Necessary Conditions for Ductile Flow of a Tensile Composite Rod

The upper bound approach is applied to the problem of deriving the conditions which promote ductile flow (i.e., flow which incurs no void formation) in a composite rod undergoing a tensile test. The conditions for homogeneous deformation and for nonhomogeneous deformation without void formation, including the case of nondeforming particles, are obtained as particular cases of ductile flow. The composite material under study is a homogeneous soft matrix with hard inclusions. The relative strength of the reinforcing particles, the geometrical parameters, and the possibility of testing under pressure are all included in the analysis. These factors appear in the equations expressing the necessary conditions for ductile flow and the expression for the composite strength. A detailed algorithm is provided for translating in graphical form the necessary conditions for ductile flow. The calculation of the flow pattern parameters is also simpler when the graphs are used. Two typical graphs are presented showing the dependency of the expected strength on such factors as external pressure and particle strength.