Combined photoelastic and electrical-analog method for solution of plane-stress plasticity problems

A new application of the electrical-analog method is introduced for the evaluation of the\(\varepsilon _z - principal\) strain, normal to the surface of a thin sheet loaded under conditions of plane stress in plasticity. The analogy relating the two physical phenomena of\(\varepsilon _z - strain\) distribution in a plane-stress plastic field and the potential φ of a plane electrostatic field is based on the assumption that the Cartesian components of strain parallel to the surface of the body vary along the thickness of the strip. They are expressed as a sum of a term independent ofz and a second term, which is a second degree function of thez-coordinate normal to the surface of the body. The boundary conditions of the\(\varepsilon _z - strain\) distribution may be easily determined by a photoelastic method using birefringent coatings cemented on the surface of the metallic specimens. Then, the electrical analogy can be applied for the evaluation of the\(\varepsilon _z - strain\) distribution all over the field. The graphited paper was used as conducting surface in the application of the analogy. The values of\(\varepsilon _z - strain\), together with data obtained by the birefringent coating and concerning the two other Cartesian components of strain, yield an explicit analytic solution of the elastic-plastic plane-stress problem. The method is applied to a plane-stress restricted plasticity problem of a thin slab, with two semicircular grooves in pure tension. The results were compared with those obtained by a photoelastic pointwise solution using normal and oblique incidence. The agreement between these results shows the accuracy of the method.