Size effect and asymptotic matching analysis of fracture of closed-cell polymeric foam

The effect of structure size on the nominal strength of closed-cell PVC foam (Divinycell H100) is investigated experimentally, theoretically and numerically. Two types of size effect are considered––Type I, characterizing failure of structures with large cracks or notches, and Type II, characterizing failure at crack initiation. Geometrically similar single edge-notched prismatic specimens of cross section widths 6.35, 43.9 and 305 mm, are tested under tension. The results are shown to agree with Bažant’s law for type I energetic (deterministic) size effect derived by asymptotic matching of a solution by equivalent linear elastic fracture mechanics for large sizes and plastic crack solution for small sizes (in the derivation, the statically indeterminate size-dependent lateral shift of the axial load resultant due to rotational end restrain is taken into account). Fitting this law, previously verified for many quasibrittle materials, to the test results furnishes the values of the fracture energy of the foam as well as the characteristic size of the fracture process zone of foam. The size effect method of measuring the fracture characteristics of foam is further supported by analysis of recent notched beam tests of Zenkert and Bäcklund. Furthermore, it is shown that compressed V-notched specimens exhibit no size effect. Subsequently, the size effect of Type II is studied using previous test data of Fleck, Olurin and co-workers for dissimilar long holed panels having different width and different diameter-width ratios. An asymptotic matching formula for this type of size effect (similar to a previously derived formula for kink band failure of fiber composites) is set up and is shown capable of matching the test data well. But its verification as a predictive tool cannot yet be claimed because of inaccurate asymptotic properties of the available energy release function. Finally, the size effect of Type I is analyzed using the eigenvalue method for the cohesive crack model and the numerical results are shown to agree again with both Bažant’s size effect law and the test results.     

Size effect in quasibrittle failure: Analytical model and numerical simulations using cohesive zone model

The recent rewriting of the Ba?ant’s size effect law (Morel, 2008) which has suggested the existence of an additional asymptotic regime for intermediate structure sizes is now compared to numerical simulations of fracture of geometrically similar notched structures of different sizes extending over 2.4 decades. The quasibrittle fracture behavior is simulated through cohesive zone model (bilinear softening) using a constant set of cohesive parameters whatever the specimen size D is. The R-curves resulting from the load–displacement responses are estimated and appear as size-independent. On this basis, the different asymptotic regimes expected for the size effect on fracture properties at peak load such as the relative crack length, the resistance to crack growth and the nominal strength are shown in fair agreement with the size effect observed on the results obtained from numerical simulations.     

岩石断裂尺寸效应测试装置研制及实验研究

面向岩石断裂尺寸效应研究的实验装置需求,针对现有技术中三点弯曲装置对多组尺寸岩石试件适应性差、最小跨距的测试量程不足等问题,研制了一种可灵活用于岩石断裂尺寸效应测试的三点弯曲装里.装置采用"两体分离式"的设计,三种不同型号的滚子与压头体、支座体配合使用,有效避免了不同尺寸试件采用同一直径滚子测试带来的实验精度问题;同时...     

无腹筋RC悬臂梁抗剪强度及尺寸效应理论研究

不同于混凝土材料,钢筋混凝土(RC)构件的破坏模式与机制更为复杂,采用混凝土材料尺寸效应理论难以描述构件的尺寸效应行为。我国相关规范中并没有系统考虑构件尺寸及纵筋率对RC梁抗剪承载力的影响。为研究剪跨比及纵筋率对无腹筋RC梁剪切破坏及抗剪强度尺寸效应的影响,采用三维细观数值模拟方法,建立了RC梁剪切破坏力学分析模型,研究了剪跨比及纵筋率对RC梁剪切破坏及抗剪强度尺寸效应的影响机制与规律。研究结果表明,RC梁抗剪强度表现出极为显著的尺寸效应现象;RC梁抗剪强度随剪跨比的增大而减小,随纵筋率的增大而增大;剪跨比较小时,纵筋率对抗剪强度的影响尤为显著。此外,基于Ba■ant材料层次尺寸效应律,提出了考虑剪跨比及纵筋率影响的RC梁抗剪强度尺寸效应理论公式。对比试验结果,验证了所提公式的准确性与合理性。     

Interplay of size effects in concrete specimens under tension studied via computational stochastic fracture mechanics

