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Different deformation modes may occur under different conditions, as can be depicted using a deformation mechanism map. Permanent deformation is irreversible; the deformation stays even after removal of the applied forces, while the temporary deformation is recoverable as it disappears after the removal of applied forces.
An idealized uniaxial stress-strain curve showing elastic and plastic deformation regimes for the deformation theory of plasticity. There are several mathematical descriptions of plasticity. [12] One is deformation theory (see e.g. Hooke's law) where the Cauchy stress tensor (of order d-1 in d dimensions) is a function of the strain tensor ...
In physics and continuum mechanics, deformation is the change in the shape or size of an object. It has dimension of length with SI unit of metre (m). It is quantified as the residual displacement of particles in a non-rigid body, from an initial configuration to a final configuration, excluding the body's average translation and rotation (its rigid transformation). [1]
Once the yield point is passed, some fraction of the deformation will be permanent and non-reversible and is known as plastic deformation. The yield strength or yield stress is a material property and is the stress corresponding to the yield point at which the material begins to deform plastically.
Deformation mechanism maps provide a visual tool categorizing the dominant deformation mechanism as a function of homologous temperature, shear modulus-normalized stress, and strain rate. Generally, two of these three properties (most commonly temperature and stress) are the axes of the map, while the third is drawn as contours on the map.
Initially, this permanent deformation is non-uniformly distributed along the sample. During this process, dislocations escape from Cottrell atmospheres within the material. The resulting slip bands appear at the lower yield point and propagate along the gauge length, at constant stress, until the Lüders strain is reached, and deformation ...
For example, consider a spring that has Q and q as, respectively, its force and deformation: The spring stiffness relation is Q = k q where k is the spring stiffness. Its flexibility relation is q = f Q, where f is the spring flexibility. Hence, f = 1/k. A typical member flexibility relation has the following general form:
In the latter case, the deformation gives rise to reaction forces that oppose the compression forces, and may eventually balance them. [4] Liquids and gases cannot bear steady uniaxial or biaxial compression, they will deform promptly and permanently and will not offer any permanent reaction force.