数Williams单元(简记W单元)在分析断裂问题中,利用Williams级数建立裂尖奇异区的位移场,通过求解广义刚度方程可直接获得应力强度因子(stress intensity factors,SIFs),具有高精高效性;但W单元需满足奇异区内裂纹面自由的边界条件,故在分析裂纹面加载的问题中受限.该文基于SIFs互等,在等效奇异区范围中,将裂纹面的荷载等效为奇异区外围边界裂纹面上的集中力,避免奇异区内裂纹面受荷,故采用W单元即可简便计算.算例分析表明:等效奇异区尺寸取裂纹长度的1/20,等效荷载系数P建议取2.0,W单元计算精度均满足1%的误差限,证明该文在奇异区裂纹面受荷等效处理方法上具有合理性、通用性,克服了W单元在分析裂纹面加载问题的局限性.     

扁球壳在热-机械荷载作用下的稳定性分析

基于扁壳几何非线性理论,应用虚功原理和变分法推导了均匀变温场中圆底扁薄球壳在均布外侧压力作用下的位移型几何非线性控制方程.考虑周边不可移简支边界条件,运用打靶法计算获得了不同几何参数的扁球壳轴对称弯曲变形的数值结果.定义了壳体临界几何参数.考察了壳体几何参数对平衡路径和临界荷载的影响.当壳体几何参数大于壳体临界几何参数时,上临界荷载随几何参数的增加单调增加,下临界荷载在很小范围内随几何参数的增加而增加,之后随几何参数的增加而减小.给定几何参数时,考察了不同均匀温度变化对壳体临界几何参数、临界荷载和平衡构型的影响.均匀升温使上临界荷载显著增加,使下临界荷载和临界几何参数显著减小.     

弹性地基输流管道的耦合模态颤振分析

推导出了弹性地基输流管道的固-液耦合振动微分方程,用幂级数法计算了Winkler模型地基和双参数模型地基输流管道的临界流速和复频率,分析了弹性地基对输流管道静力稳定性与动力稳定性的影响.结果表明,与不考虑弹性地基的情况相比较,弹性地基的作用可使管道发生静力失稳和动力失稳的临界流速增大,并且增大弹性地基参数可提高静力失稳和动力失稳的临界流速,从而推迟发散与颤振的发生.当质量比β较大时,管道会在某个地基参数组合下,在发生静力失稳后,会在较高流速下出现再稳定和再发散现象,然后发生耦合模态颤振.     

薄板热力耦合的屈曲分析

基于Rayleigh-Ritz理论,采用有限元方法,推导了薄板在热力耦合载荷作用下屈曲临界载荷的表达式.假设力载荷与热载荷同时加载,采用MATLAB编译环境编写的有限元程序求解薄板结构在热力耦合载荷作用下的屈曲临界载荷.在做屈曲分析时,热载荷以温度场的形式施加到节点上.采用非均匀温度场加载,分析了力载荷分量与热载荷分量对薄板结构失稳的影响.研究结果表明,随着给定温度载荷、力载荷的增加或者降低,临界载荷随之增加或者降低,它们几乎呈线性变化.     

Interlaminar Crack Propagation Analysis of ENF Specimens Based on the Cohesive Zone Model北大核心CSCD

Based on the classical laminated plate theory and the cohesive zone model, a theoretical model for general delamination cracked laminates was established for crack propagation of pure mode Ⅱ ENF specimens. Compared with the conventional beam theory, the proposed model fully considered the softening process of the cohesive zone and introduced the nonlinear behavior of ENF specimens before failure. The predicted failure load is smaller than that under the beam theory and closer to the experimental data in literatures. Compared with the beam theory with only fracture toughness considered, the proposed model can simultaneously analyze the influences of the interface strength, the fracture toughness and the initial interface stiffness on the load-displacement curves in ENF tests. The results show that, the interface strength mainly affects the mechanical behavior of specimens before failure, but has no influence on crack propagation. The fracture toughness is the main parameter affecting crack propagation, and the initial interface stiffness only affects the linear elastic loading stage. The cohesive zone length increases with the fracture toughness and decreases with the interface strength. The effect of the interface strength on the cohesive zone length is more obvious than that of the fracture toughness. When the adhesive zone tip reaches the half length of the specimen, the adhesive zone length will decrease to a certain extent. Copyright ©2022 Applied Mathematics and Mechanics. All rights reserved.     

Analysis of anti-plane interface cracks in one-dimensional hexagonal quasicrystal coating

The displacement discontinuity method is extended to study the fracture behavior of interface cracks in one-dimensional hexagonal quasicrystal coating subjected to anti-plane loading. The Fredholm integral equation of the first kind is established in terms of displacement discontinuities. The fundamental solution for anti-plane displacement discontinuity is derived by the Fourier transform method. The singularity of stress near the crack front is analyzed, and Chebyshev polynomials of the second kind are numerically adopted to solve the integral equations. The displacement discontinuities across crack faces, the stress intensity factors, and the energy release rate are calculated from the coefficients of Chebyshev polynomials. In combination with numerical simulations, a comprehensive study of influencing factors on the fracture behavior is conducted.     

