- Email: [email protected]
Fatigue Life Predictions of Adhesive Joint of Sheet Steels
Available online at www.sciencedirect.com
ScienceDirect Procedia Engineering 133 (2015) 518 – 527
6th Fatigue Design conference, Fatigue Design 2015
Fatigue Life Predictions of Adhesive Joint of Sheet Steels HongTae Kanga,*, Zhen Lia, A.K. Khosrovanehb, Byeongwook Kanga, Ziang Lia a
The University of Michigan-Dearborn, 4901 Evergreen Road, Dearborn, MI 48128, USA b General Motors LLC., 30001 VanDyke Road, Bldg 2-10, Warren, MI 48090, USA
Abstract Structural adhesive is widely employed in vehicle structures to enhance noise-vibration and crashworthiness performance. It is also known that structural durability is enhanced with application of structural adhesive. Many researchers have reported the fatigue performance of adhesive joints, but the test results showed noticeable scatter, making it hard to develop a fatigue life prediction method. This study fabricated cross-tension specimens joined with either adhesive only or adhesive with a spot-weld joint. These specimens were subjected to a 45-degree loading direction with respect to adhesive joint plane. The materials used for the specimens were various sheet steels, including mild steel, DP, and ultra-high strength steel. Fatigue tests were conducted for the specimens and a stress-life curve was constructed using a structural stress method. The test results were also correlated with a fracture mechanics approach. Both of the approaches showed reasonable correlation with the test results. © by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2015 2015Published The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of CETIM. Peer-review under responsibility of CETIM Keywords: Adhesive joint; Structural stress method; Fatigue life prediction; Sheet steels
1. Introduction Structural adhesives are widely employed in the construction of vehicle structures to improve crashworthiness, noise and vibration, and durability performances. Recently, the application of structural adhesives has become more common in joining dissimilar materials in vehicle structures. Since structural adhesives started being employed in vehicle structures, many researchers [1–7] investigated the strength and fatigue performance of the joints. Then the research interest shifted to the development of methods for fatigue life prediction of the joints [8–14]. Most of the
* Corresponding author. Tel.: 1-313-593-1878; fax: 1-313-593-5386. E-mail address: [email protected]
1877-7058 © 2015 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of CETIM
doi:10.1016/j.proeng.2015.12.623
HongTae Kang et al. / Procedia Engineering 133 (2015) 518 – 527
research [10, 12–14] was conducted with fracture mechanics concepts to predict the fatigue life of adhesive joints. Tomioka and co-workers [9] and Hong and Forte [11] used structural-stress concepts to predict fatigue life of the adhesive joints. Some research efforts [15–17] were also devoted to developing proper representations of the adhesive layer in finite element (FE) models. Non-linear characteristics of the adhesive materials were the main focus in the development of the proper representation of the joints in FE models. This study was conducted to develop a fatigue life prediction method using a structural stress method [18] for adhesive joints between sheet steels. To construct the structural stress versus life curve of the adhesive joints, coupon specimens were constructed for joining DP600 to DP600 and HSLA340 to HSLA340. Then, the S-N curve was used to predict fatigue life of adhesive joints between a mild steel and an ultra-high strength steel for validation of the structural stress method. The adhesive joints for the validation are subjected to cross-tension loading with 45-degree angle. The predicted fatigue life using the structural stress method correlates reasonably well with the fatigue test results of the cross-tension specimen geometry. 2. Specimen dimensions and experimental results The adhesive with spot welded joint specimens were constructed for DP600 to DP600 and HSLA340 to HSLA340 with lap-shear (LS) and coach-peel (CP) specimen geometries [19]. Also, the adhesive-only joint specimens were constructed for DP600 to DP600 with lap-shear specimen geometry. The sheet thickness used in this study was 1.53 mm for DP600 and HSLA340 steels. The adhesive material used in this study was EFTEC EFBOND WC2309 structural adhesive. The spot weld diameter was 7 mm for the adhesive joint with a spot weld. The specimen dimensions and geometries are shown in Fig. 1 [20]. The area to which the adhesive was applied was the overlapped region of the specimens.
Fig. 1. Dimensions and geometries of lap-shear and coach-peel specimens [20].
