## Abstract

Increased interest in compact heat exchangers (CHXs) to serve as intermediate heat exchangers of very high temperature reactors resulted in significant research and development on their design, analysis, and construction. Printed circuit heat exchangers are a type of CHXs with high thermal efficiency and compactness achieved through diffusion bonding a stack of etched plates with millimeter scaled channels. The diffusion bonding process changes the microstructural and mechanical properties of the wrought metal plates. The current nonnuclear design code ASME section VIII, division 1 captures the material property change through a “joint efficiency factor.” However, the current nuclear design code ASME section III, division 5 does not address or support the diffusion bonded material properties. Hence, there is a need to develop allowable stresses, isochronous curves, and fatigue life curves for various diffusion bonded alloys. In this study, Alloy 800H material was selected to establish the diffusion bonded material properties under tension, creep, fatigue, and creep-fatigue loads at elevated temperatures in the range 550–760 °C. A set of tests on diffusion bonded Alloy 800H (DB 800H) were performed and the acquired data are used in developing allowable stresses S_{y}, S_{u}, S_{r}, S_{m}, S_{t}, S_{mt}, S_{o}, isochronous curves and fatigue life curves according to the ASME section III, division 5 requirements. This paper also presents detailed procedures used in developing the ASME code section III division 5 design provisions for diffusion bonded Alloy 800H.

## 1 Introduction

The operation temperature of generation IV (gen. IV) very high temperature reactors (VHTRs) ranges from 550 °C–950 °C [1–3]. Such elevated operation temperatures impose challenges in designing intermediate heat exchangers, which transfers heat from primary loop to secondary loop [1]. Traditional heat exchangers, such as shell and tube heat exchangers, are inefficient and bulky and hence are uneconomical. Printed circuit heat exchangers (PCHEs) are compact heat exchangers (CHXs) with a very high surface area for heat transfer. PCHEs are highly efficient and compact, making them an ideal option for Gen. IV power plants [4,5]. Typical PCHE consists of a channeled core attached to a set of headers for hot and cold fluid inlets and outlets. The steps to construct a PCHE are discussed below.

The first step is the photochemical etching of the thin plates. The photochemical etching process results in two sets of channeled plates with hot and cold fluid flow channel patterns. The typical channel dimensions range from 0.5 mm to 2 mm [4,6,7]. The next fabrication step stacks alternate hot and cold fluid plates inside a vacuum furnace and subjected to specified compressive stress at a specified temperature for a specified period. The compressive stress at elevated temperature promotes the atomic diffusion and grain growth across plate interface, consequently bonds all plates in a single monolithic PCHE core with thousands of millimeter scaled channels. Usually, multiple PCHE channeled cores are welded together to form the core of a PCHE unit. In the final fabrication step, headers are welded to the PCHE core for the inlet and outlet of hot and cold fluids.

The diffusion bonding process used in fabricating PCHE cores is an innovative technique that changes the plate alloy's microstructure, resulting in changes in its physical and mechanical properties. The microstructural and property changes of diffusion bonded Alloy 617, 316H, and Haynes 230 have been demonstrated [6,8–10]. The authors have determined the mechanical properties of diffusion bonded 800H (DB 800H) through a series of tension tests at elevated temperatures [11]. A summary of the tension test results are shown in Table 1. The reduction in strengths of the DB 800H can be observed by comparing the strengths of the wrought base metal Alloy 800H (BM 800H) as shown in Fig. 1. The current ASME section VIII nonnuclear design code captures such material property change by implementing the “joint efficiency factor” of 0.7 on all allowable stresses. The ASME section III design code does not specify any guidelines for incorporating material property change due to diffusion bonding. Also, in the ASME code there are no provisions to capture the diffusion bonded material performance at elevated temperatures, especially in the creep regime. Hence, developing allowable stresses, isochronous curves, and fatigue life curves of various diffusion bonded alloys is essential. Including such diffusion bonded material properties in the ASME code section III division 5 will allow analysis and design of PCHEs for nuclear service.

T (°C) | E (GPa) | σ (MPa)_{y} | σ (MPa)_{u} | % elongation |
---|---|---|---|---|

20 | 197 | 187 | 528 | 51.2 |

20 | 193 | 160 | 507 | 55.6 |

20 | 195 | 178 | 527 | 51.5 |

20 | 199 | 185 | 531 | 55.1 |

450 | 168 | 123 | 453 | 57.9 |

450 | 179 | 125 | 451 | 55.1 |

500 | 173 | 125 | 411 | 37.5 |

550 | 168 | 116 | 326 | 35.8 |

550 | 154 | 116 | 330 | 35.9 |

600 | 158 | 121 | 317 | 22.7 |

650 | 159 | 110 | 295 | 20.4 |

650 | 159 | 113 | 290 | 20.6 |

700 | 148 | 111 | 227 | 13.5 |

760 | 144 | 95 | 145 | 16.3 |

760 | 134 | 120 | 170 | 15.0 |

760 | 134 | 103 | 163 | 15.7 |

760 | 132 | 97 | 153 | 14.3 |

T (°C) | E (GPa) | σ (MPa)_{y} | σ (MPa)_{u} | % elongation |
---|---|---|---|---|

20 | 197 | 187 | 528 | 51.2 |

20 | 193 | 160 | 507 | 55.6 |

20 | 195 | 178 | 527 | 51.5 |

20 | 199 | 185 | 531 | 55.1 |

450 | 168 | 123 | 453 | 57.9 |

450 | 179 | 125 | 451 | 55.1 |

500 | 173 | 125 | 411 | 37.5 |

550 | 168 | 116 | 326 | 35.8 |

550 | 154 | 116 | 330 | 35.9 |

600 | 158 | 121 | 317 | 22.7 |

650 | 159 | 110 | 295 | 20.4 |

650 | 159 | 113 | 290 | 20.6 |

700 | 148 | 111 | 227 | 13.5 |

760 | 144 | 95 | 145 | 16.3 |

760 | 134 | 120 | 170 | 15.0 |

760 | 134 | 103 | 163 | 15.7 |

760 | 132 | 97 | 153 | 14.3 |

Keating et al. [13] investigated the current state of ASME code section III for PCHE design and analysis and provided a list of ASME code gaps to be addressed. The gaps relevant to this study, listed below, indicate the information needed to be developed for diffusion bonded alloys:

Allowable stress and material property data of diffusion bonded materials.

