MESHLESS METHOD FOR 2D MIXED-MODE CRACK PROPAGATION BASED ON VORONOI CELL

A meshless method integrated with linear elastic fracture mechanics (LEFM) is presented for 2D mixed-mode crack propagation analysis. The domain is divided automatically into sub-domains based on Voronoi cells, which are used for quadrature for the potential energy. The continuous crack propagation is simulated with an incremental crack-extension method which assumes a piecewise linear discretization of the unknown crack path. For each increment of the crack extension, the meshless method is applied to carry out a stress analysis of the cracked structure. The J-integral, which can be decomposed into mode I and mode II for mixed-mode crack, is used for the evaluation of the stress intensity factors (SIFs). The crack-propagation direction, predicted on an incremental basis, is computed by a criterion defined in terms of the SIFs. The flowchart of the proposed procedure is presented and two numerical problems are analyzed with this method. The meshless results agree well with the experimental ones, which validates the accuracy and efficiency of the method.     

Minimum theorems in incremental linear elastic fracture mechanics

The crack propagation problem for linear elastic fracture mechanics has been studied by several authors exploiting its analogy with standard dissipative systems theory (see e.g. (Nemat-Nasser et al., 1980, Nguyen, 2000, Maugin, 1992, Bourdin et al., 2008, Salvadori, 2008). This approach is here further advanced, by noting that Stress Intensity Factors (SIFs) asymptotic expansion (Amestoy et al., 1986, Amestoy and Leblond, 1992) enjoys a Colonnetti’s decomposition (Colonnetti, 1918, Colonnetti, 1950) interpretation. As a consequence, minimum theorems are derived in terms of crack tip “quasi static velocity”. They are reminiscent of Ceradini’s theorem (Ceradini, 1965, Ceradini, 1966) in plasticity.     

弹塑性双材料界面裂纹的渐近分析

本文通过精确的数学分析,对于遵循塑性形变理论的幂硬化材料界面裂纹,求得了裂纹面面力自由和裂纹面无摩擦接触两种情况下的分离变量形式的全连续HRR 型奇性渐近解,这种全连续的奇性渐近解只对特殊的混合参数M'才存在.对任意指定的混合参数M',我们进一步求得了含弱间断的分离变量形式的HRR 型奇性渐近解(?)我们得到的所有解均保证了界面处的面力连续条件和位移连续条件,且不出现弹性双材料界面裂纹问题中所常见的应力振荡奇性和裂纹面相互嵌入的不合理现象.     

损伤材料裂纹尖端附近的应力场

本文导出了损伤材料的全量理论,导出了全量公式中H的渐近表达式;最后得到损伤材料平面应变条件下的裂纹尖端的应力应变场。     

Stress field of a damaged material near the crack tip

In this paper, a deformation theory of plasticity for damaged materials is proposed. An asymptotic expression forH near a crack tip is obtained. Finally, the stress and strain fields near the crack tip are presented.     

Failure analysis of stainless steel at elevated temperatures

In this paper, particular emphasis has been put on gathering information on the phenomena that take place at the crack tip of a crack propagating at 1100°F. Since the experimental program was directed toward studying crack propagation in tubing, the tests were conducted on rings.From the experimentally obtained data and from the correlation with the theoretically predicted values, the following picture emerges for the fracture behavior with full plasticity present. There is a region surrounding the crack tip where very large plastic deformations take place. This region is surrounded by a much larger region where the loading is nearly proportional and the behavior can be predicted well by the results of the deformation theory of plasticity and the theory of singularity fields. As the crack propagation initiates, there is a drastic change in the crack-tip configuration. The crack tip does not blunt and a fairly sharp crack-tip region is observed. The crack tip carries a large deformation field of a far more localized nature than that observed at the initiation of the crack growth.Paper was presented at 1978 SESA Spring Meeting held in Wichita, KS on May 14–19.     

The role of macroscopic hardening and individual length-scales on crack tip stress elevation from phenomenological strain gradient plasticity

This paper quantifies the effect of strain gradient plasticity (SGP) on crack tip stress elevation for a broad range of applied loading conditions and constitutive model parameters, including both macroscopic hardening parameters and individual material length-scales controlling gradient effects. Finite element simulations incorporating the Fleck-Hutchinson SGP theory are presented for an asymptotically sharp stationary crack. Results identify fundamental scaling relationships describing (i) the physical length-scales over which strain gradients are prominent, and (ii) the degree of stress elevation over conventional Hutchinson-Rice-Rosengren (HRR) fields. Results illustrate that the three length-scale theory predicts much larger SGP effects than the single length-scale theory. Critically, the first length-scale parameter dominates SGP stress elevation: this suggests that SGP effects in fracture can be predicted using the length-scales extracted from nanoindentation, which exhibits similar behavior. Transitional loading/material parameters are identified that establish regimes of SGP relevance: this provides the foundation for the rational application of SGP when developing new micromechanical models of crack tip damage mechanisms and associated subcritical crack propagation behavior in structural alloys.     

