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Numerical simulation on residual stress distribution of hard-face-welded steel specimens with martensite transformation
Materials Science and Engineering A364 (2004) 244–248
Numerical simulation on residual stress distribution of hard-face-welded steel specimens with martensite transformation Qing Xiang Yang a,∗ , Mei Yao a , Joongkeun Park b b
a College of Materials Science and Engineering, Yanshan University, Qinhuangdao, Hebei 066004, PR China Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology, Taejon 305-701, South Korea
Received 13 February 2003; received in revised form 8 August 2003
Abstract FEM models are established for calculations of the temperature fields during cooling and the internal stress field of a medium–high carbon steel specimen after hard-face-welding (hardfacing) by using an electrode with lower carbon content. The martensite transformations in both welded metal and matrix are considered in the model for calculation of the internal stress field. The validity of these models was verified by the experimental results of temperature field, as well as the residual (internal) stress field, determined at the surface of the specimen. Based on the calculated results, the effect of martensite transformation points on the residual stress fields is analyzed. © 2003 Elsevier B.V. All rights reserved. Keywords: Numerical simulation; Residual stress; Hard-facing metal; Martensitic transformation; Medium–high carbon steel
1. Introduction Hard-face-welding (hardfacing) is a technique widely used for the repairing of damaged metal parts made of medium–high/high carbon steels, such as mill rollers, tools and dies [1–3]. These steels, as well as the hardfaced metal, normally have carbon content higher than 0.50% and contain Cr, Mo, V and other alloying elements. After hardfacing, in the welding metal and the heat-affected zone (HAZ) of specimen, there often occurs martensite with high hardness, which is quite sensitive to formation of cold crack. The most effective technological measures for prevention of crack formation are the pre-heating and the afterward re-heat-treatments, which, however, are quite inconvenient or even impossible in some cases. Then, it is of great significance to investigate new kinds of electrode, by using that, the hardfacing can be carried out without or with low temperature pre-heating, as well as without or with simple afterward heat-treatments. The formation of cold cracks during welding is in general a function of three main factors that are the formation of martensite with high hardness, the existence of hydrogen ∗ Corresponding author. Tel.: +86-335-805-5593; fax: +86-335-805-7075. E-mail address: [email protected] (Q.X. Yang).
0921-5093/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2003.08.024
and the occurrence of tensile residual stress [4]. The existence of hydrogen can be limited by baking the electrodes. The sensitivity of martensite to crack formation is mainly dependent on its carbon content, which will not be changed in matrix metal during welding, but, in welding metal, it can be controlled by adjusting the chemical compositions of used electrode [5]. Nevertheless, the carbon content in welding metal should be kept on a needed level to guarantee the wear resistance of the hardfacing layer. Another factor influencing the crack formation is the occurrence of tensile residual stress after welding [6]. The residual stress at room temperature after welding is the retained internal stress, which occurs due to the non-simultaneity of temperature change and phase transformation at different sites of specimen during cooling. Upon cooling after hardfacing, the metal is shrunk due to the temperature lowering; while, austenite is slightly denser than martensite, and therefore, during the phase transformation, there is a net volume increase. Then, the formation of the internal stress, as well as the residual stress, should be able to be adjusted by adjusting the martensite transformation in the welding metal, which is dependent mainly to the chemical compositions of welding metal. The direct measurement of temperature during cooling is quite difficult and the direct measurement of internal stress is simply impossible, so the investigation of the temperature fields, as well as the internal/residual stress
Q.X. Yang et al. / Materials Science and Engineering A364 (2004) 244–248
fields during hardfacing is a complex problem and has not been deeply studied. Recently, some attempts are carried out to calculate the temperature and the internal stress fields by FEM [7–9], which should be an effective technique to resolve above-mentioned problem. In this paper, a numerical simulation to calculate the internal and residual stress distributions on simplified hardfacing specimens is carried out and the calculated results are verified by some experimental data; and then, the effect of martensite transformation is discussed. The results of this paper are important for the chemical composition design of new types of hardfacing electrode, which can be used under simplified pre-heating and afterward heat-treatment procedures.
