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Effect of hardness to fracture toughness for spot welded steel sheets
Materials & Design Materials and Design 27 (2006) 21–30 www.elsevier.com/locate/matdes
Effect of hardness to fracture toughness for spot welded steel sheets Ibrahim Sevim
*
Department of Mechanical Engineering, Engineering Faculty, Mersin University, 33343 Ciftlikkoy, Mersin, Turkey Received 30 March 2004; accepted 9 September 2004 Available online 2 November 2004
Abstract The hardness of the spot welded nugget is considered as an important parameter in the computation of stress intensity factors. A novel approach, which employs the hardness of the nugget, is developed to obtain the stress intensity factors. The results are compared with the previous results on the computation of stress intensity factors. 2004 Elsevier Ltd. All rights reserved. Keywords: Stress intensity factor for spot weld; Fracture toughness; Vickers hardness; Crack length; Strain energy release rate
1. Introduction Spot welding is widely used in joining metal sheets. This technique is commonly used in automotive industry and for manufacturing house appliances due to its high efficiency in manufacturing thin metal sheets. A wide variety of metal sheets up to 3 mm thickness can be handled by the spot welding method. Spot welded materials may be exposed to different forces. Factors, such as, shear stress on resistance spot welding zone, sheet thickness, multi welding and the width of the welding zone are important parameters that affect fatigue life. Fatigue life for a spot weld is often expressed in terms of stress density, or stress intensity factor. These quantities are used to predict fatigue life of resistance spot welding. In order to determine fracture parameters, such as, notch stress on spot-welded joints, stress intensity factor, and J-integral, fracture mechanics is employed. In his review on spot welding Davidson [1] quotes works on stress density performed by Kan [2], and Wilson and Fine [3]. Kan [2], used the finite element method to obtain stress density at the elastic-plastic
*
Tel.: +90 324 361 0033; fax: +90 324 361 0032. E-mail address: [email protected].
0261-3069/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.matdes.2004.09.008
stress zone under the influence of variable shear loads. Wilson and Fine [3], defined stress density around the spot weld by relating stress density and spot welding fatigue of the smooth samples used in Neuber analysis. Pan and Sheppard [4], discussed the formation of capillary cracks and tried to estimate the stress intensity factors for these capillary cracks. Darwish et al. [5], investigated the variation of welding current, electrode force, and weld application time with failure rate. Chang et al. [6], investigated the hardness of metal, heat effect zone, spot welding and the adhesive layer for lap joint welding. For spot welded joints, the linear fracture mechanical approach is used [7]. In fracture mechanics, the stress intensity at the tip of sharp crack is expressed through stress intensity factors. The fracture mechanics theory is used to estimate stress intensity factors for spot weld joints under shear-tensile stress. The details of this method are given in Section 2. The formation of a crack at the spot weld is related to the nugget structure. Chandel and Garber [8] estimated weld strength in terms of weld current and current cycle for spot welds of different microstructures. For spot welded zinc coated HSLA steel, Zuniga and Sheppard [9] stated that both rupture stress and yield stress of the zone exposed to heat are dependent on the hardness.
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I. Sevim / Materials and Design 27 (2006) 21–30
In this paper, we discuss fracture mechanics briefly in Section 2. Section 3 describes the experimental work. In Section 4, the data from the experiment are used to validate the new formulation and the results are discussed. The last section is devoted to conclusions and discussions.
stress intensity factor equations for spot weld using the equations for elliptical relations given in [11,12]: " 0:397 # F D KI ¼ ; ð1Þ 0:341 3=2 t ðD=2Þ K II ¼
2. Fracture mechanics approach The fracture of a material is studied in three different modes [10]. These are opening mode, sliding mode, and tearing mode, (Fig. 1) with associated intensity factors, where KI, KII, KIII, respectively. Fracture mechanics analysis is necessary in assessments of fatigue strength and fatigue life predictions of spot-welded joints and structures. The typical loading condition of tensile-shear (Fig. 2) is considered here which corresponds directly to commonly used test specimens for fatigue life predictions of spot-welded joints and structures. The main purpose in fracture mechanics analysis is to determine fracture parameters such as notch stress, stress intensity factors and J-integral on spot-weld. Pook [11] was the first to study the numerical computation of stress intensity factors for spot weld. Pook [11] analyzed fatigue behavior at the spot weld in a fracture mechanics framework based on the stress intensity factor equations. Pook developed the following
"
F ðD=2Þ
3=2
0:710 # D 0:282 þ 0:162 ; t
ð2Þ
where F is the applied load per spot weld, D is the weld diameter, t is the sheet thickness. Radaj [12] used fatigue-strength approach for local stresses at spot-weld joints. Zhang [13–15] studied the spot weld joints between sheets of dissimilar materials and different thickness. He found the relations between the J-integrals and stress intensity factors for sheets of either the same thickness or different thickness. He offers equations to compute the stress intensity factors for spot welds of dissimilar materials. pffiffiffi 3F pffi ; KI ¼ ð3Þ 2pD t 2F pffi ; pD t pffiffiffi 2F pffi : ¼ pD t
K II ¼
ð4Þ
K III
ð5Þ
The total energy release rate in combined mode cracking can easily be obtained by adding the energies from the different modes i.e. [16] 1 m2 K 2III 2 2 K I þ K II þ ; G ¼ J ¼ GI þ GII þ GIII ¼ E 1m ð6Þ
Fig. 1. The three modes of fracture: KI, opening mode; KII, sliding mode; KIII, tearing mode [10].
where KI, KII and KIII are stress intensity factors for modes I, II and III as shown in Fig. 3. There are few works on the relation between the hardness and the shear-tensile stress for spot welded joints. Zhou et al. [17] gave the following
Fig. 2. The spot welded experiment sample prepared according to mode II [19,20].
I. Sevim / Materials and Design 27 (2006) 21–30
Using (3)–(5) and (11), we obtain the following modified expressions for stress intensity factors, KI, KII and KIII pffiffiffi 3C D pffi ; KI ¼ ð12Þ 8H t
Fig. 3. Tensile loading of the spot-welded part [20].
H ¼ cry ;
23
ð7Þ C D pffi ; 2H t pffiffiffi 2C D pffi ; ¼ 4H t
where ry is the yield strength and c is a constant. Zuniga and Sheppard [9] perform experiments on a zinc-coated HSLA steel using the simulated heat effect zone samples, and suggested the following relationship for zinc-coated HSLA:
K II ¼
ð13Þ
K III
ð14Þ
ry ¼ 14:7 þ 2:568H ;
ð8Þ
ruts ¼ 65:8 þ 2:563H ;
ð9Þ
where C, H, D, and t are, respectively, the positive shear stress coefficient introduced in (11), the average Vickers hardness of the nugget, the nugget diameter, and sheet thickness.
where ruts is the ultimate strength, and H is Vickers hardness. Voort [18] gave the following equation for tensile stress TS n2 H 12:5ðn 2Þ ½1 ðn 2Þ TS ¼ ; ð10Þ 2:9 1 ðn 2Þ where H is Vickers hardness and n is Meyer strain-hardening coefficient. We suggest the following relation for spot welded joints (Fig. 4) fs ¼
4F ¼ CH 1 pD2
ð11Þ
where F is the load at failure, D is weld diameter, C is a positive constant, H is the average Vickers hardness and fs is the shear stress at the weld nugget material. We will refer to C as the shear stress coefficient.
5000 5500 6000 6500 500 Coefficient of Correlation 450
7000
3. Experimental work Resistance spot welded joints may be exposed to stress under tensile-shear conditions. The experiment is designed to determine the relation for the variation of the fracture toughness, KIC, KIIC, KIIIC, with the Vickers hardness, H, of the welding zone. The crack lengths, aIC, aIIC, aIIIC, can be computed using (21). 3.1. Materials The 1010, 1030, 1040, 1050 and 50 CrV4 steel sheets of 3 mm thickness are used in the experiment. The chemical properties of these steels are listed in Table 1.
