A micro-macro confined compressive fatigue creep failure model in brittle solids

Abstract Fatigue properties under cyclic static compressive loading and unloading (i.e., compressive fatigue/cyclic creep properties) have an important meaning for evaluation of lifetime in brittle solids containing numerous microcracks. The total deformation during cyclic static compression consists of time-independent elastic, time-dependent viscoelastic, time-dependent viscoplastic and time-independent plastic deformations. In this study, the viscoplastic and plastic deformations are collectively called as plastic deformation below. The plastic deformation dominates the lifetime of brittle solids. The rebound of elastic and viscoelastic deformations at static unloading is widely studied. However, the rebound of plastic deformation at static unloading is rarely studied under constant lateral confining pressure, and the total time-dependent deformation during cyclic static compressive failure also is rarely studied in theory. Furthermore, the rebound of plastic deformation has a great significance for cyclic static compressive failure, and microcrack variable influences seriously plastic mechanical properties of brittle solids. However, the theoretical relationship between plastic deformation rebound and microcrack variable in brittle solids during a cyclic static compressive failure is rarely established. In this study, an analytical solution is proposed by coupling the confined cyclic static loading and unloading path, the Hooke-Kelvin viscoelastic model and the formulated micro-macro model, which explains the total time-dependent visco-elastic-plastic deformation caused by microcracks variable during cyclic static compressive failure. Effects of residual static axial stress after unloading and confining pressure on cyclic creep failure are studied. Irreversible elastic and viscoelastic deformations caused by residual static stress after unloading are illustrated. An interesting rebound phenomenon of plastic deformation induced by microcrack recovery is found. A critical value of axial stress causing a rebound of plastic deformation is also found. Effects of parameters Δσ1a, Δσ1b, and Δt in cyclic static loading and unloading path on the mechanical properties of cyclic static compressive failure are discussed. The proposed theoretical model provides a certain help for evaluation and prediction of fatigue lifetime in brittle solid engineering.