Development of a Two-Parameter Model (Kmax, ΔK) for Fatigue Crack Growth Analysis

Abstract

It is generally accepted that the fatigue crack growth depends on the stress intensity factor range (ΔK) and the maximum stress intensity factor (K_max). Numerous driving forces were introduced to analyze fatigue crack growth for a wide range of stress ratios. However, it appears that the effect of the crack tip stresses and strains need to be included into the fatigue crack growth analysis as well. Such an approach can be successful as long as the stress intensity factors are correlated with the actual elastic-plastic crack tip stress-strain field. Unfortunately, the correlation between the stress intensity factors and the crack tip stress-strain field is often altered by residual stresses induced by reversed plastic deformations. A two-parameter model (ΔK_tot, K_max,tot) based on the elastic-plastic crack tip stress-strain history has been proposed. The applied stress intensity factors (ΔK_appl, K_max,appl) were modified and converted into the total stress intensity factors (ΔK_tot, K_max,tot) in order to account for the effect of local crack tip stresses and strains on the fatigue crack growth. The fatigue crack growth was regarded as a process of successive crack re-initiations in the crack tip region and predicted by simulating the stress-strain response in the material volume adjacent to the crack tip and estimating the accumulated fatigue damage. The model was developed to predict the mean stress effect for steady-state fatigue crack growth and to determine the fatigue crack growth under simple variable amplitude loading histories. Moreover, the influence of the applied compressive stress on fatigue crack growth can be explained with the proposed two-parameter model. A two-parameter driving force in the form of: Δκ = K_max,tot^p ΔK_tot^(1-p) was derived based on the local stresses and strains at the crack tip using the Smith-Watson-Topper (SWT) fatigue damage parameter: D = σ_maxΔε/2. The parameter p is a function of material cyclic stress-strain properties and varies from 0 to 0.5 depending on the fatigue crack growth rate. The effects of the internal (residual) stress induced by the reversed cyclic plasticity manifested themselves in the change of the resultant (total) stress intensity factors driving the crack. Experimental fatigue crack growth data sets for two aluminum alloys (7075-T6 and 2024-T351), two steel alloys (4340 and 4140), and one titanium alloy (Ti-6Al-4V) were used for the verification of the model under constant amplitude loading. This model was also capable of predicting variable-amplitude fatigue crack growth. Experimental fatigue crack growth data sets after single overloads for the aluminum alloy 7075-T6, steel alloy 4140, and titanium alloy Ti-6Al-4V were also used for the verification of the model. The results indicate that the driving force Δκ can successfully predict the stress ratio R effect and also the load-interaction effect on fatigue crack growth.