# Thermostructural Analysis of Plate-Type Heat Exchanger Prototypes Considering Weld Properties

Authors: Kee-nam Song; Sung-deok Hong
Journal: Science and Technology of Nuclear Installations
 (2012)

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## Abstract

The mechanical properties in a weld zone are different from those in the parent material owing to their different microstructures and residual weld stresses. Welded plate-type heat exchanger prototypes made of Hastelloy-X alloy were manufactured, and performance tests on the prototypes were performed in a small-scale nitrogen gas loop at the Korea Atomic Energy Research Institute. Owing to a lack of mechanical properties in the weld zone, previous research on the strength analyses of the prototypes was performed using the parent material properties. In this study, based on the mechanical properties of Hastelloy-X alloy obtained using an instrumented indentation technique, strength analyses considering the mechanical properties in the weld zone were performed, and the analysis results were compared with previous research. As a result of the comparison, a thermostructural analysis considering the weld material properties is needed to understand the structural behavior and evaluate the structural integrity of the prototype more reliably.


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## Body

## 1. Introduction

Researches demonstrating the massive production of hydrogen using a very high temperature reactor (VHTR) designed for operation at up to 950°C have been actively carried out worldwide. In the intermediate loop of a nuclear hydrogen program as shown in Figure1, a process heat exchanger (PHE) is a key component for transferring the high heat generated in a very high temperature reactor to a chemical reaction yielding a large quantity of hydrogen. The Korea Atomic Energy Research Institute (KAERI) has recently established a small-scale nitrogen gas loop [1] for the performance test of VHTR components and has manufactured two kinds of welded plate-type PHE prototypes, a 3 kW class and a 10 kW class, made of Hastelloy-X alloy.Figure 1
Nuclear hydrogen system.Figure2 shows the overall dimensions of the two types of plate-type PHE prototypes, and their inner components. Grooves 1.0 mm in diameter are machined into the flow plate for the primary coolant (nitrogen gas) as shown in Figure 3(a). Waved channels are bent into the flow plate for the secondary coolant (SO3 gas) as shown in Figure 3(b). Twenty flow plates for the primary and secondary coolants are stacked in turn for the 3 kW class plate-type PHE prototype, and forty flow plates for the primary and secondary coolants are stacked in turn for the 10 kW class plate-type PHE prototype. The flow plates are also bonded along the edge of the flow plate using a solid-state diffusion bonding method. After stacking and bonding the flow plates, the outside of the PHE prototypes is covered with a Hastelloy-X alloy plate 3.0 mm thick and is welded along its edges using gas tungsten arc welding with argon as a shielding gas.Overall dimension and parts of the plate-type PHE prototypes: (a) 3 kW class PHE prototype and (b) 10 kW class PHE prototype.
(a)
(b)Flow plates of plate-type PHE prototypes: (a) primary flow plate and (b) secondary flow plate.
(a)
(b)The microstructures in the weld zone, including the weld (or fusion zone) and heat-affected zone (HAZ), are different from those in the parent material, as shown in Figure4 [2]. Consequently, the mechanical properties in the weld zone are different from those in the parent material to a certain degree owing to different microstructures and residual welding stresses. When a welded structure is loaded, the mechanical behavior of the welded structure might differ from the case of a structure with homogeneous mechanical properties. Nonetheless, structural analyses [3–7] of the plate-type PHE prototypes were carried out using only the parent material properties owing to a lack of mechanical properties in the weld zone. Usually, the best way to obtain the mechanical properties in the weld zone is by taking tensile test specimens from the fusion zone and HAZ, and by performing a standard tensile test. However, when the weld zone is very narrow and the interfaces are not clear, it is difficult to take tensile test specimens from the weld zone. The reason for this is that the mechanical properties in the base material are usually used for structural analyses of the welded structure. As an aside, it has recently been determined that the ball indentation technique has the potential to be an excellent substitute for a standard tensile test, especially in the case of small specimens or property-gradient materials such as welds [8]. The weld mechanical properties of the Hastelloy-X plate were then obtained [9] using an instrumented indentation technique.Figure 4
Microstructure near the weld [2].In this study, to investigate the effect of the weld material properties on the mechanical behavior of the plate-type PHE prototypes, strength analyses considering the weld mechanical properties obtained using an instrumented indentation technique are performed, and the analysis results are compared with previous research using only the parent material properties.


