基于单元破裂的岩石裂纹扩展模拟方法

传统离散元方法在处理破裂问题时, 采用界面上的准则进行判断, 裂纹只能沿着单元边界扩展. 当物理问题存在宏观或微观裂隙时, 在界面上应用准则具有其合理性; 而裂纹沿着单元边界扩展, 使得裂纹路径受网格影响较大, 扩展方向受到限制. 针对上述情况, 可以基于单元破裂的方式, 构建连续- 非连续单元法, 并应用于岩石裂纹扩展问题的模拟. 该方法在连续计算时, 将单元离散为具有物理意义的弹簧系统, 在局部坐标系下由弹簧特征长度、面积求解单元变形和应力, 通过更新局部坐标系和弹簧特征量, 可进一步计算块体大位移、大转动, 连续问题计算结果与有限元一致, 同时提高了计算效率. 在此基础上, 引入最大拉应力与莫尔—库伦的复合准则, 判断单元破裂状态和破裂方向, 并采用局部块体切割的方式, 在单元内形成初始裂纹. 裂纹两侧相应增加新的计算节点, 同时引入内聚力模型描述裂纹两侧的法向、切向作用与张开度及滑移变形之间的关系. 按此方式, 裂纹尖端处的扩展路径可穿过单元内部和单元边界, 在扩展方向的选取上更为准确. 最后, 通过三点弯曲梁、单切口平板拉伸、双切口试样等典型数值试验, 模拟裂纹在拉伸、压剪等各种应力状态下的扩展问题, 并对岩石单轴压缩试验的破坏过程进行模拟, 分析裂纹形成与应力—应变曲线各阶段之间的对应关系. 结果表明: 连续—非连续单元法通过单元内部破裂的方式, 可以显示模拟裂纹萌生、扩展、贯通直至形成宏观裂缝的过程.      

Application of scaled boundary finite element method in static and dynamic fracture problems

The scaled boundary finite element method (SBFEM) is a recently developed numerical method combining advantages of both finite element methods (FEM) and boundary element methods (BEM) and with its own special features as well. One of the most prominent advantages is its capability of calculating stress intensity factors (SIFs) directly from the stress solutions whose singularities at crack tips are analytically represented. This advantage is taken in this study to model static and dynamic fracture problems. For static problems, a remeshing algorithm as simple as used in the BEM is developed while retaining the generality and flexibility of the FEM. Fully-automatic modelling of the mixed-mode crack propagation is then realised by combining the remeshing algorithm with a propagation criterion. For dynamic fracture problems, a newly developed series-increasing solution to the SBFEM governing equations in the frequency domain is applied to calculate dynamic SIFs. Three plane problems are modelled. The numerical results show that the SBFEM can accurately predict static and dynamic SIFs, cracking paths and load-displacement curves, using only a fraction of degrees of freedom generally needed by the traditional finite element methods.The project supported by the National Natural Science Foundation of China (50579081) and the Australian Research Council (DP0452681)The English text was polished by Keren Wang.     

Numerical modeling of discrete multi-crack growth applied to pattern formation in geological brittle media

We describe a finite element-based method to propagate multiple fractures simultaneously. The algorithm is iterative and it simulates sub-critical quasi-static crack propagation. The matrix is homogeneous and isotropic, and behaves linear elastically. The algorithmic cornerstones are a failure criterion, a propagation criterion, and a propagation angle. Fracture geometries are kept track of independently of the mesh allowing geometric handling of fracture arrest, closure, and coalescence. Fracture aperture is an emergent property of the model. The mesh is adaptively remeshed to capture variations in the geometry and displacement field. Generated patterns reproduce observed crack paths in physical experiments. Algorithm efficiency scales linearly. The model reproduces en-echelon crack linkage, fracture hooking, and orthogonal tip approximation patterns. Our numerical experiments closely match physical experiments. Remeshing consumes <2% of the total computational time demonstrating current computational capabilities allow for discrete crack propagation to be viable for multiple crack propagation.     

