Practical failure analysis of resistance spot welded advanced high-strength steel sheets

Accepted Manuscript Practical failure analysis of resistance spot welded advanced high-strength steel sheets Kwansoo Chung, Wooram Noh, Xin Yang, Heung Nam Han, Myoung-Gyu Lee PII:

S0749-6419(16)30258-3

DOI:

10.1016/j.ijplas.2016.10.010

Reference:

INTPLA 2117

To appear in:

International Journal of Plasticity

Received Date: 4 March 2016 Revised Date:

29 August 2016

Accepted Date: 27 October 2016

Please cite this article as: Chung, K., Noh, W., Yang, X., Han, H.N., Lee, M.-G., Practical failure analysis of resistance spot welded advanced high-strength steel sheets, International Journal of Plasticity (2016), doi: 10.1016/j.ijplas.2016.10.010. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Practical Failure Analysis of Resistance Spot Welded Advanced HighStrength Steel Sheets

Myoung-Gyu Leec,# a

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Kwansoo Chunga,*, Wooram Noha,c, Xin Yangb, Heung Nam Hana, and

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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 Department of Materials Science and Engineering, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul 136-701, Republic of Korea

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August 25, 2016

*

Corresponding author. Tel.: +82-2-880-7189; Fax: +82-2-885-1748 E-mail address: [email protected] (K. Chung)

#

Co-corresponding author. Tel.: +82-2-3290-3269; Email: [email protected] (M. G. Lee)

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Abstract In this study, a practical numerical procedure to analyze the failure behavior of resistance spot welded structures, especially for structures composed of advanced highstrength steels (AHSS) sheets, was developed for the first time. The root cause of the

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difference in failure modes between the welded structures of AHSS and conventional mild steel sheets was also elucidated. Given that the characterization of detailed mechanical properties of base sheets and weld nuggets is extremely complex, considerable effort was exerted to identify and properly simplify critical mechanical

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properties that are essential for failure analysis. This was achieved by developing a simple but effective experimental procedure to characterize the key properties by

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mainly utilizing standard and miniature-specimen tensile tests that are commonly available in any laboratory. In this study, two AHSS sheet grades, TRIP980 and DP980, as well as a conventional mild steel (GMW2) sheet grade were considered. The study involved the macroscopic characterization of mechanical properties including hardening behavior and fracture criterion. Furthermore, electron backscattered diffraction analysis of the base sheets and weld nuggets was also performed. The failure mode and strength

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of the lap-shear and U-shape tension tests were then analyzed for similar welded sheets under quasi-static loading conditions.

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Keywords: Advanced high strength steels; Resistance spot welding; Hardening

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deterioration; Miniature test; Fracture criterion

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1. Introduction

Electrical resistance spot welding was invented by Elihu Thomson in 1877. It has been widely used to join sheet metal parts in mass production environments and facilitate the

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automation of high-speed welding operations. In the automotive industry, resistance spot welding is extensively utilized to assemble various steel sheet parts and involves the application of more than three thousand spot welds per vehicle. The use of advanced high-strength steel (AHSS) sheets for fabricating the chassis and hang-on parts of

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automobiles has increased in the automotive industry, in order to cope with global environmental regulations. This is because the use of the AHSS sheets allows the

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reduction of automotive weight, thereby improving fuel efficiency without sacrificing passenger safety. AHSS sheets differ significantly from conventional mild steel sheets in various aspects including chemical composition and tensile strength (Lee et al., 2009; Mahnken et al., 2009; Kim et al., 2011). However, electrical resistance spot welding continues to be among the most viable options for the effective and economical assembly of various AHSS and mild steel parts to produce complete automotive bodies.

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Additionally, spot welded structures have a significant effect on the crashworthiness of vehicles. It is therefore important to develop a tool to properly evaluate the failure behavior of welded structures, particularly with respect to AHSS sheets. Furthermore, it is necessary to elucidate the differences in failure behavior between the welded

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structures of AHSS and conventional mild steel sheets.

Typically, electrical resistance spot welding processes are optimized by empirical tests involving various combinations of process parameters, such as weld current, number of impulses, welding time, and electrode force, while considering their effects on weld nugget sizes, weld strength, and impact on the performance of welded structures (Savage et al., 1978; Dickinson et al., 1980; Jou, 2001; Cho and Rhee, 2003; Tumuluru, 2006). Previous studies also employed finite element simulations to optimize the welding process, wherein the temperature distribution and associated residual stresses were analyzed to predict the size and shape of the weld nugget under an axisymmetric

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condition (Nied, 1984; Na and Park, 1996).

With respect to the performance evaluation of spot welded structures, coupon tests were

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commonly employed to experimentally measure the failure strength and failure modes at welded joints. Several types of spot welded coupons were subjected to opening, shear, or combined loading conditions (Zuniga and Sheppard, 1997; Lee et al., 1998; Chao, 2003b; Pouranvari et al., 2012; Acharya and Ray, 2013). Typically, two failure modes are involved in a coupon test, namely interfacial failure and pull-out failure. Interfacial

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failure involves a crack that penetrates through the weld nugget in a brittle failure mode. In contrast, a pull-out failure involves a crack that develops at the base sheet around the

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weld nugget and leaves a hole in the base sheet (usually with the weld nugget intact). Generally, pull-out failure is preferred to interfacial failure given its higher load-bearing and energy absorption capacities due to its ductile failure mode. An industrial standard provides process optimization guidance to avoid interfacial failure (American National Standard, 2002). Generally, spot welded joints grow stronger with increases in the nugget size and promote pull-out failure (Aslanlar, 2006; Oikawa et al., 2006;

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Khodabakhshi et al., 2015). Although extant studies developed empirical force-based failure criteria for spot welded joints under various combined axial and shear loading conditions, they did not focus on any specific spot weld mechanical properties or failure

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modes (Wung et al., 2001; Song and Huh, 2011).

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There were considerable efforts to analytically and numerically predict failure behavior in a coupon test. For example, an analytical method utilized fracture mechanics based on the stress intensity factor and J-integral to predict failure strength for interfacial cracks (Zhang, 1997, 1999). With respect to pull-out failure, lower bound limit load analysis was performed while considering sheet thickness and weld nugget diameter under combined opening and shear static loading conditions given a rigid circular cylinder for a weld nugget (Lin et al., 2002; Lin et al., 2003). These studies on interfacial and pull-out failures were later combined (Chao, 2003a). In numerical studies,

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a common practice involves applying the same properties for the base sheet and weld nugget with the assumption of rigidity for the faying surface at the welded joint to avoid failure at the weld nugget. Properties of elasticity (Deng et al., 2000) or elasto-plasticity (Radakovic and Tumuluru, 2008) were commonly applied for both the base and the

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weld. This was followed by the application of the Gurson model (Gurson, 1977) that accounted for hardening deterioration associated with micro-void development (Yang et al., 2010). A method, assuming identical elasto-plasticity properties for both the base and weld, was utilized for both the analysis of the impact test with a coupon test

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containing a single spot (Chen and Deng, 2000) and a crash box test with multiple spots

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(Xiang et al., 2006).

Typically, numerical analyses ignore the weld properties either by assuming that the weld properties are identical to those of the base sheet combined with an assumed rigid faying surface or by assuming that the rigid property of the weld nugget could be reasonably justifiable for mild steel sheets wherein pull-out failure is most common. However, the spot welded joints of AHSS sheets (that have higher strength and lower

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ductility when compared with mild steel sheets) quite often fail with unfavorable failure modes (Shi and Han, 2008). Thus, this requires a more sophisticated numerical failure

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analysis in which weld properties are properly accounted for.

Several studies characterized the microstructures and mechanical properties of spot welded joints of AHSS sheets. Adonyi and Blodgett (2006) and Hernandez et al. (2010)

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experimentally simulated the microstructures of welded joints using a Gleeble simulator to measure the mechanical properties. Tong et al. (2005) and Tao et al. (2007) developed a miniature specimen test and measured the stress-strain curves of the heat-affected zones (HAZ) and fusion zones (FZ) in addition to the stress-strain curves of the base sheet. Furthermore, they used scanning electron microscopy (SEM) and digital image correlation (DIC) techniques to investigate the material flow inside the miniature specimen. Micro-indentation tests were also performed to determine the toughness and the diameter of the FZ (Marya et al., 2006; Sun et al., 2008). However, extant research

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has not focused on failure behavior analysis of weld joints in coupon tests by utilizing the measured properties of welded joints. Hence, the primary objective of the present study involves developing a numerical procedure that enables the failure analysis of welded structures, and especially that of AHSS sheets. Additionally, the study objective

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included examining the root cause of the differences in the failure modes of AHSS and those of conventional mild steel sheets. Both failure modes and failure strength were considered during the evaluation of the failure behavior.