## 2. Weld Material Properties

Hastelloy-X is a nickel-chromium-iron-molybdenum alloy that possesses an exceptional combination of oxidation resistance, fabricability, and high-temperature strength. The chemical composition, physical properties, and mechanical properties of Hastelloy-X alloy extracted from a website [11] are summarized in Tables 1, 2, and 3, respectively. Figure 5 shows one of the specimens taken from the welded Hastelloy-X alloy plate and its indented positions for determining the mechanical properties of the parent material, weld (or fusion zone), and HAZ of the Hastelloy-X alloy strip with a 3 mm thickness. Since the measured mechanical properties have certain variations in each zone, it is necessary to set a reference value in each zone. In this study, an average value is set as the reference value in each zone. The average values of the mechanical properties in the parent material, weld, and HAZ of the welded Hastelloy-X alloy strip are obtained using the measured data. Based on the average mechanical properties in the parent material of the Hastelloy-X alloy strip, normalizing factors are obtained in the weld (or fusion zone) and HAZ to be later utilized in a strength analysis. Table 4 shows the normalizing factors, in other words, the normalized mechanical properties, of the parent material, weld, and HAZ on the weld cross-section of the weld mockup [10]. According to Table 4, the mechanical properties in the weld, HAZ, and parent material differ to a certain degree and therefore might affect the structural behavior of the plate-type PHE prototypes when considering the weld mechanical properties. The weld mechanical properties used in this study therefore include the effect of different microstructures as well as the residual welding stress, as they were obtained from the weld specimen.Table 1
Nominal chemical composition (wt%) of Hastelloy-X alloy.
Ni
Cr
Fe
Mo
Co
W
C
Mn
Si
B
47
22
18
9
1.5
0.6
0.10
1
1
0.008Table 2
Physical properties of Hastelloy-X alloy.
Temperature (°C)
Modulus ofelasticity (GPa)
Poisson'sratio
Thermal conductivity (W/m·°C)
Specific heat (J/kg·K)
Coefficient of thermal expansion (10−6/°C)
20
205
0.3
11.6
486
—
100
202
0.3
12.9
—
13.3
200
195
0.3
14.6
490
14.0
300
190
0.3
16.3
—
14.3
400
183
0.3
17.9
494
14.5
500
177
0.3
19.5
—
14.7
600
168
0.3
21.1
498
15.1
700
161
0.3
22.9
—
15.7
800
153
0.3
24.6
515
16.0
900
145
0.3
26.3
—
16.3
1000
135
0.3
27.9
544
16.7Table 3
Mechanical properties of Hastelloy-X alloy.
Temperature (°C)
Yield stress (MPa)
Ultimate tensile strength (MPa)
20
379
767
538
245
614
649
244
581
760
237
463
871
194
310
982
91
177
1093
43
97Table 4
Normalized mechanical properties of Hastelloy-X alloy.
Yield stress
Ultimate tensile strength
Parent material
1.000
1.000
HAZ
0.962
0.998
Weld
1.094
1.120Figure 5
Indented position in a welded Hastelloy-X alloy strip [10].


## 3. Finite Element Modeling

Finite element (FE) modeling is carried out using the commercial code, I-DEAS. For the sake of simplicity and an understanding of the overall behavior of the plate-type PHE prototypes, the FE models are formulated with linear solid elements including brick elements, wedge elements, and tetrahedron elements. The structural FE model of the 3 kW class PHE prototype is formulated using 830,304 brick elements, whereas the structural FE model of the 10 kW class PHE prototype is formulated using 870,696 brick elements. The weld zone including the weld bead (or fusion zone or weld) and HAZ of the plate-type PHE prototypes are modeled as shown in Figure6, where the weld bead along the edges of the prototypes and the HAZ of the inner weld bead are represented. However, the chamfering (or rounding) along the edge of the prototypes is not considered in the FE model for the sake of simplicity.FE models in the weld: (a) 3 kW class PHE prototype and (b) 10 kW class PHE prototype.
(a)
(b)Figure7 shows the input data of the primary/secondary flow plates for a thermal analysis under a gas loop test condition of 850°C [6, 12], and Figure 8 shows the displacement constraint conditions considering the pipeline stiffness of the small-scale nitrogen gas loop [13].Boundary conditions of primary/secondary coolant for a thermal analysis: (a) 3 kW class PHE prototype and (b) 10 kW class PHE prototype.
(a)
(b)Figure 8
Boundary conditions for a structural analysis.


