# Neutron Stress Measurement of W/Ti Composite in Cryogenic Temperatures Using Time-of-Flight Method

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Preparation of Fiber Reinforced Material

#### 2.2. In Situ Thermal Stress Measurement

_{1}axis is defined as parallel to the longitudinal direction of the tungsten fibers. The x

_{2}and x

_{3}axes are normal to the fiber direction. When stresses are calculated by Hooke’s equation, the strains in the three directions of x

_{1}, x

_{2}, and x

_{3}are required. In this measurement, it was assumed that stresses and strains were almost equal in the x

_{2}and x

_{3}directions. Therefore, only two directions in the x

_{1}axis and the x

_{2}axis were measured by the neutron diffraction.

_{1}direction), and the S-direction is the fiber normal direction (x

_{2}= x

_{3}).

_{0}sample of the titanium. This sample was manufactured by the spot weld of titanium plates without tungsten fibers. Figure 4b is the W/Ti composite material evaluated in this study. Figure 4c is a tungsten sample for d

_{0}measurement, in which tungsten fiber is loosely wrapped around a titanium plate. These three samples were pasted to a copper plate by glue and tape. Figure 4d shows the sample setting condition on the cryostat cooling head. In this photograph, three samples were fixed with a thin white tape, so that they did not fall off from the copper plate due to shrinkage of cooling cycles. This white tape is a water leak prevention tape used for water pipe leaks. These measurement techniques are used by JAEA staff who assist the measurement on site. Such know-how is very important for actual measurement, and the authors were provided with full support by JAEA staff.

_{0}measurement. However, the measurement accuracy of the measurement results deteriorated because the peaks of titanium and tungsten overlapped. In neutron stress measurement, d

_{0}measurement in a stress-free state is very important. As an improvement method, when measuring d

_{0}of several materials, it is necessary to measure the samples separately for d

_{0}measurement without combining them.

_{1}parallel to the longitudinal fiber direction and σ

_{2}normal to the longitudinal fiber direction were measured using Hooke’s Equation (1).

_{W}= 5% in this calculation. The initial stresses needed to calculate the residual stresses were supposed at the room temperature 300 K position. The measurement values in both the tungsten fiber and the titanium matrix were used for these initial residual stresses.

## 3. Results

#### 3.1. Diffraction Profile by the Time-of-Flight Method

#### 3.2. Strain Calculation by the TOF Method

_{0}samples) when the temperature was changed. For the same sample, the measurement was performed exactly at the same position. Moreover, the data analysis was conducted to refine the lattice constant using the Pawley method with many peaks; therefore. the effect of the energy distribution was also very small.

#### 3.3. Results of Thermal Strains

#### 3.4. Results of Thermal Stress Alterations

## 4. Discussion

_{Ti-initila}= 56 MPa for titanium and σ

_{W-initial}= −963 MPa for tungsten from the result of the stress measurement.

_{Ti-initial}= 56 MPa of the titanium matrix and the initial stress σ

_{W-initial}= −963 MPa of the tungsten fiber obtained from the measurement results is discussed. In general, residual stress in composite materials is considered to be dynamically balanced inside the material. The internal stress is balanced by being distributed according to the volume fraction of each phase composing the material. In the case of W/Ti composites, it is believed that the residual stresses of the titanium matrix and tungsten fibers are balanced according to the volume fraction of the titanium matrix and the tungsten fibers. This compound rule is represented by the following formula:

_{Ti}× V

_{Ti}= 56 × 0.95 = 53.2 and the second term is σ

_{W}× V

_{W}= 963 × 0.05 = 48.15, which are very close values. According to the calculation result of Equation (5), the calculated volume fraction of tungsten fibers is slightly larger than 5%, which was 5.5%. For example, if the volume fraction of tungsten fibers is increased or decreased by 1%, the above magnitude relationship of stress values is a large variation. From this result, it can be confirmed that these measurements succeeded in accurately evaluating the stress balance between the titanium matrix and the tungsten fibers in this measurement.

## 5. Conclusions

- (1)
- Regarding the initial residual stress in the fiber longitudinal direction, compressive stresses existed in tungsten fibers, and tensile stresses existed in the titanium matrix.
- (2)
- Thermal residual stresses in tungsten fibers and the titanium matrix were changed to other states depending on temperature changes.
- (3)
- The main factor of thermal stress alterations was the difference in thermal expansion between tungsten fiber and titanium matrix, and the effect in the longitudinal direction of the fibers was dominant.
- (4)
- The alterations in thermal stresses followed the same path during temperature rise and temperature drop in the thermal cycle changes.
- (5)
- The simple elastic calculations and the measured results showed very good agreement, confirming the high measurement accuracy of the time-of-flight method using TAKUMI.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Schematic diagram of (

**a**) 0.5 mm thick titanium plate with tungsten fibers wound at regular intervals and sandwiched between other 0.2 mm thick titanium plates; (

**b**) seven layers of these materials prepared in (

**a**) are stacked up and spot-welded; (

**c**) the overlapping condition of the welded part in the continuous spot-welding method, and the welding path on the surface of W/Ti composite.

