Experimental and Theoretical Assessment of Brittle Fracture in Engineering Components Containing a Sharp V-Notch

A criterion was proposed to predict brittle fracture in engineering components containing sharp V-shaped notches and subjected to mixed mode I/II loading. The criterion, called SV-MTS, was developed based on the maximum tangential stress (MTS) criterion proposed originally for analyzing crack problems. The curves which are obtained from the SV-MTS criterion could be used conveniently to predict the fracture resistance and also the notch bifurcation angle in sharp V-notched components under pure mode II and also mixed mode loading. To evaluate the validity of the proposed criterion, a set of fracture tests were conducted on a new test specimen, called sharp V-notched Brazilian disc (SV-BD), under mixed mode loading conditions. It is shown that the experimental results obtained from PMMA specimens are in very good agreement with the curves of SV-MTS criterion.     

Fracture analysis of U-notched disc-type graphite specimens under mixed mode loading

Fracture phenomenon was investigated both experimentally and theoretically for a type of coarse-grained polycrystalline graphite weakened by a U-shaped notch under mixed mode loading. First, 36 disc-type graphite specimens containing a central U-notch, so called in literature as the U-notched Brazilian disc (UNBD), were prepared for four different notch tip radii and the fracture tests were performed under mode I and mixed mode I/II loading conditions. Then, the experimentally obtained fracture loads and the fracture initiation angles were predicted by using the U-notched maximum tangential stress (UMTS) and the newly formulated U-notched mean stress (UMS) fracture criteria. Both the criteria were developed in the form of the fracture curves and the curves of fracture initiation angle, in terms of the notch stress intensity factors (NSIFs). The results showed that while the criteria could predict successfully the experimental notch fracture toughness values, the UMS criterion provides slightly better predictions than the UMTS criterion, particularly for shear-dominant deformations. Also, found in this research was that the curves of fracture initiation angle were almost identical for the two criteria which both could predict well the experimental results.     

On determination of mode II fracture toughness using semi-circular bend specimen

The cracked semi-circular specimen subjected to three-point bending has been recognized as an appropriate test specimen for conducting mode I, mode II and mixed mode I/II fracture tests in brittle materials. The manufacturing and pre-cracking of the specimen are simple. No complicated loading fixture is also required for a fracture test. However, almost all of the theoretical criteria available for mixed mode brittle fracture fail to predict the experimentally determined mode II fracture toughness obtained from the semi-circular bend (SCB) specimen. In this paper, a modified maximum tangential stress criterion is used for calculating mode II fracture toughness K_IIc in terms of mode I fracture toughness K_Ic. The modified criterion is used for predicting the reported values of mode II fracture toughness for two brittle materials: a rock material (Johnstone) and a brittle polymer (PMMA). It is shown that the modified criterion provides very good predictions for experimental results.     

Mixed mode (I and II) crack tip fields in bulk metallic glasses

Stationary crack tip fields in bulk metallic glasses under mixed mode (I and II) loading are studied through detailed finite element simulations assuming plane strain, small scale yielding conditions. The influence of internal friction or pressure sensitivity on the plastic zones, notch deformation, stress and plastic strain fields is examined for different mode mixities. Under mixed mode loading, the notch deforms into a shape such that one part of its surface sharpens while the other part blunts. Increase in mode II component of loading dramatically enhances the normalized plastic zone size, lowers the stresses but significantly elevates the plastic strain levels near the notch tip. Higher internal friction reduces the peak tangential stress but increases the plastic strain and stretching near the blunted part of the notch. The simulated shear bands are straight and extend over a long distance ahead of the notch tip under mode II dominant loading. The possible variations of fracture toughness with mode mixity corresponding to failure by brittle micro-cracking and ductile shear banding are predicted employing two simple fracture criteria. The salient results from finite element simulations are validated by comparison with those from mixed mode (I and II) fracture experiments on a Zr-based bulk metallic glass.     