Creep–fatigue curves of diffusion bonded materials.

Isochronous curves of diffusion bonded materials.

This study addresses these gaps for diffusion bonded Alloy 800H (DB 800H). A set of tensile, fatigue, creep, and creep-fatigue tests were performed on diffusion bonded 800H at elevated temperatures. The data developed are presented and discussed in Ref. [11]. This dataset is used to develop the allowable stresses, isochronous curves, fatigue life curves, and creep-fatigue damage envelop. The methodology used and material properties of DB 800H developed is discussed below.

## 2 Experimental Data Developed

A diffusion bonded solid block (200 × 200 × 200 mm dimensions) of Alloy 800H fabricated by Vacuum Process Engineering Inc. (VPE, Sacramento, CA) was acquired. Plates of 1.6 mm thickness were diffusion bonded together following ASME section VIII, division 1, code case 2621-1. Diffusion bonding methodologies and parameters are the proprietary information of the company and hence cannot be presented. Various ASTM standard specimens were fabricated from the diffusion bonded block using wire electrical discharge machining. A set of tension, fatigue, creep, and creep-fatigue tests were performed. The readers are referred to Ref. [11] for the mechanical tests and scanning electron microscope examinations performed and corresponding results with critical discussions on the performance of diffusion bonded Alloy 800H (DB 800H). A summary of the tensile test performed and results are shown in Table 1. Creep test results under prescribed stresses at different temperatures are presented in Table 2. Readers are referred to Ref. [11] for DB800H creep tests, which showed primary, secondary, and small tertiary creep regime. Few tests did not show significant tertiary creep regime. All tests failed through bond delamination mechanism with small reduction in area. Strain controlled fatigue and creep–fatigue experimental results are presented in Tables 3 and 4, respectively. Table 4 shows the positive strain peak dwell period, *t*_{dwell}, prescribed in each test to determine the influence of creep–fatigue interaction on rupture life.

T (°C) | σ | $t1%$ | t_{ter} | t_{rup} |
---|---|---|---|---|

550 | 180 | 231 | — | 1773 |

550 | 197 | 8.9 | — | 887.85 |

550 | 197 | 231.9 | — | 2441^{a} |

600 | 138 | 0.1 | — | 1306^{a} |

650 | 100 | — | — | 1522^{a} |

650 | 114 | 816.3 | — | 1306^{a} |

650 | 116 | 39 | — | 301 |

650 | 160 | 20 | — | 57^{b} |

700 | 68 | — | — | 1261^{a} |

760 | 40 | 494.5 | 593 | 1002.7 |

760 | 40 | 2170 | 1750 | 2624 |

760 | 46 | 190.9 | 275 | 706.2 |

760 | 46 | 212.7 | 278 | 960.8 |

760 | 62 | 21.25 | 79 | 129 |

760 | 68 | 35.5 | 93 | 180 |

760 | 68 | 7.6 | 69 | 81.0 |

760 | 68 | 9.8 | 46 | 80.9 |

T (°C) | σ | $t1%$ | t_{ter} | t_{rup} |
---|---|---|---|---|

550 | 180 | 231 | — | 1773 |

550 | 197 | 8.9 | — | 887.85 |

550 | 197 | 231.9 | — | 2441^{a} |

600 | 138 | 0.1 | — | 1306^{a} |

650 | 100 | — | — | 1522^{a} |

650 | 114 | 816.3 | — | 1306^{a} |

650 | 116 | 39 | — | 301 |

650 | 160 | 20 | — | 57^{b} |

700 | 68 | — | — | 1261^{a} |

760 | 40 | 494.5 | 593 | 1002.7 |

760 | 40 | 2170 | 1750 | 2624 |

760 | 46 | 190.9 | 275 | 706.2 |

760 | 46 | 212.7 | 278 | 960.8 |

760 | 62 | 21.25 | 79 | 129 |

760 | 68 | 35.5 | 93 | 180 |

760 | 68 | 7.6 | 69 | 81.0 |

760 | 68 | 9.8 | 46 | 80.9 |

Creep tests discontinued before rupture at this time.

Specimen failed in primary creep regime.

T (°C) | $\epsilon \u02d9$ (/s) | $\epsilon r$ | $Nf1$ | $Nf2$ | $Nf3$ |
---|---|---|---|---|---|

550 | 0.001 | 0.006 | 4732 | 6254 | 3413 |

650 | 0.001 | 0.006 | 2213 | 1893 | 2147 |

760 | 0.001 | 0.006 | 476 | 452 | 323 |

T (°C) | $\epsilon \u02d9$ (/s) | $\epsilon r$ | $Nf1$ | $Nf2$ | $Nf3$ |
---|---|---|---|---|---|

550 | 0.001 | 0.006 | 4732 | 6254 | 3413 |

650 | 0.001 | 0.006 | 2213 | 1893 | 2147 |

760 | 0.001 | 0.006 | 476 | 452 | 323 |

T (°C) | $\epsilon \u02d9r$ | $\epsilon r$ | t_{dwell} | $Nf1$ | $Nf2$ | $Nf3$ |
---|---|---|---|---|---|---|

