Creep life assessment of aero-engine recuperator based on continuum damage mechanics approach

Abstract

The creep life of an aeroengine recuperator is investigated in terms of continuum damage mechanics by using finite element simulations. The effects of the manifold wall thickness and creep properties of brazing filler metal on the operating life of the recuperator are analyzed. Results show that the crack initiates from the brazing filler metal located on the outer surface of the manifold with the wall thickness of 2 mm and propagates throughout the whole region of the brazing filler metal when the creep time reaches 34900 h. The creep life of the recuperator meets the requirement of 40000 h continuous operation when the wall thickness increases to 3.5 mm, but its total weight increases by 15%. Decreasing the minimum creep strain rate with the enhancement of the creep strength of the brazing filler metal presents an obvious effect on the creep life of the recuperator. At the same stress level, the creep rupture time of the recuperator is enhanced by 13 times if the mismatch between the minimum creep rate of the filler and base metal is reduced by 20%.

Key words： creep; life assessment; brazed joint; continuum damage mechanics; aeroengine recuperator

1 Introduction

With the rapid development of the aviation industry, the demand for environment friendly aircraft and low-emission aeroengines is more stringent than ever before [1–3]. In accordance with the statistics from the International Council on Clean Transportation, the CO₂ emissions from all commercial operations amounted to 918 million tons in 2019, an increase of 29% since 2013. Emissions from passenger transport accounted for 85% [4]. The incorporation of recuperator into the aeroengine can be an effective means to address these problems [5,6], which can remarkably improve the fuel efficiency by more than 10% [1].

Many studies have investigated the application of intercooler recuperated aeroengines [7,8]. However, most of them focused mainly on the engine thermal cycle analysis and parameter optimization [9–13], and few studies explored the engine failures and material optimization at high temperature for long-time operation. A profile tube type recuperator of high efficiency was developed by Motoren-und Turbinen-Union Friedrichshafen GmbH company under the support of Clean Program (component validator for an environmentally friendly aeroengine) [14,15]. The recuperator operating at high temperature and external load conditions is manufactured by brazing Inconel 625 alloy. As the weakest region, brazed joints mostly experience creep failures [16–18]. Therefore, much attention should be paid to the creep failure of brazed joints of the recuperator [19]. Zhang et al. [20] found that the maximum creep deformation is located in the middle of the compressor discharge air passages after 40000 h, and selecting superalloy containing creep resistant element Nb is a more suitable option for the recuperator. Jiang et al. [21] showed that a large residual stress can be introduced in the brazed joints due to the mismatch of the properties between the brazing filler metal and base metal. Shi et al. [22] investigated the creep rupture properties of nickel-based directionally solidified superalloy brazed joints. The results show that the fracture occurs in the brazing filler metal and all brazed joints exhibit a considerably lower creep life compared with that of the base metal. Ma et al. [23] found that the stress at the inner fin and tube joints will be larger, and the creep strain in and around the brazed joints is larger than that of the base metal due to the discontinuous change in structure. Chen et al. [24] investigated the creep crack growth behavior of the brazed joints. A proper mismatch design between the brazing filler metal and base metal should be considered in the creep life assessment and design. Therefore, the design of brazed joints against creep failure by optimizing their materials and dimensions should be explored to ensure the long-term safety and reliability of the recuperator.

Different from the base metal, the tertiary creep stage of the filler metal occupies a small proportion of the whole life. Cadek [25] and Kassner [26] proved that the creep rupture time of metal materials is inversely proportional to the power function of the minimum creep rate of the second stage. Sklenička et al. [27] studied the creep behavior of P92 steel pipe elbows at 600 and 650 °C by uniaxial tensile creep test with local induction heating. The creep rupture time of the pipes at different locations is prolonged with the increase in creep rupture strain. At the same minimum creep rate, the increase in the creep rupture strain of internal bending pipe by 2.7% increases the creep life by 4.7%. Vrchovinsky et al. [28] obtained a more uniform recrystallized grain structure by cold rolling process. The results show that the creep life increases from 3234 to 3961 h and the rupture strain increases by 1.07% with the increase in cold reduction from 4.8% to 15%. The creep life assessment of the recuperator involves a number of influencing factors, such as the geometrical size and creep performance of the filler metal. However, the influence of these parameters, especially the creep properties of filler metals, on the creep life of the recuperator has not been well understood.

