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Within the branch of materials science known as material failure theory, the Goodman relation (also called a Goodman diagram, a Goodman-Haigh diagram, a Haigh diagram or a Haigh-Soderberg diagram) is an equation used to quantify the interaction of mean and alternating stresses on the fatigue life of a material. [1]
In statistics, Goodman and Kruskal's gamma is a measure of rank correlation, i.e., the similarity of the orderings of the data when ranked by each of the quantities. It measures the strength of association of the cross tabulated data when both variables are measured at the ordinal level .
Although Goodman and Kruskal's lambda is a simple way to assess the association between variables, it yields a value of 0 (no association) whenever two variables are in accord—that is, when the modal category is the same for all values of the independent variable, even if the modal frequencies or percentages vary. As an example, consider the ...
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.
Common factors that have been attributed to low-cycle fatigue (LCF) are high stress levels and a low number of cycles to failure. Many studies have been carried out, particularly in the last 50 years on metals and the relationship between temperature, stress, and number of cycles to failure.
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Since the equations naturally split into direct and quadrature components, many reactances come in pairs, one for the direct axis (with the index d), one for the quadrature axis (with the index q). In the machines with a cylindrical rotor the air gap is uniform, the reactances along the d and q axes are equal, [ 4 ] and d/q indices are ...
These matrices are traceless, Hermitian, and obey the extra trace orthonormality relation, so they can generate unitary matrix group elements of SU(3) through exponentiation. [1]