10 Failure Theories of a Lamina 10.1 Basic Equations In this chapter we present various failure theories for one single layer of the composite laminate,usually called a lamina.We use the following notation throughout this chapter for the various strengths or ultimate stresses: of:tensile strength in longitudinal direction. of:compressive strength in longitudinal direction. :tensile strength in transverse direction. o:compressive strength in transverse direction. 2:shear strength in the 1-2 plane. where the strength means the ultimate stress or failure stress,the longitudinal direction is the fiber direction(1-direction),and the transverse direction is the 2-direction(perpendicular to the fiber). We also use the following notation for the ultimate strains: ultimate tensile strain in the longitudinal direction. ef:ultimate compressive strain in the longitudinal direction. ultimate tensile strain in the transverse direction. e8: ultimate compressive strain in the transverse direction. ultimate shear strain in the 1-2 plane. It is assumed that the lamina behaves in a linear elastic manner.For the longitudinal uniaxial loading of the lamina (see Fig.10.1),we have the following elastic relations: OT =E1eT (10.1) of =Eref (10.2)10 Failure Theories of a Lamina 10.1 Basic Equations In this chapter we present various failure theories for one single layer of the composite laminate, usually called a lamina. We use the following notation throughout this chapter for the various strengths or ultimate stresses: σT 1 : tensile strength in longitudinal direction. σC 1 : compressive strength in longitudinal direction. σT 2 : tensile strength in transverse direction. σC 2 : compressive strength in transverse direction. τ F 12 : shear strength in the 1-2 plane. where the strength means the ultimate stress or failure stress, the longitudinal direction is the fiber direction (1-direction), and the transverse direction is the 2-direction (perpendicular to the fiber). We also use the following notation for the ultimate strains: εT 1 : ultimate tensile strain in the longitudinal direction. εC 1 : ultimate compressive strain in the longitudinal direction. εT 2 : ultimate tensile strain in the transverse direction. εC 2 : ultimate compressive strain in the transverse direction. γF 12 : ultimate shear strain in the 1-2 plane. It is assumed that the lamina behaves in a linear elastic manner. For the longitudinal uniaxial loading of the lamina (see Fig. 10.1), we have the following elastic relations: σT 1 = E1εT 1 (10.1) σC 1 = E1εC 1 (10.2)