FATIGUE STRENGTH PREDICTION OF SPOT-WELDED JOINTS USING SMALL SPECIMEN TESTING

Transcription

1 FATIGUE STRENGTH PREDICTION OF SPOT-WELDED JOINTS USING SMALL SPECIMEN TESTING E. Nakaama*, M. Fukumoto*, M. Miahara*, K. Okamura*, H. Fujimoto* and K. Fukui** *Corporate Research & Development Laboratories, Sumitomo Metal Industries, Ltd., 1-8, Fuso-Cho, Amagasaki, Hogo , Japan **Steel Sheet, Plate, Titanium & Structural Steel Compan, Sumitomo Metal Industries, Ltd., , Harumi, Chuo-ku, Toko , Japan Abstract It is well known that fatigue strength of spot weld of high strength steel sheet is not improved, compared with that of mild steel sheet. In this stud, the dominant factors and the effects of steel grade on spot weld fatigue strength are investigated. Firstl, small specimens with total length of less than 3mm are taken from the spot weld of mild steel sheet (27MPa-grade) and high strength steel sheet (59MPa-grade). And then, tensile and high ccle fatigue properties are individuall evaluated b newl-developed testing technique. Secondl, finite element analses of tensile-shear specimen of spot-welded joints under cclic loading are carried out and fatigue limit of the joints are predicted, using the above-mentioned local material strength properties and considering calculated welding residual stresses around spot weld. Predicted result of mild steel is higher than that of 59MPa-grade steel, which coincides with eperimental results. It is clarified that the fatigue strength of HAZ, which is the crack initiation site in joint, is almost equal in both steels. Furthermore, it is also shown that large tensile residual stress ma occur and it could decrease the joint fatigue strength in the case of 59MPa-grade steel. 1. Introduction Recentl, the application of high strength steel sheets has been increasing for weight reduction of automotive structures. In general, the fatigue strength of steel sheet is increased with its tensile strength, whereas the fatigue strength of spot weld, which is the most general joining method, shows little improvement [1]. Thus, evaluation and improvement of spot weld fatigue strength of high strength steel is an important issue. Man studies on the fatigue strength prediction of spot weld have been reported. Among them, however, elastic stress analses or fracture mechanics approaches were mainl emploed, assuming small scale ielding in fatigue loading [2, 3]. In addition, there are few researches on the fatigue strength assessment with consideration of welding residual stress since the residual stress analsis is quite complicated [4]. Therefore, the dominant factors and the effect of steel grade have not been clarified. Spot weld consists of base metal, heat affected zone (HAZ), weld metal what we call nugget, and so on. Therefore, evaluation of the local fatigue strength properties in each region will lead to better understanding of the steel grade effect on joint fatigue strength. In the previous stud, the present authors developed the tensile testing technique for small specimen with total length of less than 3mm taken from each region in spot weld, and stress-strain relationships and ductilit were successfull measured [5]. In the present stud, firstl, fatigue testing method for small specimen was developed on the basis of the tensile test method, and then the local material strength properties of spot weld of mild steel and high strength steel were individuall measured. Secondl, with these material data, finite element analses of tensile-shear spot-welded joints under cclic loading were carried out and the fatigue limit was predicted, considering the numericall estimated residual stress b the welding process simulation which has been developed b some of the present authors [6]. Lastl, the predicted results were verified b comparing with the eperimental results and the effect of steel grade on joint fatigue strength were investigated. 2.1 Tensile test Test Method 2. Test method for small specimen and test results Firstl, the tensile test technique and test results will be described. In this stud, 27MPa-grade steel (mild steel) and 59MPa-grade high strength steel (59MPa steel) were used. The thickness of both steel sheets is 1.2mm. The chemical compositions and the spot welding conditions are listed in Table 1 and Table 2, respectivel.

