How is toughness related to the energy needed to extend a crack?

In materials testing, toughness is fundamentally related to the energy required to propagate a crack through a material. According to the theory established by A.A. Griffith, spontaneous crack growth occurs when the energy released from the material's elastic field balances the work required to create new fracture surfaces.1

Engineers improve a material's toughness by engineering microstructures that either resist crack propagation or absorb energy during the process. Mechanisms such as crack deflection, crack bridging, and microcracking increase the energy needed for a crack to advance by creating more fracture surface area or exerting closing forces on the crack tip. Similarly, transformation toughening utilizes phase changes to induce volume expansions that exert a closing force on the crack, thereby increasing the resistance to propagation.2

While fracture toughness is often quantified as a stress-intensity factor ($K_{Ic}$) representing the critical point where crack propagation becomes rapid, this value is intrinsically tied to the material's ability to absorb energy and resist the advancement of a crack under stress.12