In this study, the creep life of an aeroengine recuperator was investigated on the basis of continuum damage mechanics (CDM) and the finite element method. The creep deformation and damage of the recuperator were analyzed by using the modified Liu–Murakami creep damage model proposed by Zhang et al. [29]. The effect of the creep properties of filler metals on the creep life of the recuperator was evaluated. Recommendations for the life assessment and structural design will be provided for the aeroengine recuperator at high temperature.

2 Finite element analysis

2.1 Model description

The geometric model of the recuperator is established according to Ref. [1], and its dimensions are shown in Fig.1 and Tab.1. h_{\text{La}}, b, d, s, and t are the cross section dimensions of U-shaped heat exchange tubes; H and T are the overall dimensions of U-shaped heat exchange tubes; and D, L, and S are the inside diameter, length, and wall thickness of manifold, respectively. The heat transfer tubes and the manifolds are joined by brazing technology. In this study, the brazed filler is BNi-2, and the base material is Inconel 625.

Fig.1 Motoren-und Turbinen-Union Friedrichshafen GmbH recuperator geometry.

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Tab.1 Geometric model dimensions of the aeroengine recuperator

Material	hLa	d	s	b	t	T	H	L	D	S
Inconel 625	6.0 mm	1.56 mm	0.1 mm	2.70 mm	5.52 mm	290 mm	78.24 mm	690 mm	50.0 mm	2.0 mm

A one-eighth finite element model is established for the recuperator due to the structural symmetry, as shown in Fig.2. The element type of this model is C3D8R, which has a total of 142376 elements and 183693 nodes. The brazed joint is similar to a sandwich structure, which mainly includes a base metal zone, a diffusion zone, and a brazing filler metal zone [30]. The thicknesses of the brazing filler metal and diffusion zone metal are 100 and 70 μm, respectively. The diffusion zone is divided into zones 1 and 2, which are 35 μm in thickness. The element size used in this study can guarantee the calculation accuracy of the stress and creep damage analyses [31].

Fig.2 Three-dimensional finite element model and meshing of recuperator for the aeroengine: (a) one-eighth model of recuperator, (b) tube sheet, (c) brazing filler metal, and (d) detail of brazed joints.

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Fig.3 shows the boundary conditions applied to the recuperator for simulations. In the simulation of brazing residual stress, X, Y, and Z axisymmetric boundary conditions are attached to planes 1, 3, and 4, respectively. In the process of thermal stress and creep damage, plane 1 is subjected to fully constrained (encastré) boundary conditions. Plane 2 is constrained by X-direction displacement and X-, Y-, and Z-direction rotation, and Y and Z axisymmetric boundary conditions are established for planes 3 and 4, respectively. The design temperature is 650 °C, which is slightly higher than the actual operating temperature, and the internal pressure of 3 MPa is applied to the internal faces of tubes and manifolds [14].

Fig.3 Boundary conditions of the recuperator.

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2.2 Thermal stress calculation

The material properties are assumed to be isotropic and temperature-dependent. The total strain ({\epsilon }_{\text{total}}) can be decomposed into elastic strain ({\epsilon }^{\text{e}}), plastic strain ({\epsilon }^{\text{p}}), thermal strain ({\epsilon }^{\text{th}}), and creep strain ({\epsilon }^{\text{c}}), which can be expressed as Eq. (1):

(1){\epsilon }_{\text{total}}={\epsilon }^{\text{e}}+{\epsilon }^{\text{p}}+{\epsilon }^{\text{th}}+{\epsilon }^{\text{c}}.

The elastic strain is numerically analyzed on the basis of the isotropic Hooke’s law with temperature-dependent Young’s modulus and Poisson’s ratio. A rate-independent plastic model with von Mises yield surface, temperature-dependent mechanical properties, and isotropic hardening model is employed to calculate the plastic strain. The thermal strain is calculated by using the temperature-dependent coefficient of thermal expansion (CTE).

The mechanical properties of the substrate material and brazing filler metal can be obtained by experimental tests in accordance with the corresponding standards. However, acquiring the brazing diffusion zone properties directly is difficult due to the thin thickness of this layer in the brazed joints. The diffusion zone is similar to the functionally graded material, which is widely believed that the mechanical properties (e.g., Young’s modulus, CTE, density, Poisson’s ratio, and creep stress exponent) are distributed in the power law form along the thickness direction [32,33]. In this study, the diffusion zone of the brazed joints is regarded as the functionally graded material, and its mechanical property calculation is based on Eq. (2) [31]:

(2)Mat=M\exp (c\cdot y),

where M and c are the material constants, Mat is the mechanical properties of the diffusion zone, and y is the thickness of the diffusion zone, as shown in Fig.4. The mechanical properties of the substrate material and brazing filler metal, such as elastic modulus, CTE, yield stress, and Poisson’s ratio, are from Ref. [34] and Special Metals Corporation group of companies, as shown in Fig.5.

