A new method for evaluating fracture toughness of brittle materials

A new testing procedure is suggested for measuring the fracture toughness of brittle materials as superconductors and ceramics. The idea is to perform a compression test on a subcompact square specimen which contains a central hole. The presence of the hole induces a tensile stress at a certain small region attached to the hole. In this region an artificial notch is introduced such that the fracture path satisfies a pure tensile opening mode (mode I) to which the linear fracture mechanics rules apply. The stress distribution on the fracture plane guarantees a certain amount of stable crack extension. The relationship between the critical compressive load and the stress intensity factor is formulated via an available Green function along with a numerical solution (FEM with ANSYS code). The testing procedure is demonstrated with specimens made of two types of tungsten carbide which differ by their grain size only. Test results are examined via fracture toughness and strength values produced by other conventional methods and the agreement is very good. The geometry and loading direction enable the fracture toughness results to be relatively insensitive to the notch tip radius and the crack length, thereby relaxing the requirements for accurate measurements.The small size of the suggested specimen (12.70mm×12.70mm×5mm) and the avoidance of gripping interfaces provide the major cost-wise advantages.     

Generalized fracture toughness of brittle materials

A generalization of the concept of fracture toughness of brittle materials, when subjected to multiaxial loadings, is presented. The theory characterizes the fracture strength of materials under any combination of the three basic modes of crack surfaces displacement.With reference to three-dimensional loading systems, the fracture toughness may be represented, in theK ₁ K ₂ K ₃ Cartesian orthogonal space, by a surface Fracture Envelope characteristic for a specified material, whose equation is determined by the (symmetric) fracture toughnessK _1c and Poisson's ratio .It is shown that the most general fracture process, resulting from the combination of the opening mode of the tangential stress component and the tearing mode of the antiplane shear, may be conveniently analyzed with the aid of the generalized fracture toughness concept. From the knowledge of the Fracture Envelope relative to a structural material, a simple fracture criterion permits forecasting crack propagation for any combination of loads and geometries.The theory is applied to mixed-mode problems to define the analytic threshold of fatigue crack growth.

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Résumé On présente une généralisation du concept de ténacité à la rupture de matériaux fragiles soumis à des contraintes multiaxiales. La théorie proposée caractérise la résistance à la rupture des matériaux sous toutes les combinaisons possibles des trois modes de base des déplacements des surfaces d'une fissure. Par rapport à un système de mise en charge à deux dimensions, la ténacité à la rupture peut être représentée dans un espace orthogonal cartésienK ₁ K ₂ K ₃ par une Enveloppe de Rupture caractéristique d'un matériau donné dont l'équation est déterminée par la ténacité à la rupture symétriqueK _c et le module de Poisson .On montre que le processus de rupture le plus général qui résulte de la combinaison d'une ouverture sous l'effet de la composante tangentielle de la contrainte et d'un arrachement sous l'effet du cisaillement antiplanaire peut être analysé d'une manière satisfaisanteà l'aide du concept de ténacité à la rupture généralisée. A partir de la connaissance de l'Enveloppe de Rupture relative à un matériau de construction déterminé, un critère simple de rupture permet de prévoir la propagation d'une fissure pour toutes combinaisons de contraintes et de géométries.La théorie est appliquée à des problèmes de fissure suivant des modes mixtes en vue de définir de manière analytique le seuil de propagation d'une fissure de fatigue.

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Operated for the U.S. Department of Energy, Contract No. DE-AC12-76N00052.     

Method of fracture toughness testing of brittle nonmetallic materials

Strength of Materials -     

A method for fracture toughness assessment by the scatter of hardness characteristics

A stable correlation between the material fracture toughness characteristics and statistical parameters of scatter of hardness values has been established. __________ Translated from Problemy Prochnosti, No. 6, pp. 5–12, November–December, 2007.     

Fracture toughness determination of brittle materials using small to extremely small specimens

Diametral compression of a grooved, disc shaped specimen is used to determine fracture toughness. This method's most important features are that extremely small specimens can be used and no knowledge of material properties is needed. It is suitable for many brittle materials, e.g. glass, cemented carbides, ceramics, many geological, mining and building materials, perspex-like plastics, etc.     