Fracture-mode map of brittle coatings: Theoretical development and experimental verification

Brittle coatings, upon sufficiently high indentation load, tend to fracture through either ring cracking or radial cracking. In this paper, we systematically study the factors determining the fracture modes of bilayer material under indentation. By analyzing the stress field developed in a coating/substrate bilayer under indentation in combination with the application of the maximum-tensile-stress fracture criterion, we show that the fracture mode of brittle coatings due to indentation is determined synergistically by two dimensionless parameters being functions of the mechanical properties of coating and substrate, coating thickness and indenter tip radius. Such dependence can be graphically depicted by a diagram called ‘fracture-mode map’, whereby the fracture modes can be directly predicated based on these two dimensionless parameters. Experimental verification of the fracture-mode map is carried out by examining the fracture modes of fused quartz/cement bilayer materials under indentation. The experimental observation exhibits good agreement with the prediction by the fracture-mode map. Our finding in this paper may not only shed light on the mechanics accounting for the fracture modes of brittle coatings in bilayer structures but also pave a new avenue to combating catastrophic damage through fracture mode control.     

Determination of mode II fracture toughness for U-shaped notches using Brazilian disc specimen

A brittle fracture criterion is proposed for predicting fracture toughness of U-shaped notches under pure mode II loading. The criterion, called UMTS, is developed based on the maximum tangential stress (MTS) criterion. The UMTS criterion can be generally used for determining the mode II fracture toughness of U-notched components as well as the fracture initiation angle in U-shaped notches under pure mode II loading. To verify the validity of the proposed criterion, a set of experiments were carried out on the U-notched Brazilian disc (UNBD) specimens made of PMMA and also soda-lime glass. It is shown that there is a good agreement between the results of the UMTS criterion and the experimental results both for fracture toughness and for the fracture initiation angle under pure mode II conditions.     

Analysis of fracture initiation angle in some cracked ceramics using the generalized maximum tangential stress criterion

Brittle fracture in ceramics sometimes occurs under combined opening-sliding (or mixed mode I/II) crack deformation. In this paper, a generalized maximum tangential stress criterion is employed for predicting the fracture initiation angle under mixed mode I/II loading in some brittle ceramics including alumina, zirconia, soda lime glass and three silicon based ceramics. The experimental results reported for the fracture angles in these ceramics have been obtained from fracture tests on the centrally cracked circular disc (often called the Brazilian disc). Very good agreement is shown to exist between the experimental results and the theoretical predictions. According to the fracture model, the mixed mode fracture angle is strongly dependent on the elastic T-stress in the tested ceramics. The negative T-stress that exists in the Brazilian disc specimen can be the main influencing parameter for decreasing the fracture initiation angle in the investigated ceramics.     

Influence of the root radius of crack-like notches on the fracture load of brittle components

Narrow notches often cause damage that can lead to the destruction of components. The stress field in the vicinity of such crack-like notches in two-dimensional (2D) structures is similar to the stress field around equivalent cracks. Therefore similar investigations are necessary to predict the fracture load for components with cracks or narrow notches. Thus, the asymptotical stress field for a narrow notch with a rounded notch root is deduced from an Airy’s stress function. Based on this stress field a fracture criterion is developed. Comparing the theoretical fracture limit curves derived from the fracture criterion with experimental results it can be shown that for brittle material the local stress state at the fracture initiation point is the same for mode I, mixed-mode and mode II loading.     

Rectangular tensile sheet with a center notch root crack

This paper deals with the rectangular tensile sheet with a center notch crack. Such a crack problem is called a center notch crack problem for short. By using a hybrid displacement discontinuity method (a boundary element method) proposed recently by Yan, two center notch models are analyzed in detail. By changing the geometrical forms and parameters of the center notch, and by comparing the SIFs of the center notch crack problem with those of the center cracked plate tension specimen (CCT), which is a model frequently used in fracture mechanics, the effect of the geometrical forms and parameters of the center notch on the stress intensity factors (SIFs) of the center cracked plate tension specimen, is revealed. Some geometric characterestic parameters are introduced here, which are used to formulate the notch length and the branch crack length, which are to be determined in mechanical machining of the center cracked plate tension specimen. So we can say that the geometric characterestic parameters and the formulae used to determine the notch length and the branch crack length presented in this paper perhaps have some guidance role for mechanical machining of the center cracked plate tension specimen. In addition, the numerical investigation proves that the conventional angular notched specimen is much less sensitive to the size of notch than is the circular notched specimen.     

