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ScienceDirect Procedia CIRP 42 (2016) 679 – 684
18th CIRP Conference on Electro Physical and Chemical Machining (ISEM XVIII)
Numerical and Experimental Studies of Electro-Thermal Machining for Melting Notch Tip in Steel Strip Thomas Jin-Chee Liu*, Chun-Der Cheng, Ji-Fu Tseng, Li-Wei Chen, Po-Heng Chen Department of Mechanical Engineering, Ming Chi University of Technology, Taishan, Taipei, Taiwan * Corresponding author. Tel.: +886-2-29089899 ext 4569. E-mail address:
[email protected]
Abstract This paper presents the finite element analyses and experimental studies of the melting notch tip in the steel strip under the electro-thermal machining associated with high electric current. Under the electric load, a hot spot occurs at the notch tip due to the electric current density concentration and Joule heating effect. This hot spot will melt when the applied electric energy is sufficient. Numerical results predict the temperature field and melting size of the hot spot. Experimental studies show the hot spot, melting area, solidification, shrinking hole and heat affected zone around the notch tip under the electro-thermal machining. The results of this study provide the concepts for increasing the fatigue life or stopping the crack propagation. © 2016 2016The TheAuthors. Authors. Published by Elsevier © Published by Elsevier B.V. B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of 18th CIRP Conference on Electro Physical and Chemical Machining (ISEM XVIII) Keywords: electro-thermal machining; Joule heating; notch tip; heat affected zone; shrinking hole.
1. Introduction Stress concentration is a key issue in the structural engineering problems. It occurs near the corner, fillet, hole, notch and crack tip. The high stress not only induces the failure problem but also reduces the fatigue life of the structure. Especially, the tensile stress can make the structure broken and cracking. It needs to be avoided.
[1-9]. As shown in Fig. 1, when a cracked structure is subjected to the electric load, the electric current density concentrates at the crack tip. Due to the Joule heating, the electric current density concentration causes the hot spot at the crack tip zone. When large electric energy is applied, the crack tip area can melt. The melting zone can shrink to be a hole after the cooling process. This shrinking hole, like a drilled hole, can reduce the stress concentration and remove the stress singularity at the crack tip [7,9]. If the hole is not created, it can remain a heat affected zone (HAZ) with higher strength and compressive stresses [1,9]. This HAZ can also stop or retard the crack growth.
Fig. 1. (a) electric current density concentration; (b) hot spot at crack tip.
Over the past decades, many researches reported that the Joule heating effect can induce the compressive stresses, local hot spot or melting area at the crack tip in the metal structures
Fig. 2. Hot spot at notch tip.
2212-8271 © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of 18th CIRP Conference on Electro Physical and Chemical Machining (ISEM XVIII) doi:10.1016/j.procir.2016.02.301
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For a notch with a round tip, the stress concentration exists at the tip zone. To reduce the stress level or increase the local strength property, the high electric load, i.e. the electrothermal machining, can be adopted. Similar to the crack problem, the electric current density concentration and hot spot also occur at the notch tip as shown in Fig. 2. Using the electro-thermal machining, the HAZ with compressive stresses or a shrinking hole can be created as shown in Fig. 3. Both of them are good for the structure’s life because the tensile stress level can be reduced.
Table 1. Material constants of SUS 304 stainless steel [10]. mass density
8000 kg/m3
thermal conductivity k
16.2 W/(m-K) @0~100 C 21.5 W/(m-K) @500 C
specific heat Cp
500 J/(kg-K)
resistivity
7.210-7 -m @20 C 7.810-7 -m @100 C 8.610-7 -m @200 C 1010-7 -m @400 C 11.610-7 -m @650 C
melting point
1400 C
coefficient of thermal expansion T
1.7310-5 1/C @100 C 1.7810-5 1/C @315 C 1.8710-5 1/C @400 C
Young's modulus E yielding strength SY Poisson's ratio
193 GPa 215 MPa 0.29
3. Principles of analyses Fig. 3. (a) HAZ; (b) shrinking hole at notch tip.
This paper investigates the electro-thermal machining process for the notch problem. The finite element analyses and experimental studies are used for this research. The results of this study can provide the concepts for increasing the fatigue life or stopping the crack propagation.