Fig.4 Calculation method of the diffusion zone properties of brazed joints.

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Fig.5 High-temperature mechanical properties of the different materials: (a) elastic modulus, (b) coefficient of thermal expansion, (c) yield strength, and (d) Poisson’s ratio.

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2.3 Creep and damage calculation

The modified Liu–Murakami creep damage constitutive model proposed by Zhang [31] is adopted for the creep strain. This model combines the advantages of Kachanov–Rabotnov and Liu–Murakami constitutive models, which avoid the difficulty of convergence caused by the large ratio of ({\sigma }_{\text{I}}/\phantom{{\sigma }_{\text{I}}{\sigma }_{\text{eq}}}{\sigma }_{\text{eq}}), which can be expressed as follows:

(3){\dot{\epsilon }}_{ij}^{\text{c}}=\frac{3}{2}{B}_{0}m{\sigma }_{\text{eq}}^{n_0-1}{S}_{ij}{t}^{m-1}+\frac{3}{2}B{\sigma }_{\text{eq}}^{n-1}{S}_{ij}\exp \left[\frac{2\left(n+1\right)}{\text{π}\sqrt{1+3/n}}{\omega }^{3/2}\right],

(4)\dot{\omega }=\frac{A\left[1-\exp \left(-q\right)\right]}{q}{\left({\sigma }_{\text{r}}\right)}^p\exp (q\omega ),

(5){\sigma }_{\text{r}}=\alpha {\sigma }_{\text{I}}+(1-\alpha ){\sigma }_{\text{eq}},

where t is time, A, B, p, and q are material constants, n is the stress exponent of the material at the secondary creep stage, {\sigma }_{\text{eq}} is the von Mises stress, {\sigma }_{\text{I}} is the maximum principal stress, m, B₀, and n₀ are the material constants at the primary creep stage, and {\sigma }_{\text{r}} is the reference stress under multiaxial creep (equivalent stress), S_{ij} and {\epsilon }_{ij}^{\text{c}} are the deviatoric stress and deviatoric strain, respectively, {\dot{\epsilon }}_{ij}^{\text{c}} and \dot{\omega } are the derivative of {\epsilon }_{ij}^{\text{c}} and \omega with respect to time, \omega denotes the damage state parameter ranging from 0 to 1 (\omega =0 represents that no damage exists; \omega =1 indicates the failure of the material), and α is the material constant ranging from 0 to 1. The creep parameters of the Inconel 625 and BNi-2 are presented in Tab.2 [31,35]. In the damage analysis, an integration point will lose its load-carrying capacity if the damage variable \omega reaches to the critical value of 0.99 [36]. Accordingly, the creep crack will be deemed to initiate and the length of the element will be deemed as the crack increment when all the integration points of an element have failed in this manner. This treatment method for crack length has been widely adopted in the numerical simulations of creep crack growth [37–41].

Tab.2 Creep properties of different materials [31,35]

Material	B0	n0	m	A	B	n	p	q	α
BNi-2	1.562 × 10−7	1.965	0.29	7.899 × 10−9	8.017 × 10−11	2.92	2.70	3.2307	0.15
Inconel 625	‒	‒	‒	3.589 × 10−26	9.541 × 10−35	11.56	8.68	6.1550	0.15
Diffusion zone 1	1.562 × 10−7	1.965	0.29	3.570 × 10−12	9.000 × 10−15	4.12	3.62	4.8000	0.15
Diffusion zone 2	‒	‒	‒	8.000 × 10−20	1.200 × 10−25	8.20	6.48	9.1000	0.15

3 Results and discussion

3.1 Stress distribution

Fig.6 shows the variation of von Mises stress and maximum principal stress distributions with the creep exposure time of the recuperator under the design conditions (650 °C, 3 MPa). The maximum von Mises stress is located at the connection between the tube sheet and the first tube at the early stage, and the peak stress is about 359.6 MPa, which is higher than the yield stress of the Inconel 625. When the creep time is about 19910 h, the peak stress is located in the first tube of the recuperator due to the creep relaxation effect, as shown in Fig.6(a), and the maximum von Mises stress is about 167.3 MPa. For the maximum principal stress, the peak stress is 612.4 MPa at the early stage of the design operating conditions, and it is about 507.8 MPa when the creep exposure time is 19910 h, as shown in Fig.6(b). The locations of the maximum principal stress are mostly the same as that of the maximum von Mises stress under the same creep time.

