Assessing the Effects of Residual Stresses on the Fatigue Strength of Spot Welds

Residual stress at the nugget's edge was taken into consideration in the evaluation of fatigue strength for spot welds of various shapes and dimensions

BY D. H. BAE, I. S. SOHN, AND J. K. HONG

ABSTRACT. This paper presents a welded structures, accurate stress analysis tion, he proposed material properties be method for fatigue strength assessment of and systematic fatigue strength assess- considered in modeling the weld nugget spot welds, which incorporates the effects ment are needed. Since it is very difficult and the methodology for modeling the of welding residual stress. Residual stress to determine directly the fatigue design electrode. Kim and Eager (Ref. 10) inves- analysis with a welding thermal history criteria for actual structures, it is a typical tigated transient temperature response was evaluated first, and then stress analy- practice to assess fatigue strengths using during spot welding using high-speed cin- sis for fatigue was performed. mock-up specimens with structural and ematography and infrared emission mon- First, the residual stresses of spot welds mechanical characteristics similar to the itoring. Huh and Kang (Ref. 6) developed were calculated using a nonlinear finite el- actual structures (Refs. 1, 2). a three-dimensional (3-D) FEA model for ement analysis (FEA). To validify the FEA Many investigators have numerically electro-thermal analysis of the resistance results, the calculated residual stresses and experimentally assessed fatigue spot welding process. were compared to those measured by X- strength and provided considerable data For fatigue analyses, the stress cate- ray diffraction. The residual stress distrib- on the fatigue strength of various spot- gories are generally evaluated by using a utions showed good agreement between welded joints (Refs. 2, 3). To apply the nominal stress, a structural hot spot stress, calculations and measurements. Then, to data into the fatigue design of actual spot- and a notch stress with consideration of evaluate the fatigue strength of spot welds, welded thin sheet structures, welding stress concentration effects. The choice of stress analyses were performed under ten- residual stress should be properly consid- stress category depends on the method sile loading on various dimensions and ered since it affects fatigue crack initiation used to express the fatigue strength data in shapes of spot welds. and propagation at the nugget edge of a the fatigue assessment (Ref. 11). Among Based on the results, the stress ampli- spot weld. Nevertheless, there are very few these categories, nominal stress and notch tude ((Ya-res)' which took into considera- fatigue strength assessments that consider stress can be considered as the mechanical tion welding residual stress at the nugget welding residual stress because welding parameters for fatigue strength assess- edge of a spot weld, was calculated using a residual stress analysis is quite compli- ment of a spot-welded joint. modified Goodman equation. Using the cated (Refs. 4-6). In this paper, the maximum stress stress amplitude (Ya-res at the nugget edge, Research on welding residual stress range at the edge of the spot weld nugget, the load range (AP)-fatigue life (Nf) rela- analysis is summarized as follows: Tsai et instead of nominal stress, was correlated tions from the fatigue tests can be re- al. (Ref. 7) proposed an FEA model for with the fatigue strength of a spot weld. A placed by the Ga.res -Nf relations. weld nugget generation in the resistance nonlinear FEA was conducted to simulate It was found the proposed stress am- spot welding process. Anastassiou et al. welding residual stress generated by ther- plitude (Ga_res) provided a systematic and (Ref. 8) performed an experimental inves- mal cycles during the spot welding process accurate evaluation of fatigue strength of tigation on welding residual stress and mi- and then the calculated residual stresses spot-welded joints with various dimen- crostructure distribution in spot-welded were compared with experimental data sions and shapes. steel sheets and showed residual stress dis- measured by the X-ray diffraction method tribution was high tensile stress at the cen- to validate the numerical results. Based on Introduction ter and compressive stress near the notch the results, the stress amplitude (O'a_res) root where a fatigue crack initiates. Nied with consideration to welding residual Fatigue strength of spot-welded joints (Ref. 9) investigated the FEA modeling of stress at the edge of the spot weld nugget affects the structural rigidity and durabil- the resistance spot welding process for nu- was calculated using a modified Goodman ity of spot-welded structures, and thus it is merical stress analysis. In this investiga- equation. Then the fatigue load range an important factor in determining safety (AP)-fatigue life (Nf) relations obtained and structural integrity. To determine de- from the fatigue test for spot welds of var- sign criteria for long fatigue life for spot- KEY WORDS ious dimensions and shapes were placed into the stress amplitude (cra.res)-fatigue life (Nf) relation. D. H. BAE ([email protected]) is Professor, Spot Welds School of Mechanical Engineering, Fatigue Strength SungKyunKwan University, Suwon-City. Kyunggi- Residual Stress Welding Residual Stress Do, South Korea. 1. S. SOHN Maximum Principal Stress Analysis (issohn~ mail.osan-c.ac.kr) is Professor, Dept. of Finite Element Method Machine Design Engineering, Osan College, X-Ray Diffraction FEA Model and Assumptions Osan-City, Kyunggi-Do, South Korea. J. K. HONG is Research Scientist, Battelle Memorial Spot welding is a material joining tech- Institute, Cohtmbus, Ohio. nology using electrical resistance heat of ml:l$.1 JANUARY 2003 A 250 I = 2 l Thermal Expansion Coemcient I --4 ~ 200 8o- ~150 1 ...... i ...... 1 v~' o ~100 ==>- Young's Modulus p~ 50 :.,,..." >-