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Given the primary objective, it is imperative to measure the mechanical properties of spot welded joints in order to address fracture. However, it is extremely complex to

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characterize detailed mechanical properties of base sheets and weld nuggets. Therefore, the second objective of the study involved identifying and adequately simplifying critical mechanical properties that are essential for failure analysis. This was followed by the development of a simple but effective experimental procedure to characterize the main mechanical properties. Particularly, the study focused on procedures, such as the

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simple tension tests, which can be easily conducted in commonly available facilities.

The identified simple but critical mechanical properties consisted of two elements, namely the hardening behavior and fracture criteria of base sheets and weld nuggets.

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With respect to the base sheet, given the assumption of isotropy for purposes of simplicity, the numerical inverse method (Chung et al., 2011) applied for the standard

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simple tension test was utilized to characterize hardening with strain-rate sensitivity and deterioration (or softening) associated with micro-crack development (Gurson, 1977; Sánchez et al., 2008; Li et al., 2011; Fritzen et al., 2012; Khan and Liu, 2012; Matsuno et al., 2015). Furthermore, with respect to the fracture criterion, the effective fracture strain that was dependent on the stress triaxiality was utilized by simplifying the original version (Bai and Wierzbicki, 2009; ABAQUS, 2010; Dunand and Mohr, 2011; Brünig et al., 2013; Mohr and Marcadet, 2015) as a modified damage model (Chung et al. 2011). The dimensions of the weld nugget (with HAZ and FZ) were measured based

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on hardness distribution measurements and optical microscopic observations. The hardening behavior and the fracture criterion of the weld nugget were inversely characterized with a newly designed miniature simple tension test. Microstructural analysis was also performed for both base sheets and weld nuggets using an electron

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backscatter diffraction (EBSD) system to understand the mechanical properties in further detail. The characterized properties were then applied to analyze failure behavior in both coupon tests of the lap-shear and U-shape tension joints, thereby covering two extreme deformation modes. In the study, TRIP980 (transformation induced plasticity

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steel) and DP980 (dual phase steel) sheets were considered as AHSS sheets. A conventional mild steel known as GMW2 was used for comparison. The welded joints

under quasi-static conditions.

2. Finite Element Models

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consisted of similar welds using the same steel sheets. All experiments were performed

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Finite element (FE) simulation was used to characterize the mechanical properties and to analyze the failure behavior of constituent material elements in the spot welded joints. With respect to elasticity, isotropic linear elasticity with an assumed Poisson’s ratio of 0.33 was used. With respect to plasticity, an isotropic yield function, von Mises yield

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criterion, with isotropic hardening was used for both the base sheets and weld nuggets in the spot welded joints. The strain-rate sensitivity of the hardening behavior was only

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considered for base sheets as discussed in the following section. A commercial FE program of ABAQUS/Explicit (ABAQUS, 2010) successfully performed simulations for each case with 3D 8-node linear brick elements with reduced integration (C3D8R). The ductile damage model option offered by the FE program was also adopted for failure analysis resulting from the difference between the relative ductility of each material. Element size and mass scaling parameters were appropriately selected by considering solution accuracy and computational costs. Specifically, the semi-automatic mass scaling option was used for the mass scaling scheme. In this option, the element

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mass was scaled if the stable time increment calculated in the simulation was below a certain minimum time increment or a target time increment. With respect to the simulation of the simple tension test, constant cross head speeds of 0.05 mm/s and 0.0005 mm/s were used as boundary conditions for the standard specimen and the

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proposed miniature specimen, respectively. The boundary conditions are shown in Figure 1 (a) and (b). Mesh dimensions of 0.2 x 0.2 x 0.1 mm3 were used to model the gauge region of the standard specimen and base material (BM) area of the miniature specimen. In contrast, the mesh dimensions of the center region in the weld nugget of

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the miniature specimen were 0.048 x 0.068 x 0.080 mm3. The target time increments in the mass scaling scheme were set as 0.001 s and 0.0001 s for the standard specimen and

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the miniature specimen, respectively. With respect to the single welded coupons of the U-shape and the lap-shear welded specimens, tension tests were numerically performed with the boundary conditions shown in Figure 1 (c) and (d), in which the moving surface of each coupon was maintained at a speed of 0.02 mm/s. A target time increment of 0.0001 s identical to that used in the miniature tension test was utilized to simulate both coupon tension tests because the mesh size near the center of the welded joint was

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similar to that of the center in the weld nugget for the miniature specimen.

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3. Characterization of Mechanical Properties: Base sheets

Three automotive sheets were considered as the base materials of the resistance spot

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welded (RSW) joints in this study, namely TRIP980 with a thickness of 1.2 mm, DP980 with a thickness of 1.6 mm, and GMW2 with a thickness of 1.2 mm. The chemical compositions of the three base sheets are listed in Table 1. A standard simple tension test was performed to characterize the mechanical properties of the base sheets. The test was then iteratively simulated following an inverse numerical procedure detailed in this study for characterization of hardening behavior and fracture criteria. The hardening behavior considered strain-rate sensitivity along with hardening deterioration observed after the ultimate tensile strength (UTS).

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3.1. Standard simple tension test

An Instron 8801 universal tensile machine was used to perform the standard simple

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tension test as per the ASTM E 8M standard. As show in Figure 2, specimens prepared by electrical discharge machining (EDM) were used for the standard simple tension test. The engineering strain was measured using an extensometer with a gauge length of 50.0 mm. In order to evaluate anisotropy, tensile tests were performed along 0° (RD), 45°

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(DD), and 90° (TD) from the rolling direction (RD) with a constant cross head speed of 0.05 mm/s. Each test was repeated thrice and the test results indicated good duplication

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such that a representative curve was plotted for each direction in Figure 3. The tests results confirmed that the directional difference was minimal for the three base sheets. Basic properties including Young’s modulus (E), yield stress (YS), and uniform deformation limit strain corresponding to the ultimate tensile strength (UTS) were obtained along RD as summarized in Table 2. Additionally, the directional R-values, each of which corresponded to a width-to-thickness plastic strain ratio for each direction,

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are also summarized in Table 2. Although the hardening behavior was almost isotropic, the R-values in Table 2 showed some anisotropy. However, the preliminary analysis on the fracture performance of the considered weld joints indicated that the simulation results did not significantly improve when an anisotropic yield function, the Hill1948

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criterion (Hill, 1948), was used. Therefore, mechanical properties were assumed as

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isotropic for all the base sheets for purposes of simplicity.

Given that the strain-rate sensitivity significantly affected post-uniform deformation behavior, the strain-rate sensitivity was estimated by performing the simple tension test along RD as shown in Figure 3. With respect to relatively low strain rates in the range of quasi-static loading conditions, a simple tension test was performed with four constant cross head speeds of 0.05 mm/s, 0.5 mm/s, 5.0 mm/s, and 50 mm/s approximately corresponding to the engineering strain rates of 0.001 /s, 0.01 /s, 0.1 /s and 1.0 /s, respectively, given a gauge length of 50.0 mm.