245
Table 2 Parameters for residual stress determining by X-ray method Parameter’s name
Parameter
Target material Tube volume (kV) Tube current (mA) Diffraction crystal plane 2θ scanning angle Numbering time (s) Stress parameter (MPa per degree) Stress determining method
CrKa 25 5 (211)α 0.1◦ 1 −318 Fixing method
2. Experimental and calculation procedures Specimens used for testing and calculations were made of hot roller steel 60CrMnMo with chemical compositions given in Table 1. The dimensions of specimens are 90 mm × 90 mm × 24 mm. A small hole with diameter of 22 mm and depth of 2 mm was machined in the center of the upper face of the specimens. A commercial electrode marked D397 and a specially designed cracking-resistant electrode adding RE (rare earth) and Ni were adopted to fill the small hole by using arc-welding technology. The chemical compositions of the hardfacing metals by using different electrodes are determined beforehand and are also given in Table 1. The hardfacing were carried out with electric current of 100 A. In all cases, the operating time is 16 s. After the operation, the temperature fields around the welding point during cooling process were measured at given moments by using an infrared thermo-vision analyzer of type 780. After cooling to the room temperature, it has been found that at the specimen, hardfaced by using electrode D397, both the hot cracks (in the middle region of the hardfacing metal) and the cold cracks (near the boundary of the hardfacing metal and the HAZ of matrix metal) were observed [10], while at the specimen hardfaced by using cracking-resistant electrode, no cracking has been detected [11]. For specimens with cracks, there is nonsense to study the residual stress field, then the determination of residual stress only carried out on the specimen hardfaced by using the cracking-resistant electrode. The residual stress field was determined by an X-ray residual stress analyzer of type AST × 2001 and the parameters for determining the residual stress are listed in Table 2. The experimental data of temperature and residual stress fields
Fig. 1. Mesh division.
were used to verify the calculated results. The numerical simulations of temperature and internal stress fields are carried out by using a commercial software ANSYS for FEM calculation. Because of little effect of temperature on the sides of specimen, the square specimen can be simplified to the disc one with diameter equal to the side length of square specimen. In this case, the temperature and internal stress fields can be treated as the axial symmetry ones. The FEM mesh division is given in Fig. 1 (241 elements are divided and 263 nodes are formed), in which the hardfacing region is shown by dotted lines. During calculation, some thermo-physical and mechanical parameters were supposed as constant: the density, ρ = 7.85×10−6 kg/mm3 ; the elastic modulus, E = 2×105 MPa and the Poisson’s ratio, ν = 0.3. Other parameters [12–16] are given in Table 3, in which, the exchanging coefficient (α) is calculated by following equation [17]: α = 2.2(Tw − Tc )0.25 + 4.6 × 10−8 (Tw2 + Tc2 )(Tw + Tc ) (1)
Table 1 Chemical compositions of matrix steel and hardfacing metal (wt.%) Materials
C
Cr
Mn
Mo
Ni
Si
S
P
RE
60CrMnMo Hard-facing metal when the electrode D397 is used Hard-facing metal when the cracking-resistant electrode is used
0.64 0.57 0.54
1.04 1.95 1.80
1.88 2.36 1.10
0.22 0.66 0.52
– – 1.70
0.33 0.54 0.64
0.038 0.035 0.032
0.016 0.04 0.03
– – 0.085
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Table 3 Thermo-physical and mechanical parameters of 60CrMnMo steel used for FEM calculation [12–16] Temperature (◦ C)
Parameter
Thermal conduction coefficient (λ) (×10−3 W/mm ◦ C) Average heat capacity (c) (×10−3 J/kg ◦ C) Specific enthalpy (H) (×103 J/kg) Exchanging coefficient (α) (×10−6 W/mm2 ◦ C)
200
400
600
800
1000
1200
1400
1600
41.9 0.502 100 18.85
39.4 0.536 214 33.44
32.3 0.586 352 55.95
29.1 0.695 557 88.92
26.5 0.674 674 134.6
29.4 0.670 804 195.4
29.4 0.670 804 273.4
29.4 0.670 804 370.9
Fig. 2. Region division for internal stress field calculation. A1, hardfacing metal; A2, HAZ; A3, matrix steel 60CrMnMo.
