Brittle Fracture Criterion Research Articles

Mode II notch fracture toughness measurement for key-hole notches by the disk test

A new version of the well-known Brazilian disk specimen weakened by a dumbbell-shaped slit with two key-shaped ends, called key-hole notched Brazilian disk specimen, made of polymethylmethacrylate, was utilized to measure experimentally the notch fracture toughness for key-hole notches of various radii and different lengths under pure mode I and pure mode II loading conditions. The experimental values of the mode II notch fracture toughness/mode I notch fracture toughness ratio were theoretically estimated by means of two brittle fracture criteria, namely, the maximum tangential stress and the mean stress criteria. Two groups of critical distances were used in the criteria. The first one was equal to that for sharp crack and the second one was directly determined from the mode I fracture tests. It was found that while both the criteria could estimate the experimental results satisfactorily, the agreement between the theoretical and the experimental results is excellent when one deals with larger notch lengths. Also found in the research was that choosing any of the critical distance groups did not affect the theoretical predictions significantly, meaning that the critical distances of sharp crack could be used in fracture prediction of key-hole notches.

Experimental and theoretical investigation of brittle fracture in key-hole notches under mixed mode I/II loading

The Brazilian disk specimen weakened by a central dumbbell-shaped slit with two key-shaped ends and made of PMMA is employed to perform mixed mode I/II brittle fracture experiments on key-hole notches for various notch lengths and radii and, also, different mode mixity ratios. The load-carrying capacity of the specimen resulting from the test machine at the onset of sudden fracture is theoretically predicted by means of a well-known brittle fracture criterion, namely the local strain energy density criterion. A good agreement is found to exist between the theoretical and the experimental results.

Griffith criterion for brittle fracture in graphene.

There are prevailing concerns with the critical dimensions when conventional theories break down. Here we find that the Griffith criterion remains valid for cracks down to 10 nm but overestimates the strength of shorter cracks. We observe the preferred crack extension along the zigzag edge in graphene, and explain this phenomenon by local strength-based failure rather than energy-based Griffith criterion. These results provide a mechanistic basis for reliable applications of graphene in miniaturized devices and nanocomposites.

Rock bridge fracture model and stability analysis of surrounding rock in underground cavern group

Many hydropower stations in southwest China are located in regions of brittle rock mass with high geo-stresses. Under these conditions deep fractured zones often occur in the sidewalls of the underground caverns of a power station. The theory and methods of fracture and damage mechanics are therefore adopted to study the phenomena. First a flexibility matrix is developed to describe initial geometric imperfections of a jointed rock mass. This model takes into account the area and orientation of the fractured surfaces of multiple joint sets, as well as spacing and density of joints. Using the assumption of the equivalent strain principle, a damage constitutive model is established based on the brittle fracture criterion. In addition the theory of fracture mechanics is applied to analyze the occurrence of secondary cracks during a cavern excavation. The failure criterion, for rock bridge coalescence and the damage evolution equation, has been derived and a new sub-program integrated into the FLAC-3D software. The model has then been applied to the stability analysis of an underground cavern group of a hydropower station in Sichuan province, China. The results of this method are compared with those obtained by using a conventional elasto-plastic model and splitting depth calculated by the splitting failure criterion proposed in a previous study. The results are also compared with the depth of the relaxation and fracture zone in the surrounding rock measured by field monitoring. The distribution of the splitting zone obtained both by the proposed model and by the field monitoring measurements are consistent to the validity of the theory developed herein.

Theoretical and experimental investigation of brittle fracture in V-notched PMMA specimens under compressive loading

The aim of the present investigation was twofold. First, to prepare a new set of experimental data on brittle fracture of blunt V-notches under compression and second to develop stress-based criteria for predicting the compressive notch fracture toughness of blunt V-notches. A new test specimen, called V-notch stepped cottage (VSC) specimen, made of PMMA was proposed to perform fracture experiments under compression. Two brittle fracture criteria, namely the point-stress (PS) and the mean-stress (MS) criteria, were also developed to estimate the experimental results. It was demonstrated that the experimental results could be satisfactorily predicted by using the two criteria.

