基于一类非局部宏-微观损伤模型的混凝土典型试件力学行为模拟

混凝土是一类典型的准脆性材料, 其受力过程中的非线性分析与裂纹模拟依然是具有挑战性的问题. 经典的断裂力学与损伤力学分别从间断与连续的视角对裂纹拓扑进行了描述, 是早期人们研究固体破坏问题的有力工具. 21世纪以来, 相场理论和近场动力学在预测裂纹的萌生、扩展与非线性分析方面取得了重要的进展. 最近, 结合统一相场理论与近场动力学的基本思想, 发展了一类非局部宏-微观损伤模型. 该模型引入物质点偶的概念来刻画由于变形引起的微细观损伤, 对微细观损伤在作用域中进行加权平均得到定量描述物质不连续程度的拓扑损伤. 通过具有物理机制的能量退化函数, 将拓扑损伤嵌入到连续介质-损伤力学的框架中, 这使得该模型在进行非线性分析的同时可以自然地进行裂纹模拟, 而毋须预设初始裂纹与裂纹扩展路径. 本文考虑细观物理参数的空间变异性, 采用非局部宏-微观损伤模型进行混凝土试件受力全过程的精细化模拟. 通过一维建模标定模型细观参数, 并探讨了细观参数与混凝土材料细观物理-几何特性之间的内在关联, 在此基础上采用二维模型进行精细化分析. 进而, 考察了材料参数空间变异性对混凝土单轴受拉试件和带缺口三点弯曲试件力学行为的重要影响. 本文的研究工作为非局部宏-微观损伤模型细观参数的试验标定与复杂应力状态下混凝土等准脆性材料的非线性力学行为研究提供了有意义的参考.      

Numerical study of failure behaviour of pre-cracked rock specimens under conventional triaxial compression

Macroscopic pre-existing flaws play an important role in evaluating the strength and the failure modes of a heterogeneous rock mass. Crack initiation, propagation and coalescence from macroscopic pre-existing flaws are considered in a 3-D numerical model (RFPA3D) to investigate their effects on the underlying failure modes of rock. A feature of the code RFPA3D is that it can numerically simulate the evolution of cracks in three-dimensional space, as well as the heterogeneity of the rock mass. Three types of flaw geometries were evaluated numerically against experimental results: Type A for intact specimen, and Types B and C for flawed cylindrical specimens with different macroscopic pre-existing flaws, respectively. The effect of confining pressure on the fracture evolution was also considered. Numerical results showed that both the ligament angle and the flaw angle of two pre-existing cracks can affect the uniaxial compressive strength of the specimen and the mechanism of fracture evolution. In addition, both the uniaxial compressive strength and the accumulated acoustic emission increase with increasing heterogeneity.     

镁合金MB2在高应力三轴度下的拉伸破坏行为研究

通过光滑试件及不同曲率半径缺口圆柱试件的拉伸试验,实现对镁合金MB2的单向及多向应力状态加载。结合数值模拟分析,研究了不同试件在拉伸加载过程中应力状态的变化。以应力三轴度为参数,给出了镁合金MB2等效破坏应变的变化规律,在应力三轴度-等效破坏应变空间建立了镁合金MB2的失效破坏准则。利用扫描电镜对试件断口形貌进行观察,分析了导致材料宏观延性变化的微观损伤机理,对不同应力状态下镁合金MB2的失效破坏行为做出了合理解释。     

混凝土高温动态劈拉行为细观数值分析

为研究高温作用下混凝土的动态劈裂拉伸破坏行为,考虑了力学性能的高温退化与应变率增强效应的联合作用,结合混凝土材料内部非均质性,建立了细观尺度数值分析模型与方法。将该数值方法分为两个步骤:首先对混凝土进行热传导行为模拟,进而将输出结果作为初始条件对混凝土动态劈裂拉伸行为进行细观模拟。在模拟结果与已有试验现象良好吻合的基础上,分析了高温下混凝土动态劈裂拉伸行为及其细观破坏机制,对比了不同应变率及加热温度下混凝土的劈裂拉伸应力-应变关系,揭示了混凝土应变率效应与温度退化效应的相互影响规律。研究结果表明:(1) 高温作用后,试件损伤区域较常温下更集中;(2) 名义应变率较大时,破坏过程急促,常温下骨料发生破坏,而经历高温后骨料基本没有破坏;(3) 由于混凝土试件细观结构的非均质性,其内部应力呈枣核状不连续分布;(4) 相比于应变率效应,混凝土劈裂拉伸强度受温度退化作用的影响更显著。     