J 0 0 200 400 600 800 1000 Temperature (°C)

Fig. 1 -- Three-dimensional nonlinear FEA model used for welding resid- B ual stress analysis of a spot-welded joint. 1.6 0.055 1.4 nducti~ty 0.05 1.2 0.045 metallic material. During the resistance Fig. 2 (Ref. 12). The ~ 0.04 spot welding process, expansion and yield strength of shrinkage of the material occurs due to the SPCC rapidly 0.8 ..... )...... eat 0.035 o thermal cycle. Thus, welding residual decreased when "6"= 0.6 0.03 the temperature 3 stress and electrode indentation remain at o~ 0.4 0.025 3 the spot weld after the spot welding reached more than vo • process. 400°C and the spe- 0.2 0.02 In this paper, welding residual stresses cific heat increased 0 200 400 600 800 1000 were analyzed both numerically and with temperature Temperature ('(3) experimentally. The numerical analysis but rapidly changed procedure for determining welding near 800°C. The Fig. 2 -- Temperature-dependent material properties employed in nonlin- residual stress on spot welds consists of thermal expansion ear FEA. A -- Mechanical properties; B -- thermal properties. two parts: one is thermal analysis and the coefficient linearly other is mechanical analysis. Once the increased to 200°C temperature is calculated from thermal and thermal conduc- analysis, then the mechanical analysis tivity decreased at is conducted with the corresponding more than 200°C temperature histories. and slightly increased at more than 800°C. Results of Numerical Residual The 3-D FEA model employed in the Young's modulus decreases almost lin- Stress Analysis present work is shown in Fig. 1. Solid brick early with temperature. elements were used for upper and lower Generally, a welding nugget is gener- The temperature profiles taken at the plate modeling. The total number of ele- ated by thermal cycles of heating and cool- nugget center, the nugget edge, and loca- ments and nodes are 4300 and 6151, re- ing of the spot welding process. In this tions 5 mm away from the nugget center spectively. The weld nuggets were pre- analysis, however, nugget temperature of the inner and outer surfaces of the pared using multipoint constraints of the distributions were calculated using the plate are shown in Fig. 3. The peak tem- element nodes on the contact surface to heat block element within ABAQUS, perature was around 1300°C at the nugget prevent the incursion between the upper which can be referred to Huh and Kang center of the inner surface, 700°C at the and lower elements during the welding (Ref. 6) and RWMA (Ref. 13).ABAQUS, nugget center of the outer surface, and process. A sufficiently fine mesh at the a commercial FEA package, was em- 400°C at the nugget edge of both inner nugget was generated to obtain more ac- ployed for the transient temperature and and outer surfaces. curate results. Each plate was divided into subsequent residual stress analysis. The temperature distribution on the four layers to show the nugget generation process. The boundary conditions of the FEA model were the same as those of the Table 1 -- Chemical Composition of SPCC (wt-%) test condition. The material used for both FEA model C Si Mn P S Ni AI Fe and fatigue specimen is a cold-rolled sheet SPCC 0.12 0.01 0.127 0.015 0.007 0.025 0.045 Rem steel called SPCE, widely used for an automobile body. The chemical composition and mechanical properties of the specimen at room temperature are given in Table 2 -- Mechanical Properties of SPCC Table 3 -- Welding Condition of SPCC Tables 1 and 2, respectively. The spot welding condition was defined as the same Tensile Yield Elongation Electrode Welding Welding as in an actual automobile body assembly Strength Strength Force Current Time facility, which is described in Table 3. The (MPa) (MPa) (%) (N) (kA) (Cycles) temperature-dependent material proper- SPCC 307 168 47 Welding ties applied for the FEA are shown in condition 1962 8.3 15