550 | 0.001 | 0.006 | 600 s | 282 | 297 | 258 |

650 | 0.001 | 0.006 | 300 s | 87 | 127 | 133 |

650 | 0.001 | 0.006 | 600 s | 113 | — | — |

760 | 0.001 | 0.006 | 120 s | 77 | 111 | 76 |

760 | 0.001 | 0.006 | 600 s | 60 | — | — |

T (°C) | $\epsilon \u02d9r$ | $\epsilon r$ | t_{dwell} | $Nf1$ | $Nf2$ | $Nf3$ |
---|---|---|---|---|---|---|

550 | 0.001 | 0.006 | 600 s | 282 | 297 | 258 |

650 | 0.001 | 0.006 | 300 s | 87 | 127 | 133 |

650 | 0.001 | 0.006 | 600 s | 113 | — | — |

760 | 0.001 | 0.006 | 120 s | 77 | 111 | 76 |

760 | 0.001 | 0.006 | 600 s | 60 | — | — |

## 3 Allowable Stresses of DB 800H

[13]

where $Si,DB$ is the allowable stress of DB 800H, *S _{i}* is the calculated lower bound allowable stress from DB 800H tests (see below Secs. 3.1 and 3.2, $Si,BM$ is allowable stress of wrought base metal Alloy 800H (BM 800H), and

*i*is the selected allowable stress type. The detailed procedure in the allowable stress calculations and related discussions are presented below.

### 3.1 Yield Stress, $Sy$.

where *S*_{DB} and *C _{i}* are model parameters determined by fitting experimental yield stresses through a gradient descent method, and optimum parameters are listed in Table 5. The allowable yield stresses are then determined based on Eq. (1). The allowable yield stress values of DB 800H determined are listed in Table 6. A comparison of the test yield stresses to the allowable yield stresses determined is shown in Fig. 2.

Parameters | S_{y} | S_{u} |
---|---|---|

S_{DB} | 155 | 375 |

C_{0} | 0.006027 | 0.002156 |

C_{1} | −0.00022 | −1.4 × 10^{−5} |

C_{2} | −2.2 × 10^{−6} | −2.6 × 10^{−6} |

C_{3} | 8.22 × 10^{−9} | 1.42 × 10^{−8} |

C_{4} | −1 × 10^{−11} | −2.5 × 10^{−11} |

C_{5} | 4.39 × 10^{−15} | 1.24 × 10^{−14} |

Parameters | S_{y} | S_{u} |
---|---|---|

S_{DB} | 155 | 375 |

C_{0} | 0.006027 | 0.002156 |

C_{1} | −0.00022 | −1.4 × 10^{−5} |

C_{2} | −2.2 × 10^{−6} | −2.6 × 10^{−6} |

C_{3} | 8.22 × 10^{−9} | 1.42 × 10^{−8} |

C_{4} | −1 × 10^{−11} | −2.5 × 10^{−11} |

C_{5} | 4.39 × 10^{−15} | 1.24 × 10^{−14} |

T (°C) | S_{y} | S_{u} | S_{m} | S_{o} |
---|---|---|---|---|

20 | 126.0 | 315.0 | — | — |

450 | 86.0 | 280.4 | 69.7 | 66.7 |

475 | 85.6 | 280.0 | 69.3 | 66.1 |

500 | 85.2 | 278.0 | 69.0 | 66.4 |

525 | 84.7 | 274.1 | 68.9 | 59.3 |

550 | 84.0 | 268.1 | 68.0 | 52.9 |

575 | 83.0 | 259.8 | 67.2 | 47.2 |

600 | 81.8 | 249.1 | 66.3 | 42.2 |

625 | 80.2 | 236.1 | 65.0 | 37.7 |

650 | 78.1 | 221.2 | 63.3 | 32.2 |

675 | 75.7 | 204.7 | 61.3 | 26.8 |

700 | 72.8 | 187.0 | 56.1 | 22.3 |

725 | 69.4 | 165.0 | 49.5 | 18.6 |

750 | 65.6 | 144.3 | 43.3 | 15.5 |

T (°C) | S_{y} | S_{u} | S_{m} | S_{o} |
---|---|---|---|---|

20 | 126.0 | 315.0 | — | — |

450 | 86.0 | 280.4 | 69.7 | 66.7 |

475 | 85.6 | 280.0 | 69.3 | 66.1 |

500 | 85.2 | 278.0 | 69.0 | 66.4 |

525 | 84.7 | 274.1 | 68.9 | 59.3 |

550 | 84.0 | 268.1 | 68.0 | 52.9 |

575 | 83.0 | 259.8 | 67.2 | 47.2 |

600 | 81.8 | 249.1 | 66.3 | 42.2 |

625 | 80.2 | 236.1 | 65.0 | 37.7 |

650 | 78.1 | 221.2 | 63.3 | 32.2 |

675 | 75.7 | 204.7 | 61.3 | 26.8 |

700 | 72.8 | 187.0 | 56.1 | 22.3 |

725 | 69.4 | 165.0 | 49.5 | 18.6 |

750 | 65.6 | 144.3 | 43.3 | 15.5 |

### 3.2 Ultimate Tensile Stress, $Su$.

where *S*_{DB} and *C _{i}* are model parameters determined by fitting the experimental ultimate tensile stresses, and model parameters are listed in Table 5. The allowable ultimate stresses are then determined based on Eq. (1). The allowable ultimate stress values of DB 800H determined are listed in Table 6. A comparison of ultimate stresses from the tests to the allowable ultimate stresses determined is shown in Fig. 2.

