Formulation of Strain Fatigue Criterion Based on Complex Numbers

Area of Science:

• Materials Science
• Mechanical Engineering
• Solid Mechanics

Background:

• Multiaxial fatigue criteria often face mathematical challenges when combining normal and shear strain vectors.
• Existing methods use weighting factors to define equivalent strain, which can oversimplify the distinct physical nature of normal (longitudinal) and shear (rotational) strains.

Purpose of the Study:

• To develop a new method for combining different strain types in fatigue analysis.
• To address the physical inaccuracies of using simple vector addition or weighting factors for normal and shear strains.

Main Methods:

• A complex number system was employed to represent strain components.
• Normal strain was assigned as the real part, and shear strain as the imaginary part of a complex number.
• This complex number representation was applied to analyze simple load states.

Main Results:

• The proposed complex number approach successfully integrates normal and shear strains.
• For simple load cases like pure bending and pure torsion, the derived equivalent strain expression matches previously established criteria (e.g., Macha's).

Conclusions:

• The complex number method offers a more physically grounded approach to combining normal and shear strains in multiaxial fatigue.
• This method provides a unified framework for fatigue analysis, potentially improving accuracy in predicting material failure under complex loading conditions.