WELDING JOURNAL Eiz~..'l 1400 ~'~-'" ~--@"-Q + Outer-center 1200 .:' • + Outer-nuggetedge O 1000 :' "o o Outer-5mm ::' ---o-- Inner.center :~ 800 ..: • ..-D-. Inner-nuggetedge

I.- 400 ,oo

0 0.5 1 1.5 Time. sec.

Fig. 3 -- Temperature profiles on the inner and outer surfaces of the plate. Fig. 4 -- Temperature distribution on the nugget cross section.

15o ~.~p 'I 1 p t ,4,,M-~pI ¢ OTR-EXP(omax) o OTR-FEM(omax) #. 100 j o o OTR (Ref.8) $ • INR-EXP(omax) U~ 50 ~ ~ D INR-FEM(omax) o I o ,$ In-planebending moment In-#ane force and 0t ~ o o out of plane bending moment ! ~b $ * 8 -50 ~] [] o [] o Q: In-plane bending force $ P: in-plane shear force -100 • M: out-of plane bending moment 0 1 2 3 4 Radialdistance from nuggetcenter, rnm

Fig. 5 -- Welding residual stress distributions of the spot weld (outer sur- Fig. 6 -- Inner forces acting on the nugget. face, OTR; inner surface, INR; experimental data, EXP; FEA results, FEM). outer surface is lower than on the inner compression) on the outer and inner sur- surface of the lower plate. Since its influ- surface due to heat transfer from the outer face, respectively. Welding residual ence is believed to be insignificant, it was surface of the nugget to both upper and stresses on the outer surface show high not considered in this study. lower electrodes, which are cooled by cir- tension at the nugget center and compres- culating water. However, both inner and sion around the nugget edge. Comparison of the Numerical and outer surface temperature distributions at Experimental Results the nugget edge show similar results. Fig- Measurement of Residual Stresses Using ure 4 shows the temperature distribution X-Ray Diffraction Method The calculated welding residual on the nugget cross section after the weld- stresses on the inner and outer surface of ing nugget has been generated. To validate the numerical results, weld- spot-welded joints were compared to In general, since fatigue crack initia- ing residual stresses were also experimen- measured values and data by Anastassiou, tion occurs at the nugget edge on the inner tally analyzed using the X-ray diffraction et al. (Ref. 8) in Fig. 5. Welding residual surface of the loading side, it would be rea- method. The X-ray diffraction unit used is stresses measured in experiment were sonable to look at the stress at the fatigue the MSF-2M type by Rigaku Co. of Japan. about +70 MPa (in tension) at the outer crack initiation location to assess the fa- Welding residual stresses were measured surface of the nugget center and -75 MPa tigue strength of spot welds. Therefore, in with the following conditions and proce- (in compression) at the inner surface. In this investigation, welding residual dures: the projected area was 2 mm 2 and the numerical analysis, the values were ap- stresses at the nugget edge on the inner the X-ray was exposed to the inner and proximately +40 MPa (in tension) at the surface were analyzed both numerically outer surfaces of the nugget area in four outer surface of the nugget center and -40 and experimentally. different angles and three times, respec- MPa (in compression) at the inner surface Calculated residual stresses at the tively. Their mean values were applied to of the nugget center. Both the numerical nugget center show +40 MPa (in tension) calculate welding residual stresses using and the experimental results showed high and -40 MPa (in compression) on the the sin20 method. Note that in the process tension at the outer surface of the nugget outer and inner surface, respectively. of cutting off the upper plate of the spot- center and compression around the Also, calculated welding residual stresses welded joint under wet conditions, ma- nugget edge. Calculated and measured at the nugget edge are approximately -17 chining can influence welding residual residual stresses at the nugget edge on MPa (in compression) and -38 MPa (in stresses at the nugget edge on the inner outer surface were -17 MPa (in compres-