We attempt the identification, study and modeling of possible sources of size effects in concrete structures acting both separately and together. We are particularly motivated by the interplay of several identified scaling lengths stemming from the material, boundary conditions and geometry. Methods of stochastic nonlinear fracture mechanics are used to model the well published results of direct tensile tests of dog-bone specimens with rotating boundary conditions. Firstly, the specimens are modeled using microplane material law to show that a large portion of the dependence of nominal strength on structural size can be explained deterministically. However, it is clear that more sources of size effect play a part, and we consider two of them. Namely, we model local material strength using an autocorrelated random field attempting to capture a statistical part of the complex size effect, scatter inclusive. In addition, the strength drop noticeable with small specimens which was obtained in the experiments is explained by the presence of a weak surface layer of constant thickness (caused e.g., by drying, surface damage, aggregate size limitation at the boundary, or other irregularities). All three named sources (deterministic-energetic, statistical size effects, and the weak layer effect) are believed to be the sources most contributing to the observed strength size effect; the model combining all of them is capable of reproducing the measured data. The computational approach represents a marriage of advanced computational nonlinear fracture mechanics with simulation techniques for random fields representing spatially varying material properties. Using a numerical example, we document how different sources of size effects detrimental to strength can interact and result in relatively complex quasibrittle failure processes. The presented study documents the well known fact that the experimental determination of material parameters (needed for the rational and safe design of structures) is very difficult for quasibrittle materials such as concrete.     

准脆性材料抗压强度能量平衡尺寸效应模型

针对现有尺寸效应模型难以体现准脆性材料完整的抗压强度尺寸效应变化规律及其内在机理, 本文通过分析准脆性材料单轴压缩破坏过程中能量输入、储存、整体和局部能量耗散, 建立体现整体和局部损伤的力学模型及描述上述能量演化过程的双线性名义和真实应力应变曲线, 在此基础上确定了名义应力最大时输入能量、储存弹性能、整体和局部能量耗散的表达式, 最后基于能量平衡原理建立抗压强度尺寸效应模型. 抗压强度能量平衡尺寸效应模型能完整体现名义抗压强度尺寸效应, 即随试样尺寸增大, 名义抗压强度在试样尺寸小于等于局部损伤区尺寸时为真实强度, 然后逐渐减小, 最终当试样尺寸趋于无穷大时趋于弹性极限强度; 抗压强度能量平衡尺寸效应模型也能同时体现高径比和试样直径对名义强度的影响, 其包含的参数具有明确的物理意义, 可以反映真实强度、弹性极限强度、名义损伤模量非线性、局部损伤区大小和方向对准脆性材料名义抗压强度尺寸效应的影响; 通过把抗压强度能量平衡尺寸效应模型和现有尺寸效应模型应用于预测各种材料尺寸效应试验和数值模拟数据, 结果表明: 抗压强度能量平衡尺寸效应模型能很好描述试验和数值模拟尺寸效应的非线性变化规律及内在机理, 和现有尺寸效应模型相比, 其总体平均误差最小, 且小于5%.      

On a 2D hydro-mechanical lattice approach for modelling hydraulic fracture

A 2D lattice approach to describe hydraulic fracturing is presented. The interaction of fluid pressure and mechanical response is described by Biot's theory. The lattice model is applied to the analysis of a thick-walled cylinder, for which an analytical solution for the elastic response is derived. The numerical results obtained with the lattice model agree well with the analytical solution. Furthermore, the coupled lattice approach is applied to the fracture analysis of the thick-walled cylinder. It is shown that the proposed lattice approach provides results that are independent of the mesh size. Moreover, a strong geometrical size effect on nominal strength is observed which lies between analytically derived lower and upper bounds. This size effect decreases with increasing Biot's coefficient.     

Influence of narrow starter notches on the initial crack growth resistance curve of ceramics

In experimental R-curve investigations crack development usually starts from notches. The validity of R-curves depends on the size of the notch root radius. This influence is completely ignored in most cases. In this theoretical study it is shown how the notch radius affects the formally computed crack resistance curve. First, the influence of the notch radius on the starting point of the R-curve, the so-called crack-tip toughness K _I0, will be addressed. Then, the effect of the notch on the shielding stress intensity factor will be discussed, and, finally, the influence on T-stress and the consequences on local path stability will be shown.     