Fracture assessment of VO-notches under mode II loading: Experiments and theories

In the present investigation, two brittle fracture criteria were suggested to predict the onset of brittle fracture in engineering components weakened by V-notches with end holes (VO-notches) under pure mode II loading. These criteria, called VO-MTS and VO-MS were developed based on the two well-known failure concepts of the maximum tangential stress (MTS) and the mean stress (MS), respectively. In order to evaluate the accuracy of the criteria, 72 new brittle fracture tests were conducted at room temperature on the new disk type specimen containing a central slit, called the VO-notched Brazilian disk (VO-BD) specimen, made of PMMA. First, the experimental fracture loads were converted to the corresponding mode I and mode II notch fracture toughness (NFT) values and the important ratio mode II NFT/mode I NFT was experimentally achieved. Then, the theoretical values of the ratio were predicted by means of the VO-MTS and the VO-MS criteria. It was found that both the criteria could provide very good predictions to the experimental results of the ratio mode II NFT/mode I NFT, as well as those of the fracture initiation angle. Also, found in this research was that one can utilize the critical distances of sharp crack in the fracture predictions of VO-notches.

Fracture Study on Key-Hole Notches Under Tension: Two Brittle Fracture Criteria and Notch Fracture Toughness Measurement by the Disk Test

Notch fracture toughness expressions were developed for predicting tensile fracture in members containing key-hole notches based on the point stress and the mean stress criteria. The criteria were verified by using the experimental results obtained from new fracture tests on the key-hole notched Brazilian disk specimens, made of PMMA. It was found that the mean stress criterion predicts the experimental results very well. Also, found in this research was that while the point stress model provides generally satisfactory estimations, except for a special case, the accuracy of this criterion enhances as the notch radius increases.

Closed-form expressions of mode I apparent notch fracture toughness for key-hole notches

Two closed-form expressions were developed in this research to estimate the mode I apparent notch fracture toughness of brittle materials weakened by key-hole notches based on the well-established brittle fracture criteria, namely, the point stress and the mean stress. The theoretical models were verified using the experimental results reported in open literature dealing with tensile fracture in rectangular isostatic graphite plates containing central key-hole notches of various notch tip radii. A very good agreement was found to exist between the predictions of both the models and the experimental results. The results showed that while the accuracy of each model was different for various notch tip radii, total accuracies of the two models were almost equal (both about 93%) demonstrating their effectiveness. Using such expressions, it is expected that one can simply estimate the load-carrying capacity of brittle and quasi-brittle components weakened by key-hole notches under mode I loading.

Stress-based criteria for brittle fracture in key-hole notches under mixed mode loading

Abstract Two stress-based failure criteria were developed in the present research to predict mixed mode I/II brittle fracture in engineering components weakened by a key-hole notch. The first criterion was based on the well-established maximum tangential stress (MTS) concept, successfully proposed and utilized several times in recent years for different notch features. The second one was on the basis of the mean-stress (MS) concept which has been frequently used for predicting pure mode I fracture in notched domains. The results of the criteria were represented in the form of fracture curves and the curves of fracture initiation angle in terms of the notch stress intensity factors. To verify the validity of the fracture models, the theoretical predictions were compared with a large bulk of experimental data, reported in literature, on the fracture of rectangular isostatic graphite plates weakened by central key-hole notches of five different tip radii. It was found that while the total accuracies of the criteria are very good, for small notch tip radii, the MTS criterion provides generally better mixed mode notch fracture toughness results than the MS criterion. Conversely, the MS criterion works much better than the MTS model for larger notch tip radii. Dealing with fracture initiation angle, both the criteria could estimate the experimental results successfully.

Brittle fracture in V-notches with end holes

In the present research, two brittle fracture criteria were developed in terms of the notch stress intensity factors to predict mode I fracture in engineering components weakened by V-notches with end holes (VO-notches). The criteria were based on the point stress and the mean stress failure concepts. To evaluate the validity of the criteria, first, 36 new fracture tests were conducted on a new notched specimen, namely the Brazilian disk containing central V-notch with end hole (VO-BD specimen) made of polymethyl-metacrylate. Three notch angles and four notch radii were considered in the experiments. Then, the experimentally obtained fracture loads were converted to the corresponding mode I notch fracture toughness values by mean of the finite element method in order to compare the test results with the theories. It was found that very good agreement exists generally between the experimental and theoretical results. Also, found in this research was that by increasing the VO-notch angle, the accuracy of the mean stress criterion decreases, particularly for larger notch radii. Although the accuracy of the criteria depends significantly on the notch geometry, except for the angle 90°, the average discrepancies of the mean stress criterion were less than 8.5% as well as those of the point stress criterion for the entire angles showing acceptable accuracy of the predictions.

