Fatigue Damage Assessment of Tensile Specimen Considering Opening Stress in Crack Propagation Stage

Abstract

Most of the structures in service are subjected to cyclic loading of variable amplitude. The effect of load interaction is necessary to accurately predict the fatigue life of components in design phase. In the present paper, a fatigue damage methodology under complex loading history is proposed considering two stages of damage process and considering the effect of sequence of loading. This is further modified by considering opening stress in crack propagation stage. The proposed methodologies are compared with the linear damage rule by illustrating an example of dynamically induced stress in a slender bar under uniform axial time varying force. The effect of various influencing parameters on fatigue life of bar is also studied. The proposed methodologies are further validated using experimental fatigue test results. The comparison shows a good agreement between theoretical and experimental results. It is found that conventional Miner’s rule estimates higher damage index compared to the proposed methodology.

Appendix

At instant t = 0, consider the bar is straight and at rest so that displacement and velocity of the bar are given as

$$u\left( {x,0} \right) = \sum\limits_{i = 1}^{\infty } {\phi_{i} \left( x \right)\eta_{i} \left( 0 \right)}$$

(27)

$$\dot{u}\left( {x,0} \right) = \sum\limits_{i = 1}^{\infty } {\phi_{i} \left( x \right)\dot{\eta }_{i} \left( 0 \right)}$$

(28)

Multiplying Eqs. (27) and (28) by ϕ_k(x) and integrating in the domain along with the orthogonality condition of normal modes, one obtains two linear simultaneous equations with unknowns A′ and B′. On solving, constants of integrations are obtained as

$$\begin{aligned} & A_{i}^{\prime } = - \frac{1}{{\omega_{i}^{2} }}\sqrt {\frac{2}{\rho AL}} \sum\limits_{j = 1}^{n} {\frac{{P_{j} \sin \phi_{j} }}{{\sqrt {\left( {1 - r_{j}^{2} } \right)^{2} + \left( {2\xi r_{j} } \right)^{2} } }}} \\ & B_{i}^{\prime } = \frac{1}{{\omega_{di} }}\left\{ {\xi_{i} \omega_{i} A_{i}^{\prime} - \frac{1}{{\omega_{i}^{2} }}\sqrt {\frac{2}{\rho AL}} \sum\limits_{j = 1}^{n} {\frac{{P_{j} \omega_{j} \cos \phi_{j} }}{{\sqrt {\left( {1 - r_{j}^{2} } \right)^{2} + \left( {2\xi r_{j} } \right)^{2} } }}} } \right\} \\ \end{aligned}$$

(29)