Modelling the R-curve effect and its specimen-dependence

This paper explores the specimen-dependence of the resistance (R-) curve for fracture of materials showing a pronounced R-curve effect. Using a cohesive zone framework, this paper demonstrates how to effectively predict the R-curve for a specimen type whose deformation is shear-dominated (compact tension, CT) from the R-curve of a specimen type whose deformation is bending-dominated (double cantilever beam, DCB). The mathematical relationships between crack extension and crack opening displacements for both CT and DCB specimens are first derived and related to a tri-linear cohesive law. Experimental tests for intralaminar fracture of CFRP are carried out and analysed. Using, as input, the experimental results from the DCB specimen, the cohesive law is shown analytically and using Finite Element (FE) to reproduce accurately the R-curve for the DCB and also to predict accurately the R-curve for the CT specimens.     

Bilinear softening parameters and equivalent LEFM R-curve in quasibrittle failure

For composites and adhesive joints, the determination of the cohesive zone parameters from Double Cantilever Beam specimens loaded with pure moments is now well established and documented. However, for quasibrittle materials used in Civil Engineering such as concrete or wood, the difficulty to apply a pure bending moment lies inappropriated the method used for composites. Nevertheless, the one-to-one correspondence which exists between the R-curve and the softening curve is here revisited and adapted for any kind of specimen geometry and for the bilinear approximation of the softening function, well-known to successfully describe the failure of a wide group of quasibrittle materials. It is shown that even though the connections between the cohesive parameters and the ‘equivalent LEFM’ R-curve are geometry and material dependent, their trends are preserved whatever the specimen geometry and the material are. The outline of a general estimation procedure of the cohesive zone parameters funded on the equivalent LEFM R-curve is proposed.     

点阵材料微极连续介质模型的应力优化设计

在将二维周期性点阵类材料等效为具有非局部化本构的微极连续介质的基础上,运用优化技术,探讨了基于材料相对密度和微单胞特征尺度两类变量的优化结构应力的方法,给出了针对最小化结构关键部位应力、结构最大应力最小化、最大化结构关键部位安全储备三类特定目标的结构与材料一体化协同优化结果．利用圆板小孔应力集中的数值算例验证了方法的有效性．     

基于努氏硬度表征大块金属玻璃的力学性能

采用多种载荷对14种大块金属玻璃进行努氏硬度测试,结果表明努氏硬度随载荷的增加而降低,最后趋于稳定,即材料受到正压痕尺寸效应的影响,并利用Meyer定律、弹塑性变形模型、Hays-Kendall模型和比例试样阻力模型对这种现象进行了解释,因此在压痕表面未产生裂纹时应采用较大载荷下趋于稳定的硬度值对杨氏弹性模量E和屈服强...     

Size Effect on The Bending And Tensile Strength of Micromachined Polysilicon Films for MEMS

I. INTRODUCTION Microelectromechanical systems (MEMS) have achieved impressive progress and become a very area of research. But long-term durability of various MEMS devices requires a fundamental understaof the fatigue and fracture characteristics of su…     

试样疲劳性能尺度效应的概率控制体积方法

试样尺度、缺口和加载方式通常对材料的疲劳性能具有重要影响. 因此,发展关联试样尺度、缺口和加载方式对疲劳强度影响的方法对于从材料疲劳性能到结构件疲劳性能的预测具有重要意义.首先,采用旋转弯曲加载和轴向加载方式对不同几何形状EA4T车轴钢试样进行了疲劳实验.实验结果表明, 由于试样尺度的增加,轴向加载下狗骨形试样的疲劳强度明显低于沙漏形试样; 相同寿命下,缺口显著降低试样的疲劳强度. 疲劳断口扫描电镜观测结果表明,疲劳裂纹均起源于试样表面.沙漏形试样和狗骨形试样疲劳断口大多只有一个裂纹源,而缺口试样疲劳断口均具有多裂纹源特征. 然后,采用概率控制体积方法研究了试样尺度、缺口和加载方式对疲劳强度的影响,并与临界距离和应变能密度方法进行了比较. 结果表明,概率控制体积方法能够更好地关联试样尺度、缺口和加载方式对EA4T车轴钢疲劳强度的影响.最后, 提出一种基于控制体积的结构件疲劳强度预测方法,并用于具有不连续高应力区域车轴钢试样的疲劳强度预测,预测结果与实验结果 吻合.      

