Understanding basic stress, strain and external loading principals is fundamental to sheet metal bending and forming theory. Forming or sheet metal processes result in surface forces acting on the applied material. These fundamentals start with stress since it denotes force per unit area.
Formulas Behind Sheet Metal Bending Theory
Formula for stress:
Force usually comes in compression, tension, shear or torsional loads. There are a few additional formulas for force calculations one of which is oblique stress:
Building on this theory we have Hooke’s Law. This fundamental law demonstrates that strain is directly proportional to stress, and resulted in the modulus of elasticity equation:
Subsequently, nominal strain is defined as the change in gauge length:
As a result, true strain is:
From this equation, a curve can be plotted which is referred to as the stress-strain curve. The curve can be represented as:
Where k= the strength coefficient and n = strain-hardening (work hardening) exponent. Most metals have a value between .10 to .50. A value of 0 would denote perfect plastic solid and 1 would be elastic solid. From this curve came the term ductility which defines the ability of a metal to plastically deform without breaking or fracturing. Ductility is typically described in terms of elongation and percentage of elongation which is:
With l₀ being the original gauge length and l𝑓 is the length at the fracture. Ductile materials such as plastic typically show large deformations before fracture but brittle materials have little to no ductility.
How Formulas Influence Design
Henceforth, from all of these equations and research about materials there are some basic sheet metal production and forming theories that have come about. Some simple design principles to keep in mind are:
T denotes thickness of material
Additional sheet metal bending theories exist for minimum distance between edges and radii such as:
In conclusion, these highlight many of the most basic and elementary sheet metal theories. There are obviously other theories as well, but these tables provide a solid starting position. Please leave a comment or question down below and subscribe to our newsletter for continuous updates.