基于颗粒流的混凝土材料数值实验研究

混凝土材料是一种典型的非均质材料,其力学行为和破坏过程很复杂.本文利用PFC颗粒流软件的内嵌fish语言编写了骨料生成程序、边界条件控制程序,程序模拟了MTS伺服功能,实现了虚拟的混凝土单轴压缩试验.相对于一般有限元程序投放的骨料,文中骨料可以破裂.在生成的数值试件基础上,设计了单级配和全级配混凝土单轴压缩试验,并对其破裂形态、裂纹扩展过程、应力应变曲线和破裂过程能量变化规律进行了研究.利用该虚拟试验平台,可对混凝土的动、静力学特性进行系统研究.     

3D Strain Field Evolution and Failure Mechanisms in Anisotropic Paperboard

Background

Experimental analyses of the 3D strain field evolution during loading allows for better understanding of deformation and failure mechanisms at the meso- and microscale in different materials. In order to understand the auxetic behaviour and delamination process in paperboard materials during tensile deformation, it is essential to study the out-of-plane component of the strain tensor that is, in contrast to previous 2D studies, only achievable in 3D.

Objective

The main objective of this study is to obtain a better understanding of the influence of different out-of-plane structures and in-plane material directions on the deformation and failure mechanisms at the meso- and microscale in paperboard samples.

Methods

X-ray tomography imaging during in-situ uniaxial tensile testing and Digital Volume Correlation analysis was performed to investigate the 3D strain field evolution and microscale mechanical behaviour in two different types of commercial paperboards and in two material directions. The evolution of sample properties such as the spatial variation in sample thickness, solid fraction and fibre orientation distribution were also obtained from the images. A comprehensive analysis of the full strain tensor in paperboards is lacking in previous research, and the influence of material directions and out-of-plane structures on 3D strain field patterns as well as the spatial and temporal quantification of the auxetic behaviour in paperboard are novel contributions.

Results

The results show that volumetric and deviatoric strain, dominated by the out-of-plane normal strain component of the strain tensor, localize in the out-of-plane centre already in the initial linear stress-strain regime. In-plane strain field patterns differ between samples loaded in the Machine Direction (MD) and Cross Direction (CD); in MD, strain localizes in a more well-defined zone close to the notches and the failure occurs abruptly at peak load, resulting in angular fracture paths extending through the stiffer surface planes of the samples. In CD, strain localizes in more horizontal and continuous bands between the notches and at peak load, fractures are not clearly visible at the surfaces of CD-tested samples that appear to fail internally through more well-distributed delamination.

Conclusions

In-plane strain localization preceded a local increase of sample thickness, i.e. the initiation of the delamination process, and at peak load, a dramatic increase in average sample thickening occurred. Different in-plane material directions affected the angles and continuity of the in-plane strain patterns as well as the sample and fracture properties at failure, while the out-of-plane structure affected how the strain fields distributed within the samples.

     

多轴加载下混凝土细观破坏模拟的强度准则探讨

实际工程结构中混凝土材料大多处于双轴或三轴的复杂应力状态,已有的细观力学数值研究工作大多针对单轴加载问题,对于双轴或者三轴加载条件下混凝土破坏模拟的研究相对较少。复杂受力条件下的混凝土材料破坏模拟中,细观组分强度准则选取的合理与否将成为混凝土破坏模式及宏观力学性能数值研究准确和成功与否的关键。本文旨在探讨单轴强度准则,如最大拉应变准则在多轴加载条件下混凝土破坏过程研究中运用的合理性。鉴于此,首先在细观尺度上建立了混凝土试件的二维随机骨料模型,分别采用弹性损伤本构关系模型及塑性损伤本构关系模型来描述细观组分(即砂浆基质)的力学性能,对双轴加载条件下混凝土的细观破坏过程进行数值模拟,对比了单轴强度准则和多轴强度准则下混凝土试件破坏路径及宏观应力-应变关系的差异。数值结果表明,简单的单轴强度准则难以反映双轴加载下混凝土内部应力状态的复杂性,不宜采用单轴强度准则来描述多轴加载下混凝土的破坏行为。     