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3.2. Numerical inverse calibration of hardening behavior and fracture criterion

With respect to hardening behavior, the most common practice involves characterizing

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hardening only up to the UTS point corresponding to the uniform deformation limit and extrapolating the data to cover the range beyond its limit. In this study, this common practice was followed initially to characterize the hardening behavior up to the UTS point for all the test results by assuming that the distribution and the rate of strain were

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homogeneous and constant within the gauge length for each test such that algebraic characterization was possible without numerical analysis. Then, the hardening behavior

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of the base sheet up to the UTS point was fitted to the following Swift hardening law with a strain-rate sensitivity of the power law type:

•

where

 ε&  &   ε0 

m

(1)

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σ = K (ε 0 + ε )

n

denotes the time derivative. The effective stress ( σ ) and the effective plastic

strain rate ( ε& ) were based on the von Mises yield function. Furthermore, ε&0 denotes

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the reference strain rate of 0.001 /s and σ 0 denotes the reference value for ε& = ε&0 . The strain-rate sensitivity exponent, denoted by m , was calculated as an average value for the effective strain and strain rate by considering the hardening curves measured with

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various strain rates as given by the following expression:

m=

ln (σ σ 0 ) ln ( ε& ε& )

(2)

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The Swift constants and the strain-rate sensitivity exponents are listed in Table 2. The numerical simulation in this section and in subsequent sections involved implementing

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the strain-rate sensitivity of the base sheet to the FE model.

A common practice included extrapolating the hardening behavior obtained up to the UTS point to cover the range beyond UTS. However, the extrapolated hardening

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behavior did not account for the hardening deterioration (softening) often observed to occur after UTS for reasonably ductile sheets since micro-voids develop to form macrocracks (Gurson, 1977; Malcher et al., 2014). Therefore, the hardening behavior with softening after the UTS point was characterized in conjunction with the fracture

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criterion by utilizing the numerical inverse method (Chung et al., 2011). The numerical inverse method is an iteration scheme that identifies the unknown mechanical properties

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of materials by minimizing the differences in the macroscopic mechanical behavior of the specimen between simulations and experiments. In this study, hardening behavior and fracture criterion of participating material elements of several similar welded joint were determined by using the numerical inverse method for a simple tension test with several types of welded specimens.

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The numerical procedure to obtain the hardening behavior of the base sheet used the hardening curve up to the UTS point and extrapolated hardening beyond the UTS point as an initial guess, and the simulated uniaxial engineering stress-strain curve was iteratively fitted to the experimental curve with a given tolerance. The simulated

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engineering stress-strain curves with the initially extrapolated hardening did not match well with the experimental engineering stress-strain curves as shown in Figure 4 for all

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three base sheets. Therefore, simulation was iteratively performed with modified hardening data considering added softening until the simulated and experimental engineering data corresponded as shown in Figure 4. The calculated true stress-strain curve represented softening after UTS, which was physically feasible given the microvoid formation prior to the final fracture. The error between simulated and experimental data was evaluated as follows:

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φ=∑ i

yisim − yiexp yiexp

(3)

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where yisim and yiexp denote the simulated and measured values of engineering stresses at the i-th data point, respectively. On the range from the deviation point to fracture point in Figure 4, the hardening curve was iteratively modified and optimized until φ

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was less than the given tolerance of 0.001.

The calibrated true stress-strain hardening data as shown in Figure 4 demonstrated that

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hardening softened from deviation points after UTS points till failure was encountered for all three sheets. The calibrated hardening curve with softening was provided as pairs of equivalent plastic strain and stress for isotropic plasticity.

With respect to the fracture criterion, the effective fracture strain, ε F , which is dependent on the stress-triaxiality, denoted by η (defined as the ratio of the

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hydrostatic stress with respect to the yield stress, σ ii / 3σ ), was utilized. The ductile damage model was given by the code (ABAQUS, 2010). With respect to the macrocrack formation, the following accumulative condition was applied:

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dε = 1.0 ε F (η )

(4)

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ω = ∫ dω = ∫

where ω denotes the damage parameter. It should be noted that ε F (η ) in Eq. (4) corresponds to the value obtained under the assumed proportional deformation condition, and its state is defined by stress-triaxiality. However, the integrated criterion in Eq. (4) accounts for the deformation path change (details may be found in Chung et al. (2011)). With respect to ε F (η ) in Eq. (4), rigorous characterization of the dependence of this term on η

requires extensive experimental effort involving

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specimens with various shapes (Bai and Wierzbicki, 2009; Dunand and Mohr, 2011). Moreover, even the measured fracture criterion is often a subject of controversy with respect to its accuracy or validity, especially if failure is preceded by strain localization, which is a usual occurrence for most ductile sheets. Therefore, the fracture criterion was

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mainly applied in this study as a tool to conveniently quantify the relative ductility of material elements that compete for failure in the welded joints. Additionally, considerable efforts were exerted to simplify the criteria such that the resulting criteria could be calibrated by only using the simple tension data, while still enabling the

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successful failure analysis of the welded joints for all the cases considered in this study. The efforts involved extensive numerical trials of various simplified criteria for the weld

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nuggets and for the base sheets until proper failure simulations of the welded joints were achieved.

The fracture criterion ultimately obtained for the base sheet after the simplification effort is shown in Figure 5 (a), which consists of three regions. The simplified criterion assumed the following first-order inverse function for the region beyond the simple

C

η

(5)

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ε F (η ) =

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tension mode (η ≥ 0.333 ) with a constant C as shown below.

Furthermore, a constant effective fracture strain, denoted by D, was assumed for the

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negative stress-triaxiality region ( −0.333 ≤ η ≤ 0 ) as a half value of ε F η =0.333 . In the transition zone ( 0 ≤ η ≤ 0.333 ), a second-order polynomial function connecting the two zones

was

assumed,

and

therefore,

ε F (η ) = 9(ε F η = 0.333 − ε F η =0 )η 2 + ε F η =0 .

Consequently, there was only one constant, denoted by C , to characterize in this simplified fracture criterion.

Thus, the constant C in Eq. (5) for the region beyond the simple tension mode was

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calibrated based on simple tension data. Following the characterization of the hardening data with softening, the criterion specified in Eq. (4) was iteratively performed numerically with various C values such that failure occurred, with ω = 1.0 , at the assumed failure points (x-marked) in the experimental engineering stress-strain curves

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as shown in Figure 4. The calibrated C values of the three base sheets are listed in Table 3, while the apparent effective fracture strains obtained after accounting for the deformation mode change in Eq. (4) are shown in Figure 6 (Chung et al., 2011). The deformation mode changed from the mode of the high fracture strain to that of the low

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fracture strain in the critical element due to strain localization during the simple tension test. Hence, the apparent fracture strain (dotted lines) affected by the mode change

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increased when compared with that obtained without any mode change (solid lines).

Strain localization accompanied all three base sheets before fracture occurred as experimentally observed in Figure 7. The simulated effective strain development of the critical element with the maximum effective strain, denoted by ε cri , was compared with the average effective strain of its neighbors, denoted by ε avr , within a distance of 2.5

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mm. The results of the comparison also confirmed strain localization prior to fracture (Chung et al., 2014a; Chung et al., 2014b) as shown in Figure 6. That is, the critical element initially deformed in conjunction with its neighbors but deformation was eventually localized at the critical element while that of all neighboring elements

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virtually stopped before fracture. The critical element was located at the middle surface of the center of the specimen. Furthermore, Figure 6 suggested that identification of

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exact effective fracture strains was not feasible and the calibrated values shown here were an approximation in principle as measured based on the x marks shown in Figure 4. This was due to strain localization prior to fracture. The simulated specimen shapes corresponded well with experiments at the moment of failure in Figure 7, and this partially validated the simulation. For the evaluation of deformations in the local areas in the sample surface, the DIC technique has been often used. However, the main objective of this study did not involve examining the deformation of complex individual material. Instead, this study focused on capturing the relative ductility of constituent material elements in the welded joints. Therefore, the comparison of specimen shapes

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between the simulation and experiment can also partially validate the usefulness of the proposed model.

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4. Characterization of Mechanical Properties: Electrical Resistance Spot Welded Joints

Table 4 summarizes the welding process conditions applied to fabricate the spot welded

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joints. A pneumatic pedestal welder with high frequency direct current (HFDC) power source was used. All spot welds were produced with standard dome-shaped electrodes

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(MWZ-6006) with a 4.8 mm diameter flat on the weld face. A similar spot welded joint was fabricated for each base sheet, while two weld current conditions, namely 5.0 kA and 6.0 kA, were employed for TRIP980 such that the joints exhibited different failure modes in the coupon tests. With respect to AHSS sheets, such as TRIP980 and DP980, desirable welding process conditions tended to have lower weld current or shorter welding time when compared with those of mild steel sheets such as GMW2. This is

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because the AHSS had a larger amount of carbon equivalents as shown in Table 1. These resulted in higher electrical resistance and increased heat generation, and thus often required stronger electrode force to prevent expulsion (Oikawa et al., 2006). Consequently, the weld current for the TRIP980 weld was lower than that of the GMW2

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weld. The weld current for the DP980 weld was larger than those of the other two welds since it had higher thickness, while a higher electrode force was also required to prevent

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expulsion.

