PSI - Issue 42

Florian Garnadt et al. / Procedia Structural Integrity 42 (2022) 1113–1120 F. Garnadt et al. / Structural Integrity Procedia 00 (2019) 000–000

1114

2

(a)

(b)

Strain �

Notch Support

with notch

without notch

Cycles N

Fig. 1. (a) Turbine shaft as an example of a component with notches as design features; (b) Schematic fatigue life curves showing the lifetime beneficial e ff ect of notch support.

by Fig. 1 (b) are utilized to determine the number of cycles to crack initiation. While determining such curves for a specific material and temperature, the impact of the stress gradient on crack initiation and growth from the notch root is generally neglected. Here, standardized un-notched specimens are typically used. If the e ff ect of notch support is considered in the determination of fatigue life curves, the cycle number will increase for the same crack depth at the same local loading level as indicated by the shifted curve in Fig. 1 (b). The e ff ect is based on a reduced short crack growth rate due to the stress gradient induced by the notch. The combination of the local strain concept for crack initiation and a fracture mechanical approach for crack prop agation at notches was used by e.g., Dowling (1979) and Vormwald (1989). However, the focus was on materials applied at room temperature. Within this paper a model for short crack growth under combined creep and low cycle fatigue (LCF) loading at high temperature will be described. The results and findings will be validated by experimental crack growth measurements using round bar specimens with a circumferential notch. Furthermore, the transferabil ity and applicability of this approach will be demonstrated by further tests and computations for a component-like structure.

Nomenclature

a n

Crack depth

Notch support factor

t Time ( C t ) avg Creep crack tip loading F Force K t , I

Notch factor based on first principal stress

N R

Cycle number

Load ratio

T

Temperature Displacement

U

d a d N

Crack growth rate

Strain range

∆ ε ∆ J

Fatigue crack tip loading

˙ ε

Strain rate

χ I ∗ () e ff

Normalized stress gradient based on first principle stress

E ff ective value () eq , loc Local equivalent value () glob Global value () x mm Up to x mm crack depth () 5% 5% load drop criterion