Simple and effective failure analysis of dissimilar resistance spot welded advanced high strength steel sheets

International Journal of Mechanical Sciences 121 (2017) 76–89

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Simple and effective failure analysis of dissimilar resistance spot welded advanced high strength steel sheets

MARK

⁎

Wooram Noha,d, Wonjae Kima, Xin Yangb,1, Moonjin Kangc, Myoung-Gyu Leed, , ⁎ Kwansoo Chunga, a Department of Materials Science and Engineering, Research Institute of Advanced Materials, Engineering Research Institute, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 151-742, Republic of Korea b General Motors China Science Lab, Shanghai 200120, China c Advanced Welding & Joining R & BD Group, Korea Institute of Industrial Technology, 156 Gaetbeol-ro, Yeonsu-gu, Incheon 406-840, Republic of Korea d Department of Materials Science and Engineering, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul 136-701, Republic of Korea

A R T I C L E I N F O

A B S T R A C T

Keywords: Advanced high strength steels Dissimilar weld Failure analysis Mechanical properties of weld Numerical inverse approach

The failure of welded structures was analyzed considering dissimilar combinations of advanced high strength steels (AHSS) and a conventional mild steel. A method to characterize the mechanical properties of hardening behavior along with the deterioration associated with micro-void development and fracture criterion based on a modified damage model was applied by employing simple but effective experimental and numerical inverse procedure. The proposed procedure was solely based on standard and miniature simple tension tests for base sheets and weld nuggets, respectively. The identified plastic and failure properties were applied to the analysis of the failure mode and strength in the two well-accepted coupon tests of lap-shear and U-shape tension tests for DP980-TRIP980 and GMW2-TRIP980 dissimilar welded sheets. The analysis confirmed that the distinct failure behavior in the coupon tests for the two dissimilar weld cases was mainly due to the competition between the element with high strength/low ductility and the element with low strength/high ductility.

1. Introduction Recently, advanced high strength steels (AHSS) have been increasingly used for automotive parts to improve the fuel efficiency of automobiles by reducing their weight, while ensuring passenger safety. The two most frequently used AHSS in the automotive industry are dual phase (DP) steel and transformation induced plasticity (TRIP) steel. DP and TRIP steels offer good combinations of strength and formability. The mixed microstructure of soft ferrite and hard martensite in DP steel leads to enhanced ductility and work hardening. In contrast, the transformation of metastable retained austenite into martensite during straining in TRIP steel results in improved ductility and toughness. Resistance spot welding (RSW) is the most widely used method for joining sheet metal parts in the automotive industry. RSW is still the favored process for joining AHSS sheets, although their mechanical and welding properties are very different from low carbon steel sheets [1,2]. In general, AHSS sheets contain a higher amount of carbon and austenitic phase stabilizers, which leads to hard microstructures in the weld region owing to high cooling rates. Consequently, the characterization and evaluation of the mechanical properties and ⁎

1

failure behavior of welded joints, particularly for AHSS sheets, are critical issues. The welding characteristics and performance are known to be influenced by various combinations of process parameters. These parameters include weld current and time, the number of impulses, and the electrode force, which have been optimized either by experiments [3–5] or by employing finite element simulations [6,7]. The structures welded by RSW have heterogeneous microstructures, which make prediction of mechanical properties and failure modes challenging. The failure strength and modes at welded joints can be evaluated experimentally by coupon tests [8,9]. There are two failure modes in coupon tests: interfacial failure and pull-out failure. The crack in the first mode penetrates through the weld nugget in a rather brittle failure mode. However, in the latter mode, the crack develops at the base sheet around the weld nugget, leaving a hole in the base sheet. In general, the pull-out failure mode is favored than the interfacial failure mode because of its greater load-carrying capacity and energy absorption as well as its rather ductile failure manner. It is reported that the weld size has a significant impact on the failure mode, and the transition from interfacial to pull-out modes can be obtained by increasing the weld size [10,11]. There have been empirical force-

Corresponding authors. E-mail addresses: [email protected] (M.-G. Lee), [email protected] (K. Chung). Present address: Shandong Automotive Technology & Research Center, Dezhou, Shandong Province 253400, China.

http://dx.doi.org/10.1016/j.ijmecsci.2016.12.006 Received 21 March 2016; Received in revised form 6 December 2016; Accepted 12 December 2016 Available online 21 December 2016 0020-7403/ © 2016 Elsevier Ltd. All rights reserved.

