Hertzian fracture at unloading

Hertzian fracture through indentation of flat float glass specimens by steel balls has been examined experimentally. Initiation of cone cracks has been observed and failure loads together with contact and fracture radii determined at monotonically increasing load but also during unloading phases. Contact of dissimilar elastic solids under decreasing load may cause crack inception triggered by finite interface friction and accordingly the coefficient of friction was determined by two different methods. In order to make relevant predictions of experimental findings, a robust computational procedure has been developed to determine global and local field values in particular at unloading at finite friction. It was found that at continued loading it is possible to specify in advance how the contact domain divides into invariant regions of stick and slip. The maximum tensile stress was found to occur at the free surface just outside the contact contour, the relative distance depending on the different elastic compliance properties and the coefficient of friction. In contrast, at unloading invariance properties are lost and stick/slip regions proved to be severely history dependant and in particular with an opposed frictional shear stress at the contact boundary region. This causes an increase of the maximum tensile stress at the contour under progressive unloading. Predictions of loads to cause crack initiation during full cycles were made based on a critical stress fracture criterion and proved to be favourable as compared to the experimental results.     

脆性断裂的非局部力学理论

本文提出一种脆性材料断裂的非局部力学理论,内容包括:Ⅰ、Ⅱ、Ⅲ型Griffith裂纹的非局部弹性应力场,裂纹尖端邻域非局部弹性应力场的渐近形式,脆性开裂的最大拉应力准则。文中给出了这种理论应用于三种基本型裂纹和Ⅰ-Ⅱ、Ⅰ-Ⅲ复合型裂纹临界开裂条件的计算结果,并把它们与一些试验资料和最小应变能密度因子理论进行了对比。     

A nonlocal theory for brittle fracture

In this paper, a nonlocal theory of fracture for brittle materials has been systematically developed, which is composed of the nonlocal elastic stress fields of Griffith cracks of mode-I, II and III, the asymptotic forms of the stress fields at the neighborhood of the crack tips, and the maximum tensile stress criterion for brittle fracture. As an application of the theory, the fracture criteria of cracks of mode-I, II, III and mixed mode I–II, I–III are given in detail and compared with some experimental data and the theoretical results of minimum strain energy density factor.     

断裂力学判据的评述

从Inglis 和Griffith 的著名论文到Irwin 和Rice 等的奠基性贡献,对断裂力学中的线弹性断裂力学的K判据,界面断裂力学的G判据,和弹塑性断裂力学的J 判据作了扼要的综述. 介绍了在界面断裂力学G判据的基础上提出的界面断裂力学的K判据,以说明断裂力学的判据存在改进的可能性. 在综述中归纳出断裂力学判据中目前还没有较好解决的几个问题. 在总结以往断裂力学研究经验的基础上,指出裂纹端应力奇异性的源是对断裂力学判据存在的问题作进一步研究的切入点. 探讨了裂纹端应变间断的奇点是裂纹端应力奇异性的源的问题,从而对裂纹端应力强度因子的物理意义进行了讨论. 最后,阐述了进行可靠的裂纹端应力场的弹塑性分析是改进弹塑性断裂力学判据的关键,而进行可靠的裂纹端应力场的弹塑性分析的前提是要通过裂纹端应力奇异性的源的研究来获得作用在裂纹端的造成裂纹端应变间断的有限值应力.      

Stress and failure analysis of a glass-epoxy composite plate with a circular hole

Experimental and finite-element analyses are presented for the anisotropic states of stress, strain and fracture of a glass-epoxy plate containing a circular hole and subjected to uniaxial tension. Strains were experimentally measured using foil gages, moiré and birefringent coating. Stresses are computed in the linear range from the measured strains. While the hole reduces the plate strength by a factor of two, the maximum tensile strain at fracture is greater than the ultimate strain in a plate without a hole. Fracture consists of crack initiation at the hole boundary but off the horizontal axis. Away from the hole, failure is accompanied by considerable delamination. Discontinuous crack propagation is present.     