页岩水力压裂中多簇裂缝扩展的全耦合模拟

水平井和水力压裂是页岩气开发中的关键技术。对水力压裂中多簇裂缝同时扩展的物理过程进行了数值模拟。采用扩展有限元法(XFEM)模拟岩石中裂缝沿着任意路径扩展,采用有限体积法(FVM)模拟裂缝中流体的流动,并且考虑井筒中流体流动以及在各簇裂缝间的流量动态分配。通过牛顿迭代对全耦合物理过程进行数值求解,重点研究了初始长度不同的两条裂缝的扩展过程,证明较大的射孔摩阻能促进两条裂缝的同时扩展。并通过算例证明了本方法的精度和有效性。     

岩石偏心圆孔单裂纹平台圆盘的动态裂纹扩展与止裂

针对平台圆环构型的优点, 提出偏心圆孔单裂纹平台圆盘(cracked eccentrically holed flattened disc, CEHFD), 该试样具有更长的断裂路径。利用霍普金森压杆加载系统, 径向冲击CEHFD试样, 完成Ⅰ型动态断裂实验。砂岩试样表面粘贴应变片和裂纹扩展计, 用于监测裂纹动态起裂、扩展和止裂的全过程。实验表明, 在整个断裂过程中, 裂纹非匀速扩展, 裂纹扩展速度在裂纹起裂后加速上升, 在裂纹止裂前有明显的减速, 与地震时断层的动态破裂全过程完全吻合。采用实验-数值-解析法得到动态应力强度因子, 其时间历程呈现先增大后减小的趋势。根据断裂过程不同时刻, 得到相应的动态起裂韧度、扩展韧度及止裂韧度。在动态断裂全过程中, 动态扩展韧度为速度的函数, 变化趋势与速度一致, 随着时间先增大后减小; 动态起裂韧度大于动态止裂韧度, 止裂韧度随着裂纹最大扩展速度的增大而降低, 并且有较大的离散性。     

冲击载荷作用下准脆性连续体破裂问题研究

在连续体动力问题中心差分算法的基础上,引进准脆性材料的破坏准则,节点单元的破裂算法、离散子块的接触搜索及接触力计算等,对准脆性连续体在冲击载荷作用下的破裂破坏问题进行数值模拟.通过数值算例,给出结构在冲击载荷作用下裂纹产生和扩展的模拟结果图,初步验证程序的正确性和可应用性,为模拟连续体转变为非连续体这一复杂物理过程提出新方法和新思路.     

混凝土双K断裂参数计算的半解析有限元法

混凝土裂缝扩展的双$K$断裂准则，用于描述混凝土结构裂缝的起裂、稳定扩 展和失稳断裂. 其相应的双$K$断裂参数(起裂断裂韧度$K_{\rm IC}^{\rm ini} $和失 稳断裂韧度$K_{\rm IC}^{\rm un}$)一般通过简便的试验和基于虚拟裂缝扩展粘 聚力的解析方法确定. 利用平面扇形域哈 密顿体系的方程，通过分离变量法及共轭辛本征函数向量展开法，以解析的方法推导出基于混 凝土虚拟裂缝扩展线性粘聚力模型的平面裂缝解析元列式. 将该解析元与有限元相结合，构成 半解析的有限元法，可求解任意结构几何形状的混凝土平面裂缝双$K$断裂参数的计算问题. 数值计算结果表明半解析有限元法对该类问题的求解是十分有效的.     

整体加筋壁板裂纹扩展轨迹模拟及控制分析

应用有限元方法并结合裂纹扩展方向判据分析模拟了飞机整体加筋壁板裂纹的扩展轨迹,与实验结果对比证明此方法的有效性;并通过壳单元模型和粘聚区渐进损伤模型详细讨论了影响整体加筋壁板裂纹扩展的筋条参数,研究了壁板筋条对裂纹止裂的控制,并对不同参数下裂纹的应力强度因子和扩展情况作对比分析.文章所述方法和结论对于飞机整体加筋壁板的损伤容限设计具有指导意义.     

