A finite element model to investigate the performance of hybrid structure under lowvelocity impact loading was developed and validated using a building-block approach. The hybrid structure consisted of a composite patch adhesively bonded to a metal substrate. Each component of the model was validated individually to accurately capture the behavior and damage mechanisms of each material. Interlaminar composite damage and adhesive damage were modeled with cohesive zone theory. Hashin failure criteria with energy dissipation based damage evolution modeled intralaminar damage in the composite. The Johnson-Cook plasticity model captured the metal substrate's behavior. Each component was assembled into a hybrid structure model that captured the interactions between the damage modes. Once the hybrid model was validated with experimental results, a sensitivity study was performed on various input parameters to provide guidance for optimized design of composite patches subjected to low-velocity impact loading.
NomenclatureA, B, C, m, n = Johnson-Cook material constants a 0 = initial crack length BK = Benzeggagh-Kenane C v = empirical variable adjusting for void content CDM = continuum damage mechanics CFRP = carbon-fiber reinforced polymer CZT = cohesive zone theory d = length of the lever arm in MMB test D = damage variable DCB = double cantilever beam E m = Young's Modulus of matrix E 1 , E 1f = Young's Modulus of ply or fiber, longitudinal orientation E 2 , E 2f = Young's Modulus of ply or fiber, transverse orientation E 3 = Young's Modulus of ply, out-of-plane orientation ENF = end-notched flexure F = applied load FRP = fiber reinforced polymer G c = critical fracture energy G f c , G f t = energy dissipation rate, longitudinal (fiber) compressive or tensile G I , G II = Mode I or II fracture energy G Ic , G IIc = Mode I critical fracture energy G m = shear modulus, matrix G m c , G m t = energy dissipation rate, transverse (matrix) compressive or tensile G shear = total shear fracture energy G T = total fracture energy G 12 , G 12f 2 G 13 = transverse shear modulus G 23 , G 23f = out-of-plane shear modulus of ply or fiber GFRP = glass-fiber reinforced polymer h = thickness of adhered plies K = penalty stiffness , = fiber or matrix bulk modulus L = length of half span for DCB, ENF, MMB tests , = Mode I or II cohesive zone length L e = length of each element LEFM = linear elastic fracture mechanics M = length of cohesive zone parameter MMB = mixed mode bending N e = number of elements in the cohesive zone S L , S Lm = longitudinal shear strength of ply or matrix S T = transverse shear strength S 0 , S a = maximum traction, Mode II; max. traction from coarse mesh refinement, Mode II t, t n , t s , t t = traction, Mode I, Mode II, or Mode III traction T = homologous temperature T c = thickness of adhesive layer ̅ = traction without damage application, Mode I T 0 , T a = maximum traction, Mode I; max. traction from coarse mesh refinement, Mode I = effective traction at damage inititiation V f = fiber volume ratio V m = ma...