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dures that use commonly available facilities such as a universal tensile machine. The key mechanical properties identified by the practical procedure are the hardening behavior and fracture criteria of base sheets and weld nuggets. For the hardening behavior, the strain rate sensitivity as well as the deterioration associated with micro-void development [22,37,38] was characterized along with the fracture criteria. For this purpose, the numerical inverse method [39] was applied to the standard simple tension test for base sheets and miniature simple tension test for the weld nugget. For the fracture criterion, the effective fracture strain, which is dependent on the stresstriaxiality, was utilized by simplifying the original version [40–43] of the damage model [39,44]. The dimensions of the weld nugget were determined using the measured hardness distribution and optical microscopic observation. The characterized properties were then applied to the analysis of the failure behavior in both coupon tests of the lap-shear and U-shape tension tests. Regarding the base material, TRIP980 and DP980 sheets were the AHSS sheets and GMW2 was the conventional mild steel considered. DP980-TRIP980 and GMW2TRIP980 combinations were utilized in the investigation of dissimilar welded joints.

based failure criteria for spot welded joints under various combinations of axial and shear loading conditions, but they did not refer to any specifics on the mechanical properties of spot welds or failure modes [12,13]. There have been substantial efforts, both analytical and numerical, in predicting failure behavior in coupon tests. The analytical methods include classical brittle fracture mechanics based approaches to interfacial failure [14,15], lower bound limit load analysis for pull-out failure under combined opening and shear static loading conditions [16–18], and a combination of these two approach for interfacial and pull-out failure [19]. In the numerical approaches, identical properties for the base sheet and the weld nugget assuming rigidity for the faying surface at the welded joint were used to avoid fracture through the weld nugget. Elastic [20], elasto-plastic [21], and elastic-plastic with hardening deterioration by the Gurson model [22,23] are examples of numerical approaches. These simplifying assumptions might be justifiable for mild steel sheets, in which the pull-out failure is favored owing to the low strength of the ductile base sheet. However, more sophisticated failure analysis is required to properly account for the mechanical properties of AHSS sheets, which have a higher strength with relatively lower ductility than those of mild steel sheets [24]. There have been several studies on the microstructures and mechanical properties of spot welded joints of AHSS sheets. The mechanical properties and the microstructures of welded joints of DP and austenitic stainless steels were measured with the Gleeble simulator [25]. Tong et al. [26] and Tao et al. [27] developed a miniature test to obtain stress–strain curves of the heat affected zones (HAZs) and fusion zones (FZs) as well as the base material (BM) by using scanning electron microscopy and digital image correlation techniques. Micro-indentation tests have also been used to determine the toughness and diameter of the FZ [28,29]. In these studies, there were no attempts to investigate the characteristics in failure mode with different combinations of base sheets. The literature on the RSW of dissimilar combinations and the effect of microstructures on the performance of dissimilar welds is limited. Hernandez et al. [30] investigated the failure mode of dissimilar combinations of DP600-DP780 and DP600-TRIP780. They found that the pull-out failure mode was activated when DP600 was paired with DP780 and TRIP780, and compared the results with the DP600 similar weld. Similar work on the susceptibility of the interfacial failure mode in dissimilar TRIP and non-TRIP steel combinations was undertaken by Hilditch et al. [31]. Marashi et al. [32] investigated the mode of failure and characteristics of FZ for the RSW of austenitic stainless steel and low carbon steel. They concluded that the spot weld strength in the pull-out mode was influenced by the strength and FZ size of the low carbon steel. Transition from interfacial failure to pull-out failure of dissimilar combination of DP600 and low carbon steel was also examined by Pouranvari [33] with varying size of FZ and lap-shear specimen turned out to have greater tendency to fail in pull-out failure than cross-tension specimen. More recently, the effects of the welding parameters on the microstructure, weld nugget size and mechanical properties were analyzed. Wei et al. [34] investigated similar and dissimilar combinations of DP1000 and TRIP980, while Khodabakhshi et al. [35] took a look into those of ultra-fine grained and coarse grained low carbon steel sheets. In their work, the relationship between the microstructure and hardness in different zones of spot welds was established. The common aspect of the aforementioned efforts is that the failure behavior of weld joints was analyzed without knowledge of the measured properties of welded joints. To overcome the limitations of previous studies, the present authors [36] analyzed the failure behavior of welded structures, especially AHSS sheets, where the failure modes and failure strength of spot welded joints were considered. However, that study focused only on similar welds. In the present study, the critical mechanical properties of dissimilar spot welded joints, including failure properties, were measured by effective experimental proce-

2. Finite element modeling Mechanical properties and failure performance of spot welded joints were analyzed with finite element (FE) simulations. All constituent materials of the spot welded joints were assumed to be isotropic linear elastic and isotropic hardening rule with von Mises isotropic yield function was adopted. Strain-rate sensitivities were considered only for the base material zones, while the FZs and HAZs of all weld nuggets were assumed to be strain-rate insensitive. Numerical simulations were carried out with a commercial dynamic explicit FE software, ABAQUS/ Explicit [44]. For acceptable solution accuracy with computational efficiency, simulations were conducted with a mass scaling which would scale density of the element if the stable time increments were less than a prescribed target time increment. The FE model for each case consisted of three-dimensional eight-node linear continuum elements with a reduced integration (C3D8R). For the simple tension of a standard specimen, the constant cross-head speed of 0.05 mm/s was set as a boundary condition, in which the element size of 0.20×0.20×0.10 mm3 was used for the gauge region of the specimen with the target time increment of 0.001 s. Meanwhile, the speed of 0.0005 mm/s was prescribed as the boundary condition for the simple tension test of a miniature specimen cut from a single spot welded stack which will be introduced in the later section. The element size of 0.048×0.068×0.080 mm3 was used near the center of the welded joint as shown in Fig. 1 with the target time increment of 0.0001 s. With respect to the single welded coupons such as the lap-shear and U-shape tension specimens, the tensile simulation was executed by moving the clamping region of each coupon at the constant speed of 0.02 mm/s as shown in Fig. 2. The simulations adopted the mesh size and the mass scaling scheme comparable to the tension test for the miniature specimen. 3. Characterization of mechanical properties 3.1. Base sheets 3.1.1. Standard tensile test Three automotive sheets were considered as the base sheets for RSW joints: TRIP980 (1.2 mm thick), DP980 (1.6 mm thick), and GMW2 (1.2 mm thick). The chemical compositions of the three sheets are listed in Table 1. Different thicknesses involve different amount of rolling, which would affect the microstructure, especially grain structures. The RSW is mainly to assemble completed automotive parts, which often have different thicknesses. Especially when parts are made of different steels, the parts more often than not have different thicknesses. The 77