近场动力学在断裂力学领域的研究进展

近场动力学采用非局部积分计算节点内力, 利用统一数学框架描述空间连续与非连续, 避免了非连续区局部空间导数引起的应力奇异, 数值上具有无网格属性, 可自然模拟材料结构的断裂问题. 本文概述了近场动力学的弹性本构力模型, 系统介绍了近场动力学临界伸长率、临界能量密度以及材料强度相关的键失效准则. 详细介绍了近场动力学在断裂力学领域的研究进展, 包括断裂参数能量释放率与应力强度因子的求解、J积分、混合型裂纹、弹塑性断裂、黏聚力模型、动态断裂、材料界面断裂以及疲劳裂纹扩展等. 最后讨论了断裂问题近场动力学研究的发展方向.      

Estimation of Fracture Toughness of Metallic Materials Using Instrumented Indentation: Critical Indentation Stress and Strain Model

We propose a generalized approach based on fracture mechanics and contact mechanics to estimate the fracture toughness in metallic materials from instrumented indentation testing. Models were developed for brittle and ductile fracture. Different criteria were applied to each model to determine the critical fracture point during indentation. For brittle fracture, the critical fracture point was defined in terms of the critical mean pressure; for ductile fracture, the critical fracture point was derived from fracture strain and critical plastic zone size. Each fracture criterion was used to determine the indentation fracture energy corresponding to the fracture energy required for crack extension. The fracture toughness was estimated for various metallic materials using each model and compared with standard fracture toughness tests.     

裂纹动态起始问题的研究进展

力图就前人提出的冲击载荷下裂纹的起始判据进行较全面的综述．这些较著名的判据有：（１）动态应力强度因子判据；（２）动态Ｊ积分判据；（３）最小作用量判据；（４）极小作用时间判据等．简要介绍了近年来有关裂纹在冲击载荷（特别是短脉冲）下动态起始的一些重要实验和实验中所发现的一些重要结论．实验公认，一般对于小范围屈服而言，材料的动态断裂韧性随加载（应变）率的提高而减小，此时材料的断裂形式为解理型；而对于大范围屈服则韧性随加载率的提高而增大，此时材料的断裂形式为纤维型．特别指出，Ｂｒｏｗｎ大学的平板撞击实验表明，裂纹在起始时，观察到一个不再满足二分之一阶奇异性的“尖峰”，按Ｃｌｉｆｔｏｎ和Ｆｒｅｕｎｄ等人所给出的模型，在裂纹起始断裂瞬间，在裂纹顶端会突然形成一个小洞，该洞的半径作为一个参数等于二相粒子的间距．     

Stress pulses emitted during fracture in tension

This paper is concerned with the stress pulses which are emitted during the tensile fracture of glass rods of rectangular cross-section. Both a longitudinal and a flexural pulse were observed. The experimentally recorded pulse shapes are found to be in close agreement with those predicted by using a theoretical model proposed by Phillips and Kolsky. It is shown that the deviations noted in the earlier work with circular glass rods are due, primarily, to the effect of crack bifurcation and not to the geometry of the cross-section. Further, the phenomenon of crack bifunction is found to depend upon the magnitude of the applied stress required to initiate fracture, and to be essentially independent of the section geometry.     

Mixed mode fatigue crack growth in test coupons made from 2024-T3 aluminum

In this paper, two different fracture criteria are applied to determine the crack trajectory or angle of crack propagation in test specimens containing inclined cracks emanating from open holes. Also, different crack growth rate models are assumed for each criterion. The maximum principal stress criterion is used with a crack growth-rate equation based on an effective stress intensity factor. The strain energy density criterion is used with a crack growth-rate equation corresponding to an effective strain energy density factor. The crack growth-rate models for each criterion were constructed using unpublished fatigue crack growth data for 2024-T3 aluminum.     

Combined compressive-shear fracture of rocks

Investigations are made on the combined compressive-shear fracture of rocks. Three types of specimens are considered. They involve no precracking, fatigue crack, and mechanically cut crack. The critical shear stress and critical stress intensity factor of diorite-porphyrite are obtained.Fracture pattern in rocks under compressive-shear loading is determined experimentally based upon which fracture criterion is assumed. Significant information on the stability of rock mass and mechanism of tectonic fracture can be gained.     

