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Fatigue has traditionally been associated with the failure of metal components which led to the term metal fatigue. In the nineteenth century, the sudden failing of metal railway axles was thought to be caused by the metal crystallising because of the brittle appearance of the fracture surface, but this has since been disproved. [ 1 ]
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]
The fatigue limit or endurance limit is the stress level below which an infinite number of loading cycles can be applied to a material without causing fatigue failure. [1] Some metals such as ferrous alloys and titanium alloys have a distinct limit, [ 2 ] whereas others such as aluminium and copper do not and will eventually fail even from ...
[2] [3] The law provides a mathematical model to predict the number of cycles to failure (N) based on the applied stress amplitude (). A High Cycle Fatigue Test is used to determine material behaviour under repetitive cyclic loads. This test aims to establish the stress-cycles-to-failure characteristics of materials, primarily utilising an ...
An example of these stress/strain calculations for a simple leadless chip component is shown in the following equation: = (+ + + + ()) Here α is the CTE, T is temperature, L D is the distance to the neutral point, E is elastic modulus, A is the area, h is the thickness, G is shear modulus, ν is Poisson's ratio , and a is the edge length of ...
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 -0.5 to -0.7. Small c results in long ...
This simplification allows the number of cycles until failure of a component to be determined for each rainflow cycle using either Miner's rule to calculate the fatigue damage, or in a crack growth equation to calculate the crack increments. [2] Both methods give an estimate of the fatigue life of a component.
Paris' law (also known as the Paris–Erdogan equation) is a crack growth equation that gives the rate of growth of a fatigue crack. The stress intensity factor K {\displaystyle K} characterises the load around a crack tip and the rate of crack growth is experimentally shown to be a function of the range of stress intensity Δ K {\displaystyle ...