Meaning
Non-dimensional geometric metrics that quantify the severity of a multi-axial stress state are defined as the ratio of hydrostatic pressure to equivalent von mises stress. Mechanical designers use the stress triaxiality ratio to evaluate whether a molded part will fail in a ductile or brittle manner under localized loads. This value varies across the geometry of a part, with high values indicating a strong resistance to plastic flow.
The limit of this ratio determines where voids grow rapidly within the polymer matrix.
Deformation Mechanism
High values of the stress triaxiality ratio promote brittle fracture by preventing the shear deformation that allows polymers to yield and draw. Sharp internal corners and thickness transitions in injection molded parts generate these high-triaxiality regions. Modifying the tooling to include generous radii reduces this ratio and improves impact resistance.
Simulation Application
Finite element models calculate the local triaxiality to predict damage initiation sites in complex structures. This simulation helps locate the precise areas where structural reinforcement is needed.
Material Response
Ductile polymers like polycarbonate undergo a dramatic transition to brittle failure when this ratio exceeds a threshold. Fillers and glass fibers further restrict the material’s ability to deform, lowering the allowable triaxiality before microcracking begins. Regrind resins are particularly sensitive to these triaxial stress states because of their reduced molecular weight and lower fracture toughness.