where Tw is temperature of specimen and Tc is that of environment. During calculation of internal stress field, the martensite transformations in specimen were taken into account. Based on the features of phase transformation, the whole specimen can be divided into three regions: the hardfacing metal region (A1), in which the martensite transformation occurs at higher temperature; the HAZ (A2) near the hardfacing metal with pick temperature higher than AC3 , in which the martensite transformation occurs at lower temperature and the zone of matrix (A3) far from hardfacing metal with temperature lower than AC3 , in which the martensite transformation dose not occur. During calculations of internal stress field, the different features of these three regions should be considered comprehensively. According to the calculated results of temperature field, the dimensions of heat-affected zone can be determined. A simplified division of these three regions is shown in Fig. 2. The martensite transformation temperatures Ms and Mf of matrix steel 60CrMnMo, as well as those of hardfacing metals, were determined by using tangent method from
the dilatometric curves obtained on a high speed automatic dilatometer of type Formaster-D and are given in Table 4. It can be seen, the heating temperature has little effect on the martensite temperatures, especially higher than 1000 ◦ C. In this work, the martensite temperatures determined after heating at 1000 ◦ C were used for internal stress field calculation. The expansion coefficients needed for calculations can also be obtained based on the dilatometric curves and are listed in Table 5. The internal stress field induced during cooling after hardfacing is also related to the yield strengths (σ s ) of the matrix and hardfacing metal. It is assumed [17] that the steel becomes ideal-plastic (σ s gets to zero) when the temperature is higher than 600 ◦ C. When the temperature is lower than that, the σ s increases with the decrease of temperature. In regions A1 and A2, when the austenite–martensite phase transformation occurs, the yield strength will be changed sharply and increase with the transformed amount of martensite. The values of yield strength of these three regions used for calculations of internal stress fields are given in Table 6.
3. Results and analyses 3.1. Temperature fields Comparisons between measured and calculated results of temperature fields on the surface of hardfaced specimen are shown in Fig. 3. Fig. 3(a) shows the temperature fields of hardfacing metal at t = 18 and 35 s (2 and 19 s after welding operation) and Fig. 3(b) shows the temperature history at r = 0 (the center of hardfacing metal) and r = 14 mm (HAZ). It can be seen, that there are little differences between the measured and the calculated results. This fact indicates that the model used for temperature field calculations is correct and obtained results can be used for further calculation of internal stress field of specimens after hardfacing.
Table 4 Martensite transformation temperatures of different materials Materials (◦ C)
Steel 60CrMnMo
T Ms Mf
800 230 135
1000 225 130
1200 215 125
Hard-facing metal welded by using electrode
Hard-facing metal welded by high cracking resistance with RE and Ni
800 348 232
800 330 228
1000 345 225
1200 338 225
1000 325 223
1200 322 160
Q.X. Yang et al. / Materials Science and Engineering A364 (2004) 244–248
247
Table 5 Expansion coefficient used for the calculation of internal stress field (10−6 /◦ C) T (◦ C) A1 region
50 10.5
100 11.8
150 12.9
220 13.9
225 −11.7
300 −11.7
325 −11.7
330 15.9
550 16.5
600 16.7
650 16.7
1600 16.7
T (◦ C) A2 region
50 10.5
125 11.8
130 −11.7
200 −11.7
225 −11.7
230 14.7
300 15.4
350 15.9
500 16.5
600 16.7
650 16.7
1600 16.7
T (◦ C) A3 region
50 10.5
100 11.8
150 12.9
200 13.9
250 14.7
300 15.4
350 15.9
400 16.2
550 16.5
600 16.7
650 16.7
1600 16.7
1600 calculated t = 18s
1600
1200
calculated r = 14mm
measured t = 18s measured t = 35s 800
1200
measured r = 0mm
T, 0C
T, 0C
calculated r = 0mm
calculated t = 35s
