With the fundamental objective of establishing the universality of the Griffith energy competition to describe the growth of large cracks in solids not just under monotonic but under general loading conditions this paper puts forth a generalization of the classical Griffith energy competition in nominally elastic brittle materials to arbitrary non-monotonic quasistatic loading conditions which include monotonic and cyclic loadings as special cases. Centered around experimental observations the idea consists in: i) viewing the critical energy release rate Gc not as a material constant but rather as a material function of both space X and time t ii) one that decreases in value as the loading progresses this solely within a small region around crack fronts with the characteristic size of such a region being material specific and iii) with the decrease in value of Gc being dependent on the history of the elastic fields. By construction the proposed Griffith formulation is able to describe any Paris-law behavior of the growth of large cracks in nominally elastic brittle materials for the limiting case when the loading is cyclic. For the opposite limiting case when the loading is monotonic the formulation reduces to the classical Griffith formulation. Additional properties of the proposed formulation are illustrated via a parametric analysis and direct comparisons with representative fatigue fracture experiments on a ceramic mortar and PMMA.