2 Table 1. Chemical compositions of steels tested (mass%). Steel C Si Mn P S Mild MPa Table 2. Welding conditions. Steel Mild 59MPa Electrode force (N) 343 Welding time (ccle* 1 ) 14 Hold time (ccle* 1 ) 3 Welding current* 2 (A) *1: 1 ccle = 1/6 sec. *2: Values for obtaining 4.7mm nugget diameter. Figure 1 shows the shape and dimensions of the tensile specimen. The specimen has the thickness of.3mm and the gage section.5mm in length and.3mm in width. The cross section of the spot weld and the sampling locations of specimens are shown in Fig. 2. Nugget specimens were taken from the middle section of nugget as loading ais was parallel to sheet thickness direction. As to HAZ specimen, the loading ais was parallel to the hoop direction of spot weld in order to eclude the corona bond and to minimize microstructure variation within specimen. In addition, the test section of HAZ specimen was fit to the edge of sheet separation, which is the crack initiation site of the actual joint. Specimens of base metal were taken far awa from spot weld and loading ais was perpendicular to sheet thickness direction. All specimens were manufactured b wire electric discharge machining. Heat input during specimen machining was kept low b enough cooling so as to prevent an changes in microstructure and hardness. Figure 3 shows the hardness distribution on the cross-sectional surface in spot weld. Hardness in the weld is much higher than that of base metal because microstructure in welded region was changed into martensite, which has ver high hardness, due to etremel rapid cooling during welding process. A large hardness gradient is seen in HAZ region, which ma be caused b the variation of cooling rate. The weld hardness of 59MPa steel is higher than mild steel since 59MPa steel includes grater carbon content as shown in Table 1. Since the tensile specimen is too small in dimension, gripping methods normall used for standard size specimens, such as clamping or pinning, are not applicable. Therefore, the testing grips for the small specimen were speciall developed [5]. Figure 4 is the magnified view of the specimen and the grips. The grip has minute projections designed to fit for shoulders of the specimen. B hooking the specimen at these projections, tensile load can be applied without bending or twisting specimen. R.25 Base metal HAZ Sampling location of specimen Corona bond Weld metal (Nugget) 2.4 Thickness.3 1mm Fig. 1. Shape and dimensions of tensile specimen (unit:mm). 5 Edge of sheet separation Vickers hardness mild steel 59MPa steel Distance from the center of nugget (mm) Fig. 3. Hardness distribution in spot weld. Fig. 2. Cross section of spot weld and sampling location of specimens. Specimen Base metal Grip Grip Base metal 5mm Fig. 4. Magnified view of tensile specimen and test grips.

3 Testing machine used was Ttron TM 25 (MTS sstems corp.) with maimum load capacit of ±25N. The actuator is mounted on the air bearing to reduce friction and small sample testing can be performed with precision. Tensile test condition was set b actuator displacement speed,.1mm/s, and tensile load was applied up to rupture. All tensile tests were conducted in air and at ambient temperature. Strain in test results described below is the nominal value calculated from the gage length of specimen and the actuator displacement. But it should be noted that non-contact strain measurement in test section was additionall carried out b 2D- ESPI sstem (Dantec Ettemeer GmbH) which utilizes laser speckle interferometr and the above-mentioned nominal strain was confirmed to be sufficientl accurate b comparing with the measured value Test results Figure 5 is an eample of ruptured specimen (HAZ of mild steel). All specimens were ruptured within the test section and tensile tests were successfull carried out. Stress-strain relationships of base metal, HAZ and nugget are shown in Fig. 6 and mechanical properties of each specimen are given in Table 3. Tensile strength of base metal shows good agreement with the values measured b JIS No.5 standard tpe specimen with gage section 5mm in length and 25mm in width, mild steel: 343MPa, 59MPa steel: 591MPa, which indicates that the valid test results were obtained. Moreover, tensile strength of nugget well coincides with the estimated values based on the conversion table between hardness and tensile strength (SAE J 417), mild steel: 15MPa, 59MPa steel: 124MPa. This means that the strength of solidified metal can be accuratel evaluated from hardness. The tensile strength of HAZ and nugget is much higher than that of base metal, but elongation is lower. This is because microstructure in HAZ and nugget is mainl martensite as previousl mentioned. The strength of HAZ is lower than nugget. The sampling location of HAZ specimen is slightl apart from nugget and the maimum temperature and cooling rate during welding is lower than nugget, which ma decrease martensite volume fraction in HAZ microstructure. 