Fatigue tests of the specimens were conducted at test frequency of 7 or 10 Hz [19]. The fatigue failure criterion is the full separation of the specimen into two pieces. The runout is defined as 3 million cycles and marked with
519
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arrows in Fig. 2. The fatigue test results of the specimens are presented in load range versus cycle to failure as shown in Fig. 2. The upper group of data points in Fig.2 is from LS specimens and the lower group of data points in the same figure is from CP specimens. As shown in Fig. 2, no differences are observed between adhesive-only joints and adhesive with a spot weld joints in fatigue performance of LS specimens. The test results also show that the sheet strength of the joints does not affect the fatigue strength of the adhesive with a spot weld joints in CP and LS specimens. This is the same observation as with the fatigue performance of spot-weld only joints [20]. The slope of the load range versus fatigue life is very flat, and noticeable scatter is observable in the CP and LS specimen geometries. The slope in the CP specimen results is flatter than that of the LS specimens. The failure mode of the adhesive with spot weld joint is shown in Fig. 3 [19]. The failure mechanism is very similar to that of the adhesiveonly joint since the majority of the applied load is carried by the adhesive regions. Only after the adhesive region in front of the spot weld fails does the spot weld take the applied load. 1.E+05
DP600_LS_Adhesive Only_1.53mm DP600_LS_Adhesive+Spotweld_1.53mm DP600_CP_Adhesive+Spotweld_1.53mm HSLA340_CP_Adhesive+Spotweld_1.53mm HSLA340_LS_Adhesive+Spotweld_1.53mm
Load Range, N
1.E+04
1.E+03
1.E+02 1.E+03
1.E+04
1.E+05
Cycles to Failure Fig. 2. Fatigue test results of LS and CP specimens.
1.E+06
1.E+07
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(a)
(b) Fig. 3. Typical failure modes of adhesive with a spot weld for HSLA340 (a) CP; (b) LS [19].
3. Structural stress calculation 3.1. Structural stress equation This study used a structural stress concept to develop a fatigue life prediction method for adhesive-only joints and adhesive with spot weld joints between sheet steels. This structural stress concept is widely used for fatigue life prediction of spot welded joints [21–23]. The biggest advantage of the structural stress concept is that structural stress is a lot less sensitive in the mesh sizes than stresses obtained from finite element analysis. The structural stress method used in this study was originally proposed by Rupp and co-workers [18] and modified by nCode [24] for taking account of the effect of sheet thickness and spot-weld diameter on the structural stress. The modified structural stress method for a spot welded joint is briefly summarized below. The structural stresses in the radial direction are calculated from the forces and moments acting on the circular weld nugget sitting on a circular plate, as shown in Fig. 4 [23]. The radial structural stresses ( σ r ) due to the forces in the x- and y-directions are calculated as follows:
§F · σ r FX ¨ X ¸ PFXY © πdt ¹
(1)
§F · σ r FY ¨ Y ¸ PFXY © πdt ¹
(2)
§k F · σ r FZ ¨ 1 2 Z ¸ PFZ © t ¹
PFXY PFZ
if FZ ! 0 or 0 if FZ d 0
SFFXY d DEFXY t TEFXY
SFFZ d DEFZ t TEFZ
(3) (4) (5)
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where σ r FX and σ r FY are the radial stresses due to forces ( ܨ ܨ ) in the X- and Y-directions,
respectively. The diameter of the circular weld nugget is “d” and the thickness of the circular plate is “t.” σ r FZ is
the radial structural stress due to a normal force FZ on the weld nugget and k1 (=1.744) is a parameter that depends on the ratio of the nugget radius and specimen length from the center of the nugget to the edge of the grip area. ܲி ܲி are the correction parameters of the radial structural stresses for the different sheet thicknesses and the weld nugget diameters. SFFXY is the empirical scale factor for force in the X and Y directions. DEFXY and DEFZ are the diameter exponents for the forces in the X, Y, and Z directions, respectively. The thickness exponents are defined as TEFXY and TEFZ. The radial structural stresses due to the applied moments with respect to the local X- and Y-directions ( M X and
M Y , respectively), occur at the edge of the weld nugget and are expressed as:
σ r M X
k2MX PMXY , dt 2
(6)
σ r M Y
k2MY PMXY , dt 2
(7)
PMXY
SFMXY d DEMXY t TEMXY
(8)
where k 2 (=1.872) is a parameter that depends on the ratio of the nugget radius and specimen span. PMXY represents the correction parameters of the radial structural stresses for the different sheet thicknesses and weld nugget diameters. SFMXY is the empirical scale factor for the moment with respect to the X and Y directions. DEMXY is the diameter exponent for the moments with respect to the X and Y directions. The thickness exponent for the moments is defined as TEMXY.
