The influence of grain size on the flow stress of a copper-3.2 at. % tin solid solution

Abstract

The slope, k F , of the Petch relationship between flow stress, σ f , and grain size, d − 1 2 , has been investigated as a function of temperature in an alloy containing 3.2 at. % of tin in copper. It was found that K F remained almost constant up to a critical temperature, T crit , which was defined by the onset of repeated yielding. It then increased in magnitude by a factor of 2 and decreased again at a rate inversely proportional to the square of the temperature, T −2. The exact form of this relationship depended upon the strain at which the measurements were made. It is suggested that the increment of flow stress introduced by the presence of grain boundaries is controlled by the stress required to generate dislocations from an unpinned source. At temperatures below T crit , the friction stress which opposes a glide dislocation is equal to that which opposes a dislocation at its source, and any temperature dependence of K F arises from the temperature dependence of the shear modulus. At temperatures above T crit , the concentration of solute atoms around a dislocation at its source is considered to be higher than that around a gliding dislocation and the friction stress on the source is greater. This leads to the sudden increase of K F at the critical temperature. The magnitude of the difference between the two friction stresses, τ x , is considered to depend upon the mobility of the solute.