A Conjecture to Derive An Equation of Motion For Dynamic Fracture

Crack propagation is hypothesized as being a discontinuous process and by decoupling in time the (macroscopic) dynamic energy release rate, Gd, from the (microscopic) J-integral a discrete non-linear equation is obtained having the form of a logistic map. Applying this equation to fracture in amorphous brittle materials (in particular PMMA) it shows that for an accelerating crack, propagation changes from a continuous process in time to a discontinuous one concomitant with instabilities in velocity related to macroscopic branching.