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Plane Strain

Definition - What does Plane Strain mean?

Plain strain is the deformation of a body in which the displacements of all points in the body are parallel to a given plane, and the values of these displacements do not depend on the distance perpendicular to the plane.

Plane strain is commonly used to analyze deformation or fracture of materials. It is also used in examination of shape/size changes in two dimensions.

Plane strain is also known as plane deformation.

Corrosionpedia explains Plane Strain

Plain strain is a stress state in which the strains are biaxial, so that the associated stresses are triaxial. It is especially important in the interior of cracked materials under stress where through-the-thickness strains are constrained.

Plane strain is a very specific condition under which a material can withstand without fracture. Plane strain is often applicable to very thick materials. Plain strain can be idealized as long wire with stresses acting perpendicular to its length. Therefore the strain or displacement along the length is zero.

In fact, material away from the free surfaces of a relatively thick component is not free to deform laterally as it is constrained by the surrounding material. The stress state under these conditions tends to triaxial and there is zero strain perpendicular to both the stress axis and the direction of crack propagation when a material is loaded in tension. Under plane-strain conditions, materials behave essentially elastic until the fracture stress is reached and then rapid fracture occurs. Since little or no plastic deformation is noted, this mode of fracture is known as brittle fracture.

Since the displacement in one of the directions is negligible compared to the other two, the plane strain condition is valid when:

  • One of the dimensions is much larger than the other two
  • In-plane forces do not vary along the largest dimension
  • Forces acting normal to the section plane are negligible

Plane strain is applicable to rolling, drawing and forging where flow in a particular direction is constrained by the geometry of the machinery, e.g. a well-lubricated die wall. Anti-plane strain is another special state of strain that can occur in a body, for instance in a region close to a screw dislocation.

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