Fracture toughness and crack morphology in indentation fracture of brittle materials

The relationship between the indentation fracture toughness, K _c, and the fractal dimension of the crack, D, has been examined on the indentation-fractured specimens of SiC and AIN ceramics, a soda-lime glass and a WC-8%Co hard metal. A theoretical analysis of the crack morphology based on a fractal geometry model was then made to correlate the fractal dimension of the crack, D, with the fracture toughness, K _IC, in brittle materials. The fractal dimension of the indentation crack, D, was found to be in the range 1.024–1.145 in brittle materials in this study. The indentation fracture toughness, K _c, increased with increasing fractal dimension, D, of the crack in these materials. According to the present analysis, the fracture toughness, K _IC, can be expressed as the following function of the fractal dimension of the crack, D, such that $$In K_{IC} = {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}\{ In[2\Gamma E/(1 - \nu ^2 )] - (D - 1)In r_L \}$$ Where Γ is the work done in creating a unit crack surface, E is Young's modulus, v is Poisson's ratio, and r _L is r _min/r _max, the ratio of the lower limit, r _min, to the upper limit, r _max, of the scale length, r, between which the crack exhibits a fractal nature (r _min ?r?r _max). The experimental data (except for WC-8%Co hard metal) obtained in this study and by other investigators have been fitted to the above equation. The factors which affect the prediction of the value of K _IC from the above equation have been discussed.     

Effect of loading rate on dynamic fracture initiation toughness of brittle materials

Numerical simulation is carried out to investigate the effect of loading rate on dynamic fracture initiation toughness including the crack-tip constraint. Finite element analyses are performed for a single edge cracked plate whose crack surface is subjected to uniform pressure with various loading rate. The first three terms in the Williams’ asymptotic series solution is utilized to characterize the crack-tip stress field under dynamic loads. The coefficient of the third term in Williams’ solution, A ₃, was utilized as a crack tip constraint parameter. Numerical results demonstrate that (a) the dynamic crack tip opening stress field is well represented by the three term solution at various loading rate, (b) the loading rate can be reflected by the constraint, and (c) the constraint A ₃ decreases with increasing loading rate. To predict the dynamic fracture initiation toughness, a failure criterion based on the attainment of a critical opening stress at a critical distance ahead of the crack tip is assumed. Using this failure criterion with the constraint parameter, A ₃, fracture initiation toughness is determined and in agreement with available experimental data for Homalite-100 material at various loading rate.     

Simple bond energy approach for non-destructive measurements of the fracture toughness of brittle materials

A simple bond breakage model for computing the fracture surface energy and toughness of a wide variety of brittle materials is presented and correlated against values reported in the literature for the single crystalline forms of these same materials. The correlation shows that this simple model can provide an accurate estimate for both the fracture surface energy and toughness of these materials. It is further shown that this simple model can be extended to amorphous materials with reasonable accuracy by normalizing the fracture surface energy of the crystalline material by the ratio of the density of the amorphous material vs. the density of the single crystalline material. Applications to thin film low-k materials and capabilities for non-destructive measurements are also discussed.     

Fracture toughness and absorbed energy measurements in impact tests on brittle materials

Previous work on impact testing has shown that the energy/unit area (w) normally measured in notched impact tests is dependent on specimen geometry. A fracture mechanical analysis has now been developed to account for the observed dependence ofw on notch size. A correction factor () has been derived to accommodate notch effects and this allows for the calculation of the strain energy release-rateG directly from the measured fracture energies.Tests on PMMA have shown that corrected results are independent of specimen geometry and theG _c for PMMA has been evaluated as 1.04 × 10³ J m^–2. The experimental results show that there is an additional energy term which must be accounted for and this has been interpreted here as being due to kinetic energy losses in the specimens. A conservation of momentum analysis has allowed a realistic correction term to be calculated to include kinetic energy effects and the normalized experimental results show complete consistency between all the geometries used in the test series.It is concluded that the analysis resolves many of the difficulties associated with notched impact testing and provides for the calculation of realistic fracture toughness parameters.     

A modified Kolsky method for determining the shear strength of brittle materials

Technical Physics Letters - A new modification of the Kolsky method is proposed, according to which a loaded sample is arranged in an obliquely cut tube casing. Using this configuration, it is...     

A new method of fracture toughness determination in brittle ceramics by open-crack shape analysis

Improvement of the fracture toughness of high-quality ceramics remains one of the most important goals in materials development. An associated problem is the accurate measurement of fracture toughness in such brittle or semi-brittle ceramics, particularly in small samples encountered in material development. Previously used methods relying on measurement of the size of fracture mirrors, the indentation load and crack length in Vickers hardness-induced cracking, and a variant of similar techniques, have all been less than satisfactory in discriminating quantitative differences among materials. A hitherto unused technique of inferring the fracture toughness in samples from measurements of open-crack flank displacements, which we have developed, avoids most of the theoretical and experimental difficulties of other methods. While it is somewhat intensive in terms of evaluation and requires high resolution of open cracks, the technique is fundamentally the soundest of all techniques and is capable of furnishing discriminating results. We present results of its application to the measurement of some model materials such as soda–lime glass, single-crystal silicon, alumina, and a reaction-bonded silicon nitride whose porosity would ordinarily present difficulties with other methods. This revised version was published online in November 2006 with corrections to the Cover Date.     

