Constitutive modeling of size effect on deformation behaviors of amorphous polymers in micro-scaled deformation

Abstract

With the advantages of high-formability, low-cost and unique physical properties, polymers have been widely used in microforming of polymeric components for a large scale of applications in many fields including micro-optics, microfluidic and sensors, etc. In micro-scale, the deformation behaviors of polymers are observed to be size-dependent. Conventional constitutive models of polymers, however, cannot predict and represent those size-dependent behaviors well. To address this issue, a constitutive model with consideration of size effect for amorphous polymers in micro-scale was developed in this research. Firstly, on the basis of the couple stress theory, the impact of rotational gradients was taken into consideration and a strain gradient “elastic-viscoplastic” constitutive model was proposed to quantitatively describe the size-dependent behaviors of amorphous polymers in micro-scale. After that, four point micro-bending experiments were implemented on poly (methyl methacrylate) (PMMA) films with thickness varying from the millimeter scale to micrometer scale. The size effect of PMMA in micro-scale was further illustrated and the proposed strain gradient “elastic-viscoplastic” model was finally validated and verified for the capability of modeling of the size effect of amorphous polymers in micro-scaled deformation. This research thus advances the understanding of the size effect and the strain gradient based mechanical behaviors of amorphous polymers and facilitates its applications in industries.