PSI - Issue 74

Karel Slámečka et al. / Procedia Structural Integrity 74 (2025) 85 – 90 Karel Slámečka / Structural Integrity Procedia 00 (202 5 ) 000 – 000 ( , )= ∙ � 2√ � ,

88 4

(1)

where C ( x , t ) is the nitrogen concentration at depth x (Fig. 2) and time t , C s is the surface concentration, and D is the diffusion coefficient. Here, C s defines the DZ properties at the CL/DZ interface. The thermal expansion mismatch between Ti and DZ was characterized by the differential parameter Δα = α Ti – α DZ . In the simulations, Δα varied between 0.5 and 2.5 µstrain/°C to capture uncertainty in the N-rich zone. Table 2. Material parameters used in simulations. E : Young's modulus, μ : Poisson’s ratio, σ y : yield strength, E t : tangent modulus, α : coefficient of thermal expansion. Subscripts 20 and 700 denote properties at room temperature (20 °C) and at 700 °C, respectively. * CL/DZ interface values; † Sakamoto et al. (2023) , Sl ámečka et al. (2024) ; ‡ Gobbi et al. (2019). Parameter Ti * DZ (Ti + N) ‡ CL (TiN) E 20 / E 700 (GPa) 120 / 80 132 / 88 550 µ (–) 0.361 0.361 0.25 σ y20 / σ y700 (MPa) † 300 / 100 400 / 130 – E t20 / E t700 (MPa) † 725 / 72.5 1000 / 100 – α 20 / α 700 (µstrain/°C) 8.5 / 10.3 6.0–8.0 / 7.8–9.8 9.35

3. Results and discussion 3.1. Cooling stresses

Fig. 3 shows the residual stress profiles obtained after cooling from the stress-free nitriding temperature to room temperature, plotted across the smallest neck cross-section , which is where cracks are both expected and observed (Fig. 1c). The curves illustrate how the coating architecture and the thermal expansion mismatch between the Ti core and the DZ ( Δ α ) influence the distribution of tensile and compressive stress zones.

Fig. 3. Residual stress profiles predi cted across the smallest neck cross -section after cooling from nitriding temperatures of (a) 500 °C, (b) 600 °C, and (c) 700 °C. Dotted vertical lines indicate the location of the CL/DZ and DZ/Ti interfaces. σ 1 , σ 2 , σ 3 : principal stresses.