7500
8000
8500
9500 10000 500
Materials Pair 50CrV4-1010
R f = 0.80 s
450
50CrV4-1030
400
Tensile-Shear Stress, fs ,(MPa)
9000
50CrV4-1040 50CrV4-1050
350 300
fs=1562443. H
-1
400 350 300
250
250
200
200
150
150
100
100
50
50
0 5000
5500
6000
6500
7000
7500
8000
8500
9000
0 9500 10000
Vickers Hardness, H (MPa) Fig. 4. Tensile-shear stress, fs versus Vickers hardness, H.
24
I. Sevim / Materials and Design 27 (2006) 21–30
Table 1 The chemical compositions of experiment sample (wt%) Alloys
C (%)
Si (%)
Mn (%)
P (%)
S (%)
Cr (%)
Mo (%)
Ni (%)
Al (%)
Cu (%)
Ti (%)
V (%)
1010 1030 1040 1050 50CrV4
0.107 0.328 0.402 0.506 0.523
0.11 0.069 0.247 0.252 0.394
0.413 0.673 0.82 0.654 0.915
0.019 0.015 0.012 0.014 0.021
0.025 0.019 0.028 0.006 0.027
– – 0.025 0.251 0.917
0.003 0.001 0.001 0.002 0.025
– – 0.003 – 0.034
0.032 – 0.014 0.006 –
0.031 0.037 0.032 0.017 0.183
0.002 0.002 0.001 0.002 –
– 0.005 0.003 0.006 0.095
3.2. Shape and dimensions of a weld-bonded lap joint Resistance spot weld is applied to 3 mm thickness 1010, 1030, 1040, 1050 and 50CrV4 steel sheets. The dimensions of the metal sheets and the position of the spot weld are shown in Fig. 2 (DIN 50124 DVS 29.2). These numbers are selected such that the edge effects are minimum, and the fracture should occur at the welding zone in a tensile shear experiment. Also only the tensile-shear force should be effective. 3.3. Spot-welding machine A 180 kV spot welding machine was used in the experiment. The electrodes are made of copper alloy having a spherical tip with a diameter of 16 mm. The electrode for resistance spot welding machine was loaded with a constant 7500 N force in the same direction of the electrode. Welding currents were measured to be 13 and 18 kA. The welding process was performed for 30 welding cycles. Nugget diameter changed in the range 8–13 mm due to changes in the welding current and the properties of the material. 3.4. Instron testing machine The resistance spot welded parts were tested for tensile-shear as shown in Fig. 3. Tensile-shear force was the maximum rupture force value read on the testing machine scale. During the tensile experiment, all parts were at constant speed of 7 mm/s. The welded surface of the material has the chemical properties given in Table 2. 3.5. The computation of fracture toughness of spot-welded steel sheets The rupture force for the welded parts was determined by the data from the tensile-shear force experi-
ment. From the welding zones of the ruptured parts, the nugget diameters were measured. The diameters were measured three times and the arithmetical mean of these three measurements is assigned as the nugget diameter. For the case in Figs. 2 and 3, (1)–(5), and (12)–(14) are used to calculate the fracture toughness, KIC, KIIC, KIIIC, according to Modes I, II, III. 3.6. Hardness analysis of heat affected zone of the spot weld The heat effected zone of the spot weld was etched using abrasive papers of 80–1200 mesh, and then 0.3 lm diamond paste. The Vickers hardness of the surface was measured at every 0.5 mm under the load 98.0665 N. The standard deviations and arithmetic means of the measured data were computed, and the results were combined to obtain a hardness value for the ruptured samples.
4. Results and discussion The stress intensity factors are calculated using (12)– (14) from the experimental data for the parts shown in Figs. 2 and 3. For comparison, the same quantities are calculated using (1)–(5). Some selected data are given in Table 3. It is clear from Table 3 that the differences (DF) are considerably high. This is true for other approach detailed in the literature [13]. The fracture toughness values computed using (3)–(5) are closer (18%) to the computed values using (12)–(14) (Table 3). We believe that the difference comes from measurement errors for nugget hardness. The results in Table 3 are demonstrated graphically in Figs. 5–7, 9 and 11. The graphs are generated using the curve fitting technique via the least squares method [21] (see Fig. 8 , 10 and 12).
Table 2 The chemical compositions of welding zone (wt%) Alloys
C (%)
Si (%)
Mn (%)
P (%)
S (%)
Cr (%)
Mo (%)
Ni (%)
Al (%)
Cu (%)
Ti (%)
V (%)
50CrV4-1010 50CrV4-1030 50CrV4-1040 50CrV4-1050
0.315 0.425 0.463 0.514
0.252 0.231 0.321 0.323
0.665 0.794 0.868 0.784
0.020 0.018 0.017 0.018
0.026 0.023 0.028 0.017
0.458 0.458 0.471 0.584
0.014 0.013 0.013 0.014
0.017 0.017 0.019 0.017
0.016 – 0.007 0.003
0.10 0.11 0. 108 0.1
0. 001 0. 001 0.004 0. 001
0.05 0.05 0.049 0.050
Table 3 Computed fracture toughness (KIC, KIIC, KIIIC) values based on the (1)–(5) and (12)–(14), and the differences (DF = K(1 5) K(12 14)) Materials pair
Estimated using Eqs. (1), (2)
Estimated using Eqs. (3)–(5)
Estimated using Eqs. (12)–(14)
Rupture force, F (kN)
Nugget diameter, D (mm)
Sheet thickness, t (mm)
Hardness, Hv (MPa)
KIC (MPa m1/2)
KIIC (MPa m1/2)
KIIIC (MPa m1/2)
KIC (MPa m1/2)
KIIC (MPa m1/2)
KIIIC (MPa m1/2)
KIC (MPa m1/2)
KIIC (MPa m1/2)
KIIIC (MPa m1/2)
21,850 21,580 16,818 19,613 19,123 17,044 18,152 18,090 19,700 18,829 19,152 17,083 18,700 22,050 18,633 16,279 13,882 12,490 14,960 14,300
11 11 8.5 8.3 10 9 10.5 9.8 11 11 11.5 11 11 11.8 11 9.6 9 8.5 10 9
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
6404 6404 6374 5246 6374 6610 7325 6815 7060 7531 7570 8100 7570 6835 7060 8129 8129 8482 8433 7845
30.62 30.24 31.33 37.50 29.77 29.80 26.78 28.80 27.61 26.39 25.56 23.94 26.21 28.60 26.11 26.51 24.27 23.26 23.29 25.01
36.93 36.47 37.71 45.16 35.84 35.87 32.26 34.66 33.29 31.82 30.85 28.87 31.60 34.55 31.49 31.91 29.21 28.00 28.04 30.09
– – – – – – – – – – – – – – – – – – – –
10.00 9.87 9.95 11.89 9.62 9.53 8.70 9.29 9.01 8.61 8.38 7.81 8.55 9.40 8.52 8.53 7.76 7.39 7.52 7.99
23.08 22.80 22.99 27.46 22.22 22.01 20.09 21.45 20.81 19.89 19.35 18.05 19.75 21.71 19.68 19.70 17.92 17.07 17.38 18.46
16.32 16.12 16.25 19.41 15.71 15.56 14.20 15.16 14.71 14.06 13.68 12.76 13.96 15.35 13.91 13.93 12.67 12.07 12.29 13.05
10.60 10.60 8.23 9.77 9.68 8.40 8.85 8.88 9.62 9.02 9.38 8.38 8.97 10.66 9.62 7.29 6.83 6.18 7.32 7.08
24.50 24.50 19.01 22.56 22.37 19.42 20.44 20.50 22.22 20.83 21.66 19.36 20.72 24.62 22.22 16.84 15.78 14.29 16.91 16.36
17.32 17.32 13.44 15.95 15.81 13.73 14.45 14.49 15.70 14.72 15.31 13.69 14.65 17.40 15.70 11.90 11.16 10.10 11.95 11.56
DF = Eq. (1) Eq. (12) (MPa m1/2)
DF = Eq. (2) Eq. (13) (MPa m1/2)
DF = Eq. (3) Eq. (12) (MPa m1/2)
DF = Eq. (4) Eq. (13) (MPa m1/2)
DF = Eq. (5) Eq. (14) (MPa m1/2)
20.02 19.64 23.1 27.73 20.09 21.4 17.93 19.92 17.99 17.37 16.18 15.56 17.24 17.94 16.49 19.22 17.44 17.08 15.97 17.93
12.43 11.97 18.7 22.6 13.47 16.45 11.82 14.16 11.07 10.99 9.19 9.51 10.88 9.93 9.27 15.07 13.43 13.71 11.13 13.73
–0.6 0.73 1.72 2.12 0.06 1.13 0.15 0.41 0.61 0.41 –1 0.57 0.42 1.26 1.1 1.24 0.93 1.21 0.2 0.91
1.42 1.7 3.98 4.9 0.15 2.59 0.35 0.95 1.41 –0.94 2.31 1.31 0.97 2.91 2.54 2.86 2.14 2.78 0.47 2.1
1 1.2 2.81 3.46 0.1 1.83 0.25 0.67 0.99 –0.66 1.63 0.93 0.69 2.05 1.79 2.03 1.51 1.97 0.34 1.49
I. Sevim / Materials and Design 27 (2006) 21–30
50CrV4-1010 50CrV4-1010 50CrV4-1010 50CrV4-1010 50CrV4-1010 50CrV4-1030 50CrV4-1030 50CrV4-1030 50CrV4-1030 50CrV4-1030 50CrV4-1040 50CrV4-1040 50CrV4-1040 50CrV4-1040 50CrV4-1040 50CrV4-1050 50CrV4-1050 50CrV4-1050 50CrV4-1050 50CrV4-1050
Measured data
25
26
I. Sevim / Materials and Design 27 (2006) 21–30 5000 5500 6000 6500 20 Coefficient of Correlation 18 R K = 0.80
7000
7500
8000
8500
9000
50CrV4-101 0
IC
Fracture Toughness KIC, (MPa.m1/2)
9500 10000 20
Materials Pair 50CrV4-103 0
16
50CrV4-104 0
K IC=63840 .H
14
-1
50CrV4-105 0
18 16 14
12
12
10
10
8
8
6
6
4
4
2
2
0 5000
5500
6000
6500
7000
7500
8000
8500
9000
0 9500 10000
Vickers Hardness, H (MPa) Fig. 5. According to (12); fracture toughness, KIC, versus Vickers hardness, H.
