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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]
Load an initial force: Rockwell hardness test initial test force is 10 kgf (98 N; 22 lbf); superficial Rockwell hardness test initial test force is 3 kgf (29 N; 6.6 lbf). Load main load: reference below form / table 'Scales and values'. Leave the main load for a "dwell time" sufficient for indentation to come to a halt.
The range equation reduces to: = where =; here is the specific heat constant of air 287.16 J/kg K (based on aviation standards) and = / = (derived from = and = +). c p {\displaystyle c_{p}} and c v {\displaystyle c_{v}} are the specific heat capacities of air at constant pressure and constant volume respectively.
In the above equation, F could be in N and d in mm, giving HV in the SI unit of MPa. To calculate Vickers hardness number (VHN) using SI units one needs to convert the force applied from newtons to kilogram-force by dividing by 9.806 65 (standard gravity). This leads to the following equation: [4]
ASTM Specification E384, for example, states that the load range for microhardness testing is 1 to 1000 gf. For loads of 1 kgf and below, the Vickers hardness (HV) is calculated with an equation, wherein load (L) is in grams force and the mean of two diagonals (d) is in millimeters:
This formula was derived in 1744 by the Swiss mathematician Leonhard Euler. [2] The column will remain straight for loads less than the critical load. The critical load is the greatest load that will not cause lateral deflection (buckling). For loads greater than the critical load, the column will deflect laterally.
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 ...
The other method, namely the secant method, uses the compliance-crack length equation given by ASTM standard to calculate effective crack length from an effective compliance. Compliance at any point in Load vs displacement curve is essentially the reciprocal of the slope of the curve that ensues if the specimen is unloaded at that point.