# 1: Analysis of Deformation Processes

Learning Objectives

• Appreciate different approaches, including their inherent assumptions, that can be used to model plastic flow in metal forming operations.
• Gain an insight into these approaches and how they can provide estimates of the necessary deformation loads for different metal forming operations.
• Recognise the relative importance and limitations of the different approaches, ranging from simple work analyses to hodographs, and to become familiar with their use.

## Before You Start

You should be familiar with the contents of the Theory of Metal Forming – Stress States and Yielding Criteria TLP and the concepts of stress and strain.

• 1.1: Introduction to Analysis of Deformation Processes
• 1.2: Lévy-Mises Equations
Once the yield criterion is satisfied, we can no longer expect to use the equations of elasticity. We must develop a theory to predict plastic strains from the imposed stresses.
• 1.3: Slip Line Field Theory
This approach is used to model plastic deformation in plane strain only for a solid that can be represented as a rigid-plastic body. Elasticity is not included and the loading has to be quasi-static. In terms of applications, the approach now has been largely superseded by finite element modelling, as this is not constrained in the same way and for which there are now many commercial packages designed for complex loading (including static and dynamic forces plus temperature variations).
• 1.4: Work Formula Method
When deforming a body, work has to be done by the applied forces. In the simplest case, the work done can be estimated from the magnitude of the applied stress(es) and the extent of the deformation. This is analogous to simple mechanics in which the work done is equal to force applied multiplied by the distance moved. Clearly, this simple approach assumes, in the first instance, that all the work done by the applied forces results in deformation; this can be called “useful” work.
• 1.5: Limit Analysis
• 1.6: Finite Element Method
• 1.7: Hencky Relations
• 1.8: Deeper Questions