Fracture Toughness KIIC, (MPa.m1/2)
5000 5500 6000 6500 40 Coefficient of Correlation R K = 0.80 36 IIC
7000
32
7500
8000
K IIC =147 44 0.H
8500
9000
9500 10000 40 Materials Pair 36 50CrV4-1010
50CrV4-1030
-1
50CrV4-1040 50CrV4-1050
28
32 28
24
24
20
20
16
16
12
12
8
8
4
4
0 5000
5500
6000
6500
7000
7500
8000
8500
9000
0 9500 10000
Vickers Hardness H, (MPa) Fig. 6. According to (13); fracture toughness, KIIC, versus Vickers hardness, H.
The following equations are obtained by curve fitting in Figs. 5–7:
K III P K IIIC :
ð16cÞ
K IC ¼ 63840H 1 ;
ð15aÞ
The following expressions for KI, KII and KIII are used:
K IIC ¼ 147440H 1 ;
ð15bÞ
pffiffiffiffiffiffiffiffiffi K I ¼ s paIC ;
ð17aÞ
K IIIC ¼ 104240H 1 :
ð15cÞ
pffiffiffiffiffiffiffiffiffiffi K II ¼ s paIIC ;
ð17bÞ
pffiffiffiffiffiffiffiffiffiffiffiffi K III ¼ s paIIIC ;
ð17cÞ
The fracture of a spot weld occurs when the following conditions are satisfied [20]: K I P K IC ;
ð16aÞ
K II P K IIC ;
ð16bÞ
where s is the applied shear stress, and aIC, aIIC, aIIIC are crack lengths parallel to the fracture axis in the heat affected zone.
I. Sevim / Materials and Design 27 (2006) 21–30 5000 5500 6000 6500 30 Coefficient of Correlation R K = 0.80 27
7000
7500
8000
8500
9000
9500 10000 30
Materials Pair 50CrV4-1010
IIIC
Fracture ToughnessKIIIC, (MPa.m1/2)
27
50CrV4-1030
24
K IIIC =104 240 .H
-1
50CrV4-1040 50CrV4-1050
21
27 24 21
18
18
15
15
12
12
9
9
6
6
3
3
0 5000
5500
6000
6500
7000
7500
8000
8500
9000
0 9500 10000
Vickers Hardness H, (MPa)
Strain Energy Release Rate GC, (MPa.m)
Fig. 7. According to (14); fracture toughness, KIIIC, versus Vickers hardness, H.
5000 5500 6000 6500 0.010 Coefficient of Correlation 0.009 R G =0 .80
7000
7500
8000
8500
9000
9500 10000 0.010
Materials Pair 50CrV4-1010
IC
50CrV4-1030
0.008
50CrV4-1040 50CrV4-1050
0.007
0.009 0.008 0.007 0.006
0.006
G C=1826 67. H
0.005
-2
0.005
0.004
0.004
0.003
0.003
0.002
0.002
0.001
0.001
0.000 5000
5500
6000
6500
7000
7500
8000
8500
9000
0.000 9500 10000
Vickers Hardness, H (MPa) Fig. 8. According to (6); strain energy release rate, GC, versus Vickers hardness, H.
Since the plastic deformation takes place during fracture, the applied shear stress, s s ffi syield ;
ð18Þ
where syield is a stress which includes the increase in the yield stress due to deformations in a small region of the spot weld. syield and the hardness H of the material is related by the following. syield ¼ H :
ð19Þ
Using (17), one can obtain the following equations for stress intensity factors pffiffiffiffiffiffiffiffiffi K I ¼ H paIC ; ð20aÞ pffiffiffiffiffiffiffiffiffiffi K II ¼ H paIIC ;
ð20bÞ
pffiffiffiffiffiffiffiffiffiffiffiffi K III ¼ H paIIIC :
ð20cÞ
Substituting (20) into (15), the following equations are obtained: pffiffiffiffiffiffiffiffiffi H paIC ¼ 63840H 1 ; ð21aÞ pffiffiffiffiffiffiffiffiffiffi H paIIC ¼ 147440H 1 ;
ð21bÞ
pffiffiffiffiffiffiffiffiffiffiffiffi H paIIIC ¼ 104240H 1 :
ð21cÞ
Rearranging (21), the following conditions for crack lengths (aIC, aIIC, aIIIC) 2 1 63840 ð22aÞ aIC P p H
28
I. Sevim / Materials and Design 27 (2006) 21–30 5000 50
5500
6000
7000
7500
8000
8500
9000
IC
9500 10000 50
Material Pair 50CrV4-1010
Coefficients of Correlation R K , R K =0.98
45
Fracture Toughness,KIC, KIIC, (MPa.m1/2)
6500
IIC
45
50CrV4-1030
40
50CrV4-1040 50CrV4-1050
35
40 35
30
30
25
25
20
20
15
15
10
K IC=1968 47 .H
-1
K IIC =2373 00 .H
10
-1
5 0 5000
5
5500
6000
6500
7000
7500
8000
8500
0 9500 10000
9000
Vickers Hardness H, (MPa) Fig. 9. According to (1) and (2); fracture toughness, KIC, K
5000 5500 6000 6500 0.040 Coefficient of Correlation 0.036 R G =0 .98
7000
7500
8000
IIC,
8500
Strain Energy vRelease RateGC, (MPa.m)
IIC
versus Vickers hardness, H.
9000
9500 10000 0.040 Materials Pair 0.036 50CrV4-1010 50CrV4-1030
0.032
50CrV4-1040 50CrV4-1050
0.028 0.024
0.032 0.028 0.024
0.020
G C=775534. H
-2
0.020
0.016
0.016
0.012
0.012
0.008
0.008
0.004
0.004
0.000 5000
5500
6000
6500
7000
7500
8000
8500
9000
0.000 9500 10000
Vickers Hardness, H (MPa) Fig. 10. According to (1), (2) and (6); strain energy release rate, GC, versus Vickers hardness, H.
