Orientation, polarity and chirality of interface toughness

The toughness of an interface is usually reported as one number, yet patterning can make it a function of the direction in which the crack grows. An interface patterned with two elastic–brittle materials, joining the plate arms of a double cantilever beam through a compliant bondline, is studied with its toughness regarded as such a function. The function splits into an orientation part, a polarity part, which changes sign under reversal, and a chiral part, which distinguishes mirror-image directions; the point group of the pattern decides which parts exist. Whereas a crack tip in a layered solid must cross every layer, a crack front on an interface averages the bond along its length. With equal bond stiffness the peak toughness is therefore the rule of mixtures on the toughest straight cross-section normal to the growth direction, counted within a front lag of a quarter of the elastic process zone. This rule predicts the peak from the pattern alone, to a median of 0.9 % at moderate toughness contrast, and gives way to individual pinning, at large contrast or on sparse thin lines, and, in wider specimens, to a front that turns toward nearly aligned tough lines and gains up to 18 % over the rule. Four consequences follow. The same tough inclusions at the same area fraction give a weakly or a strongly directional interface depending only on the lattice on which they are arranged. A straight line of tough material wider than a fraction of the elastic process zone, not connectivity, reaches the toughness of the tough material. Disorder at fixed area fraction turns designed anisotropy into sample-to-sample scatter. Within the range of the rule the peak is polar only through a stiffness contrast, with a bound that does not contain the toughness contrast, so a bondline patterned in stiffness alone is the strongest diode, with a ratio of the peaks in opposite directions that grows with the stiffness contrast and is bounded by two. The dissipated energy, the work supplied minus the elastic energy stored per unit area of crack, is found to be polar as well.