A concise review about fracture assessments of brittle solids with V-notches

A concise review of recent studies about the fracture assessments of elastic brittle solid materials containing V-notches is presented. In this preliminary and brief survey, elastic stress distributions in V-notched solids are discussed first. The concept of notch stress intensity factor is introduced. Combine the digital image correlation method with numerical computation techniques to analyze the stress distribution near the notches. Fracture criteria such as strain energy density, J-integral, theory of critical distance are used.However, various new materials are developed in different engineering fields, thus, the establishment of reliable and accurate material strength theory or failure criterion is imperative. Therefore, predicting fracture for various modern materials would require more experiments to infer material dependent parameters in the local fracture model.     

脆性材料裂纹与损伤相互作用的试验研究

为研究岩石等脆性材料的损伤对裂纹动态扩展的影响,采用动态透射焦散线方法,模拟脆性材料裂纹与损伤相互作用的动态过程,进行多种损伤情况下有机玻璃试样裂纹动态扩展过程试验研究,讨论不同类型损伤对脆性材料裂纹动态扩展规律的影响和裂纹与损伤相互作用的机制。试验结果表明:不同类型的损伤对裂纹扩展影响不同,除裂纹型损伤外,其他几种类型损伤的存在均会引起裂纹扩展出现短暂停滞,停滞时间与损伤的尺寸及距离扩展裂纹路径的距离有关系;裂纹扩展路径上存在单个圆孔时会影响裂纹扩展速度,裂纹消耗能量增大;而多个圆孔情况下,材料局部弱化,裂纹扩展速度增大,而裂纹扩展消耗能量降低;表面损伤和局部贯通裂纹的尺寸、相对裂纹扩展路径距离等影响裂纹扩展速度,但能量消耗并未增大;对称裂纹相互竞争,同步扩展,裂纹尖端位置或裂纹长度的微小差别(例如裂纹长度相差3.68%)就会对裂纹起裂产生明显影响,导致2个裂纹起裂时间不同,裂纹扩展以后,先起裂的裂纹尖端应力强度因子大说明能量集中到相应裂纹尖端,从而越有利于该裂纹的扩展,扩展速度也就越大(相差约38.9%),相同条件下裂纹扩展所消耗的能量也越大。     

模拟脆性材料动态裂纹扩展的非连续变形分析方法

非连续变形分析方法(DDA)属于隐式离散元法,通过引入虚拟节理可以模拟材料从连续到破坏全过程.尝试将DDA方法应用于脆性材料动态裂纹扩展问题.采用基于Voronoi多边形离散的DDA方法进行模拟.由于Voronoi多边形会存在较多短边,采用原始DDA程序计算时短边会优先发生破坏.针对该问题通过引入均布弹簧算法,在一定程...     

钢框架梁柱节点脆性断裂原因及新型节点形式

针对节点受力机理的复杂性,分析了地震中钢框架梁柱节点脆性断裂的原因,并提出了新型的节点形式,如加强型节点和削弱型节点,以防止节点发生脆性破坏,改善节点的抗震性能。     

从应用角度考虑塑料压力管的力学破坏问题

建立和完善快速裂纹增长危险和长期寿命—长期强度性能的质量监控体系对塑料压力管持续发展至关重要。聚氯乙烯管材的抗冲击性能、Ｃ 环法断裂韧性、聚乙烯管的断裂伸长率数据在应用中都有明确的针对性。拉伸屈服强度、打压爆破压力、Ｉｚｏｄ 或Ｃｈａｒｐｙ 抗冲击强度、Ｂｅｌｌ 法耐环境应力开裂性数据等与塑料压力管实际应用关系不大。塑料管的耐老化性能及焊接质量与力学破坏有关,是需要重视的问题。塑料压力管在其适用范围内,有足够的承压能力和刚性,满足实际使用的需要。     

A continuous/discontinuous deformation analysis (CDDA) method based on deformable blocks for fracture modeling

In the framework of finite element meshes, a novel continuous/discontinuous deformation analysis (CDDA) method is proposed in this paper for modeling of crack problems. In the present CDDA, simple polynomial interpolations are defined at the deformable block elements, and a link element is employed to connect the adjacent block elements. The CDDA is particularly suitable for modeling the fracture propagation because the switch from continuous deformation analysis to discontinuous deformation analysis is natural and convenient without additional procedures. The SIFs (stress intensity factors) for various types of cracks, such as kinked cracks or curved cracks, can be easily computed in the CDDA by using the virtual crack extension technique (VCET). Both the formulation and implementation of the VCET in CDDA are simple and straightforward. Numerical examples indicate that the present CDDA can obtain high accuracy in SIF results with simple polynomial interpolations and insensitive to mesh sizes, and can automatically simulate the crack propagation without degrading accuracy.     