Asymptotic fields for interface crack in elastic-plastic material

Exact mathematical analyses are presented for interface crack between dissimilar elastic-plastic materials. The deformation theory of plasticity is used. For two kinds of boundary conditions on crack faces: (1) traction free and (2) frictionless contact, the asymptotic separable solutions of the HRR type with full continuity are obtained, which exist only for special mixity parameterM ^p. For any assignedM ^p, the separable solutions of the HRR type which contained weak discontinued line are further obtained. All of our results not only satisfy the continuity of displacements and that of tractions on the interface, but also they are free of oscillatory singularity and interpenetration of crack faces.This investigation is supported by the National Natural Science Foundation of China     

金属材料疲劳损伤的宏细观理论

工程结构的疲劳损伤发展过程经历了由初始缺陷的形成、裂纹的稳态扩展直到最后失效的不同发展阶段,通常疲劳损伤的演化可以概括为以下几个阶段:(1) 亚结构和微观结构的变化引起永久损伤的形成,产生微观裂纹;(2) 微观缺陷的长大会合形成主裂纹;(3) 主裂纹稳态扩展;(4) 结构失稳或完全失效.首先论述了疲劳裂纹扩展的物理机制,并从细观和宏观两个方面总结了处理疲劳裂纹问题的最新研究成果,对位错力学在处理短裂纹扩展问题中的应用,以及无位错区(DFZ)在疲劳裂纹扩展中的作用进行了较详细讨论.      

EXPERIMENTAL AND THEORETICAL INVESTIGATIONS ON THE VELOCITY OSCILLATIONS OF DYNAMIC CRACK PROPAGATING IN BRITTLE MATERIAL TENSION

设计了一种精确测量裂纹在预拉伸带板中的传播速度的实验装置, 系统研究了裂纹在受不同预加载荷作用的不同尺寸的有机玻璃 板中的传播行为.实验结果表明:在一个细长、上下表面固定的带板中, 裂纹速度分为加速和稳定2个阶段.在稳定速度阶段, 裂纹平均速度v₀ 是预加载荷在板中储存的弹性能Wh的增函数.由于此时裂纹处于自相似传播阶段, 可以认为材料的动态断裂能G_c是裂纹传播速度v₀的增函数, 即材料存在"速度增韧性".当裂纹传播速度达到一定阈值, 裂纹的传播速度出现明显的振荡现象, 裂纹的振荡周期与断裂面出现的周期性沟槽的尺度一致.在更高的预加能量下, 裂纹传播路径出现弯曲、微分岔以及宏观分岔现象.建立了一个描述裂纹在带板中的直线传播行为的动力学模型, 并用这个模型模拟裂纹在传播过程中的速度振荡现象.     

CTS试件中复合型疲劳裂纹扩展

针对复合型循环载荷作用下的金属构件中的裂纹扩展问题进行了实验分析和理论建模. 首先 采用紧凑拉剪试件(CTS)和 Richard研制的复合型载荷加载装置，对承受复合型循环载荷的裂纹进行了实验研究. 实验选择了两种金属材料试件，分别承受3种形式的复合型循环载荷的作用，在裂纹尖端具 有相同的初始应力场强度的条件下考察复合型循环载荷对裂纹扩展规律的影响. 实验结果表明，疲劳裂纹的扩展速率与加载角度有关. 对于同样金属材料的试件，当裂尖处 初始应力场强度相等时，载荷越接近于II型，裂纹增长速率越快. 采用等效应力强度 因子(I型和II型应力强度因子的组合)、裂纹扩展速率及复合强度等参数，以实验数据为 基础，建立了一个疲劳裂纹扩展模型，用来预测裂纹在不同模式疲劳载荷作用下的扩展速率. 为验证其有效性，该模型被应用于钢制试件的数值模拟计算中. 实验结果与模拟计算曲线保 持一致，表明该模型可以用来估算带裂纹金属构件的寿命.     

复合型裂纹断裂和扩展速率试验夹具及裂纹长度测量方法

本文设计了复合型裂纹断裂和扩展试验夹具及试样,借助此夹具可以在拉压疲劳试验机上进行多种复合型裂纹断裂及扩展速率试验,针对此夹具和试样提出了复合型裂纹长度测量的显微镜直读比拟法,并应用设计的夹具和提出的裂纹长度测量方法的MTSnew810上进行了多种复合型裂纹扩展速率试验,获得了复合型裂纹扩展的a-N曲线及一些新的结果。     

模拟裂纹扩展的单位分解扩展无网格法

单位分解扩展无网格法(PUEM)是一种求解不连续问题的新型无网格方法.其基于单位分解思想,通过在传统无网格法的近似函数中加入扩展项来反映由裂纹所产生的不连续位移场.详细描述了水平集方法,PUEM不连续近似函数的构造及控制方程的离散.针对裂纹扩展问题,提出了一种十分简单的水平集更新算法;讨论了不同的节点数、高斯积分阶次以及围线积分区域对应力强度因子计算结果的影响,并给出了合理的参数;模拟了边裂纹和中心裂纹的扩展问题,并与XFEM的数值结果进行了比较.数值算例表明,本文方法具有较高的计算精度,是模拟裂纹扩展非常有效的方法,具有广阔的应用前景.     

