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In engineering and materials science, a stress–strain curve for a material gives the relationship between stress and strain. It is obtained by gradually applying load to a test coupon and measuring the deformation , from which the stress and strain can be determined (see tensile testing ).
In the above definitions of engineering stress and strain, two behaviors of materials in tensile tests are ignored: the shrinking of section area; compounding development of elongation; True stress and true strain are defined differently than engineering stress and strain to account for these behaviors. They are given as
In mechanics, strain is defined as relative deformation, compared to a reference position configuration. Different equivalent choices may be made for the expression of a strain field depending on whether it is defined with respect to the initial or the final configuration of the body and on whether the metric tensor or its dual is considered.
The nominal stress = is the transpose of the first Piola–Kirchhoff stress (PK1 stress, also called engineering stress) and is defined via = = = or = = = This stress is unsymmetric and is a two-point tensor like the deformation gradient.
Stress–strain analysis (or stress analysis) is an engineering discipline that uses many methods to determine the stresses and strains in materials and structures subjected to forces. In continuum mechanics , stress is a physical quantity that expresses the internal forces that neighboring particles of a continuous material exert on each other ...
The strain can be decomposed into a recoverable elastic strain (ε e) and an inelastic strain (ε p). The stress at initial yield is σ 0 . Work hardening , also known as strain hardening , is the process by which a material's load-bearing capacity (strength) increases during plastic (permanent) deformation.
The tensile strength can be quoted as either true stress or engineering stress, but engineering stress is the most commonly used. Fatigue strength is a more complex measure of the strength of a material that considers several loading episodes in the service period of an object, [ 6 ] and is usually more difficult to assess than the static ...
The Ramberg–Osgood equation was created to describe the nonlinear relationship between stress and strain—that is, the stress–strain curve—in materials near their yield points. It is especially applicable to metals that harden with plastic deformation (see work hardening), showing a smooth elastic-plastic transition.