E43 Fracture - Cortex

Topic

The fracturing of the crust of a loaf of bread, a cookie, a chip, or a piece of chocolate describes how this brittle material breaks under an applied load: Griffith's fracture mechanics establishes that any fracture in such a crust begins at an inherent imperfection—such as a crack, pore, or fissure—from which the crack propagates as soon as the elastic energy released during cracking exceeds the surface energy required to create the resulting fracture surface. If the crust contains a more severe imperfection, the crack will consequently begin to propagate from it with less released elastic energy.

The stress intensity factor of the crust quantifies the stress concentration accumulating at the crack tip; it increases with both the applied stress and the square root of the crack size. When this factor reaches the critical value corresponding to the crust's fracture toughness, the crack propagates spontaneously through the material. A larger crack or higher applied stress causes the stress intensity factor to reach the fracture toughness threshold more quickly.

A crispy crust possesses low fracture toughness, characteristic of a brittle material; it breaks with minimal release of elastic energy and allows the crack to propagate rapidly, producing the characteristic sound heard when biting into it. In contrast, a moist crust possesses higher fracture toughness because the water plasticizes the starch and gluten network, absorbing additional elastic energy and thereby arresting the crack before it can propagate as far as it would in a crisp crust. The fact that the crust absorbs more water increases its fracture toughness, which in turn means it is no longer perceived as crisp.

The modulus of rupture of the crust—measured via a three-point bending test—is the standard metric for the fracture resistance of a baked good or biscuit; it correlates well with the sensory perception of crispness. A high modulus of rupture combined with low fracture energy (a parameter established by another model in this set) indicates a brittle, crisp fracture. This combination of high modulus of rupture and low fracture energy results in a crust that feels crisp when bitten.

Thus, based on the stress intensity factor and fracture toughness introduced earlier, the crack propagation speed through the crust ultimately dictates the sensory experience of biting into it: a crack propagating rapidly generates a high-frequency sound perceived as crispness, whereas a soft crust propagates the crack slowly, producing no appreciable sound upon biting. The fact that this crust is more fragile—characterized by the lower fracture toughness used to initiate this model—causes the crack to propagate through it more rapidly; consequently, the sound produced upon biting into it is higher-pitched and distinctly crisp.

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