Plasticity in forming

Solid-state forming of metallic materials relies on their ability to undergo large-scale irreversible deformation, known as "plastic deformation", above a certain level of stress. This capacity is limited only by the phenomena of "damage" and "fracture".

The aim of this article is therefore to present the set of equations describing the field of velocities v and stresses σ, during the plastic flow of metallic materials in various processes such as rolling, forging, drawing, stamping, machining...

Plasticity theory allows us to analyze metal behavior on three scales:

• on an overall process scale:

  • assessment of strengths and energy required,

  • study of flow morphology and geometric evolution of the part,

  • assessment of process limits (maximum possible reductions),

  • assessing the shape of free surfaces and the risk of defects ("dog bone" edges when rolling thick plates, filling defects caused by deep engravings or folds in hot forging, etc.);

• on the local scale of the element of matter, assumed to be continuous and homogeneous:

  • assessment of the stress and strain (and even temperature) fields that determine the quality of the final product: microstructure, mechanical properties, residual stress, damage (cracks),

  • assessment of the risk of highly localized heterogeneities appearing as a result of flow localization (shear bands) or the appearance of mechanical instabilities initiating fracture;

• on a microscopic scale:

  • understanding the evolution of microstructure elements: inclusions and internal porosity,

  • modeling the evolution of metal roughness, which determines the aesthetic appearance of the part and the intensity of friction and tool wear.

In addition, to fully understand its capabilities in the analysis and interpretation of "complex" mechanical tests, the reader may wish to refer to the following files:

• hardness tests [M 4 154] at