Finite element simulations of Tennessee marble under plane strain laboratory testing: Effects of sample–platen friction on shear band onset

Abstract

We use the finite element method to analyze a non-associated Drucker–Prager elastic–plastic material relation for Tennessee marble under plane strain laboratory test conditions. We study how the sample–platen interface boundary conditions affect the development of stress and strain in the sample and prediction for the onset of shear banding according to the Rudnicki–Rice theory. Samples that are bonded with the platen (corresponding to an infinite coefficient of friction (COF)) have all their maximum interface stresses at the outside upper corner of the test piece. When the COF is finite the stresses are not maximum in the corner but just inside of it, with the exception of the in-plane lateral normal stress, which has its maximum along the vertical centerline. Both the interface COF and the aspect ratio (the height/width ratio) affect the whole-sample axial stress–strain curves and the onset of localization. For an aspect ratio of 2.25, simulations with different COFs have whole-sample axial nominal stress versus strain curves that are coincident until late in the loading program. Then, in the vicinity of localization (near peak), these curves separate slightly from each other and the onset of localization occurs at different stress and strain values. Specifically, the stress and strain at localization onset decrease with increasing COF (from 0.01 to infinity in separate simulations) from the values for the frictionless interface. Although we focus on the 2.25 aspect ratio, our analyses with three other ratios (1.875, 1.5, and 1.0) with fixed COF show that localization onset occurs at progressively higher axial nominal stress and strain as the aspect ratio is decreased. Lastly, we find that a lower sample aspect ratio facilitates localization near the outside of the sample and close to the sample–platen interface, while the higher aspect ratio favors the onset of shear banding in the sample center. Our results demonstrate that modest variations in sample–platen friction do not significantly alter the nominal stress–strain curves but they can affect the onset and location of localization.