Fig.6 (a) von Mises stress and (b) maximum principal stress distributions of the recuperator of aero engine under different creep exposure times.

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Two paths are set along the thickness and length of brazed joints zone to further understand the stress distribution, as shown in Fig.7. The variation of the von Mises stress and maximum principal stress along path 1 is shown in Fig.8. The von Mises stress decreases from the initial 200 MPa to about 17 MPa, and the maximum principal stress is in the compressive stress, which is reduced by 80 MPa. High stress values are maintained at all points at 0 h, and stress relaxation appears in all areas with the extension of time. For the stress distribution of brazed joints along path 2 (Fig.9), the von Mises stress in the BNi-2 region is consistent with that in path 1, which decreases from 200 to 17 MPa and reaches 0.3 MPa after 40000 h. The BNi-2 surrounds the oval pipe along the length direction, the maximum principal stress at the end of the pipe is larger than that in the middle region, but the relaxation still occurs with the increase in time.

Fig.7 Paths along the thickness and circumferential direction of the brazed joints.

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Fig.8 (a) von Mises stress and (b) maximum principal stress distributions along path 1 of the brazed joints.

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Fig.9 (a) von Mises stress and (b) maximum principal stress distributions along path 2 of the brazed joints.

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3.2 Creep damage distribution

The creep damage result of the whole recuperator structure at 40000 h is shown in Fig.10. For the creep damage of brazed joints, the damage degrees of the different regions are as follows: BNi-2 > diffusion zone 1 > diffusion zone 2 > Inconel 625, in which BNi-2 first reaches the damage threshold value of 0.99. At the same stress level, Inconel 625 alloy has better creep resistance, and its maximum damage value is only 0.092 at 40000 h.

Fig.10 Creep damage in (a) Inconel 625, (b) BNi-2, and diffusion zones (c) 1 and (d) 2 at 40000 h.

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3.3 Effect of manifold wall thickness

The thickness of the manifold has a great influence on the generation and redistribution of stress in brazed joints. Yu et al. [42] show that for single crystal nickel-based alloys DD5, the stress intensity factor at the crack tip decreases remarkably with the increase in the specimen thickness at the same stress level, which leads to the prolongation of rupture time. Tab.3 shows the element numbers and node numbers in the finite element model of the recuperator under the different wall thicknesses of 2.0, 2.5, 3.0, and 3.5 mm. Fig.11 and Fig.12 show the creep damage distribution of BNi-2 with time under the different wall thicknesses of 2.0, 2.5, 3.0, and 3.5 mm. The creep damage first occurs at the top and bottom of the oval BNi-2 region near the side of the heat exchanger tube, and the failure zone extends from the edge to the middle of tube. When the creep time is 40000 h, the wall thickness of the manifold increases from 2.0 to 3.5 mm, and the circumferential crack length along path 2 decreases from 2.0 to 1.5 mm. Similarly, the damage area reduces with the increase in wall thickness. Fig.13 shows the variation of crack length with time in the BNi-2 region. When the wall thickness of manifold is 2 mm, the crack initiation time is 1910 h, and the creep crack length extends to 2.78 mm in the BNi-2 region after 40000 h continuous operation. The crack initiation time is 4910 h, and the creep crack length is only 1.16 mm after the same creep time when the manifold wall thickness increases to 3.5 mm, an increase of 75% in wall thickness. Increasing the manifold wall thickness by 75% can prolong the creep life of the whole structure by 1.4 times. However, the prolonged life is achieved at the cost of increasing recuperator weight. In this case, the total weight of the recuperator increases by approximately 15%.

Tab.3 Finite element model dimensions of manifold at different wall thicknesses

Thickness/mm	Element number	Node number	Minimum mesh size/(μm × μm × μm)
2.0	142376	183693	202 × 35 × 327
2.5	143824	185023	202 × 35 × 406
3.0	144728	186641	202 × 35 × 484
3.5	145664	187815	202 × 35 × 562

Fig.11 Creep damage distributions of BNi-2 with different wall thicknesses of manifold at 40000 h: (a) 2.0 mm, (b) 2.5 mm, (c) 3.0 mm, and (d) 3.5 mm.

