Considère

Considère, or the Considère criterion, is a stability criterion used in material science to predict the onset of necking in ductile metals under uniaxial tension. It is named after the French metallurgist Albert Considère, who formulated the idea in the late 19th century. The criterion provides a simple local condition to determine when uniform elongation becomes unstable and a neck forms.

Mathematically, necking begins when the true stress sigma_t, as a function of true plastic strain epsilon_p, has a slope equal to the current stress: d sigma_t / d epsilon_p = sigma_t. In terms of the common true-stress versus true-strain curves, this means the work-hardening rate (the slope) has fallen to the level of the stress itself. When the derivative is greater than the current stress, uniform deformation can be maintained; when it reaches equality, the material loses stability and necking localizes.

Applications of the Considère criterion include predicting the maximum stable elongation in tensile tests and informing metal-forming processes. It is typically applied using experimentally obtained true stress–true strain data to estimate the onset of necking in quiescent, rate-independent, isotropic materials under uniaxial loading.

Limitations should be noted. The criterion assumes homogeneous material properties, rate independence, and simple uniaxial loading with negligible thermal or rate effects. It does not account for strain-rate sensitivity, thermal softening, multi-axial stress states, or complex geometries encountered in real components. Extensions exist for generalized, rate-dependent plastics and non-uniaxial loading, but the basic Considère condition remains a foundational reference for necking onset in ductile metals.