### 3.3 Time-Independent Allowable Stress, $Sm$.

*S _{m}* is the time-independent allowable stress determined per HBB-2160(d)(3), and is the minimum of

The product of one-third of the minimum tensile strength at room temperature and the tensile strength reduction factor [Table HBB-3225-2, ASME BPVC.III.5-2017];

The product of one-third of the minimum tensile strength at specified temperature and the tensile strength reduction factor [Table HBB-3225-2, ASME BPVC.III.5-2017];

The product of two-thirds of the minimum yield strength at room temperature and the yield strength reduction factor [Table HBB-3225-2, ASME III.5-2017];

The product of 90% of yield strength at specified temperature and the yield strength reduction factor [Table HBB-3225-2, ASME III.5-2017]

The yield strength and ultimate strength reduction factor for long time elevated temperature service for DB 800H are not available; hence, wrought base metal Alloy 800H reduction factors from Table HBB-3225-2 are used for DB 800H.

### 3.4 Primary Membrane Allowable Stress $So$.

*S _{o}* is the maximum allowable limit of the primary membrane stress to be used as a reference for stress calculations under design loading [17]. The provisions per HBB-3221(b)(1) These stresses are determined as follows:

- (1)
For temperatures below the range where creep and stress rupture strength governs, the

*S*is:_{o}the specified minimum tensile strength at room temperature divided by 3.5

the tensile strength at specified temperature divided by 3.5

two-thirds of the specified minimum yield strength at room temperature

two-thirds of the yield strength at specified temperature

As per ASME code section III, creep effects in Alloy 800H are neglected below 425 °C (800 °F); hence, below 425 °C, tension test data are used to calculated

*S*as follows:_{o}

- (2)
For temperatures in the range where creep and stress rupture strength governs,

*S*is calculated as follows:_{o}100% of the average stress to produce a creep rate of 0.01%/1000 h

100

*F*_{avg}% of the average stress to cause rupture at the end of 100,000 h, where for temperatures below 815 °C (1500 °F)*F*_{avg}is 0.67.80% of the minimum stress to cause rupture at the end of 100,000 h

The power law function is fitted to the test data as shown in Fig. 3. The power law function was fitted by using the wrought metal data. By keeping the stress exponent same, linear fitting parameter was determined. Ideally, a large creep dataset would be needed to determine the power term, which would capture the dislocation mechanisms at lower stresses accurately. Due to limited creep tests on DB 800H, the power exponent of wrought metal was used. By extrapolation, the stress to produce creep rate of 0.01%/1000 h is calculated. The final values of *S*_{0} after accounting the maximum bound of 0.7 reduction factor are presented in Table 6.

### 3.5 Time and Temperature-Dependent Allowable Stress $Sr$.

The creep rupture data of DB 800H is used to calculate the Larson Miller Parameter using Eq. 4. In this equation, *T* is absolute temperature in *Kelvin*(*K*), *t* is rupture time in h, and *C* is a constant set to 15.21, which is determined for BM 800H by Swindeman [18]. The linear regression equation (Eq. (5)) is used to fit the calculated Larson Miller parameter (LMP) data from creep rupture tests shown with cross sign “X” in Fig. 4. LMP calculated based on data shown in cross sign “X” are used to estimate the rupture life of few tests. These tests were discontinued once test time exceeded the expected rupture life. These discontinued tests DB 800H (D) are shown with plus sign “+” in Fig. 4. Note that DB 800H (D) was not used to calculate the fitting line shown in Fig. 4. The X-ray scans of specimens showed microvoid distributed at diffusion bonds, which may change creep performance from specimen to specimen [11]. Hence, these tests served as validation for interpolated creep life and statistical study to ensure the LMP fit rupture predictions are reasonable. More creep tests will change LMP parameters, and improve rupture life predictions and allowable stress reliability.

*a*

_{0}and

*a*

_{1}are calculated for the LMP values for the time of 1% strain, time of onset of tertiary creep, and time of rupture, and presented in Table 7. The standard error of estimate is calculated per Eq. (6) [17]

Data type . | C
. | a_{0}
. | a_{1}
. | SEE . |
---|---|---|---|---|

1% strain | 18.12 | 43325 | −12962 | 0.543357 |

Tertiary creep | 14.35 | 27539 | −6001.7 | 0.235697 |

Creep rupture | 15.21 | 29070 | −6210.4 | 0.201313 |

Data type . | C
. | a_{0}
. | a_{1}
. | SEE . |
---|---|---|---|---|

1% strain | 18.12 | 43325 | −12962 | 0.543357 |

Tertiary creep | 14.35 | 27539 | −6001.7 | 0.235697 |

Creep rupture | 15.21 | 29070 | −6210.4 | 0.201313 |

where *N _{d}* is the number of data points and

*D*is the degree-of-freedom calculated as a total constraint number in Larson Miller parameter and degree of the regression equation. The LMP function has one constant

_{f}*C*, and first-order regression equation is used (Eq. (5)); hence, the degree-of-freedom in above equation is two [19]. An adjustment of 1.65 multiple of standard error of estimate (SEE) is applied to logarithmic time to represent the 95% lower bound of stress data. This procedure results in the calculation of the minimum stress to cause 1% strain for a given time and temperature. The same procedure is used with creep data of tertiary creep and for creep rupture life by using Eqs. (4) and (5) to calculated minimum stress for tertiary creep and creep rupture. The calculated regression coefficients of DB800H are presented in Table 7.

The maximum value of minimum stress to rupture is bounded by the upper stress limit of *S _{u}*/1.1. The proposed minimum stress to rupture values of diffusion bonded 800H material is presented in Table 8.