measured r = 14mm 800
400
0
400
0
5
(a)
10 15 20 25 30 35 40 45 r, mm
0
0
20
(b)
40
60
80 100 120 140 160 t, s
Fig. 3. Comparison of measured and calculated results of temperature fields on the surface of specimen. (a) Temperature fields of hardfacing metal at t = 18 and 35 s (2 and 19 s after welding operation). (b) Temperature history at r = 0 (the center of hardfacing metal) and r = 14 mm (HAZ). Table 6 Yield strength (σ s ) used for the calculation of internal stress field (MPa) [17] T (◦ C) A1 region
100 2400
225 2400
325 400
550 400
600 0
1600 0
T (◦ C) A2 region
100 2400
130 2400
225 400
550 400
600 0
1600 0
T (◦ C) A3 region
100 1200
300 800
550 650
600 20
1000 0
1600 0
on tendency. There are two peaks of tensile residual stress appeared. One is located in the center of hardfacing metal, and another is in the HAZ near the hardfacing metal. These are just the positions where the cracks being often observed. Then, this procedure can be used for further modeling-calculation of residual stress fields with different features of martensite transformation of hardfacing metal. 3.3. Effect of martensite temperatures of hardfacing metal on residual stress fields
3.2. Residual (internal) stress fields
The change of martensite transformation temperatures will cause the change of the residual stress distribution. As shown in Table 4, the martensite transformation temperature Ms of hardfacing metal welded by using electrode D397 is 345 ◦ C, while, by using cracking-resistant hardfacing electrode with addition of Ni and RE elements, it is 325 ◦ C. The
The calculated residual stress distribution and measured data on the surface of specimen after hardfacing are shown in Fig. 4. It can be seen, that the calculated results of the residual fields is in accordance with the measured ones
600
Calculated
400
Measured
200 0 -200 -400 0
(a)
800 700 600 500 400 300 200 100 0 -100 -200
Calculated Measured
Stress ,MPa
Stress, MPa
800
5
10 15 20 25 30 35 40 45 r, mm
(b)
0
5
10 15 20 25 30 35 40 45 r, mm
Fig. 4. Comparison of measured and calculated results of residual stress distribution. (a) Radial stress and (b) tangential stress.
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Q.X. Yang et al. / Materials Science and Engineering A364 (2004) 244–248
(a)
Ms = 345 °C Ms = 335 °C Ms = 325 °C Ms = 315 °C
t = 180s
Ms = 345 °C Ms = 335 °C Ms = 325 °C Ms = 315 °C
900 700 Stress,MPa
Stress,MPa
1100 800 700 600 500 400 300 200 100 0 -100 -200 0
500 300 100
-100 5 10 15 20 25 30 35 40 45 r,mm
-300 0
(b)
5 10 15 20 25 30 35 40 45 r,mm
Fig. 5. Residual stress fields on the surface of specimen with different Ms temperatures of welding metal. (a) Radial stress and (b) tangential stress.
residual stress field calculations by using these data, as well as other two values of Ms , 335 and 315 ◦ C, have been carried out and are given in Fig. 5. It can be seen, with the lowering of Ms of hardfacing metal, the peak values of tensile residual stress at dangerous positions reduce. When Ms is equal to 315 ◦ C, the residual tensile stress in the center of hardfacing metal even becomes compressive, which is considered to be benefit to avoid the occurrence of cracks. This fact should be another important reason for the different cracking behaviors of specimens welded by using electrode D397 and cracking-resistant electrode and should be taken into account during the chemical composition design of the electrode. 4. Conclusions 1. The calculated results of temperature and residual stress field of hardfaced specimen are in accordance with the experimental data, which proves that the proposed procedures are correct. 2. Two peak values of tensile residual stress appear on the surface of the specimen. One is located in the center of hardfacing metal and another is located in the HAZ near hardfacing metal. 3. With the lowering of the martensite transformation temperature Ms , the peak values of tensile residual stress at dangerous positions reduce, which is considered to be benefit to avoid the occurrence of cold cracks.
