Distributed dislocation-residual stress model of cold rolled strips based on the complex variable function method of plane elasticity

In order to reveal the formation mechanism of the manifested waves of cold rolled strips,the distributed dislocation was calculated by using measured residual stress,and a distributed dislocation-residual stress model was proposed. The stress field of an elastic plane with a typically distributed dislocation in the straight boundary was analyzed using the complex variable function method of plane elasticity,and the interaction was studied between the stress fields due to several straight lines with the distributed dislocation.In combination with measured data,the actual distributed dislocation which corresponds to a small relative error of residual stress was calculated in a general way. The form of the deflection function was shown by analyzing the distributed dislocation,which coincides with the actual buckling mode.