数字图像技术在节理岩体裂纹扩展试验中的应用研究

含倾斜裂纹的岩石在单轴压缩下,会发生翼裂纹扩展并逐步损伤破坏。对含预制裂纹的类岩石脆性试件进行单轴压缩试验,采用两台高分辨率相机连续捕捉图像,经过数字图像相关技术(DIC)处理,得到了试件的全局应变场演化过程图,试验结果表明:当荷载达到一定阶段,裂纹端部观察到了明显的微破裂区,其形状为绕裂纹尖端逆时针转动82°的椭圆;荷载增大到最大荷载的85.6%时,微破裂聚集成核,端部开始形成宏观翼裂纹,裂纹的扩展过程就是高应变区不断蔓延的过程,也是微破裂不断发育、成核的过程;次生微破裂区以及反翼微破裂区发育缓慢,且形成过程中也受到了拉伸应力作用,翼裂纹是试件的主要破坏模式。最后基于线弹性断裂力学,比较了裂纹尖端周围应力和应变的变化规律,给出了采用应变方法分析裂纹起裂扩展的理论依据,并且验证了DIC系统试验结果的可靠性。     

Phenomena and theoretical analysis for the failure of brittle rocks

Rockburst, an unstable failure of brittle rocks, has been greatly concerned in rock mechanics and rock engineering for more than 100 years. The current understanding on the mechanical mechanism of rockburst is based on the Coulomb theory, i.e. compressive-shear failure theory. This paper illustrates a series of tensile and tensile-shear fracture phenomena of rockburst, and proposes a methodology for the analysis of fracture mode and its energy dissipation process based on Griffith theory. It is believed that: (1) the fracture modes of rockburst should include compressive-shear, tensile-shear and pure tensile failures; (2) the rupture angle of rock mass decreases with the occurrence of tensile stress; (3) the proportion of kinetic energy in the released strain energy from a rockburst may be much larger than that transferred into surface energy; and (4) the understanding on the tensile and tensile-shear failure modes of rockburst may change the basic thinking of rockburst control, i.e. from keeping the reduction in initial compressive stress σ3 to restricting the creation of secondary tensile stress.     

场富集有限元方法模拟多裂纹起裂、扩展和连接过程

研究含多裂纹岩石的力学响应和裂纹行为对岩体结构的设计与稳定性分析具有重要的指导意义。提出了场富集有限元方法研究脆性岩石材料中多裂纹的演化规律,包括裂纹的起裂、扩展和连接过程。提出了多裂纹在扩展过程中出现的各种交汇情况的解决方案。场富集有限元方法可以直接处理复杂的交叉裂纹,而不需要像扩展有限元一样引入额外的富集函数。通过数值算例,充分说明了场富集有限元方法在处理各种复杂裂纹系统扩展演化方面的能力。     

类岩石脆性材料非闭合裂纹的Ⅰ-Ⅱ压剪复合型断裂准则研究

实际工程中,结构体裂纹常处于拉剪和压剪复合受力状态,研究适合于复合型裂纹的断裂准则和裂纹扩展机理具有重要的理论意义和实用价值。以Ⅰ-Ⅱ复合型裂纹为研究对象,基于线弹性理论,在考虑裂纹几何特征及受力形式的基础上,系统介绍了裂纹应力强度因子（SIF）的理论解。提出了适用于Ⅱ型断裂的径向剪应力准则和双剪应力准则。对于Ⅰ-Ⅱ复合型裂纹,提出用等效Ⅰ、Ⅱ型SIF比值与Ⅰ、Ⅱ型断裂韧度比值的关系判定裂纹断裂类型,并分别选择适合于Ⅰ、Ⅱ型断裂的断裂准则,计算了裂纹断裂扩展理论角度。理论断裂角与预制非闭合裂纹类岩石脆性材料压剪断裂试验结果符合得较好。     

