Image based computations of lineal path probability distributions for microstructure representation

Lineal path probability distributions are statistical descriptors that are useful for microstructure representation. It is shown that complete orientation dependent lineal path probability distributions of any three-dimensional microstructure can be estimated from the two-dimensional vertical sections. A digital image based technique is presented for computation of the direction dependent lineal path probability distributions from the vertical metallographic sections. The technique has been utilized for estimation of the lineal path probabilities in isotropic and anisotropic microstructures of Ti–6Al–4V–1.0B alloys containing TiB whiskers.