Combination of fracture and damage mechanics for numerical failure analysis

A new approach for the analysis of crack propagation in brittle materials is proposed, which is based on a combination of fracture mechanics and continuum damage mechanics within the context of the finite element method. The approach combines the accuracy of singular crack-tip elements from fracture mechanics theories with the flexibility of crack representation by softening zones in damage mechanics formulations. A super element is constructed in which the typical elements are joined together. The crack propagation is decided on either of two fracture criteria; one criterion is based on the energy release rate or the J-integral, the other on the largest principal stress in the crack-tip region. Contrary to many damage mechanics methods, the combined fracture⧹damage approach is not sensitive to variations in the finite element division. Applications to situations of mixed-mode crack propagation in both two- and three-dimensional problems reveal that the calculated crack paths are independent of the element size and the element orientation and are accurate within one element from the theoretical (curvilinear) crack paths.     

致密砂岩巷道模型试件动态起裂及止裂全过程分析

为了开展在不同冲击载荷作用下巷道围岩内裂纹的起裂、扩展及止裂等问题，以可调速冲击试验机进行动态加载试验，采用致密青砂岩制作裂纹巷道模型试件，并利用裂纹扩展计分别记录了动态起裂、扩展、止裂等时刻，对裂纹扩展速度的变化规律进行分析；随后采用AUTODYN有限差分法软件进行相应的数值模拟，数值模拟得到的裂纹扩展路径与试验结果基本一致。经过两者对比分析可知:随着冲击载荷作用的增加，裂纹平均扩展速度逐渐增大，随后趋于稳定值；预制裂纹的起裂时间随着冲击速度载荷的增加而逐渐降低，并在稳定值上下波动；随着冲击速度载荷的增加，裂纹扩展路径过程中的止裂时段逐渐变短。     

An investigation of the step-wise propagation of a mode-II fracture in a poroelastic medium

In this paper we use an eXtended Finite Element Method based model for the simulation of shear fracture in fully saturated porous materials. The fracture is incorporated as a strong discontinuity in the displacement field by exploiting the partition of unity property of finite element shape functions. The pressure is assumed to be continuous across the fracture. However, the pressure gradient, i.e. the fluid flow, can be discontinuous. The failure process is described by the cohesive zone approach and a Tresca fracture condition without dilatancy. We investigate the propagation of a shear fracture under compression asking the question whether or not a Tresca criterion can result in stepwise propagation in a poroelastic medium. In order to evaluate possible numerical artefacts, we also look at the influence of the element size and the magnitude of a time increment. The performance of the X-FEM model and the influence of the pore pressure on the fracture propagation are addressed. Our simulations do not show evidence for step wise progression in mode II failure.     

采用压缩单裂纹圆孔板确定岩石动态起裂、扩展和止裂韧度

爆炸、冲击、地震等人为或自然灾害不可避免,经常造成大量土木工程设施的破坏,因此岩石在动态载荷作用下的行为受到特别关注.岩石动态断裂韧度是评价岩石抵抗裂纹动态起裂、扩展和止裂性能的材料参数,开展岩石动态断裂韧度测试方法的研究对相关理论基础和实验技术的要求较高.岩石动态断裂韧度分为动态起裂、动态扩展、动态止裂三种,虽然关于动态起裂和动态扩展的研究已有一些成果,对岩石动态止裂的研究仍是一个难题,至今几乎无人问津.研究表明,在分离式霍普金森压杆撞击压缩单裂纹圆孔板岩石试样的I型动态断裂试验中,动态起裂、扩展、止裂的全过程可以由黏贴在压缩单裂纹圆孔板试样上的裂纹扩展计监测,岩石的动态起裂、扩展、止裂韧度可以用实验-数值-解析法确定.特别值得一提的是首次测出了岩石的动态止裂韧度.裂纹扩展计信号还显示,压缩单裂纹圆孔板在止裂后,停止的裂纹还会再次动态起裂、扩展并超出裂纹扩展计的检测范围.从能量的角度分析了动态止裂的过程,指出测试动态止裂韧度时要注意的一些问题.结果显示,岩石动态起裂韧度和动态扩展韧度分别随动态加载率和裂纹扩展速度的增大而增大,岩石动态起裂韧度略大于动态止裂韧度.      

