Plastic bending is a nonlinear behavior particular to members made of ductile materials that frequently achieve much greater ultimate bending strength than indicated by a linear elastic bending analysis. It is a well-established concept in structural engineering and materials science.
In both plastic and elastic bending analyses of a straight beam, it is assumed that the strain distribution is linear about the neutral axis (plane sections remain plane). In an elastic analysis, this assumption leads to a linear stress distribution, but in a plastic analysis, the resulting stress distribution is nonlinear and dependent on the beam's material.
Mechanism: Plastic bending begins when an applied moment causes the outside fibers of a cross-section to exceed the material's yield strength. The cross-section does not yield uniformly; rather, the outer regions yield first, redistributing stress and delaying failure beyond what would be predicted by elastic analytical methods. The stress distribution from the neutral axis follows the same shape as the material's stress-strain curve (assuming a non-composite cross-section). After a cross-section reaches a sufficiently high condition of plastic bending, it acts as a plastic hinge.
Limiting Strength: The limiting plastic bending strength (see Plastic moment) is generally considered an upper limit to a beam's load-carrying capability at a particular cross-section. However, a beam may fail due to global or local instability (e.g., local buckling, local crippling, or global lateral-torsional buckling) before the plastic moment is reached at any point along its length.
Important Considerations:
- The deflections necessary to develop the stresses indicated in a plastic analysis are often excessive, potentially to the point of incompatibility with the structure's function.
- Working materials into the plastic range can lead to permanent deformation, so additional analyses may be required at limit load to ensure no detrimental permanent deformations occur.
- The large deflections and stiffness changes associated with plastic bending can significantly alter the internal load distribution, particularly in statically indeterminate beams.
History: Plastic theory was validated around 1908 by C. v. Bach.
