PSI - Issue 34

D. Rigon et al. / Procedia Structural Integrity 34 (2021) 154–159 D. Rigon and G. Meneghetti / Structural Integrity Procedia 00 (2021) 000–000

156

3

Technology Material

definition of l ferritic grain size Austenitic grain size

Wrought

Ferritic steels

Austenic stainless steels

Pearlitic steels pearlite colony size Dual-phase (ferritic-martensitic) steels Ferritic grain size (with ferrite percentage higher than 50%) Martensitic steels martensite lath widths (or packet size of martensite laths) Bainitic steels bainite packet size Titanium alloys width of α lamellae

AM

MS (as-built/aged)

Subgrain cell size/martensite lath width Subgrain cell size/martensite lath width Subgrain cell size/martensite lath width

17PH4

316

Ti6Al4V

width of α lamellae

10.0 12.0 14.0 16.0

10.0 12.0 14.0 16.0

Serie2 Serie3 Serie4 CM & AM R ≈ 0 CM R = -1 CM & AM R ≈ 0.5

Serie1 Serie2 Serie4 CM & AM R ≈ 0 CM R = -1 CM & AM R ≈ 0.5

0.5 ]

0.5 ]

0.0 2.0 4.0 6.0 8.0

0.0 2.0 4.0 6.0 8.0

ΔK th,LC,R [MPa∙m

ΔK th,LC,R [MPa∙m

Circle size is proportional to HV values

Circle size is proportional to l 0.3 values

50

500

0.1

1

10

100

1000

l [ μm]

HV

Fig. 1. Threshold SIF of long cracks for CM and AM materials taken from the literature versus the microstructural length parameter l and Vickers hardness for different load ratios load (from (Rigon and Meneghetti 2020, 2021)).

Fig. 1 summarises the experimental data collected from the literature and enables one to appreciate a certain correlation among ΔK th,LC , l and HV. In particular, Fig. 1a shows that ΔK th,LC,exp increases with l , where the circle sizes are proportional to HV, while the opposite trend can be observed in Figs. 1b where ΔK th,LC decreases with HV and the circle sizes are proportional to l raised to 0.3 to accommodate the entire range of l values. In light of these observations, the following empirical bi-parametric equation has been proposed (Rigon and Meneghetti 2020, 2021): ∆K th,LC, (R) = α R · l β R + γ R ·HV δ R (1) where α R , β R , γ R , δ R are coefficients that depend on the load ratio R and are to be fitted with the relevant set of data. Units of ΔK th,LC,(R) , l and HV used to calibrate Eq. (1) are [MPa√m], [μm] and [kgf/mm 2 ] . To calibrate the empirical model , only references reporting ΔK th,LC,exp evaluated at growth rates between 10 -10 and 10 -11 m/cycle, the microstructural length parameter l and HV were taken into account for the analysis. Eq. (1) was fitted on the collected experimental results by using the curve fitting toolbox of Matlab® software and by setting the n onlinear least squares fitting method. For each load ratio set of data, the fitting provided the following estimating equations: ∆K th,LC, (R=-1) = 4.5 · l 0.127 +229·HV -0.81 (2) ∆K th,LC, (R=0) = 1.82 · l 0.165 +53.52·HV -0.53 (3)