2 1 147440 ; p H
ð22bÞ
2 1 104240 P : p H
ð22cÞ
aIIC P
aIIIC
It is clear from (22) that the crack length becomes smaller as hardness increases. This kind of small cracks may be present at a spot weld under shear-tensile stress or they may be created as soon as the shear-tensile stress is applied to the spot weld [20,22]. It is clear from Figs. 5–7 that the fracture toughness and hardness are inversely proportional to each other
for a spot-welded pair. The variables that affects the microstructure of the welding zone are welding current, the cycle of the current, holding time, the chemical structure of the alloy, and the cooling rate of the weld zone. Different microstructures arise depending on these parameters. Each different structure has its own hardness value. In this study, we used a 50CrV4 metal sheet for the spot weld pair. The hardness at the welding zone takes high values, since an alloy microstructure is formed in the welding zone of a 50CrV4 sheet, and the cooling rate is slower for 50CrV4 alloy [20]. Nugget is the zone where the metal pair melts. That zone has the properties of a die cast structure when it
Fracture Toughness,KIC, KIIC, KIIIC (MPa.m1/2)
I. Sevim / Materials and Design 27 (2006) 21–30 5000 5500 6000 6500 40 Coefficients of Correlation 36 R K , R K , R K = 0. 96 IC
IIC
7000
7500
8000
8500
29
9000
9500 10000 40
Material Pair 50CrV4-1010
IIIC
32 K =63845.H -1 IIC
KIIC=147440.H
-1
KIIIC=104260.H
-1
50CrV4-1040 50CrV4-1050
28
36
50CrV4-1030 32 28
24
24
20
20
16
16
12
12
8
8
4
4
0 5000
5500
6000
6500
7000
7500
8000
8500
0 9500 10000
9000
Vickers Hardness H, (MPa) Fig. 11. According to (3)–(5); fracture toughness, KIC, KIIC, KIIIC, versus Vickers hardness, H.
5000 5500 6000 6500 0.010 Coefficient of Correlation 0.009 R =0 .96
7000
7500
8000
8500
9500 10000 0.010
Materials Pair 50CrV4-1010
GC
Strain Energy Release RateGC, (MPa.m)
9000
50CrV4-1030
0.008
0.009 0.008
50CrV4-1040
0.007
50CrV4-1050
0.006
0.007 0.006
0.005
GC =182666. H
-2
0.005
0.004
0.004
0.003
0.003
0.002
0.002
0.001
0.001
0.000 5000
5500
6000
6500
7000
7500
8000
8500
9000
0.000 9500 10000
Vickers Hardness, H (MPa) Fig. 12. According to (3)–(6); strain energy release rate, GC, versus Vickers hardness, H.
hardens. In this structure; inclusions, incoherent particles and embrittled grain are present. These properties accelerate the crack development, which causes a fracture in spot weld. Garh [23] shows that the fracture toughness reduces while the hardness increases for plastic, ceramic, and metallic alloys. The computed ratio of the stress intensity factors using (1) and (2) is found as KI ¼ 0:83 ð23Þ K II and the ratios using (3)–(5) are as KI K III ¼ 0:433; ¼ 0:707: K II K II
ð24Þ
According to (12)–(14), the ratios are found to be as follows KI K III ¼ 0:433 ¼ 0:707: ð25Þ K II K II Eqs. (3)–(5) give the same values as (12)–(14). Any stress intensity factor for a given mode can easily be computed using (24) or (25) provided that the stress intensity factor for a specific mode is known. For example, if KI is known then it is a simple matter to compute KII and KIII. The correlation coefficient for the values of (1)–(5) is smaller than the correlation coefficient for (12)–(14). This is due to the errors in the measurement for Vickers hardness.
30
I. Sevim / Materials and Design 27 (2006) 21–30
5. Conclusions We offered (12)–(14) to compute fracture toughness for low carbon alloy steel. The computed values are comparable with the values obtained using (3). However, the values obtained from (1) and (2) demonstrate significant differences up to 18%. In (11), we introduce the shear stress coefficient C for spot weld pairs. We calculated, approximately, C = 1.56 · 106 (MPa)2 for low carbon alloy steels (Fig. 4). Similarly, the other coefficients related with C can be used to verify this value (Figs. 5–7 and Eq. (22)). For other materials, C should be determined using proper experimaental data. The crack formation, which may cause fracture, at spot weld joints is highly dependent on hardness H. Higher H values cause a decrease in fracture toughness of the spot weld for smaller crack lengths. Fracture toughness or stress intensity factors can easily be computed using (24) or (25), provided that the values for any one of the three modes are known. Acknowledgement The author is grateful to Dr. Hu¨seyin Canbolat of Electrical and Electronics Engineering Department for his suggestions to improve the results and for his assistance in typing and correcting the English manuscript. References [1] Davidson JAA. Review of the fatigue properties of spot welded sheet steels. SAE technical paper series. Paper No. 830033, 1984. [2] Kan YR. Fatigue resistance of spot welds-an analytical study. Metal Eng 1976(November):26–6. [3] Wilson RB, Fine TE. Fatigue behavior of spot welded high strength steel joints. SAE technical paper series. Paper No. 810354. [4] Pan N, Sheppard SD. Stress intensity factors in spot welds. Eng Fract Mech 2003;70:671–84.
[5] Darwish SM, Soliman MS, Al-Fahead AM. Manufacturing and characteristics of brass damping sheets. J Mater Process Technol 1998;79:66–71. [6] Chang B, Yaowu Shi Y, Lu L. Studies on the stress distribution and fatigue behavior of weld-bonded lap shear joints. J Mater Process Technol 2001;108:307–13. [7] Paris PC, Erdogˇan F. A Critical analysis of crack propagation laws. Trans ASME J Basic Eng 1693;84(4):528. [8] Chandel RS, Garber S. Mechanical and metallurgical aspects of spot-welded joints in heat-treated low-carbon mild steel sheet. Met Technol 1974(September):418–24. [9] Zuniga SM, Sheppard SD. Determining the constitutive properties of the heat-affected zone in a resistance spot weld. Model Simul Mater Sci Eng 1995;3:391–416. [10] Lawn B. Fracture of brittle solids printed in Great Britain, 2nd ed. Cambridge: University Press; 1993. [11] Pook LP. Fracture mechanics analysis of the fatigue behaviour of spot welds. Int J Fract 1975;11:173–6. [12] Radaj D. Strength assesment for spot-welded joints on the local stresses. Schweissen Schneiden & Transl DVS Welding Cutting 1989;1:E10–E13. [13] Zhang D. Stress intensities at spot welds. Int J Fract 1997;88:167–85. [14] Zhang D. Stress intensities derived from stresses around a spot weld. Int J Fract 1999;99:239–57. [15] Zhang D. Fracture mechanics solutions to spot welds. Int J Fract 1997;88:167–85. [16] Broek D. Elementary engineering fracture mechanics. Leyden: Noordhoff International Publishing; 1974. [17] Zhou M, Hu JS, Zhang H. Critical specimen sizes for tensile-shear testing of steel sheets. Welding Res Suppl 1999(September):305s–313s. [18] Voort GFV. Metallography principles and practice. ASM; 1999. [19] Eryu¨rek BI. Study of contact resistance in electrical resistance _ _ ¨ . Faculty of Mech Eng, Istanbul; spot weld. Ph.D. Thesis, I.T.U 1976 [in Turkish]. [20] Sevim I. Effect of abrasive particle size on wear resistance for _ ¨ . Fen Bilimleri abrasive wear of steels. Thesis of Ph.D. I.T.U _ Enstitu¨su¨ ISTANBUL-1998 [in Turkish]. _ [21] Ko¨ksal BA. Istatislik Analiz Metodları (Methods of statistical analysis) C ¸ agˇlayan Kitabevi. ISTANBUL-1995 [in Turkish]. [22] Odabası D, Su S. Comparison of the reciprocating and continuous two-body abrasive wear behavior of solitio-treated and age hardened 2014 Al alloy. Wear 1997;208:25–35. [23] Zum Gahr KH. Microstructure and wear of materials. Elsevier Science Publishers B.V; 1987.