中心直裂纹平台巴西圆盘复合型动态应力强度因子

为了指导用中心直裂纹平台巴西圆盘(CSTFBD)试样进行岩石复合型动态断裂 试验,利用有限元法首先验证了文献中对中心直裂纹巴西圆盘(CSTBD)得到的有关结果,分析 比较了不同无量纲裂纹长度(即裂纹半长和圆盘半径之比)时两种圆盘的I, II型动态应力 强度因子的时间历程,发现两者的差异大部分在10{\%}以内,同时验证了该文数值方法的可 靠性. 然后讨论了CSTFBD试样I, II型动态应力强度因子的复合比、起裂角以及纯II型加 载角. 研究成果可为复合型动态断裂试验中CSTFBD试样的加工、试样上应变片的粘贴、起裂 方向和起裂时间的估计等提供参考.     

Mode II fracture-parameter estimates for concrete from beam specimens

At the present time, work on determination of fracture parameters for concrete subjected solely to mode I deformation states has advanced to the point where standard methods of testing and data evaluation have been proposed. Thus, many researchers are now considering the dual problems of (1) determination of fracture parameters for mode II deformation and (2) the need for this information (or put another way—the possible application of this information). In fact, the physical testing arrangements for mode II testing with no influence of mode I are not obvious; compromises must be made which will lead to approximations—perhaps fairly gross—in the estimates of mode II fracture parameters. Herein are presented experimental and analytical results for fracture parameters for beams loaded in antisymmetric four-point bending with a single-edge starter notch located in a region of high-shear and low-bending moment. This study complements another, presented elsewhere, in which beams in three-point bending were used with notches located off center. From this study, which included tests on 18 beam specimens, the following conclusions are reached. The beams must be tested in strain control. Crack initiation started in mode II but quickly changed to a mixed mode (although finite-element calculations indicate mode I is dominant). The fracture energy associated with the onset of unstable crack propagation is much larger than normally obtained for mode I—this is thought to be due to extensive aggregate interlock forces not present in normal bending or direct tension tests. Probably this type of testing arrangement is not suitable for determination of mode II fracture parameters because propagation does not occur under mode II conditions.     

Experimental and numerical investigation of concrete properties effects on fracture toughness under complex loading

Abstract

This article is presenting the common experimental specimen for determining the fracture toughness of the first pure mode and second pure mode. The Notched beam is chosen from a presented common specimen in the form of three-point flexure beam and four-point flexure beam that were built in the concrete laboratory. For prevention of cracks growth, a critical load of first pure mode and the second pure mode of each specimen computed. Obtained results are used for computing the fracture toughness. For the purpose of investigating the effective fracture parameters in the suggested specimen, finite element analysis on the mentioned geometry is performed. Obtained results show that different parameters are effective on the fracture toughness including crack length, cement percentage, water and the thickness of biggest used aggregate in the sand. Also with changing each of these parameters, the fracture mechanic properties are changed. Each of these effects is examined separately in this article and the conclusions presented in tables and figures.

Communicated by Dumitru Caruntu.     