2.2 Fatigue test Secondl, fatigue test technique and test results will be shown. The steels tested and the sampling method of specimen are all same as the tensile test described in the previous section. Here, HAZ, which is the crack initiation site of joint, is focused on and its fatigue strength is investigated. Stress σ (MPa) Base metal HAZ Nugget Bold : Mild steel Thin : 59MPa steel 5µm Fig. 5. Ruptured specimen after tensile test (mild steel, HAZ) Strain ε (%) Fig. 6. Stress-strain relationships. Table 3. Tensile strength and ductilit of each specimen. Specimen Tensile strength (MPa) Elongation (%) Reduction of area (%) Base metal Mild steel HAZ Nugget Base metal MPa steel HAZ Nugget

4 2.2.1 Test method When the tensile specimen shown in Fig. 1 is subjected to fatigue loading, the specimen is frequentl fractured in the curved area because of stress concentration. In this case, applied stress at the fracture position cannot be precisel estimated since the stress concentration factor varies according to the contact state between specimen shoulders and the grip projections. Thus, an hourglass-shape specimen was designed in order to fracture in the center portion. The shape and dimensions of fatigue specimen is illustrated in Fig.7. The stress concentration factor at the minimum width section is 1.23, which ma be low enough to regard the specimen as smooth. Using the same testing grip as the tensile test in Fig. 4, fatigue test under tension-tension loading can be conducted, but tension-compression loading test, which is essential for fatigue propert evaluation, cannot be performed. Therefore, a new test grip was designed for compressive loading. The magnified view of the specimen and the grips are shown in Fig. 8. The specimen shoulders are hooked at the projections of grips, and at the same time, the specimen is held from the back side in both ends. In this manner, the application of compressive loading to the small specimen was achieved. Stress waveform for fatigue test was sine at a frequenc of 1Hz. Two kinds of stress ratio, R=.1 (tension-tension) and R=-1 (tensioncompression) were emploed. All fatigue tests were conducted in air and at ambient temperature Test results An eample of ruptured specimen after fatigue test is shown in Fig. 9. All fatigue specimens were successfull ruptured at the center of the test section. Figure 1 shows S-N diagrams of HAZ specimen. Stress amplitude in ordinate indicates the nominal value, that is to sa, stress concentration of the specimen is not taken into account. It is found that the fatigue strength of mild steel and 59MPa steel are almost equal in both stress ratio R=.1 and 1 although the tensile strength of 59MPa steel is much higher than mild steel as shown in Fig. 6. The reason of these test results is presumed as follows. As mentioned before, the tensile strength of HAZ specimen is lower than nugget, which indicates that HAZ microstructure includes not onl hard phases such as martensite but also soft phases such as ferrite. In addition, 59MPa steel has greater carbon content and hardness of martensite itself ma be higher than mild steel, which results in larger hardness difference between hard and soft phases in 59MPa steel. In consequence, stress concentration in soft phases is severer and crack initiation is promoted in 59MPa steel. In this work, as described above, it was clarified that the fatigue strength of HAZ of spot weld, which is the crack initiation site in joint, was approimatel equal in mild steel and high strength steel (59MPa-grade) tested in this stud. R.2.6 Specimen Grip Grip R Thickness.3 5mm Fig. 7. Shape and dimensions of fatigue specimen (unit:mm). 5µm Fig. 9. Ruptured specimen after fatigue test (59MPa steel, HAZ). R = -1, σ a = 297MPa, N f = ccle. Stress amplitude σ a (MPa) Fig. 8. Magnified view of fatigue specimen and test grips R=.1 R=-1 open : Mild steel solid : 59MPa steel Number of ccles to fracture N f (ccle) Fig. 1. S-N diagrams of HAZ specimen.