岩石紧凑拉伸断裂过程及其尺寸效应的三维数值模拟

采用最近开发的三维岩石破裂过程分析软件RFPA3D模拟单边裂纹紧凑拉伸断裂过程。试验中五个不同尺寸的岩样具有相同的力学性质参数分布,模拟结果得到了裂纹扩展中的应力场、位移场和声发射的空间分布以及单边裂纹扩展贯通的过程。单边裂纹拉伸断裂的路径是一个复杂的空间三维曲面,三维裂纹比二维裂纹更为复杂。分析了岩石试样的峰值强度和试样尺寸之间的关系。随着岩样尺寸的增加,峰值强度逐渐减小,并且延性破坏特征更加明显,模拟结果满足岩石的尺寸效应规律。最后模拟了三组不同均匀性的试样拉伸破坏过程,结果表明细观上的非均匀性对岩石尺寸效应有很大影响,随着非均匀性的增加,岩石宏观强度随之提高,即使在均匀材料中一样存在尺寸效应。     

三维四向编织复合材料的拉伸尺寸效应研究

通过对三维四向碳/环氧编织复合材料的拉伸实验,观测了不同几何尺寸的试件的破坏模式和断口形貌,得到了材料在拉伸载荷下不同的破坏机理以及材料的力学性能与试件几何尺寸的相关性,研究表明材料随着内部单胞数量的增加材料的弹性模量递减,而剪切模量和泊松比递增的变化规律,通过体积平均法从理论上预报了材料的弹性性能,预报结果与实验结果相符,实验和理论所获结论为进一步进行材料的刚度和强度预报以及强度准则的建立奠定了必要的实验和理论基础.     

An Experimental Method to Determine the Tensile Strength of Concrete at High Rates of Strain

In the present work, dynamic tensile strength of concrete is experimentally investigated by means of spalling tests. Based on extensive numerical simulations, the paper presents several advances to improve the processing of spalling tests. The striker is designed to get a more uniform tensile stress field in the specimen. Three methods proposed in the literature to deduce the dynamic strength of the specimen are discussed as well as the use of strain gauges and a laser extensometer. The experimental method is applied to process data of several tests performed on wet micro-concrete at strain rates varying from 30 to 150/s. A significant increase of the dynamic tensile strength with strain-rate is observed and compared with data of the literature. In addition, post-mortem studies of specimens are carried to improve the analysis of damage during spalling tests.     

三维非均匀脆性材料破坏过程的数值模拟

采用有限元方法模拟了三维均匀固体材料在宏观等效力学性质和破坏过程。首先采用格形（lattice）方法把试件离散成三维均匀网格,在每个单元格中将材料按照均匀处理,根据给定的统计规则来确定不同单元格中的材料常数以反映材料的非均匀性。然后对非均匀脆性材料选用简单的本构关系与断裂准则,采用自适应选取载荷步长对试件进行加载,通过非平衡迭代技术对刚度矩阵进行不断修正,实现了非均匀脆性材料的弹性行为及破坏过程的数值模拟。在此基础上,通过数值计算研究了材料的非均匀分布对宏观等效力学性质和破坏过程的影响,给出了破坏全过程的非线性载荷－位移曲线以及不同载荷阶段的三维损伤破坏的演化图。     

