Yield Surfaces for Anisotropic Plates

Aerospace systems are incorporating composite materials into their structures. The composite materials are often anisotropic in mechanical response due to their geometric layout. For many years, the failure surfaces of anisotropic materials were thought to be characterizable by a quadratic function in the stress, referred to as a Tsai-Wu yield surface, or, in a more restrictive form, a Tsai-Hill yield surface. Such a representation does not work for materials that are strong in two directions and weak in one direction, which is the case of most interest since it represents fiber/epoxy composite plates. This paper demonstrates the impossibility of modeling the failure surface with either the Tsai-Wu or Tsai-Hill failure surfaces. A yield surface is presented based on the lemniscate, which is quartic in the stress. This new yield surface addresses the case of strong in two directions and weak in one.