Brittle fracture in rounded-tip V-shaped notches

Two failure criteria are proposed in this paper for brittle fracture in rounded-tip V-shaped notches under pure mode I loading. One of these criteria is developed based on the mean stress criterion and the other based on the point stress criterion which both are well known failure criteria for investigating brittle fracture in elements containing a sharp crack or a sharp V-notch. To verify the validity of the proposed criteria, first the experimental data reported by other authors from three-point bend (TPB) and four-point bend (FPB) tests on PMMA at −60 °C and Alumina–7% Zirconia ceramic are used. Additionally, some new fracture tests are also carried out on the rounded-tip V-notched semi-circular bend (RV-SCB) specimens made of PMMA for various notch opening angles and different notch tip radii. A very good agreement is shown to exist between the results of the mean stress criterion and the experimental data.     

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.     

Fracture of V-notched specimens under mixed mode (I + II) loading in brittle materials

The purpose of this research is threefold. First, to provide experimental results of fracture loads for V-notched beams loaded under mixed mode. Second, to check the suitability of fracture criteria based on the cohesive zone model and strain energy density when applied to those samples. And, third, to suggest a very simple fracture criterion, based on the dominance of the local mode I, for notched samples (with different V-notch angles and notch root radii) loaded under mixed (I + II) mode. This proposal unifies predictions for the experimental results obtained under mode I and mixed mode loading. To this end, 36 fracture tests on V-notched beams were performed and reported: three V-notched angles were investigated (90°, 60°, 30°, four different loadings (mixed modes I and II) were selected and three samples were tested for each configuration.     

Fracture assessment of Brazilian disc specimens weakened by blunt V-notches under mixed mode loading by means of local energy

The main purpose of this research is to re-analyse experimental results of fracture loads from blunt V-notched samples under mixed mode (I + II) loading considering different combinations of mode mixity ranging from pure modes I to II. The specimens are made of polymethyl-metacrylate (PMMA) and tested at room temperature. The suitability of fracture criterion based on the strain energy density (SED) when applied to these data is checked in the paper. Dealing with notched samples, characterized by different notch angles and notch root radii, the SED criterion used in combination with the concept of local mode I, valid in the proximity of the zone of crack nucleation, permits to provide a simple approximate but accurate equation for the SED in the control volume. This proposal unifies predictions for the experimental results obtained under modes I, II and mixed mode loading.     

Sudden Fracture from U-Notches in Fine-Grained Isostatic Graphite Under Mixed Mode I/II Loading

The U-notched maximum tangential stress (UMTS) criterion, proposed originally and utilized previously by the author and his co-researcher for predicting mixed mode I/II fracture in plexi-glass (PMMA) and also pure mode II fracture in PMMA and soda-lime glass, was employed to estimate the experimental results reported in literature dealing with brittle fracture of many U-notched fine-grained isostatic graphite plates under combined tensile/shear loading conditions. By using the fracture curves of the UMTS criterion, which can predict the onset of brittle fracture in terms of the notch stress intensity factors (NSIFs) in the entire domain from pure mode I to pure mode II, the mixed mode fracture toughness (i.e. the load-bearing capacity) of U-notched graphite plates was successfully estimated.     

Brittle failures at rounded V-notches: a finite fracture mechanics approach

Finite Fracture Mechanics (FFM) is applied to investigate the brittle failure behavior of rounded V-notched elements subjected to mode I loading. According to the criterion, fracture does not propagate continuously, but by finite crack extensions, whose value is determined by the contemporaneous fulfilment of a stress requirement and an energy balance. Consequently, the crack advance becomes a structural parameter. By assuming the generalized apparent stress intensity factor as the governing failure parameter, as expected for a brittle structural behavior, the expression of the apparent generalized fracture toughness as a function of the material properties as well as of the notch opening angle and root radius is achieved. FFM predictions are then successfully compared to experimental data available in the Literature and to results provided by other theoretical approaches based on a critical distance.     

