Strain hardening in biaxially stretched elastomers undergoing strain-induced crystallization

Abstract

We reveal strain hardening due to strain-induced crystallization (SIC) in both cross-linked natural rubber (NR) and its synthetic analogue (IR) under planar extension, a type of biaxial stretching where the rubber is stretched in one direction while maintaining the dimension in the other direction unchanged. Utilizing a bespoke biaxial tensile tester, planar extension tests were conducted on geometrically designed and optimally shaped sheet specimens to achieve a uniform and highly strained field. Evident strain hardening due to SIC was observed in both stretching (x) and constrained (y) directions when the stretch (λ_x) exceeded a critical value λ_x,c. The λ_x,c value aligned with the onset stretch of SIC in planar extension, as determined by wide-angle X-ray scattering measurements. Interestingly, the nominal stress ratio between the constrained (σ_y) and stretching (σ_x) axes as a function of λ_x exhibited a distinct minimum near λ_x,c. This minimum signifies that the increment of σ_x induced by an increase in λ_x surpasses that of σ_y before strain hardening (λ_x < λ_x,c), while the relationship is reversed in the strain hardening region (λ_x > λ_x,c). The λ_x,c value in planar extension (4.7 for IR and 4.5 for NR) was slightly lower than that in uniaxial extension (5.7 for IR and 5.2 for NR). This difference in λ_x,c values can be explained by considering a single mechanical work required for strain hardening, owing to the relatively small dissimilarities between the two stretching modes. This investigation contributes significantly to the understanding of SIC phenomena in biaxial stretching, and provides valuable insights for predicting the mechanical response of SIC rubber under various deformation conditions.