# Smart Stress Annihilation in Steels Using Residual Stress Distribution Monitoring and Localized Induction Heating

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Heat Dissipation and Distribution

^{−1}, which is given by:

^{−7}H/m). Similar eddy current effects can also be considered for pulsed-current waveforms, to the extent that a pulsed-field may be considered as a summary of the harmonic sinusoidal fields [18]. Depth $\mathsf{\delta}$ in most steels is from a few tens to a few hundreds of microns for a frequency regime in the order of several kHz, which is typically used in induction heating. The value of the excitation frequency is determined based on the depth of the desired heat treatment of the steel. For simplicity reasons, we assume that the microstructure of the steel under treatment does not have a significant effect on the eddy current distribution and $\mathsf{\delta}$ when the induced eddy current amplitude, I

_{o}, is in the order of tens of Amperes.

^{−3}m, $\mathsf{\sigma}$~2 × 10

^{6}S/m, ${\mathsf{\mu}}_{\mathrm{r}}$~100–4000.

## 3. Experimental Set-Up and Results

## 4. Discussion

^{2}, then 900 U-shaped conductors are needed to heat-treat the surface of the steel effectively. Suppose that all conductors have to transmit their maximum power at the same time, the total amount of power required is 900 kW, bearing in mind that 1 kW per conductor is required to achieve 570 °C in the under-treatment steel. The amount of required power is less than the power required for a normal furnace to heat a large batch of steel. Additionally, the cost of an RF current generator of 1 MW power is not dramatically high and is certainly lower than the cost of custom ovens for the same purpose. However, bearing in mind that only selected areas of the steel will need thermal treatment, the amount of power required for stress annihilation is considerably smaller. This is an excellent advantage of the proposed technique.

## 5. Future Work

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**The experimental set-up: (

**a**) permeability distribution monitoring; (

**b**) induction heating and temperature monitoring. In the insets, the sensor, the camera, and the single turn induction coil are illustrated.

**Figure 3.**Permeability distribution in low carbon steel coupon (arbitrary units), measured before the treatment, corresponding to a rather homogeneous stress distribution along the centerline.

**Figure 4.**Temperature distribution during the induction heating of AISI 1008 steel using an: (

**a**) Induction coil at $\mathrm{d}=10\mathrm{mm}$ from the under-treatment surface, during heating for ${\mathrm{t}}_{\mathrm{o}}=3\mathrm{s}$; (

**b**) induction coil at $\mathrm{d}=10\mathrm{mm}$ from the under-treatment surface, one minute after heating for ${\mathrm{t}}_{\mathrm{o}}=3\mathrm{s}$; (

**c**) induction coil at $\mathrm{d}=0.2\mathrm{mm}$ from the under-treatment surface, one minute after heating for ${\mathrm{t}}_{\mathrm{o}}=3\mathrm{s}$; (

**d**) the V-shaped or U-shaped conductor at $\mathrm{d}=0.2\mathrm{mm}$ from the under-treatment surface, one minute after heating for ${\mathrm{t}}_{\mathrm{o}}=3\mathrm{s}$.

**Figure 5.**The V-shaped or U-shaped conductor is providing the local magnetic flux density inducing eddy currents for localized heat treatment, used for the results of Figure 4d.

**Figure 6.**Transmission electron microscopy micrographs of the heat-treated AISI 1008 steel before (

**a**) and after (

**b**) heat treatment. The dislocation forests have been reduced after heat treatment for ${\mathrm{t}}_{\mathrm{o}}=3\mathrm{s}$ with the inductive heater at $\mathrm{d}=0.2\mathrm{mm}.$

**Figure 7.**Permeability dependence on the position of measurement for the test coupon of low carbon steel: (

**a**) Use of the one-turn coil at d = 0.2 mm and (

**b**) use of the V-shape or U-shaped conductor of Figure 5.

**Figure 8.**Permeability measurements along the AISI 1008 steel coupon correlated with residual stresses: (

**a**) Initially monitored stress distribution in the stress relieved steel coupon (black points); (

**b**) after beating the surface with the steel sphere; and (

**c**) after localized heat treatment in the vicinity of the trace of the steel sphere. An improvement in the stress distribution of more than 90% can be observed.

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**MDPI and ACS Style**

Liang, K.; Tsarabaris, P.; Ktena, A.; Bi, X.; Hristoforou, E.
Smart Stress Annihilation in Steels Using Residual Stress Distribution Monitoring and Localized Induction Heating. *Metals* **2020**, *10*, 838.
https://doi.org/10.3390/met10060838

**AMA Style**

Liang K, Tsarabaris P, Ktena A, Bi X, Hristoforou E.
Smart Stress Annihilation in Steels Using Residual Stress Distribution Monitoring and Localized Induction Heating. *Metals*. 2020; 10(6):838.
https://doi.org/10.3390/met10060838

**Chicago/Turabian Style**

Liang, Kaiming, Panagiotis Tsarabaris, Aphrodite Ktena, Xiaofang Bi, and Evangelos Hristoforou.
2020. "Smart Stress Annihilation in Steels Using Residual Stress Distribution Monitoring and Localized Induction Heating" *Metals* 10, no. 6: 838.
https://doi.org/10.3390/met10060838