S_{r} | |||||||||
---|---|---|---|---|---|---|---|---|---|

Time | |||||||||

T (°C) | 1 h | 3 h | 10 h | 30 h | 100 h | 300 h | 1000 h | 3000 h | 10,000 h |

500 | 252.7 | 252.7 | 252.7 | 252.7 | 252.7 | 252.7 | 252.7 | 224.7 | 192.6 |

525 | 249.2 | 249.2 | 249.2 | 249.2 | 249.2 | 249.2 | 216.3 | 187.4 | 159.3 |

550 | 243.7 | 243.7 | 243.7 | 243.7 | 243.7 | 212.1 | 180.6 | 155.9 | 131.8 |

575 | 236.2 | 236.2 | 236.2 | 236.2 | 207.9 | 178.5 | 151.2 | 129.5 | 109.1 |

600 | 226.4 | 226.4 | 226.4 | 207.9 | 175.0 | 149.8 | 126.0 | 107.8 | 90.3 |

625 | 214.7 | 214.7 | 207.2 | 176.4 | 147.7 | 126.0 | 105.0 | 88.9 | 74.2 |

650 | 201.1 | 201.1 | 176.4 | 149.8 | 124.6 | 105.0 | 87.5 | 73.5 | 60.9 |

675 | 186.1 | 181.3 | 150.5 | 126.7 | 105.0 | 88.2 | 72.8 | 60.9 | 50.4 |

700 | 170.0 | 154.7 | 128.1 | 107.1 | 88.2 | 73.5 | 60.2 | 50.4 | 41.3 |

725 | 150.0 | 132.3 | 108.5 | 90.3 | 74.2 | 61.6 | 49.7 | 41.3 | 33.6 |

750 | 131.2 | 113.4 | 92.4 | 76.3 | 62.3 | 51.1 | 41.3 | 34.3 | 27.3 |

S_{r} | |||||||||
---|---|---|---|---|---|---|---|---|---|

Time | |||||||||

T (°C) | 1 h | 3 h | 10 h | 30 h | 100 h | 300 h | 1000 h | 3000 h | 10,000 h |

500 | 252.7 | 252.7 | 252.7 | 252.7 | 252.7 | 252.7 | 252.7 | 224.7 | 192.6 |

525 | 249.2 | 249.2 | 249.2 | 249.2 | 249.2 | 249.2 | 216.3 | 187.4 | 159.3 |

550 | 243.7 | 243.7 | 243.7 | 243.7 | 243.7 | 212.1 | 180.6 | 155.9 | 131.8 |

575 | 236.2 | 236.2 | 236.2 | 236.2 | 207.9 | 178.5 | 151.2 | 129.5 | 109.1 |

600 | 226.4 | 226.4 | 226.4 | 207.9 | 175.0 | 149.8 | 126.0 | 107.8 | 90.3 |

625 | 214.7 | 214.7 | 207.2 | 176.4 | 147.7 | 126.0 | 105.0 | 88.9 | 74.2 |

650 | 201.1 | 201.1 | 176.4 | 149.8 | 124.6 | 105.0 | 87.5 | 73.5 | 60.9 |

675 | 186.1 | 181.3 | 150.5 | 126.7 | 105.0 | 88.2 | 72.8 | 60.9 | 50.4 |

700 | 170.0 | 154.7 | 128.1 | 107.1 | 88.2 | 73.5 | 60.2 | 50.4 | 41.3 |

725 | 150.0 | 132.3 | 108.5 | 90.3 | 74.2 | 61.6 | 49.7 | 41.3 | 33.6 |

750 | 131.2 | 113.4 | 92.4 | 76.3 | 62.3 | 51.1 | 41.3 | 34.3 | 27.3 |

### 3.6 Temperature and Time-Dependent Allowable Stress $St$.

*S _{t}* are the temperature and time-dependent allowable stresses, which are determined using data from long-term, constant load, uniaxial tests. Per HBB-3221(b)(1), for each specific time

*t*,

*S*is the smallest of the following values:

_{t}100% of the average stress required to obtain a total (elastic, plastic, primary, and secondary creep) strain of 1%;

80% of the minimum stress to cause initiation of tertiary creep;

67% of the minimum stress to cause rupture

Similar to the *S _{r}* determination in Sec. 3.5, the Larson Miller parameter (Eq. (4)) and liner fitting function (Eq. (5)) with respective SEE values are used to calculate the minimum stresses of tertiary creep and rupture. For calculating average stress for 1% strain, no SEE values are used, but the rest of the calculation procedure remains the same as for

*S*. The final calculated

_{r}*S*values are tabulated in Table 9.

