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.     

Prediction of intrinsic fracture toughness for brittle materials from the apparent toughness of notched-crack specimen

In this investigation, fracture process zone model is used to establish a new relationship to predict the intrinsic fracture toughness from the apparent fracture toughness of a notched-crack specimen. The parameters needed in the proposed model are very rare, such as, the fracture process zone size of materials, the notch radius. Specimens made up of two kinds of polycrystalline alumina and one soda-lime glass with notch radii as small as a few micrometer are used to verify the predictions of this model. Besides, the results also show that fracture toughness of ceramics decreases with the decreasing of notch root radius. Under condition of the radius of crack tip is not greater than the averaged grain size, the apparent toughness can be approximately regarded as the fracture toughness of the materials.     

A new method to estimate the plane strain fracture toughness of materials

Although the testing method for fracture toughness K_IC has been implemented for decades, the strict specimen size requirements make it difficult to get the accurate K_IC for the high‐toughness materials. In this study, different specimen sizes of high‐strength steels were adopted in fracture toughness testing. Through the observations on the fracture surfaces of the K_IC specimen, it is shown that the fracture energy can be divided into 2 distinct parts: (1) the energy for flat fracture and (2) the energy for shear fracture. According to the energy criterion, the K_IC values can be acquired by small‐size specimens through derivation. The results reveal that the estimated toughness value is consistent with the experimental data. The new method would be widely applied to predict the fracture toughness of metallic materials with small‐size specimens.     

Application of the small punch test to determine the fracture toughness of metallic materials

A new methodology to determine the elasto‐plastic fracture toughness, J_Ic, by means of notched small punch tests (SPT) samples is reported. Standard SPT samples were used after being longitudinally notched machined from the centre of one side of the sample to the centre of the opposite side, producing a notch depth‐to‐thickness ratio a/t= 0.4. The onset of crack initiation was experimentally determined directly from the experimental load‐displacement plot of the test and also with the aid of scanning electron microscope observations performed on different samples, with tests being interrupted at different percentages of the maximum registered load. The test was also modelled using finite element analysis and the J‐integral was evaluated as a contour integral in ABAQUS. The obtained results were compared with the critical J values of the steel determined using standard tests (J–R curves) and the differences found were duly justified.     

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.     

A new method to determine the un-poled elastic properties of ferroelectric materials

Abstract

Piezoelectric devices with complex electrode geometries often contain ferroelectric regions that experience little or no electric field and remain unpolarised. Since the un-poled and poled material properties differ it is desirable to account for these regions in a device when developing predictive models or to design piezoelectric transducers. The lack of published data on the elastic properties for un-poled ferroelectrics, specifically the numerous commercial compositions such as lead zirconate titanate, reflects the difficulty of experimental measurement. In this work, a method for predicting un-poled properties from more commonly available poled data has been developed. A new method of calculating these properties is presented which provides a rapid and practical solution to the problem of evaluating the isotropic stiffness and Poisson’s ratio for an un-poled ferroelectric material. The way in which this calculation has been derived and validated is presented and detailed comparisons are made with alternative methods and experimental data.     

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...     

Modeling the brittle–ductile transition in ferritic steels. Part II: analysis of scatter in fracture toughness

A dislocation simulation model has been proposed to predict the brittle–ductile transition in ferritic steels in Part I. Here we extend the model to address the problem of inherent scatter in fracture toughness measurements. We carried out a series of Monte Carlo simulations using distributions of microcracks situated on the plane of a main macrocrack. Detailed statistical analysis of the simulation results showed the following: (a) fracture is initiated at one of the microcracks whose size is at the tail of the size distribution function, and (b) the inherent scatter arises from the distribution in the size of the critical microcrack that initiates the fracture and not from the variation of the location of the critical microcrack. Utilizing the weakest-link theory, Weibull analysis shows good agreement with the Weibull modulus values obtained from fracture toughness measurements.     

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.