On T-Stresses Near V-Notches

The second term of stress field around a sharp V-notch under mode I loading was investigated. It was found that in the Cartesian coordinate system, unlike the T-stress in cracked bodies, the second term of Williams’ expansion in all three stress components is nonzero and its value depends on the distance from the notch tip. Thus, according to the stress based fracture criteria, in addition to the singular term, the first non-singular term may also play an important role in brittle fracture of sharp V-notched components under mode I loading.     

Failure assessment of notched polycrystalline graphite under tensile-shear loading

The fracture load and the fracture initiation angle were experimentally measured for a V-notched specimen made of polycrystalline graphite under combined tensile-shear loading. The experimental results were obtained for several specimens with different notch angles and various notch tip radii. The experimental observations showed that for a constant notch tip radius, the fracture load in pure tensile loading conditions decreases as the notch angle increases. Moreover, for a constant notch angle, as the notch tip radius increases the fracture load in graphite specimens enhances in the entire domain between pure tensile and pure shear loading conditions. A recently developed failure criterion was then used to estimate the experimental values of the notch fracture resistance and the fracture initiation angle for the tested graphite specimens. The experimental results could be estimated very well by using the results of the proposed criterion.     

The role of T-stress in brittle fracture for linear elastic materials under mixed-mode loading

The purpose of this paper is to revisit the maximum tensile stress (MTS) criterion to predict brittle fracture for mixed mode conditions. Earlier experimental results for brittle fracture of polymethylmethacrylate (PMMA) using angled cracked plates are also re-examined. The role of the T -stress in brittle fracture for linear elastic materials is emphasized. The generalized MTS criterion is described in terms of mode I and II stress intensity factors, K _I and K _II and the T- stress (the stress parallel to the crack), and a fracture process zone, r _c . The generalized MTS criterion is then compared with the earlier experimental results for PMMA subjected to mixed mode conditions. It is shown that brittle fracture can be controlled by a combination of singular stresses (characterized by K ) or non-singular stress ( T -stress). The T -stress is also shown to have an influence on brittle fracture when the singular stress field is a result of mode II loading.     

T应力对Ⅰ-Ⅱ复合型裂纹扩展的影响

利用最大周向正应力判据MTS重新分析研究了脆性破坏的Ⅰ-Ⅱ复合型裂纹扩展,其中考虑了平行于裂纹方向的非奇异项T应力。以平板中的斜裂纹处于双向受力为研究对象,通过两个方向力的不同组合以及裂纹与受力方向的夹角变换得到包括纯I型和纯II型在内的Ⅰ-Ⅱ复合型裂纹,分析了T应力对裂纹扩展方向以及断裂时的应力强度因子的影响,并将预测结果与现有的实验数据进行了比较。在此基础上,给出了不同T应力条件下通用的Ⅰ-Ⅱ复合型裂纹扩展条件,可用于给定几何试件的脆性断裂判定。分析结果表明:裂纹尖端非奇异项T应力对裂纹扩展的影响是不可忽略的,尤其是对II型断裂的影响更为明显。     

The role of first non‐singular stress terms in mixed mode brittle fracture of V‐notched components: an experimental study

This paper investigates the effects of the first non‐singular stress terms on the fracture assessment of sharp V‐notches under mixed mode loading. First, numerical studies have been performed on a fracture test configuration called single V‐notched ring (SVR) specimen. Then, the notch stress intensity factors as well as the coefficients of the first non‐singular stress terms, which are vital parameters in brittle fracture of V‐notched components, were calculated via a finite element over‐deterministic algorithm for a wide range of loading and geometry conditions. The obtained results demonstrate that the SVR specimen is able to provide a complete range of mode mixities from pure mode I to pure mode II loading conditions. The numerical results, next, have been converted to dimensionless parameters and are illustrated in several graphs. Indeed, these graphs can be easily employed by the engineers for rapid calculation of the corresponding notch stress intensity factors and the coefficients of the first non‐singular stress terms in the SVR specimen. The obtained fracture parameters are then submitted to the maximum tangential stress criterion to assess the effects of the first non‐singular terms on fracture behaviour of the specimen. Finally, an experimental study has been performed on the SVR specimen made of Nayriz Marble rock for two notch angles with a complete range of mode mixities. The obtained experimental data confirm the significant role of the first non‐singular stress terms. In fact, these results show that considering only the singular stress terms may induce an average error of 38% in the predicted fracture loads, which can be decreased to about 12% just by adding the contribution of the first non‐singular terms to the maximum tangential stress criterion.     

