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In a 1961 paper, P. C. Paris introduced the idea that the rate of crack growth may depend on the stress intensity factor. [4] Then in their 1963 paper, Paris and Erdogan indirectly suggested the equation with the aside remark "The authors are hesitant but cannot resist the temptation to draw the straight line slope 1/4 through the data" after reviewing data on a log-log plot of crack growth ...
Figure 1: Typical plot of crack growth rate versus the stress intensity range. The Paris–Erdogan equation fits the central linear region of Regime B. A crack growth equation is used for calculating the size of a fatigue crack growing from cyclic loads. The growth of a fatigue crack can result in catastrophic failure, particularly in the case ...
In fracture mechanics, a crack growth resistance curve shows the energy required for crack extension as a function of crack length in a given material.For materials that can be modeled with linear elastic fracture mechanics (LEFM), crack extension occurs when the applied energy release rate exceeds the material's resistance to crack extension .
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The stress intensity factor at the crack tip of a compact tension specimen is [4] = [() / / + / / + /] where is the applied load, is the thickness of the specimen, is the crack length, and is the effective width of the specimen being the distance between the centreline of the holes and the backface of the coupon.
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.
Primary cracks (Figure 1) form when the tensile stress at the outer surface of the concrete reaches the tensile strength of concrete. When a primary crack forms, the concrete in the vicinity of the crack is relieved of any tension, resulting in a stress free zone near the crack.
In fracture mechanics, the energy release rate, , is the rate at which energy is transformed as a material undergoes fracture.Mathematically, the energy release rate is expressed as the decrease in total potential energy per increase in fracture surface area, [1] [2] and is thus expressed in terms of energy per unit area.