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Failure criteria in this case are related to microscopic fracture. Some of the most popular failure models in this area are the micromechanical failure models, which combine the advantages of continuum mechanics and classical fracture mechanics . [ 1 ]
Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics to characterize the material's resistance to fracture .
Mechanics (from Ancient Greek μηχανική (mēkhanikḗ) 'of machines') [1] [2] is the area of physics concerned with the relationships between force, matter, and motion among physical objects. [3]
In solid mechanics, the yield point can be specified in terms of the three-dimensional principal stresses (,,) with a yield surface or a yield criterion. A variety of yield criteria have been developed for different materials.
In continuum mechanics, the maximum distortion energy criterion (also von Mises yield criterion [1]) states that yielding of a ductile material begins when the second invariant of deviatoric stress reaches a critical value. [2] It is a part of plasticity theory that mostly applies to ductile materials, such as some metals.
Continuum mechanics is valid for a bending beam. The stress at a cross section varies linearly in the direction of bending, and is zero at the centroid of every cross section . The bending moment at a particular cross section varies linearly with the second derivative of the deflected shape at that location.
Figure 1: View of Drucker–Prager yield surface in 3D space of principal stresses for =, =. The Drucker–Prager yield criterion [1] is a pressure-dependent model for determining whether a material has failed or undergone plastic yielding.
Thus, this maintenance is desired to be performed infrequently, even when such increased intervals cause increased complexity and cost to the overhaul. Crack growth, as shown by fracture mechanics, is exponential in nature; meaning that the crack growth rate is a function of an exponent of the current crack size (see Paris' law). This means ...