Y
Fig. 4. Circular plate model for a spot weld joint [23].
Subsequently, the radial structural stresses, except for the stress due to the normal force, are calculated incrementally along the circumference of the weld nugget by the angle θ . Here, θ is the angle as measured from a reference axis in the plane of the weld nugget. The resulting equivalent structural stresses as a damage parameter are then calculated by the appropriate combination and superposition of local radial structural stresses along the circumference of the weld nugget, as shown below:
σ eq θ σ r FX cosθ σ r FY sinθ σ r FZ σ r M X sinθ σ r M Y cosθ
(9)
Finally, the maximum radial structural stress is determined for the given applied load from the equivalent structural stresses calculated using Equation (7). The maximum radial structural stress range versus fatigue life of
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the specimens tested is then plotted on log-log coordinates, resulting in an S-N curve for a given joint, and is fitted using equation (8) below:
'V eqmax where 'V eq
max
A N f
b
(10)
is the maximum structural stress range, N f is the number of cycle to failure, “A” is the coefficient,
and “b” is the exponent.
3.2. Constructing S-N curve using the structural stress range To construct the S-N curve of adhesive joints with and without a spot weld using the structural stress equations explained in the previous section, it is necessary to develop finite element (FE) models for the specimen types considered in this study. In the FE models of these specimens, the adhesive area is represented with the area contact method (ACM), consisting of a hexagonal element with rigid connection elements between steel sheets. A typical representation of ACM is shown in Fig. 5. The forces and moments at nodes are then transformed to the center of the surfaces that contact with steel sheets, presented with shell elements. These forces and moments are used to calculate the structural stress of Equation (7). Fig. 6 shows FE models of LS and CP specimens, and Fig. 7 shows the structural stress range versus the number of cycle to failure of the specimens. The element size in the FE models is 5 mm by 5 mm, and the overlapping region to which adhesive is applied is connected with ACM.
Fig. 5. A typical ACM representation in FE model [24].
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Fig. 6. FE models of CP and LS specimen.
4. Validation of the structural stress approach for adhesive joints The S-N curve developed from LS and CP specimens of DP600 and HSLA340 sheet steels is used to predict fatigue life of an adhesive joint with and without a spot weld. The specimens are constructed with cross-tension (CT) geometry, as shown in Fig. 8. Various strengths of steels are joined with adhesive only and with adhesive with a spot weld. Sheet thicknesses of the loading part (1.6 mm) and the constrained part (1.2 mm) are different. These combinations of specimens provide better data to validate the structural stress approach. The predicted life versus test life of the CT specimens is shown in Fig. 9. The dotted line represents a perfect correlation between the predicted life and the test life. The two solid lines present the upper and lower factor of 3. As shown in Fig. 9, the structural stress method works fairly well except in the long-life region. Many things contribute to making the difference between the predicted life and the test life. The most important factor for this difference is that the slopes of LS and CP in the S-N curve are actually different. This study, however, did not distinguish the difference in the slopes of the S-N curve since whether the joint in a real structure is in LS condition or CP condition cannot be identified. Usually, S-N slopes for LS specimens and CP specimens are the same in S-N curve of spot-weld joints. Another contributing factor for this difference could be the equations of the structural stresses used in this study. These equations were developed for spot-weld joints, and the mechanics at the adhesive joint are definitely different from those of a spot-weld joint. This study ignores the differences and assumes that the same equations could represent the fatigue characteristics of adhesive joints. Thus, it is necessary to conduct further studies in prediction of fatigue life of adhesive joints with and without a spot weld.