References [1] S. Kumar, D.P. Moudal, H.K. Khaira, A.K. Jha, J. Mater. Eng. Perform. 8 (6) (1999) 711–715. [2] J.-K. Kim, S.-J. Kim, Wear 237 (2) (2000) 217–222. [3] R. Dasgupta, B.K. Prasad, A.K. Jha, Mater. Transact. 39 (12) (1998) 1191–1196. [4] D. Uwer, H. Hohne, Schweissen und Schneiden 43 (4) (1991) E66– E69. [5] S. Christov, M. Lozev, Fiziko-khimicheskaya Mekhanika Materialov 28 (2) (1992) 44–50. [6] Y. Arai, M. Kikuchi, T. Watanabe, Int. J. Press. Vessels Piping 63 (3) (1995) 237–248. [7] L. Wikander, L.N. Karlsson, Mater. Sci. Eng. 22 (4) (1994) 845– 864. [8] J.B. Roelens, Weld. Res. Abroad 42 (8) (1996) 17–24. [9] M. Mochizuki, N. Satiti, H. Vozumi, Transact. Japan Soc. Mech. Eng. Part A 62 (595) (1996) 808–813. [10] Q.X. Yang, X.J. Ren, M. Yao, J. Rare Earths 16 (4) (1998) 295. [11] Q.X. Yang, A.R. Wang, M. Yao, Welding Technol. (China) 1997;(12):29. [12] B.M. Dimuqiake, Calculation Handbook of Heating Furnace and Heat Treatment Furnace, Mechanical Industry Publisher, Beijing, 1989, p. 102. [13] Editorial Committee of Practical Handbook of Engineering Materials, Practical Handbook of Engineering Materials, Chinese Standard Publisher, 1988, p. 78. [14] F.H. Wohlbier, Trans. Tech. Pub, Ohio, 1975–1978. [15] Y.S. Touloudian, Thermo-physical Properties of Matter, Plenum, NewYork, 1970–1975. [16] K. Easterling, Introduction of Welding Physical Metallurgy, Mechanical Industry Publisher, Beijing, 1989, p. 45. [17] Z. Liu, Z.J. Wu, Numerical Simulation of Heat Treatment Process, Science Publisher, Beijing, 1996, p. 66.
Numerical simulation on residual stress distribution of hard-face-welded steel specimens with martensite transformation Qing Xiang Yang a,∗ , Mei Yao a , Joongkeun Park b b
a College of Materials Science and Engineering, Yanshan University, Qinhuangdao, Hebei 066004, PR China Department of Materials Science and Engineering, Korea Advanced Institute of Science and Technology, Taejon 305-701, South Korea
Received 13 February 2003; received in revised form 8 August 2003
Abstract FEM models are established for calculations of the temperature fields during cooling and the internal stress field of a medium–high carbon steel specimen after hard-face-welding (hardfacing) by using an electrode with lower carbon content. The martensite transformations in both welded metal and matrix are considered in the model for calculation of the internal stress field. The validity of these models was verified by the experimental results of temperature field, as well as the residual (internal) stress field, determined at the surface of the specimen. Based on the calculated results, the effect of martensite transformation points on the residual stress fields is analyzed. © 2003 Elsevier B.V. All rights reserved. Keywords: Numerical simulation; Residual stress; Hard-facing metal; Martensitic transformation; Medium–high carbon steel
1. Introduction Hard-face-welding (hardfacing) is a technique widely used for the repairing of damaged metal parts made of medium–high/high carbon steels, such as mill rollers, tools and dies [1–3]. These steels, as well as the hardfaced metal, normally have carbon content higher than 0.50% and contain Cr, Mo, V and other alloying elements. After hardfacing, in the welding metal and the heat-affected zone (HAZ) of specimen, there often occurs martensite with high hardness, which is quite sensitive to formation of cold crack. The most effective technological measures for prevention of crack formation are the pre-heating and the afterward re-heat-treatments, which, however, are quite inconvenient or even impossible in some cases. Then, it is of great significance to investigate new kinds of electrode, by using that, the hardfacing can be carried out without or with low temperature pre-heating, as well as without or with simple afterward heat-treatments. The formation of cold cracks during welding is in general a function of three main factors that are the formation of martensite with high hardness, the existence of hydrogen ∗ Corresponding author. Tel.: +86-335-805-5593; fax: +86-335-805-7075. E-mail address: [email protected] (Q.X. Yang).
0921-5093/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2003.08.024
and the occurrence of tensile residual stress [4]. The existence of hydrogen can be limited by baking the electrodes. The sensitivity of martensite to crack formation is mainly dependent on its carbon content, which will not be changed in matrix metal during welding, but, in welding metal, it can be controlled by adjusting the chemical compositions of used electrode [5]. Nevertheless, the carbon content in welding metal should be kept on a needed level to guarantee the wear resistance of the hardfacing layer. Another factor influencing the crack formation is the occurrence of tensile residual stress after welding [6]. The residual stress at room temperature after welding is the retained internal stress, which occurs due to the non-simultaneity of temperature change and phase transformation at different sites of specimen during cooling. Upon cooling after hardfacing, the metal is shrunk due to the temperature lowering; while, austenite is slightly denser than martensite, and therefore, during the phase transformation, there is a net volume increase. Then, the formation of the internal stress, as well as the residual stress, should be able to be adjusted by adjusting the martensite transformation in the welding metal, which is dependent mainly to the chemical compositions of welding metal. The direct measurement of temperature during cooling is quite difficult and the direct measurement of internal stress is simply impossible, so the investigation of the temperature fields, as well as the internal/residual stress
Q.X. Yang et al. / Materials Science and Engineering A364 (2004) 244–248
fields during hardfacing is a complex problem and has not been deeply studied. Recently, some attempts are carried out to calculate the temperature and the internal stress fields by FEM [7–9], which should be an effective technique to resolve above-mentioned problem. In this paper, a numerical simulation to calculate the internal and residual stress distributions on simplified hardfacing specimens is carried out and the calculated results are verified by some experimental data; and then, the effect of martensite transformation is discussed. The results of this paper are important for the chemical composition design of new types of hardfacing electrode, which can be used under simplified pre-heating and afterward heat-treatment procedures.
