Verification of brittle fracture criteria for elements with V-shaped notches

In this paper an analysis of crack initiation in plane elements with V-shaped notches under biaxial loading (mode I and II) was presented. The following fracture criteria were used to evaluate the critical loads and directions of crack initiation: strain energy release rate criterion; strain energy density criterion; modified McClintock's stress criterion; non-local stress criterion.Results of numerical analysis obtained using the boundary element method and path independent H and J integrals were compared with experimental data.     

Investigation of mixed mode brittle fracture in rounded-tip V-notched components

A criterion is proposed for brittle fracture analysis in rounded-tip V-notched components. This criterion, called RV-MTS, is developed based on the maximum tangential stress (MTS) criterion proposed earlier for investigating mixed mode brittle fracture in sharp cracks. Using the RV-MTS criterion, a set of fracture curves is presented based on the notch stress intensity factors (NSIFs) for predicting mixed mode and also pure mode II fracture toughness of rounded-tip V-notches. The criterion is also able to predict fracture initiation angles under mixed mode loading. The validity of the criterion is evaluated by several fracture tests performed on the rounded-tip V-notched Brazilian disc (RV-BD) specimens made of PMMA. A good agreement is shown to exist between the theoretical predictions and the experimental results for various notch opening angles and different notch radii.     

Brittle fracture assessment of engineering components in the presence of notches: a review

Brittle fracture of notched components has been widely investigated in recent decades both experimentally and theoretically. This is because of designers' concern about catastrophic failure in notched engineering components made of brittle or quasi‐brittle materials. Up to now, extensive studies have been performed on brittle fracture analysis of engineering components weakened by notches of various features under mode I, mode II, mode III and mixed mode loading conditions. In the present paper, the attempt is made to review the research articles published in the open literature on brittle fracture assessment of notched components by means of notch fracture mechanics concepts. The main focus of this paper is on the stress‐based fracture criteria, which are the basis of authors' experience in recent years.     

V形刻槽爆破机理动态数值模拟分析

文章以花岗岩荒料开采中的切割爆破工程实践为研究对象,为分析V形刻槽爆破成缝机理及爆破参数改变对刻槽爆破效果影,响等内容,建立了各向同性脆性材料的多刻槽孔准平面应变模型,以显式动力分析有限元程序ANSYS／LS-DYNA为模拟运算工具,详细计算了在动载作用下槽孔周围及双孔连心线上岩体的动态应力分布与变化规律,并运用断裂力学理论分析刻槽爆破动态成缝机理。     

Influence of sub-micrometer notches on the fracture of single crystal silicon thin films

The influence of notches on the fracture of single crystal silicon thin films was investigated. The tests were conducted on notched and smooth tensile specimens micromachined on a silicon wafer. The specimen geometry was 100 μm long, 50 μm wide and 5 μm thick. For the notched specimen, a V‐shaped sub‐micrometer notch was introduced on one edge of it by using a focused ion beam (FIB) process. The notch lengths ranged from 0.07 to 1.3 μm. Four types of specimens with different surfaces and tensile orientations were tested. The smooth specimens showed scattered fracture strengths and ‘collapsed’ fractures. For the restrictive‐shaped notches, the critical length was 0.5 μm. The short‐notched (<0.5 μm) specimens also showed ‘collapsed’ fractures, and the stress concentrations on notch tips decreased their fracture strengths. For the long‐notched (>0.5 μm) specimens, the notch was equivalent to a crack in the Griffith model and the crack mainly propagated on {111} cleaved planes.     

Sharp V‐notches in viscoplastic solids: Strain energy rate density rule and fracture toughness

Different from Neuber's rule or Glinka's energy method which are always adopted to characterize the notch tip field under elastoplastic condition, in this paper, the strain energy rate density (SERD) rule is used for viscoplastic materials. In particular, based on the definition of generalized notch stress intensity factor (G‐NSIF) for sharp V‐notch in viscoplastic solids, the concept of SERD for sharp V‐notch in viscoplastic solids is presented. Subsequently, by taking as a starting point the SERD, the averaged strain energy density (SED) for sharp V‐notch in viscoplastic solids is derived with integration of time. The fracture toughness relation between sharp V‐notch specimens and crack specimen in viscoplastic materials is given based on the transformation of SERD. A numerical approach is presented to compute the SERD and SED based on finite element method. Some crucial comments on the G‐NSIF have been discussed. Some typical solutions for SERD and SED for sharp V‐notched specimens are investigated.     

Dynamic Fracture of Nominally Brittle Materials

Current understanding of dynamic fracture mechanisms and the methods of modeling are reviewed critically. Experimental methods used in dynamic fracture investigations and key experimental observations are reviewed. This is followed by a critical review of the dynamic fracture models. Mechanistic and phenomenological models as well as discrete and continuum models and their ability to reproduce experimental results are discussed.     