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/ ~ ~~ i_~ _ ' Outer suffGce i Inner surface ~_ ,, P I- Inner surface II I'l II ii_ i~p ~I~ Outer surface T 0n=6mm o=1.250. 2.5°. 5 °, 75 °

Boundary condition: out of plane displacements are fixed on side CD, all displacements are fixed at point E

Fig. 7-- Stress analysis model of lB-type spot-welded joint. Fig. 8 -- Stress distribution around the spot weld of lB-type spot-welded lap joint subjected to tensile shear load. sion) and -14 MPa (in compression), re- plicated pattern of spectively. Also, calculated and measured deformation (Ref. 3000 15). Fatigue cracks A residual stresses at the nugget edge on the & inner surface were -38 MPa (in compres- are generally gener- 2500 sion) and -70 MPa (in compression), re- ated at the nugget spectively. edge on the inner z 2oo0 Such a discrepancy between the nu- surface and propa- I0 I ¢I merical and experimental values for weld- gated to the outer ~ 15o0 ing residual stresses may be attributed to surface of the plate _o by this deformation ew=30mm, t=-lmm. 6=1.25 ° • ~11 the difference between the conditions of • a mechanism and ~ 1000 • w'=30mrn, t=-lmm. 0=2.5 ° • the numerical analysis and the experi- & w=30mm, t=-Imm. 0=5,0 ° • & ment. The nugget metal was actually stress concentration. < • w=30mm, t=lmm, e=7.5 ° pressed out by the electrode force and Therefore, it is very s00 x w--40mm, t=lmm, 9=2,5" [] w=60mm, t=l mm, 9=25 ° thermal expansion. However, such actual important to calcu- & w=30mm, t=-2mm, 9=2,5* welding conditions and various thermal late the accurate 0 and physical properties were neglected in stress and strain dis- 1.E+04 1.E+05 1.E+06 1.E+07 the process of the FEA. Also, the effect of tributions around Number of cycles to failure, Nf (cycles) phase transformation during the welding the weld nugget for a reasonable fatigue process and the release of residual stress Fig. 9 -- AP-Nf relation of lB-type spot-weMed lap joints. when cutting off the plate with wet ma- strength assessment. chining were not considered in the FE In this study, a analysis. In spite of the discrepancy, the 3-D FE model was residual stress distributions show reason- used to calculate the stress distribution. Di- applied to each fatigue specimen. able agreement between the calculations mensions of the reference model are plate ABAQUS, a commercial FEA package, was and measurements. thickness, t, 1 mm; plate width, w, 30 mm; used for the stress analysis. The stress analy- specimen lapped length, 2L, 30 mm; and sis model is drawn in Fig. 7. Stress Analysis Considering the joint angle between upper and lower plate, Welding Residual Stress 0, 2.5 deg. Three-dimensional solid brick el- Results of Stress Analysis ements were used for the FEA model. The Stress Analysis Model total numbers of elements and nodes used Stress distributions around the weld of were 1164 and 1992, respectively. The IB-type spot-welded joint subjected to ten- In order to evaluate the fatigue upper and lower plates had only one layer sile shear load are shown in Fig. 8. It shows strength of spot-welded joints, stress of solid brick element and the weld nugget stress concentration occurs at the nugget analysis was also performed. The model is area had a refined mesh. The nugget size edge on the loading side of the plate and a spot-welded bus window pillar joint sus- was modeled with the same diameter of ranges from -20 to 40 deg, which is affected taining in-plane bending force by warping electrode used in industrial fields, and the by the joint angle. When the joint angle was of the body structure. When the external weld nugget was modeled using multipoint more than 5 deg, tensile stresses were si- tensile shear load is applied to the in-plane constrains for the nodes of the upper and multaneously generated at the nugget edge bending (IB) type single spot-welded lap lower elements on the contact surface. in the opposite side as well as in the loading joint, three kinds of internal forces act on Boundary conditions and load conditions side. This phenomenon is due to the fact the spot-weld: in-plane shear force (P), in- were assumed as the same as those for the that out-of-plane bending and in-plane plane bending force (Q), and out-of-plane fatigue tests. Fatigue strength was actually bending deformation increase with the joint bending moment (M), as illustrated in Fig. assessed with the mechanical parameter angle increases. It is known that other geometrical factors such as plate thickness and 6. These internal forces give a very com- and it was calculated with the actual load