5 3. Fatigue limit prediction of spot-welded joint In this chapter, fatigue limit of tensile-shear specimen of spot-welded joints will be predicted, based on results of finite element analses. The tensile-shear specimen represented in Fig. 11 is 26mm in length and 4mm in width. The length of lapped region in loading direction is 4mm. Figure 12 shows relationships between load range and fatigue lives at a force ratio.1, evaluated on the basis of JIS Z 3138 Method of Fatigue Testing for Spot Welded Joint. It is found that fatigue strength of mild steel is slightl higher than 59MPa steel. 3.1 Analsis model Figure 13 shows a finite element model for tensile-shear specimen of the joint. Considering the geometric smmetr, onl a half of the specimen was modeled with three-dimensional 8 nodes heahedral elements. HAZ was divided into three element groups which were named HAZ1, HAZ2 and HAZ3 since hardness changed dramaticall within HAZ. The minimum mesh size in HAZ1 is approimatel 15µm, which is equivalent to several grains size in the actual joint. Stress-strain relationships in Fig. 6 were given to base metal, HAZ1 (corresponding to the sampling location of HAZ specimen) and nugget. Stress-strain relationships of HAZ2 and HAZ3 were computed from that of HAZ1, assuming that stress in plastic deformation region is proportional to hardness. One side of model was fied and cclic loading corresponding to the fatigue limit in Fig. 12 was applied to the other side. The commercial FEM code ABAQUS was used for the analses. The cross section of joint after fatigue test in the vicinit of crack initiation site is represented in Fig. 14. It is confirmed that the corona bond is separated b fatigue loading in most cases as this figure. In order to simulate this fracture mode, corona bond in analsis model was also separated b setting the duplicate nodes on upper and lower sheet as shown in Fig. 13. In this stud, all region in corona bond was separated, that is to sa, upper and lower sheet were jointed in onl nugget elements. 3.2 Analsis result Figure 15 is an eample of analsis results. This figure indicates distribution of Mises equivalent stress at the maimum load on the smmetrical surface. The stress values at the corner node were used for fatigue limit prediction of the joint. 4 Loading direction Lapped region Spot weld Load range L (N) Force ratio =.1 Mild steel 59MPa steel Fig. 11. Tensile-shear specimen of spot-welded joint Number of ccles to failure N f (ccle) Fig. 12. L-N diagrams of joint. Cclic load HAZ2 HAZ3 Smmetrical plane HAZ1 Base metal HAZ1 z Fied Spot weld Nugget Nugget Corona bond ( : duplicate node) Fig. 13. FE model of tensile-shear specimen.

6 Loading direction (MPa) (Mises equivalent stress) Crack initiation site Propagation Corona bond (separated) 25µm Corona bond Stress evaluation point 5µm Fig. 14. Cross section in the vicinit of the crack initiation site (mild steel). Fig. 15. Distribution of Mises equivalent stress around the sheet separation edge (mild steel). 3.3 Residual stress As mentioned in introduction, it is important to evaluate and consider residual stress for accurate assessment of fatigue strength of weldment. In this stud, the finite element simulation method of spot welding process developed b Fukumoto et al. [6] was emploed. This method is based on the coupled electrical-thermal-mechanical analses, and man phenomena which ma occur during welding process, namel, solid/liquid phase change, phase transformation and changes in mechanical properties, are taken into consideration. In addition, the validit of analsis results such as nugget formation have been confirmed b comparing with eperimental results (see reference [6] for details). An aismmetrical model is shown in Fig. 16. The model includes a pair of the dome tpe electrodes and two sheets of 1.2mm thickness. Figure 17 represents distribution of radial stress σ after welding in mild steel and 59MPa steel. Large tensile stress appears around the spot weld in both steels. Firstl, nugget shape was defined as a contour line indicating liquid phase fraction of.8, and secondl, residual stress at the nugget edge on the interface between upper and lower sheets was etracted. Finall, the residual stress was added to the stress b fatigue loading analses of the joint in each component σ, σ and τ. 3.4 Stress parameter for fatigue limit prediction In tensile-shear specimen of joint, upper and lower sheets are offset from the center plane of nugget. Therefore, spot weld rotates as applied load increases and this deformation behavior leads to multiaial stress state at the crack initiation site. Furthermore, as described below, the residual stress brings about a comple stress state and then causes change in the orientation of the principal stress aes during fatigue loading, which is called non-proportional stress state. Generall, fatigue damage under non-proportional stress cannot be estimated with validit b the common parameters for multiaial stress state, k (MPa) (a) Nugget edge Electrode Two sheets (MPa) (b) Nugget edge Electrode Fig. 16. Aismmetrical model for spot welding simulation. Fig. 17. Distribution of radial residual stress after welding. (a) Mild steel, (b) 59MPa steel.

