Similarity and size effects in the quasi-static testing of notched specimens - a review

Abstract

The question of similarity or non-similarity or size effects in deformation and failure is a long-standing problem which has gained recently considerable attention because of its importance for the transferability of mechanical test results of geometrically similar, scaled down structural models to full scale structures using similitude laws. Moreover, it concerns also the validity of the use of small scale laboratory type test results as a basis for the computational modelling of large scale components. Special attention has to be given to structures with strain concentrators, such as holes or notches, which are susceptible to excessive strains, damage, and crack initiation. These mechanisms and the non-uniformity of the associated stress and strain distributions (stress and strain gradients) may induce size effects which are more pronounced than for uniform distributions. In support of the EU-Project LISSAC (Limit Strains for Severe Accident Conditions), a literature survey was performed concerning mechanical test results of geometrically similar, bluntly or sharply notched specimens made of metallic materials, predominantly steel. In most cases the specimens are of relatively simple shape, such as circular tension specimens with a circumferential V- or U-notch, single-edge-notched bend specimens with rectangular cross sections, compact tension specimens, and others. The review has to be restricted to quasi-static loading conditions. Attention is focussed on test results of specimens of nominally the same material which are geometrically similar to a very large extent. Results of primary interest are: Records representing normalized loads or stresses versus normalized displacements or strain measures based on load-point displacement, notch opening, or crack extension. Specific quantities derived from these, such as absorbed energies up to fracture, maximum load, or crack initiation, normalized displacements or strains at maximum load or at a sudden load drop. Reduction of area or diametrical strain at a notch as well as relative notch mouth opening after fracture. Crack initiation and crack propagation behaviour. Although not part of the primary interest, the size influence on characteristic quantities of Linear Elastic Fracture Mechanics and Elastic-Plastic Fracture Mechanics is also considered to some extent: The critical stress intensity factor or strain energy release rate at initiation of crack extension, appropriate for brittle response of essentially elastic materials, and the path-independent J-contour integral as well as the crack-tip opening displacement for elastic-plastic material behaviour; moreover, the size influence on records representing the J-contour integral or the crack-tip opening displacement versus the crack extension (resistance curves) are also examined where available. A number of influences are pointed out which may affect all these results. They come from intended variations of the test conditions (e.g. temperature, testing rate, notch sharpness) or are undesirable ones and difficult to control (e.g. macroscopic material inhomogeneity, testing machine effects). In the course of a previous literature survey, references on size effects in notched specimens had been found and this search was extended by the computerized support of several data banks. The results of about 30 research activities are reviewed selectively in chronological order, with the first publication in 1932 and the last one in 2001; but certainly, the cited literature is not exhaustive. The annotated review closes with discussions and conclusions referring to specific results of the various publications, as related to the various issues mentioned above.