WELDING JOURNAL mI,',lil~.l 200 r 500- . ~m.t-lmm, e-12s' l ; .~-~m:t=-lmm,e=ta~" " " -- o, • ~3Q'r~.t-l~.e-2s" 180 ..... : ' ' • w=30mm, t=-lmm, 6=2.5* 1 -- 160 ...... i , & w=30mm, ~--lmra, 0=5.0* i .... o,-~, 400 ; ...... X ~30'nm.l'll~.~7S" c°= I e w=30mm, t=lmm, 0=7.5* ,~ 140 ~ ...... X~40mm, t=lmm, e=2.5" " j • ~EG'nmt-1~.~25" ~ ~ 12 ~ ow--60mm, t=-lmm, B=2.5* F 8 ,~ 0 l ...... AW=30mm, t=2mm, e=2.5* " ! "o ,,~ 100 I ...... o ~30mm.I~ 1~, Bsl ~5" x ~7~ 80 / - * ..... r~: ...... XL - • a ~3omm,t,,l~S*~O* m,~ /

11 0 ~'''tx'- ~ ~30~ t=Zmm,e=2 5" 20 ...... o i ol 1 .E+O4 1 .E+05 1 .E+06 1 .E+07 1 E+04 1E~5 1.E'*06 1 E+07 Number of cycles to failure, Nf ~ O' cycl~ to failure, I~ (cyc~)

Fig. 10 -- Representation in the Aa,,_r~.,.-Nfrelation of various IB-type spot- Fig. 11 -- Comparison of the Ga-N/ relation and the ~,res-Nf relation of weMed lap joints. various IB-type spot-weMed lap joints.