## 4. Thermal/Strength Analysis and Discussion

### 4.1. Thermal Analysis

Based on the input data shown in Figure6 and the material properties of Hastelloy-X alloy in Table 2, thermal analyses are carried out using I-DEAS/TMG Ver. 6.1 [14]. Figure 9 shows the steady-state thermal analysis results [6, 12] of the plate-type PHE prototypes under the test condition of a small-scale nitrogen gas loop. According to Figure 9, the temperature distributions are nearly symmetrical along the vertical axis owing to external thermal convection and the effects of gravity.Temperature contours of outer PHEs: (a) 3 kW class PHE prototype [6] and (b) 10 kW class PHE prototype [12].
(a)
(b)


### 4.2. Structural Analysis

Based on the steady-state thermal analysis results and imposing the displacement constraint conditions shown in Figure8, steady-state thermostructural analyses on the PHE prototypes are carried out using ABAQUS Ver. 6.8 [15]. The mesh patterns in the FE models including the node and element numbering are identical for I-DEAS and ABAQUS. The material properties in Table 2 are used as the parent material properties, while the mechanical properties in the weld and HAZ are generated by multiplying the parent material properties with the normalizing factors in Table 3. According to the test conditions of the small-scale nitrogen gas loop, the in/outflow pressures for the primary and secondary coolant are 3.0 MPa and 0.1 MPa, respectively, as shown in Figure 7. The bilinear stress-strain curve of Hastelloy-X for an elastic-plastic structural analysis extracted from a website [11] is shown in Figure 10.Figure 10
Bilinear stress-strain curve for an elastic-plastic analysis [10].


#### 4.2.1. Analysis Results of the 3 kW Class PHE Prototype

Figure11 shows the stress distributions from an elastic analysis using the parent material properties. A maximum local stress of 272.33 MPa occurs around the edge between the top plate and side plate, that is, the welded zone, which exceeds the yield stress of the parent material (237.88 MPa at 746°C) [11] by 14.48%. Since the elastic stress distributions using the material properties in the weld zone are the same as those shown in Figure 11 owing to the use of the same elastic modulus in the elastic analysis, the maximum local stress of 272.33 MPa exceeds the yield stress of the weld material (260.24 MPa) by only 4.64%. Thus, a smaller degree of excess yield stress is attributed to a larger yield stress of the weld material than the parent material.Figure 11
Overall stress contours of a 3 kW class PHE prototype from an elastic analysis using the parent material properties [6].Figure12 shows the stress distributions using the parent material properties from an elastic-plastic analysis. A maximum local stress of 242.60 MPa around the edge between the top and side plates, that is, the welded zone, exceeds the yield stress of the parent material (237.63 MPa at 750°C) by 2.09%. Figure 13 shows the stress distributions using the weld material properties from an elastic-plastic analysis. A maximum local stress of 266.19 MPa exceeds the yield stress of the weld material (260.61 MPa at 740.70°C) by 2.14%. The degree of excess yield stress on the weld (fusion zone) is changed for the analysis results using the weld material properties as compared to using the parent material properties. This is attributed to a larger yield stress in the weld than in the parent material.Figure 12
Overall stress contours of a 3 kW class PHE prototype from an elastic-plastic analysis using the parent material properties [6].Figure 13
Overall stress contours of a 3 kW class PHE prototype from an elastic-plastic analysis using the weld material properties.Figure14 shows the stress distributions on the weld bead and in the HAZ from an elastic-plastic analysis using the weld material properties. In the HAZ, a maximum local stress of 235.47 MPa exceeds the yield stress of the weld material (228.65 MPa at 749.22°C) by 2.98%, while a maximum stress of 239.17 MPa using the parent material properties exceeds the yield stress of the parent material (237.68 MPa) by only 0.63%. The degree of excess yield stress in the HAZ is increased for the analysis results using the weld material properties compared to using the parent material properties. This is attributed to a smaller yield stress in the HAZ than that in the parent material. The thermostructural analysis results of the 3 kW class PHE prototype are briefly summarized in Table 5.Table 5
Analysis results of 3 kW class PHE prototype.
Maximum local stress
Yield stress (MPa)
Percentage exceeding the yield stress (%)
Stress (MPa)
Location
Temperature (°C)
Parent
Weld
HAZ
Parent
Weld
HAZ
Elastic analysis
272.33
Weld
746.00
237.88
260.24
14.48
4.64
Elastic-plastic analysis
Weld
Using parent material  properties
242.60
Weld
750.00
237.63
2.09
Using weld material properties
266.19
Weld
740.70
260.61
2.14
HAZ
Using parent material properties
239.17
HAZ
237.68
0.63
Using weld material properties
235.47
HAZ
749.22
228.65
2.98Figure 14
Stress contours of a 3 kW class PHE prototype in the weld zone from an elastic-plastic analysis using the weld material properties.