Effect of hardness to fracture toughness for spot welded steel sheets Ibrahim Sevim
*
Department of Mechanical Engineering, Engineering Faculty, Mersin University, 33343 Ciftlikkoy, Mersin, Turkey Received 30 March 2004; accepted 9 September 2004 Available online 2 November 2004
Abstract The hardness of the spot welded nugget is considered as an important parameter in the computation of stress intensity factors. A novel approach, which employs the hardness of the nugget, is developed to obtain the stress intensity factors. The results are compared with the previous results on the computation of stress intensity factors. 2004 Elsevier Ltd. All rights reserved. Keywords: Stress intensity factor for spot weld; Fracture toughness; Vickers hardness; Crack length; Strain energy release rate
1. Introduction Spot welding is widely used in joining metal sheets. This technique is commonly used in automotive industry and for manufacturing house appliances due to its high efficiency in manufacturing thin metal sheets. A wide variety of metal sheets up to 3 mm thickness can be handled by the spot welding method. Spot welded materials may be exposed to different forces. Factors, such as, shear stress on resistance spot welding zone, sheet thickness, multi welding and the width of the welding zone are important parameters that affect fatigue life. Fatigue life for a spot weld is often expressed in terms of stress density, or stress intensity factor. These quantities are used to predict fatigue life of resistance spot welding. In order to determine fracture parameters, such as, notch stress on spot-welded joints, stress intensity factor, and J-integral, fracture mechanics is employed. In his review on spot welding Davidson [1] quotes works on stress density performed by Kan [2], and Wilson and Fine [3]. Kan [2], used the finite element method to obtain stress density at the elastic-plastic
*
Tel.: +90 324 361 0033; fax: +90 324 361 0032. E-mail address: [email protected].
0261-3069/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.matdes.2004.09.008
stress zone under the influence of variable shear loads. Wilson and Fine [3], defined stress density around the spot weld by relating stress density and spot welding fatigue of the smooth samples used in Neuber analysis. Pan and Sheppard [4], discussed the formation of capillary cracks and tried to estimate the stress intensity factors for these capillary cracks. Darwish et al. [5], investigated the variation of welding current, electrode force, and weld application time with failure rate. Chang et al. [6], investigated the hardness of metal, heat effect zone, spot welding and the adhesive layer for lap joint welding. For spot welded joints, the linear fracture mechanical approach is used [7]. In fracture mechanics, the stress intensity at the tip of sharp crack is expressed through stress intensity factors. The fracture mechanics theory is used to estimate stress intensity factors for spot weld joints under shear-tensile stress. The details of this method are given in Section 2. The formation of a crack at the spot weld is related to the nugget structure. Chandel and Garber [8] estimated weld strength in terms of weld current and current cycle for spot welds of different microstructures. For spot welded zinc coated HSLA steel, Zuniga and Sheppard [9] stated that both rupture stress and yield stress of the zone exposed to heat are dependent on the hardness.
22
I. Sevim / Materials and Design 27 (2006) 21–30
In this paper, we discuss fracture mechanics briefly in Section 2. Section 3 describes the experimental work. In Section 4, the data from the experiment are used to validate the new formulation and the results are discussed. The last section is devoted to conclusions and discussions.
stress intensity factor equations for spot weld using the equations for elliptical relations given in [11,12]: " 0:397 # F D KI ¼ ; ð1Þ 0:341 3=2 t ðD=2Þ K II ¼
2. Fracture mechanics approach The fracture of a material is studied in three different modes [10]. These are opening mode, sliding mode, and tearing mode, (Fig. 1) with associated intensity factors, where KI, KII, KIII, respectively. Fracture mechanics analysis is necessary in assessments of fatigue strength and fatigue life predictions of spot-welded joints and structures. The typical loading condition of tensile-shear (Fig. 2) is considered here which corresponds directly to commonly used test specimens for fatigue life predictions of spot-welded joints and structures. The main purpose in fracture mechanics analysis is to determine fracture parameters such as notch stress, stress intensity factors and J-integral on spot-weld. Pook [11] was the first to study the numerical computation of stress intensity factors for spot weld. Pook [11] analyzed fatigue behavior at the spot weld in a fracture mechanics framework based on the stress intensity factor equations. Pook developed the following
"
F ðD=2Þ
3=2
0:710 # D 0:282 þ 0:162 ; t
ð2Þ
where F is the applied load per spot weld, D is the weld diameter, t is the sheet thickness. Radaj [12] used fatigue-strength approach for local stresses at spot-weld joints. Zhang [13–15] studied the spot weld joints between sheets of dissimilar materials and different thickness. He found the relations between the J-integrals and stress intensity factors for sheets of either the same thickness or different thickness. He offers equations to compute the stress intensity factors for spot welds of dissimilar materials. pffiffiffi 3F pffi ; KI ¼ ð3Þ 2pD t 2F pffi ; pD t pffiffiffi 2F pffi : ¼ pD t
K II ¼
ð4Þ
K III
ð5Þ
The total energy release rate in combined mode cracking can easily be obtained by adding the energies from the different modes i.e. [16] 1 m2 K 2III 2 2 K I þ K II þ ; G ¼ J ¼ GI þ GII þ GIII ¼ E 1m ð6Þ
Fig. 1. The three modes of fracture: KI, opening mode; KII, sliding mode; KIII, tearing mode [10].
where KI, KII and KIII are stress intensity factors for modes I, II and III as shown in Fig. 3. There are few works on the relation between the hardness and the shear-tensile stress for spot welded joints. Zhou et al. [17] gave the following
Fig. 2. The spot welded experiment sample prepared according to mode II [19,20].
I. Sevim / Materials and Design 27 (2006) 21–30
Using (3)–(5) and (11), we obtain the following modified expressions for stress intensity factors, KI, KII and KIII pffiffiffi 3C D pffi ; KI ¼ ð12Þ 8H t
Fig. 3. Tensile loading of the spot-welded part [20].
H ¼ cry ;
23
ð7Þ C D pffi ; 2H t pffiffiffi 2C D pffi ; ¼ 4H t
where ry is the yield strength and c is a constant. Zuniga and Sheppard [9] perform experiments on a zinc-coated HSLA steel using the simulated heat effect zone samples, and suggested the following relationship for zinc-coated HSLA:
K II ¼
ð13Þ
K III
ð14Þ
ry ¼ 14:7 þ 2:568H ;
ð8Þ
ruts ¼ 65:8 þ 2:563H ;
ð9Þ
where C, H, D, and t are, respectively, the positive shear stress coefficient introduced in (11), the average Vickers hardness of the nugget, the nugget diameter, and sheet thickness.
where ruts is the ultimate strength, and H is Vickers hardness. Voort [18] gave the following equation for tensile stress TS n2 H 12:5ðn 2Þ ½1 ðn 2Þ TS ¼ ; ð10Þ 2:9 1 ðn 2Þ where H is Vickers hardness and n is Meyer strain-hardening coefficient. We suggest the following relation for spot welded joints (Fig. 4) fs ¼
4F ¼ CH 1 pD2
ð11Þ
where F is the load at failure, D is weld diameter, C is a positive constant, H is the average Vickers hardness and fs is the shear stress at the weld nugget material. We will refer to C as the shear stress coefficient.
5000 5500 6000 6500 500 Coefficient of Correlation 450
7000
3. Experimental work Resistance spot welded joints may be exposed to stress under tensile-shear conditions. The experiment is designed to determine the relation for the variation of the fracture toughness, KIC, KIIC, KIIIC, with the Vickers hardness, H, of the welding zone. The crack lengths, aIC, aIIC, aIIIC, can be computed using (21). 3.1. Materials The 1010, 1030, 1040, 1050 and 50 CrV4 steel sheets of 3 mm thickness are used in the experiment. The chemical properties of these steels are listed in Table 1.
