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The stress–strain curve for a ductile material can be approximated using the Ramberg–Osgood equation. [2] This equation is straightforward to implement, and only requires the material's yield strength, ultimate strength, elastic modulus, and percent elongation.
A more meaningful representation of ductility would be obtained by identifying the strain at the onset of necking, which should be independent of sample dimensions. This point can be difficult to identify on a (nominal) stress-strain curve, because the peak (representing the onset of necking) is often relatively flat.
Hollomon's equation is a power law relationship between the stress and the amount of plastic strain: [10] σ = K ϵ p n {\displaystyle \sigma =K\epsilon _{p}^{n}\,\!} where σ is the stress, K is the strength index or strength coefficient, ε p is the plastic strain and n is the strain hardening exponent .
Toughness is related to the area under the stress–strain curve. In order to be tough, a material must be both strong and ductile. For example, brittle materials (like ceramics) that are strong but with limited ductility are not tough; conversely, very ductile materials with low strengths are also not tough. To be tough, a material should ...
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.
The Considère construction for prediction of the onset of necking, expressed as the gradient of the (true) stress-strain curve falling to the true stress, for a material conforming to the Ludwik-Hollomon relationship, with the parameter values shown. The condition can also be expressed in terms of the nominal strain:
The critical value of stress intensity factor in mode I loading measured under plane strain conditions is known as the plane strain fracture toughness, denoted . [1] When a test fails to meet the thickness and other test requirements that are in place to ensure plane strain conditions, the fracture toughness value produced is given the ...
Δε p /2 is the plastic strain amplitude; Δε e /2 is the elastic strain amplitude; 2N is the number of reversals to failure (N cycles); ε f ' is an empirical constant known as the fatigue ductility coefficient defined by the strain intercept at 2N =1; c is an empirical constant known as the fatigue ductility exponent, commonly ranging from ...