A model of void coalescence in columns

Void coalescence in columns (or necklace coalescence) is a computationally confirmed and physically observed mechanism of void link-up in metal alloys and polymers that has received little attention in the literature. Here, analytical treatment of the phenomenon proceeds from first principles of limit analysis and homogenization theories. A cylindrical unit cell embedding a cylindrical void of finite height is considered under axially symmetric loading. Two types of trial velocity fields are used in seeking an upper bound to the yield criterion corresponding to the particular regime of coalescence in columns. For each type, exact expressions of the overall yield criterion are obtained, albeit in implicit form when using continuous fields. Upon comparison with other modes of yielding allowing for void growth and coalescence in layers, an actual effective yield domain is obtained so as to ascertain regimes of stress state and microstructural states where void coalescence in columns prevails. The predictions are also assessed against finite element based limit analysis.