Fracture morphology of tensile cracks and rupture velocity

Desiccation cracks in starch-water mixtures are studied with respect to morphological features, mainly plumose structures, on their faces. Specimens have diameters of 50-100 mm and thicknesses of 2-40 mm. Structures similar to those on joints in rocks are found. Rupture velocities are measured from videos and estimated from photos. Rupture covers the range from spontaneously nucleating, dynamic cracks with velocities of 100-200 mm/s to quasi-static cracks with velocities of 0.1 mm/s and less. Plumose lines give the rupture direction, and their relation to rupture velocity is similar to the relation between seismic rays and seismic wave velocity. A ray-tracing method from seismology is used to calculate plumose lines for depth-dependent rupture velocity. Moreover, an inverse method, based on finite difference travel times and conjugate gradients, is developed to invert a set of measured plumose directions into a rupture-velocity distribution which can also depend on the horizontal coordinate on the rupture surface. The main results of this paper are as follows. (1) Plumose lines can successfully be inverted into relative rupture velocity. (2) In thin starch layers (thickness less than 0.2 times diameter), rupture velocity decreases from top to bottom by a factor of 2-5, following a decrease of tensile stress due to the increase in water concentration. (3) Horizontal variation of rupture velocity reflects horizontal variation of stress, including stress relaxation due to the propagating crack, and ranges from dynamic to quasi-static velocities. (4) In thick starch layers (thickness about 0.5 times diameter), rupture is predominantly quasi-static. (5) Starch cracks sometimes have a fringe zone where topographic amplitudes are higher and rupture velocities lower than on the main part of the crack; this probably also applies to joints in rocks and their fringe zones. (6) Starch-water mixtures at rupture have a Poisson ratio close to 0.5. Cracks in starch are closest to subsidence or diagenesis joints in sedimentary rocks.