基于统一强度理论抗滑桩桩间距的计算

在已有抗滑桩桩间距研究的基础上,对桩间土拱进行受力分析。从侧阻力条件和土拱强度条件两个方面对抗滑桩桩间距进行了计算,将统一强度理论引入土拱强度的分析,藉此分别判断拱顶前缘、后缘及拱脚处土体是否处于临界状态,可得3个桩间距值,取相应的最小桩间距作为设计桩间距。此方法对于滑坡推力的矩形、三角形和梯形分布形式均适用,并可考虑土体自重应力的影响,同时可推及锚索抗滑桩桩间距的计算。对两个计算实例进行了分析,本方法的计算值与已有计算值或设计值的比较表明本方法效果良好。具体计算中统一强度参数b取0.2~0.7较为合适,滑坡推力为矩形分布时b值约为0.3,滑坡推力为三角形分布时b值约为0.6,滑坡推力为梯形分布时b值介于两者之间。     

防护结构设计中应变速率效应问题

在防护结构设计中，通常是采用材料的动力强度和动力弹性模量以考虑应变速率效应问题。应用所提出的应变速率相关材料模型，对核武器及常规武器爆炸作用下的钢结构和钢筋混凝土结构进行速率相关分析，并与考虑材料强度提高的速率无关分析对比。两种分析结果表明，对于钢结构，两种计算结果相差不大；而对于钢筋混凝土结构．两种计算结果相差较大，而且目前防护结构设计方法偏于保守。     

基于自动分组遗传算法的建筑结构体系与构件尺寸协同优化设计

研究了利用结构优化方法实现建筑结构体系选择的问题。文中建立了可以覆盖框架、框架-剪力墙和巨型结构三种体系的优化模型,并采用自动分组遗传算法求解,实现了结构体系与构件尺寸的协同优化。文章特别设计了三类模块,每类模块通过专门构造的含有多个分量的设计变量来表示,按一定方式组合这些模块可得到不同体系的结构。巨型结构中,巨型构件的设计变量表示方法和惯性矩计算方法满足提出的三条假设。基于精心构造的设计变量和三条相关假设,文中建立了以结构总材料用量最少为目标,考虑强度、刚度、分组及构造要求等约束条件的优化模型,采用自动分组遗传算法研究了40层、10层、6层三种高度建筑的优化设计。在相同外荷载条件下,它们的最优设计分别为巨型结构、框架-剪力墙和框架结构。     

Fracture resistance and strength of two-phase WC–Ni alloy

Microcracking near a crack tip in a material with microinhomogeneity is regarded as a stochastic process. Both the critical deformation energy density and minimum ligament size of a structural element at global failure are related to a fracture resistance parameter which depends also on the strength. This parameter is also known as the critical energy density factor. For composites it is shown that transition of material behaviour from one structural state to another could alter the fracture resistance depending on character of the critical defect size and strength. The theoretical result is shown to be in agreement with the experimental data.     

Mechanical Properties of two novel planar lattice structures

Two novel statically indeterminate planar lattice materials are designed: a new Kagome cell (N-Kagome) and a statically indeterminate square cell (SI-square). Their in-plane mechanical properties, such as stiffness, yielding, buckling and collapse mechanisms are investigated by analytical methods. The analytical stiffness is also verified by means of finite element (FE) simulations. In the case of uniaxial loading, effective modulus, yield strength, buckling strength and critical relative density are compared for various lattice structures. At a critical relative density, the collapse mode will change from buckling to yielding. Elastic buckling under macroscopic shear loading is found to have significant influence on failure of lattice structures, especially at low relative densities. Comparison of the analytical bulk and shear moduli with the Hashin–Shtrikman bounds indicates that the mechanical properties of the SI-square honeycomb are relatively close to being optimal. It is found that compared with the other existing stretching-dominated 2D lattice structures, the N-Kagome cell possesses the largest continuous cavities for fixed relative densities and wall thicknesses, which is convenient for oil storage, disposal of heat exchanger, battery deploying and for other functions. And the initial yield strength of the N-Kagome cell is slightly lower than that of the Kagome cell. The SI-square cell has similar high stiffness and strength as the mixed cell while its buckling resistance is about twice than that of the mixed cell.