Analysis of strain distribution during tensile deformation of sheet steel and determination of uniform elongation using a constitutive equation

Uniform strain distribution in a tensile specimen during an initial stage of tensile deformation of sheet steel breaks down into the localization of strain after the maximum load point corresponding to uniform elongation. These deformation behaviors were analyzed by a simplified constitutive equation derived from a thermally activated process of dislocation movement, The average deformation behavior measured at fixed gage length is co-related with the local deformation behaviors by means of the equality of load applied on a tensile specimen. Relation between local strain and local strain rate derived from this co-relation exhibits an U-shaped curve which goes through a point of average strain and strain rate, which composes a straight line at fixed strain rate on this strain and strain rate diagram. The U-shaped curve becomes tangent to the straight line expressing average strain and strain rate relation at a strain corresponding to the uniform elongation. Development of strain fluctuation imposed at a local point was analyzed on this diagram. At smaller average strain which corresponds to the left half of the U-shaped curve, the local strain higher than the average exhibits local strain rate lower than the average, which results in a convergence of strain fluctuation and thus uniform deformation, On the other hand, at higher average strain, the local strain higher than the average exhibits local strain rate higher than the average, which results in a divergence of strain fluctuation and the development of localized deformation. Uniform elongation is defined as the strain at the boundary of convergence and divergence of local strain fluctuation.