7500
8000
8500
9500 10000 500
Materials Pair 50CrV4-1010
R f = 0.80 s
450
50CrV4-1030
400
Tensile-Shear Stress, fs ,(MPa)
9000
50CrV4-1040 50CrV4-1050
350 300
fs=1562443. H
-1
400 350 300
250
250
200
200
150
150
100
100
50
50
0 5000
5500
6000
6500
7000
7500
8000
8500
9000
0 9500 10000
Vickers Hardness, H (MPa) Fig. 4. Tensile-shear stress, fs versus Vickers hardness, H.
24
I. Sevim / Materials and Design 27 (2006) 21–30
Table 1 The chemical compositions of experiment sample (wt%) Alloys
C (%)
Si (%)
Mn (%)
P (%)
S (%)
Cr (%)
Mo (%)
Ni (%)
Al (%)
Cu (%)
Ti (%)
V (%)
1010 1030 1040 1050 50CrV4
0.107 0.328 0.402 0.506 0.523
0.11 0.069 0.247 0.252 0.394
0.413 0.673 0.82 0.654 0.915
0.019 0.015 0.012 0.014 0.021
0.025 0.019 0.028 0.006 0.027
– – 0.025 0.251 0.917
0.003 0.001 0.001 0.002 0.025
– – 0.003 – 0.034
0.032 – 0.014 0.006 –
0.031 0.037 0.032 0.017 0.183
0.002 0.002 0.001 0.002 –
– 0.005 0.003 0.006 0.095
3.2. Shape and dimensions of a weld-bonded lap joint Resistance spot weld is applied to 3 mm thickness 1010, 1030, 1040, 1050 and 50CrV4 steel sheets. The dimensions of the metal sheets and the position of the spot weld are shown in Fig. 2 (DIN 50124 DVS 29.2). These numbers are selected such that the edge effects are minimum, and the fracture should occur at the welding zone in a tensile shear experiment. Also only the tensile-shear force should be effective. 3.3. Spot-welding machine A 180 kV spot welding machine was used in the experiment. The electrodes are made of copper alloy having a spherical tip with a diameter of 16 mm. The electrode for resistance spot welding machine was loaded with a constant 7500 N force in the same direction of the electrode. Welding currents were measured to be 13 and 18 kA. The welding process was performed for 30 welding cycles. Nugget diameter changed in the range 8–13 mm due to changes in the welding current and the properties of the material. 3.4. Instron testing machine The resistance spot welded parts were tested for tensile-shear as shown in Fig. 3. Tensile-shear force was the maximum rupture force value read on the testing machine scale. During the tensile experiment, all parts were at constant speed of 7 mm/s. The welded surface of the material has the chemical properties given in Table 2. 3.5. The computation of fracture toughness of spot-welded steel sheets The rupture force for the welded parts was determined by the data from the tensile-shear force experi-
ment. From the welding zones of the ruptured parts, the nugget diameters were measured. The diameters were measured three times and the arithmetical mean of these three measurements is assigned as the nugget diameter. For the case in Figs. 2 and 3, (1)–(5), and (12)–(14) are used to calculate the fracture toughness, KIC, KIIC, KIIIC, according to Modes I, II, III. 3.6. Hardness analysis of heat affected zone of the spot weld The heat effected zone of the spot weld was etched using abrasive papers of 80–1200 mesh, and then 0.3 lm diamond paste. The Vickers hardness of the surface was measured at every 0.5 mm under the load 98.0665 N. The standard deviations and arithmetic means of the measured data were computed, and the results were combined to obtain a hardness value for the ruptured samples.
4. Results and discussion The stress intensity factors are calculated using (12)– (14) from the experimental data for the parts shown in Figs. 2 and 3. For comparison, the same quantities are calculated using (1)–(5). Some selected data are given in Table 3. It is clear from Table 3 that the differences (DF) are considerably high. This is true for other approach detailed in the literature [13]. The fracture toughness values computed using (3)–(5) are closer (18%) to the computed values using (12)–(14) (Table 3). We believe that the difference comes from measurement errors for nugget hardness. The results in Table 3 are demonstrated graphically in Figs. 5–7, 9 and 11. The graphs are generated using the curve fitting technique via the least squares method [21] (see Fig. 8 , 10 and 12).
Table 2 The chemical compositions of welding zone (wt%) Alloys
C (%)
Si (%)
Mn (%)
P (%)
S (%)
Cr (%)
Mo (%)
Ni (%)
Al (%)
Cu (%)
Ti (%)
V (%)
50CrV4-1010 50CrV4-1030 50CrV4-1040 50CrV4-1050
0.315 0.425 0.463 0.514
0.252 0.231 0.321 0.323
0.665 0.794 0.868 0.784
0.020 0.018 0.017 0.018
0.026 0.023 0.028 0.017
0.458 0.458 0.471 0.584
0.014 0.013 0.013 0.014
0.017 0.017 0.019 0.017
0.016 – 0.007 0.003
0.10 0.11 0. 108 0.1
0. 001 0. 001 0.004 0. 001
0.05 0.05 0.049 0.050
Table 3 Computed fracture toughness (KIC, KIIC, KIIIC) values based on the (1)–(5) and (12)–(14), and the differences (DF = K(1 5) K(12 14)) Materials pair
Estimated using Eqs. (1), (2)
Estimated using Eqs. (3)–(5)
Estimated using Eqs. (12)–(14)
Rupture force, F (kN)
Nugget diameter, D (mm)
Sheet thickness, t (mm)
Hardness, Hv (MPa)
KIC (MPa m1/2)
KIIC (MPa m1/2)
KIIIC (MPa m1/2)
KIC (MPa m1/2)
KIIC (MPa m1/2)
KIIIC (MPa m1/2)
KIC (MPa m1/2)
KIIC (MPa m1/2)
KIIIC (MPa m1/2)
21,850 21,580 16,818 19,613 19,123 17,044 18,152 18,090 19,700 18,829 19,152 17,083 18,700 22,050 18,633 16,279 13,882 12,490 14,960 14,300
11 11 8.5 8.3 10 9 10.5 9.8 11 11 11.5 11 11 11.8 11 9.6 9 8.5 10 9
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
6404 6404 6374 5246 6374 6610 7325 6815 7060 7531 7570 8100 7570 6835 7060 8129 8129 8482 8433 7845
30.62 30.24 31.33 37.50 29.77 29.80 26.78 28.80 27.61 26.39 25.56 23.94 26.21 28.60 26.11 26.51 24.27 23.26 23.29 25.01
36.93 36.47 37.71 45.16 35.84 35.87 32.26 34.66 33.29 31.82 30.85 28.87 31.60 34.55 31.49 31.91 29.21 28.00 28.04 30.09
– – – – – – – – – – – – – – – – – – – –
10.00 9.87 9.95 11.89 9.62 9.53 8.70 9.29 9.01 8.61 8.38 7.81 8.55 9.40 8.52 8.53 7.76 7.39 7.52 7.99
23.08 22.80 22.99 27.46 22.22 22.01 20.09 21.45 20.81 19.89 19.35 18.05 19.75 21.71 19.68 19.70 17.92 17.07 17.38 18.46
16.32 16.12 16.25 19.41 15.71 15.56 14.20 15.16 14.71 14.06 13.68 12.76 13.96 15.35 13.91 13.93 12.67 12.07 12.29 13.05
10.60 10.60 8.23 9.77 9.68 8.40 8.85 8.88 9.62 9.02 9.38 8.38 8.97 10.66 9.62 7.29 6.83 6.18 7.32 7.08
24.50 24.50 19.01 22.56 22.37 19.42 20.44 20.50 22.22 20.83 21.66 19.36 20.72 24.62 22.22 16.84 15.78 14.29 16.91 16.36
17.32 17.32 13.44 15.95 15.81 13.73 14.45 14.49 15.70 14.72 15.31 13.69 14.65 17.40 15.70 11.90 11.16 10.10 11.95 11.56
DF = Eq. (1) Eq. (12) (MPa m1/2)
DF = Eq. (2) Eq. (13) (MPa m1/2)
DF = Eq. (3) Eq. (12) (MPa m1/2)
DF = Eq. (4) Eq. (13) (MPa m1/2)
DF = Eq. (5) Eq. (14) (MPa m1/2)
20.02 19.64 23.1 27.73 20.09 21.4 17.93 19.92 17.99 17.37 16.18 15.56 17.24 17.94 16.49 19.22 17.44 17.08 15.97 17.93
12.43 11.97 18.7 22.6 13.47 16.45 11.82 14.16 11.07 10.99 9.19 9.51 10.88 9.93 9.27 15.07 13.43 13.71 11.13 13.73
–0.6 0.73 1.72 2.12 0.06 1.13 0.15 0.41 0.61 0.41 –1 0.57 0.42 1.26 1.1 1.24 0.93 1.21 0.2 0.91
1.42 1.7 3.98 4.9 0.15 2.59 0.35 0.95 1.41 –0.94 2.31 1.31 0.97 2.91 2.54 2.86 2.14 2.78 0.47 2.1
1 1.2 2.81 3.46 0.1 1.83 0.25 0.67 0.99 –0.66 1.63 0.93 0.69 2.05 1.79 2.03 1.51 1.97 0.34 1.49
I. Sevim / Materials and Design 27 (2006) 21–30
50CrV4-1010 50CrV4-1010 50CrV4-1010 50CrV4-1010 50CrV4-1010 50CrV4-1030 50CrV4-1030 50CrV4-1030 50CrV4-1030 50CrV4-1030 50CrV4-1040 50CrV4-1040 50CrV4-1040 50CrV4-1040 50CrV4-1040 50CrV4-1050 50CrV4-1050 50CrV4-1050 50CrV4-1050 50CrV4-1050
Measured data
25
26
I. Sevim / Materials and Design 27 (2006) 21–30 5000 5500 6000 6500 20 Coefficient of Correlation 18 R K = 0.80
7000
7500
8000
8500
9000
50CrV4-101 0
IC
Fracture Toughness KIC, (MPa.m1/2)
9500 10000 20
Materials Pair 50CrV4-103 0
16
50CrV4-104 0
K IC=63840 .H
14
-1
50CrV4-105 0
18 16 14
12
12
10
10
8
8
6
6
4
4
2
2
0 5000
5500
6000
6500
7000
7500
8000
8500
9000
0 9500 10000
Vickers Hardness, H (MPa) Fig. 5. According to (12); fracture toughness, KIC, versus Vickers hardness, H.