7 such as equivalent stress or maimum principal stress [7]. In this stud, thus, the concept of critical plane [7] is emploed. (1) As shown in Fig. 18, normal stress σ θ acting on the plane with angle θ measured counterclockwise from the Y ais is computed b following equation at stress evaluation position. ( σ + σ ) ( σ σ ) σ θ = + cos2θ + τ sin2θ (1) 2 2 (2) The critical plane is defined as the plane on which total range of normal stress shows the maimum, and then normal stress on this critical plane is used for fatigue limit prediction. The variation of normal stress with angle is shown in Fig. 19. It is noted that the stress which does not consider the residual stress, namel, the stress generated onl b fatigue loading is represented in the case of mild steel, whereas the stress in 59MPa steel includes the residual stress. As to mild steel, the peak normal stress denoted b open circles at maimum force is above the horizontal line indicating.2% proof stress. In this stud, therefore, the tensile residual stress is assumed to be released b fatigue loading and its effect is neglected. In the case of 59MPa steel, on the contrar, the maimum normal stress still eists below the lateral line. Thus, the tensile residual stress is taken into consideration. In both steels, there is a difference in the angle with peak stress between at the maimum and the minimum force. These results mean that the principal stress direction rotates and the stress state is non-proportional. The angle with the maimum stress range is about 12 degrees, which is determined as the direction of the critical plane. As shown in Fig. 14, the crack propagation direction in actual spot weld is about 12 degrees from the original interface between upper and lower sheets corresponding to the Y ais in Fig. 18, and the above critical plane is proved to be valid from the standpoint of the failure mode. 3.5 Predicted results Fatigue limit diagrams of HAZ specimen and stress analsis results are represented in Fig. 2. The curved lines denote Gerber diagrams, which connects tensile strength on the X ais and fatigue limit under stress ratio of -1 on the Y ais b parabola. It is noted that fatigue limit of HAZ specimen is the product of nominal stress and the stress concentration factor, In addition, two kinds of analsis result are plotted. The circular smbols indicate the normal stress on the critical plane which does not consider the residual stress and the stress b the triangular smbols include the residual stress. In the analsis of spot-welded joints, the force corresponding to the fatigue limit of the actual joint was applied and it follows that the fatigue limit θ σ θ σ τ τ Fig. 18. Definition of angle and stress acting on the plane. θ σ Normal stress σ θ (MPa) 1 (a) at Maimum force at Minimum force Total range Normal stress σ θ (MPa) 1 σ.2 5 σ.2 5 without residual stress Angle θ (deg) Fig. 19. Change in normal stress with angle. (a) Mild steel, (b) 59MPa steel. (b) at Maimum force at Minimum force Total range including residual stress Angle θ (deg) Stress amplitude σ a (MPa) R=-1 Test results b small specimen Analsis result (without residual stress) Analsis result (including residual stress) R=.1 Dashed line:σ m +σ a =σ.2 ( ) (a) TS (b) TS Mean stress σ m (MPa) Mean stress σ m (MPa) Fig. 2. Fatigue limit diagrams and analsis results. (a) Mild steel, (b) 59MPa steel. Stress amplitude σ a (MPa) Test results b small specimen Analsis result (without residual stress) Analsis result (including residual stress) R=-1 R=.1 ( ) Dashed line:σ m +σ a =σ.2

