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1 Summary of Elasticity Theory: Basic Concepts
1.8 Permanent Deformations
Changes in distances between individual particles of a body before and after loading
ceases to act characterize the permanent or plastic deformation. For example, the
section OL in Fig. 1.4 represents, at a specific scale, relative permanent (plastic)
deformation caused by stress σ L .
Due to elastic after-effect, permanent deformations almost always decrease with
time. This process is accelerated when the body is heated. Deformations disappearing due to elastic after-effect are referred to unstable permanent deformations.
Permanent deformations that cannot be eliminated by the above method are called
stable permanent deformations.
1.9 Elastic Limit
Maximum stress when stable permanent deformations are still seen is called [5] the
natural elastic limit. At stresses not exceeding the natural elastic limit, unstable
permanent deformations occur, which have specific limit values for each material.
For practical determination of the elastic limit, the permanent deformation is
conditionally set based on the technical capabilities of measuring it. The value
determined in this manner is called the conditional elastic limit. In engineering,
the elastic limit is frequently identified with the proportionality limit.
1.10 Elastic Shear Deformation
Assume that the homogeneous stressed state in a body is created by elongation in a
single direction by stress σ 1 = p and compression in a perpendicular direction by
stress σ 2 = −p (Fig. 1.5a).
By projecting all forces to the normal line to the section equally inclined to the
directions of elongation and compression, we can easily make sure that there will
be no normal stresses in these sections. This indicates that the stress vector on these
areas is located in the section plane.
The forces acting on the element ABCD cut from the body by the abovementioned equally inclined sections will look as shown in Fig. 1.5b, (strain state).
Internal forces act on the surface of this element, which lie in the planes it is confined
by. Such forces are called tangential, and their values belonging to the unit of
surface area are referred to as tangential stresses.
1 Summary of Elasticity Theory: Basic Concepts
1.8 Permanent Deformations
Changes in distances between individual particles of a body before and after loading
ceases to act characterize the permanent or plastic deformation. For example, the
section OL in Fig. 1.4 represents, at a specific scale, relative permanent (plastic)
deformation caused by stress σ L .
Due to elastic after-effect, permanent deformations almost always decrease with
time. This process is accelerated when the body is heated. Deformations disappearing due to elastic after-effect are referred to unstable permanent deformations.
Permanent deformations that cannot be eliminated by the above method are called
stable permanent deformations.
1.9 Elastic Limit
Maximum stress when stable permanent deformations are still seen is called [5] the
natural elastic limit. At stresses not exceeding the natural elastic limit, unstable
permanent deformations occur, which have specific limit values for each material.
For practical determination of the elastic limit, the permanent deformation is
conditionally set based on the technical capabilities of measuring it. The value
determined in this manner is called the conditional elastic limit. In engineering,
the elastic limit is frequently identified with the proportionality limit.
1.10 Elastic Shear Deformation
Assume that the homogeneous stressed state in a body is created by elongation in a
single direction by stress σ 1 = p and compression in a perpendicular direction by
stress σ 2 = −p (Fig. 1.5a).
By projecting all forces to the normal line to the section equally inclined to the
directions of elongation and compression, we can easily make sure that there will
be no normal stresses in these sections. This indicates that the stress vector on these
areas is located in the section plane.
The forces acting on the element ABCD cut from the body by the abovementioned equally inclined sections will look as shown in Fig. 1.5b, (strain state).
Internal forces act on the surface of this element, which lie in the planes it is confined
by. Such forces are called tangential, and their values belonging to the unit of
surface area are referred to as tangential stresses.