We first review Puck and Schürmann's progressive failure criteria for three-dimensional deformations of unidirectional fiber-reinforced composites, and then simplify these for plane stress deformations. These criteria have been implemented as an USDFLD subroutine in the commercial software, ABAQUS/Standard. Several example problems have been analyzed with the developed software, and for some problems computed results have been compared with those obtained by using the CLPT for stress analysis and Puck and Schürmann's criteria for failure analysis. A close agreement between the two set of results verifies the implementation of the failure criteria in the software, ABAQUS. These examples illustrate that the ultimate failure load is significantly higher than that when the failure initiates first which is usually called the first ply failure load.
NomenclatureA,B,C = three modes of failure in matrix A (R) = reduced stiffness parameter in N 2 /mm 2 B (R) ,C (R) = reduced stiffness parameters in N 2 /mm D (R) = reduced stiffness parameter in N 2 /mm 3 E 1 ,E 2 = elastic moduli in the longitudinal and the transverse directions, respectively, within a ply, GPa FI = Dimensionless failure index; 0 ≤ FI < 1 no failure, FI = 1 at failure initiation f(σ 22 ) = ( )( ) ( ) G 12 = shear modulus in the x 1 -x 2 plane, GPa H = laminate thickness, mm M = applied moment, N-mm/mm M o = applied moment at damage initiation, N-mm/mm M x = bending moment resultant, N-mm/mm ( ) ( ) ( ) = inclination parameters are slopes of the failure surface in stress space at σ nn =0, dimensionless N x = in-plane force resultant in x-direction, N/mm N xy = in-plane force resultant in x-y plane, N/mm S = compliance matrix S L = in-plane shear strength, MPa S T = shear strength transverse to the fibers in the failure plane, MPa ̅ = shear strength S L as a function of the normal stress σ 22 , MPa ̅ = shear strength S T as a function of the normal stress σ 22 , MPa 2 S = shear strength resultant in the failure plane for σ 22 = 0 or σ nn =0, MPa ̅ = Shear strength resultant S as a function of the normal stress σ 22 or σ nn , MPa T= transformation matrix for transforming from global to local coordinate system T σi = transformation matrix for transforming stresses from global to local coordinate system T εi = transformation matrix for transforming strains from global to local coordinate system ̅ = stiffness matrix X C = absolute value of the compressive strength in the fiber direction, MPa X T = absolute value of the tensile strength in the fiber direction, MPa, Y C