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Fig. 1. Finite element meshes of the modified miniature test for (a) the top view and (b) the side view.

was applied to iteratively determine the hardening behavior as well as the fracture criteria. The mechanical properties for the base sheet (and also for the weld nugget shown in the later section) consisted of the hardening behavior up to the UTS point, hardening deterioration (or softening after UTS) by the damage accumulation, and final fracture controlled by the fracture criterion proposed in later section. In this

sheets investigated in the present work are all for real parts made of commercial automotive sheets. In such a case, the difference in the chemical compositions of different steels would be more important than the difference in thickness (unless the difference is significant). For the mechanical properties of the base sheets, the standard simple tension test was conducted, and an inverse numerical procedure

Fig. 2. Specimen configuration (unit: mm) and finite element meshes for (a)–(b) the lap-shear tension test and (c)–(d) the U-shape tension test.

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Table 1 Chemical compositions of the base sheets. [wt%]

TRIP980 DP980 GMW2

C

Mn

P

S

Si

Cr

Al

Ni

Mo

N

0.20 0.10 0.010

1.82 2.20 0.70

0.017 0.008 0.080

0.0043 0.0020 0.025

1.49 0.050 0.30

– 0.24 –

0.046 0.040 0.010

– 0.020 –

– 0.35 –

0.0039 – –

⎛ ε ̇ ⎞m σ = K (ε0 + ε )n ⎜ ⎟ ⎝ ε0̇ ⎠

study, motived by the previous work by Chung et al. [39], simplified approach using an inverse identification of parameters for the mechanical properties was applied by using combined experiment and simulation. First, the correct hardening curve is obtained from the uniaxial tension test only up to UTS point (or uniform deformation range). Then, the initial guess for the hardening behavior beyond UTS, by simple extrapolation, is applied and the hardening after UTS point is iteratively corrected to predict the prescribed force-displacement curve (or engineering stress-engineering strain curve). During this iteration, the simplified failure model is also applied together to identify the parameters for the criterion. The reliability of the proposed inverse identification approach was well validated by comparing the measured force-displacement curves and the displacements at fractures in Chung et al. [39]. Also, the commonly used extrapolation without any hardening deterioration (for example, simple extrapolations by using either Swift type or Voce type hardening models, or their combined hardening model) couldn’t predict the force-displacement (or engineering stress-strain curve) well, in particular after UTS point till failure [39]. For the simple tension experiments, the Instron 8801 tensile machine following the ASTM E 8 M standard was used. The strain was measured with an extensometer having a gauge length of 50.0 mm. The tensile tests confirmed that the directional difference in the hardening behavior was minimal, while the R -values showed some anisotropy, as shown in Table 2. Considering that this anisotropy has little effect on the failure analysis of the current study compared to other mechanical properties, the three base sheets were assumed to be isotropic for simplicity. To consider the effect of the strain rate on the post-uniform deformation behavior, the simple tension tests were also carried out with four different cross-head speeds: 0.05, 0.5, 5.0, and 50 mm/s, which correspond to engineering strain rates of 0.001, 0.01, 0.1, and 1.0/s, respectively. Each test was repeated at least 3–5 times for the same condition to secure reliability of the tested results. The basic mechanical properties measured with an engineering strain rate of 0.001/s are summarized with the strain rate sensitivity in Table 2.

where the strain rate sensitivity exponent, m , is the average for the effective strain and strain rate, considering the hardening curves measured with various strain rates; i.e.,

m=

ln(σ / σ0 ) ln(ε ̇/ ε0̇ )

(2)

where σ and ε ̇ are the effective stress and the effective strain rate, respectively, and ε0̇ and σ0 are the reference strain rate of 0.001/s and the reference stress for ε ̇ = ε0̇ , respectively. The Swift constants and the strain rate sensitivity are listed in Table 2. In this study, hardening behavior with softening after UTS due to micro-void development before macro-cracks [22] was characterized with an appropriate fracture criterion utilizing the numerical inverse method proposed by Chung et al. [39]. This avoids the common practice of extrapolating the hardening behavior after UTS with an arbitrary function, because of which the hardening deterioration cannot be represented. The simulation of the simple tension tests was performed iteratively in order to consider softening. The hardening data was initially extrapolated from the data obtained up to UTS and iteratively modified until the calculated and experimental force– displacement curves fit together. The calibrated true stress–strain curves for the three sheets in Fig. 3 demonstrate that hardening softens from the deviation points after UTS until failure is encountered.