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1.E+03
Structural Stress Range (MPa)
DP600_LS_AdhesiveOnly_1.53mm DP600_LS_Adhesive+Spotweld_1.53mm DP600_CP_Adhesive+Spotweld_1.53mm HSLA340_CP_Adhesive+Spotweld_1.53mm HSLA340_LS_Adhesive+Spotweld_1.53mm
1.E+02
1.E+01
1.E+00 1.E+03
1.E+04
1.E+05
1.E+06
Cycles to Failure Fig. 7. Structural stress range versus fatigue life of CP and LS specimens.
Fig. 8. Cross-Tension specimens.
1.E+07
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1.E+07 980 spcc
1.E+06
440 590
Predicted Life, Cycle
1470 1.E+05
1.E+04
1.E+03
1.E+02 1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E+07
Test Life, Cycle Fig. 9. Comparison between predicted life and test life using the structural stress method.
5. Summaries and Conclusions The application of structural adhesives is being increased to enhance crashworthiness, noise and vibration, and structural durability performance. Many researchers [1–7] have reported the fatigue performance of structural adhesive joints with or without a spot weld. However, information on the fatigue life prediction methods for these joints is very limited. Thus, this study revisited the fatigue test results for adhesive joints with and without a spot weld in LS and CP specimen geometries and investigated the applicability of a structural stress method developed for spot weld joints to predict the fatigue life of these joints. The structural stress-based S-N curve was developed from fatigue test results of LS and CP specimens for DP600 and HSLA340 and applied to predict fatigue life of CT specimens of various steels. The structural stress method used in this study predicts reasonably well the fatigue life of adhesive joints with and without a spot weld in the short-life region. From the study conducted, the following conclusions are drawn: x The structural stress method can be applied to predict fatigue life of adhesive joints with or without a spot weld regardless of the specimen geometry. x For the high-cycle region, it is necessary to improve the accuracy of the fatigue life prediction.
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References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24]
B.H. Chang, Y.W. Shi, S.J. Dong, A Study on the Role of Adhesives in Weld-Bonded Joints, Welding Journal Research Supplement 78 (199) 275-s-279-s. A. Melander, J. Linder, H. Stensio, M. Larsson, A. Gustavsson, A., G. Bjorkman, How Defects in an Adhesive Layer Influence the Fatigue Strength of Bonded Steel-Sheet Specimens, Fatigue and Fracture Engineering and Material Structures 22 (1999) 421-426. X. Long, S.K. Khanna, Fatigue Performance of Spot Welded and Weld Bonded Advanced High Strength Steel Sheets, Science and Technology of Welding and Joining 13 (2008) 241-247. S. Sam, M. Shome, Static and Fatigue Performance of Weld Bonded Dual Phase Steel Sheets, Science and Technology of Welding and Joining 15 (2010) 242-247. W. Xu, L. Liu, Y. Zhou, H. Mori, D.L. Chen, Tensile and fatigue properties of weld-bonded and adhesive-bonded magnesium alloy joints, Material Science & Engineering A 563 (2013) 125-132. S.H. Chowdhury, D.L. Chen, S.D. Bhole, X. Cao, P. Wanjara, Lap shear strength and fatigue behavior of friction stir spot welded dissimilar magnesium-to-aluminum joints with adhesive, Material Science & Engineering A 562 (2013) 53-60. W. Lai, J. Pan, Failure mode and fatigue behavior of weld-bonded lap-shear specimens of magnesium and steel sheets, International Journal of Fatigue 75 (2015) 184-197. N. Tomioka, J. Niisawa, H. Kitagawa, Stress analysis and fatigue strength on adhesive joints, SAE Technical Paper No. 931886, 1993. J.K. Shang, R.A. Chernenkoff, Fatigue life prediction methods for adhesive-bonded sheet-aluminum joints, SAE Technical Paper No. 960575, 1996. J.A. Harris, R.H. Martin, Development of a life assessment method for bonded and weld-bonded automotive structures, SAE Technical Paper No. 980692, 1998. J.K. Hong, T. Forte, Development of fatigue evaluation procedure for weld-bonded joints using the Battelle structural stress method, SAE Technical Paper No. 2012-01-0477, 2012. P. Hayes, G. Bjorkman, A. Blows, T. Mumford, P. Briskham, A fracture mechanics approach to durability calculations for adhesive joints, SAE Int. J. Mater. Manf. 5(1) (2012) 