各向异性对平板裂纹扩展路径的影响研究

近场动力学理论克服了经典连续介质力学在模拟裂纹扩展方面的不足。本文基于微梁键构建了一般各向异性近场动力学平面模型,并探讨了各向异性对于裂纹扩展路径的影响。首先,建立一般各向异性的微梁键,并基于插值法建立了一般各向异性近场动力学平面模型的应变能密度表达式;然后,利用应变能密度互等原理求解出近场动力学平面本构模型的一般各向异性参数;最后,通过带初始切口的平板断裂实验研究了不同各向异性参数对于平板裂纹扩展路径的影响。     

动载荷作用下裂隙岩体的止裂机理分析

为深层次了解裂隙岩体在动载荷作用下的动态断裂特性及止裂机理,采用TWSRC（tunnel with single radial crack）构型进行中低速冲击实验,选择砂岩作为原材料制作裂隙岩体试样,以落锤冲击试验装置与裂纹扩展计实验系统对裂纹的动态起裂、扩展及止裂过程进行全过程监测,重点研究动态破裂过程的破裂行为及止裂现象。使用有限差分法程序进行数值模拟,验证冲击实验结果的科学性与准确性。研究发现:裂隙岩体的动态断裂过程是由起裂加速-高速扩展-缓慢减速-止裂-再次起裂加速-再次高速扩展等多次循环的过程构成,且止裂区间尺寸为微秒量级;裂隙岩体止裂位置的穿晶断裂比例远小于初始起裂点,青砂岩动态断裂过程的穿晶断裂比例稍大于黑砂岩;裂隙岩体中止裂点再次起裂所需的能量,远小于预制裂纹初始起裂所需要的能量。     

Plasticity induced fatigue crack growth retardation model for steel elements reinforced by composite patch

Fatigue tests on notched steel plates reinforced by composite patch showed that the application of carbon fiber reinforced polymers (CFRP) strips with pretension of the overlays prior to bonding. This resulted in a significant amount of additional fatigue life. In particular, the pre-tension produces a compressive field in the steel plate which reduces the stress ratio that enhances crack growth retardation. The fatigue crack propagation rate is postulated to be a function of the effective strain energy density factor range. Fatigue crack growth data showed that standard crack growth retardation model cannot be used to evaluate the minimum effective stress. Hence, an ad hoc plasticity model is introduced and validated using experimental results. The proposed technique is an extension of the well know Newman’s model. The bridging effect due to the reinforcing strips is analytically modeled in order to estimate the reduction of crack opening displacement and finally the magnification of the crack growth retardation. Numerical and experimental results match well and show a significant influence of the pre-tension level on the expected fatigue crack growth rate of a reinforced steel plate.     

对裂纹扩展规律Paris公式物理本质的探讨

首先讨论了著名力学家K.Krausz和A.S.Krausz关于Paris公式物理本质研究的成果，从材料的微观结构和裂纹尖端的应力场出发，应用位错动力学理论，热激活能理论和速率过程理论对疲劳裂纹扩展规律进行了微观到宏观的探讨。最终推导出疲劳裂纹扩展速率的一个解析表示式，该式严格地定了Paris公式的两个试验常数，赋予了Paris公式明确的物理意义，从而真实地揭示了Paris公式的物理本质，为这一经验的普遍规律奠定了理论基础。     

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。     

单边裂纹通电瞬间裂尖处应力场的复变函数解

本文应用复变函数中的Schwarz-Christoffel变换方法，在具单边裂纹的导电薄板通电瞬间温度场复变函数解的基础上，推导出用复变函数表示的应力场的表达式，并且给出算例，通过理论计算得知；当对具有单边裂纹的导电薄板通入适当密度的电流时，裂尖处温度急剧升高并熔化便裂尖变钝。同时，在裂尖周围形成了有利于遏制裂纹扩展的压应力场，有效地防止了裂纹沿其主方向和其它方向延伸。从理论上证明了电磁热效应在裂尖处产生高温形成焊口的同时，压应力场的形成是遏制裂纹扩展的主要因素之一。理论计算结果与实验结果比较吻合，为这一止裂方法的应用打下了理论基础。     

Temperature field at time of pulse current discharge in metal structure with elliptical embedding crack

Theoretical analysis is made on the temperature field at the time of pulse current discharge in a metal structure with an elliptical embedding crack. In finding the temperature field, analogy between the current flow through an elliptical embedding crack and the fluid flow through a barrier is made based on the similarity principle. Boundary conditions derived from this theory are introduced so that the distribution of current density and the temperature field expressions can be obtained. The study provides a theoretic basis to the applications of stopping spatial crack with electromagnetic heating.