M4 Strain Hardening (Work Hardening)

Topic

The accumulated plastic deformation of this metal—beyond the yield point established by another model in this set—progressively increases its strength, as described by the Hollomon equation; this strain hardening (or work hardening) means that, to continue deforming plastically beyond that point, the metal requires increasing stress rather than continuing to deform under the same constant stress. Consequently, the greater the accumulated plastic deformation, the higher the metal's strength becomes at that moment, according to the Hollomon equation.

However, the Hollomon equation does not accurately describe this strain hardening if expressed in terms of engineering stress and strain—quantities directly measured by another model in this set—because these engineering values ​​relate force and elongation to the specimen's original dimensions, which are no longer valid once significant plastic deformation has occurred. Instead, it is necessary to first convert engineering stress and strain into true stress and true strain, both of which are referenced to the specimen's actual cross-section and length at any given moment. Greater accumulated plastic deformation increases the discrepancy between engineering values ​​and their corresponding true values, thereby making this conversion increasingly necessary for an accurate description of strain hardening.

At the microstructural level, this strain hardening is governed by the multiplication and interaction of dislocations—a process described by the Kocks-Mecking model (another distinct model within this set): as the metal's dislocation density rises with accumulated plastic deformation, each moving dislocation encounters more obstacles posed by existing dislocations, requiring greater stress to continue moving. The fact that this dislocation density—according to that same Kocks-Mecking model—is higher for a given accumulated plastic strain results in a correspondingly more pronounced work hardening.

Consequently, the parameters introduced at the start of this model—accumulated plastic strain and work hardening—are directly measured using another model within this same set: the one describing the tensile test for this metal. It is the engineering stress-strain curve recorded beyond the yield point during that tensile test which, once converted to true stress and true strain, reveals the progression of this work hardening and allows the Hollomon equation—introduced at the beginning of the model—to be fitted to those same data.

ID:4436