PurposeThe stress state near the notch affects fatigue damage directly, but quantifying the stress field is difficult. The purpose of this study is to provide a mathematical description method of the stress field near the notch to achieve a reliable assessment of the fatigue life of notched specimens.Design/methodology/approachFirstly, the stress distribution of notched specimens of different materials and shapes under different stress levels is investigated, and a method for calculating the stress gradient impact factor is presented. Then, the newly defined stress gradient impact factor is used to describe the stress field near the notch, and an expression for the stress at any point along a specified path is developed. Furthermore, by combining the mathematical expressions for the stress field near the notch, a multiaxial fatigue life prediction model for notched shaft specimens is established based on the damage mechanics theory and closed solution method.FindingsThe stress gradient factor for notched specimens with higher stress concentration factors (V60-notch, V90-notch) varies to a certain extent when the external load and material change, but for notched specimens with relatively lower stress concentration factors (C-notch, U-notch, stepped shaft), the stress gradient factor hardly varies with the change in load and material, indicating that the shape of the notch has a greater influence on the stress gradient. It is also found that the effect of size on the stress gradient factor is not obvious for notched specimens with different shapes, there is an obvious positive correlation between the normal stress gradient factor and the normal stress concentration factor compared with the relationship between the shear stress gradient factor and the stress concentration factor. Moreover, the predicted results of the proposed model are in better agreement with the experimental results of five kinds of materials compared with the FS model, the SWT model, and the Manson–Coffin equation.Originality/valueIn this paper, a new stress gradient factor is defined based on the stress distribution of a smooth specimen. Then, a mathematical description of the stress field near the notch is provided, which contains the nominal stress, notch size, and stress concentration factor which is calculated by the finite element method (FEM). In addition, a multiaxial fatigue life prediction model for shaft specimens with different notch shapes is established with the newly established expressions based on the theory of damage mechanics and the closed solution method.

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PurposeEngineering components/structures are usually subjected to complex and variable loads, which result in random multiaxial stress/strain states. However, fatigue analysis methods under constant loads cannot be directly applied to fatigue life prediction analysis under random loads. Therefore, the purpose of this study is how to effectively evaluate fatigue life under multiaxial random loading.Design/methodology/approachFirst, the average phase difference is characterized as the ratio of the number of shear strain cycles to the number of normal strain cycles, and the new non-proportional additional hardening factor is proposed. Then, the determined random typical load spectrum is processed into a simple variable amplitude load spectrum, and the damage in each plane is calculated according to the multiaxial fatigue life prediction model and Miner theory. Meanwhile, the cumulative damage can be calculated separately by projection method. Finally, the maximum projected cumulative damage plane is defined as the critical plane of multiaxial random fatigue.FindingsThe fatigue life prediction capability of the method is verified based on test data of TC4 titanium alloy under random multiaxial loading. Most of the predicting results are within double scatter bands.Originality/valueThe objective of this study is to provide a reference for the determination of critical plane and non-proportional additional hardening factor under multiaxial random loading, and to promote the development of multiaxial fatigue from experimental studies to practical engineering applications.

PurposeUnder multiaxial random loading, the material stress–strain response is not periodic, which makes it difficult to determine the direction of the critical plane on the material. Meanwhile, existing methods of constant loading cannot be directly applied to multiaxial random loading; this problem can be solved when an equivalent stress transformation method is used.Design/methodology/approachFirst, the Liu-Mahadevan critical plane is introduced into multiaxial random fatigue, which is enabled to determine the material's critical plane position under random loading. Then, an equivalent stress transformation method is proposed which can convert random load to constant load. Meanwhile, the ratio of mean stress to yield strength is defined as the new mean stress influence factor, and a new non-proportional additional strengthening factor is proposed by considering the effect of phase differences.FindingsThe proposed model is validated using multiaxial random fatigue test data of TC4 titanium alloy specimens and the results of the proposed model are compared with that based on Miner's rule and BSW model, showing that the proposed method is more accurate.Originality/valueIn this work, a new multiaxial random fatigue life prediction model is proposed based on equivalent stress transformation method, which considers the mean stress effect and the additional strengthening effect. Results show that the predicted fatigue lives given by the proposed model are in well accordance with the tested data.

PurposeDue to the limitation of experimental conditions and budget, fatigue data of mechanical components are often scarce in practical engineering, which leads to low reliability of fatigue data and reduces the accuracy of fatigue life prediction. Therefore, this study aims to expand the available fatigue data and verify its reliability, enabling the achievement of life prediction analysis at different stress levels.Design/methodology/approachFirst, the principle of fatigue life probability percentiles consistency and the perturbation optimization technique is used to realize the equivalent conversion of small samples fatigue life test data at different stress levels. Meanwhile, checking failure model by fitting the goodness of fit test and proposing a Monte Carlo method based on the data distribution characteristics and a numerical simulation strategy of directional sampling is used to extend equivalent data. Furthermore, the relationship between effective stress and characteristic life is analyzed using a combination of the Weibull distribution and the Stromeyer equation. An iterative sequence is established to obtain predicted life.FindingsThe TC4–DT titanium alloy is selected to assess the accuracy and reliability of the proposed method and the results show that predicted life obtained with the proposed method is within the double dispersion band, indicating high accuracy.Originality/valueThe purpose of this study is to provide a reference for the expansion of small sample fatigue test data, verification of data reliability and prediction of fatigue life data. In addition, the proposed method provides a theoretical basis for engineering applications.