_{t}S_{t} | ||||||||
---|---|---|---|---|---|---|---|---|

Time | ||||||||

T (°C) | 1 h | 10 h | 30 h | 100 h | 300 h | 1000 h | 3000 h | 10,000 h |

500 | 89.6 | 89.6 | 89.6 | 87.3 | 81.8 | 76.1 | 71.3 | 66.4 |

525 | 88.2 | 88.2 | 84.7 | 78.7 | 73.5 | 68.3 | 63.8 | 59.3 |

550 | 86.8 | 82.0 | 76.5 | 70.9 | 66.1 | 61.2 | 57.1 | 52.9 |

575 | 86.1 | 74.2 | 69.1 | 63.9 | 59.4 | 54.9 | 51.1 | 47.2 |

600 | 78.5 | 67.2 | 62.4 | 57.5 | 53.4 | 49.3 | 45.8 | 42.2 |

625 | 71.3 | 60.8 | 56.3 | 51.8 | 48.0 | 44.2 | 41.0 | 37.7 |

650 | 64.8 | 55.0 | 50.9 | 46.7 | 43.2 | 39.6 | 36.7 | 33.6 |

675 | 58.9 | 49.8 | 45.9 | 42.1 | 38.8 | 35.5 | 32.8 | 30.0 |

700 | 53.6 | 45.1 | 41.5 | 37.9 | 34.9 | 31.9 | 29.4 | 26.8 |

725 | 48.7 | 40.8 | 37.5 | 34.1 | 31.4 | 28.6 | 26.3 | 23.4 |

750 | 44.2 | 36.9 | 33.8 | 30.8 | 28.2 | 25.6 | 23.5 | 19.4 |

S_{t} | ||||||||
---|---|---|---|---|---|---|---|---|

Time | ||||||||

T (°C) | 1 h | 10 h | 30 h | 100 h | 300 h | 1000 h | 3000 h | 10,000 h |

500 | 89.6 | 89.6 | 89.6 | 87.3 | 81.8 | 76.1 | 71.3 | 66.4 |

525 | 88.2 | 88.2 | 84.7 | 78.7 | 73.5 | 68.3 | 63.8 | 59.3 |

550 | 86.8 | 82.0 | 76.5 | 70.9 | 66.1 | 61.2 | 57.1 | 52.9 |

575 | 86.1 | 74.2 | 69.1 | 63.9 | 59.4 | 54.9 | 51.1 | 47.2 |

600 | 78.5 | 67.2 | 62.4 | 57.5 | 53.4 | 49.3 | 45.8 | 42.2 |

625 | 71.3 | 60.8 | 56.3 | 51.8 | 48.0 | 44.2 | 41.0 | 37.7 |

650 | 64.8 | 55.0 | 50.9 | 46.7 | 43.2 | 39.6 | 36.7 | 33.6 |

675 | 58.9 | 49.8 | 45.9 | 42.1 | 38.8 | 35.5 | 32.8 | 30.0 |

700 | 53.6 | 45.1 | 41.5 | 37.9 | 34.9 | 31.9 | 29.4 | 26.8 |

725 | 48.7 | 40.8 | 37.5 | 34.1 | 31.4 | 28.6 | 26.3 | 23.4 |

750 | 44.2 | 36.9 | 33.8 | 30.8 | 28.2 | 25.6 | 23.5 | 19.4 |

### 3.7 Primary Membrane Allowable Stress $Smt$.

*S _{mt}* is the allowable limit of general primary membrane stress, to be used as a reference for stress calculations for the actual service life under the level A and B service loading.

*S*is determined as the lower value of

_{mt}*S*(time-independent) and

_{m}*S*(time-dependent), and is documented in Table 10.

_{t}S_{mt} | |||||||||
---|---|---|---|---|---|---|---|---|---|

Time | |||||||||

T (°C) | 1 h | 3 h | 10 h | 30 h | 100 h | 300 h | 1000 h | 3000 h | 10,000 h |

500 | 69.0 | 69.0 | 69.0 | 69.0 | 69.0 | 69.0 | 69.0 | 69.0 | 66.4 |

525 | 68.6 | 68.6 | 68.6 | 68.6 | 68.6 | 68.6 | 68.3 | 63.8 | 59.3 |

550 | 68.0 | 68.0 | 68.0 | 68.0 | 68.0 | 66.1 | 61.2 | 57.1 | 52.9 |

575 | 67.2 | 67.2 | 67.2 | 67.2 | 63.9 | 59.4 | 54.9 | 51.1 | 47.2 |

600 | 66.2 | 66.2 | 66.2 | 62.4 | 57.5 | 53.4 | 49.3 | 45.8 | 42.2 |

625 | 64.9 | 64.9 | 60.8 | 56.3 | 51.8 | 48.0 | 44.2 | 41.0 | 37.7 |

650 | 63.3 | 59.9 | 55.0 | 50.9 | 46.7 | 43.2 | 39.6 | 36.7 | 33.6 |

675 | 58.9 | 54.4 | 49.8 | 45.9 | 42.1 | 38.8 | 35.5 | 32.8 | 30.0 |

700 | 53.6 | 49.3 | 45.1 | 41.5 | 37.9 | 34.9 | 31.9 | 29.4 | 26.8 |

725 | 48.7 | 44.7 | 40.8 | 37.5 | 34.1 | 31.4 | 28.6 | 26.3 | 23.4 |

750 | 43.3 | 40.6 | 36.9 | 33.8 | 30.8 | 28.2 | 25.6 | 23.5 | 19.4 |

S_{mt} | |||||||||
---|---|---|---|---|---|---|---|---|---|

Time | |||||||||

T (°C) | 1 h | 3 h | 10 h | 30 h | 100 h | 300 h | 1000 h | 3000 h | 10,000 h |

500 | 69.0 | 69.0 | 69.0 | 69.0 | 69.0 | 69.0 | 69.0 | 69.0 | 66.4 |

525 | 68.6 | 68.6 | 68.6 | 68.6 | 68.6 | 68.6 | 68.3 | 63.8 | 59.3 |

550 | 68.0 | 68.0 | 68.0 | 68.0 | 68.0 | 66.1 | 61.2 | 57.1 | 52.9 |

575 | 67.2 | 67.2 | 67.2 | 67.2 | 63.9 | 59.4 | 54.9 | 51.1 | 47.2 |

600 | 66.2 | 66.2 | 66.2 | 62.4 | 57.5 | 53.4 | 49.3 | 45.8 | 42.2 |

625 | 64.9 | 64.9 | 60.8 | 56.3 | 51.8 | 48.0 | 44.2 | 41.0 | 37.7 |

650 | 63.3 | 59.9 | 55.0 | 50.9 | 46.7 | 43.2 | 39.6 | 36.7 | 33.6 |

675 | 58.9 | 54.4 | 49.8 | 45.9 | 42.1 | 38.8 | 35.5 | 32.8 | 30.0 |

700 | 53.6 | 49.3 | 45.1 | 41.5 | 37.9 | 34.9 | 31.9 | 29.4 | 26.8 |

725 | 48.7 | 44.7 | 40.8 | 37.5 | 34.1 | 31.4 | 28.6 | 26.3 | 23.4 |

750 | 43.3 | 40.6 | 36.9 | 33.8 | 30.8 | 28.2 | 25.6 | 23.5 | 19.4 |

## 4 Isochronous Curves

*E*is elastic modulus at a given temperature

*C*

_{1},

*C*

_{2}, and

*C*

_{3}are calculated using Eq. (10). These parameters are calculated using the strain versus time history from creep tests. A gradient optimization algorithm available in matlab is implemented to determine an optimum parameter set. Equation (9) can simulate the creep strains for a selected time and stress value