Fracture mechanics analysis of thin coatings under plane-strain indentation

A combined experimental/analytical work is carried out to elucidate the fracture resistance of a thin, hard coating bonded to a semi-infinite substrate due to indentation by a cylindrical surface. The bending of the coating under the softer substrate induces concentrated tensile stress regions at the lower and upper surfaces of the coating, from which cracks may ensue. The evolution of such damage in a model transparent system (glass/polycarbonate) is viewed in situ from below and from the side of the specimen. The critical load needed to initiate a crack on the lower coating surface generally increase proportionally to the coatings thickness, d. An interesting departure from this trend occurs for thin coatings, where the fracture load, although marred by a large scatter, increases somewhat with decreasing d. The fracture data for the upper coating surface are limited to relatively thick coatings due to the recurrence of premature failure from the coating edges. The behavior in this range is similar to that for the lower surface crack, albeit with an order of magnitude greater fracture resistance.A fracture mechanics analysis in conjunction with FEM is performed to elucidate the stress intensity factors responsible for crack propagation. A crack normal to the coating surface is assumed to emanate either from the lower or upper surface of the coating. A major feature of the solution is the occurrence of a bending-induced compression stress field over a region ahead of the crack tip. This effect, which become more dominant as the ratio between the contact length and the coating thickness is increased, tends to delay the onset of crack propagation, especially for the lower surface crack. Consequently, in applications associated with large indenters, thin and/or tough coatings and stiff substrates, cracking from the upper coating surface may precede that from the lower surface. An interesting feature of this crack shielding mechanism is that when the coating surface contains a distribution of flaws rather than a single crack, small flaws in this population may be more detrimental than large ones. Incorporation of these aspects into the analysis leads to a good correlation with the test results. In the special case of line loading, which constitutes a lower bound for the critical loads, a closed-form, approximate solution for the stress intensity factors or the critical loads are obtained.Plane-strain indentation, although less common than spherical indentation, allows for characterizing the fracture resistance of opaque films through observation from the specimen edge. This approach is not easily implemented to thin films (i.e., less than about a hundred microns), however.     

Nonlocal theory solution of two collinear cracks in the functionally graded materials

In this paper, the interaction of two collinear cracks in functionally graded materials subjected to a uniform anti-plane shear loading is investigated by means of nonlocal theory. The traditional concepts of the nonlocal theory are extended to solve the fracture problem of functionally graded materials. To make the analysis tractable, it is assumed that the shear modulus varies exponentially with the coordinate vertical to the crack. By use of the Fourier transform, the problem can be solved with the help of a pair of triple integral equations, in which the unknown variable is the displacement on the crack surfaces. To solve the triple integral equations, the displacement on the crack surfaces is expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularity is present near the crack tips. The nonlocal elastic solutions yield a finite hoop stress at the crack tip, thus allowing us to use the maximum stress as a fracture criterion in functionally graded materials. The magnitude of the finite stress field depends on the crack length, the distance between two cracks, the parameter describing the functionally graded materials and the lattice parameter of the materials.     

基于GMTS准则的岩石复合型断裂机理研究

使用国际岩石力学协会规定的半圆盘岩石试件,加工不同倾角的直裂纹试样,通过三点弯曲加载试验得到不同I-II复合比断裂的断裂韧性和初始断裂角．传统裂纹扩展准则忽视了常数项即T应力及更高阶项的影响,导致该扩展准则的理论预测结果存在较大缺陷,本文通过考虑常数项,建立广义最大周向应力准则(GMTS)．在此基础上,分别采用传统的裂纹扩展准则和考虑T应力的裂纹扩展准则预测不同复合比裂纹的断裂韧性和初始扩展角,然后对比理论预测结果和实验结果．分析可得：常数项即T应力对断裂的临界应力强度因子和初始断裂角的影响是不可忽略的,且II型断裂占比较大时影响更大,广义最大周向应力准则预测值与实验测试结果之间的误差最小．     