4.1. Dimensions of weld nuggets

The shapes and dimensions of the weld nuggets were determined based on optical microscopic observations as well as the hardness distribution measurements performed across the cross-sections of the welded joints. The samples were prepared by grinding and polishing to obtain uniform roughness in the range of 1 µm. For the optical

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microscopy, the micro polished cross-section was etched with LePera’s reagent (LePera, 1980). With respect to the micro Vickers hardness test, the hardness distribution was measured across the cross-section of the welded joint with 0.2 mm intervals. An

indentation, as marked by the dots in Figure 8.

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indentation force of 0.978 N (100 gf) and a dwell time of 10 s were employed per

The measured hardness values in Figure 8 were mainly distinct in two zones especially for AHSS. Therefore, all the spot welded joints were assumed to comprise of two zones

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with respect to their mechanical properties for purposes of simplicity. These zones included the base material (BM) zone and the weld nugget zone in which the heat-

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affected zone (HAZ) and the fusion zone (FZ) shared the same properties. The assumed boundaries of the two zones were marked with dotted lines as shown in the optical microscopic images in Figure 8. Additionally, since the change in the weld had virtually no effect on the hardness values for the weld nuggets of TRIP980 as shown in Figure 8 (a) and (b), the same mechanical properties were assumed for both weld nuggets with differences only in their dimensions. The shape of the weld nugget was assumed as an

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axisymmetric barrel shape with dimensions that are schematically illustrated in Figure 9. The dimensions averaged from three measurements per each welded joint are

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summarized in Table 5.

4.2. Modified miniature test

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A newly designed miniature specimen was used to characterize the mechanical behavior of the welded joint. The new specimen was fabricated with two base sheets that were aligned along RD and then spot welded together in the middle as shown in Figure 10. The new specimen was tapered around the weld nugget such that the major deformation and failure were induced at the weld nugget due to non-uniform deformation. In contrast to the previous miniature specimen (Tong et al., 2005) that was solely made of the weld nugget and was extremely small, the modified specimen contained the weld nugget in the middle surrounded by the base sheet such that the total size was not as small as that

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of the previous specimen. Hence, this was not strictly a miniature test in a figurative sense. However, it was easy to install the specimen to perform the tensile test using typical universal tensile test machines. The deformation of the specimens was measured using an extensometer with a gauge length of 25.0 mm. The extensometer was installed

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to assess the combined deformation of the weld nugget and the base sheet in the midportion of the specimen as shown in Figure 10 (c) and (d). Deformation of the specimen during the miniature test was affected not only by the geometry of the specimen but also by the difference in the material properties between the base material and weld nugget

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of the welded joint. Therefore, it was essential to analyze the mechanical behavior of the

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weld nugget by applying the inverse calibration method to the miniature test.

Miniature tension tests were performed with four constant cross head speeds of 0.0005 mm/s, 0.005 mm/s, 0.05 mm/s, and 0.5 mm/s approximately corresponding to the engineering strain rates of 0.0003 /s, 0.003 /s, 0.03 /s, and 0.3 /s at the weld nugget (based on the numerical simulation), respectively. These tests were conducted to evaluate the overall strain-rate sensitivity of the weld nugget under quasi-static loading

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conditions. The experimental results shown in Figure 11 confirmed that the weld nuggets had virtually no strain-rate sensitivity when compared with that of the base sheets. Therefore, the weld nuggets of all the welded joints considered in this study

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were assumed to be strain-rate insensitive and isotropic for purposes of simplicity.

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4.3. Numerical inverse calibration of hardening behavior and fracture criterion

During the modified miniature test, deformation was non-uniformly distributed throughout the specimen although it was mainly concentrated at the weld nugget. Therefore, in a manner similar to that applied for the base sheet, the numerical inverse method was applied to characterize the mechanical properties of the weld nugget. This involved applying the mechanical properties that were inversely calibrated previously to the base material zones. For purposes of simplicity, it was assumed that the weld zone and the base sheet shared identical isotropic elastic properties for each weld. The

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findings indicated that the inversely calibrated hardening behavior was extremely sensitive to weld nugget geometries and especially the dent size and depth. Therefore, additional care was employed to provide accurate dimensions of the weld nuggets as

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shown in Figure 9 and listed in Table 5.

The inverse calibration method was used to characterize the fracture criterion as well as the hardening data of each weld nugget. Various hardening curves were iteratively tested for the weld nugget, which was assumed as a zone, until φ in Eq. (3) was less

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than the given tolerance of 0.001. The simulated curve matched well with the measured force-displacement curve as shown in Figure 11. Figure 12 shows the resulting

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calibrated hardening curves of the weld nuggets and those of the base sheets for comparison purposes.

As previously discussed, a major simplification effort was applied to the fracture criterion of the weld nugget. As shown in Figure 5, the fracture criterion ultimately obtained for the weld nugget after the simplification effort also consisted of three

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regions. Here, the same simplified dependence of the effective fracture strain ε F (η ) on the stress-triaxiality as that of the base sheet was assumed. However, the only exception included that there were two sets of ε F (η ) for the region beyond the simple tension

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mode (η ≥ 0.333 ). In this region, Eq. (5) was employed for the ductile weld zone of the GMW2 weld nugget but all the other weld nuggets that did not possess similarly high ductility could be characterized by the following expression as depicted in Figure 5 with

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n = 3.0 .

ε F (η ) =

K exp( K ×η n / K )

(6)

Consequently, there was only one constant, C or K , that required characterization in the simplified fracture criteria for the weld zones of the welded joints.

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The hardening curves and the fracture criteria of the base sheets and the hardening curves of their weld zones as previously characterized were employed to inversely calibrate the fracture criteria of the weld zones for the welded joints such that failure

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occurred (with ω = 1.0 ) at the assumed failure points marked by x in the measured force-displacement curves as shown in Figure 11. With respect to the TRIP980 welded joint, the miniature test showed brittle fracture with good duplication as shown in Figure 11 (a) such that it was easy to identify the failure point. However, with respect to

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other welded joints, the measured force-displacement curves did not show good duplication after maximum force points despite performing repeated tests with the same

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cross head speed. Therefore, failure was assumed to occur at the point where the divergence of experimental curves commenced as shown in Figure 11 (b) and (c). The calibrated parameters for the effective fracture strain of each weld nugget are listed in Table 3. The apparent effective fracture strains accounting for the change of the deformation mode are depicted in Figure 12.

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As summarized in Figure 12, the mechanical properties were extremely distinct for the base sheets and their weld nuggets. The TRIP980 weld was so strong but so brittle compared to its base sheet, significantly sacrificing its ductility. With respect to the GMW2, its weld was stronger than the base but it was so ductile, not sacrificing its

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ductility. It was observed that the DP980 weld mainly lost its ductility with little increase in strength, even though there was strength boost only in the early stage soon

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after initial yielding, which was captured in the hardness test shown in Figure 8. Overall, the strength of all the bases and weld zones shown in Figure 12 reasonably matched well with the hardness test results shown in Figure 8. In contrast to the base sheets, the hardening behavior of all the weld nuggets did not accompany hardening deterioration till the macro-crack formation. Figure 12 also showed that the ductility in terms of the fracture criteria displayed a more or less inverse coordination with strength.

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5. Microstructure Analysis

The measured mechanical properties at the macroscopic level were compared with the microstructures. The microstructures were examined by the electron backscatter

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diffraction (EBSD) system (TSL OIMTM, Japan) equipped with a SU-70 field emission scanning electron microscope (Hitachi, Japan). Specimens were mechanically ground and electrolytically polished in a solution consisting of 10% perchloric acid and 90% ethanol. A critical misorientation angle of 15° was used for the identification of the

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grains.

