Creep damage laws for bonded joints under pure mode I loading

Nowadays, adhesively bonded joints constitute an emergent area, being applied in several industries, especially in the aviation sector. Research has been developed on the analysis of the mechanical behaviour of bonded joints, while establishing fracture characterisation in pure modes I and II, and in mixed-mode I + II. Despite of the significant developments in analysing of bonded joints under quasi-static and fatigue conditions, few studies have addressed other mechanical phenomena such as creep. On creep analysis, developments have been presented on damage modelling of metallic materials, including the use of cohesive zone modelling (CZM). This study presents an adaptation of the Kachanov-Rabotnov and Liu-Murakami damage models, including rheological parameters by using Maxwell, Voigt-Kelvin, and Burgers constitutive equations when creep loading is considered. Other stress degradation effects due to creep phenomena are also considered, incorporating power law and sin-hyperbolic based models. Twelve damage models are derived: Kachanov-Rabotnov-Maxwell (KRM), Kachanov-Rabotnov-Voigt-Kelvin (KRVK), Kachanov-Rabotnov-Burgers (KRB), Kachanov-Rabotnov-Maxwell-Sun (KRMS), Kachanov-Rabotnov-Voigt-Kelvin-Sun (KRVKS), Kachanov-Rabotnov-Burgers-Sun (KRBS), Liu-Murakami-Maxwell (LMM), Liu-Murakami-Voigt-Kelvin (LMVK), Liu-Murakami-Burgers (LMB), Liu-Murakami-Maxwell-Hyperbolic (LMMH), Liu-Murakami-Voigt-Kelvin-Hyperbolic (LMVKH), and Liu-Murakami-Burgers-Hyperbolic (LMBH). Resulting damage laws are appropriate for adhesives, but also for ductile polymers in general. The implementation of the derived laws in CZM was demonstrated, being capable of modelling primary, secondary, and tertiary creep phases under pure mode I loading. A parametric analysis was also performed, assessing the level of creep damage rate induced by each parameter and their effect on the creep curve shape. A theoretical basis was established in this study for further analysis of creep loaded adhesively bonded joints using CZM, where mixed-mode I + II can be considered in the future.