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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 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]
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]
In addition, small crack growth data may be needed to match the increased rate of growth seen with small cracks. [39] Typically, a cycle counting technique such as rainflow-cycle counting is used to extract the cycles from a complex sequence. This technique, along with others, has been shown to work with crack growth methods. [40]
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Plot of Load vs. Displacement. The energy release rate is defined [3] as the instantaneous loss of total potential energy per unit crack growth area , , where the total potential energy is written in terms of the total strain energy , surface traction , displacement , and body force by