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The influence of material inertia on neck development in a notched round baris analyzed numerically. Dynamic axisymmetric calculations are carried out forisotropically hardening elastic-viscoplastic solids so that both materialstrain rate sensitivity and material inertia are accounted for. The focus is onthe effect of bar size on whether the notch triggers necking or neckinginitiates away from the notch. The governing equations are presented innon-dimensional form and two key non-dimensional groups that involve bothmaterial and loading parameters are identified. For both non-dimensionalgroups, with all parameters fixed except for bar size, it is found that forsufficiently small bars, the notch triggers necking, whereas for sufficientlylarge bars necking ultimately occurs away from the notch. With materialproperties fixed, for one non-dimensional group the transition to necking awayfrom the notch corresponds to increasing imposed velocity whereas for the othernon- dimensional group this transition takes place for decreasing imposedstrain rate. Both these transitions correspond to increasing bar size. Theresults indicate that this transition is governed by material inertia but thebar size at which it occurs depends on the material properties, particularlystrain hardening and strain rate hardening.

Effect of size on necking of dynamically loaded notched bars