冲击加载下巷道内裂纹的扩展特性及破坏行为

为了开展含预制裂纹的巷道模型试样在冲击载荷下的动态断裂响应实验,选用青砂岩作为模型材料制作巷道模型试样,以可调速落锤冲击实验机作为冲击加载装置进行试样的动态断裂实验,分析冲击载荷作用下的巷道内裂纹的扩展规律。采用裂纹扩展计及应变片测试系统监测裂纹的起裂时间、扩展速度及止裂时间,并借助于AUTODYN、ABAQUS有限元数值分析软件对实验模型进行数值模拟,计算裂纹的动态起裂韧度、动态扩展韧度、动态止裂韧度等断裂参数。结果表明:巷道内裂纹在扩展路径过程中存在着明显的止裂现象;采用实验-数值方法能够较好地得出裂纹的起裂韧度、扩展韧度和止裂韧度等参数。另外,对止裂现象进行了初步的分析,讨论了试样内应力反射波与透射波对止裂问题的影响。     

Crack kinking in sandwich structures under three-point bending

Sandwich beams under three-point bending containing cracks in the core material very close to the upper skin interface are investigated. The cracks considered parallel or with an imperceptible inclination to the longitudinal beam axis and at different distances from the upper skin interface, are analyzed with static non-linear elastic two and three dimensional finite element analyses. From the proposed analyses stress intensity factors are calculated using linear elastic fracture mechanics. It is demonstrated that the crack propagation on the compression side of the core is mainly subjected in shear. The strain energy density criterion is used in order to determine the angle of kinking of the crack into the core.     

A simple model of the double cantilever beam crack propagation specimen

A very simple model of the double cantilever beam (dcb) dynamic crack propagation specimen is studied. The main assumption on which the model is based is that the arms of the dcb specimen deform as shear beams. The particular problem studied is the dynamic growth of a sharp crack from a blunt pre-crack with the ends of the specimen arms held at a fixed separation distance. It is demonstrated that this simple model predicts crack motion which is qualitatively consistent with the results of more detailed numerical analyses of the problem and with experimental results. The analysis employs an energy balance crack propagation criterion and both constant specific fracture energy and a class of crack speed dependent fracture energies are considered. Among the features exhibited by the model is that, for constant specific fracture energy, the crack tip speed is constant from initiation up to arrest. On the other hand, for the same geometry and loading conditions, but a strongly crack speed dependent specific fracture energy, the crack speed decreases gradually between fracture initiation and crack arrest.     

基于碎点法的动态断裂分析

工程中的冲击防护结构在撞击、爆炸等冲击载荷下可能发生动态断裂并最终破坏, 抑制结构的动态断裂是提升结构防护能力的重要手段, 为此需要准确预测结构在动态载荷下的断裂行为. 数值仿真是预测动态断裂的重要手段, 然而当前工程中常用的有限元法在模拟断裂方面仍存在网格畸变和难以显式引入裂纹等问题. 碎点法是近年来提出的一种不连续型伽辽金弱形式无网格方法, 适合模拟断裂问题, 本文提出一种显式动力学格式的碎点法并将该方法应用于动态断裂分析. 一方面, 碎点法参考弱形式无网格类方法, 将求解域离散为空间中的节点和子域, 并基于支持域内的节点群构造子域的位移试函数, 因此该方法的子域具有抵抗畸变的能力. 另一方面, 碎点法参考间断伽辽金有限元法, 使用分片连续的位移试函数, 并引入内部界面数值通量修正保证方法的一致性和稳定性, 因此该方法易于在结构中显式引入裂纹. 本文首先介绍碎点法的核心思想和离散形式, 接着推导了动力学碎点法弱形式动量方程, 然后建立了碎点法的显式动力学求解格式, 最后通过算例验证动力学碎点法预测应力波传播和动态断裂行为的能力.      

