The use of critical stress intensity factor to quantify "hardness" and "crunchiness" objectively

A simple test from materials science, in which a notched beam is bent so that the notch increases in length due to the propagation of a crack, allows determination of a parameter called the Critical Stress Intensity Factor in Mode I fracture, K-IC, by means of which the conditions under which the crack will propagate can be quantified. This is shown to track sensory hardness of several apples, carrot, celery and cucumber with remarkable precision, a result predicted by theoretical analysis due to Lucas et al. (2002). Hardness and crunchiness are shown to be indistinguishable and therefore must be identical. Therefore, a mechanical test can reliably replace a sensory test resulting in quicker, cheaper and more accurate estimate of a sensory parameter.