The chevron folding instability in thermoplastic elastomers and other layered materials

When thermoplastic elastomers (TPEs) such as styrene-isoprene-styrene or styrene-butadiene-stryrene copolymers in an aligned lamellar or hexagonal morphology are stretched perpendicularly to the plates or rods, then above a critical stress the lamellae or cylinders buckle to form a chevron or zig-zag structure. We examine this instability both analytically and using finite element analysis. In the analytic work we treat the elastomer as if it were a homogeneous anisotropic material and describe the chevron formation in terms of strain fields at length scales larger than that of the microphase pattern. We find that in order to do this one must respect the underlying microphase structure in two respects: (i) in terms of a statement as to how the material anisotropy rotates with the material; and (ii) in terms of additional `material moduli' which represent couplings between the macroscopic strain fields and deformations that occur at the microphase length scale. We define moduli which relate to hard phase bending and to displacement of the soft phase relative to the hard phase. The analytical results are tested by comparison with finite element models which solve for the microscopic strain field, and which allow the examination of post-buckling behaviour. We find that for perfectly aligned TPEs there is a geometric instability towards a sinusoidal buckling profile, which evolves into the chevron shape on further strain beyond the instability. The buckling is associated with a sharp turnover in the stress-strain curve. We also set our work in the context of treatments of similar buckling instabilties found in the fields of structural geology and liquid crystals.