Verification of Brittle Fracture Criteria for Bimaterial Structures

Abstract The increasing application of composite materials in the construction of machines causes strong need for modelling and evaluating their strength. There are many well known hypotheses used for homogeneous materials subjected to monotone and cyclic loading conditions, which have been verified experimentally by various authors. These hypotheses should be verified also for composite materials. This paper provides experimental and theoretical results of such verifications for bimaterial structures with interfacial cracks. Three well known fracture hypotheses of: Griffith, McClintock and Novozhilov were chosen. The theoretical critical load values arising from each hypotheses were compared with the experimental data including uni and multi-axial loading conditions. All tests were carried out with using specially prepared specimens of steel and PMMA.

Strain energy density to assess mode II fracture in U-notched disk-type graphite plates

The brittle fracture criterion, namely the strain energy density (SED) over a control volume, which embraces the notch edge, is utilized in the present research to assess the experimentally obtained fracture loads of several U-notched Brazilian disk (UNBD) specimens made of a type of commercial graphite under pure mode II loading. The results show that the SED criterion could successfully predict the fracture loads of graphite specimens for different notch tip radii with an average discrepancy of about ±10%. It is proved in this investigation that not only the SED criterion works well on brittle fracture of notched graphite components under pure mode I, mixed mode I/II and pure mode III loading conditions, but also under pure mode II loading.

CTOD-FADの検討（第一報）

Recently, the risk of the brittle fracture is increasing because of expansion of the use of structure in low temperature, such as LNG pipe, ships in ice sea, and use of thick plate with upsizing of container ship. Although, CTOD design curve by WES 2805 in Japan and FAD by BS 7910 in United Kingdom are used as fracture evaluation of brittle fracture, unified and reliable criteria are needed in international community. For this reason, new fracture assessment criteria, CTOD-FAD, with feature of CTOD design curve and FAD is proposed in this study. CTOD-FAD is analytically and experimentally generated and verified for structure model with through thickness crack in this paper. As a result, it is proved that it is possible to evaluate more accurately by using CTOD-FAD compared with existing criteria for many types of structure.

Pure shear fracture study in a brittle graphite material containing a U-notch

A disc-type specimen containing a central bean-shaped slit, called the U-notched Brazilian disc specimen, was utilized to measure experimentally the mode II notch fracture toughness of a type of commercial polycrystalline graphite. First, 24 U-notched Brazilian disc graphite specimens were fabricated for four different notch tip radii, and the monotonic fracture tests were performed under pure mode I and pure mode II loading conditions; 12 for each loading mode. The recorded fracture loads were converted to the corresponding notch fracture toughness values, and the ratio mode II notch fracture toughness/mode I notch fracture toughness was experimentally determined. Then, assuming that the experimental values of mode I notch fracture toughness are known, the mode II notch fracture toughnesses were theoretically predicted by means of two brittle fracture criteria, namely the existing U-notched maximum tangential stress and the newly developed U-notched mean stress. A very good agreement was found to exist between the theoretical and the experimental results. Also, found in this research was that both the criteria could predict well the experimentally measured fracture initiation angles.

A meshfree study of the Kalthoff–Winkler experiment in 3D at room and low temperatures under dynamic loading using viscoplastic modelling

A new model for studying the fracturing of metals under impact using Smoothed Particle Hydrodynamics is presented. The model combines a temperature and strain rate dependent flow stress with a criterion for brittle fracture and is suitable for metallic materials undergoing high strain rate loadings. First, the well documented Kalthoff–Winkler experiment was used to validate our approach. A series of simulations was then conducted to model the behaviour of a 4340 steel at 223K (−50°C) under different impact speeds to investigate the simultaneous effect of temperature and impact velocity towards the failure of the material. In some cases a lower temperature brought about failure for the same impact velocity, highlighting the role of combining factors in failure analysis. This paper demonstrates the relevance of SPH in the prediction of the initiation and propagation of brittle cracks in structures, thus opening new areas for future research.

