# fracture_mechanics_crack_initiation¶

class reliability.PoF.fracture_mechanics_crack_initiation(P, A, Sy, E, K, n, b, c, sigma_f, epsilon_f, Kt=1.0, q=1.0, mean_stress_correction_method='modified_morrow', print_results=True)

This function uses the material properties, the local cross sectional area, and force applied to the component to determine how many cycles until crack initiation (of a 1mm crack). Units should always be in MPa (and mm^2 for area). This function may be used for an un-notched or notched component. If the component is un-notched, the parameters q and Kt may be left as their default values of 1.

While there are formulas to find the parameters q and Kt, these formulas have not been included here so that the function is reasonably generic to different materials and geometries. Resources for finding some of these parameters if they are not given to you: q = 1/(1+a/r) Where r is the notch radius of curvature (in mm), and a is 0.025*(2070/Su). Su is the ultimate strength in MPa. This only applies to high strength steels where Su>550MPa. Kt ==> https://www.efatigue.com/constantamplitude/stressconcentration/ This website will provide you with the appropriate Kt for your notched geometry.

Inputs: P - Force applied on the component [units of MPa] A - Cross sectional area of the component (at the point of crack initiation) [units of mm^2] Sy - Yield strength of the material [units of MPa] E - Elastic modulus (Young’s modulus) [units of MPa] K - Strength coefficient of the material n - Strain hardening exponent of the material b - Elastic strain exponent of the material c - Plastic strain exponent of the material sigma_f - Fatigue strength coefficient of the material epsilon_f - Fatigue strain coefficient of the material q - Notch sensitivity factor (default is 1 for no notch) Kt - stress concentration factor (default is 1 for no notch) mean_stress_correction_method - must be either ‘morrow’, ’modified_morrow’, or ‘SWT’. Default is ‘modified_morrow’ as this is the same as the uncorrected Coffin-Manson relationship when mean stress is zero.

Outputs: The results will be printed to the console if print_results is True The following results are also stored in the calculated object. sigma_max sigma_min sigma_mean epsilon_max epsilon_min epsilon_mean cycles_to_failure

Example usage: fracture_mechanics_crack_initiation(P=0.15, A=5*80, Kt=2.41, q=0.9857, Sy=690, E=210000, K=1060, n=0.14, b=-0.081, c=-0.65, sigma_f=1160, epsilon_f=1.1,mean_stress_correction_method=’SWT’)