3.1.3. Fracture criterion for base sheets In this study, a fracture criterion was applied to practically quantify the relative ductility of material elements that compete for failure in the welded joints. For this purpose, the criterion was simplified to make calibration possible by using only simple tension data, while still enabling the failure analysis of the welded joints to be carried out successfully. The effective fracture strain, εF , which is dependent on the stresstriaxiality, η , defined as the ratio of the hydrostatic stress to the equivalent stress, σii /3σ , was utilized as a fracture criterion. In addition, the following accumulative condition was used for the macro-crack formation;

3.1.2. Hardening behavior with softening after ultimate tensile strength (UTS) The hardening behavior of the base sheet was fitted to the Swift hardening law up to the UTS with a strain rate sensitivity of the power law type:

ω=

∫ dω= ∫ εdε(η) = 1.0 F

Table 2 Mechanical properties of the base sheets. Dir.

E [GPa]

YS [MPa]

UTS [MPa]

Uniform def. limit

TRIP980 DP980 GMW2

RD RD RD

205 198 117

767 792 156

999 1120 289

14.8% 7.43% 26.6%

m

R

TRIP980 DP980 GMW2

Swift constants K [MPa] ε0 1480 0.00468 1600 0.000193 571 0.0162

0.00427 0.00166 0.0203

0.886 0.753 2.16

n 0.119 0.101 0.313

(1)

(3)

where ω is a damage parameter. The integrated criterion in Eq. (3) accounts for the deformation path change detailed in Chung et al. [39]. Rigorous characterization of εF (η) has been proposed by Bai and Wierzbicki [40] and Dunand and Mohr [41]. However, their methods require extensive experimental efforts involving specimens with various shapes. Moreover, for most ductile sheets, even the accuracy or validity of the measured fracture criterion is often controversial because the failure is preceded by strain localization. In this study, the fracture criterion, which consists of the three regions shown in Fig. 4, was used for simplification. The criterion assumed a first order inverse function with a constant C for the region beyond the simple tension mode (η ≥ 0.333): 79

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Fig. 5. Identified fracture criteria of base sheets along with apparent fracture strain based on deformation history.

εF (η) = 9(εF η =0.333 − εF η =0 )η2 + εF η =0 . With this simplification, only the constant C is iteratively determined numerically with various trial values such that failure occurs, with ω = 1.0 , at the assumed failure point (marked “x”) in the experimental hardening curve. In Fig. 5, the criterion specified in Eq. (3) with deformation history of the critical element is shown after the hardening data with softening was characterized. The calibrated C values of the three base sheets are listed in Table 3. Fig. 5 shows that the apparent fracture strain (dotted lines) affected by the mode change becomes larger than that obtained without any mode change (solid lines) owing to the strain localization [39]. 3.2. Electrical resistance spot welded joints 3.2.1. Weld condition Two types of dissimilar spot welded joints, DP980-TRIP980 and GMW2-TRIP980, were considered. The welding process conditions are listed in Table 4. The welding parameters for current RSW process were iteratively determined to produce enough size of weld nugget in practice, which could resist larger load until fracture. Higher weld current and longer weld time increased the size of weld nugget in general, but expulsion could occur if Joule heat energy was too large and electrode force was too small to prevent fusion liquid from leaking. Fabrication of weld nugget with DP980-TRIP980 combination required longer welding time and stronger electrode force than that with GMW2TRIP980 combination. Because DP980 has the largest thickness among three steel sheets in this study, more electric energy was necessary to accomplish the enough nugget size for DP980-TRIP980 combination. Furthermore, expulsion during RSW for DP980-TRIP980 was prevented by pushing electrode with larger force. It was known that higher content of carbon equivalents in AHSS operates as larger electric resistivity and makes expulsion occur at ease [11], which resulted in larger electrode force to fabricate DP980-TRIP980 spot weld nugget. Meanwhile, for the case of GMW2-TRIP980 combination, GMW2 is a conventional mild steel showing less content of carbon equivalents and thickness of two constituent sheets is smaller than that of DP980, as shown in Table 1. As a result, short welding time and moderate electrode force were enough to produce required size of weld nugget.

Fig. 3. Comparison of experiment and simulation of the standard tension tests for (a) engineering stress–strain curves and (b) the calibrated hardening curves.

3.2.2. Dimensions of weld nuggets The dimensions of the weld nuggets were determined from optical microscopic observation as well as from the hardness distribution across the cross sections of the welded joints. For the optical microscopic observation, the micro-polished cross section was etched with LePera's reagent [45]. The hardness distribution was measured across the cross section of the welded joint at 0.2 mm intervals by employing a 0.978 N (100 gf) indentation force and 10 s of dwell time for each indentation, represented with dots in Fig. 6.