Brittle fracture considerations of two external notches under combined loading

The interaction behavior of two external notches, modeled by plane hyperbolas, is analyzed using the strain energy density failure criterion[1,2]. It is shown that the pure shear and normal loadings may be combined to the case of inclined or off-axis loading of this double-notch geometry. The crack trajectory emanating from the notch surface is assumed for most cases to follow a path along which the material elements experience more volume change than shape change. This is determined by taking the minimum values of the strain energy density function. The failure loads are obtained by holding the critical strain energy density function constant and are shown to vary with the angle between the inclined load and the major axis of the notch. The variations will depend on the aspect ratios of the notches. Graphical plots of the crack trajectories for different loading angles are displayed. The double-notch geometry is such that only local trajectory information can be gleaned from the initial state. Numerical results of failure load, fracture angle, etc. are given for notches with different degrees of bluntness.     

Brittle Fracture of a Lifting Stud During Assembly Operations

A lifting stud from a stator frame broke during assembly operations. The part was hot rolled from a 50 W grade low-carbon steel (according to the Canadian standard CSA G40.21-04), which is the equivalent of AISI 1022 grade. Complete metallurgical characterization of the material showed that the chemical and mechanical requirements of the aforementioned standard were met. Moreover, the tensile testing showed that the material had good ductility. Fractographic investigation, both at the macroscale and microscale levels, indicated that the lifting stud failed under bending overload, in a brittle mode. It was found that brittle behavior of the ductile material was caused by the sudden application of the load combined with triaxial stresses promoted by the threaded geometry.     

Fracture of components with V-shaped notches

An experimental and numerical study was performed to ascertain the influence of V-notches on the strength of different brittle materials. Critical loads were computed using the cohesive process zone model that allows extension of classical methods, based on linear elastic fracture mechanics, to rounded V-notches and contained plasticity. A large experimental programme, with more than one hundred tests, was performed with PMMA samples to support the numerical predictions. All the experimental results are reported. In addition, experimental results of notched steel samples, performed by Strandberg, [Engng. Fract. Mech. 69 (2002) 403], and notched samples made with expanded PVC foams, performed by Grenestedt, Hallström and Kuttenkeuler [Engng. Fract. Mech. 54 (1996) 445], are in very good agreement with the numerical computations, adding further support to the cohesive process zone model.     

Three-dimensional linear elastic distributions of stress and strain energy density ahead of V-shaped notches in plates of arbitrary thickness

This paper presents an analytical solution, substantiated by extensive finite element calculations, for the stress field at a notch root in a plate of arbitrary thickness. The present approach builds on two recently developed analysis methods for the in-plane stresses at notch root under plane-stress or plane strain conditions, and the out-of-plane stresses at a three-dimensional notch root. The former solution (Filippi et al., 2002) considered the plane problem and gave the in-plane stress distributions in the vicinity of a V-shaped notch with a circular tip. The latter solution by Kotousov and Wang (2002a), which extended the generalized plane-strain theory by Kane and Mindlin to notches, provided an expression for the out-of-plane constraint factor based on some modified Bessel functions. By combining these two solutions, both valid under linear elastic conditions, closed form expressions are obtained for stresses and strain energy density in the neighborhood of the V-notch tip. To demonstrate the accuracy of the newly developed solutions, a significant number of fully three-dimensional finite element analyses have been performed to determine the influences of plate thickness, notch tip radius, and opening angle on the variability of stress distributions, out-of-plane stress constraint factor and strain energy density. The results of the comprehensive finite element calculations confirmed that the in-plane stress concentration factor has only a very weak variability with plate thickness, and that the present analytical solutions provide very satisfactory correlation for the out-of-plane stress concentration factor and the strain constraint factor.     

Generalized stress intensity factors of V-shaped notch in a round bar under torsion, tension, and bending

In this study, generalized stress intensity factors K_I,λ1, K_II,λ2, and K_III,λ4 are calculated for a V-shaped notched round bar under tension, bending, and torsion using the singular integral equation of the body force method. The body force method is used to formulate the problem as a system of singular integral equations, where the unknown functions are the densities of body forces distributed in an infinite body. In order to analyze the problem accurately, the unknown functions are expressed as piecewise smooth functions using three types of fundamental densities and power series, where the fundamental densities are chosen to represent the symmetric stress singularity and the skew-symmetric stress singularity. Generalized stress intensity factors at the notch tip are systematically calculated for various shapes of V-shaped notches. Normalized stress intensity factors are given by using limiting solutions; they are almost determined by notch depth alone, and almost independent of other geometrical parameters. The accuracy of Benthem-Koiter’s formula proposed for a circumferential crack is also examined through the comparison with the present analysis.     