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The orientation image maps of the welds shown in Figure 13 confirmed that the FZs of the AHSS weld nuggets (but not those of the GMW2 weld) were transformed to the martensite structure. With respect to the TRIP980 welds fabricated with 5.0 kA and 6.0 kA, the same constituent phases were observed with only slight differences in grain size. This validated their assumed similar mechanical properties based on their similar hardness values. With respect to the FZs fully transformed to the martensite, the FZ

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hardness of the TRIP980 weld was considerably higher than that of the DP980 weld as summarized in Table 6. This implied that the differences in their hardness and strengths could be attributed to the difference in the carbon contents of their base sheets (which were 0.20 and 0.10 wt% C). As the increasing carbon content was frozen in the

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martensite, it became stronger and tended to be more brittle (Smith, 1993). With respect to the FZ strength of the DP980 weld, its strength increase due to the martensite

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formation was not as significant because the base sheet already contained the martensite. Additionally, the GMW2 weld involved a FZ that was made only with bainite and acicular ferrite with deficiency of carbon content. The carbon content of the GMW2 was just 0.010 wt % and was not enough to form the martensite (Smith, 1993), resulting in the weakest among all the FZs.

As discussed earlier, the welded joints were assumed to comprise of two zones, the base sheet and weld nugget zones without distinction between FZ and HAZ. The

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microstructural constituents as well as the grain sizes of HAZs indicated an intermediate state in-between the states of BM and FZ. Thus, the hardness distribution was also in-

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between that of BM and FZ as summarized in Table 6 and Figure 13.

6. Failure Analysis of Coupon Tests: Lap-shear and U-shape Tension Tests

The failure behavior of the resistance spot welded joints in the coupon tests was

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analyzed utilizing calibrated mechanical properties including the hardening behavior and the fracture criteria of three base sheets and their weld zones. The coupon tests

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involved the execution of the commonly employed lap-shear and the U-shape tension tests with the specimen configuration and fixtures as shown in Figure 14. Mechanical extensometers with gauge lengths of 81.0 mm and 12.5 mm were used to measure the displacement of the lap-shear and the U-shape tensile tests, respectively. All the tests were repeated five times under a quasi-static loading condition with a tensile speed of 0.02 mm/s. Force-displacement test data and failure modes are summarized in Figure 15

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and Figure 16 for the lap-shear and U-shape tension tests, respectively. Additionally, detailed quantitative evaluations for the predictions of failure mode, peak load, and displacement at failure for each case are listed in Table 7. These figures revealed that the repeated tests showed good duplication of the failure mode for each material sample

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with a distinct failure mode. For both the coupon tests, the GMW2 and DP980 welded samples showed all pull-out and interfacial modes, respectively. However, the TRIP980

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welded samples showed mixed results involving interfacial modes for both coupon tests with 5.0 kA and for the U-shape test with 6.0 kA and a pull-out mode for the lap-shear test with 6.0 kA.

FE analysis simulated the two coupon tests under proper boundary conditions with the mechanical properties of the constituent materials characterized in the previous sections. As shown in Figure 15 and Figure 16, from an engineering practice viewpoint, the simulated force-displacement curves corresponded fairly well with the experimental

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curves for both the coupon tests, especially with respect to the failure strength and failure mode. As shown in Table 7, the predictions for the measured load at the peak were better than those of its displacement. The averaged errors of the load at the peak between the experiment and simulation were 5.92 % for lap-shear and 13.5 % for the U-

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shape tension tests. Meanwhile, relatively larger averaged errors for the displacement at fracture of 13.2 % and 29.8 % were observed for the lap-shear and U-shape tension tests, respectively. Furthermore, in Figure 15 and Figure 16, deformation of the element for the base and weld nugget zones of each weld joint with maximum strain were traced by

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using the numerical analysis and compared at the moment of failure with the x and

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small reverse triangle marks that denoted fracture and non-fracture, respectively.

Typically, failure in the coupon test is the result of competition between the zone with high strength/low ductility and the zone with low strength/high ductility. In principle, deformation is concentrated at the zone with low strength. However, if the zone with low strength is sufficiently ductile, then brittle failure occurs at the zone with high strength when the zone with high strength is relatively too low in ductility. If

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concentrated deformation at the zone with low strength is relatively large when compared to its ductility and the zone with high strength withstands small deformations despite its brittle nature, then rather ductile failures occur at the zone with the low

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strength.

With respect to the GMW2 sheet, the competition for failure between the zone with high

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strength/low ductility and the zone with low strength/high ductility was absent since the weld nugget was stronger than the base sheet without sacrificing significant ductility. Therefore, strain was localized in the base sheet for both coupon tests. In contrast, there was virtually no deformation in the weld nugget, and this resulted in pull-out failure modes for both the coupon tests as shown in Figure 15 (j)~(l) and Figure 16 (j)~(l). The simulated failure modes complied well with the experiments as shown in Figure 17 (g)~(h) and Table 7. With respect to both the coupon tests, the simulated forcedisplacement curves corresponded with the experiment, and this was particularly

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applicable for failure strength in which the prediction of failure strength had errors less than 11.6 %. However, the value of the error exceeded 17.7 % for the prediction of the displacement at the peak. The results suggested that ductility was good for both the base and the weld nugget for the GMW2 case involving a conventional mild steel sheet.

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Hence, detailed fracture criteria were not required and the weaker strength of the base sheet was the main cause of inducing pull-out failure. This type of analysis could justify the common practice employed in previous studies wherein rigidity for the weld nugget was assumed to artificially induce pull-out failure (Chao, 2003b; Lin et al., 2003).

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Furthermore, the early interfacial failure was averted with a sufficiently high constant D with an assumed value (that was a half value of ε F η =0.333 ) in the negative stress-

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triaxiality region such that the pull-out failure was achieved. In order to simulate the gradual force decline with the pull-out failure mode in the lap-shear test, the resistance to the macro-crack propagation was considered in the simulation by adding the linear gradual decline of the stress in the base sheet property following the macro-crack formation with ω = 1.0 in Eq. (4) as shown in Figure 4. The added resistance to the macro-crack propagation improved the simulation result with a gradual decline in the

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force for the lap-shear test. However, it did not affect the results for the standard simple tension test and the U-shape test wherein the crack propagation was minimal.

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In the joint of the DP980 sheet, the competition for failure between the zone with high strength/low ductility and the zone with low strength/high ductility was absent. This could be because unlike the case of the GMW2 joint, the weld nugget was less ductile

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than the base without the added strength boost. Therefore, the numerical analysis predicted the interfacial failure modes for both the coupon tests as expected. The simulation results agreed well with the experiments for the failure modes and predicted the flow tendency of the force-displacement curves for both coupon tests as shown in Figure 15 (g)~(i), Figure 16 (g)~(i), and Figure 17 (e)~(f). The prediction error was less than 2.71 % especially at the peak loads as listed in Table 7. In the GMW2 case, the weaker base sheet was the main driver of all pull-out failures for both tests as an extreme. In contrast, in the DP980 case, the lower ductility of the weld nugget led to all

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interfacial failures in both tests and signified another extreme.

In the TRIP980 case, the same conditions including the mechanical properties were applied to simulate the cases with 5.0 kA and 6.0 kA with differences only in their

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dimensions as listed in Table 5. In contrast to the two extreme cases with GMW2 and DP980 in which either ductility or strength was similar or distinct, the weld nugget was much stronger with much lower ductility when compared to the base sheet for the TRIP980 case as a mixture of the two extremes. Additionally, the failure mode was also

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mixed and resulted from the competition for failure between the weld nugget with high strength/low ductility and the base zone with relatively low strength/high ductility. The

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case with 5.0 kA involved simulations and experiments that showed interfacial failure in both tests. With respect to the stronger weld nugget, the nugget deformed less when compared with the base. However, it was small in size and extremely brittle such that the nugget failed in both tests as shown in Figure 15 (a)~(c), Figure 16 (a)~(c), and Figure 17 (a)~(b). In the case with 6.0 kA involving the stronger nugget, the nugget deformed less when compared with the base and it was extremely brittle. However, the

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nugget was sufficiently large to avoid failure in one of the two tests. That is, it survived in the lap-shear test but failed in the U-shape test as shown in Figure 17 (c)~(d). This difference in the failure mode was ascribed to the critical deformation mode difference in the two tests. The critical deformation mode of the U-shape test in the weld nugget

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with the maximum strain involved a stress-triaxiality close to 1.0, in which there was virtually no ductility. Therefore, the weld nugget failed as shown in Figure 16 (d)~(f).