Fig. 4. Stress-triaxiality dependent effective fracture strain.

εF (η) =

C η

(4)

For the negative stress-triaxiality region (−0.333 ≤ η ≤ 0 ), a constant effective fracture strain D was assumed as a half value of εF η=0.333. Lastly, in the transition zone (0 ≤ η ≤ 0.333), a second order polynomial function connecting the two zones was assumed, 80

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Table 3 Parameters for the effective fracture strains of the base sheets and the weld zones. Material Parameter

C K D

Base sheet

Weld zones

TRIP980

DP980

GMW2

0.333

0.527

0.682

0.500

0.791

1.02

HAZ TRIP980

HAZ DP980

5.65 0.123

3.25 0.505

HAZ GMW2

FZ DP980-TRIP980

FZ GMW2-TRIP980

4.02 0.347

4.13 0.325

0.833 1.25

Table 4 Electrical resistance spot welding process conditions. Parameter Material

Dissimilar spot weld

DP980TRIP980 GMW2TRIP980

Weld current [kA]

Number of impulse

Impulse welding time [ms]

Electrode force [kN]

7.5

3

100

3.6

7.5

1

170

2.6 Fig. 7. Cross-section view of the assumed axisymmetric barrel shape of the dissimilar spot weld nugget. Table 5 Dimensions of the axisymmetric barrel shapes of the weld nuggets. [mm]

U-A U-B C D E U-F U-T U-R1 U-R2 L-A L-B L-F L-T L-R1 L-R2

Dissimilar spot welds DP980 (U)-TRIP980(L)

GMW2 (U)-TRIP980(L)

6.48 7.07 4.27 6.16 0.0630 0.160 1.60 4.49 2.50 6.02 =U-B 0.221 1.20 1.63 1.86

6.20 6.70 5.24 6.70 0.0323 0.183 1.20 3.01 2.45 =U-A =U-B 0.173 1.20 =U-R1 2.59

3.2.3. Modified miniature test In order to identify the mechanical behavior of the welded joint, a miniature specimen was newly designed. The new specimen was spot welded together in the middle after the two sheets were aligned along the rolling direction, as shown in Fig. 8. A tapered shape was introduced around the weld nugget to produce major deformation and failure at the weld nugget as a consequence of non-uniform deformation. Deformation of the specimen was measured using an extensometer with a gauge length of 25.0 mm, as shown in Fig. 8(b). Because the deformation in the miniature test was affected not only by the geometry of the specimen but also by the material property difference at the constituent zones of the welded joint, a numerical inverse method was applied to analyze the mechanical behavior of each zone for the miniature test. The overall strain rate sensitivity of the weld nugget was evaluated by the miniature tension tests with four constant cross-head speeds of 0.0005, 0.005, 0.05, and 0.5 mm/s. They approximately correspond to the engineering strain rates of 0.0003, 0.003, 0.03, and 0.3/s at the weld nugget, respectively. Each test was repeated at least three to five times for the same condition. The experimental results shown in Fig. 9 confirmed that the weld nuggets have virtually no strain rate sensitiv-

Fig. 6. Optical microscopic observation and Vickers hardness distribution for dissimilar spot welded joints of (a) DP980-TRIP980 and (b) GMW2-TRIP980.

Five distinct zones were identified for the description of the mechanical properties considering the measured hardness values in each dissimilar welded joint: one FZ, two BMs, and two HAZs for each BM side as shown in Fig. 6. The weld nugget shape was assumed to be an axisymmetric barrel, whose dimensions are schematically shown in Fig. 7 and listed as the average values of the three measurements for each welded joint in Table 5.

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3.2.4. Numerical inverse calibration of hardening behavior and fracture criterion The numerical inverse method was used to identify the mechanical properties of the welded joints in a similar manner as the identification for the base sheets. The ABAQUS/Explicit FE software was utilized for numerical simulations. The elastic properties of HAZs in each dissimilar weld were assumed to be the same as those of the base sheets neighboring the HAZs. In addition, the FZs of dissimilar welds were assumed to share the same elastic properties as TRIP980. A preliminary finding was that the calibrated hardening behavior was very sensitive to the weld nugget geometries such as the dent size and depth; therefore, extra care was taken to provide accurate dimensions of the weld nuggets, which are shown in Fig. 7 and listed in Table 5. The fracture criterion and hardening data of each welded joint were characterized using the inverse calibration method. In this study, five distinct zones were assumed in each weld nugget for their mechanical property description as plotted in Fig. 6. The hardness values of HAZs that neighbor TRIP980, DP980, and GMW2 in both spot welded joints were shown in Fig. 6. From the independent work of the present authors [36] for the similar spot welds for TRIP980-TRIP980, DP980DP980, and GMW2-GMW2, the hardness values of HAZs in the current dissimilar welds were comparable to those of weld nuggets in similar spot welds, as listed in Table 6. The hardness values of DP980 FZ and HAZ in DP980 side are 430 Hv and 420 Hv, respectively, and those of TRIP980 FZ and HAZ in TRIP980 side are the same as 530 Hv. Also, the hardness values of GMW2 FZ and HAZ in GMW2 side are 180 Hv and 150 Hv, respectively. Therefore, it is a reasonable assumption that the mechanical properties of HAZs in dissimilar welds can be approximated as those of weld nuggets in similar spot welded joints. The mechanical properties of the weld nuggets in similar weld nuggets were identified using the same inverse calibration method until the simulated curve matched the measured force–displacement curve well. The similar weld nugget was assumed as a single zone in the calibration for simultaneous consideration of HAZ and FZ because the size of HAZ was observed to be very narrow and its hardness value as well as microstructural constituent showed the intermediate state between BM and FZ. The hardening behavior and fracture criteria of HAZs in dissimilar welded joints were employed, as shown in Fig. 10 and Table 3. Applying the properties characterized to the HAZs as well as to the BMs from the previous section, an inverse calibration was iteratively carried out with various trial hardening curves for the FZs until the simulated curves converged to the measured force–displacement curves in Fig. 9. The calibrated hardening curves of the FZs for both spot welded joints are plotted in Fig. 10. The simplified fracture criterion for the FZ consists of three regions as shown in Fig. 4. The same simplified dependence of the effective fracture strain εF (η) on the stress-triaxiality was assumed here as done for the base sheet. Eq. (5) was suggested for both FZs of dissimilar weld nuggets, which were not so ductile:

