Polymer glasses have numerous advantageous mechanical properties in comparison to other materials. One of the most useful is the high degree of toughness that can be achieved due to significant yield occurring in the material. Remarkably, the onset of plasticity in polymeric materials is very poorly quantified, despite its importance as the ultimate limit of purely elastic behavior. Here we report the results of a novel experiment which is extremely sensitive to the onset of yield and discuss its impact on measurement and elastic theory. In particular, we use an elastic instability to locally bend and impart a textit{local} tensile stress in a thin, glassy polystyrene film, and directly measure the resulting residual stress caused by the bending. We show that plastic failure is initiated at extremely low strains, of order $10^{-3}$ for polystyrene. Not only is this critical strain found to be small in comparison to bulk measurement, we show that it is influenced by thin film confinement - leading to an increase in the critical strain for plastic failure as film thickness approaches zero.
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