215-225. T. Walander, A. Eklind, T. Carberger, U. Stigh, Fatigue damage of adhesive layers – experiments and models, Procedia Materials Science 3 (2014) 829-834. W. Lai, J. Pan, Stress intensity factor solutions for adhesive-bonded lap-shear specimens of magnesium and steel sheets with and without kinked cracks for fatigue life estimations, Engineering Fracture Mechanics 131 (2014) 454-470. R.H. Andruet, D.A. Dillard, S.M. Holzer, Two- and three- dimensional geometrical nonlinear finite elements for analysis of adhesive joints, International Journal of Adhesion & Adhesives 21 (2001) 17-34. D. Castagnetti, E. Dragoni, Standard finite element techniques for efficient stress analysis of adhesive joints, International Journal of Adhesion & Adhesives 29 (2009) 125-135. X. He, A review of finite elements analysis of adhesively bonded joints, International Journal of Adhesion & Adhesives 31(2011) 248-264. A. Rupp, K. Storzel, V. Grubisic, Computer aided dimensioning of spot-welded automotive structures, SAE Technical Paper No. 950711, 1995. S.K. Khanna, Fatigue testing and failure characterization of spot welded dual phase, Final Report for Auto/Steel Partnership, 2004. J. Bonnen, H. Agrawal, M. Amaya, R. Mohan Iyengar, H. Kang, A.K. Khosravaneh, T. Link, H. Shih, M. Walp, B. Yan, Fatigue of advanced high strength steel spot welds,” SAE 2006 Transactions Journal of Materials & Manufacturing (2007) 726-744. P. Dong, A structural stress definition and numerical implementation for fatigue analysis of welded joints, International Journal of Fatigue 23 (2001) 865-876. S.D. Sheppard, Further refinement of a methodology for fatigue life estimation in resistance spot weld connections, Advances in Fatigue Lifetime Prediction Techniques: 3rd Volume, ASTM STP 1292, American Society for Testing and Materials, Philadelphia, 265-282, 1996. H. Kang, Fatigue prediction of spot welded joints using equivalent structural stress, Materials and Design 28 (2007) 837-843. DesignLife Theory Manuals, HBM-nCode, 2014.
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ScienceDirect Procedia Engineering 133 (2015) 518 – 527
6th Fatigue Design conference, Fatigue Design 2015
Fatigue Life Predictions of Adhesive Joint of Sheet Steels HongTae Kanga,*, Zhen Lia, A.K. Khosrovanehb, Byeongwook Kanga, Ziang Lia a
The University of Michigan-Dearborn, 4901 Evergreen Road, Dearborn, MI 48128, USA b General Motors LLC., 30001 VanDyke Road, Bldg 2-10, Warren, MI 48090, USA
Abstract Structural adhesive is widely employed in vehicle structures to enhance noise-vibration and crashworthiness performance. It is also known that structural durability is enhanced with application of structural adhesive. Many researchers have reported the fatigue performance of adhesive joints, but the test results showed noticeable scatter, making it hard to develop a fatigue life prediction method. This study fabricated cross-tension specimens joined with either adhesive only or adhesive with a spot-weld joint. These specimens were subjected to a 45-degree loading direction with respect to adhesive joint plane. The materials used for the specimens were various sheet steels, including mild steel, DP, and ultra-high strength steel. Fatigue tests were conducted for the specimens and a stress-life curve was constructed using a structural stress method. The test results were also correlated with a fracture mechanics approach. Both of the approaches showed reasonable correlation with the test results. © by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2015 2015Published The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of CETIM. Peer-review under responsibility of CETIM Keywords: Adhesive joint; Structural stress method; Fatigue life prediction; Sheet steels
1. Introduction Structural adhesives are widely employed in the construction of vehicle structures to improve crashworthiness, noise and vibration, and durability performances. Recently, the application of structural adhesives has become more common in joining dissimilar materials in vehicle structures. Since structural adhesives started being employed in vehicle structures, many researchers [1–7] investigated the strength and fatigue performance of the joints. Then the research interest shifted to the development of methods for fatigue life prediction of the joints [8–14]. Most of the
