A Model for Fatigue Crack Growth in the Paris Regime under the Variability of Cyclic Hardening and Elastic Properties

Abstract

Over the last 60 years, several models have been developed governing different zones of fatigue crack growth from the threshold zone to final failure. The best known model is the Paris law and a number of its based on mechanical, metallurgical and loading parameters governing the propagation of cracks. This paper presents an analytical model developed to predict the fatigue crack propagation rate in the Paris regime, for different material properties, yield strength (σy), Young’s modulus (E) and cyclic hardening parameters (K’, n’) and their influence by variability. The cyclic plastic deformation at a crack tip or any other cyclic hardening rule may be used to reach this objective, for to investigate this influence, these properties of the model are calibrated using available experimental data in the literature. This FCGR model was validated on Al-alloys specimens under constant amplitude load and shows good agreement with the experimental results.

Prediction of Fatigue Crack Growth Rate and Stress Intensity Factors Using the Finite Element Method

“…where a is the length of the crack, N is the number of cycles, C is the Paris constant, and m is the Paris exponent. Both C and m are dependent strongly on the cyclic hardening exponent and mechanical properties [42], and they are obtained experimentally. Several authors [43,44] identified a very consistent empirical relationship between Paris' law parameters, which was supported by experimental results, such as [45,46].…”

Analytical modeling of fatigue crack growth in plastically pre‐strained steels

“…This observation suggests as a physical interpretation that the growth rate of cracks is significantly influenced by the cyclic strain hardening characteristics at the material crack tip. This phenomenon has been extensively studied in literature through analytical efforts as well as experimental results, and it has been found to have a direct impact on FCGR [25][26][27]65 and has been associated with the crack closure phenomenon. 66 Furthermore, Equation ( 25), considering the stress ratio effect, may be appropriately modified to also include the residual stresses effect in FCGR analysis.…”

Quasi-in-situ observation of fatigue crack growth behavior of friction stir welded 2024-T4 joint

“…The values of 'm' and 'C' are listed in table 1. The value of 'm' is crucial in determining the fatigue crack resistance [23][24][25]. The corresponding modeling equations for selected C(T) samples are shown as equations (5) to (8).…”