Failure criteria for brittle elastic materials

The validity of several known failure initiation criteria at reentrant corners in brittle elastic materials is examined and a simple one is proposed. Their predictions, under mode I stress field, are compared to experimental observations carried out on PMMA (polymer) and Alumina-7%Zirconia (ceramic) V-notched specimens. Because all realistic V-notched reentrant corners are blunt, a detailed experimental procedure has been followed, focusing on specimens with different notch tip radii. It is demonstrated that by assuming a sharp V-notch, some failure criteria predict reasonably well the experimental findings, and that corrections are needed in order for these to take into consideration the realistic radius at the notch tip.     

A generalised notch stress intensity factor for U-notched components loaded under mixed mode

A novel notch stress intensity factor (NSIF) for U-notched specimens loaded under mixed mode is examined in this article. The concept is based on the averaged strain energy density criterion, or alternatively on the cohesive zone model, as well as the equivalent local mode approach. To a certain extent, it is a generalisation of Glinka’s NSIF for mode I, where σ_tip is replaced by σ_max.The applicability of a fracture criterion based on this new NSIF is checked against 171 fracture tests with PMMA (at −60 °C) performed on U-notched specimens, with different notch root radii and loaded under mixed mode. The asymptotic behaviour of the new NSIF as the notch becomes a crack (when the notch root radius tends to zero) or when the notch disappears (when the notch root radius tends to infinity) is also discussed.     

Mixed Mode Brittle and Ductile Fracture of a High Strength Rotor Steel at Room Temperature

The mixed mode fracture of a high strength rotor steel has been investigated at room temperature using single edge notched specimens. In mode I, and for limited amounts of shear loading, the steel exhibited cleavage fracture. For conditions near mode~II ductile fracture occurred. A transition from brittle to ductile fracture occurred for mixed mode loading. Finite element analysis provided estimates of the extent of near crack tip yielding and elastic-plastic stress intensity factors. Test results agreed with the maximum tensile stress (MTS) criterion for small scale yielding for limited amounts of shear loading. The load for mode II fracture was lower than predicted from the MTS criterion, but higher than predicted from plastic collapse predictions. Observed fracture angles where in broad agreement with the predicted fracture mechanisms. The load for the transition from brittle to ductile fracture was found to agree approximately with the predicted load. This revised version was published online in July 2006 with corrections to the Cover Date.     

A critical shear displacement criterion for ductile–brittle transition under mixed mode I and II loading

Abstract

Micromechanisms producing ductile and brittle damage operate in parallel at a crack tip. The dominant mode of failure depends upon which of the two (ductile or brittle) damage parameters first reaches its critical value. This has been shown by a study of ductile–brittle transition behaviour in HY100 steel under mixed mode I and II loading. The transition from ductile to brittle behaviour in HY100 steel was found to be affected by mixed mode I and II ratio (ratio of imposed tensile and shear loading) in a manner such that with increasing shear the transition temperature decreased. In the present paper, a criterion is proposed based on the shear strain ahead of a notch tip, to predict the fracture behaviour at any given temperature and mixed mode ratio.     