Fig. 8. Specimen configuration of the newly designed miniature test (unit: mm) for (a) the top view and (b) the side view of the specimen.

14000 12000

Force (N)

10000 8000 6000 0.0005 mm/s 0.005 mm/s 0.05 mm/s 0.5 mm/s Simulation Fracture (=1.0)

4000 2000 0 0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Displacement (mm)

(a) 14000 0.0005 mm/s 0.005 mm/s 0.05 mm/s 0.5 mm/s Simulation Fracture (=1.0)

12000

Force (N)

10000 8000 6000

εF (η) =

4000

0 0.2

0.4

0.6

0.8

1.0

1.2

1.4

(5)

with n = 3.0 . Consequently, there was only one constant, K , in the simplified fracture criteria for the FZs of dissimilar welded joints. Employing the hardening curves and fracture criteria of the three base sheets and their HAZs as well as the hardening curves of the FZs previously identified, the fracture criteria of the FZs were inversely calibrated for the welded joints. This action was performed such that failure occurred (with ω = 1.0 ) at the points (marked “x”) in the measured force–displacement curves as shown in Fig. 9. For the welded joints, in which the measured force–displacement curves did not show good duplication after the maximum force points even for repeated tests, failure was assumed to occur at the point where the experimental curves started to diverge. Because the mechanical properties of HAZs in dissimilar welds were comparable to those of similar weld nuggets from the authors’ preliminary study, the fracture criteria of the FZs of

2000

0.0

K exp(K × ηn / K )

1.6

Displacement (mm)

(b) Fig. 9. Force–displacement curves for dissimilar spot welded joints of (a) DP980-TRIP980 and (b) GMW2-TRIP980.

ity. Therefore, it was assumed for simplicity that all the constituent zones of the weld nuggets are strain rate insensitive as well as isotropic.

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Table 6 Hardness values and microstructures of the spot welded joints. Similar spot welded jointsa

BM

HAZ

FZ

Grain size (μm) Hardness (Hv) Constituent phases

4.5 350 Ferrite+bainite +retained austenite

6.4 Intermediate Ferrite+bainite

10.3 530 Martensite

Grain size (μm) Hardness (Hv) Constituent phases

4.7 350 Ferrite+bainite +retained austenite

7.6 Intermediate Ferrite+bainite

14.0 530 Martensite

DP980-DP980

Grain size (μm) Hardness (Hv) Constituent phases

3.5 340 Ferrite+martensite

11.2 Intermediate Ferrite+martensite

24.1 430 Martensite

GMW2-GMW2

Grain size (μm) Hardness (Hv) Constituent phases

34.4 100 Ferrite

54.5 Intermediate Ferrite+bainite

79.2 180 Bainite+acicular ferrite

TRIP980-TRIP980 (5.0 kA)

TRIP980-TRIP980 (6.0 kA)

Dissimilar spot welded joints DP980-TRIP980

HAZ of DP980

HAZ of TRIP980

FZ

Grain size (μm) Hardness (Hv) Constituent phases

12.4 420 Ferrite+martensite HAZ of GMW2

9.0 530 Ferrite+bainite HAZ of TRIP980

17.2 470 Martensite FZ

Grain size (μm) Hardness (Hv) Constituent phases

54.5 150 Ferrite

7.1 530 Ferrite+bainite

32.3 430 Martensite

Dissimilar spot welded joints GMW2-TRIP980

a

Chung et al. [36].

