Interaction of Tire Material and Design

Abstract

Abstract An analytical study based on the Halpin-Tsai equations in their complex form has been conducted over a reasonably practical range of variables typical of a composite construction involving steel-cord reinforcement in a rubber matrix. Curves are presented which show the influence of several material properties on the composite characteristics of bias-angle constructions. From these curves, it is possible to deduce the influence of these constituent material properties on the overall composite response. The most significant deductions from these results are: (1). The elastic extension modulus of the composite, E′, is highly dependent on the bias angle and moderately dependent on the volume fraction of cord. On the other hand, E′ is essentially independent of the loss modulus of the matrix E″r. (2). The elastic shear modulus of the composite, G′, is also dependent on the bias angle and volume fraction of cord, but independent of the loss modulus of rubber. Also G′ is symmetric about a 45 degree bias angle. (3). The loss modulus in tension of the composite, E″, is highly dependent on the bias angle and moderately dependent on the volume fraction of cord and loss modulus of the matrix. (4). The loss modulus in shear of the composite, G″, is dependent on the bias angle and volume fraction of cord and nearly independent of the loss modulus of the matrix except at bias angles near zero and 90 degrees. (5). The loss tangent in tension of the composite, tan ΔE′ is highly dependent on the bias angle from 0 to 20 degrees and is approximately a constant for all other bias angles. The magnitude of the constant value is the same as tan δr of the matrix. (6). The loss tangent in shear of the composite, tan ΔG′ is nearly a constant except for very small or very large bias angles. The magnitude of this constant is approximately the small value of the loss modulus of the cord. Also tan ΔG is symmetric about 45 degrees. (7). For most bias angles, the loss tangent of the composite in shear is much less than the loss tangent of the composite in tension.