Fracture at V-notches with contained plasticity

Fracture at V-notches with contained plasticity was studied. The tested material was a soft annealed tool steel, AISI O1, at −50°C. The material behaviour at this temperature was brittle for a standard fracture toughness test and ductile for a tensile test. Single-edge notched tension and three-point bend specimens were tested, with notch angles ranging from 0° to 140°. For the same notch angle, both brittle and ductile fracture occurred depending on the geometry. However, transferability between different geometries prevailed if the fracture was brittle.Fracture loci derived from simple point-stress or mean-stress criteria were fitted to the experimental results. The trend of the experimental results was followed well even though the fracture loci were derived under the assumption of linear elastic stresses. However, a fracture criterion based on the fracture toughness and a tension test alone will provide a conservative fracture locus.The effect of introducing a notch radius on the used fracture criteria is discussed within the context of linear elastic analysis. As expected, a mean-stress criterion is more sensitive to changes in the notch radius than a point-stress criterion. For both criteria, the sensitivity for changes in the notch radius is less for larger notch angles.     

State‐of‐the‐art review on the local strain energy density concept and its relation to the J‐integral and peak stress method

The local average strain energy density (SED) approach has been proposed and elaborated by Lazzarin for strength assessments in respect of brittle fracture and high‐cycle fatigue. Pointed and rounded (blunt) V‐notches subjected to tensile loading (mode 1) are primarily considered. The method is systematically extended to multiaxial conditions (mode 3, mixed modes 1 and 2). The application to brittle fracture is documented for PMMA flat bar specimens with pointed or rounded V‐notches inclusive of U‐notches. Results for other brittle materials (ceramics, PVC, duraluminum and graphite) are also recorded. The application to high‐cycle fatigue comprises fillet‐welded joints, weld‐like shaped and V‐notched base material specimens as well as round bar specimens with a V‐notch. The relation of the local SED concept to comparable other concepts is investigated, among them the Kitagawa, Taylor and Atzori–Lazzarin diagrams, the Neuber concept of fictitious notch rounding applied to welded joints and also the J‐integral approach. Alternative details of the local SED concept such as a semicircular control volume, microrounded notches and slit‐parallel loading are also mentioned. Coarse FE meshes at pointed or rounded notch tips are proven to be acceptable for accurate local SED evaluations. The peak stress method proposed by Meneghetti, which is based on a notch stress intensity factor consideration combined with a globally even coarse FE mesh and is used for the assessment of the fatigue strength of welded joints, is also presented.     

Brittle Mixed-Mode (I+II) Fracture: Application of the Equivalent Notch Stress Intensity Factor to Cracks Emanating from Notches

In the present paper, crack initiation in mixed-mode (I+II) fracture has been studied using notched circular ring specimens. A new criterion of brittle mixed-mode (I+II) fracture based on the notch tangential stress and the volumetric approach has been developed. The critical value of the equivalent notch stress-intensity factor has been considered as fracture toughness in mixed-mode (I+II) fracture.     

Interface crack initiation at V-notches along adhesive bonding in weakly bonded polymers subjected to mixed-mode loading

In this paper, interface crack initiation at V-notches along adhesive in bonded Polycarbonate (PC) and Poly Methyl Methacrylate (PMMA) subjected to mixed-mode loading conditions was investigated based on a combined experimental, finite element and matched asymptotic analysis. The V-notch specimens with an adhesive interface starting from its tip made at different notch angles were tested under three-point bending conditions. The experimental observations show that the specimens mainly fail by cracks along the interface. Also, the load at the crack initiation increases when the notch angle increases. The computational results are then used to explain and to correlate with the experimental data. A two-fold criterion developed by Leguillon (Eur J Mech A/Solids 21:61?C72 2002) that requires a simultaneous satisfaction of both Griffith energy and stress conditions for the crack initiation at a notch in the specimen made of a homogeneous brittle material is first extended for V-notch specimens under mixed-mode loading conditions and then used to estimate the crack initiation load. The estimated loads appear to agree well with the experimental data. Finally, an inverse method is proposed to estimate the values of fracture toughness at different mode mixity ratios.     

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.