welds and the FZs in the similar spot welds are similar as listed in Table 6. From the preliminary study with the similar welds for TRIP980, DP980, and GMW2, it was observed that the microstructures of their HAZs in the current dissimilar welds were different from those of the corresponding FZs in the similar welds; i.e., HAZs consisted of weaker phases and smaller grains compared to the corresponding FZs [36]. However, the effects of the weaker phases and the small-sized grains on their mechanical properties were more or less compensated, which can be explained by the grain size effect on strength; i.e., considering the classical Hall-Petch relationship [46,47], the strength of polycrystals increases as the square root of grain size decreases. Therefore, the lower strength of weaker phases could be compensated by their smaller grain size. From that, the assumption used in the inverse method might be justified.

dissimilar welded joints could be calibrated considering the fracture criteria of HAZs. The fracture criteria of HAZs were determined from the inverse calibration for similar welded joints for TRIP980, DP980, and GMW2. The calibrated values of each FZ are listed in Table 3, while the apparent effective fracture strains accounting for the change of the deformation mode are depicted in Fig. 10. As shown in Fig. 10, the strength and ductility of the FZ for each dissimilar spot welded joint are positioned in between those of its HAZs. Overall, the strengths of all the base and weld zones consistently matched the hardness test results shown in Fig. 6. It is notable that the hardening behavior of the weld zones did not show hardening deterioration up to macro-crack formation, which is different from the hardening behavior of the base sheets. 3.3. Microstructure analysis

4. Failure analysis of coupon tests for dissimilar spot welded joints

The macroscopic mechanical properties were compared with microstructures of constituent zones. Microstructures were examined by an electron backscatter diffraction system (TSL OIMTM, Japan) equipped with an SU-70 field emission scanning electron microscope (Hitachi, Japan). Specimens were mechanically ground and electrolytically polished in a solution of 10% perchloric acid and 90% ethanol. A critical misorientation angle of 15° was used for the identification of grains. As Fig. 11 indicates, the orientation image maps of the welds confirmed that the FZs of all weld nuggets were transformed to the martensitic structure. In addition, the strength of the FZ in the DP980TRIP980 weld was larger than that of the FZ in the GMW2-TRIP980 weld, which is mainly due to the small supply of the carbon content from the GMW2 base sheet. The dissimilar welded joints in this study are comprised of five zones, which were characterized from the optical microscopic observation and hardness measurement (see Section 3.2.2). The HAZs of base sheets in dissimilar welded joints were assumed to have similar mechanical properties as their FZs in the similar welded joints. This is because the hardness values of the HAZs in dissimilar spot

The failure behavior of dissimilar RSW joints in the coupon tests was analyzed by using the calibrated mechanical properties described in the previous sections for both base sheets and weld zones. In the coupon tests, the lap-shear and the U-shape tension tests were considered with the specimen configuration shown in Fig. 2. The displacements during the lap-shear and the U-shape tensile tests were measured by the extensometers with gauge lengths of 81.0 mm and 12.5 mm, respectively. Under the quasi-static tensile loading condition with a cross-head speed of 0.02 mm/s, both coupon tests were repeated two or three times for dissimilar welded joints. The force–displacement data and deformation modes are summarized in Fig. 12 and Fig. 13 for the lapshear and U-shape tension tests, respectively. In these figures, the deformation of the critical element with maximum strain for each constituent zone was compared at the moment of failure with the “x” and small inverted triangle marks to identify fractures and non83

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





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Fig. 10. True stress–strain curves and the fracture criteria of the constituent zones of the dissimilar welded joints for (a)–(b) DP980-TRIP980 and (c)–(d) GMW2-TRIP980.

Regarding the welded joint of GMW2-TRIP980, all the experimental results and simulation results showed almost the same force-displacement curves with the pull-out failure modes for the lap-shear and Ushape tension tests, as shown in Fig. 12(d) and Fig. 13(d), respectively, along with Fig. 14(c)–(d). Competition for failure here was between the HAZ of the TRIP980 zone with its high strength/low ductility and the GMW2 base zone with its low strength/high ductility as shown in Fig. 10(c)–(d). Failure eventually occurred at the GMW2 sheet owing to its lowest strength, as shown in Fig. 12(e)–(f) and Fig. 13(e)–(f). The results suggested that if welded with AHSS, the conventional mild steel sheet would be more likely to fail with the pull-out mode, justifying the conventional method of modeling pull-out failure by assuming rigidity for its weld nugget. Failure in the coupon test was mainly the result of competition between the zone with high strength/low ductility and the zone with low strength/high ductility. There were eight material zones: BMs of TRIP980, DP980, and GMW2; HAZs of TRIP980, DP980, and GMW2; and FZs of DP980-TRIP980 and GMW2-TRIP980. These eight zones were contested for four cases: two dissimilar welded joints with two coupon tests for each joint. Among the eight material zones, the GMW2 base zone was the most vulnerable to failure with its lowest strength,

