A surface crack of length a_i (mm) was detected in a C-frame of rectangular section ( depth of section AB (h), measured from point A to B and  thickness of the section AB (b)) made of a steel alloy (yield strength=860 in MPa and fracture toughness = K_ic in MPa.m^-0.5 . The C-frame is subjected to  a variable load P that acts in the directions as shown and it fluctuates from P_min to P_max (in N) .

Data (based on the student number last digit):

In the region of crack propagation, the values measured for the relationship between da/dN and DKi  in this alloy were: (Hint: use it to determine the Paris coefficient C and exponent m)

Table 1.                                                         

Hint: as the geometric factor Y depends on the crack length… then use the initial crack a_i to calculate the Y₁ for the different loads. Use the Y₁’s to determine the final crack size a_f1.

With a_f1  calculate again the geometric factors Y₂’s.. Take the average (Y₁+Y₂)/2 as the final value of the geometric factor Y.  calculate the final crack length  a_f

Determine the following with at least 4 decimal places of accuracy:

Area of the rectangular section (in 10^-4 m²)

The coefficient of the Paris equation (in 10^-12 for K_i in MPa.m^-½ )

The maximum axial stress (in MPa)

Using a_i

Using a_f

Using a_average

The life of the component in number of cycles