While calculating the isochronous curves, a stress value is selected, and creep strains are calculated at different times. Eq. (11) is a stress function in terms of plastic strain; hence, this equation is solved numerically to determine the plastic strain values corresponding to a stress. By fitting the experimental responses from tension tests, parameters of Eq. (11) are evaluated for a specified temperature as shown in Table 11.

i | 1 | 2 | 3 | 4 |
---|---|---|---|---|

$Bi(1)$ | 3.128 | 0.17229 | 0.037567 | 0.004503 |

$Bi(2)$ | −0.3547 | −0.000654 | 0.013289 | 0.00498 |

$Bi(3)$ | 0.5551 | 0.026628 | −0.029622 | 0.048257 |

$Bi(4)$ | −0.4807 | −0.093665 | 0.006146 | −0.101054 |

$Bi(5)$ | 0 | 0.05869 | 0.005120 | 0.054705 |

i | 1 | 2 | 3 | 4 |
---|---|---|---|---|

$Bi(1)$ | 3.128 | 0.17229 | 0.037567 | 0.004503 |

$Bi(2)$ | −0.3547 | −0.000654 | 0.013289 | 0.00498 |

$Bi(3)$ | 0.5551 | 0.026628 | −0.029622 | 0.048257 |

$Bi(4)$ | −0.4807 | −0.093665 | 0.006146 | −0.101054 |

$Bi(5)$ | 0 | 0.05869 | 0.005120 | 0.054705 |

The creep test provides a time history data, from which strain value at desired time is extracted from experiments and used to fit the isochronous curves simulation. The proposed isochronous curves are compared against the test data from tension tests (hot tension curve) and from the creep tests at different times in Fig. 5. In this figure, a good comparison between simulated isochronous curves and test data at 550 °C, 650 °C, and 760 °C is observed. Hence, the equation set presented above with the optimized parameter set is used to simulate the isochronous curves at intermediate temperatures for diffusion bonded Alloy 800H as shown in Figs. 6(a)–6(c).

## 5 Fatigue Curves

The design fatigue curves in section III, division 5, figure HBB-T-1420-1C correlate the strain range versus the fatigue life, *N _{f}*. These curves are developed from hundreds of fatigue tests. A reduction factor of “2” on stress in the high-cycle fatigue regime and “20” on fatigue life in the low-cycle fatigue regime are usually used to develop the fatigue curves of metals.

Only a few fatigue tests have been conducted on DB 800H at three temperatures. Ideally, these few tests are not enough to generate a new set of design fatigue curves. Hence, a reduction factor of 10 is used on the life of wrought base metal 800H fatigue curves and compared to the DB 800H fatigue test data in Fig. 7. In this figure, a reduction factor of 10 on wrought base metal 800H (BM 800H) life bounds the lower values of the DB 800H test life. Hence, for the S–N curves of DB 800H, it is proposed to use the figure HBB-T-1420-1C and a reduction factor, *R _{f}* = 10, to develop S-N curves of DB 800H. Table 12 shows the S–N curve values of DB 800H. These proposed fatigue curves of DB 800H can be revised as a large set of test data becomes available.

Number of cycle | 538 °C | 649 °C | 760 °C |
---|---|---|---|

10 | 0.01160 | 0.00932 | 0.00774 |

20 | 0.00849 | 0.00678 | 0.00562 |

40 | 0.00660 | 0.00533 | 0.00469 |

100 | 0.00515 | 0.00417 | 0.00388 |

200 | 0.00454 | 0.00366 | 0.00349 |

300 | 0.00433 | 0.00347 | 0.00309 |

400 | 0.00409 | 0.00327 | 0.00270 |

1000 | 0.00293 | 0.00234 | 0.00212 |

2000 | 0.00243 | 0.00197 | 0.00183 |

4000 | 0.00212 | 0.00175 | 0.00164 |

10,000 | 0.00194 | 0.00155 | 0.00149 |

Number of cycle | 538 °C | 649 °C | 760 °C |
---|---|---|---|

10 | 0.01160 | 0.00932 | 0.00774 |

20 | 0.00849 | 0.00678 | 0.00562 |

40 | 0.00660 | 0.00533 | 0.00469 |

100 | 0.00515 | 0.00417 | 0.00388 |

200 | 0.00454 | 0.00366 | 0.00349 |

300 | 0.00433 | 0.00347 | 0.00309 |

400 | 0.00409 | 0.00327 | 0.00270 |

1000 | 0.00293 | 0.00234 | 0.00212 |

2000 | 0.00243 | 0.00197 | 0.00183 |

4000 | 0.00212 | 0.00175 | 0.00164 |

10,000 | 0.00194 | 0.00155 | 0.00149 |

## 6 Creep–Fatigue Damage

*N*) summation for multiple strain ranges. Estimated fatigue life for DB 800H is obtained from Fig. 7. The second term calculates the creep damage, a ratio of $\Delta t$, time increment at a stress

_{r}*σ*and

*t*, estimated rupture life at the stress from Table 8

_{r}The above equation's stress values can either be imported from creep–fatigue tests or a material model that can simulate the stress relaxation history for the dwell period. The following discussion presents the material model and associated calculations.