2. Case study In Fig. 4, it shows the geometry and other conditions for the case study of this paper. The steel strip has the dimensions WL and thickness e. The notch length and notch angle are respectively denoted as a and . R is the radius of the round notch tip. The strip is subjected to a direct current (DC) i0. In Table 1, it lists the material data of the SUS 304 stainless steel strip [10]. The elasto-plastic stress-strain relation with the tangent modulus ET=0.05E is considered in the analysis.
For the multi-physical analyses, the matrix-form equation describing the thermo-electro-structural coupled-field is as follows [11]: && C 0 M 0 0 U 0 0 0 T t && tu C C & & 0 0 0 V 0 0
& K K ut 0 U & 0 T 0 K t & 0 0 V 0
0 U F 0 T Q v K V I
(1)
whereU, T, V, F, Q and I are the vector forms of the displacement, temperature, electric potential, force, heat flow rate and electric current, respectively. The material constant matrices M, C, Ct, Ctu, K, Kt, Kut and Kv are the structural mass, structural damping, thermal specific heat, thermostructural damping, structural stiffness, thermal conductivity, thermo-structural stiffness and electric conductivity, respectively. The coupled heat flow matrix Q contains the effects of the thermal loading and Joule heating. Ctu and Kut are thermo-structural coupled terms. Eq. (1) is a directly coupled nonlinear equation which is solved using the NewtonRaphson iterative method [11]. The Joule heating is the main principle of the electrothermal machining process. It is described as follows [12,13] q& J
2
(2)
Also, the transient heat transfer is described as follows q kT k 2T q& C p
Fig. 4. Case study.
(3) T t
(4)
where , J, q , k, T, q& , , Cp and t are the resistivity, electric current density, heat flux, thermal conductivity, temperature, heat generation of Joule heating, mass density, specific heat and time, respectively.
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4. Experimental method There are two types of SUS 304 steel strips as shown in Fig. 5. Type A strip is thinner and will be subjected to low electric load for the accuracy validation between experimental and numerical results. Type B strip is thicker and will be subjected to high electric load for the electro-thermal machining. The geometry parameters of the strips are listed in Table 2.
For high electric load experiments, the resistance spot welding (RSW) machine is used to be the power supplier. Fig. 7 shows the experimental facilities.
Fig. 6. Experimental facilities for low electric load.
Fig. 5. (a) Type A strip for low electric load; (b) Type B strip for high electric load. Table 2. Geometry parameters of strips.
Fig. 7. Experimental facilities for high electric load.
parameter
Type A
Type B
L
240 mm
100 mm
W
8 mm
8 mm
a
4 mm
4 mm
20
20
e
0.05 mm
1 mm
R
0.2 mm
0.2 mm
In Fig. 6, it shows the experimental facilities for low electric load in this study. The direct current (DC) power supplier provides the electric load applying on the steel strip. The strip will be heated and the thermal camera (designed by FLIR Co.) can capture the surface temperature. To capture the thermal image, the strip must be coated by the black paint.
5. Finite element method The finite element software ANSYS is adopted for the numerical analyses. In ANSYS, the element type SOLID226 with the thermo-electro-structural coupled-field formulation is used for the modeling. In Figs. 8 and 9, it shows the finite element models of the steel strips. The following conditions are considered in the finite element analysis: (1) Three-dimensional analysis (2) Thermo-electro-structural coupled-field (3) Transient heat transfer (initial condition: 25 C) (4) Convection on air/strip interface (natural convection coefficient: 25 W/(m2-K)) (5) Steady electric current (DC current) (6) Elasto-plastic material property (7) Both ends of the strip are fixed
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a
b
experimental data may be induced by the disturbance from the surrounding air. In addition, the temperature contours from the finite element analysis and thermal camera are shown respectively in Figs. 11 and 12. Both contours are similar. A hot spot exists at the notch tip zone due to the electric current density concentration and Joule heating effect. The finite element result in Fig. 13 proves the electric current density concentration at the notch tip. The analyses and results in this section provide the research foundation for the problem under high electric load.
