Dilatational bands in rubber-toughened polymers

A Mechanical Model for the Onset of Damage in Rubber Modified Amorphous Polymers

“…4), typically less than 1% of the particle volume, can be neglected for the calculation of stresses and energies. The energy dissipation is here proportional to the surface of the void, as opposed to the notably different result given in a previous paper [2], where this energy is proportional to the volume of the void according to the term 4rG x&3/3, which corresponds to a particular value of the limiting extension ratio (ha = 5) of the rubber.…”

“…applied at infinity inner void surface (stretched) potential energy outside the particle (external forces and matrix) elastic shear energy in the particle after void appearance energy dissipated in void formation volume of the ith particle specific surface energy of the rubber homogenised shear modulus of a blend shear modulus of the rubber Poisson's ratio of the rubber particle temperature elastic energy inside the particle before void appearance elastic hydrostatic energy in the particle after the void appearance volume fraction of particles in the matrix total volume of particles and matrix surface tension of the rubber extension ratio at the inner void surface shear modulus of the matrix Poisson's ratio of the matrix In many polymers toughened by rubber particles, it is known that, at medium loading rates, damage occurs through cavity formation in the particles [I] and subsequent yielding of the matrix around the particles [2]. Yielding occurs after cavity formation owing to the relatively large and instantaneous decrease of the hydrostatic tension stress in a particle where a void is developing.…”

Modeling and Simulation of Mechanical Properties of Nano Particle Modified Polyamide 6

“…In this section, the cavitation criteria are introduced. A model of particle cavitation is advanced by Lazzeri and Bucknall [8]. Two assumed preconditions are  the largest defects of inclusions are micro holes with nanometer-ordered dimensions  the releasing of stored volumetric energy should be big enough to widen the surface area of holes and to extend the surrounding layers of inclusions for the expansion of micro holes.…”

Micromechanics, macromechanics and constitutive modeling of the elasto-viscoplastic deformation of rubber-toughened glassy polymers

“…" reduced elastic stiffness, * decreased yield stress, " reduced post-yield softening, " reduced strain-hardening, and Lazzeri and Bucknall [43] modeled the matrix pressure dependence on the onset of macroscopic yield of a porous glassy polymer containing spherical voids. These modifications might make a "Gurson-type" model more suitable for the application to rubber-toughened polycarbonate.…”

“…McClintock ( for by Steenbrink, et al (1997), and the pressure dependence of yield has been accounted for by Lazzeri and Bucknall (1993). These modifications might make the…”