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Crack growth equations are used to predict the crack size starting from a given initial flaw and are typically based on experimental data obtained from constant amplitude fatigue tests. One of the earliest crack growth equations based on the stress intensity factor range of a load cycle is the Paris–Erdogan equation [2]
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 ...
Therefore, a more general theory of crack growth is needed for elastic-plastic materials that can account for: the local conditions for initial crack growth which include the nucleation, growth, and coalescence of voids (decohesion) at a crack tip. a global energy balance criterion for further crack growth and unstable fracture.
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.
Fastran was written in the 1980s by James C. Newman while at NASA and is an acronym derived from NASA FATIGUE CRACK GROWTH STRUCTURAL ANALYSIS. [2] Crack closure was first observed by Wolf Elber as propping open a crack tip resulting in a reduction of the full stress intensity range or crack tip driving force. [3]
where is the Young's modulus of the material, is the surface energy per unit area of the crack, and is the crack length for edge cracks or is the crack length for plane cracks. The quantity σ π a {\displaystyle \sigma {\sqrt {\pi a}}} is postulated as a material parameter called the fracture toughness .
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The specimen showing stable crack growth shows an increasing trend in fracture toughness as the crack length increases (ductile crack extension). This plot of fracture toughness vs crack length is called the resistance (R)-curve. ASTM E561 outlines a procedure for determining toughness vs crack growth curves in materials. [17]
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