Fig. 12 Examples of the assessment of the present simulation for the
cracked area plotted against number of loading cycles for repeated
two-step loading block tests compared with the corresponding behavior
due to the application of CAL having the two involved stress amplitudes.
Figure 12 presents the cracked area against the corresponding number of
cycles as a result of the present assessment for six examples out of the
virtual tests involved in Fig. 11 together with their corresponding CAL
virtual tests. The arrowed symbols in Fig. 11 refer to the examples
presented in Fig. 12. A vertical line G-G is drawn in each figure to
indicate Nf experimentally obtained in the case of the
presented repeated two-step block loading. The value of\(\sum\frac{N}{N_{f}}\ \) for each experiment is typed in Fig. 12.
The runs due to the CSA virtual tests result in their corresponding
duration of Nf which are used, here, to
calculate\(\ \sum\frac{N}{N_{f}}\ \). The theoretical summations
are generally less than 1. This is justified in Fig. 12 which shows the
behavior due to repeated two-step loading blocks. The line representing
a repeated two-step loading blocks lies between the two corresponding
CAL lines. For its corresponding three runs, the specimens in each
example utilized the same surface configuration. Experimentally,
summations equal to and greater than 1 are possible since specimens with
different surface configurations are tested and calculations rely on CAL
endurance data extracted from average fitted lines.
The four block parameters\(\text{\ σ}_{o_{1}}\),\(\text{\ N}_{1}\),\(\sigma_{o_{2}}\)and \(N_{2}\) have influences
on\(\ \sum\frac{N}{N_{f}}\) . Keeping three of those parameters
unchanged, such an influence of changing the fourth parameter follows.
For \(\text{\ σ}_{o_{1}}\)greater than\(\text{\ σ}_{o_{2}}\), the
previous discussion on the present results relevant to TSL tests with
H-L sequence implies that \(\ \sum\frac{N}{N_{f}}\) in repeated
two-step loading block decreases with
increasing\(\frac{N_{1}}{\ N_{f_{1}}}\) ,\(\ \frac{N_{2}}{N_{f_{2}}}\)and\(\text{\ σ}_{o_{1}}\)and with a decrease in\(\text{\ σ}_{o_{2}}\).
The present simulation with its devised software is capable to perform a
detailed parametric study for recognizing the contribution of each of
the above parameters.
The present results together with those of its conjugate article52 are encouraging the present authors to work on
checking the invoked model against other materials and geometries.
Actually, the available four experimental data 3presented in Fig. 1 for comparison cover a lifetime range from
104 cycles to 107 cycles. The grey
line in Fig. 1 presents the endurance line fitting those experimentally
obtained point. Despite Fig. 1 shows good proximity between experimental
data and the present model, it should be noted that the experimental
data represent a small sample to be used as comparison, at maximum it
can be stated as a possible indicator of compatibility. The same
scenario is observed in Fig. 10, aggravated by the tiny available sample
related to the experimental data. Of course, validation of the proposed
model needs more comparative experimental sampling. Based on the above
argument, the authors are working to check the model with sufficient
experimental data on other two-phase and single phase materials
available in the literature. That would be a strength of the model.
Relevant experimental data are numerous in the literature, e.g.55, 60-65. Further, those publications specifically
contain many test results with H-L and L-H load sequences. However, a
problem exists. The input data necessary for the application of the
model are the main parameters controlling the fatigue life of un-notched
test specimens, i.e. (1) some metallurgical details of the tested
material in terms of the existing phases with their percentage, grain
size and mechanical properties, (2) specimen’s size, (3) specimen’s
surface roughness, (4) loading pattern. Unfortunately, metallurgical
details as mentioned above and/or surface roughness are not provided. At
present, this unable the use of those test results to check the
predictive abilities of the present model. However, the present
algorithm can easily perform some comparative scenarios between two or
more numerical simulations, considering different values of the missing
data in a trial for their reasonable evaluation. This will facilitate
the checking step.
The algorithm outlined by the flow chart in Fig. 2 applies the present
model on the limited case of un-notched round specimens in push-pull
loading. However, the concepts of the model can manipulate other
uniaxial testing conditions, i.e. rotating bending moment and pure
twisting moment. In this case, the algorithm needs some alterations to
accommodate such conditions. For that objective, some numerical analyses
should be performed for necessary deformation parameters around the tips
of neighboring short surface cracks in the case of different types of
uniaxial loading. Based on the above arguments, the authors will work to
expand the application of the proposed model to other experimental tests
with uniaxial loading.