PSI - Issue 76

D. Kaschube et al. / Procedia Structural Integrity 76 (2026) 19–26

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To measure applicability, the sum squared distances from the ideal line can be used as a measure of error. The closer R 2 is to 1, the more suitable the model is. Equation 2 is used to calculate the suitability of the Morrow relationship. This method uses the mean stress σ m to count for the mean strain influence which only works well up to about 10 4 cycles, as the mean stress is comparably low in HCF, especially in tension-release test mode. The poor R 2 value of 0 . 3998 shows that this method is way too non-conservative in case of tension mean strain. Since taking the mean stress into account does not lead to a satisfactory result, it makes sense to use the stress amplitude together with the mean stress to correct expectations. For this reason, the SWT model uses the maximum stress σ max , see Equation 3. In the case of compressive stress, this leads to a shift to the non-conservative side, but results in an increase in R 2 to 0 . 9377, see Figure 3c. The prediction in the case of tensile mean strain is also more successful, but with an R 2 of 0 . 7707 it is still low and remains on the non-conservative side. The model of Ince and Glinka, described with Equation 4, is a combination of the Morrow and the SWT model and therefore not suitable in this case, see Figure 3d. Figure 3e shows the influence of the Walker model, based on di ff erent values for γ . This parameter is a value expressing the mean stress sensitivity of a material, but does not take into account that a material can react di ff erently to tensile and compressive mean stress. For this reason, di ff erent methods were tested to calculate γ . The first method, based on Equation 7, yields a γ of 0 . 67. This value produces a very good result ( R 2 = 0 . 9444) in the case of com pressive strains, but performs poorly in the case of tensile strains. The second method, a regression with all available values from Table 1 according to the method of Dowling, Dowling (2009), yields a γ of 0 . 40. With this value, the R 2 values for tension and compression become almost equal. It is therefore the optimal value if one wishes to evaluate tensile and compressive stresses equally using the Walker method. The optimal value for γ when evaluating tensile strain alone is approximately 0 . 10, yielding an R 2 of0 . 9047.This γ value indicates the material’s significant sensitivity to tensile stress. The modified Smith Watson Topper model provides the best prediction of fatigue strength behaviour when tensile and compressive stresses are considered together. As Equation 8 shows, it includes a sensitivity factor which, in this case, is also called γ as in the Walker model, but is calculated di ff erently, see Equation 9. The use of this model provides the best results for compressive strain and, with an R 2 of 0 . 8447, also performs better than the Walker model with γ determined specifically for this purpose by means of regression.

5. Conclusion

The results of this study confirm that the Co ffi n-Manson model, as anticipated, fails to represent the mean strain influence in fatigue behaviour for CMF-manufactured Ti6Al4V, since it does not incorporate any mean strain cor rection. In contrast, the correction models—Morrow, Smith-Watson-Topper (SWT), Ince-Glinka, Walker, and the Modified Smith-Watson-Topper (MSWT)—were systematically evaluated for their e ff ectiveness. The Morrow and SWT models o ff er some improvement, with SWT generally performing better for tensile mean strains, while the Ince-Glinka approach was not suitable for the present dataset. The Walker model’s accuracy depends significantly on the selection of the γ parameter, and determining this parameter by regression requires comprehensive datasets that are often unavailable in practice. Moreover, the complexity of the Walker model’s application can limit its practical usability for engineers. The Modified Smith-Watson-Topper (MSWT) model stands out by combining simplicity in calculation with reli able prediction accuracy. The MSWT utilizes a straightforward equation for γ , based solely on the material’s ultimate and yield strengths, making it easy to apply even when detailed regression data is lacking. Among all tested mean strain correction approaches, the MSWT delivers the best balance of simplicity and predictive accuracy. Taken together, these findings show that the MSWT model provides an e ffi cient and robust method for estimating fatigue life under varying mean strains in Ti6Al4V manufactured with cold metal fusion, and is recommended for practical engineering applications using this additive manufacturing process.