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The critical deformation mode of the lap-shear test in the weld nugget with the maximum strain involved a stress-triaxiality of 0.6, in which there was some amount of ductility, although it was still brittle. Therefore, the weld nugget survived as shown in Figure 15 (d)~(f). The analysis suggested that the U-shape test could be more vulnerable to interfacial failure when compared with the lap-shear test in general.

Overall, the mixed failure modes and the force-displacement curves of both coupon tests with 5.0 kA and 6.0 kA cases could be predicted with the FE model proposed in

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this study. Figure 17 (a)~(d) showed good matches in the failure modes between the experiment and simulation. Furthermore, the predicted force-displacement curves corresponded to the measured ones with a margin as shown in Figure 15 (a)~(f) and Figure 16 (a)~(f). Similar observations for the welded joints of GMW2 and DP980

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indicated that the peak loads of the coupon tests were predicted closer to the measured values. However, relatively larger errors were observed with respect to the prediction of displacements at failure as listed in Table 7. In the force-displacement curve of the lapshear test with the 6.0 kA case that failed in the pull-out mode, the decline in the force

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after the maximum point was gradual with a pull-out failure occurring in the GMW2 case. A linear gradual decline of the stress in the base sheet property occurred after the

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macro-crack formation was added to emulate the resistance to the macro-crack propagation. This improved the simulation result as shown in Figure 15 (d).

7. Conclusions

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In this study, the failure behavior of welded structures was investigated with a newly proposed experimental procedure that was simple but effective. The procedure was predominantly based on a simple tension test to characterize critical mechanical properties. Two AHSS sheet grades, namely TRIP980 and DP980, were considered

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in conjunction with a conventional mild steel sheet grade (GMW2). Four welded joints of the three base sheets were fabricated. The failure behavior of these joints

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was evaluated with two coupon tests, namely the lap-shear and U-shape tension tests. Both the tests also only required the use of a simple tension test facility.


The simple tension test results were analyzed using a numerical inverse method to evaluate the strength and ductility of the material elements comprising the welded joints in terms of their hardening behavior and fracture criteria. The fracture criterion was mainly utilized in this study to conveniently quantify the relative ductility difference between the participating material elements competing for failure. The

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fracture criterion involved was the stress-triaxiality dependent effective fracture strain. It was therefore significantly simplified from the original version such that the

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criterion could be calibrated by only using the simple tension test.


The standard tensile specimen and a newly designed miniature specimen were used to perform the simple tension tests to determine the mechanical properties of the base material and its weld nugget. The two AHSS base sheets showed superior strength with less ductility when compared to that of the GMW2 in which hardening

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deterioration associated with micro-cracks development was observed along with rate sensitivity. An isotropic assumption for all three base sheets was made for

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purposes of simplicity. The strengths of TRIP980 and DP980 were comparable, and their fracture criteria showed that TRIP980 had the lowest ductility.


The dimensions of the weld nugget were measured based on hardness distribution measurements and optical microscopic observations. The hardening behavior and the

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fracture criterion of the weld nugget were inversely characterized with a newly designed miniature simple tension test. In contrast to the base sheets, the weld nuggets did not show strain-rate sensitivity or hardening deterioration. In a manner similar to the base materials, the weld nuggets of the AHSS sheets also showed larger

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strength and lower ductility than those of GMW2. Given that an increase in carbon content generally leads to strong and brittle martensite, the weld nugget of TRIP980

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had the highest strength and lowest ductility. Although there was a strength increase from the formation of bainite and acicular ferrite in the weld nugget of GMW2, the ductility was preserved and was almost identical to the base material owing to grain growth and an absence of martensite due to the low amount of carbon content.


From the engineering practice viewpoint, there was a reasonable degree of agreement between the experimental results and the simulations in terms of the failure modes and failure strengths of both the coupon tests of each welded joint. This partially

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validated the calibrated properties applied to the welded joint. Failure modes were perfectly predicted with the proposed simplified modeling. The comparison of the predicted loads at the peak indicated relative averaged errors of 5.92 % and 13.5 %, for the lap-shear and U-shape tension tests, respectively. Nevertheless, the prediction

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for the displacements at the failure indicated larger differences when compared with those of the peak load, and this could be due to the simplified material model used in this study.

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Comparative analysis based on the experiment and numerical simulation suggested that a proper characterization of the simplified mechanical properties of the weld

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nugget and the base material was critical to predict the failure mode. The failure mode of the weld structure was determined by the relative differences in the strength and ductility of the base sheet and the weld nugget. In all the cases considered in the present study, the base sheet strength was weaker, and therefore the strain was localized at the base, which in turn possibly led to the pull-out mode unless the weld nugget was extremely brittle. With respect to the GMW2 weld, there was no sacrifice

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of ductility at the weld nugget. Thus, its failure resulted in the pull-out mode for all the coupon tests. In the AHSS welds, there was a significant decrease in ductility at the weld nugget such that it resulted in the interfacial failure: DP980 and TRIP980

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(with 5.0 kA) in both coupon tests. However, in the case of the TRIP980 (with 6.0 kA) with a larger weld nugget size, interfacial failure was avoided in the lap-shear

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test (as an exception).


The simplified procedure proposed in this study was reasonably successful in examining a rather complex phenomenon, both qualitatively as well quantitatively as a first approximation. This could be because the study mainly required the relative formability of participating material elements. It did not require the absolute formability of participating material elements, which involves significantly more sophisticated material and fracture models. Therefore, the proposed approach for the characterization of mechanical properties could be useful in the future as a first trial

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procedure when the further failure analysis of spot welded structures with various AHSS sheets is involved. This could be particularly applicable given the

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convenience wherein only a simple tension test facility is required.

Acknowledgement

The authors would like to thank Dr. Kathy Wang of General Motors Company for her

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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

Research

Foundation

of

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gratefully appreciated. MG Lee appreciates support by the funding through the National Korea

(NRF-2012R1A5A1048294)

and

(NRF-

2014R1A2A1A11052889). HN Han was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the

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Ministry of Science, ICT and Future Planning (NRF-2013R1A2A2A01008806).

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Savage, W., Nippes, E., Wassell, F., 1978. Dynamic contact resistance of series spot welds. Welding Journal 57, 43s-50s. Shi, Y., Han, Z., 2008. Effect of weld thermal cycle on microstructure and fracture toughness of simulated heat-affected zone for a 800MPa grade high strength low alloy steel. Journal of Materials Processing Technology 207, 30-39. Smith, W.F., 1993. Structure and properties of engineering alloys, 2 ed, McGraw-Hill, pp. 1-44. Song, J.H., Huh, H., 2011. Failure characterization of spot welds under combined axial– shear loading conditions. International Journal of Mechanical Sciences 53, 513-525. Sun, X., Stephens, E.V., Khaleel, M.A., 2008. Effects of fusion zone size and failure mode on peak load and energy absorption of advanced high strength steel spot welds under lap shear loading conditions. Engineering Failure Analysis 15, 356-367. Tao, H., Tong, W., Hector, L.G., Zavattieri, P.D., 2007. Uniaxial Tensile and Simple Shear Behavior of Resistance Spot-Welded Dual-Phase Steel Joints. Journal of Materials Engineering and Performance 17, 517-534. Thomson, E., 1889. Electrical welding-machine. US Patent US398913 A. Tong, W., Tao, H., Zhang, N., Jiang, X., Marya, M.P., Hector Jr, L.G., Gayden, X.Q., 2005. Deformation and fracture of miniature tensile bars with resistance-spot-weld microstructures. Metallurgical and Materials Transactions A 36, 2651-2669. Tumuluru, M.D., 2006. Resistance spot welding of coated high-strength dual-phase steels. Welding Journal 85, 31-37. Wung, P., Walsh, T., Ourchane, A., Stewart, W., Jie, M., 2001. Failure of spot welds under in-plane static loading. Experimental Mechanics 41, 100-106. Xiang, Y., Wang, Q., Fan, Z., Fang, H., 2006. Optimal crashworthiness design of a spot-welded thin-walled hat section. Finite Elements in Analysis and Design 42, 846855. Yang, X., Xia, Y., Zhou, Q., 2010. A simplified FE model for pull-out failure of spot welds. Engineering Fracture Mechanics 77, 1224-1239. Zhang, S., 1997. Stress intensities at spot welds. International Journal of Fracture 88, 167-185. Zhang, S., 1999. Stress intensities derived from stresses around a spot weld. International Journal of Fracture 99, 239-257. Zuniga, S., Sheppard, S.D., 1997. Resistance spot weld failure loads and modes in overload conditions. ASTM special technical publication 1296, 469-489.

