Extension of Griffith's theory of rupture to three dimensions

Comparison of the Conventional and Mechanochemical Syntheses of Cyclodextrin Derivatives

Many scientists are working hard to find green alternatives to classical synthetic methods. Today, state-of-the-art ultrasonic and grinding techniques already drive the production of organic compounds on an industrial scale. The physicochemical and chemical behavior of cyclodextrins often differs from the typical properties of classic organic compounds and carbohydrates. The usually poor solubility and complexing properties of cyclodextrins can require special techniques. By eliminating or reducing the amount of solvent needed, green alternatives can reform classical synthetic methods, making them attractive for environmentally friendly production and the circular economy. The lack of energy-intensive synthetic and purification steps could transform currently inefficient processes into feasible methods. Mechanochemical reaction mechanisms are generally different from normal solution-chemistry mechanisms. The absence of a solvent and the presence of very high local temperatures for microseconds facilitate the synthesis of cyclodextrin derivatives that are impossible or difficult to produce under classical solution-chemistry conditions. Although mechanochemistry does not provide a general solution to all problems, several good examples show that this new technology can open up efficient synthetic pathways.

The Strength of Fibres in All-Ceramic Composites

When considering the strength of a fibre reinforced ceramic composite, it is often assumed that the fibres retain their full strength of several GPa after cracking of the weaker matrix. The strength of the composite after matrix cracking is then calculated by the rule of mixtures as the product of fibre volume fraction and fibre strength. This paper demonstrates that such a calculation is not consistent with the principles of fracture mechanics for an isolated fibre embedded in an elastic matrix of the same elastic modulus, because the strength of the fibre is much reduced by the stress concentration arising from the matrix crack. Experimental measurements of the strength of a glass fibre embedded in a brittle matrix support the theory. The case of a fibre in a matrix of different elastic modulus is also considered, together with the proDlem of cracking along the fibre-matrix interface.

Weibull Modulus of Toughened Ceramics

The influence of toughness on the Weibull modulus of ceramics is discussed. It is shown that an increase in toughness does not give a higher Weibull modulus if the ceramic is truly brittle, following the Griffith criterion of fracture. However, R curve behaviour, such as that shown by tetragonal zirconia, by Dugdale material, or by fibrous ceramic composites, leads to an improved Weibull modulus. Theoretical argument and experimental results support these conclusions.