Investigation of Size Effects on Process Models for Plane Strain Microbending

Accurate process models provide vital information in the design of manufacturing processes. To characterize bending operations, analytical models have been developed and shown to predict the peak bending forces fairly accurately for sheets in the macro or mesoscale (i.e. sheets with a large number of grains through the thickness). However, whether these models also accurately predict bending forces for sheets in the microscale (i.e. sheets with approximately ten grains or less through the thickness) has not been evaluated. The present study is aimed at investigating the use of two such models from previous work with microscale bending data. In addition, using these previous models as a foundation, additional bending force models were developed to predict the bending force specifically for microscale bending operations. Data analysis showed that the process models from past research, which provide accurate results for macroscale bending, over predict the peak force required for bending microscale sheets. These process models assume a non-linear strain distribution through the thickness and a curved formed wall. The two models developed in this research provide accurate results for the microscale bending tests, however, they under predict the peak force for the macroscale bending operation. These developed process models assume a linear strain distribution through the thickness and a straight formed wall. The linear strain distribution is more appropriate for the microscale bending process as there are few grains through the thickness and the strain in individual grains varies linearly across the grain. The straight formed wall is more appropriate for the microscale bending process as there is not sufficient distance to warrant a curved formed wall assumption. These differences represent size effects for assumptions in the process models. The material used for these investigations was Brass (CuZn15). The sheets had between 2 and 50 grains through the thickness with grain sizes of between 10 μm and 71 μm.