*σ*

_{max}at zero dwell time to

*σ*at time

*t*

_{dwell}, stress at the end of strain dwell is obtained as

where $M=\u2212N\u2212a1T+1$ and *σ*_{end} is stress at the end of strain dwell per Eq. (19). Note that the $C*=C+1.65\xd7SEE$ for creep rupture per Table 7 to calculated the 95% lower bound of stress rupture. This equation calculates the creep damage during stress relaxation of strain dwell in a cycle. Multiplying this equation with the cycle number in the creep–fatigue test gives the total creep damage accumulated in the test specimen till rupture.

The model parameters *N* and *K* in Eq. (17) are determined for three temperatures (Table 13) based on relaxation histories obtained from experiments. As the *N* and *K* parameters are determined, the creep damage accumulation in creep–fatigue test specimens can be calculated using Eq. (21). The fatigue damage in creep–fatigue test specimens can be calculated by using the first term in Eq. (13) as stated earlier. As sufficient test data are not available to develop a creep–fatigue envelope for DB 800H, the calculated creep–fatigue damages of DB 800H specimens at three temperatures are compared against the creep–fatigue envelope of BM 800H from ASME section III, division 5, HBB-T-1420-2 in Fig. 8. This figure shows that the DB 800H test specimens creep–fatigue damage accumulations up to rupture fall outside the BM 800H ASME code creep–fatigue damage envelop. This indicates that the BM 800H envelope can be used for design and analysis of PCHE constructed of diffusion bonded 800H.

## 7 Discussion, Conclusions, and Future Work

This study developed material properties and design curves of diffusion bonded Alloy 800H (DB 800H) to design and analyze PCHE following the ASME code section III division 5 provision. To facilitate this development, a set of tension, creep, fatigue, and fatigue–creep tests on DB 800H, and few fatigue and creep–fatigue tests on wrought 800H ASTM standard specimens were conducted by the authors [11]. The material properties and design curves development were motivated by the ASME code gap analysis by Keating et al. [13]. Hence, this study addressed the material property-related gaps toward developing ASEM code section III division 5 design and analysis methodology for PCHE.

The allowable stresses of DB800H are developed following the procedure of ASME section III HBB-3221(b). First, the allowable stresses *S _{y}*,

*S*,

_{u}*S*, and

_{m}*S*are developed based on the tension test data. Following the allowable stresses,

_{o}*S*,

_{r}*S*, and

_{t}*S*are developed based on the creep test data. The LMPs are determined and fitted with a linear function for these three time and temperature-dependent allowable stresses. A SEE calculates the lower bound of rupture stresses from the LMP plot. A joint efficiency factor of 0.7 bounds the calculated allowable stresses to maintain consistency with the existing joint efficiency factor for nonnuclear components provided in section VIII, division 1. The calculated allowable stresses are tabulated similarly as in ASME code.

_{mt}The tension tests at various temperatures and creep strain time histories are then used to determine the isochronous curves for DB 800H for the temperature range 510 °C–760 °C up to 10,000 h. With the small number of fatigue and creep–fatigue test data of DB 800H developed, it was not possible to develop fatigue curves and creep–fatigue envelopes for DB 800H. An extensive set of data are needed for the development of these curves and envelope. Hence, fatigue design (S–N) curves of DB 800H are proposed based on the BM 800H ASME curves in section III, division 5, figure HBB-T-1420-1C with a reduction factor of 10. These S–N curves are observed to bind the lower values of the DB 800H fatigue test data. When the creep–fatigue damage accumulations in the DB 800H test specimens are calculated and compared to the ASME BM 800H creep–fatigue envelope (Fig. HBB-T-1420-2), it is observed that the BM 800H envelope can be used PCHE design unlit sufficient data are available to develop a DB 800H envelop.

It is also noted here that the material properties and design curves proposed in this study for DB 800H are based on a limited set of tests. As more test data become available, the proposed allowable stresses and design curves can be reevaluated and revised as needed. The creep test data for developing the time and temperature-dependent allowable stresses and isochronous curves are limited to 1000 h of rupture life. The LMPs are determined and fitted with a linear equation to interpolate for intermediate temperatures and extrapolate allowable stresses up to 10,000 h. The equations developed should not be used to extrapolate the creep life of DB800H beyond 10,000 h. Creep tests with a target rupture life of 10,000–30,000 h will be needed to extend the allowable stresses to longer creep life.

It is demonstrated that a reduction factor of 10 on BM 800H fatigue curves bounds the DB 800H fatigue life data. Only a few fatigue tests, all tested with a strain range of 0.6%, were performed. Hence, additional fatigue tests on DB 800H with smaller and larger strain ranges would be needed to evaluate the proposed fatigue curves. Similarly, additional creep–fatigue tests can facilitate the development and evaluation of the creep-fatigue envelope of DB 800H. Note that all experiments conducted in this study were focused on solid ASTM specimens. This study does not focus on the influence of channels. The presence of channels may change the local stress flow during the diffusion bonding process, which may result in different bond properties than the solid diffusion bonded regions. A series of tests at elevated temperatures are needed on diffusion bonded specimens with channels to address the effect of stress concentrations near channel corners on the proposed allowable stresses and design life presented in this study.

## Acknowledgment

This research is being performed using funding received from the DOE Office of Nuclear Energy's Nuclear Energy University Program under an Integrated Research Program entitled “ASME Code Application of the Compact Heat Exchanger for High Temperature Nuclear Service” (NEUP-16-10714) with the award number DE-NE0008576, and “Advancements toward ASME Nuclear code case for compact heat exchangers” (IRP-17-14227) with the award number DE-NE0008714. Authors would like to acknowledge Mr. Aaron Wildberger from Vacuum Process Engineering for his help with the diffusion bonded Alloy 800H block fabrication.

## Funding Data

Office of Nuclear Energy (Grant Nos. DE-NE0008576 and DE-NE0008714; Funder ID: 10.13039/100006147).

## References

**139**(1), p.