Analytical investigation of some critical plane approaches under biaxial stress state

Determining the fatigue damage to the machine and machine parts in the case of variable loading has great importance in engineering. Several reasons such as material properties, mean stress value, number of cycles, stress range and design parameters affects the fatigue life of structural elements. In multiaxial stress state examination of the fatigue behavior of materials is essential to minimize the risk that are caused by design and to increase the material strength. The first fatigue test was carried out during 1860s and 1870s on wagon axles by German Engineer August Wöhler. S-N diagram is the basis of fatigue criteria and S N curve is still used in today. Late 19th century theories that show the effects of mean stress are introduced mainly by Gerber and Goodman. Due to the material fatigue behavior can not be visually observed; analytical calculations, numerical calculations, experimental approaches and finite element-based methods are developed. Today, many fatigue testing machines are used and improved with developing technology. However; multiaxial fatigue experiments for proportional and non-proportional loadings are costly and time consuming. Equivalent stress hypothesis, fracture plane estimates are used for material fatigue life calculations. Critical plane approaches are developed for determining the maximum damage level and determine crack initiation plane and crack progression surface. Critical plane approaches are seperated into three main group: stress based approaches, strain based approaches and strain energy based approaches. Stress based approaches which calculate fatigue life with the aid of other material parameters are the most frequently applied variants of critical plane approaches. Using stress based fatigue approaches, fatigue life of materials are calculated and maximum damage plane is estimated under combination of, for example, bending and torsion. Stress based approaches use parameters such as amplitude of normal stress, mean stress values, maximum shear stress and octahedral shear stress. It is aimed to obtain most appropriate results for the experimental results by using critical plane approaches defined with different material parameters. In the present studies, stress states are investigated using Rotvel's, Nishihara's and Kawamoto's experiment data. The test results are compared with analytical results. In this study, critical plane approaches are examined in detail and each critical plane approach's parameters are defined. Then critical plane orientation is calculated with appropriate criteria by defining the experimental inputs used in the present studies under non-proportional and proportional high cycle loadings. To sum up analytical calculations are evaluated and it is decided whether it is suitable for certain stress state.