245
Table 2 Parameters for residual stress determining by X-ray method Parameter’s name
Parameter
Target material Tube volume (kV) Tube current (mA) Diffraction crystal plane 2θ scanning angle Numbering time (s) Stress parameter (MPa per degree) Stress determining method
CrKa 25 5 (211)α 0.1◦ 1 −318 Fixing method
2. Experimental and calculation procedures Specimens used for testing and calculations were made of hot roller steel 60CrMnMo with chemical compositions given in Table 1. The dimensions of specimens are 90 mm × 90 mm × 24 mm. A small hole with diameter of 22 mm and depth of 2 mm was machined in the center of the upper face of the specimens. A commercial electrode marked D397 and a specially designed cracking-resistant electrode adding RE (rare earth) and Ni were adopted to fill the small hole by using arc-welding technology. The chemical compositions of the hardfacing metals by using different electrodes are determined beforehand and are also given in Table 1. The hardfacing were carried out with electric current of 100 A. In all cases, the operating time is 16 s. After the operation, the temperature fields around the welding point during cooling process were measured at given moments by using an infrared thermo-vision analyzer of type 780. After cooling to the room temperature, it has been found that at the specimen, hardfaced by using electrode D397, both the hot cracks (in the middle region of the hardfacing metal) and the cold cracks (near the boundary of the hardfacing metal and the HAZ of matrix metal) were observed [10], while at the specimen hardfaced by using cracking-resistant electrode, no cracking has been detected [11]. For specimens with cracks, there is nonsense to study the residual stress field, then the determination of residual stress only carried out on the specimen hardfaced by using the cracking-resistant electrode. The residual stress field was determined by an X-ray residual stress analyzer of type AST × 2001 and the parameters for determining the residual stress are listed in Table 2. The experimental data of temperature and residual stress fields
Fig. 1. Mesh division.
were used to verify the calculated results. The numerical simulations of temperature and internal stress fields are carried out by using a commercial software ANSYS for FEM calculation. Because of little effect of temperature on the sides of specimen, the square specimen can be simplified to the disc one with diameter equal to the side length of square specimen. In this case, the temperature and internal stress fields can be treated as the axial symmetry ones. The FEM mesh division is given in Fig. 1 (241 elements are divided and 263 nodes are formed), in which the hardfacing region is shown by dotted lines. During calculation, some thermo-physical and mechanical parameters were supposed as constant: the density, ρ = 7.85×10−6 kg/mm3 ; the elastic modulus, E = 2×105 MPa and the Poisson’s ratio, ν = 0.3. Other parameters [12–16] are given in Table 3, in which, the exchanging coefficient (α) is calculated by following equation [17]: α = 2.2(Tw − Tc )0.25 + 4.6 × 10−8 (Tw2 + Tc2 )(Tw + Tc ) (1)
Table 1 Chemical compositions of matrix steel and hardfacing metal (wt.%) Materials
C
Cr
Mn
Mo
Ni
Si
S
P
RE
60CrMnMo Hard-facing metal when the electrode D397 is used Hard-facing metal when the cracking-resistant electrode is used
0.64 0.57 0.54
1.04 1.95 1.80
1.88 2.36 1.10
0.22 0.66 0.52
– – 1.70
0.33 0.54 0.64
0.038 0.035 0.032
0.016 0.04 0.03
– – 0.085
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Q.X. Yang et al. / Materials Science and Engineering A364 (2004) 244–248
Table 3 Thermo-physical and mechanical parameters of 60CrMnMo steel used for FEM calculation [12–16] Temperature (◦ C)
Parameter
Thermal conduction coefficient (λ) (×10−3 W/mm ◦ C) Average heat capacity (c) (×10−3 J/kg ◦ C) Specific enthalpy (H) (×103 J/kg) Exchanging coefficient (α) (×10−6 W/mm2 ◦ C)
200
400
600
800
1000
1200
1400
1600
41.9 0.502 100 18.85
39.4 0.536 214 33.44
32.3 0.586 352 55.95
29.1 0.695 557 88.92
26.5 0.674 674 134.6
29.4 0.670 804 195.4
29.4 0.670 804 273.4
29.4 0.670 804 370.9
Fig. 2. Region division for internal stress field calculation. A1, hardfacing metal; A2, HAZ; A3, matrix steel 60CrMnMo.