* Corresponding author. Tel.: 1-313-593-1878; fax: 1-313-593-5386. E-mail address: [email protected]
1877-7058 © 2015 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of CETIM
doi:10.1016/j.proeng.2015.12.623
HongTae Kang et al. / Procedia Engineering 133 (2015) 518 – 527
research [10, 12–14] was conducted with fracture mechanics concepts to predict the fatigue life of adhesive joints. Tomioka and co-workers [9] and Hong and Forte [11] used structural-stress concepts to predict fatigue life of the adhesive joints. Some research efforts [15–17] were also devoted to developing proper representations of the adhesive layer in finite element (FE) models. Non-linear characteristics of the adhesive materials were the main focus in the development of the proper representation of the joints in FE models. This study was conducted to develop a fatigue life prediction method using a structural stress method [18] for adhesive joints between sheet steels. To construct the structural stress versus life curve of the adhesive joints, coupon specimens were constructed for joining DP600 to DP600 and HSLA340 to HSLA340. Then, the S-N curve was used to predict fatigue life of adhesive joints between a mild steel and an ultra-high strength steel for validation of the structural stress method. The adhesive joints for the validation are subjected to cross-tension loading with 45-degree angle. The predicted fatigue life using the structural stress method correlates reasonably well with the fatigue test results of the cross-tension specimen geometry. 2. Specimen dimensions and experimental results The adhesive with spot welded joint specimens were constructed for DP600 to DP600 and HSLA340 to HSLA340 with lap-shear (LS) and coach-peel (CP) specimen geometries [19]. Also, the adhesive-only joint specimens were constructed for DP600 to DP600 with lap-shear specimen geometry. The sheet thickness used in this study was 1.53 mm for DP600 and HSLA340 steels. The adhesive material used in this study was EFTEC EFBOND WC2309 structural adhesive. The spot weld diameter was 7 mm for the adhesive joint with a spot weld. The specimen dimensions and geometries are shown in Fig. 1 [20]. The area to which the adhesive was applied was the overlapped region of the specimens.
Fig. 1. Dimensions and geometries of lap-shear and coach-peel specimens [20].
Fatigue tests of the specimens were conducted at test frequency of 7 or 10 Hz [19]. The fatigue failure criterion is the full separation of the specimen into two pieces. The runout is defined as 3 million cycles and marked with
519
520
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arrows in Fig. 2. The fatigue test results of the specimens are presented in load range versus cycle to failure as shown in Fig. 2. The upper group of data points in Fig.2 is from LS specimens and the lower group of data points in the same figure is from CP specimens. As shown in Fig. 2, no differences are observed between adhesive-only joints and adhesive with a spot weld joints in fatigue performance of LS specimens. The test results also show that the sheet strength of the joints does not affect the fatigue strength of the adhesive with a spot weld joints in CP and LS specimens. This is the same observation as with the fatigue performance of spot-weld only joints [20]. The slope of the load range versus fatigue life is very flat, and noticeable scatter is observable in the CP and LS specimen geometries. The slope in the CP specimen results is flatter than that of the LS specimens. The failure mode of the adhesive with spot weld joint is shown in Fig. 3 [19]. The failure mechanism is very similar to that of the adhesiveonly joint since the majority of the applied load is carried by the adhesive regions. Only after the adhesive region in front of the spot weld fails does the spot weld take the applied load. 1.E+05
DP600_LS_Adhesive Only_1.53mm DP600_LS_Adhesive+Spotweld_1.53mm DP600_CP_Adhesive+Spotweld_1.53mm HSLA340_CP_Adhesive+Spotweld_1.53mm HSLA340_LS_Adhesive+Spotweld_1.53mm
Load Range, N
1.E+04
1.E+03
1.E+02 1.E+03
1.E+04
1.E+05
Cycles to Failure Fig. 2. Fatigue test results of LS and CP specimens.
1.E+06
1.E+07
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(a)
(b) Fig. 3. Typical failure modes of adhesive with a spot weld for HSLA340 (a) CP; (b) LS [19].