脆性材料断裂韧性测定的山形缺口试件和方法

本文扼要地介绍了测定新型结构陶瓷、高强度金属、以及其他脆性材料断裂韧性的山形缺口试件与方法。概述了这个方法的发展史、优缺点、目前研究概况、主要理论分析与实验研究成果,以及存在的问题和发展动向。     

Nanoscale Morphology in Tensile Fracture of a Brittle Amorphous Ribbon

The paper reports on the observation of nanoscale morphology on the tensile fracture surface of a brittle amorphous Fe-based ribbon. The formation of nanoscale damage cavity structure is a main characteristic morphology on the fracture surfaces. Approaching the ribbon boundary, these damage cavities assemble and form the nanoscale periodic corrugations, which are neither Wallner lines nor crack front waves. The periodic corrugations result from the interactions between the reflected elastic waves by the boundaries of amorphous ribbon and the stress fields of the crack tip.     

Analysis of a new specimen for mixed mode fracture tests on brittle materials

Numerical and experimental studies were performed on a new fracture test configuration called the diagonally loaded square plate (DLSP) specimen. The mode I and mode II stress intensity factors were computed for different crack lengths and crack orientation angles using finite element analysis. The numerical results show that the DLSP specimen is able to provide pure mode I, pure mode II and any mixed mode loading conditions in between. Fracture experiments were also conducted on Plexiglas using the DLSP specimen. It is shown that the results obtained from the fracture tests are consistent very well with mixed mode fracture theories.     

Using torsional bar testing to determine fracture toughness

A new method to determine fracture toughness K _IC of materials is introduced. A round-rod specimen having a V-grooved spiral line with a 45° pitch is tested under pure torsion. An equibiaxial tensile/compressive stress state is effectively created to simulate conventional test methods using a compact-type specimen with a thickness equivalent to the full length of the spiral line. K _IC values are estimated from the fracture load and crack length with the aid of a three-dimensional finite element analysis. K _IC of 7475-T7351 aluminium is estimated to be 51.3 MPa √m, which is higher than the vendor's value in the TL orientation by ∼0.8% and higher than 0.5T compact tension (CT) value by 6%; A302B steel yields 54.9 MPa √m being higher than CT test value by ∼2%. Good agreement between the K _IC values obtained by different methods indicates the proposed method is sound and reliable.     

The Equivalent Strain Energy Density approach re-formulated and applied to sharp V-shaped notches under localized and generalized plasticity

In the case of a rounded notch, the stress and strain at the notch tip can be determined by the traditional Neuber rule or by the Equivalent Strain Energy Density (ESED) approach, as formulated by Glinka and Molski. In the latter case the elastoplastic strain energy density at the notch tip is thought of as coincident with that determined under purely elastic conditions. For sharply V‐shaped notches this approach is not directly applicable, since the strain energy density at the notch tip tends toward infinity both for a material obeying an elastic law and a material obeying a power hardening law. By using the notch stress intensity factors, the present paper suggests a re‐formulation of the ESED approach which is applied no longer at the notch tip but to a finite size circular sector surrounding the notch tip. In particular we have adopted the hypothesis that, under plane strain conditions, the value of the energy concentration due to the notch is constant and independent of the two constitutive laws. When small scale yielding conditions are present, such a hypothesis immediately results in the constancy of the strain energy averaged over the process volume. As a consequence, plastic notch stress intensity factors valid for sharp V‐shaped notches can be predicted on the basis of the linear elastic stress distributions alone.     

Mixed mode fracture toughness as a separation parameter when cutting polymers

Material separation at the tool edge during the cutting of polymers has been interpreted using fracture mechanics. The different types of chip that can be produced in the same material under different conditions reflect the cube–square scaling inherent in elastoplastic fracture mechanics. In the case of PMMA, it is shown that both globally-elastic brittle spalls and continuous ribbons formed by plastic shear may be produced merely by altering the depth of cut. In the case of LLDPE and Nylon 66, only continuous chips are formed as it was not possible to take the large depths of cut required in the sledge microtome used for experiments. The shape of the discrete brittle spalls arises because the loading of the tool edge on the workpiece is asymmetrical, resulting in both Mode I and Mode II displacements. The same loading applies when ductile chips are formed. Results seem to show that measured fracture toughnesses when chips form in shear can vary with tool rake angle (or equivalently with primary shear plane angle) and a model (based on a rule of mixtures of critical crack tip opening displacements) is presented that may explain the variation.     

A criterion for brittle fracture in U-notched components under mixed mode loading

A failure criterion is proposed for brittle fracture in U-notched components under mixed-mode static loading. The criterion, called UMTS, is developed based on the maximum tangential stress criterion and also a criterion proposed in the past for mode I failure of rounded V-shaped notches [Gomez FJ, Elices M. A fracture criterion for blunted V-notched samples. Int J Fracture 2004;127:239-64]. Using the UMTS criterion, a set of fracture curves are derived in terms of the notch stress intensity factors. These curves can be used to predict the mixed mode fracture toughness and the crack initiation angle at the notch tip. An expression is also obtained from this criterion for predicting fracture toughness of U-notched components in pure mode II loading. It is shown that there is a good agreement between the results of UMTS criterion and the experimental data obtained by other authors from three-point bend specimens.