U形切口的有限断裂准则

有限断裂力学准则综合了应力和能量参数,假设裂纹或切口端部有限裂纹长度的增长．特别地,该有限裂纹的长度不是材料的基本常数,而是与构件的结构有关．基于U形切口两种形式：点方式和线方式有限断裂准则,对文献中的铝合金U形切口三点弯曲断裂实验进行了分析验证．一方面基于材料的断裂韧度和抗拉强度,预测切口件断裂载荷;另一方面根据几组不同的切口根部半径及其对应的临界切口应力强度因子,同时估算材料的断裂参数：断裂韧度和抗拉强度．将点方式和线方式两种不同形式有限断裂准则的预测结果,与平均周向应力准则、最大周向应力准则以及文献中相关结果进行了比较得出：无论是预测断裂载荷还是估算材料断裂参数,线方式有限断裂准则,与文献中相关结果比较吻合,尤其是估算的断裂韧度精度较高．     

Pitting formation under rolling contact

The mechanism of pitting caused by rolling contact is analyzed using the fracture mechanics approach. The governing factors are the initial crack length, crack angle, contact force, friction, strain hardened layer, and the hydraulic pressure of trapped fluid acting on the crack surface. Mode I and II stress intensity and the strain energy density factors are calculated by application of the two-dimensional finite element method. The strain energy density criterion is applied to show that shallow angle crack under small rolling contact force and friction enhances the probability of pitting under the roller’s running surface. The presence of a strain hardened surface layer also tends to affect the fracture behavior. The analytical results agree well with the experimental observations.     

Non-local criteria for the borehole problem: Gradient Elasticity versus Finite Fracture Mechanics

Two nonlocal approaches are applied to the borehole geometry, herein simply modelled as a circular hole in an infinite elastic medium, subjected to remote biaxial loading and/or internal pressure. The former approach lies within the framework of Gradient Elasticity (GE). Its characteristic is nonlocal in the elastic material behaviour and local in the failure criterion, hence simply related to the stress concentration factor. The latter approach is the Finite Fracture Mechanics (FFM), a well-consolidated model within the framework of brittle fracture. Its characteristic is local in the elastic material behaviour and non-local in the fracture criterion, since crack onset occurs when two (stress and energy) conditions in front of the stress concentration point are simultaneously met. Although the two approaches have a completely different origin, they present some similarities, both involving a characteristic length. Notably, they lead to almost identical critical load predictions as far as the two internal lengths are properly related. A comparison with experimental data available in the literature is also provided.

     

Material plasticity dependence of mixed mode fatigue crack growth in commonly used engineering materials

In this paper, an investigation of fatigue crack propagation in rectangular plates containing an inclined surface crack is presented. A criterion for the three-dimensional stress state is proposed to predict fatigue crack initiation angles. It is assumed that the direction of crack initiation coincides with the direction of the minimum radius of the plastic zone defined by the von Mises yield criterion. The maximum energy release rate criterion, i.e., G_max criterion, is extended to study the fatigue crack growth characteristics of mixed mode cracks. A modification has been made to this criterion to implement the consideration of the plastic strain energy. Subsequently, this concept is applied to predict crack growth due to fatigue loads. Experiments for checking the theoretical predictions from the proposed criterion have been conducted. The results obtained are compared with those obtained using the commonly employed fracture criteria and the test data.     

Dynamic interfacial debonding initiation induced by an incident crack

When a crack propagates towards a weak interface, interface debonding may occur before the incident crack reaches the interface. This phenomenon refers to the “Cook–Gordon mechanism”. In this investigation, an equivalent dynamic Cook–Gordon mechanism is studied both experimentally and analytically. Two strength-based criteria incorporating dynamic fracture mechanics analysis are proposed to predict the initiation location of interface debonding ahead of a dynamic incident crack. As validation, a comparison is made between the analytical predictions and experimental measurements. Results show that the strength-based criteria can effectively predict the initiation of interface debonding. Meanwhile, effects of the stress intensity factor and the T stress of the incident crack, on the interfacial debonding initiation are investigated. It is concluded that high-stress intensity factors of the incident cracks will easily induce interfacial debonding initiation, and changing the T stress is an effective way to control interfacial debonding initiation. Furthermore, high-interfacial tensile strengths rather than shear strengths, tend to suppress interfacial debonding initiation induced by a mode-I incident crack.