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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.
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 stretch ratio or extension ratio (symbol λ) is an alternative measure related to the extensional or normal strain of an axially loaded differential line element. It is defined as the ratio between the final length l and the initial length L of the material line.
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.
Experimentally, stress relaxation is determined by step strain experiments, i.e. by applying a sudden one-time strain and measuring the build-up and subsequent relaxation of stress in the material (see figure), in either extensional or shear rheology. a) Applied step strain and b) induced stress as functions of time for a viscoelastic material.
Total strain energy theory – This theory assumes that the stored energy associated with elastic deformation at the point of yield is independent of the specific stress tensor. Thus yield occurs when the strain energy per unit volume is greater than the strain energy at the elastic limit in simple tension.
In the strain hardening method, the slope of strain hardening region (above the natural draw ratio) in the true stress-strain curves is calculated and used as a measure of ESCR. This slope is called the strain hardening modulus (G p). The strain hardening modulus is calculated over the entire strain hardening region in the true stress strain curve.
For two-dimensional, plane strain problems the strain-displacement relations are = ; = [+] ; = Repeated differentiation of these relations, in order to remove the displacements and , gives us the two-dimensional compatibility condition for strains