width also affect stress concentration where (~a-rc,s and (~rc's are the stress ampli- joints. Thus, in the present test, the pin around the nugget edge (Ref. 16). tudes, which consider welding residual joint grips were used to remove the effects stress and welding residual stress at the of in-plane bending deformation and Calculation of the Stress Amplitude nugget edge of the spot weld, respectively. force (Ref. 16). Considering Welding Residual Stress In Equation 2, G,.re s iS defined as Fatigue tests were conducted under the following conditions: frequency (r") was 25 Among the stress categories, the nomi- Gmean+Gres) Hz, cyclic loading form was Sine wave, and nal stress and the notch stress can be con- a =S e 1 normal load ratio was 0 since it is known sidered as mechanical parameters for sys- a -res Sl I that the influence of the frequency for fa- tematic fatigue strength assessment of f( (3) tigue strength at room temperature and in spot-welded joints. As mentioned previ- When the normal load ratio, R (= air is negligible (Refs. 16, 17). The number ously, nominal stress (G, = P/W.t, Wiswidth amin/Crm,x) becomes zero, then G,...... = of cycles to failure was determined as the of plate, and t is plate thickness) of the plate Gmax/2. Therefore, the stress amplitude, cycles when a fatigue crack appeared on is considerably influenced by geometrical which considers welding residual stress, the outer surface of the specimen and factors such as the plate thickness and the can be written as when its length was equal to nugget diam- width. Therefore, it is proposed to use the eter. Fatigue limit of each specimen was maximum principal stress at the nugget 2S,,-(G,,,~+ 2Gres) determined as the load that did not initi- edge on the inner surface of IB-type spot- ate a crack at 107 cycles. welded lap joints. The stress amplitude G a -res = Se 2S, (£~a-res)' which considers welding residual f (4) Fatigue Test stress, was calculated using the modified Goodman equation that follows. Load Range (AP)-Fatigue Life The fatigue test results for various IB- (Nf) Relation type spot-welded joints are shown in Fig. 9 as AP-Nf relations. The influence of the Ga F (Ymean = ], (1) Specimens and the Testing Method geometrical factors on fatigue strength S e S. can be observed. In higher loads and where aa = ~max - Groin ," Dimensions and shapes of the speci- shorter life ranges, the influence of the 2 mens were the same as those in the FEA plate thickness is not clearly observed due models. The welding conditions followed to the complicated deformation charac- Gma x + Gmi n Gmean -- were from the recommendation of teristics of the thin plate. However, in 2 RWMA (Ref. 13) class-C, illustrated in lower loads and longer life ranges, it is Table 3. The diameter of the electrode clearly revealed. The fatigue strength con- S e is fully reversed fatigue strength at a used for spot-welding was 6 mm, a typical siderably increases with the plate thick- given number of cycles; S u is ultimate size for an actual application. The fatigue ness under the same loading condition stress; O'm/. and G,,ax denote the minimum testing machine used is a servo-hydraulic due to the increase of bending rigidity of and maximum stresses, respectively. The power system (MTS, capability 98 kN). Fa- the plate. For the same thickness, the fa- modified Goodman equation considering tigue tests, such as tensile shear (TS) type tigue life decreases with the joint angle of welding residual stress, which was pro- specimens, are generally conducted with the specimen due to the fact that torque of posed in this study, can be written as simple plate grips (Refs. 14-15). However, the weld nugget by in-plane bending de- in the case of IB-type spot-welded joints formation linearly increases with the joint ~a-res ~ (Gmean+Gres)_ 1 subjected to tension-shear load, the sim- angle. However, the influence of the plate ple grip cannot be used due to in-plane width on fatigue strength is not clearly Se St, (2) bending deformation of spot-welded lap identified. Since the data of the AP-Nf re-