**Figure 2.**SEM photographs of the W/Ti composite: (

**a**) a photograph of the cross-section of the W/Ti composite; (

**b**) SEM component analysis focusing on the boundary between the titanium matrix and the tungsten fibers.

**Figure 3.**Schematic diagram of (

**a**) coordinate system of W/Ti composite, and (

**b**) sample setting and neutron measurement image.

**Figure 4.**Photograph of the sample condition for the neutron measurement: (

**a**) d

_{0}sample of the titanium manufactured by the spot weld of titanium plates without tungsten fibers; (

**b**) the W/Ti composite material; (

**c**) tungsten sample for d

_{0}measurement, where tungsten fiber is loosely wrapped around a titanium plate; (

**d**) the sample setting condition on the cryostat cooling head. Three samples were fixed with a thin white water leak prevention tape.

**Figure 5.**Schematic diagram of the temperature vs. time program for the in situ stress measurement of the W/Ti composite.

**Figure 6.**One example of the diffraction profile measured using the time-of-flight method of TKUMI. These diffraction profiles were peak-fitted using the Z-Rietveld software.

**Figure 7.**Comparison of the diffraction peaks in N-direction and S-direction. (

**a**) N-direction: W110 and W220 appear. (

**b**) S-direction: W110 and W220 disappear, and W200 appears.

**Figure 8.**Alterations of thermal strains determined from the results of the diffraction peak measurements of (

**a**) the titanium matrix and (

**b**) the tungsten fibers in the W/Ti composite.

**Figure 9.**Stress alterations of the titanium matrix in the W/Ti composite: (

**a**) the longitudinal direction of tungsten fibers; (

**b**) the normal direction.

**Figure 10.**Stress alterations of tungsten in W/Ti composites: (

**a**) the longitudinal direction of the tungsten fiber; (

**b**) the normal direction.

**Figure 11.**Comparison of calculated results from Equation (2) and measurement results in the longitudinal fiber direction: (

**a**) results of the titanium matrix; (

**b**) results of the tungsten fibers.

Welding voltage (V) & current (A) | 200, 8.5 |

Welding pressure (kN) | 1.9 |

Holding time (msec.) | 200 |

Diameter of electrode (mm) | 11 |

MLF beam power | 600 kW | ||

Measurement material | W/Ti composite | ||

Slit system | Incident slit: 5 × 10 mm Detected 90° A, B banks | ||

Measurement method | Time of Flight (TOF) | ||

Measurement time | 600 sec./profile | ||

Tungsten: | |||

E: 388.69, ν: 0.2833 | |||

Young’s modulus E (GPa) Poisson’s ratio ν | Titanium: | ||

hkl, | E, | ν | |

100, | 110.86, | 0.3290 | |

002, | 128.35, | 0.2976 | |

101, | 123.41, | 0.3061 | |

102, | 126.83, | 0.3002 | |

Macro, | 114.70, | 0.3217 |

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**MDPI and ACS Style**

Nishida, M.; Harjo, S.; Kawasaki, T.; Yamashita, T.; Gong, W.
Neutron Stress Measurement of W/Ti Composite in Cryogenic Temperatures Using Time-of-Flight Method. *Quantum Beam Sci.* **2023**, *7*, 8.
https://doi.org/10.3390/qubs7010008

**AMA Style**

Nishida M, Harjo S, Kawasaki T, Yamashita T, Gong W.
Neutron Stress Measurement of W/Ti Composite in Cryogenic Temperatures Using Time-of-Flight Method. *Quantum Beam Science*. 2023; 7(1):8.
https://doi.org/10.3390/qubs7010008

**Chicago/Turabian Style**

Nishida, Masayuki, Stefanus Harjo, Takuro Kawasaki, Takayuki Yamashita, and Wu Gong.
2023. "Neutron Stress Measurement of W/Ti Composite in Cryogenic Temperatures Using Time-of-Flight Method" *Quantum Beam Science* 7, no. 1: 8.
https://doi.org/10.3390/qubs7010008