Radiation embrittlement modelling in multi-scale approach to brittle fracture of RPV steels

The purpose of the present article is to develop a multi-scale brittle fracture modelling for irradiated RPV materials. For this development, applicability of local brittle fracture criteria for radiation embrittlement modelling is analysed through comparison of the predicted and test results on radiation embrittlement of RPV steels in terms of ductile-to-brittle transition temperature and fracture toughness. The influence of radiation-induced defects on the processes of cleavage microcrack nucleation and propagation is clarified. The physical-and-mechanical models of the effect of irradiation-induced defects on cleavage microcrack nucleation are developed on the basis of dislocation and brittle fracture theories. Stress-and-strain controlled fracture criterion is developed that allows the adequate prediction of radiation embrittlement by various mechanisms. The differences and commonalities are revealed in the nature of material embrittlement due to cold work and neutron irradiation. The mechanism is explained of significant recovery of fracture resistance properties with simultaneous increase of fraction of intercrystalline fracture after post-irradiation annealing. Engineering approach for prediction of the temperature dependence of fracture toughness as a function of neutron fluence is justified.

A ductile–brittle fracture model for material ductile damage in plastic deformation based on microvoid growth

The fracture of ductile solids has frequently been observed to result from the large growth and coalescence of microscopic voids, a process enhanced by the superposition of hydrostatic tensile stresses on a plastic deformation field. The ductile growth of voids is treated here as a problem in continuum plasticity. In this paper, a ductile–brittle fracture criterion derived from a microvoid mechanical model is proposed for microdamage and fracture of metallic material under large elastic–plastic deformation and has been proved to be effective in the analysis of metal forming process. Using this criterion, the analyses of microdamage and ductile–brittle fracture for tensile specimens in complex stress-states have been carried out. The results from these analyses on damage development and fracture are in good agreement with the experimental ones, and from microview point are reasonable for cracked specimens.

Effect of non-singular stress on the brittle fracture of V-notched structure

The traditional brittle fracture criteria for V-notched structures are established on the base of the singular stress field at a V-notch tip where only two singular stress terms are adopted. The non-singular stress terms also play a significant role in determining the stress and strain fields around a V-notch tip, which in turn could affect the fracture character of V-notched structures predicted by the fracture mechanics criteria. In this paper, the effect of the non-singular stress on the brittle fracture properties for the V-notch problem is discussed. Firstly, the stress field around a V-notch tip is described by the Williams asymptotic expansions. At the same time, the stress field far from the V-notch tip is modeled by the conventional boundary element method since there is no stress singularity. By the combination of the Williams asymptotic expansions and the boundary integral equations, the complete stress field at a V-notch tip including several non-singular stress terms can be obtained. Then, three different brittle fracture criteria are introduced to predict the critical loading and initial crack propagation direction of V-notched structures under mixed-mode loading. Comparing with the existed experimental results, it can be found that the degree of accuracy of the predicted results when taking into account the non-singular stress terms is much higher than the predicted ones neglecting the non-singular stress.

Investigation of liquid LBE embrittlement effects on irradiated ferritic/martensitic steels by slow-strain-rate tensile tests

In the present work, LBE (lead–bismuth eutectic) embrittlement effects on ferritic/martensitic (FM) steels have been studied by conducting slow-strain-rate tensile (SSRT) testing on T91 and F82H steels either in Ar or in liquid LBE after irradiation to doses up to about 20dpa in a mixed spectrum of spallation neutrons and high energy protons. SSRT tests were performed at temperatures in the range of 150–500°C. Tests in Ar revealed significant irradiation-induced hardening and embrittlement effects (loss of ductility) as compared to the unirradiated ones. Tests in LBE showed additional embrittlement effects induced by LBE, which increased with irradiation-induced hardening. As a consequence, the fracture strain of irradiated specimens was reduced to a very low level of about 2–3%. A combination of the model of adsorption-induced reduction in cohesion of atomic bonds and the Kelly–Tyson–Cottrell criterion (σ/τ⩾σmax/τmax) for brittle cleavage fracture was used to interpret qualitatively the observation reported in the present paper.

Hydrogen effect on shearing and cleavage of Al: A first-principles study

We report on first-principles calculations of the effect of a (111) hydrogen layer embedded in Al on generalized stacking fault energies and cleavage energy for different choices of the slip and cleavage planes. It is shown that the H layer softens Al against shear by reducing the stable and unstable stacking fault energies relative to pure Al. This finding points to a possible enhancement of plasticity of Al by H. The H layer also reduces the cleavage energy on the (111) plane. The reductions in the cleavage energy and unstable stacking fault energy compensate each other and produce only a moderate change in the Rice criterion of ductile versus brittle fracture.