离散大块体断裂破坏分析方法研究

一般离散单元计算方法(包括DDA方法)受离散块体低阶线性位移近似的限制,在模拟开裂过程时,需要将大部分实际上连续的区域离散化,离散方式对分析结果有显著影响。为了建模时利用真实结构面来构造块体系统,提高大块体位移应力分析精度,有必要引进新的位移近似假设。本项研究在块体内引入无网格法位移模式,以离散节点位移自由度代替原基本块体自由度,并在此基础上进行块体内非贯穿裂纹扩展和强度破坏分析。为此建立的无网格法裂纹扩展分析算法,采用满足单位分解条件的特殊增强型函数表达裂纹周围应力场的非连续、奇异特性,将对应的扩展自由度动态映射到裂纹周围的节点上,统一按DDA法隐式迭代方式求解,实现块体裂纹扩展和强度分析,相关算例结果显示该算法是合理有效的。     

相场断裂模型分步算法在ABAQUS中的实现

 首次基于ABAQUS平台实现相场断裂模型的分步算法,利用UMAT/VUMAT子程序接口对非线性平衡方程进行隐式/显式求解,提出位移场和相场的分步求解算法。准静态加载下的I和II型裂缝扩展问题、冲击荷载作用下的I型动态裂缝分叉和II型动态裂缝扩展问题,计算所得结果与已有文献和试验成果基本一致,说明了方法的可靠性;同时,对岩石力学领域中的双平行翼型裂缝相交和动态裂缝三维曲面扩展等问题,也利用该方法进行模拟。计算实例表明,结构储存的较高弹性应变能是脆性材料动态裂缝分叉的主要原因,而相场断裂模型是一种能够计算包括裂缝起裂、相交、分叉和三维曲面扩展的有效断裂计算方法,借助通用有限元平台可以方便地实现其分步算法。     

页岩水力压裂裂缝形态的试验研究

为深入认识页岩储层水力裂缝延伸规律及其空间形态,采用真三轴岩土工程模型试验机、压裂泵压伺服控制系统、Disp声发射定位系统和工业CT扫描技术,建立了一套室内页岩水力压裂大型物理模拟试验方法,并通过试验后页岩试样水力裂缝的延伸与空间展布规律,初步探讨了页岩水力压裂网状裂缝的形成机理。结果表明：裂缝延伸时泵压曲线典型的锯齿状波动与裂缝网络的形成密切相关,是页岩体积压裂的一个明显特征。页岩层理面的发育程度、泵压大小和地应力状态对裂缝形态有显著影响,水力裂缝在层理面内的分叉、转向进而沟通天然裂缝是形成裂缝网络的关键,而层理面过弱或过强都不利于网状裂缝的形成;对层理面胶结强度适中的地层,地应力对裂缝的延伸有较大影响;在低排量且维持较低泵压时,裂缝易于转向,且更易形成网状裂缝,而达到体积压裂。建立的页岩水力压裂物理模拟试验方法及试验结果可为页岩气压裂优化设计等提供技术支持。     

基于3D-ILC单轴拉伸双平行内裂纹扩展规律研究

多裂纹相互作用是断裂力学研究的重要内容,但是针对单轴拉伸下的三维多内裂纹相互作用研究较少。基于3D-ILC技术,在完整立方体试件中生成三维双平行内裂纹,对不同错距d开展单轴拉伸试验,分析了断裂过程、应力云纹、起裂与破坏荷载及断口特征,基于M积分和MTS准则开展裂纹扩展路径及相互作用模拟。结果表明：①内裂纹错距为2 mm时相互“吸引”,错距为6与10 mm先相互“吸引”后“排斥”;②三维双内裂纹单轴拉伸下具有“合并分界”、“漏斗状”特征等断裂形态,其中裂纹中心侧发生I-II型复合断裂,外侧发生纯I型断裂;③初始应力云纹在预制裂纹尖端呈现“花瓣状”,裂纹相互“吸引”过程中应力云纹在中心侧裂纹尖端呈现“括弧状”;④试样强度与裂纹间错距成正比,错距为2,6,10 mm抗拉强度相对完整试样下降百分比分别为63.39%,50.79%,41.09%。起裂荷载与最终破坏荷载的比值分别为12.92%,15.16%,13.57%;⑤基于M积分,得出内裂纹I、II型应力强度因子分布规律,基于MTS裂纹扩展判据,实现三维双内纹的相互作用扩展全过程数值模拟,与试验一致。研究结果为三维双平行内裂纹相互作用研究提供试验与理论基础。     