Application of a new statistical function for fracture toughness to failures at microracks in brittle materials

A new statistical distribution function for fracture toughness has been derived on the basis of the self-similar nature of the mechanical behaviour of crack-tip regions. It has been used to describe statistically variable fracture-toughness data well and to give a good prediction of the effect of the crack front length, that is of the specimen size. The present paper develops on this basis a statistical criterion for failure in linearly elastic materials containing distributions of many microcracks. Data from a number of materials tested in several different laboratories are presented, as are the results of statistical tests showing the quality of the fits obtained using the new function. Some bimodal data is considered.

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Résumé On a établi une nouvelle fonction de distribution statistique pour la ténacité à la rupture, en se basant sur la nature homothétique du comportement mécanique des régions sises aux extrémités de fissures.Cette fonction est utilisée pour présenter des données de ténacité à la rupture statistiquement variables, et pour fournir une prédiction satisfaisante des effet de la longueur du front de fissuration ou de la taille de l'éprouvette.Sur cette base, on développe dans l'étude un critère statistique de rupture dans des matériaux linéaires élastiques comportant des distributions de nombreuses microfissures.Les données relatives à plusieurs matériaux essayés dans divers laboratoires sont fournies, et les résultats d'essais statistiques présentés montrent la bonne concordance à laquelle conduit l'usage de la nouvelle finction. On considère également quelques données à caractère bimodal.

     

The fractal effect of irregularity of crack branching on the fracture toughness of brittle materials

Microstructural observations of brittle materials indicated that a variety of microdefect events can be responsible not only for inelastic behaviour, but also for macroscopic crack front irregularity. This irregularity produces an increase in the fracture toughness of the material. In this paper, this irregularity is analysed by fractal geometry in a very simple manner; a fractal model of crack branching is established. Both microscopic and macroscopic analytical results show that the toughness can be raised appreciably as a fractal geometric effect of the irregularity.

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Résumé Des observations microscopiques sur des matériaux fragiles ont montré qu'une variété d'évènements à l'échelle du microdéfaut peuvent être responsables non seulement du comportement inélastique, mais aussi de l'irrégularité du front d'une fissure macroscopique. Cette irrégularité provoque un accroissement de la ténacité à la rupture du matériau. Dans cette étude, on analyse de manière très simple cette irrégularité par fractogéométrie (Mandelbrot) et on établit un modèle fractal relatif à une fissure qui se ramifie. Les résultats de l'analyse microscopique et macroscopique montrent qu'un effet fractogéométrique de l'irrégularité du front de fissure est d'accroitre de manière appréciable la ténacité.

     

Compliance calibration of the short rod chevron-notch specimen for fracture toughness testing of brittle materials

The short rod chevron-notch specimen has the advantages of (1) crack development at the chevron tip during the early stage of test loading and (2) convenient calculation of K _Ic from the maximum test load and a calibration factor which depends only on the specimen geometry and manner of loading. For generalized application, calibration of the specimen over a range of specimen proportions and chevron-notch configurations is necessary. Such was the objective of this investigation, wherein calibration of the short rod specimen was made by means of experimental compliance measurements converted into dimensionless stress intensity factor coefficients.     

On the use of short-rod/bar test specimens to determine the fracture toughness of metallic materials

The compliance calibration of a set of short-bar fracture toughness test specimens has been studied using analytical and experimental techniques. The stress intensity coefficients obtained from experimental compliance analyses were used for the assessment of fracture toughness,K _ICSB, from short-bar fracture toughness tests. Very good correlation was observed between theK _ICSB andK _IC values of a series of high chromium cast irons.K _ICSB values also correlated well withK _Q(j) values of a high strength cast aluminium alloy.

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Résumé On a étudié l'étalonnage par compliance d'une série d'éprouvettes d'essai de ténacité à la rupture en forme barreaux courts en recourant à des techniques analytique et expérimentale.Les facteurs d'intensité de contrainte dérivés des analyses expérimentales de compliance ont été utilisés pour établir la ténacité à la rupture dans le cas d'essais sur barreaux courtsK _ICSB.On a relevé une excellente corrélation entre les valeurs deK _ICSB etK _IC pour une famille de fontes á haute teneur en chrome. Les valeurs deK _ICSB ont également été trouvées en bonne corrélation avec les valeurs deK _Q(J) relatives à un alliage d'aluminium à haute résistance moulé.