3. Structural stress calculation 3.1. Structural stress equation This study used a structural stress concept to develop a fatigue life prediction method for adhesive-only joints and adhesive with spot weld joints between sheet steels. This structural stress concept is widely used for fatigue life prediction of spot welded joints [21–23]. The biggest advantage of the structural stress concept is that structural stress is a lot less sensitive in the mesh sizes than stresses obtained from finite element analysis. The structural stress method used in this study was originally proposed by Rupp and co-workers [18] and modified by nCode [24] for taking account of the effect of sheet thickness and spot-weld diameter on the structural stress. The modified structural stress method for a spot welded joint is briefly summarized below. The structural stresses in the radial direction are calculated from the forces and moments acting on the circular weld nugget sitting on a circular plate, as shown in Fig. 4 [23]. The radial structural stresses ( σ r ) due to the forces in the x- and y-directions are calculated as follows:
§F · σ r FX ¨ X ¸ PFXY © πdt ¹
(1)
§F · σ r FY ¨ Y ¸ PFXY © πdt ¹
(2)
§k F · σ r FZ ¨ 1 2 Z ¸ PFZ © t ¹
PFXY PFZ
if FZ ! 0 or 0 if FZ d 0
SFFXY d DEFXY t TEFXY
SFFZ d DEFZ t TEFZ
(3) (4) (5)
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where σ r FX and σ r FY are the radial stresses due to forces ( ܨ ܨ ) in the X- and Y-directions,
respectively. The diameter of the circular weld nugget is “d” and the thickness of the circular plate is “t.” σ r FZ is
the radial structural stress due to a normal force FZ on the weld nugget and k1 (=1.744) is a parameter that depends on the ratio of the nugget radius and specimen length from the center of the nugget to the edge of the grip area. ܲி ܲி are the correction parameters of the radial structural stresses for the different sheet thicknesses and the weld nugget diameters. SFFXY is the empirical scale factor for force in the X and Y directions. DEFXY and DEFZ are the diameter exponents for the forces in the X, Y, and Z directions, respectively. The thickness exponents are defined as TEFXY and TEFZ. The radial structural stresses due to the applied moments with respect to the local X- and Y-directions ( M X and
M Y , respectively), occur at the edge of the weld nugget and are expressed as:
σ r M X
k2MX PMXY , dt 2
(6)
σ r M Y
k2MY PMXY , dt 2
(7)
PMXY
SFMXY d DEMXY t TEMXY
(8)
where k 2 (=1.872) is a parameter that depends on the ratio of the nugget radius and specimen span. PMXY represents the correction parameters of the radial structural stresses for the different sheet thicknesses and weld nugget diameters. SFMXY is the empirical scale factor for the moment with respect to the X and Y directions. DEMXY is the diameter exponent for the moments with respect to the X and Y directions. The thickness exponent for the moments is defined as TEMXY.
Y
Fig. 4. Circular plate model for a spot weld joint [23].
Subsequently, the radial structural stresses, except for the stress due to the normal force, are calculated incrementally along the circumference of the weld nugget by the angle θ . Here, θ is the angle as measured from a reference axis in the plane of the weld nugget. The resulting equivalent structural stresses as a damage parameter are then calculated by the appropriate combination and superposition of local radial structural stresses along the circumference of the weld nugget, as shown below:
σ eq θ σ r FX cosθ σ r FY sinθ σ r FZ σ r M X sinθ σ r M Y cosθ
(9)
Finally, the maximum radial structural stress is determined for the given applied load from the equivalent structural stresses calculated using Equation (7). The maximum radial structural stress range versus fatigue life of
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the specimens tested is then plotted on log-log coordinates, resulting in an S-N curve for a given joint, and is fitted using equation (8) below:
'V eqmax where 'V eq
max
A N f
b
(10)
is the maximum structural stress range, N f is the number of cycle to failure, “A” is the coefficient,
and “b” is the exponent.