8 limit can be predicted with more accurac as the stress plot comes near toward the parabola. In the case of mild steel, the circular smbol is near the parabola, which indicates that the precision of prediction is relativel high. With regard to 59MPa steel, the triangular mark is almost upon the parabola and this means that the joint fatigue limit is successfull predicted with little error. Lastl, prediction accurac of the fatigue limit will be quantitativel eamined. As to mild steel, stress onl b fatigue loading is slightl apart from Gerber line. In this stud, the joint analses were conducted again with different loads from the eperimental fatigue limit, and then, a loading condition under which the stress value is located just on the parabola was defined as the predicted fatigue limit. Figure 21 compares the predicted with the eperimental. The evaluation error in mild steel is about 9% and the prediction accurac is satisfactor. It is found that the higher estimated value is obtained in mild steel than 59MPa steel, which coincides with the eperimental results. As discussed before, this is because the fatigue strength of HAZ is approimatel equal in both steels and the tensile residual stress increases mean stress in 59MPa steel. Fatigue limit L w (N) Eperimental Predicted Mild steel 59MPa steel Fig. 21. Comparison between eperimental and predicted results of fatigue limit of spot-welded joint. 4. Conclusions In this stud, small specimens with total length of less than 3mm were taken from each region (base metal, HAZ and nugget) of the spot weld of mild steel and high strength (59MPa-grade) steel sheets, and tensile and high ccle fatigue properties were measured b newl-developed testing method. And then, finite element analses of tensile-shear spot-welded joints under cclic loading and fatigue limit prediction were conducted with the local material strength properties, considering the residual stress estimated b spot welding process simulation. The main results are summarized as follows. (1) Tensile strength of HAZ and nugget is much higher than base metal but ductilit is lower. This is because the microstructure in HAZ and nugget region changes into martensite. (2) Fatigue strength of HAZ, which is the crack initiation site of spot weld, is almost equal in mild steel and 59MPa steel although tensile strength of 59MPa steel is higher than mild steel. (3) Utilizing stress at the crack initiation site (HAZ) with consideration of calculated residual stress and fatigue limit diagrams of HAZ, the joint fatigue limit can be accuratel estimated. Furthermore, it is predicted that mild steel ehibits higher fatigue limit than 59MPa steel, which coincides with the eperimental results. This is due to both the test results of HAZ mentioned above (2) and the effect of tensile residual stress in 59MPa steel. References 1. Lindgen, C., Sperle, J. O. and Johnson, M., Fatigue strength of Spot Welded Beams in High Strength Steels, Welding in the World, 37, 9-14 (1996). 2. Hahn, O., Gieske, D., Klasfauseweh, U. and Rohde, A., Fatigue Resistance of Spot Welds under Multiaial Loads, Welding in the World, 37, (1996). 3. Henrsson, H. -F., Fatigue Life Predictions of Spot Welds Using Coarse FE Meshes, Fatigue and Fracture of Engineering Materials and Structures, 23, (2). 4. Bae, D. H., Sohn, I. S. and Hong, J. K., Assessing the Effects of Residual Stresses on the Fatigue Strength of Spot Weld, Welding Journal, Januar, 18-s to 23-s (23). 5. Nakaama, E., Okamura, K., Miahara, M., Yoshida, M., Fukui, K. and Fujimoto, H., Prediction of Strength of Spot- Welded Joints b Measurements of Local Mechanical Properties, SAE paper Fukumoto, M., Fujimoto, H., Okamura, K. and Fukui. K., Finite Element Simulation of Resistance Spot Welding Process, SAE paper Socie, D. F. and Marquis, G. B., Multiaial Fatigue, SAE (2).