#### 4.2.2. Analysis Results of 10 kW Class PHE Prototype

Figure15 shows the stress distributions of the 10 kW class PHE prototype from an elastic analysis using the parent material properties. A maximum local stress of 331.23 MPa occurs around the edge between the top and side plates, that is, the welded zone, which exceeds the yield stress of the parent material (237.98 MPa at 744.46°C) by 39.18%. Since the stress distributions using the material properties in the weld zone are the same as those shown in Figure 15 owing to the use of the same elastic modulus in the elastic analysis, the maximum local stress of 331.23 MPa exceeds the yield stress of the weld material (260.35 MPa) by 27.22%. Thus, a smaller degree of excess yield stress is attributed to the larger yield stress of the weld material than the parent material.Figure 15
Overall stress contours of a 10 kW class PHE prototype from an elastic analysis using the parent material properties [12].Figure16 shows the stress distributions using the parent material properties from an elastic-plastic analysis. A maximum local stress of 263.65 MPa exceeds the yield stress of the parent material (236.86 MPa at 760.37°C) by 11.31%. Figure 17 shows the stress distributions using the weld material properties from an elastic-plastic analysis. A maximum local stress of 267.60 MPa occurs around the edge between the top and side plates, that is, the welded zone, which exceeds the yield stress of the weld material (260.50 MPa at 742.23°C) by 2.72%. The degree of excess yield stress on the weld (fusion zone) is decreased for the analysis results using the weld material properties compared to using the parent material properties. This is attributed to a larger yield stress in the weld than in the parent material.Figure 16
Overall stress contours of a 10 kW class PHE prototype from an elastic-plastic analysis using the parent material properties [12].Figure 17
Overall stress contours of a 10 kW class PHE prototype from an elastic-plastic analysis using the weld material properties.Figure18 shows the stress distributions on the weld bead and in the HAZ from an elastic-plastic analysis using the weld material properties. In the HAZ, a maximum local stress of 264.56 MPa exceeds the yield stress of the weld material (216.04 MPa at 792.09°C) by 22.46%, while a maximum stress of 191.88 MPa using the parent material properties is smaller than the yield stress of the parent material (224.57 MPa) by 14.56%. The degree of excess yield stress in the HAZ is increased for the analysis results using the weld material properties compared to using the parent material properties. This is attributed to a smaller yield stress in HAZ than that in the parent material. The thermostructural analysis results of the 10 kW class PHE prototype are briefly summarized in Table 6.Table 6
Analysis results of 10 kW class PHE prototype.
Maximum local stress
Yield stress (MPa)
Percentage exceeding the yield stress (%)
Stress (MPa)
Location
Temperature (°C)
Parent
Weld
HAZ
Parent
Weld
HAZ
Elastic analysis
331.23
Weld
744.46
237.98
260.35
39.18
27.22
Elastic-plastic analysis
Weld
Using parent material properties
263.65
Weld
760.37
236.86
11.31
Using weld material properties
267.60
Weld
742.23
260.50
2.72
HAZ
Using parent material properties
264.56
HAZ
216.04
22.46
Using weld material properties
191.88
HAZ
792.09
216.04
−14.56Figure 18
Stress contours of a 10 kW class PHE prototype in weld zone from an elastic-plastic analysis using the weld material properties.