3.2. Constructing S-N curve using the structural stress range To construct the S-N curve of adhesive joints with and without a spot weld using the structural stress equations explained in the previous section, it is necessary to develop finite element (FE) models for the specimen types considered in this study. In the FE models of these specimens, the adhesive area is represented with the area contact method (ACM), consisting of a hexagonal element with rigid connection elements between steel sheets. A typical representation of ACM is shown in Fig. 5. The forces and moments at nodes are then transformed to the center of the surfaces that contact with steel sheets, presented with shell elements. These forces and moments are used to calculate the structural stress of Equation (7). Fig. 6 shows FE models of LS and CP specimens, and Fig. 7 shows the structural stress range versus the number of cycle to failure of the specimens. The element size in the FE models is 5 mm by 5 mm, and the overlapping region to which adhesive is applied is connected with ACM.
Fig. 5. A typical ACM representation in FE model [24].
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Fig. 6. FE models of CP and LS specimen.
4. Validation of the structural stress approach for adhesive joints The S-N curve developed from LS and CP specimens of DP600 and HSLA340 sheet steels is used to predict fatigue life of an adhesive joint with and without a spot weld. The specimens are constructed with cross-tension (CT) geometry, as shown in Fig. 8. Various strengths of steels are joined with adhesive only and with adhesive with a spot weld. Sheet thicknesses of the loading part (1.6 mm) and the constrained part (1.2 mm) are different. These combinations of specimens provide better data to validate the structural stress approach. The predicted life versus test life of the CT specimens is shown in Fig. 9. The dotted line represents a perfect correlation between the predicted life and the test life. The two solid lines present the upper and lower factor of 3. As shown in Fig. 9, the structural stress method works fairly well except in the long-life region. Many things contribute to making the difference between the predicted life and the test life. The most important factor for this difference is that the slopes of LS and CP in the S-N curve are actually different. This study, however, did not distinguish the difference in the slopes of the S-N curve since whether the joint in a real structure is in LS condition or CP condition cannot be identified. Usually, S-N slopes for LS specimens and CP specimens are the same in S-N curve of spot-weld joints. Another contributing factor for this difference could be the equations of the structural stresses used in this study. These equations were developed for spot-weld joints, and the mechanics at the adhesive joint are definitely different from those of a spot-weld joint. This study ignores the differences and assumes that the same equations could represent the fatigue characteristics of adhesive joints. Thus, it is necessary to conduct further studies in prediction of fatigue life of adhesive joints with and without a spot weld.
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1.E+03
Structural Stress Range (MPa)
DP600_LS_AdhesiveOnly_1.53mm DP600_LS_Adhesive+Spotweld_1.53mm DP600_CP_Adhesive+Spotweld_1.53mm HSLA340_CP_Adhesive+Spotweld_1.53mm HSLA340_LS_Adhesive+Spotweld_1.53mm
1.E+02
1.E+01
1.E+00 1.E+03
1.E+04
1.E+05
1.E+06
Cycles to Failure Fig. 7. Structural stress range versus fatigue life of CP and LS specimens.
Fig. 8. Cross-Tension specimens.
1.E+07
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1.E+07 980 spcc
1.E+06
440 590
Predicted Life, Cycle
1470 1.E+05
1.E+04
1.E+03
1.E+02 1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E+07
Test Life, Cycle Fig. 9. Comparison between predicted life and test life using the structural stress method.
5. Summaries and Conclusions The application of structural adhesives is being increased to enhance crashworthiness, noise and vibration, and structural durability performance. Many researchers [1–7] have reported the fatigue performance of structural adhesive joints with or without a spot weld. However, information on the fatigue life prediction methods for these joints is very limited. Thus, this study revisited the fatigue test results for adhesive joints with and without a spot weld in LS and CP specimen geometries and investigated the applicability of a structural stress method developed for spot weld joints to predict the fatigue life of these joints. The structural stress-based S-N curve was developed from fatigue test results of LS and CP specimens for DP600 and HSLA340 and applied to predict fatigue life of CT specimens of various steels. The structural stress method used in this study predicts reasonably well the fatigue life of adhesive joints with and without a spot weld in the short-life region. From the study conducted, the following conclusions are drawn: x The structural stress method can be applied to predict fatigue life of adhesive joints with or without a spot weld regardless of the specimen geometry. x For the high-cycle region, it is necessary to improve the accuracy of the fatigue life prediction.
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