Int J Fract https://doi.org/10.1007/s10704-019-00402-9 ORIGINAL PAPER Numerical study of fatigue crack growth considering an elastic–plastic layer in mixed-mode loading Rafael Moresco · Eduardo Bittencourt Received: 25 January 2019 / Accepted: 14 November 2019 © Springer Nature B.V. 2019 Abstract In this work, crack propagation simulations in a weak surface between an elastic–plastic layer and an elastic substrate are considered. A plane strain model is used in the simulations. Fracture propagation process is taken into account by an irreversible cyclic cohesive zone model. Loading applied to the structure is rotated in order that mixed loading modes could be introduced. Besides loading, thickness of the elastic–plastic layer is also changed. All other intrinsic fracture properties are kept constant. The present work shows a direct rela- tion between mode II applied energy and the energy dissipated plastically during propagation. As a conse- quence, the introduction of mode II loading intensifies the effects of the elastic–plastic layer, resulting substan- tially larger plastic strains, more extensive crack clo- sure during unloading and smaller tractions at the crack tip when the size of the layer increases. The result is a substantial increase in the fatigue crack growth resis- tance. These effects are minimal or not observed when only mode I is considered. Keywords Fracture mechanics · Fatigue · Composites · Mixed-mode · Plasticity R. Moresco · E. Bittencourt (B) Center of Applied and Computational Mechanics, Universidade Federal do Rio Grande do Sul, Av. Osvaldo Aranha 99, Porto Alegre 90035-190, Brazil e-mail: eduardo.bittencourt@ufrgs.br R. Moresco e-mail: rafael.moresco@ufrgs.br 1 Introduction Laminar composites are widely used in industry, play- ing a key role in the design of equipments and machines. They can be exemplified by panels used in aircraft and automobile structures, microelectronic devices, etc (Groover 2007). These multi-layer structures can be shaped combining different materials or the same mate- rial in distinct orientations, allowing the union of two or more properties. A typical combination is the use of ductile layers with brittle layers, with the former permitting a greater toughness for the composite and the latter introducing another property such as a greater heat resistance, higher strength, etc. Of particular inter- est in the present study is a three-layer configuration where an elastic–plastic layer is sandwiched by elas- tic foundations. Mode I fracture studies done by Tver- gaard and Hutchinson (1994, 1996) and Lane et al. (2000), among others, indicate that a larger plastic layer leads to greater toughness due to greater plas- tic dissipation. In these studies, loading was mono- tonically applied. Considering cyclic loading, exper- imental behavior of fatigue crack growth (FCG) in aluminum-alumina configurations subjected to mode I was addressed in Cannon et al. (1991), McNaney et al. (1996) and Kruzic et al. (2004). Aluminum layer thickness effects were noticed on FCG only for near threshold regime. Otherwise FCG results showed to be nearly independent of the layer thickness. Numeri- cal simulations of equivalent cases done by Wang and 123