### 4.3. Discussions

From the results of the thermostructural analyses on the plate-type PHE prototypes, the following interesting observation was found. Even though the maximum stress exceeds the yield stress in the weld zone, the degree of excess yield stress decreases or increases owing to the different yield stresses in the weld zone, when compared with the analysis results of using the parent material properties. Consequently, a thermostructural analysis considering the weld material properties seems to be needed to understand the structural behavior and evaluate the structural integrity of the plate-type PHE prototypes more reliably.A higher amount of stress and wider high-stress region occur for the 10 kW PHE prototype compared to the 3 kW PHE prototype. This is attributed to the size effect of the prototypes under the same displacement constraint conditions.The maximum local stress occurs around the edge between the top and side plates of the plate-type PHE prototypes, that is, the welded zone. The stress that occurs around the edges in the FE model will decrease to a certain degree when considering the chamfered edges, since the edges of the PHE prototypes are chamfered realistically.


## 4.1. Thermal Analysis

Based on the input data shown in Figure6 and the material properties of Hastelloy-X alloy in Table 2, thermal analyses are carried out using I-DEAS/TMG Ver. 6.1 [14]. Figure 9 shows the steady-state thermal analysis results [6, 12] of the plate-type PHE prototypes under the test condition of a small-scale nitrogen gas loop. According to Figure 9, the temperature distributions are nearly symmetrical along the vertical axis owing to external thermal convection and the effects of gravity.Temperature contours of outer PHEs: (a) 3 kW class PHE prototype [6] and (b) 10 kW class PHE prototype [12].
(a)
(b)


## 4.2. Structural Analysis

Based on the steady-state thermal analysis results and imposing the displacement constraint conditions shown in Figure8, steady-state thermostructural analyses on the PHE prototypes are carried out using ABAQUS Ver. 6.8 [15]. The mesh patterns in the FE models including the node and element numbering are identical for I-DEAS and ABAQUS. The material properties in Table 2 are used as the parent material properties, while the mechanical properties in the weld and HAZ are generated by multiplying the parent material properties with the normalizing factors in Table 3. According to the test conditions of the small-scale nitrogen gas loop, the in/outflow pressures for the primary and secondary coolant are 3.0 MPa and 0.1 MPa, respectively, as shown in Figure 7. The bilinear stress-strain curve of Hastelloy-X for an elastic-plastic structural analysis extracted from a website [11] is shown in Figure 10.Figure 10
Bilinear stress-strain curve for an elastic-plastic analysis [10].


### 4.2.1. Analysis Results of the 3 kW Class PHE Prototype

Figure11 shows the stress distributions from an elastic analysis using the parent material properties. A maximum local stress of 272.33 MPa occurs around the edge between the top plate and side plate, that is, the welded zone, which exceeds the yield stress of the parent material (237.88 MPa at 746°C) [11] by 14.48%. Since the elastic stress distributions using the material properties in the weld zone are the same as those shown in Figure 11 owing to the use of the same elastic modulus in the elastic analysis, the maximum local stress of 272.33 MPa exceeds the yield stress of the weld material (260.24 MPa) by only 4.64%. Thus, a smaller degree of excess yield stress is attributed to a larger yield stress of the weld material than the parent material.Figure 11
Overall stress contours of a 3 kW class PHE prototype from an elastic analysis using the parent material properties [6].Figure12 shows the stress distributions using the parent material properties from an elastic-plastic analysis. A maximum local stress of 242.60 MPa around the edge between the top and side plates, that is, the welded zone, exceeds the yield stress of the parent material (237.63 MPa at 750°C) by 2.09%. Figure 13 shows the stress distributions using the weld material properties from an elastic-plastic analysis. A maximum local stress of 266.19 MPa exceeds the yield stress of the weld material (260.61 MPa at 740.70°C) by 2.14%. The degree of excess yield stress on the weld (fusion zone) is changed for the analysis results using the weld material properties as compared to using the parent material properties. This is attributed to a larger yield stress in the weld than in the parent material.Figure 12
Overall stress contours of a 3 kW class PHE prototype from an elastic-plastic analysis using the parent material properties [6].Figure 13
Overall stress contours of a 3 kW class PHE prototype from an elastic-plastic analysis using the weld material properties.Figure14 shows the stress distributions on the weld bead and in the HAZ from an elastic-plastic analysis using the weld material properties. In the HAZ, a maximum local stress of 235.47 MPa exceeds the yield stress of the weld material (228.65 MPa at 749.22°C) by 2.98%, while a maximum stress of 239.17 MPa using the parent material properties exceeds the yield stress of the parent material (237.68 MPa) by only 0.63%. The degree of excess yield stress in the HAZ is increased for the analysis results using the weld material properties compared to using the parent material properties. This is attributed to a smaller yield stress in the HAZ than that in the parent material. The thermostructural analysis results of the 3 kW class PHE prototype are briefly summarized in Table 5.Table 5
Analysis results of 3 kW class PHE prototype.
Maximum local stress
Yield stress (MPa)
Percentage exceeding the yield stress (%)
Stress (MPa)
Location
Temperature (°C)
Parent
Weld
HAZ
Parent
Weld
HAZ
Elastic analysis
272.33
Weld
746.00
237.88
260.24
14.48
4.64
Elastic-plastic analysis
Weld
Using parent material  properties
242.60
Weld
750.00
237.63
2.09
Using weld material properties
266.19
Weld
740.70
260.61
2.14
HAZ
Using parent material properties
239.17
HAZ
237.68
0.63
Using weld material properties
235.47
HAZ
749.22
228.65
2.98Figure 14
Stress contours of a 3 kW class PHE prototype in the weld zone from an elastic-plastic analysis using the weld material properties.