where Tw is temperature of specimen and Tc is that of environment. During calculation of internal stress field, the martensite transformations in specimen were taken into account. Based on the features of phase transformation, the whole specimen can be divided into three regions: the hardfacing metal region (A1), in which the martensite transformation occurs at higher temperature; the HAZ (A2) near the hardfacing metal with pick temperature higher than AC3 , in which the martensite transformation occurs at lower temperature and the zone of matrix (A3) far from hardfacing metal with temperature lower than AC3 , in which the martensite transformation dose not occur. During calculations of internal stress field, the different features of these three regions should be considered comprehensively. According to the calculated results of temperature field, the dimensions of heat-affected zone can be determined. A simplified division of these three regions is shown in Fig. 2. The martensite transformation temperatures Ms and Mf of matrix steel 60CrMnMo, as well as those of hardfacing metals, were determined by using tangent method from
the dilatometric curves obtained on a high speed automatic dilatometer of type Formaster-D and are given in Table 4. It can be seen, the heating temperature has little effect on the martensite temperatures, especially higher than 1000 ◦ C. In this work, the martensite temperatures determined after heating at 1000 ◦ C were used for internal stress field calculation. The expansion coefficients needed for calculations can also be obtained based on the dilatometric curves and are listed in Table 5. The internal stress field induced during cooling after hardfacing is also related to the yield strengths (σ s ) of the matrix and hardfacing metal. It is assumed [17] that the steel becomes ideal-plastic (σ s gets to zero) when the temperature is higher than 600 ◦ C. When the temperature is lower than that, the σ s increases with the decrease of temperature. In regions A1 and A2, when the austenite–martensite phase transformation occurs, the yield strength will be changed sharply and increase with the transformed amount of martensite. The values of yield strength of these three regions used for calculations of internal stress fields are given in Table 6.
3. Results and analyses 3.1. Temperature fields Comparisons between measured and calculated results of temperature fields on the surface of hardfaced specimen are shown in Fig. 3. Fig. 3(a) shows the temperature fields of hardfacing metal at t = 18 and 35 s (2 and 19 s after welding operation) and Fig. 3(b) shows the temperature history at r = 0 (the center of hardfacing metal) and r = 14 mm (HAZ). It can be seen, that there are little differences between the measured and the calculated results. This fact indicates that the model used for temperature field calculations is correct and obtained results can be used for further calculation of internal stress field of specimens after hardfacing.