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Fig.12 Damage distributions of BNi-2 along path 2 with different wall thicknesses of manifold: (a) 2.0 mm, (b) 2.5 mm, (c) 3.0 mm, and (d) 3.5 mm.

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Fig.13 Creep crack length variation curve of BNi-2 with time at different wall thicknesses of manifold.

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3.4 Effect of filler metal creep properties

Previous studies [43–45] showed that the creep properties of the filler metal have a great influence on the creep life of the brazed joints due to the appreciable mismatch of the creep properties between the brazing filler metal and base metal. At the same stress level of 200 MPa, the minimum creep rate and rupture time of the filler metal BNi-2 are approximately four orders of magnitude different from those of Inconel 625 alloy [31]. Improving the filler metal creep properties is of great importance so as to minimize the mismatch of the brazed joints. Four cases of the joints with improved filler metal creep properties are studied (Fig.14(a)–Fig.14(c)). Given that the steady-state creep strain rate is usually described by the Norton’s creep law, {\dot{\epsilon }}_{min}^{}=B{\sigma }^n [46], where B is the material constant, n is the creep stress index. The original creep stress exponent n of the BNi-2 is 2.92, four values of n (3.36, 3.79, 4.22, and 4.65) with an interval of 0.43 are selected to be appropriate for the present analysis. The corresponding B value for each n value is calculated by using Eqs. (3)–(5) such that the mismatch of minimum creep rate between the brazing filler metal and base metal can be reduced by 5%, 10%, 15%, and 20% at the same stress level at 650 °C. The creep rupture time is linearly related to the minimum creep rate in the logarithmic coordinate system, which satisfies the classical Monkman–Grant relationship [47], as shown in Fig.14(c). Although the creep failure strain of the modified BNi-2 remains at about 4.5%, its rupture time is effectively prolonged with the decrease in the minimum creep rate (Fig.14(d)). The creep crack length along the circumferential direction of brazed joints at creep time of 100000 h is calculated by using the same constitutive model and CDM approach, as mentioned in Section 2.1. This process is performed to further compare the effects of filler creep properties and manifold wall thickness on the life of joints. The results in Tab.4 and Fig.15 show that the failure area of the brazed joints is mainly concentrated in the brazing filler metal. When the creep time is 100000 h, the wall thickness of the manifold increases from 2.0 to 3.5 mm, and the crack length decreases from 2.99 to 2.58 mm (cases 1–3). Increasing the manifold wall thickness by 50% (case 3) can only prolong the life of the recuperator to 1.16 times. However, the creep lifetime can be enhanced by 13 times if the minimum creep rate difference between the brazing filler and base metal is reduced by 20% (case 7). In view of the trade-off relationship between creep strength and ductility in practical materials [48], decreasing the minimum creep strain rate with the enhancement of creep strength is a more effective means to deal with the weight gain and high cost problems.

Tab.4 Creep crack length along the circumferential direction of brazed joints at 100000 h: comparison of the effect of manifold wall thickness and BNi-2 creep properties

Case	Wall thickness of Inconel 625/mm	Material constant B of BNi-2	Creep stress exponent n of BNi-2	Crack initiation region	Creep crack length at 100000 h/mm	Relative value of creep crack length at 100000 h/%
1	2.0	8.017 × 10−11	2.92	BNi-2	2.99	0.00
2	2.5	8.017 × 10−11	2.92	BNi-2	2.96	−1.00
3	3.0	8.017 × 10−11	2.92	BNi-2	2.58	−13.71
4	2.0	4.700 × 10−12	3.36	BNi-2	2.42	−19.06
5	2.0	2.800 × 10−13	3.79	BNi-2	1.66	−44.48
6	2.0	1.800 × 10−14	4.22	BNi-2	1.10	−63.21
7	2.0	1.200 × 10−15	4.65	BNi-2	0.23	−92.31

Fig.14 Modified BNi-2 and Inconel 625 at 650 °C: relationship curve in double logarithmic coordinate axis of (a) the minimum creep strain rate with the applied stress, (b) the rupture time with the applied stress, (c) the creep rupture time with the minimum creep rate (the Monkman–Grant relationship); and (d) relationship curve of the creep strain with time.

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Fig.15 Degree of creep life enhancement of the recuperator.

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4 Conclusions

In this study, the creep life assessment of an aeroengine recuperator under design conditions was investigated by the finite element simulation coupled with CDM approach. Some conclusions are provided as follows:

(1) The brazed joints become the weakest part due to the mismatch of the creep properties between the brazing filler metal and base metal. The maximum damage occurs in the filler rather than in the base metal, which seriously affects the long-term life of the brazed joints.