180
Fig. 8. Type A model, (a) whole model; (b) mesh near tip region.
notch tip temperature (oC)
160 140 finite element results experimental results
120 100 80 60
a 40 20 0
20
40 60 time (s)
80
100
Fig. 10. Notch tip temperature.
b
Fig. 11. Temperature contour (C) from finite element analysis.
Fig. 9. Type B model, (a) whole model; (b) mesh near tip region.
6. Results 6.1. Type A strip under low electric load The validation of the research method is confirmed in this section. The electric load is i0 = 4 A. In Fig. 10, the notch tip temperature data from finite element analyses and experiments are compared in the time interval of 80 seconds. It shows good agreement. Both temperature curves become the steady-state condition at the last 10 seconds. The fluctuation of the
Fig. 12. Temperature contour (C) from thermal camera.
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a
Fig. 15. Steel strip with hot spot under electro-thermal machining.
b
a
b
Fig. 13. Electric current density contour (A/m2) from finite element analysis. (a) notch region; (b) tip region.
6.2. Type B strip under high electric load Using high electric load, the electro-thermal machining process can be achieved on the steel strip. Due to the Joule heating, the notch tip can melt when the electric energy is sufficient. Fig. 14 shows the steel strip fixed on two electrodes of the RSW machine. When high electric current is applied, the notch tip gets a hot spot as shown in Fig. 15. Using the electro-thermal machining with different electric currents, the notch tip property is modified as shown in Fig. 16. In Fig. 16(a), the tip zone has the surface change without any melting process under i0=500 A with the operating time t=0.3333 s. In Fig. 16(b), higher electric current causes the melting process and HAZ at the notch tip. Under i0=580 A, the shrinking hole is created. Above results prove the concepts in Fig. 3.
c
Fig. 16. Results of electro-thermal machining. (a) surface change (i0=500A); (b) HAZ (i0=540A); (c) shrinking hole (i0=580A).
Fig. 14. Steel strip and electrodes.
In the finite element analysis, the solid-liquid phase change state is not simulated. It is difficult to use the finite element analysis to prove directly the experimental results in Fig. 16. However, the temperature and stress fields can be obtained from the finite element analysis as shown in Figs. 17 and 18. Under i0=580 A, the temperature contour can be used to estimate the melting area and size after the electro-thermal machining. The stress contour of y shows the compressive stresses around the notch tip. The compressive stresses can
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reduce the tensile stress level so as to prevent from the crack initiation or growth.
In addition, the temperature contours under i0=500 A and i0=540 A are shown in Fig. 19. Comparing Figs. 17 and 19, the size of the melting area (red-color area) is larger when the electric load is higher. In Fig. 19(a), no melting area is found due to the lower electric load. This contour is identical to the photo in Fig. 16(a).
7. Conclusions
Fig. 17. Temperature contour (C) under i0=580A.
In this paper, experimental and numerical results show the melting condition, HAZ, shrinking hole, temperature, electric current, and stress fields at the notch tip. Under the electrothermal machining, the multi-physical behaviors of the notch tip can be shown or predicted. The results of this study provide the concepts for increasing the fatigue life or stopping the crack propagation in the structures. Acknowledgements The authors would like to thank the Ministry of Science and Technology in Taiwan for the financial support under contract numbers NSC 101-2221-E-131-011, MOST 1032221-E-131-015 and MOST 104-2221-E-131-030. Also, the authors appreciate the support of the research project 103Academic-Research-E-02 of Ming Chi University of Technology.
References Fig. 18. Stress contour of y (Pa) under i0=580A.
a
b
Fig. 19. Temperature contour (C). (a) i0=500 A; (a) i0=540 A.
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