Karl Kromp

Crack resistance curves of alumina and zirconia at room temperature

Ceramic three-point bend specimens were pre-cracked in a displacement-controlled test in air at room temperature to form sharp cracks of different lengths. Critical stress intensity factors (KIC were then measured as a function of sharp crack length in a fast-fracture, load-controlled test. Crack resistance curves (KIC against crack length) were determined for three commercially pure aluminas of different grain size, a debased alumina containing a glassy phase, and a partially stabilized zirconia (PSZ) material. The crack resistance curves proved to be flat for the finer-grained and the debased alumina. A steeply rising crack resistance curve was, however, observed for a pure coarse-grained alumina material which is explained by friction effects of the cracked microstructure behind the measured crack front. The effect is influenced by the test procedure itself. Though crack branching takes place the crack resistance curve of PSZ is completely flat, which is attributed to fast fracture testing where only the most dangerous flaw is activated.

R-curve evaluation with ceramic materials at elevated temperatures by an energy approach using direct observation and compliance calculation of the crack length

An experimental procedure is presented which allows the direct visual observation and measurement of crack extension in ceramic materials at high temperatures. The directly measured crack lengths, gained from displacement-controlled three-point bend tests, are compared to those calculated from the compliance. An energy approach is presented to calculateR-values from the load-displacement curves. TheseR-values for a pure alumina and an alumina containing a glassy phase, for which the load-displacement curves show non-linearity at high temperatures, are compared toK-values andJ-values. The stress intensity approach, based on traction-free surfaces, gives unrealistic data for the nonlinear behaving material owing to adhesive effects behind the actual crack front. TheJ-values, calculated by two methods developed for investigations with moving cracks, are identical to those from the energy approach.

The validity of Weibull estimators-experimental verification

A sufficiently large number of bending tests of a recrystallized silicon carbide ceramic was performed, which gave a fundamental set of strength values. From this fundamental set, arbitrary subsets of size M were chosen by a Monte-Carlo procedure and the parameters of the two-parametric Weibull distribution were calculated by the maximum likelihood method. The dependence of the statistical distribution of the two parameters, obtained by this procedure, on the size of the subset M was investigated. It was found that the variation coefficient of the scale parameter could be well described by the equations given in the literature, whereas the variation coefficient of the Weibull modulus was much higher. It has been shown that the reason for this behaviour is that the distribution of flaws and therefore the strength of the material does not perfectly obey the Weibull statistics, for which the theoretical equations were derived. Thus, in real ceramics the numerical value for the Weibull modulus obtained from a certain number of experiments is even more indeterminate than described by the theoretical solution.

Pore structure of carbon/carbon composites studied by small-angle X-ray scattering

Abstract The development of voids in the fibers and in the matrix of a carbon/carbon composite due to different temperature treatments (1800°C, 2100°C, and 2400°C) was studied by small-angle X-ray scattering (SAXS). Both the scattering of the composite and the fibers were measured, the respective part of the matrix was obtained by subtracting the scattering signal of the fiber from that of the composite. It was observed that the fibers are only slightly influenced by the heat treatment, showing a small increase of the pore size and a weakly more preferred orientation in fiber length direction. The matrix, however, exhibits a pronounced increase of pore size. In particular, large pores develop in the material as a consequence of the stress-induced graphitization of the matrix.

Prediction of strength of recrystallized siliconcarbide from pore size measurement Part I The bimodality of the distribution

The bending strength values of more than 100 specimens of a recrystallized siliconcarbide ceramic (RSiC) show a distinct bimodal Weibull distribution. By measuring the number and size of surface pores, calculating the distribution of volume pores and choosing appropriate shape factors for the pores in the volume and for those close to the surface, the two modes of the Weibull distribution of the strength values can be predicted.

Crack resistance curves of alumina at high temperatures

Ceramic three-point bend specimens were pre-cracked in a displacement-controlled test in air at room temperature to form sharp cracks of different lengths. Critical stress intensity factors (Klc) were then measured as a function of sharp crack length in a fast-fracture, load-controlled test at 900, 1000 and 1100° C. By means of these fast fracture tests, crack resistance curves (Klc against crack length) were determined for two commercially pure aluminas of different grain size and for a debased alumina containing a glassy phase. The crack resistance curve for the pure, fine grained alumina proved to be flat at 900° C, as was found for room temperature. A steeply rising crack resistance was, however, observed for the pure coarse-grained alumina at 1100° C and for the debased alumina at 1000 and 1100° C. This rise in KR curves is explained by friction effects of the cracked microstructure behind the crack front for the coarse grained alumina and by adhesive forces caused by the second phase behind the crack front for the debased alumina. These facts are proved by comparison to experiments on notched specimen and by annealing experiments. From the annealing experiments the size of the adhesive zone is estimated for the debased material.

Determination of interface parameters for carbon/carbon composites by the fibre-bundle pull-out test

In this study a new experimental technique for the measurement of the mechanical properties of the interface between the fibre bundles and the matrix of fibre (bundle) reinforced composites is proposed. The results of this fibre-bundle pull-out test with a bidirectionally layered, satin weave carbon-fibre-reinforced carbon composite, which has been graphitized at three different temperatures, are presented and interpreted within the framework of two micromechanical models.

Elastic moduli and interlaminar shear strength of a bidirectional carboncarbon composite after heat treatment

Abstract In this work a bidirectionally laminated carbon carbon composite has been heat treated (‘graphitized’) at three different temperatures (1800, 2100, and 2400 °C). The Youngs modulus, E11, the intralaminar modulus, G12, and the interlaminar shear modulus, G13, were measured by a resonant beam method for the three modifications. It is shown that an increase in the graphitization temperature leads to an increase in the Youngs modulus and a decrease in the interlaminar shear modulus. The intralaminar shear strength shows a maximum for the material heat treated at 2100 °C and increases with increasing testing temperature.

Non-contacting strain measurements of ceramic and carbon single fibres by using the laser-speckle method

A non-contacting laser correlation sensor is used to determine the strain of different ceramic (alumina, silicon carbide) and carbon fibres in a single fibre tension test. The diameter of these fibres varies from 15 to only 5 mm, which makes the application of conventional strain sensors impossible. The advantage of the non-contacting method is that the strain is directly measured and end-effects from the gripping system need not to be considered. Results for different ceramic and carbon fibres with linear and non-linear stress ‐strain curves are presented as an example. q 2003 Elsevier Ltd. All rights reserved.

Hutchinson's shear coefficient for anisotropic beams

Timoshenkos theory of vibrating beams requires a shear correction factor to correctly take into account the effects of shear deformation for different beam cross-sections. This correction is crucial for a precise determination of the shear modulus from the resonant frequencies. Hutchinsons beam theory is used to derive a new shear correction coefficient for anisotropic materials. A comparison is made with other shear coefficients for anisotropic materials published in the literature. Computer-simulated spectra are used to validate the new anisotropic shear correction coefficient.