广义扩展有限元法及其在裂纹扩展分析中的应用

结合广义有限元法(GFEM)和扩展有限元法(XFEM)的特点,提出了一种新的数值方法——广义扩展有限元法(GXFEM)。阐述了广义扩展有限元法的基本原理,对相关公式进行推导,探讨数值实施中需注意的重要问题,给出利用广义扩展有限元法进行断裂分析时应力强度因子的计算方法,编写了广义扩展有限元法程序。通过算例进行了应力强度因子的计算,模拟了结构裂纹的扩展过程。算例结果表明,利用广义扩展有限元法计算裂纹扩展问题,不需要进行过密的网格划分,且网格在裂纹扩展后无需重新剖分,具有相当高的计算精度。     

Incubation time based testing of materials

Some principal features of the behavior of materials subjected to pulsed actions are common for a number of seemingly quite different physical processes, such as dynamic fracture (starting cracks and scabbing), cavitation in liquids, and electrical breakdown in solids. In this paper, we analyze examples illustrating typical dynamic effects inherent in these processes. We propose a unified interpretation for the fracture of solids and liquids and electrical breakdown in insulators using the structural-time approach based on the concept of the fracture incubation time. The examples of different physical processes considered in the paper show the fundamental importance of investigating incubation processes preparing abrupt structural changes (fracture and phase transitions) in continua under intense pulsed actions. The fracture incubation time is evidently a universal basic characteristic of the dynamic strength and must become one of the main material parameters to be experimentally determined (measured).     

冲击载荷作用下圆孔缺陷对裂纹动态扩展行为的影响规律

空腔和裂纹缺陷通常共存于深部地下岩体中,它们共同影响着岩体的结构安全性与稳定性。为了探究动力扰动载荷下圆形空腔对裂隙岩体内裂纹扩展行为的影响规律,提出了不同圆孔倾角的直裂纹空腔圆弧开口试件（circular opening specimen with straight crack cavity, COSSCC）,利用自制大型落锤冲击实验装置进行动态加载实验,同时采用裂纹扩展计系统测试了裂纹的动态起裂时刻与裂纹扩展速度等各种断裂力学参数,随后采用有限差分软件Autodyn进行裂纹扩展路径与圆孔周围应力场的数值分析,并采用有限元软件Abaqus计算裂纹的动态起裂韧度与裂纹扩展过程中的动态扩展韧度。结果表明:（1）当圆孔倾角θ小于10°时,裂纹扩展路径会偏折并穿过圆孔表面;当圆孔倾角θ为20°与30°时,裂纹扩展路径向圆孔方向发生偏折但不会穿过圆孔,圆孔具有明显的裂纹扩展引导作用; 当圆孔倾角θ为40°与50°时,裂纹扩展路径不会发生偏折,圆孔引导作用明显减弱。（2）当裂纹扩展路径达到圆孔空腔附近时,裂纹尖端的拉伸应力区与圆孔边缘的拉伸应力区发生重合,此时裂纹扩展速度显著增大,裂纹动态断裂韧度显著减小。（3）裂纹的偏折方向与裂纹尖端最大周向应力的方向基本一致。（4）裂纹动态断裂韧度始终小于裂纹起裂韧度,且裂纹动态断裂韧度与裂纹动态扩展速度呈负相关关系。裂纹动态扩展速度越大,裂纹动态断裂韧度越小。