Multi-Axial Stress State Yield Criteria for Injection Moulded Housings
Pressure-dependent yield criteria accurately predict multi-axial housing failure, preventing costly tool steel recuts and unnecessary wall thickness.
Hydrostatic Pressure
Meaning
Isotropic mechanical stress states define the average normal stress acting uniformly across all planes passing through a specific point within a fluid, melt or solid body. Calculated as one-third of the trace of the Cauchy stress tensor, hydrostatic pressure represents the non-deviatoric stress component that alters the physical volume and intermolecular spacing of a polymer without inducing macroscopic shear shape changes. The variable governs polymer melt compressibility, volumetric shrinkage during moulding, crystallization kinetics under pressure, and the pressure-dependent yield limits of solid thermoplastics.
It ceases to govern deformation when applied to incompressible theoretical fluids, or when pure deviatoric stress states drive plastic yielding entirely through shear mechanisms without volumetric change.
Phase Behaviour
High isotropic pressure compresses free volume between polymer backbones, driving macromolecules into closer physical proximity. This volumetric contraction elevates the glass transition temperature of amorphous polymers and raises the equilibrium melting point of semi-crystalline resins, often shifting phase transition temperatures by tens of degrees Celsius under production conditions. Inside an injection mould cavity, elevated hydrostatic pressure retards molecular relaxation while accelerating crystallization nucleation rates, producing finer, denser spherulitic morphologies than those formed under ambient pressures.
As pressure rises, melt shear viscosity escalates exponentially according to the Barus equation or modified Cross-WLF models, altering flow resistance across runners and cavity walls. Decompressing the melt during cavity filling or gate freezing prompts immediate changes in specific volume governed by the resin’s pressure-volume-temperature state diagram.
Cavity Packing
Injection moulding machinery establishes intense hydrostatic pressure fields during the packing and holding phases to compensate for volumetric thermal contraction as the melt solidifies. Holding pressures ranging between fifty and one hundred and fifty megapascals force additional melt mass through the gate, preventing sink marks, internal vacuum voids and dimensional warpage in thick-walled sections. If the hydrostatic pressure profile decays prematurely due to early gate freeze-off, the trapped melt solidifies under atmospheric conditions, yielding parts with severe volumetric shrinkage and internal tensile residual stresses.
Excessive holding pressure packs the cavity beyond its volumetric shrinkage requirement, resulting in over-densification, mechanical sticking against mould cores, and cracked ejector pin locations during part demoulding.
Structural Yielding
Solid thermoplastics respond to hydrostatic stress fields with dramatic shifts in their ultimate yield and failure thresholds. While metals undergo plastic yield almost entirely via deviatoric shear stresses, solid polymers expand their yield envelopes significantly under compressive hydrostatic states. Glassy polymers such as polymethyl methacrylate deform via shear yielding under high compressive pressure, whereas triaxial tensile hydrostatic fields promote localized micro-void nucleation, craze propagation and catastrophic brittle fracture.
Finite element analyses of thick plastic components subjected to bending or point impacts must evaluate the local hydrostatic tension to predict whether ductile yielding or brittle crazing will dominate. Regrind fractions possessing internal contamination or micro-voids suffer accelerated failure under hydrostatic tension, as localized stress triaxiality drives rapid craze coalescence around low-adhesion foreign particulates.