### 4.2.2. Analysis Results of 10 kW Class PHE Prototype

Figure15 shows the stress distributions of the 10 kW class PHE prototype from an elastic analysis using the parent material properties. A maximum local stress of 331.23 MPa occurs around the edge between the top and side plates, that is, the welded zone, which exceeds the yield stress of the parent material (237.98 MPa at 744.46°C) by 39.18%. Since the stress distributions using the material properties in the weld zone are the same as those shown in Figure 15 owing to the use of the same elastic modulus in the elastic analysis, the maximum local stress of 331.23 MPa exceeds the yield stress of the weld material (260.35 MPa) by 27.22%. Thus, a smaller degree of excess yield stress is attributed to the larger yield stress of the weld material than the parent material.Figure 15
Overall stress contours of a 10 kW class PHE prototype from an elastic analysis using the parent material properties [12].Figure16 shows the stress distributions using the parent material properties from an elastic-plastic analysis. A maximum local stress of 263.65 MPa exceeds the yield stress of the parent material (236.86 MPa at 760.37°C) by 11.31%. Figure 17 shows the stress distributions using the weld material properties from an elastic-plastic analysis. A maximum local stress of 267.60 MPa occurs around the edge between the top and side plates, that is, the welded zone, which exceeds the yield stress of the weld material (260.50 MPa at 742.23°C) by 2.72%. The degree of excess yield stress on the weld (fusion zone) is decreased for the analysis results using the weld material properties compared to using the parent material properties. This is attributed to a larger yield stress in the weld than in the parent material.Figure 16
Overall stress contours of a 10 kW class PHE prototype from an elastic-plastic analysis using the parent material properties [12].Figure 17
Overall stress contours of a 10 kW class PHE prototype from an elastic-plastic analysis using the weld material properties.Figure18 shows the stress distributions on the weld bead and in the HAZ from an elastic-plastic analysis using the weld material properties. In the HAZ, a maximum local stress of 264.56 MPa exceeds the yield stress of the weld material (216.04 MPa at 792.09°C) by 22.46%, while a maximum stress of 191.88 MPa using the parent material properties is smaller than the yield stress of the parent material (224.57 MPa) by 14.56%. The degree of excess yield stress in the HAZ is increased for the analysis results using the weld material properties compared to using the parent material properties. This is attributed to a smaller yield stress in HAZ than that in the parent material. The thermostructural analysis results of the 10 kW class PHE prototype are briefly summarized in Table 6.Table 6
Analysis results of 10 kW class PHE prototype.
Maximum local stress
Yield stress (MPa)
Percentage exceeding the yield stress (%)
Stress (MPa)
Location
Temperature (°C)
Parent
Weld
HAZ
Parent
Weld
HAZ
Elastic analysis
331.23
Weld
744.46
237.98
260.35
39.18
27.22
Elastic-plastic analysis
Weld
Using parent material properties
263.65
Weld
760.37
236.86
11.31
Using weld material properties
267.60
Weld
742.23
260.50
2.72
HAZ
Using parent material properties
264.56
HAZ
216.04
22.46
Using weld material properties
191.88
HAZ
792.09
216.04
−14.56Figure 18
Stress contours of a 10 kW class PHE prototype in weld zone from an elastic-plastic analysis using the weld material properties.


