Elasto-Plastic Analysis of a Miniature Circular Disk Bending Specimen

Miniature disk bending test is used to evaluate the mechanical behavior of irradiated materials and its properties — mainly ductility loss due to irradiation in steel. In Miniature Disk Bending Machine the specimen is firmly held between the two horizontal jaws of punch, and an indentor with spherical ball travels vertically. Researchers have observed reasonable correlations between values of the yield stress, strain hardening and ultimate tensile strength estimated from this test and mechanical properties determined from the uniaxial tensile test. Some methods for the analysis of miniature disk bending, proposed by various authors have been discussed in the paper. It is difficult to distinguish between the regimes of elastic and plastic deformation since local plastic deformation occurs for very small values of load when the magnitude of spatially averaged stress will be well below the yield stress. Also, the analytical solution for large amplitude, plastic deformation becomes rather unwieldy. Hence a finite element analysis has been carried out. The finite element model, considers contact between the indentor and test specimen, friction between various pairs of surfaces and elastic plastic behavior. The load is increased in steps and converged solution has been obtained and analysis terminated at a load beyond which a stable solution cannot be obtained. A sensitivity study has been carried out by varying the various parameters defining the material properties by ±10% around the base values. This study has been carried out to generate a data base for the load-deflection characteristics of similar materials from which the material properties can be evaluated by an inverse calculation. It is seen that the deflection obtained by analytical elastic bending theory is significantly lower than that obtained by the elasto-plastic finite element solution at relatively small values of load. The FE solution and experimental results are in reasonably good agreement.