Modelling for Creep Cavitation Damage and Life of Three Metallic Materials

Figures & data

Table 1. The chemical composition (wt%) of test materials [20–23]

	OFHC copper	0.5CMV steel (S and CW)	X20 steel (series CL)	X20 steel (series CT)
C	-	0.14	0.202	0.218
Si	<0.001	0.26	0.265	0.278
Mn	-	0.59	0.657	0.645
P	-	0.009	0.0185	0.0184
S	0.0021–0.0024	0.018	0.0054	0.0049
Cr	-	0.32	11.537	11.45
Ni	<0.0005	0.19	0.709	0.699
Mo	-	0.61	1.061	1.057
Cu	Balance	0.16	0.091	0.091
Al	-	<0.01	0.0289	0.0281
Nb	-	<0.01	-	-
Ti	-	<0.01	-	-
W	-	-	0.068	0.063
V	-	0.29	0.286	0.29
Co	-	-	0.022	0.017
Fe	<0.001	Balance	Balance	Balance
Sb	<0.0005	<0.01	-	-
Pb	<0.0005	-	-	-
Sn	<0.0005	0.01	0.001	0.005
Ag	0.001	-	-	-
As	<0.003	0.02	-	-
Zn	<0.01	-	-	-

Table 2. Temperature, time and stress ranges for the assessed data in creep testing [20–23]

Quantity/material	OFHC copper	0.5CMV steel (S)	0.5CMV steel (CW)	X20 steel (CL)	X20 steel (CT)
Temperature (°C)	400–550	640–700	600–640	600–670	600
Time (h)	0.5–97.5	22–1508	545–8886	92–7566	3766
Stress (MPa)	13.8–34.5	20–160	35.7–80	80	90

Figure 1. (a) A schematic 2D illustration of creep cavities at grain boundaries, (b) a simplified 3D model of creep cavitation in a polycrystal adapted from [40] and (c) a faceted creep cavity shaped by surface diffusion in copper.

Figure 2. Creep cavitation damage (a) and (b) in HAZ of X20 steel [27], and (c) in oxygen free phosphorus doped (OFP) copper [26].

Figure 3. Observed versus predicted cavity area fraction (for copper converted from density) with classical Φ’ model and the new Φ model for OFHC copper [20] in (a) and (b), for simulated type IV HAZ of 0.5CMV steel [23] in (c) and (d), and for X20 steel [21, 22] in (e) and (f).

Figure 4. Observed versus predicted time to cavity area fraction (for copper converted from density) with classical Φ’ model and the new Φ model for OFHC copper [20] in (a) and (b), for simulated type IV HAZ of 0.5CMV steel [23] in (c) and (d), and for X20 steel [21, 22] in (e) and (f).

Figure 5. The predicted versus observed time to given cavity area fraction for 0.5CMV type IV cross-weld HAZ [23] in (a), and the predicted versus observed cavity area fraction for selected 0.5CMV type IV cross-weld HAZ [23] data in (b).

Figure 6. Predicted (with the new Φ model) and measured evolution of creep cavitation damage for restricted test series in (a) OFHC copper [20], (b) 0.5CMV simulated type IV HAZ [23], (c) cross-weld 0.5CMV steel [23] and (d) X20 steel base material [21, 22].

Table 3. Indicative values for the model parameters in Equations (2)–(5) [20–23, 51, 53]

Parameter	OFHC copper	0.5CMV steel ^1)	0.5CMV steel ^2)	X20 steel	Unit
A’	26.11	115.53	-	0.0015	1/h·MPa^2.3
n’	2.3	2.3	-	4.8	-
Q	104	174	174	174	kJ/mol·K
B(T,σ) ^3)	4.13 ·10^17 (20.7MPa/773 K) 4.75 ·10^17 (24.1MPa/773 K)	6.20 ·10^24 (60MPa/913 K)	2.35 ·10^15 (60MPa/893 K)	9.69 ·10^23 (80MPa/908 K)	1/h
m	−0.24	1.89	1.51	1.51	-
n	4.79	5.0	5.0	5.0	-
ω	0	7.56	3.69	7.34	-

^a Simulated type IV HAZ specimens in [23]

^b Type IV HAZ of cross-weld specimens in [23]

^c Values for the example test series in Figures 3 and 5

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