基于MLS的数值流形法模拟多裂纹扩展

 含多裂纹的脆性材料在伺服加载下的响应分析对结构进行性能评估具有重要意义。得益于数学覆盖和物理覆盖这两套覆盖系统,数值流形法能够很自然地模拟多裂纹的萌生与扩展。为了更好地模拟二维裂纹的交叉、汇合,采用基于移动最小二乘插值(MLS)的数值流形法(NMM)进行模拟,并对包含裂尖的物理片进行自由度扩充来模拟裂尖的奇异性,裂纹扩展中裂尖可以停留在背景网格的内部。针对多裂纹扩展中的一些数值问题,给出了相应的解决方案,并提出一个简单、能近似满足断裂韧度的多裂纹扩展算法。对几个典型多裂纹算例进行了裂纹扩展分析,结果表明所提算法是有效且鲁棒的。     

基于数字图像与数值计算的节理岩体锚固效应研究

为了研究锚杆对裂隙岩体的加固作用,通过自主研发的数字图像相关(DIC)试验技术和离散元(DEM)数值计算方法,对预置裂隙岩体试样锚固前后进行测试。从细观层次量化分析了加载过程中两类岩体(未锚固和锚固岩体)裂隙的起裂、扩展等特征,对比了数字图像测量的位移场,应变场和裂隙张开度(COD)以及数值计算得到的裂隙发育数量,区域分布和扩展方向。结果表明:基于DIC测量软件,可精确进行岩体非接触的无损测量,并且能够监测出岩体锚固这种内部隐蔽的过程;加固岩体的锚杆与裂隙交叉位置出现应变集中成核现象,定量地说明了岩体加固对裂隙的抑制作用;同时还得出岩体加固可以改变裂隙扩展类型和主裂隙发育方向。     

Implementation aspects of a phase-field approach for brittle fracture

This paper provides a comprehensive overview of a phase-field model of fracture in solid mechanics setting. We start reviewing the potential energy governing the whole process of fracture including crack initiation, branching or merging. Then, a discretization of system of equation is derived, in which the key aspect is that for the correctness of fracture phenomena, a split into tensile and compressive terms of the strain energy is performed, which allows crack to occur in tension, not in compression. For numerical analysis, standard finite element shape functions are used for both primary fields including displacements and phase field. A staggered scheme which solves the two fields of the problem separately is utilized for solution step and illustrated with a segment of Python code.     

Shear fracture (Mode II) of brittle rock

Mode II fracture initiation and propagation plays an important role under certain loading conditions in rock fracture mechanics. Under pure tensile, pure shear, tension- and compression-shear loading, the maximum Mode I stress intensity factor, K_Imax, is always larger than the maximum Mode II stress intensity factor, K_IImax. For brittle materials, Mode I fracture toughness, K_IC, is usually smaller than Mode II fracture toughness, K_IIC. Therefore, K_Imax reaches K_IC before K_IImax reaches K_IIC, which inevitably leads to Mode I fracture. Due to inexistence of Mode II fracture under pure shear, tension- and compression-shear loading, classical mixed mode fracture criteria can only predict Mode I fracture but not Mode II fracture. A new mixed mode fracture criterion has been established for predicting Mode I or Mode II fracture of brittle materials. It is based on the examination of Mode I and Mode II stress intensity factors on the arbitrary plane θ,K_I(θ) and K_II(θ), varying with θ(−180°θ+180°), no matter what kind of loading condition is applied. Mode I fracture occurs when (K_IImax/K_Imax)<1 or 1<(K_IImax/K_Imax)<(K_IIC/K_IC) and K_Imax=K_IC at θ_IC. Mode II fracture occurs when (K_IImax/K_Imax)>(K_IIC/K_IC) and K_IImax=K_IIC at θ_IIC. The validity of the new criterion is demonstrated by experimental results of shear-box testing.Shear-box test of cubic specimen is a potential method for determining Mode II fracture toughness K_IIC of rock since it can create a favorable condition for Mode II fracture, i.e. K_IImax is always 2–3 times larger than K_Imax and reaches K_IIC before K_Imax reaches K_IC. The size effect on K_IIC for single- and double-notched specimens has been studied for different specimen thickness B, dimensionless notch length a/W (or 2a/W) and notch inclination angle α. The test results show that K_IIC decreases as B increases and becomes a constant when B is equal to or larger than W for both the single- and double-notched specimens. When a/W (or 2a/W) increases, K_IIC decreases and approaches a limit. The α has a minor effect on K_IIC when α is within 65–75°. Specimen dimensions for obtaining a reliable and reproducible value of K_IIC under shear-box testing are presented. Numerical results demonstrate that under the shear-box loading condition, tensile stress around the notch tip can be effectively restrained by the compressive loading. At peak load, the maximum normal stress is smaller than the tensile strength of rock, while the maximum shear stress is larger than the shear strength in the presence of compressive stress, which results in shear failure.