## 4.2.1. Analysis Results of the 3 kW Class PHE Prototype

Figure11 shows the stress distributions from an elastic analysis using the parent material properties. A maximum local stress of 272.33 MPa occurs around the edge between the top plate and side plate, that is, the welded zone, which exceeds the yield stress of the parent material (237.88 MPa at 746°C) [11] by 14.48%. Since the elastic stress distributions using the material properties in the weld zone are the same as those shown in Figure 11 owing to the use of the same elastic modulus in the elastic analysis, the maximum local stress of 272.33 MPa exceeds the yield stress of the weld material (260.24 MPa) by only 4.64%. Thus, a smaller degree of excess yield stress is attributed to a larger yield stress of the weld material than the parent material.Figure 11
Overall stress contours of a 3 kW class PHE prototype from an elastic analysis using the parent material properties [6].Figure12 shows the stress distributions using the parent material properties from an elastic-plastic analysis. A maximum local stress of 242.60 MPa around the edge between the top and side plates, that is, the welded zone, exceeds the yield stress of the parent material (237.63 MPa at 750°C) by 2.09%. Figure 13 shows the stress distributions using the weld material properties from an elastic-plastic analysis. A maximum local stress of 266.19 MPa exceeds the yield stress of the weld material (260.61 MPa at 740.70°C) by 2.14%. The degree of excess yield stress on the weld (fusion zone) is changed for the analysis results using the weld material properties as compared to using the parent material properties. This is attributed to a larger yield stress in the weld than in the parent material.Figure 12
Overall stress contours of a 3 kW class PHE prototype from an elastic-plastic analysis using the parent material properties [6].Figure 13
Overall stress contours of a 3 kW class PHE prototype from an elastic-plastic analysis using the weld material properties.Figure14 shows the stress distributions on the weld bead and in the HAZ from an elastic-plastic analysis using the weld material properties. In the HAZ, a maximum local stress of 235.47 MPa exceeds the yield stress of the weld material (228.65 MPa at 749.22°C) by 2.98%, while a maximum stress of 239.17 MPa using the parent material properties exceeds the yield stress of the parent material (237.68 MPa) by only 0.63%. The degree of excess yield stress in the HAZ is increased for the analysis results using the weld material properties compared to using the parent material properties. This is attributed to a smaller yield stress in the HAZ than that in the parent material. The thermostructural analysis results of the 3 kW class PHE prototype are briefly summarized in Table 5.Table 5
Analysis results of 3 kW class PHE prototype.
Maximum local stress
Yield stress (MPa)
Percentage exceeding the yield stress (%)
Stress (MPa)
Location
Temperature (°C)
Parent
Weld
HAZ
Parent
Weld
HAZ
Elastic analysis
272.33
Weld
746.00
237.88
260.24
14.48
4.64
Elastic-plastic analysis
Weld
Using parent material  properties
242.60
Weld
750.00
237.63
2.09
Using weld material properties
266.19
Weld
740.70
260.61
2.14
HAZ
Using parent material properties
239.17
HAZ
237.68
0.63
Using weld material properties
235.47
HAZ
749.22
228.65
2.98Figure 14
Stress contours of a 3 kW class PHE prototype in the weld zone from an elastic-plastic analysis using the weld material properties.