Table 4 Martensite transformation temperatures of different materials Materials (◦ C)
Steel 60CrMnMo
T Ms Mf
800 230 135
1000 225 130
1200 215 125
Hard-facing metal welded by using electrode
Hard-facing metal welded by high cracking resistance with RE and Ni
800 348 232
800 330 228
1000 345 225
1200 338 225
1000 325 223
1200 322 160
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Table 5 Expansion coefficient used for the calculation of internal stress field (10−6 /◦ C) T (◦ C) A1 region
50 10.5
100 11.8
150 12.9
220 13.9
225 −11.7
300 −11.7
325 −11.7
330 15.9
550 16.5
600 16.7
650 16.7
1600 16.7
T (◦ C) A2 region
50 10.5
125 11.8
130 −11.7
200 −11.7
225 −11.7
230 14.7
300 15.4
350 15.9
500 16.5
600 16.7
650 16.7
1600 16.7
T (◦ C) A3 region
50 10.5
100 11.8
150 12.9
200 13.9
250 14.7
300 15.4
350 15.9
400 16.2
550 16.5
600 16.7
650 16.7
1600 16.7
1600 calculated t = 18s
1600
1200
calculated r = 14mm
measured t = 18s measured t = 35s 800
1200
measured r = 0mm
T, 0C
T, 0C
calculated r = 0mm
calculated t = 35s
measured r = 14mm 800
400
0
400
0
5
(a)
10 15 20 25 30 35 40 45 r, mm
0
0
20
(b)
40
60
80 100 120 140 160 t, s
Fig. 3. Comparison of measured and calculated results of temperature fields on the surface of specimen. (a) Temperature fields of hardfacing metal at t = 18 and 35 s (2 and 19 s after welding operation). (b) Temperature history at r = 0 (the center of hardfacing metal) and r = 14 mm (HAZ). Table 6 Yield strength (σ s ) used for the calculation of internal stress field (MPa) [17] T (◦ C) A1 region
100 2400
225 2400
325 400
550 400
600 0
1600 0
T (◦ C) A2 region
100 2400
130 2400
225 400
550 400
600 0
1600 0
T (◦ C) A3 region
100 1200
300 800
550 650
600 20
1000 0
1600 0
on tendency. There are two peaks of tensile residual stress appeared. One is located in the center of hardfacing metal, and another is in the HAZ near the hardfacing metal. These are just the positions where the cracks being often observed. Then, this procedure can be used for further modeling-calculation of residual stress fields with different features of martensite transformation of hardfacing metal. 3.3. Effect of martensite temperatures of hardfacing metal on residual stress fields
3.2. Residual (internal) stress fields
The change of martensite transformation temperatures will cause the change of the residual stress distribution. As shown in Table 4, the martensite transformation temperature Ms of hardfacing metal welded by using electrode D397 is 345 ◦ C, while, by using cracking-resistant hardfacing electrode with addition of Ni and RE elements, it is 325 ◦ C. The
The calculated residual stress distribution and measured data on the surface of specimen after hardfacing are shown in Fig. 4. It can be seen, that the calculated results of the residual fields is in accordance with the measured ones
600
Calculated
400
Measured
200 0 -200 -400 0
(a)
800 700 600 500 400 300 200 100 0 -100 -200
Calculated Measured
Stress ,MPa
Stress, MPa
800
5
10 15 20 25 30 35 40 45 r, mm
(b)
0
5
10 15 20 25 30 35 40 45 r, mm
Fig. 4. Comparison of measured and calculated results of residual stress distribution. (a) Radial stress and (b) tangential stress.
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Q.X. Yang et al. / Materials Science and Engineering A364 (2004) 244–248
(a)
Ms = 345 °C Ms = 335 °C Ms = 325 °C Ms = 315 °C
t = 180s
Ms = 345 °C Ms = 335 °C Ms = 325 °C Ms = 315 °C
900 700 Stress,MPa
Stress,MPa
1100 800 700 600 500 400 300 200 100 0 -100 -200 0
500 300 100
-100 5 10 15 20 25 30 35 40 45 r,mm
-300 0
(b)
5 10 15 20 25 30 35 40 45 r,mm
Fig. 5. Residual stress fields on the surface of specimen with different Ms temperatures of welding metal. (a) Radial stress and (b) tangential stress.
residual stress field calculations by using these data, as well as other two values of Ms , 335 and 315 ◦ C, have been carried out and are given in Fig. 5. It can be seen, with the lowering of Ms of hardfacing metal, the peak values of tensile residual stress at dangerous positions reduce. When Ms is equal to 315 ◦ C, the residual tensile stress in the center of hardfacing metal even becomes compressive, which is considered to be benefit to avoid the occurrence of cracks. This fact should be another important reason for the different cracking behaviors of specimens welded by using electrode D397 and cracking-resistant electrode and should be taken into account during the chemical composition design of the electrode. 4. Conclusions 1. The calculated results of temperature and residual stress field of hardfaced specimen are in accordance with the experimental data, which proves that the proposed procedures are correct. 2. Two peak values of tensile residual stress appear on the surface of the specimen. One is located in the center of hardfacing metal and another is located in the HAZ near hardfacing metal. 3. With the lowering of the martensite transformation temperature Ms , the peak values of tensile residual stress at dangerous positions reduce, which is considered to be benefit to avoid the occurrence of cold cracks.
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