Abstract The maximum hardness of a range of metals and substantially single-phase alloys was estimated by measuring the micro-hardness of surfaces strained by shot peening, by wear in stony soil, and by working with a blunted “trepanning” tool. The highest and most uniform hardness results were obtained by trepanning and these are taken as the maximum hardness, Hu. The values are compared with previous, generally lower, estimates. The strength of the material at low strain and the maximum strength are shown to be related according to the metallic structure. The mechanism of abrasive wear is considered. Wear results on hard abrasives are examined in relation to the maximum hardness. It is suggested that wearing surfaces locally reach a maximum hardness measured by Hu, but that other regions remain substantially softer. This is confirmed by the wear behaviour of the materials on soft abrasives (to be reported). Properties affecting the flow of the wearing material are discussed, and the importance of hardening and softening mechanisms due to alternating strain. Various wear and high-strain phenomena are considered including the structural transformation of two austenitic steels, temperature, strain rate and speed effects, and the mechanism that limits strength.