Birth of mesomechanics arising from segmentation and multiscaling: nano-micro-macro

Abstract

Two generic functions μ(t) and ν(t) are proposed to describe the material microstructure degradation for a given design specification concerned with fatigue crack growth. This is accomplished by applying the concept of mesomechanics supplemented by multiscaling. Linearity and superposition are preserved from the appropriate range of scale segmentation. The dual scale model of micro- and macro-cracking in fatigue is used to derive μ(t) and ν(t) using only the initial values μ(0) and ν(0) at t = 0 that is prior to the onset of material damage. Fatigue crack growth results are obtained for pre-cracked 2024-T3 and 7075-T6 aluminum panels with the respective initial crack lengths of 2.0 mm and 0.3 mm and a fatigue life of 20 years. The basic scheme relies on the use of three dual scale parameters μ*(t), σ*(t) and d*(t). Anticipated are their relative behavior referred to two scales, say micro and macro. The relations between the measured (macro) and conceptualized (micro) material parameters at least prior to damage are more forgiving and can be established as the initial conditions for the prediction. Matching of the predicted with the available macroscopic crack growth results for the 2024-T3 and 7075-T6 aluminum alloys demonstrates that the methodology spares a detailed knowledge of the complex microstructure. In principle, the scheme can also be applied to characterize the behavior of carbon nano-tube reinforced composites, however complex, from a knowledge of its macroscopic behavior by tests. The corresponding micro- and nanobehavior are assumed to be obtainable by analysis. To this end, there remains the formulation of the dual scale nano/microcracking model in fatigue.