Fracture Toughness KIIC, (MPa.m1/2)
5000 5500 6000 6500 40 Coefficient of Correlation R K = 0.80 36 IIC
7000
32
7500
8000
K IIC =147 44 0.H
8500
9000
9500 10000 40 Materials Pair 36 50CrV4-1010
50CrV4-1030
-1
50CrV4-1040 50CrV4-1050
28
32 28
24
24
20
20
16
16
12
12
8
8
4
4
0 5000
5500
6000
6500
7000
7500
8000
8500
9000
0 9500 10000
Vickers Hardness H, (MPa) Fig. 6. According to (13); fracture toughness, KIIC, versus Vickers hardness, H.
The following equations are obtained by curve fitting in Figs. 5–7:
K III P K IIIC :
ð16cÞ
K IC ¼ 63840H 1 ;
ð15aÞ
The following expressions for KI, KII and KIII are used:
K IIC ¼ 147440H 1 ;
ð15bÞ
pffiffiffiffiffiffiffiffiffi K I ¼ s paIC ;
ð17aÞ
K IIIC ¼ 104240H 1 :
ð15cÞ
pffiffiffiffiffiffiffiffiffiffi K II ¼ s paIIC ;
ð17bÞ
pffiffiffiffiffiffiffiffiffiffiffiffi K III ¼ s paIIIC ;
ð17cÞ
The fracture of a spot weld occurs when the following conditions are satisfied [20]: K I P K IC ;
ð16aÞ
K II P K IIC ;
ð16bÞ
where s is the applied shear stress, and aIC, aIIC, aIIIC are crack lengths parallel to the fracture axis in the heat affected zone.
I. Sevim / Materials and Design 27 (2006) 21–30 5000 5500 6000 6500 30 Coefficient of Correlation R K = 0.80 27
7000
7500
8000
8500
9000
9500 10000 30
Materials Pair 50CrV4-1010
IIIC
Fracture ToughnessKIIIC, (MPa.m1/2)
27
50CrV4-1030
24
K IIIC =104 240 .H
-1
50CrV4-1040 50CrV4-1050
21
27 24 21
18
18
15
15
12
12
9
9
6
6
3
3
0 5000
5500
6000
6500
7000
7500
8000
8500
9000
0 9500 10000
Vickers Hardness H, (MPa)
Strain Energy Release Rate GC, (MPa.m)
Fig. 7. According to (14); fracture toughness, KIIIC, versus Vickers hardness, H.
5000 5500 6000 6500 0.010 Coefficient of Correlation 0.009 R G =0 .80
7000
7500
8000
8500
9000
9500 10000 0.010
Materials Pair 50CrV4-1010
IC
50CrV4-1030
0.008
50CrV4-1040 50CrV4-1050
0.007
0.009 0.008 0.007 0.006
0.006
G C=1826 67. H
0.005
-2
0.005
0.004
0.004
0.003
0.003
0.002
0.002
0.001
0.001
0.000 5000
5500
6000
6500
7000
7500
8000
8500
9000
0.000 9500 10000
Vickers Hardness, H (MPa) Fig. 8. According to (6); strain energy release rate, GC, versus Vickers hardness, H.
Since the plastic deformation takes place during fracture, the applied shear stress, s s ffi syield ;
ð18Þ
where syield is a stress which includes the increase in the yield stress due to deformations in a small region of the spot weld. syield and the hardness H of the material is related by the following. syield ¼ H :
ð19Þ
Using (17), one can obtain the following equations for stress intensity factors pffiffiffiffiffiffiffiffiffi K I ¼ H paIC ; ð20aÞ pffiffiffiffiffiffiffiffiffiffi K II ¼ H paIIC ;
ð20bÞ
pffiffiffiffiffiffiffiffiffiffiffiffi K III ¼ H paIIIC :
ð20cÞ
Substituting (20) into (15), the following equations are obtained: pffiffiffiffiffiffiffiffiffi H paIC ¼ 63840H 1 ; ð21aÞ pffiffiffiffiffiffiffiffiffiffi H paIIC ¼ 147440H 1 ;
ð21bÞ
pffiffiffiffiffiffiffiffiffiffiffiffi H paIIIC ¼ 104240H 1 :
ð21cÞ
Rearranging (21), the following conditions for crack lengths (aIC, aIIC, aIIIC) 2 1 63840 ð22aÞ aIC P p H
28
I. Sevim / Materials and Design 27 (2006) 21–30 5000 50
5500
6000
7000
7500
8000
8500
9000
IC
9500 10000 50
Material Pair 50CrV4-1010
Coefficients of Correlation R K , R K =0.98
45
Fracture Toughness,KIC, KIIC, (MPa.m1/2)
6500
IIC
45
50CrV4-1030
40
50CrV4-1040 50CrV4-1050
35
40 35
30
30
25
25
20
20
15
15
10
K IC=1968 47 .H
-1
K IIC =2373 00 .H
10
-1
5 0 5000
5
5500
6000
6500
7000
7500
8000
8500
0 9500 10000
9000
Vickers Hardness H, (MPa) Fig. 9. According to (1) and (2); fracture toughness, KIC, K
5000 5500 6000 6500 0.040 Coefficient of Correlation 0.036 R G =0 .98
7000
7500
8000
IIC,
8500
Strain Energy vRelease RateGC, (MPa.m)
IIC
versus Vickers hardness, H.
9000
9500 10000 0.040 Materials Pair 0.036 50CrV4-1010 50CrV4-1030
0.032
50CrV4-1040 50CrV4-1050
0.028 0.024
0.032 0.028 0.024
0.020
G C=775534. H
-2
0.020
0.016
0.016
0.012
0.012
0.008
0.008
0.004
0.004
0.000 5000
5500
6000
6500
7000
7500
8000
8500
9000
0.000 9500 10000
Vickers Hardness, H (MPa) Fig. 10. According to (1), (2) and (6); strain energy release rate, GC, versus Vickers hardness, H.