(2) When the manifold wall thickness is 2.0 mm, the crack initiates at 1910 h. When the creep crack length is extended to 2.78 mm in the BNi-2 region, the creep time reaches 40000 h. When the manifold wall thickness is increased to 3.5 mm, the creep crack length is 1.16 mm at 40000 h, which satisfies the requirement of long-term operation. However, the total weight of the recuperator is simultaneously increased by about 15%.

(3) Decreasing the minimum creep rate with the enhancement of the creep strength of the brazing filler metal presents more evident effect on the creep life of the recuperator than increasing the manifold wall thickness. At the same stress level, the creep rupture time of the recuperator can be enhanced by 13 times if the mismatch of the minimum creep strain rate between the brazing filler metal and base metal is reduced by 20%.

The creep properties can be improved by modifying the composition of brazing filler metal, thereby improving the creep lifetime of the brazed joints. This work may serve as the basis for the development of new Ni-based brazing filler. A new Ni-based brazing filler with optimal creep properties should be explored to extend the service life of the recuperator as much as possible, which will be envisaged in the continuation of this work.

5 Nomenclature

A, q	Material constants in the Liu–Murakami damage evolution model
B	Coefficient in the secondary creep stage
B0, m	Coefficients in the primary creep stage
c	Diffusion exponent in material properties
D	Inner diameter of the manifold
L	Length of the manifold
M	Initial material properties
Mat	Material properties of the diffusion zone
n0, n	Stress exponents in the primary and secondary creep stage, respectively
p	Rupture stress exponent in stress-based models
S	Wall thickness of the manifold
Sij	Deviatoric stress
y	Thickness of the diffusion zone
\omega	Damage state parameter ranging from 0 to 1
α	Material constant of multiaxiality ranging from 0 to 1
{\epsilon }^{\text{c}}	Creep strain
{\epsilon }^{\text{e}}	Elastic strain
{\epsilon }^{\text{p}}	Plastic strain
{\epsilon }^{\text{th}}	Thermal strain
{\epsilon }_{\text{total}}	Total strain
{\dot{\epsilon }}_{min}^{}	Minimum creep strain rate
{\sigma }_{\text{eq}}	von Mises stress
{\sigma }_{\text{I}}	Maximum principal stress
{\sigma }_{\text{r}}	Reference stress under multiaxial creep (equivalent stress)

Acknowledgements

The work was supported by the National Natural Science Foundation of China (Grant No. 51675181). The authors are also grateful for the Innovation Program of Shanghai Municipal Education Commission, China (Grant No. 2019-01-07-00-02-E00068).

References

1 Salpingidou C , Misirlis D , Vlahostergios Z , Flouros M , Donus F , Yakinthos K . Conceptual design study of a geared turbofan and an open rotor aero engine with intercooled recuperated core. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2018, 232(14): 2713–2720

2 Ricco P , Skote M , Leschziner M A . A review of turbulent skin-friction drag reduction by near-wall transverse forcing. Progress in Aerospace Sciences, 2021, 123: 100713

3 Wileman A J , Aslam S , Perinpanayagam S . A road map for reliable power electronics for more electric aircraft. Progress in Aerospace Sciences, 2021, 127: 100739

4 Graver B, Rutherford D, Zheng S. CO₂ emissions from commercial aviation: 2013, 2018, and 2019. Available from International Council on Clean Transportation website, 2020

5 Ferrari M L , Sorce A , Pascenti M , Massardo A F . Recuperator dynamic performance: experimental investigation with a microgas turbine test rig. Applied Energy, 2011, 88(12): 5090–5096

6 McDonald C F , Massardo A F , Rodgers C , Stone A . Recuperated gas turbine aeroengines, Part I: early development activities. Aircraft Engineering and Aerospace Techology, 2008, 80(2): 139–157

7 Boggia S , Rüd K . Intercooled recuperated gas turbine engine concept. In: Proceedings of the 41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit. Tucson: AIAA, 2005, 4192

8 Rolt A , Baker N . Intercooled turbofan engine design and technology research in the EU framework 6 NEWAC programme. In: Proceedings of International Symposium on Air Breathing Engines. Montreal: ISABE, 2009, 1351–1360

9 Zhang C Y , Gümmer V . Performance assessment of recuperated rotorcraft powerplants: trade-off between fuel economy and weight penalty for both tubular and primary surface recuperators. Applied Thermal Engineering, 2020, 164: 114443

