What Is Elastic Deformation?

Elastic deformation is the phenomenon that the material deforms under the action of external force, and the deformation completely disappears when the external force is removed. Elastic deformation is divided into three types: linear elasticity, non-linear elasticity and hysteretic elasticity. Linear elastic deformation obeys Hooke's law, and the strain changes with the instantaneous single value of stress. Nonlinear elastic deformation does not obey Hooke's law, but still has instantaneous single value. Hysteretic deformation also conforms to Hooke's law, but does not occur at the moment of loading, and it takes a period of time to reach the stable value corresponding to Hooke's law.

When an object is subjected to external force, it will deform. If the external force is removed, the object can completely recover its original shape and size. This deformation is called elastic deformation. ^[2]

Elastic deformation in metals is achieved by changing the distance between atoms. The relationship between external forces and elastic deformation is described using Hooke's law. Hooke's law can be described as: when an object is deformed by an external force, the deformation is proportional to the external force within the elastic limit.

Under the simple conditions of unidirectional stretching, the relationship between the true normal stress _i and the true strain can be written as:

_i = C (1)

The proportionality constant C is called the elastic modulus, and it reflects the ability of a metal material to resist elastic deformation. A similar relationship holds under the simple condition of unidirectional shear, that is,

= C (2)

Where shear stress; shear strain; C shear elastic modulus. When engineering stress and strain are used, the relationship similar to formulas (1) and (2) still holds, but the proportionality constant changes slightly. It is customarily expressed by E and G, respectively. The relationship of G is:

G = E [2 (1 + )] (3)

Among them, is called the Poisson's ratio, which represents the ratio between the longitudinal deformation and the lateral deformation. Generally speaking, the elastic deformation is relatively small, especially for rigid metal materials. In this case, the difference between the engineering stress and strain and the real stress and strain is small, and E and G are equivalent to C and C , respectively. ^[2]

Under the conditions of three-way stretching or three-way compression, in addition to the shape change of the object, the volume change also occurs. For example, for an isotropic body, if subjected to a three-dimensional compressive stress P, the strain e in any main direction is:

The relative change in volume V / V is V / V = 3e = 3P (2v-1) / E, so the relationship between pressure P and volume strain is obtained as:

Among them, E / 3 (1-2v) is called bulk elastic modulus, which can be expressed by K, and the inverse of K = 1 / K, which is called volume compression coefficient. ^[2]