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Mechanical Properties vs. Grain Size

•Increased "strain to failure"

Catcalaied utraint ta failure ai a funcKon oj Ihe gmin size far naireriair, aj sew.rai fracture tr.ughne.tses /tnkćsz f>nm rej. IOA j

According to this analysis, an initial sub-critical flaw will bc clastically scrained on loading, sonie looalised straining will takc place ahead of the shatp flaw, and sonie overall straining of thc sample will be required for the flaw to grow to critical si/e. whcrc catastrophic failure will take place. In the case ot' very brittle materials this total J-integra) reduces essentially to eąuacion (xi.i) only. which corresponds closely to the Griffith crack condition. as seen in equation (xl). If wc consider that the fracture toughness and yield stress remain constanl, but that the startir.g flaw size is reduced as the grain size is decreused, then it is ncccssary to impose a higher stress, induce greater localised plasticity and morę global plasticity to grow ihe finer starting flaw to the critical crack length [106], This analysis has been carried out by Chan 1106]. with thc important results summariscd in Fig. 10, showing the inerease in fracture strain or ductility as the grain size is rcduced, for a varicty of malcrials with a rangę of values of fracture toughness. The important conclusion is thc steady inerease in strain to failure as Fig. JO. thc grain size is reduced, with a dramatic inerease once ihe grain size rcaches a value characteristic for each materiał (fracture toughness and yield stress combination).