2 1 147440 ; p H
ð22bÞ
2 1 104240 P : p H
ð22cÞ
aIIC P
aIIIC
It is clear from (22) that the crack length becomes smaller as hardness increases. This kind of small cracks may be present at a spot weld under shear-tensile stress or they may be created as soon as the shear-tensile stress is applied to the spot weld [20,22]. It is clear from Figs. 5–7 that the fracture toughness and hardness are inversely proportional to each other
for a spot-welded pair. The variables that affects the microstructure of the welding zone are welding current, the cycle of the current, holding time, the chemical structure of the alloy, and the cooling rate of the weld zone. Different microstructures arise depending on these parameters. Each different structure has its own hardness value. In this study, we used a 50CrV4 metal sheet for the spot weld pair. The hardness at the welding zone takes high values, since an alloy microstructure is formed in the welding zone of a 50CrV4 sheet, and the cooling rate is slower for 50CrV4 alloy [20]. Nugget is the zone where the metal pair melts. That zone has the properties of a die cast structure when it
Fracture Toughness,KIC, KIIC, KIIIC (MPa.m1/2)
I. Sevim / Materials and Design 27 (2006) 21–30 5000 5500 6000 6500 40 Coefficients of Correlation 36 R K , R K , R K = 0. 96 IC
IIC
7000
7500
8000
8500
29
9000
9500 10000 40
Material Pair 50CrV4-1010
IIIC
32 K =63845.H -1 IIC
KIIC=147440.H
-1
KIIIC=104260.H
-1
50CrV4-1040 50CrV4-1050
28
36
50CrV4-1030 32 28
24
24
20
20
16
16
12
12
8
8
4
4
0 5000
5500
6000
6500
7000
7500
8000
8500
0 9500 10000
9000
Vickers Hardness H, (MPa) Fig. 11. According to (3)–(5); fracture toughness, KIC, KIIC, KIIIC, versus Vickers hardness, H.
5000 5500 6000 6500 0.010 Coefficient of Correlation 0.009 R =0 .96
7000
7500
8000
8500
9500 10000 0.010
Materials Pair 50CrV4-1010
GC
Strain Energy Release RateGC, (MPa.m)
9000
50CrV4-1030
0.008
0.009 0.008
50CrV4-1040
0.007
50CrV4-1050
0.006
0.007 0.006
0.005
GC =182666. H
-2
0.005
0.004
0.004
0.003
0.003
0.002
0.002
0.001
0.001
0.000 5000
5500
6000
6500
7000
7500
8000
8500
9000
0.000 9500 10000
Vickers Hardness, H (MPa) Fig. 12. According to (3)–(6); strain energy release rate, GC, versus Vickers hardness, H.
hardens. In this structure; inclusions, incoherent particles and embrittled grain are present. These properties accelerate the crack development, which causes a fracture in spot weld. Garh [23] shows that the fracture toughness reduces while the hardness increases for plastic, ceramic, and metallic alloys. The computed ratio of the stress intensity factors using (1) and (2) is found as KI ¼ 0:83 ð23Þ K II and the ratios using (3)–(5) are as KI K III ¼ 0:433; ¼ 0:707: K II K II
ð24Þ
According to (12)–(14), the ratios are found to be as follows KI K III ¼ 0:433 ¼ 0:707: ð25Þ K II K II Eqs. (3)–(5) give the same values as (12)–(14). Any stress intensity factor for a given mode can easily be computed using (24) or (25) provided that the stress intensity factor for a specific mode is known. For example, if KI is known then it is a simple matter to compute KII and KIII. The correlation coefficient for the values of (1)–(5) is smaller than the correlation coefficient for (12)–(14). This is due to the errors in the measurement for Vickers hardness.
30
I. Sevim / Materials and Design 27 (2006) 21–30
5. Conclusions We offered (12)–(14) to compute fracture toughness for low carbon alloy steel. The computed values are comparable with the values obtained using (3). However, the values obtained from (1) and (2) demonstrate significant differences up to 18%. In (11), we introduce the shear stress coefficient C for spot weld pairs. We calculated, approximately, C = 1.56 · 106 (MPa)2 for low carbon alloy steels (Fig. 4). Similarly, the other coefficients related with C can be used to verify this value (Figs. 5–7 and Eq. (22)). For other materials, C should be determined using proper experimaental data. The crack formation, which may cause fracture, at spot weld joints is highly dependent on hardness H. Higher H values cause a decrease in fracture toughness of the spot weld for smaller crack lengths. Fracture toughness or stress intensity factors can easily be computed using (24) or (25), provided that the values for any one of the three modes are known. Acknowledgement The author is grateful to Dr. Hu¨seyin Canbolat of Electrical and Electronics Engineering Department for his suggestions to improve the results and for his assistance in typing and correcting the English manuscript. References [1] Davidson JAA. Review of the fatigue properties of spot welded sheet steels. SAE technical paper series. Paper No. 830033, 1984. [2] Kan YR. Fatigue resistance of spot welds-an analytical study. Metal Eng 1976(November):26–6. [3] Wilson RB, Fine TE. Fatigue behavior of spot welded high strength steel joints. SAE technical paper series. Paper No. 810354. [4] Pan N, Sheppard SD. Stress intensity factors in spot welds. Eng Fract Mech 2003;70:671–84.
[5] Darwish SM, Soliman MS, Al-Fahead AM. Manufacturing and characteristics of brass damping sheets. J Mater Process Technol 1998;79:66–71. [6] Chang B, Yaowu Shi Y, Lu L. Studies on the stress distribution and fatigue behavior of weld-bonded lap shear joints. J Mater Process Technol 2001;108:307–13. [7] Paris PC, Erdogˇan F. A Critical analysis of crack propagation laws. Trans ASME J Basic Eng 1693;84(4):528. [8] Chandel RS, Garber S. Mechanical and metallurgical aspects of spot-welded joints in heat-treated low-carbon mild steel sheet. Met Technol 1974(September):418–24. [9] Zuniga SM, Sheppard SD. Determining the constitutive properties of the heat-affected zone in a resistance spot weld. Model Simul Mater Sci Eng 1995;3:391–416. [10] Lawn B. Fracture of brittle solids printed in Great Britain, 2nd ed. Cambridge: University Press; 1993. [11] Pook LP. Fracture mechanics analysis of the fatigue behaviour of spot welds. Int J Fract 1975;11:173–6. [12] Radaj D. Strength assesment for spot-welded joints on the local stresses. Schweissen Schneiden & Transl DVS Welding Cutting 1989;1:E10–E13. [13] Zhang D. Stress intensities at spot welds. Int J Fract 1997;88:167–85. [14] Zhang D. Stress intensities derived from stresses around a spot weld. Int J Fract 1999;99:239–57. [15] Zhang D. Fracture mechanics solutions to spot welds. Int J Fract 1997;88:167–85. [16] Broek D. Elementary engineering fracture mechanics. Leyden: Noordhoff International Publishing; 1974. [17] Zhou M, Hu JS, Zhang H. Critical specimen sizes for tensile-shear testing of steel sheets. Welding Res Suppl 1999(September):305s–313s. [18] Voort GFV. Metallography principles and practice. ASM; 1999. [19] Eryu¨rek BI. Study of contact resistance in electrical resistance _ _ ¨ . Faculty of Mech Eng, Istanbul; spot weld. Ph.D. Thesis, I.T.U 1976 [in Turkish]. [20] Sevim I. Effect of abrasive particle size on wear resistance for _ ¨ . Fen Bilimleri abrasive wear of steels. Thesis of Ph.D. I.T.U _ Enstitu¨su¨ ISTANBUL-1998 [in Turkish]. _ [21] Ko¨ksal BA. Istatislik Analiz Metodları (Methods of statistical analysis) C ¸ agˇlayan Kitabevi. ISTANBUL-1995 [in Turkish]. [22] Odabası D, Su S. Comparison of the reciprocating and continuous two-body abrasive wear behavior of solitio-treated and age hardened 2014 Al alloy. Wear 1997;208:25–35. [23] Zum Gahr KH. Microstructure and wear of materials. Elsevier Science Publishers B.V; 1987.