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Figure 1: Boundary conditions imposed on the specimens in the finite element models for simulations of (a) standard tension, (b) miniature tension, (c) lap-shear tension and (d) U-shape tension test

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Figure 2: ASTM E 8M simple tension test specimen configuration for the base sheet

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1200

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Engineering strain (%)

Engineering strain (%)

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Figure 3: Engineering stress-engineering strain curves for (a)~(b) TRIP980, (c)~(d) DP980, (e)~(f) GMW2

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1200

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Experiment Simulation with softening Simulation with extrapolated hardening Fracture (ω ω=1.0) Deviation Point UTS

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Experiment Simulation with softening Simulation with extrapolated hardening Fracture (ω ω=1.0) Deviation Point UTS

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200 100

0

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Equivalent plastic strain

TE D

Engineering strain

Engineering stress (MPa)

1.0

SC

2400

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(b)

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Engineering stress (MPa)

(a)

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Equivalent plastic strain

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0.4

0.5

0.6

0.0

0.7

0.2

0.4

0.6

0.8

1.0

1.2

Engineering strain

Equivalent plastic strain

(e)

(f)

1.4

1.6

1.8

Figure 4: Engineering and calibrated true stress-true strain curves for (a)~(b) TRIP980, (c)~(d) DP980, (e)~(f) GMW2

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(b) Figure 5: Stress-triaxiality dependent effective fracture strain for (a) the base sheet and the ductile weld zone, (b) the brittle weld zone

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1.6

1.0

Fracture strain Deformation history Apparent fracture strain Fracture (ω ω=1.0)

1.2

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1.0

ε cri

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Effective plastic strain of critical element UTS Fracture (ω ω=1.0)

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0.8

1.0

1.2

0.0

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Triaxiality

1.0

1.0

0.8

M AN U

Equivalent plastic strain

1.2

ε cri

0.8

1.0

0.6

0.4

0.6 0.4

0.2

0.2

Effective plastic strain of critical element UTS Fracture (ω ω=1.0)

0.0

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0.4

(c) 2.5

Fracture strain Deformation history Apparent fracture strain Crack (ω ω=1.0)

EP

2.0

1.5

1.0

AC C

Equivalent plastic strain

0.8

(b)

Fracture strain Deformation history Apparent fracture strain Fracture (ω ω=1.0)

1.4

0.6

ε ave

SC

(a) 1.6

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Equivalent plastic strain

1.4

ε cri

0.4

0.6

0.8

1.0

(d) 1.0

0.8

0.6

Effective plastic strain of critical element UTS Fracture (ω ω=1.0)

0.2

0.0

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0.2

0.8

0.4

0.5

0.0

0.6

ε ave

1.0

1.2

0.0

1.4

Triaxiality

(e)

0.2

0.4

0.6

ε ave

0.8

1.0

(f)

Figure 6: The calibrated fracture criteria and the comparison of the effective plastic strains of the critical element and the neighboring elements for the standard simple tension test of (a)~(b) TRIP980, (c)~(d) DP980, (e)~(f) GMW2

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Figure 7: Specimens failed after strain localization in experiments and simulations for (a) TRIP980, (b) DP980, (c) GMW2

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Figure 8: Optical microscopic observation and Vickers hardness distribution for spot welded joints of TRIP980 with (a) 5.0 kA and (b) 6.0 kA, (c) DP980, (d) GMW2

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Figure 9: Cross-section view of the assumed axisymmetric barrel shape of spot weld nugget

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Figure 10: Specimen configuration and fixture of the newly designed miniature test (unit: mm) for (a) as-received spot welded stack, (b) the top view, (c) the side view of the specimen and (d) the specimen installed in the Instron 8801 machine

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14000 12000

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0.0005 mm/s 0.005 mm/s 0.05 mm/s 0.5 mm/s Simulation Fracture (ω ω=1.0)

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SC

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2000 1000

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(c) Figure 11: Force-displacement curves for spot welded joints of (a) TRIP980 with 6.0kA, (b) DP980, (c) GMW2

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2000

Fracture strain of weld Fracture strain of base Deformation history Apparent fracture strain Fracture (ω ω=1.0)

1.2

1800

1400 1200 1000 800 600 Weld Base Fracture (ω ω=1.0)

400 200 0 0.0

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1.2

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1200 1000 800 600

Equivalent plastic strain

True stress (MPa)

1400

Weld Base Fracture (ω ω=1.0)

400 200 0 0.6

0.8

1.0

(b)

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Equivalent plastic strain

Weld Base Fracture (ω ω=1.0)

400

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0.4

0.8

1.5

2.0

(d) Fracture strain of weld Fracture strain of base Deformation history Apparent fracture strain Fracture (ω ω=1.0)

3.0 2.5 2.0 1.5 1.0 0.5

200

0.0

1.0

Triaxiality

(c)

1200

Fracture strain of weld Fracture strain of base Deformation history Apparent fracture strain Fracture (ω ω=1.0)

1.4

Equivalent plastic strain

1400

2.0

(b)

2000

0.4

1.5

SC

(a)

0.2

1.0

Triaxiality

Equivalent plastic strain

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RI PT

Equivalent plastic strain

True stress (MPa)

1600

1.2

1.6

2.0

0.0 -0.5

0.0

0.5

1.0

1.5

2.0

Triaxiality

Equivalent plastic strain

(e)

(f)

Figure 12: Comparison of true stress-true strain curves and fracture criteria of the base sheets and the weld nuggets for (a)~(b) TRIP980, (c)~(d) DP980, (e)~(f) GMW2

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Figure 13: SEM images (70° tilted) and orientation maps of normal direction for the

AC C

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base material (BM), heat-affected (HAZ) and fusion zones (FZ) of the welded joint for (a)~(c) TRIP980 with 5.0 kA, (d)~(f) TRIP980 with 6.0kA, (g)~(i) DP980, and (j)~(l) GMW2

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Figure 14: Specimen configurations and fixtures for (a) the lap-shear tension test and (b) the U-shape tension test

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2000 Experiment 1 (interfacial) Experiment 2 (interfacial) Experiment 3 (interfacial) Experiment 4 (interfacial) Experiment 5 (interfacial) Simulation (interfacial)

18000 Force (N)

16000

Weld nugget Base TRIP Fracture (ω ω=1.0) Non-fracture

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1.2

1.0

Equivalent plastic strain

Displacement (mm)

24000 22000

Experiment 1 (pull-out) Experiment 2 (pull-out) Experiment 3 (pull-out) Experiment 4 (pull-out) Experiment 5 (pull-out) Simulation (pull-out)

20000

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Equivalent plastic strain

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True stress (MPa)

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49

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Displacement (mm)

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Equivalent plastic strain

Weld nugget Base TRIP Fracture (ω ω=1.0) Non-fracture

1800

True stress (MPa)

Weld nugget: Fracture strain Weld nugget: Apparent fracture strain Weld nugget: Deformation history Base TRIP:Fracture strain Base TRIP:Apparent fracture strain Base TRIP:Deformation history Fracture (ω ω=1.0) Non-fracture

0.6 0.4 0.2

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Equivalent plastic strain

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2.0

Triaxiality

(f)

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(e)

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Experiment 1 (interfacial) Experiment 2 (interfacial) Experiment 3 (interfacial) Experiment 4 (interfacial) Experiment 5 (interfacial) Simulation (interfacial)

20000 18000 16000 14000 12000 10000 8000 4000 2000 0 0.0

0.5

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1600

TE D

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2.5

Weld nugget Base DP Fracture (ω ω=1.0) Non-fracture

1800

True stress (MPa)