On the peculiarities of a crack growth path in anisotropic solid

One of the possibilities to increase the resistance of a structure to catastrophic fracture is to force a main line crack to deviate from its path. In this connection the influence of the elastic moduli of an anisotropic material on the possibilities of crack rotation are studied. In particular a linear elastic problem for a straight Mode I crack, located on a symmetry axis of an orthotropic plane is considered. The strength properties of the material are supposed to be isotropic. For studying a direction of a crack growth path several crack models are considered. It is shown that a thin elongated elliptical hole as a crack model leads to more plausible results concerning crack rotation conditions than an ideal cut model. The maximal tensile stresses are taken as a crack growth criterion. It is shown that for some class of orthotropic materials a crack deviates from the straight path just after it starts to grow even in the conditions of uniaxial normal tension. The problem of the stability of a straight crack path under Mode I loading is also considered. This problem is reduced to the problem of the fracture direction determination for thin elongated elliptical cavity slightly inclined to the initial direction. In the frame of the proposed approach the conditions of instability are obtained. It is shown that for some class of orthotropic materials a straight crack path is unstable in the conditions of uniaxial normal tension. This class of materials is wider than one for which a crack deviates from the straight crack path just after its start. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Electrostrictive stresses near crack-like flaws

Slit cracks in purely dielectric material systems do not perturb any applied uniform electric field. Furthermore, when the dielectric is unconstrained and does not support any conducting plates or mechanical loads, there are no additional mechanical stresses generated in the material upon introduction of the crack. This situation applies to both electrostrictive and piezoelectric materials. However, flaws which have finite thickness such as thin elliptical or ellipsoidal voids will cause severe inhomogeneous concentration of the electric field. In turn, this can generate substantial mechanical stress from electrostrictive or piezoelectric sources. The effect of an elliptical through flaw in an infinite isotropic body is considered. It is found that, in the case of thin ellipses, the near flaw tip mechanical stresses approximate the singular stresses near a slit crack with an equivalent stress intensity factor. In that sense, the flaw may be considered as a slit crack and treated in terms of linear elastic fracture mechanics. However, except for impermeable and conducting flaws, the value of the equivalent stress intensity factor depends on the aspect ratio of the flaw. As the aspect ratio of the flaw diminishes, the magnitude of the equivalent stress intensity factor falls and disappears in the limit of a slit crack. The results are used to show that a flaw-like crack in a material with a very high dielectric constant can be treated by fracture mechanics as an impermeable slit crack when the flaw aspect ratio is an order of magnitude greater than the ratio of dielectric permittivities (flaw value divided by the value for the surrounding material).     

韧脆转变的一种细观随机模糊统计分析

对不同温度和应力状态下40Cr材料进行大子样宏观试验和细观观测,提出了一种新的材料断裂韧脆转变统计随机模糊模型。该模型认为,在统计意义上,材料的韧性断裂为空穴机制,临界空穴扩张比参数可以作为韧性断裂的判据;材料的脆性断裂可以用内嵌币状裂纹的脆性断裂模型来模拟,为此测量断裂特征长度,提出并具体计算了控制币状裂纹失稳扩张的细观临界应力强度因子;在韧脆转变区域内,这两种机理并存并相互竞争,为此提出了模糊准则。对模型参数进行了测量和统计分析,给出分布规律,给出了计算断裂特征的概率模型。计算了韧脆转变区域内的细观机制变化和宏观响应。结果表明,该模型及分析方法可以很好地模拟应力状态及温度对韧脆转变的影响。     

Interpretation of parameters in phase field models for fracture

Phase field fracture models typically feature a length parameter, which controls the width of the diffuse transition zone between broken and undamaged material. In the limit case of a vanishing length parameter, these models converge to a sharp crack formulation. From this point of view, the length scale parameter is a purely auxiliary numerical quantity. However, the study of the stability of homogeneous solutions in a one dimensional setting permits a different interpretation. Since the length parameter is directly related to the critical stress at which the homogeneous solution becomes unstable and crack nucleation occurs, it can be related to the strength of the material. In this regard, the length parameter itself may be seen as a material parameter. These analytical findings are approved by finite element simulations. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Poling angle effect on two mode-III semi-permeable collinear cracks in a piezoelectric strip: Strip-saturation model

A mathematical strip-saturation model is proposed to analyze the influence of changing poling direction on two hairline electrically semi-permeable collinear cracks embedded in a piezoelectric strip. The remote boundaries of the piezoelectric strip are subjected to anti-plane mechanical and in-plane electrical loads. Fourier series method is applied to transform the model into triple series equations which are then reduced to singular integral equations using the integral equation technique. The closed-form analytical expressions are derived for saturation zones length, crack-sliding displacement (CSD), crack opening potential drop (COPD), intensity factors (IFs), and energy release rate (ERR). Influence of the poling angle on CSD, COPD, and ERR are shown graphically for various cracked piezoelectric ceramics. In addition, the numerical study is also presented for analyzing the effect of inter-crack distance and prescribed electrical and mechanical loadings on the fracture parameters. All graphical results are analyzed and compared.     

New damage evolution model of rock material

As a kind of natural engineering material with original defects, there are distinctly nonlinear and anisotropic mechanical behaviors for rock materials. Nevertheless, the rock damage mechanics can solve this problem well. However, for the complexity of mechanical property of rock material, the mature and applicable model to describe the rock failure process and the method to determine the maximum damage value have not been established very well. To solve this problem, one new damage evolution model for rock material has been proposed. In this model, the least energy consumption principle proposed to describe the fracture process of materials is used. Using the experimental data of granite sample under uniaxial compression and the results of numerical tests under uniaxial tension and uniaxial compression, this model is verified. Moreover, the results of the new model have been compared with the results of the tests (numerical test and real test) and the traditional damage model. The comparison shows that the new model has the higher accuracy and better reflects for the fracture process of the granite sample. Moreover, the released damage energies of the new model and Mazars model are different, and the released damage energy of the new model is slightly less than that of the Mazars model.