SPECIMEN CONFIGURATION
The specimens alloy has volume percentages of 70% and 30% respectively
for the ferrite and pearlite phases. The mixture rule concludes average
values for \(\sigma_{y}\) equal to 275.9 MPa,\(=\sigma_{y1}\), for the
ferrite grains and 689.7 MPa, \({=\sigma}_{y2}\), for the pearlite
grains. Search in the literature shows that values up to\(\sigma_{y1}=\ \)312 MPa and \(\sigma_{y2}=\ \)1020 MPa can be
found. Thus, standard deviations of 35.9 MPa and 331 MPa are invoked for\(\sigma_{\text{y\ }}\)of the ferrite and pearlite grains respectively.
Variations in \(\sigma_{y}\) of the grains of each phase are assumed
randomly distributed between the minimum and maximum values of the
corresponding phase. The cyclic yield stress of steel is approximately
equal to 0.6 of its monotonic yield stress 11, 12, 5,
53-55. Following that, a grain is assumed having a value of 0.6 for the
ratio of its cyclic and monotonic yield stresses.
A mean grain size of 36 µm is assumed for both phases of the alloy with
13 µm standard deviation. This accommodates surface 445 ferrite grains
and 191 pearlite grains arranged along the circumference of the specimen
minimum cross section.
The specimen surface roughness resembles micro cracks of different sizes
and locations. The model assumes the existence of multi coplanar micro
cracks along the specimen minimum circumference. The starting maximum
crack length is 0.1 µm and the crack lengths follow a normal
distribution.
Different virtual specimens were randomly prepared with the above
configuration. A virtual test starts with one of those specimens. A
specimen is subjected to a cyclic axial load with the parameters listed
in Table1.