On the evaluation of residual stresses in bi-layer materials using the bent strip method

Numerous equations can be found in the literature for calculating residual stresses in plated metals and thin film materials using the bent strip method. The residual stresses predicted by these different equations were found to vary widely, and it is clear that not all of them can be correct. The linear-elastic relations for determining residual stresses in deposits of arbitrary thickness were therefore derived from first principles, and the results obtained here agree with earlier bi-metallic beam solutions if the residual stress terms go to zero. In the general case of a non-uniform through-thickness residual stress the problem is statically indeterminate, and conditions under which a constant uniform residual stress may be assumed are discussed. Common issues associated with using finite element models to analyze deposit stresses are also addressed, along with practical considerations for specimen design. The results given here can be used to calculate residual stresses in mechanically isotropic, linear-elastic metallic, ceramic, and polymeric films using the bent strip method.