It is often much higher than what current real materials can achieve.
The lowered fracture stress is due to defects, such as interior or surface cracks.
One of the goals for the study of mechanical properties of materials is to design and fabricate materials exhibiting strength close to the theoretical limit.
When a solid is in tension, its atomic bonds stretch, elastically.
Once a critical strain is reached, all the atomic bonds on the fracture plane rupture and the material fails mechanically.
The stress at which the solid fractures is the theoretical strength, often denoted as
After fracture, the stretched atomic bonds return to their initial state, except that two surfaces have formed.
The theoretical strength is often approximated as: [1][2] where The stress-displacement, or
vs x, relationship during fracture can be approximated by a sine curve,
vs x curve can be related to Young's modulus through the following relationship: where The strain
vs x curve with Young's modulus thus becomes The sinusoidal relationship of stress and displacement gives a derivative: By setting the two
together, the theoretical strength becomes: The theoretical strength can also be approximated using the fracture work per unit area, which result in slightly different numbers.
However, the above derivation and final approximation is a commonly used metric for evaluating the advantages of a material's mechanical properties.