Energy-based yield criterion for PMMA from large-scale molecular dynamics simulations

We use molecular dynamics (MD) with the DREIDING force field to characterize the ultimate mechanical response of amorphous poly(methyl methacrylate). We characterize how volumetric and deviatoric strains contribute to yield for a wide range of loading conditions from pure deviatoric, volume-conserving cases to isotropic volume expansion. We propose and apply an energy-based yield criterion to define yield consistently for all cases. Our results show that permanent deformation occurs when either the deviatoric or volumetric strains reach critical values, except in a narrow region around the transformation between deviatoric- and volumetric-dominated yield where the two strain invariants interact. In contrast, the pressure-modified von Mises criterion is only applicable to shear-dominated loading conditions. These results provide insight into the physics of yield in amorphous polymers and provide quantitative information and guidance for physics-based yield criteria for polymer-matrix composite materials.

Figure 1

Stress along principal axis as a function of time for three different loading paths: (a) volume-conserving uniaxial, (b) pure uniaxial strain, and (c) volumetric expansion.

Figure 2

Snapshots of the MD simulations at two different times for volume-conserving uniaxial deformation (a, b) and pure uniaxial strain (c, d).

Figure 3

Deviatoric (a) and volumetric (b) stress-strain curves for the entire family of deformation paths. Curves are identified by the transverse to longitudinal strain ratios.

Figure 4

Pressure-modified von Mises plot (deviatoric stress at yield vs pressure) including our MD simulations (squares and circles) and experiments (triangles).

Figure 5

Mechanical work performed on the samples per unit volume and time for the family of the deformation paths explored. The maximum of these curves define the yield condition.

Figure 6

Deviatoric and volumetric strains at yield (a, b) and deviatoric and volumetric stresses at yield (c, d) as a function of effective deformation rate for the various deformations. Curves are identified by the transverse to longitudinal strain ratios.

Figure 7

Total mechanical work absorbed up to yield as a function of effective deformation rate for the various deformations. Curves are identified by the transverse to longitudinal strain ratios.

Figure 8

Deviatoric and volumetric yield strain (a), yield stress (b), and energy absorbed (c) as a function of transverse to longitudinal strain ratio.