On the development of creep damage constitutive equations: a modified hyperbolic sine law for minimum creep strain rate and stress and creep fracture criteria based on cavity area fraction along grain boundaries

Figures & data

Table 1. The variation of creep cavitation coefficient A [5].

Parameter	σ = 80 MPa	σ = 100 MPa	σ = 150 MPa	σ = 200 MPa	Temperatures (°C)
A	57	83	1	112	600
A	57	83	47	145	650
A	57	84	113	146	700

Figure 1. The variation of creep cavitation coefficient A with different variations of stress and temperature [6].

Figure 2. Comparison of conventional hyperbolic sine law with experiment [8] for 2·25Cr–1Mo steel [9].

Figure 3. Comparison of conventional hyperbolic sine law with experiment [10] for 0·5Cr–0·5Mo–0·25 V steel [9].

Figure 4. Comparison of modified hyperbolic sine law with the conventional one and experimental data [8] of 0·5Cr–0·5Mo–0·25 V steel [9].

Figure 5. Comparison of modified hyperbolic sine law with the conventional one and experimental data [10] of 2·25Cr–1Mo steel [9].

Table 2. The typical functions between minimum creep strain rate and stress [14].

Power law creep [15,16]
Linear +power law [17,18]
Hyperbolic sine law [3,13]

Figure 6. Experimental data of minimum strain rate and stress at 600 °C under 70–200 MPa for P91 steel [11].

Figure 7. The modelling result of conventional hyperbolic sine law compared with experimental data of P91 steel.

Figure 8. The modelling result of linear power law compared with experimental data of P91 steel.

Figure 9. The modelling result of modified hyperbolic sine law compared with experimental data for P91 steel.

Figure 10. The comparison between different function of minimum creep strain rate and applied stress for P91 steel.

Figure 11. Probability density function of cavity equivalent R for P91, experimental data from ref [21].

Table 3. The value of U′ for P91 at 600 °C.

Stress (MPa)	Rupture time (h)	U′ (h^−2)
70	80,736·8	1·2 × 10^−10
100	34,141	6·738 × 10^−10
110	21,206·3	1·746 × 10^−9
120	12,858·6	4·75 × 10^−9
140	3414·7	6·736 × 10^−8
160	971·2	8327 × 10^−7

Table 4. The value of U′ for P91 at 625 °C.

Stress (MPa)	Rupture time (h)	U′ (h^−2)
90	21,372·4	1·72 × 10^−9
100	9895·4	8·02 × 10^−9
120	1657·9	2·857 × 10^−7
140	99	1·142 × 10^−5

Figure 12. The trend of the values of U′ under different stress and temperature.

Table 5. The number of cavities at failure under a range of stress levels [12].

Stress (MPa)	Lifetime (h)	Number density of cavities (10^−5 μm^−3)
120	51,406	1·0625
135	29,466	0·6376
150	15,316	0·475
165	6779	0·45
180	2825	0·375

Table 6. The relationship between the value of A₂ and stress.

Stress (MPa)	A2
120	8·04139E-10
135	1·46871E-09
150	4·04979E-09
165	1·95844E-08
180	9·39776E-08

Figure 13. The trend of cavity nucleation rate coefficient A₂ and stress.

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