Prediction of Central Bursting in Extrusion Using Multiplicity Criterion.

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The central burst defect, also called chevron crack, in axi-symmetric extrusion is analyzed. For the prediction of central bursting the criterion based on plastic instability is used. It satisfies the sufficient condition suεu=0 for multiplicity of solution, which is derived from the discussion based on its necessary condition ΔsuΔεu=0, where su denotes the nominal stress rate, and Δ shows the difference of any two multiple solutions. Stress and strain in the specimen are evaluated using FEM. As the parameter representing the risk for the occurrence of central bursting the measure yM is introduced and it is calculated using the stress and strain on the central line of the product. When yM<0, the bursting occurs. The value of yM is shown in the range of combination between the cone angle of die and the reduction in working. From these values the working condition predicting yM=0 is interpolated for several work hardening exponents, which shows the boundary between workings with and without cracking. The boundary curve predicted is compared with experimental values obtained by Zimerman and Avitzur. The prediction is found to be, on the whole, similar to the experimental results.