BP',,P,,~-"1 JANUARY 2003 lations are widely scattered by the influ- Conclusions Fracture Mechanics 37(5): 993-951. ence of geometrical factors, it is difficult to 6. Huh, H., and Kang, W. J. 1997. Electro- determine the fatigue design criterion The following conclusions are made in thermal analysis of the electric resistance spot even with a slight change of the design. this study: welding process by a 3-D finite element 1) Welding residual stresses of spot- method. Journal of Material Processing Technol- ogy 63 ( 1-3): 672-677. Fatigue Strength Assessment welded joints were calculated by the non- 7. Tsai, C. L., Dickinson, D., and Jammal, O. Considering Welding Residual Stresses linear FEA method and compared with the experimentally measured values by the A. 1990. Study of nugget formation in resistance spot welding using finite element method. Many investigators have numerically X-ray diffraction method. The residual stress distributions show reasonable Recent Trends in Welding Science and Technol- and experimentally attempted to establish agreement between the calculations and ogy. Eds. S. A. Davis and J. M. Vitek, pp. 43-53. a reasonable fatigue design method for ASM International, Materials Park, Ohio. spot-welded lap joints. Some insightful re- measurements. 2) To develop a reasonable fatigue 8. Anastassiou, M., Babbit, M., and Lebrun, sults can be found in such publications as J. L. 1990. Residual stress and microstructure Engineenng Fracture Mechanics, Fatigue strength assessment method of spot- welded joints with various dimensions and distribution in spot-welded steel sheet: Rela- and Fracture of Engineering Materials and shapes, a stress amplitude that takes into tion with fatigue behavior. Material Science attd Structttres, Journal of JSAE, and JSAE Re- consideration welding residual stress Engineering A125: 141-156. view. However, it is still difficult to find an 9. Nied, H. A. 1984. The finite element mod- approach considering welding residual (Oa_rcs) was proposed. In this study, it is shown the proposed stress amplitude eling of the resistance spot welding process. stresses in fatigue strength assessments. (~Ja-rcs) can provide a systematic and accu- WeldhtgJouma163(4): 123-s to 132-s. Therefore, the stress amplitude ((Ya-res)' 10. Kim, E. W., and Eager, T. W. 1989. Mea- which considered welding residual stress, rate evaluation of fatigue strength of spot- welded joints with various dimensions and surement of transient temperature response was employed to establish a reasonable fa- shapes. during resistance spot welding. WeMingJournal tigue strength assessment method for spot 68(8): 303-s to 31 l-s. welds with various dimensions and shapes. 3) The fatigue strength at a fatigue limit that considers welding residual stress 11. Niemi, E. 1995. Stress Determhtation for Figure 10 shows the (Ya_res-Nf relation Fatigue Analysis of Wekled Components. Eng- of IB-type spot-welded lap joints with var- is about 25% lower than that without consideration of welding residual stresses. land: Abington Publishing pp. 3-25. ious dimensions and shapes under tensile 12. Goldsmith, A. 1961. Handbook of shear loading. Figure 11 shows the com- References Thermo Physical Properties of Solid Materials. parison between the fatigue strengths rep- Revised ed. il. The MacMillan Co, pp. 28-56. resented by stress amplitudes with and 1. Hujimoto, M. O., Mori, S. K., and Ojima, 13. RWMA, 1981. Residual ,Spot WeMing without consideration of welding residual Manual 1:119-143. stresses. Fatigue strengths from the stress M. 1985. Modeling of automobile structure members and research objects. JSAE Sympo- 14. Tomioka, N., Niisawa, J., and Bae, D. H. amplitude range that neglect welding 1988. Theoretical analysis of stress distribution residual stresses are much higher than sium, JSAE, pp. 2(I-26. 2. JSAE. 1987. Databook Fatigue Data of of single spot-welded lap joint under tension- those that consider welding residual shear load. Journal of JSAE 39: 105-112. stresses. From Fig. 10, the fatigue strength Spot-WeMedJoints. JSAE, pp. 12-185. 3. Bae, D. H. 1991. Fracture mechanical fa- 15. Bae, D. H., Niisawa, J., and Koiso, A. at fatigue limit was around 32 MPa. This 1988. On stress distribution and fatigue value is about 25% lower than that ne- tigue strength evaluation of IB-type-spot welded lap joint under tension shear load. Jour- strength of single elliptical spot-welded lap glecting welding residual stresses. This in- joint under tension shear load. JSAE Review 9 dicates that fatigue strength of IB-type nalofKSAE 13(5): 42-50. 4. Radaj, D., and Zhang, S. 1995. Gcomct- (4): 86-91. spot-welded joints could be greatly over- 16. Sohn, I. S. 1998. A study on the hltigue de- estimated by neglecting welding residual rically nonlinear behavior of spot-wclded joint in tensile and compressive shear loading. Jour- sign method and expert system development for stresses. Therefore, for determining more nal of Engineering Fracture Mechanics 51 (2): thin steel sheet spot welded lap joint. Ph.D. dis- reasonable fatigue design criterion of the sertation. SungKyunKwan University, S. Korea. spot-welded structures, the welding resid- 281-294. 5. Radaj, D., Zheng, Z., and Mochrmann, 17. Shigley, J.E., and Mischkc, C. R. 1989. ual stresses generated in the welding Mechanical Engineering Design. 5th ed., Mc- process should be considered in fatigue W. 19911. Local stress parameter at the spot weld of wMous specimens. Journal of Engineering Graw-Hill, pp. 286-288. strength assessment.

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