10 Kyprianidis K G , Rolt A M . On the optimization of a geared fan intercooled core engine design. Journal of Engineering for Gas Turbines and Power, 2015, 137(4): 041201

11 Salpingidou C , Vlahostergios Z , Misirlis D , Donnerhack S , Flouros M , Goulas A , Yakinthos K . Thermodynamic analysis of recuperative gas turbines and aero engines. Applied Thermal Engineering, 2017, 124: 250–260

12 Vlahostergios Z , Misirlis D , Flouros M , Salpingidou C , Donnerhack S , Goulas A , Yakinthos K . Development, numerical investigation and experimental validation of a new recuperator design for aero engines applications. In: Proceedings of ASME Turbo Expo 2017: Turbomachinery Technical Conference & Exposition. Charlotte: ASME, 2017, V02BT41A035

13 Kormann M , Schaber R . An intercooled recuperative aero engine for regional jets. In: Proceedings of ASME Turbo Expo 2014: Turbine Technical Conference and Exposition. Düsseldorf: ASME, 2014, V03AT07A021

14 Schoenenborn H , Ebert E , Simon B , Storm P . Thermomechanical design of a heat exchanger for a recuperative aeroengine. Journal of Engineering for Gas Turbines and Power, 2006, 128(4): 736–744

15 Goulas A , Donnerhack S , Flouros M , Misirlis D , Vlahostergios Z , Yakinthos K . Thermodynamics cycle analysis, pressure loss, and heat transfer assessment of a recuperative system for aero-engines. Journal of Engineering for Gas Turbines and Power, 2015, 137(4): 041205

16 Zhang Y C , Jiang W C , Tu S T , Zhang X C , Zhou G Y . Analysis of creep crack growth behavior of the brazed joint using continuum damage mechanics approach. In: Proceedings of the ASME 2018 Pressure Vessels and Piping Conference. Prague: ASME, 2018, 51678: V06AT06A062

17 Luo Y , Jiang W C , Zhang Y C , Zhou F , Tu S T . A new damage evolution model to estimate the creep fracture behavior of brazed joint under multiaxial stress. International Journal of Mechanical Sciences, 2018, 149: 178–189

18 Tu S T . Emerging challenges to structural integrity technology for high-temperature applications. Frontiers of Mechanical Engineering in China, 2007, 2(4): 375–387

19 Tu S T , Zhou G Y . Creep of brazed plate-fin structures in high temperature compact heat exchangers. Frontiers of Mechanical Engineering in China, 2009, 4(4): 355–362

20 Zhang D J , Zeng M , Wang J W , Wang Q W . Creep analysis of cross wavy primary surface recuperator for microturbine system. In: Proceedings of ASME Turbo Expo: Power for Land, Sea, & Air. Berlin: ASME, 2008, 899–904

21 Jiang W C , Gong J M , Chen H , Tu S T . The effect of filler metal thickness on residual stress and creep for stainless-steel plate–fin structure. International Journal of Pressure Vessels and Piping, 2008, 85(8): 569–574

22 Shi D Q , Dong C L , Yang X G , Zhang L , Hou J B , Liu Y . Experimental investigations on creep rupture strength and failure mechanism of vacuum brazed joints of a DS superalloy at elevated temperature. Materials Science and Engineering: A, 2012, 545: 162–167

23 Ma T , Chen Y T , Zeng M , Wang Q W . Stress analysis of internally finned bayonet tube in a high temperature heat exchanger. Applied Thermal Engineering, 2012, 43: 101–108

24 Chen G , Wang G Z , Xuan F Z , Tu S T . Mismatch effect in creep properties on creep crack growth behavior in welded joints. Materials & Design, 2014, 63: 600–608

25 Cadek J . Creep in Metallic Materials. Amsterdam: Elsevier, 1988, 372–692

26 Kassner M E . Fundamentals of Creep in Metals and Alloys. 3rd ed. Oxford: Butterworth-Heinemann, 2015, 261–273

27 Sklenička V , Kuchařová K , Král P , Kvapilová M , Svobodová M , Čmakal J . The effect of hot bending and thermal ageing on creep and microstructure evolution in thick-walled P92 steel pipe. Materials Science and Engineering: A, 2015, 644: 297–309

28 Vrchovinsky V , Zrnik J , Kvackaj T , Wangyao P . Effect of final cold rolled microstructures on creep deformation behavior in nickel base alloy. Journal of Metals, Materials and Minerals, 2005, 15(2): 57–68