fractures, respectively. The repeated tests showed good duplication of the pull-out failure mode for each dissimilar welded sample in both coupon tests. For the welded joint of DP980-TRIP980, FE simulations considering five distinct zones of the welded joint for the coupon tests showed good agreement with the experimental results, as shown in Fig. 12(a) and Fig. 14(a) for the lap-shear tests and in Fig. 13(a) and Fig. 14(b) for the U-shape tests. The pull-out failure mode as well as the maximum force level of the tests was predicted well. Even though the strengths of the two base sheets were similar, DP980 was better protected from failure than TRIP980 because of its larger thickness and better ductility. Ultimately, therefore, the competition for failure here was between the HAZ of TRIP980 with its high strength/low ductility and the TRIP980 base zone with its low strength/high ductility as shown in Fig. 10(a)–(b). Failure eventually occurred at the TRIP980 base zone with the pull-out for the lap-shear test as shown in Fig. 12(b)–(c), while the HAZ of the TRIP980 zone failed for the U-shape test as shown in Fig. 13(b)–(c). As shown in Fig. 14(b) for the U-shape test, the failure at the HAZ of TRIP980 did not penetrate through the FZ in the simulation so that the result was regarded as the pull-out mode with the HAZ zone failure, not the base zone failure, unlike all other pull-out failure cases. 84

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Fig. 11. SEM images (70° tilted) and orientation maps for normal direction of two heat affected zones (HAZ) and one fusion zone (FZ) of the dissimilar welded joints for (a)–(c) DP980TRIP980 and (d)–(f) GMW2-TRIP980.

employed. Two dissimilar welded joints, DP980-TRIP980 and GMW2TRIP980, were fabricated and their failure behavior was evaluated for two coupon tests, the lap-shear and U-shape tension tests, which were also based on the simple tension test. From the intensive experiments and numerical simulations, the following conclusions could be summarized:

which induced easy strain localization. Therefore, the weld joint of GMW2-TRIP980, which involved the GMW2 base zone, failed at the GMW2 base with the pull-out mode. Following the GMW2 base zone, the HAZ of TRIP980 for the DP980-TRIP980 weld was the second most vulnerable with its largest strength but with its lowest ductility. Even though the HAZ of TRIP980 was vulnerable, it was less vulnerable in the lap-shear test; therefore, the zone survived in the case of the lapshear test for the joint of DP980-TRIP980. When DP980 and TRIP980 base sheets were involved together, DP980 was better protected from failure than TRIP980 with its larger thickness and better ductility.

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5. Conclusions

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In the present study, the failure behavior of dissimilar welded structures was evaluated by a simple but efficient experimental procedure to identify critical mechanical properties of welded joints. The proposed procedure enables to use commonly available simple tension tests. TRIP980 and DP980, the two most frequently applied AHSS in the automotive industry, and a mild steel sheet, GMW2, were

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The simplified fracture criteria, defined as the stress-triaxiality dependent effective fracture strain, coupled with numerical inverse approach for the standard simple tension test and newly designed miniature simple tension test could be successfully calibrated for both base and dissimilar welded joints. The strain rate sensitivity or hardening deterioration were not shown for the weld nuggets, unlike for the base sheets. It was found that the failure behavior of each spot welded joint was attributed to competition between each constituent zone, whose critical mechanical properties were hardening behavior and the fracture criterion, represented by strength and ductility, respectively. The FZ strength of the DP980-TRIP980 weld was larger than that of

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Fig. 12. Force–displacement curves with failure modes along with hardening curves and fracture criteria at the moment of failure in the lap-shear tension test for the dissimilar spot welded joints of (a)–(c) DP980-TRIP980 and (d)–(f) GMW2-TRIP980.

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Fig. 13. Force–displacement curves with failure modes along with hardening curves and fracture criteria at the moment of failure in the U-shape tension test for the dissimilar spot welded joints of (a)–(c) DP980-TRIP980 and (d)–(f) GMW2-TRIP980.

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Fig. 14. Comparison of experimental and simulated failure modes of the dissimilar welded coupon tests; (DP980-TRIP980) the pull-out failure for both (a) lap-shear and (b) U-shape tension tests; (GMW2-TRIP980) the pull-out failure for both (c) lap-shear and (d) U-shape tension tests.

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GMW2-TRIP980 weld because of small supply of the carbon content from the GMW2 base sheet. Failure behavior in the coupon test was mainly the result of competition between the element with high strength/low ductility and the element with low strength/high ductility. The GMW2 base element was most vulnerable to failure. This is mainly because its strength was the lowest among all the considered materials, which induced easy strain localization. The HAZ of TRIP980 was more vulnerable in the U-shape tension test than in the lap-shear test because its critical deformation mode did not exhibit any ductility in the U-shape tension test.

Acknowledgement The authors would like to thank Dr. Kathy Wang of General Motors Company for her constructive advice. The supports provided by Dr. Qi Shen and Prof. Yongbing Li of Shanghai Jiaotong University for fabricating the spot welded specimens are also gratefully appreciated. MGL appreciates supports by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (MSIP) Nos. 2012R1A5A1048294 and NRF-2014R1A2A1A11052889. References [1] Lee W, Chung K-H, Kim D, Kim J, Kim C, Okamoto K, Wagoner RH, Chung K. Experimental and numerical study on formability of friction stir welded TWB sheets based on hemispherical dome stretch tests. Int J Plast 2009;25:1626–54. [2] Kim JH, Sung JH, Piao K, Wagoner RH. The shear fracture of dual-phase steel. Int J Plast 2011;27:1658–76.

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