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.