## 4.2.2. Analysis Results of 10 kW Class PHE Prototype

Figure15 shows the stress distributions of the 10 kW class PHE prototype from an elastic analysis using the parent material properties. A maximum local stress of 331.23 MPa occurs around the edge between the top and side plates, that is, the welded zone, which exceeds the yield stress of the parent material (237.98 MPa at 744.46°C) by 39.18%. Since the stress distributions using the material properties in the weld zone are the same as those shown in Figure 15 owing to the use of the same elastic modulus in the elastic analysis, the maximum local stress of 331.23 MPa exceeds the yield stress of the weld material (260.35 MPa) by 27.22%. Thus, a smaller degree of excess yield stress is attributed to the larger yield stress of the weld material than the parent material.Figure 15
Overall stress contours of a 10 kW class PHE prototype from an elastic analysis using the parent material properties [12].Figure16 shows the stress distributions using the parent material properties from an elastic-plastic analysis. A maximum local stress of 263.65 MPa exceeds the yield stress of the parent material (236.86 MPa at 760.37°C) by 11.31%. Figure 17 shows the stress distributions using the weld material properties from an elastic-plastic analysis. A maximum local stress of 267.60 MPa occurs around the edge between the top and side plates, that is, the welded zone, which exceeds the yield stress of the weld material (260.50 MPa at 742.23°C) by 2.72%. The degree of excess yield stress on the weld (fusion zone) is decreased for the analysis results using the weld material properties compared to using the parent material properties. This is attributed to a larger yield stress in the weld than in the parent material.Figure 16
Overall stress contours of a 10 kW class PHE prototype from an elastic-plastic analysis using the parent material properties [12].Figure 17
Overall stress contours of a 10 kW class PHE prototype from an elastic-plastic analysis using the weld material properties.Figure18 shows the stress distributions on the weld bead and in the HAZ from an elastic-plastic analysis using the weld material properties. In the HAZ, a maximum local stress of 264.56 MPa exceeds the yield stress of the weld material (216.04 MPa at 792.09°C) by 22.46%, while a maximum stress of 191.88 MPa using the parent material properties is smaller than the yield stress of the parent material (224.57 MPa) by 14.56%. The degree of excess yield stress in the HAZ is increased for the analysis results using the weld material properties compared to using the parent material properties. This is attributed to a smaller yield stress in HAZ than that in the parent material. The thermostructural analysis results of the 10 kW class PHE prototype are briefly summarized in Table 6.Table 6
Analysis results of 10 kW class PHE prototype.
Maximum local stress
Yield stress (MPa)
Percentage exceeding the yield stress (%)
Stress (MPa)
Location
Temperature (°C)
Parent
Weld
HAZ
Parent
Weld
HAZ
Elastic analysis
331.23
Weld
744.46
237.98
260.35
39.18
27.22
Elastic-plastic analysis
Weld
Using parent material properties
263.65
Weld
760.37
236.86
11.31
Using weld material properties
267.60
Weld
742.23
260.50
2.72
HAZ
Using parent material properties
264.56
HAZ
216.04
22.46
Using weld material properties
191.88
HAZ
792.09
216.04
−14.56Figure 18
Stress contours of a 10 kW class PHE prototype in weld zone from an elastic-plastic analysis using the weld material properties.


## 4.3. Discussions

From the results of the thermostructural analyses on the plate-type PHE prototypes, the following interesting observation was found. Even though the maximum stress exceeds the yield stress in the weld zone, the degree of excess yield stress decreases or increases owing to the different yield stresses in the weld zone, when compared with the analysis results of using the parent material properties. Consequently, a thermostructural analysis considering the weld material properties seems to be needed to understand the structural behavior and evaluate the structural integrity of the plate-type PHE prototypes more reliably.A higher amount of stress and wider high-stress region occur for the 10 kW PHE prototype compared to the 3 kW PHE prototype. This is attributed to the size effect of the prototypes under the same displacement constraint conditions.The maximum local stress occurs around the edge between the top and side plates of the plate-type PHE prototypes, that is, the welded zone. The stress that occurs around the edges in the FE model will decrease to a certain degree when considering the chamfered edges, since the edges of the PHE prototypes are chamfered realistically.


## 5. Conclusions

In this study, to investigate the effects of the weld material properties on the mechanical behavior of plate-type PHE prototypes made of Hastelloy-X, thermostructural analyses considering the weld mechanical properties were performed and the results were compared with those using the parent material properties. As a result of the analysis, the following conclusions can be drawn.(1)
While the maximum stress exceeds the yield stress in the weld zone, the degree of excess yield stress may differ owing to the different yield stresses in the weld zone.(2)
A thermostructural analysis considering the weld material properties seems to be necessary to understand the structural behavior and evaluate the structural integrity of the plate-type PHE prototypes more reliably.(3)
The stress occurring around the edges in the FE model will decrease to a certain degree when considering the chamfered edges, since the edges of the PHE prototypes are chamfered realistically.



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*Source: 726489-2012-12-11.xml*