Question

Discuss briefly what you understand by the term ‘Fatigue Failure Criteria’ (Goodman, Gerber etc.) used in design under cyclic stresses; state specifically why such criteria are needed.

Answer 1

Mean stress as well as stress amplitude exist when a component is subjected to fluctuating stresses. It has been observed that the mean stress component has an effect on fatigue failure when it is present in combination with an alternating component. The fatigue diagram for this general case is shown in Fig. below. In this diagram, the mean stress is plotted on the abscissa and stress amplitude on ordinate. The magnitudes of mean stress and stress amplitude depend upon the magnitudes of maximum and minimum force acting on the component. When stress amplitude is zero, the load is purely static and the criterion of failure is Sut or Syt. These limits are plotted on the abscissa. When the mean stress is zero, the stress is completely reversing and the criterion of failure is the endurance limit Se that is plotted on the ordinate. When the component is subjected to both components of stress, the actual failure occurs at different scattered points shown in the figure. There exists a border, which divides safe region from unsafe region for various combinations of mean stress and stress amplitude. Different criterion are proposed to construct the borderline dividing safe zone and failure zone. They include Gerber line, Soderberg line and Goodman line. AGa Syt Failure Yield line points Gerber line Goodman line Soderberg line Sy Sut C Mean stress Gerber Line: A parabolic curve joining Se on the ordinate to Sut on the abscissa is called the Gerber line. Soderberg Line A straight line joining Se on the ordinate to Syt on the abscissa is called the Soderberg line. Goodman Line A straight line joining Se on the ordinate to Sut on the abscissa is called the Goodman line.

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