29 Zhang Y C , Jiang W C , Tu S T , Zhang X C , Ye Y J . Creep crack growth behavior analysis of the 9Cr-1Mo steel by a modified creep-damage model. Materials Science and Engineering: A, 2017, 708: 68–76

30 Zhang Y C , Yu X T , Jiang W C , Tu S T , Zhang X C . Elastic modulus and hardness characterization for microregion of Inconel 625/BNi-2 vacuum brazed joint by high temperature nanoindentation. Vacuum, 2020, 181: 109582

31 Zhang Y C. Creep damage and crack growth analysis of the brazed joint under multi-axial stress state. Dissertation for the Doctoral Degree. Shanghai: East China University of Science and Technology, 2016 (in Chinese)

32 Lai H S . Estimation of Ct of functionally graded materials under small scale creep stage. Composite Structures, 2016, 138: 352–360

33 Lee K H . Analysis of a propagating crack tip in orthotropic functionally graded materials. Composites Part B: Engineering, 2016, 84: 83–97

34 Zhang Y C , Jiang W C , Tu S T , Wen J F , Woo W . Using short-time creep relaxation effect to decrease the residual stress in the bonded compliant seal of planar solid oxide fuel cell―a finite element simulation. Journal of Power Sources, 2014, 255: 108–115

35 Hyde T H, Xia L, Becker A A. Prediction of creep failure in aeroengine materials under multi-axial stress states. International Journal of Mechanical Sciences, 1996, 38(4): 385–401, 403

36 Hyde C J , Hyde T H , Sun W , Becker A A . Damage mechanics based predictions of creep crack growth in 316 stainless steel. Engineering Fracture Mechanics, 2010, 77(12): 2385–2402

37 Kim N H , Oh C S , Kim Y J , Davies C M , Nikbin K , Dean D W . Creep failure simulations of 316H at 550 °C: Part II—Effects of specimen geometry and loading mode. Engineering Fracture Mechanics, 2013, 105: 169–181

38 Mehmanparast A , Davies C M , Webster G A , Nikbin K M . Creep crack growth rate predictions in 316H steel using stress dependent creep ductility. Materials at High Temperatures, 2014, 31(1): 84–94

39 Hyde T H , Saber M , Sun W . Testing and modelling of creep crack growth in compact tension specimens from a P91 weld at 650 °C. Engineering Fracture Mechanics, 2010, 77(15): 2946–2957

40 Zhang Y C , Jiang W C , Tu S T , Zhang X C , Ye Y J , Wang R Z . Experimental investigation and numerical prediction on creep crack growth behavior of the solution treated Inconel 625 superalloy. Engineering Fracture Mechanics, 2018, 199: 327–342

41 Zhao L, Xu L Y, Han Y D, Jing H Y. Quantifying the constraint effect induced by specimen geometry on creep crack growth behavior in P92 steel. International Journal of Mechanical Sciences, 2015, 94–95: 63–74

42 Yu Z Y , Wang X M , Liang H , Li Z X , Li L , Yue Z F . Thickness debit effect in Ni-based single crystal superalloys at different stress levels. International Journal of Mechanical Sciences, 2020, 170: 105357

43 Kurata Y , Saito T , Tsuji H , Takatsu T , Shindo M , Nakajima H . Development of a filler metal for weldments of a Ni-Cr-W superalloy with high creep strength. JSME International Journal Series A: Solid Mechanics and Material Engineering, 2002, 45(1): 104–109

44 Mayr P , Cerjak H , Jochum C , Pasternak J . Long-term creep behaviour of E911 heat resistant 9% Cr steel weldments fabricated with filler metals of different creep strength. In: Proceedings of ASME Pressure Vessels and Piping Conference. San Antonio: ASME, 2007, 675–680

45 Baumgartner S , Posch G , Mayr P . Welding advanced martensitic creep-resistant steels with boron containing filler metal. Welding in the World, 2012, 56(7): 2–9

46 NortonF H. The Creep of Steel at High Temperature. New York: McGraw-Hill, 1929

47 Kim Y K , Kim D , Kim H K , Oh C S , Lee B J . An intermediate temperature creep model for Ni-based superalloys. International Journal of Plasticity, 2016, 79: 153–175

48 Ma H L , Zhao B G , Wu G Z , Li Z , Gao Y L . A SnBiAgIn solder alloy with exceptional mechanical properties by rapid quenching. Journal of Materials Science: Materials in Electronics, 2021, 32(6): 8167–8173