Brittle fracture: Variation of fracture toughness with constraint and crack curving under mode I conditions

The effect of constraint on brittle fracture of solids under predominantly elastic deformation and mode I loading conditions is studied. Using different cracked specimen geometry, the variation of constraint is achieved in this work. Fracture tests of polymethyl methacrylate were performed using single edge notch, compact tension and double cantilever beam specimens to cover a bread range of constraint. The test data demonstrate that the apparent fracture toughness of the material varies with the specimen geometry or the constraint level. Theory is developed using the critical stress (strain) as the fracture criterion to show that this variation can be interpreted using the critical stress intensity factorK _Cand a second parameterT orA ₃,whereT andA ₃are the amplitudes of the second and the third term in the Williams series solution, respectively. The implication of this constraint effect to the ASTM fracture toughness value, crack tip opening displacement fracture criterion and energy release rateG _Cis discussed. Using the same critical stress (strain) as the fracture criterion, the theory further predicts crack curving or instability under mode I loading conditions. Experimental data are presented and compared with the theory.     

Fracture investigation at V-notch tip using coherent gradient sensing (CGS)

Local deformation field and fracture characterization of mode I V-notch tip are studied using coherent gradient sensing (CGS). First, the governing equations that relate to the CGS measurements and the elastic solution at mode I V-notch tip are derived in terms of the stress intensity factor, material constant, notch angle and fringe order. Then, a series of CGS fringe patterns of mode I V-notch are simulated, and the effects of the notch angle on the shape and size of CGS fringe pattern are analyzed. Finally, the local deformation field and fracture characterization of mode I V-notch tip with different V-notch angles are experimentally investigated using three-point-bending specimen via CGS method. The CGS interference fringe patterns obtained from experiments and simulations show a good agreement. The stress intensity factor obtained from CGS measurements shows a good agreement with finite element results under K-dominant assumption.     

Dynamic fracture toughness determined from load-point displacement

The paper presents a method to determine dynamic fracture toughness using a notched three-point bend specimen. With dynamic loading of a specimen there is a complex relation between the stress-intensity factor and the force applied to the specimen. This is due to effects of inertia, which have to be accounted for to evaluate a correct value of the stress-intensity factor. However, the stress-intensity factor is proportional to the load-point displacement if the fundamental mode of vibration is predominant in the specimen. The proportionality constant depends only on the geometry and stiffness of the specimen. In the present method we have measured the applied force and load-point displacement by a modified Hopkinson pressure bar, where two-point strain measurement has been used to evaluate force and displacement for times greater than the transit time for elastic waves in the Hopkinson bar. We have compared the method with the stress-intensity factor derived from strain measurement near the notch tip and good agreement was obtained. The method is well suited for high-temperature testing and results from fracture toughness tests of brittle materials at ambient and elevated temperatures are presented.     

各向异性编织CMC弯曲断裂失效模型

通过对缺口弯曲断裂试验的研究发现，编织CMC存在两种断裂失效模式：界面主导的和纤维束主导的失效模式．针对这两种模式建立了界面失效模型和纤维束断裂失效模型．界面失效模型用半经验方法处理弱界面和大编织角度的断裂强度问题；纤维束断裂失效模型采用解析方法处理较强界面和小角度的断裂强度问题，为含有缺口试件的弯曲强度预报打下了初步的理论基础．     

一种基于SHTB的Ⅱ型动态断裂实验技术

冲击剪切载荷作用下动态断裂韧性的测定是材料力学性能和断裂行为研究中重要组成部分.为了测定材料的Ⅱ型动态断裂韧性,许多学者采用不同的试样与实验方法进行了实验,但限于实验条件,裂纹断裂模式往往是I+Ⅱ复合型,而不是纯Ⅱ型,因而不能准确测得材料的Ⅱ型动态断裂韧性.鉴于此,本文基于分离式霍普金森拉杆(split Hopkinson tension bar,SHTB)实验技术,提出一种改进的紧凑拉伸剪切(modified compact tension shear,MCTS)试样,通过夹具对MCTS试样施加约束,从而保证试样按照纯Ⅱ型模式断裂.采用实验-数值方法对MCTS试样动态加载过程进行分析,将实验测得的波形输入有限元软件ANSYS-LSDYNA,得到了裂纹尖端应力强度因子-时间曲线,并与紧凑拉伸剪切(compact tension shear,CTS)试样进行了对比.同时采用数字图像相关法进行了实验,验证了有限元分析结果.结果表明,MCTS试样在整个加载过程中K_I K_Ⅱ,裂纹没有张开;而CTS试样在同样的加载过程中K_IK_Ⅱ,出现裂纹张开现象.这说明MCTS试样能够准确地测定材料的Ⅱ型动态断裂韧性,为材料动态力学测试提供了一种有效的实验技术.     