混凝土拉伸断裂的细观数值分析

根据混凝土试件拉伸和三点弯曲的物理模型,用梁-颗粒模型BPM 2D(B eam-Particle M ode l)模拟了混凝土拉伸和三点弯曲试件微裂纹的萌生、扩展直至试件宏观破坏的全过程。在梁-颗粒模型中用三种类型梁单元形成混凝土细观数值模型,每种类型梁单元的力学性质均按韦伯(W e ibu ll)分布随机赋值以模拟混凝土细观结构的非均匀性。数值模拟结果给出了混凝土拉伸应力-应变曲线和三点弯曲载荷-位移曲线,以及混凝土试件破坏过程最大应力分布图和裂纹扩展图。数值模拟结果显示混凝土破坏过程实际上就是微裂纹萌生、扩展、贯通,直到宏观裂纹产生导致混凝土失稳断裂的过程。通过对数值模拟结果的分析,揭示出混凝土在拉伸条件下裂纹尖端的拉应力集中是裂纹扩展的动力,混凝土组成材料力学性质的非均匀性是造成裂纹扩展路径曲折的重要原因。     

石英玻璃圆环高速膨胀碎裂过程的离散元模拟

采用离散元算法模拟了石英玻璃圆环受到外加动态载荷时的力学行为. 首先基于flat-jointed粘结模型,通过标准的单轴拉压、三点弯曲等数值实验来标定了石英玻璃的微观参数. 在此模型基础上,数值模拟再现了石英玻璃圆环在不同应变率下的膨胀碎裂过程. 为定量分析数值模拟结果,需要准确确定圆环的碎裂发生时刻. 模拟发现:伴随着石英玻璃圆环的断裂,圆环外表面粒子径向膨胀速度的时程曲线会发生突然升高然后下降的跳动;详细分析表明,这种跳动源自周向的脆性断裂诱发的卸载波(周向拉伸应力急剧下降)以及伴随而来的泊松膨胀,这种径向速度跳动现象为实验中检测脆性断裂发生时刻提供了可能. 进一步的数值研究表明:(1)石英玻璃圆环的断裂应变随着应变率的提高而增大,与韧性金属材料的膨胀环实验结果一致;(2)石英玻璃圆环的碎片平均质量随着应变率的增大而减小;(3)数值计算获得的碎片平均尺寸与已有的理论和实验结果比较吻合. 利用液压膨胀环实验装置对石英玻璃圆环进行了验证性实验,回收得到的碎片形貌及碎片个数与数值模拟的结果基本一致.      

Determining material true stress–strain curve from tensile specimens with rectangular cross-section

The uniaxial true stress logarithmic strain curve for a thick section can be determined from the load–diameter reduction record of a round tensile specimen. The correction of the true stress for necking can be performed by using the well-known Bridgman equation. For thin sections, it is more practical to use specimens with rectangular cross-section. However, there is no established method to determine the complete true stress–logarithmic strain relation from a rectangular specimen. In this paper, an extensive three-dimensional numerical study has been carried out on the diffuse necking behaviour of tensile specimens made of isotropic materials with rectangular cross-section, and an approximate relation is established between the area reduction of the minimum cross-section and the measured thickness reduction. It is found that the area reduction can be normalized by the uniaxial strain at maximum load which represents the material hardening and also the section aspect ratio. Furthermore, for the same material, specimens with different aspect ratio give exactly the same true average stress–logarithmic strain curve. This finding implies that Bridgmans correction can still be used for necking correction of the true average stress obtained from rectangular specimens. Based on this finding, a method for determining the true stress–logarithmic strain relation from the load–thickness reduction curve of specimens with rectangular cross-section is proposed.     

Fracture behaviour in tension of viscoplastic porous metallic materials saturated with liquid

The present work extends the investigation which has been initiated in Parts I and II of this study (Martin, C.L., Favier, D., Suéry, M., 1997a. Viscoplastic behaviour of porous metallic materials saturated with liquid, part I: constitutive equations. Int. J. Plasticity 13, 215–235; Martin, C.L., Favier, D. Suéry, M., 1997b. Viscoplastic behaviour of porous metallic materials saturated with liquid, Part II: experimental identification on a Sn–Pb model alloy. Int. J. Plasticity 13, 237–259) to the tensile behaviour of viscoplastic porous metallic materials saturated with liquid. Simple tensile experiments together with ring extension tests are carried out to study the fracture behaviour of this class of material. Ring tests consist in applying an internal pressure on a specimen with a ring shape. A Sn–Pb model alloy with a dendritic microstructure is used to characterise the behaviour of the material up to fracture. The liquid presence is accounted for to derive the intrinsic behaviour of the solid skeleton. The collected data are then incorporated in the model framework presented in Part I. A simple modification of the model allows the treatment of the strong asymmetry between tension and compression which is exhibited by these materials.     

