Definitions

# Deformation (engineering)

In materials science, deformation is a change in the shape or size of an object due to an applied force. This can be a result of tensile (pulling) forces, compressive (pushing) forces, shear, bending or torsion (twisting). Deformation is often described in terms of strain.

As deformation occurs, internal inter-molecular forces arise which oppose the applied force. If the applied force is not too large these forces may be sufficient to completely resist the applied force, allowing the object to assume a new equilibrium state and to return to its original state when the load is removed. A larger applied force may lead to a permanent deformation of the object or even to its structural failure.

In the figure it can be seen that the compressive loading (indicated by the arrow) has caused deformation in the cylinder so that the original shape (dashed lines) has changed (deformed) into one with bulging sides. The sides bulge because the material, although strong enough to not crack or otherwise fail, is not strong enough to support the load without change, thus the material is forced out laterally. Internal forces (in this case at right angles to the deformation) resist the applied load.

The concept of a rigid body can be applied if the deformation is negligible.

## Types of deformation

Depending on the type of material, size and geometry of the object, and the forces applied, various types of deformation may result. The image to the right shows the engineering stress vs. strain diagram for a typical ductile material such as steel.

### Elastic deformation

This type of deformation is reversible. Once the forces are no longer applied, the object returns to its original shape. Soft thermoplastics and metals have moderate elastic deformation ranges while ceramics, crystals, and hard thermosetting plastics undergo almost no elastic deformation. Elastic deformation is governed by Hooke's law which states:

$sigma=Eepsilon,!$

Where $sigma$ is the applied stress, $E$ is a material constant called Young's modulus, and $epsilon$ is the resulting strain. This relationship only applies in the elastic range and indicates that the slope of the stress vs. strain curve can be used to find Young's modulus. Engineers often use this calculation in tensile tests. The elastic range ends when the material reaches its yield strength. At this point plastic deformation begins.

### Plastic deformation

This type of deformation is not reversible. However, an object in the plastic deformation range will first have undergone elastic deformation, which is reversible, so the object will return part way to its original shape. Soft thermoplastics have a rather large plastic deformation range as do ductile metals such as copper, silver, and gold. Steel does, too, but not iron. Hard thermosetting plastics, rubber, crystals, and ceramics have minimal plastic deformation ranges. One material with a large plastic deformation range is wet chewing gum, which can be stretched dozens of times its original length.

Under tensile stress plastic deformation is characterized by a strain hardening region and a necking region and finally, fracture (also called rupture). During strain hardening the material becomes stronger through the movement of atomic dislocations. The necking phase is indicated by a reduction in cross-sectional area of the specimen. Necking begins after the Ultimate Strength is reached. During necking, the material can no longer withstand the maximum stress and the strain in the specimen rapidly increases. Plastic deformation ends with the fracture of the material.

#### Metal fatigue

Another deformation mechanism is metal fatigue, which occurs primarily in ductile metals. It was originally thought that a material deformed only within the elastic range returned completely to its original state once the forces were removed. However, faults are introduced at the molecular level with each deformation. After many deformations, cracks will begin to appear, followed soon after by a fracture, with no apparent plastic deformation in between. Depending on the material, shape, and how close to the elastic limit it is deformed, failure may require thousands, millions, billions, or trillions of deformations.

Metal fatigue has been a major cause of aircraft failure, such as the De Havilland Comet, especially before the process was well understood. There are two ways to determine when a part is in danger of metal fatigue; either predict when failure will occur due to the material/force/shape/iteration combination, and replace the vulnerable materials before this occurs, or perform inspections to detect the microscopic cracks and perform replacement once they occur. Selection of materials which are not likely to suffer from metal fatigue during the life of the product is the best solution, but not always possible. Avoiding shapes with sharp corners limits metal fatigue by reducing stress concentrations, but does not eliminate it.

### Fracture

This type of deformation is also not reversible. A break occurs after the material has reached the end of the elastic, and then plastic, deformation ranges. At this point forces accumulate until they are sufficient to cause a fracture. All materials will eventually fracture, if sufficient forces are applied.

## Misconceptions

A popular misconception is that all materials that bend are "weak" and all those which don't are "strong". In reality, many materials which undergo large elastic and plastic deformations, such as steel, are able to absorb stresses which would cause brittle materials, such as glass, with minimal elastic and plastic deformation ranges, to break. There is even a parable to describe this observation (paraphrased below):

"The mighty oak stands strong and firm before the wind, while the willow yields to the slightest breeze. However, in the strongest storm, the oak will break while the willow will bend, and thus survive. So, in the end, which is the stronger of the two?"

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