Particle flow study on strength and meso-mechanism of Brazilian splitting test for jointed rock mass

A discrete element method （DEM） called particle flow code （PFC2D） was used to construct a model for Brazilian disc splitting test in the present study. Based on the experimental results of intact Brazilian disc of rock-like material, a set of micro-parameters in PFC2D that reflected the macro-mechanical behavior of rock-like materials were obtained. And then PFC2D was used to simulate Brazilian splitting test for jointed rock mass specimens and specimen containing a central straight notch. The effect of joint angle and notch angle on the tensile strength and failure mode of jointed rock specimens was detailed analyzed. In order to reveal the meso-mechanical mechanism of crack coalescence, displacement trend lines were applied to analyze the displacement evolution during the crack initiation and propagation. The investigated conclusions can be described as follows. （1） The tensile strength of jointed rock mass disc specimen is dependent to the joint angle. As the joint angle increases, the tensile strength of jointed rock specimen takes on a nonlinear variance. （2） The tensile strength of jointed rock mass disc specimen containing a central straight notch distributes as a function of both joint angle and notch angle. （3） Three major failure modes, i.e., pure tensile failure, shear failure and mixed tension and shear failure mode are observed in jointed rock mass disc specimens under Brazilian test. （4） The notch angle roles on crack initiation and and joint angle play important propagation characteristics of jointed rock mass disc specimen containing a central straight notch under Brazilian test.     

A generalized stress intensity factor to be applied to rounded V-shaped notches

In the presence of sharp (zero radius) V-shaped notches the notch stress intensity factors (N-SIFs) quantify the intensities of the asymptotic linear elastic stress distributions. They are proportional to the limit of the mode I or II stress components multiplied by the distance powered 1 − λ_i from the notch tip, λ_i being Williams’ eigenvalues. When the notch tip radius is different from zero, the definition is no longer valid from a theoretical point of view and the characteristic, singular, sharp-notch field diverges from the rounded-notch solution very next to the notch. Nevertheless, N-SIFs continue to be used as parameters governing fracture if the notch root radius is sufficiently small with respect to the notch depth.Taking advantage of a recent analytical formulation able to describe stress distributions ahead of rounded V-notches, the paper gives a generalized form for the notch stress intensity factors, in which not only the opening angle but also the tip radius dimension is explicitly involved. Such parameters quantify the stress redistribution due to the root radius with respect to the sharp notch case.     

Nonlinear interface shear fracture of end notched flexure specimens

The nonlinear analytical solutions of an end notched flexure adhesive joint or fracture test specimen with identical or dissimilar adherends are investigated. In the current study, a cohesive zone model (with arbitrary nonlinear cohesive laws) based analytical solution is obtained for the interface shear fracture of an end notched flexure (ENF) specimen with sufficiently long bond length. It is found that the scatter and inconsistency in calculating Mode II toughness may be significantly reduced by this model. The present work indicates that the Mode II toughness G_IIc under pure shear cracking condition is indeed very weakly dependent on the initial crack length. And this conclusion is well supported by the experimental results found in the literature. The parametric studies show that the interface shear strength is the most dominant parameter on the critical load. It is also interesting to note that with very short initial crack length and identical interface shear strength, higher Mode II toughness indeed cannot increase the critical load. Unlike the high insensitivity of critical load to the detailed shape of the cohesive law for Mode I peel fracture, the shape of the cohesive law becomes relatively important for the critical load of joints under pure Mode II fracture conditions, especially for joints with short initial crack length. The current study may help researchers deepen the understanding of interface shear fracture and clarify some previous concepts on this fracture mode.