Strain hardening in biaxially stretched elastomers undergoing strain-induced crystallization.

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.