基于应变能的复杂应力场低周疲劳分析

塑性应变能使材料微观组织结构发生不可逆变化,从而引起等效宏观应力,该应力随循环加载而增大．假定材料疲劳源处破坏是由最大拉应力引起的,最大等效宏观应力与外加应力叠加达到材料本征断裂应力时形成微裂纹．微裂纹引起上述两部分应力变化,继续加载直至宏观裂纹出现,从而得到材料的疲劳寿命．本文所建立的多轴疲劳寿命公式包含材料参数、拉应力以及塑性应变能等,以上数据可通过单轴疲劳数据和有限元方法获得．通过对SM45C材料的计算验证,表明该模型对多轴随机应变加载低周疲劳寿命,具有良好的预测结果．     

Application of Laser Deposition to Mechanical Characterization of Advanced High Strength Steels Subject to Non-Proportional Loading

Background

Characterization of hardening and fracture limits of advanced high strength steels (AHSSs) undergoing strain path changes (SPCs) are particularly challenging for plane strain condition, which commonly occurs in sheet metal forming. There is a need for a simple, engineering-friendly method to characterize materials subjected to complex loading paths that mimic stress conditions in actual forming processes.

Objective

Experimental additive manufacturing techniques have been applied to reinforce AHSS specimens subjected to SPCs in order to broaden capabilities for characterizing hardening behavior and fracture limits.

Methods

Hardening curves subject to SPCs (e.g. uniaxial tension or equi-biaxial tension followed by plane strain) have been obtained with a programmable biaxial tensile testing system using cruciform-shaped specimens with load-bearing arms reinforced by laser deposition. A notched specimen selectively reinforced by laser deposition was newly designed to characterize fracture limits subjected to SPCs ending with plane strain condition.

Results

Complex loading histories were successfully enabled by applying laser deposition technology. Results show that both hardening behavior and fracture limits of a TRIP-assisted steel and a dual-phase steel are dependent on loading history.

Conclusions

It appears that the laser deposition technique can be used for material characterization under specific SPCs. Hardening behavior of AHSSs under SPCs ending with plane strain is quite different from traditional uniaxial tension-uniaxial compression tests. For materials sensitive to SPCs, multi-step forming can be a great option to reach the targeted forming shape.

     

Size dependent response of large shell elements under in-plane tensile loading

Large-scale thin-walled structures with a low weight-to-stiffness ratio provide the means for cost and energy efficiency in structural design. However, the design of such structures for crash and impact resistance requires reliable FE simulations. Large shell elements are used in those simulations. Simulations require the knowledge of the true stress–strain response of the material until fracture initiation. Because of the size effects, local material relation determined with experiments is not applicable to large shell elements. Therefore, a numerical method is outlined to determine the effect of element size on the macroscopic response of large structural shell elements until fracture initiation. Macroscopic response is determined by introducing averaging unit into the numerical model over which volume averaged equivalent stress and plastic strain are evaluated. Three different stress states are considered in this investigation: uniaxial, plane strain and equi-biaxial tension. The results demonstrate that fracture strain is highly sensitive to size effects in uniaxial tension whereas in plane strain or equi-biaxial tension size effects are much weaker. In uniaxial and plane strain tension the fracture strain for large shell elements approaches the Swift diffuse necking condition.     

Modelling of crack growth by fracture damage zone

The strain energy density (SED) criterion is applied for analyzing the full range of mixed mode fracture from tensile to shear loading. A fracture damage zone (FDZ) local to the crack tip is defined and discussed in connection with the influence of crack geometry, loading and local material property. The size of FDZ tends to change continuously from statically to cyclically applied load conditions. It can be estimated from the uniaxial mechanical properties of the material. Both experimental and analytical results are examined for subcritical crack growth under static loading that depends on the type steel structures the fracture behavior of which could be represented by a single curve for the given specimen geometry.