22000

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Displacement (mm)

EP

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SC

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Equivalent plastic strain

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14000 Experiment 1 (pull-out) Experiment 2 (pull-out) Experiment 3 (pull-out) Experiment 4 (pull-out) Experiment 5 (pull-out) Simulation (pull-out)

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Triaxiality

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Weld nugget Base GMW2 Fracture (ω ω=1.0) Non-fracture

1800 1600 1400

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TE D

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Equivalent plastic strain

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True stress (MPa)

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SC

Equivalent plastic strain

1.6

2.5 2.0 1.5 1.0 0.5

0.0 -0.5

0.0

0.5

1.0

1.5

2.0

Triaxiality

EP

Equivalent plastic strain

(l)

AC C

(k)

Figure 15: 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 welded joints of TRIP980 with (a)~(c) 5.0 kA and (d)~(f) 6.0 kA, (g)~(i) DP980, (j)~(l) GMW2

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Displacement (mm)

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1.2

1.0

Equivalent plastic strain

(a)

1.0

9000 8000

Experiment 1 (interfacial) Experiment 2 (interfacial) Experiment 3 (interfacial) Experiment 4 (interfacial) Experiment 5 (interfacial) Simulation (interfacial)

7000

0.8

Force (N)

6000

0.6 0.4

5000 4000 3000

0.0 -0.5

0.0

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0.2

1.0

1.5

2.0

Triaxiality

EP

(c)

AC C

Equivalent plastic strain

Force (N)

6000

True stress (MPa)

7000

Weld nugget Base TRIP Fracture (ω ω=1.0) Non-fracture

1800

Experiment 1 (interfacial) Experiment 2 (interfacial) Experiment 3 (interfacial) Experiment 4 (interfacial) Experiment 5 (interfacial) Simulation (interfacial)

RI PT

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52

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Displacement (mm)

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Equivalent plastic strain

Weld nugget Base TRIP Fracture (ω ω=1.0) Non-fracture

1800

True stress (MPa)

Weld nugget: Fracture strain Weld nugget: Apparent fracture strain Weld nugget: Deformation history Base TRIP:Fracture strain Base TRIP:Apparent fracture strain Base TRIP:Deformation history Fracture (ω ω=1.0) Non-fracture

0.6 0.4 0.2

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1.6

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Experiment 1 (interfacial) Experiment 2 (interfacial) Experiment 3 (interfacial) Experiment 4 (interfacial) Experiment 5 (interfacial) Simulation (interfacial)

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Weld nugget Base DP Fracture (ω ω=1.0) Non-fracture

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Equivalent plastic strain

(h)

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(g)

True stress (MPa)

1600

6000

3000

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(f)

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9000 8000

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Triaxiality

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Displacement (mm)

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Weld nugget: Fracture strain Weld nugget: Apparent fracture strain Weld nugget: Deformation history Base GMW2:Fracture strain Base GMW2:Apparent fracture strain Base GMW2:Deformation history Fracture (ω ω=1.0) Non-fracture

1600 1400

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0.4

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0.8

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1.4

1.6

EP

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TE D

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Equivalent plastic strain

Equivalent plastic strain

3.0

Weld nugget Base GMW2 Fracture (ω=1.0) Non-fracture

1800

True stress (MPa)

2

SC

0.0 -1.0

Experiment 1 (pull-out) Experiment 2 (pull-out) Experiment 3 (pull-out) Experiment 4 (pull-out) Experiment 5 (pull-out) Simulation (pull-out)

RI PT

1.6

Force (N)

Equivalent plastic strain

1.8

2.5 2.0 1.5 1.0 0.5

0.0 -0.5

0.0

0.5

1.0

1.5

2.0

Triaxiality

(l)

AC C

(k)

Figure 16: 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 welded joints of TRIP980 with (a)~(c) 5.0 kA and (d)~(f) 6.0 kA, (g)~(i) DP980, (j)~(l) GMW2

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(g)

(h)

Figure 17: Comparison of experimental and simulated failure modes of the welded coupon tests for (TRIP980-5kA) the interfacial for both (a) lap-shear and (b) U-shape; (TRIP980-6kA) (c) the pull-out for lap-shear and (d) the interfacial for U-shape; (DP980) the interfacial for both (e) lap-shear and (f) U-shape; (GMW2) the pull-out for both (g) lap-shear and (h) U-shape

55

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Tables Table 1: Chemical compositions of the base sheets Mn

P

S

Si

Cr

Al

Ni

Mo

N

0.20

1.82

0.017

0.0043

1.49

-

0.046

-

-

0.0039

0.10

2.20

0.008

0.0020

0.050

0.24

0.040

0.020

0.35

-

0.010

0.70

0.080

0.025

0.30

-

0.010

-

-

-

Table 2: Mechanical properties of the base sheets

TRIP 980 DP 980 GMW2

E [GPa]

RD RD RD

205.3 198.3 116.8

YS [MPa] 767.3 791.8 156.2

Swift constants

ε0

1482.3

DP 980

1601.6

GMW2

570.52

999.0 1116 289.0

14.8 % 7.43% 26.6 %

m

R-value

0.00468

0.119

0.00427

0.000193

0.101

0.00166

0.313

0.0203

EP

TRIP 980

AC C

0.0162

Uniform def. limit

n

TE D

K [MPa]

UTS [MPa]

M AN U

Dir.

RI PT

TRIP980 (1.2 mm) DP980 (1.6 mm) GMW2 (1.2 mm)

C

SC

[wt %]

56

RD DD TD RD DD TD RD DD TD

0.886 0.970 1.019 0.753 0.960 0.867 2.157 1.772 2.823

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Table 3: Parameters for the effective fracture strains of the base sheets and the weld zones

C

K D

Weld zones

TRIP980

DP980

GMW2

0.333

0.527

0.682

0.500

0.791

TRIP980TRIP980

DP980DP980

GMW2GMW2

0.833

1.02

5.65

3.25

0.123

0.505

1.25

SC

Parameter

Base sheet

RI PT

Material

Table 4: Electrical resistance spot welding process conditions Material

Weld Impulse welding Impulse current [kA] time [ms] 5.0

TRIP980

DP980

8.5

GMW2

7.5

Electrode force [kN]

1

170

2.6

1

170

2.6

3

130

3.6

1

170

2.6

TE D

Spot weld

6.0

M AN U

Parameter

Table 5: Dimensions of the axisymmetric barrel shapes of the weld nuggets Spot welds

TRIP980 (6.0 kA)

DP980

GMW2

A

4.75

5.30

7.75

5.72

B

4.95

6.20

8.56

6.10

C

4.95

6.20

7.12

6.10

D

0.100

0.100

0.380

0.190

E

0.0900

0.0900

0.410

0.200

T

1.20

1.20

1.60

1.20

R1

10.3

1.83

3.36

3.88

R2

1.02

1.17

1.64

1.80

AC C

[mm]

EP

TRIP980 (5.0 kA)

57

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

DP980

4.5

6.4

10.3

Hardness (Hv)

350

Intermediate

530

Constituent phases

ferrite + bainite + retained austenite

ferrite + bainite

Martensite

Grain size ( m)

4.7

7.6

14.0

Hardness (Hv)

350

Intermediate

Constituent phases

ferrite + bainite + retained austenite

ferrite + bainite

Grain size ( m)

3.5

11.2

24.1

Hardness (Hv)

340

Intermediate

430

Constituent phases

ferrite + martensite

ferrite + martensite

Martensite

Grain size ( m)

34.4

54.5

79.2

Hardness (Hv)

100

Intermediate

180

Constituent phases

ferrite

ferrite + bainite

bainite + acicular ferrite

RI PT

Grain size ( m)

AC C

EP

TE D

GMW2

FZ

530

Martensite

SC

TRIP980 (6.0 kA)

HAZ

M AN U

TRIP980 (5.0 kA)

BM

58

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Table 7: Comparisons of peak loads and corresponding displacements of coupon tests between experiment and simulation

Ushape test

I

I

P

P

DP 980

I

I

GMW2

P

P

TRIP 980 with 5.0kA TRIP 980 with 6.0kA

I

I

I

I

DP 980

I

I

GMW2

P

P

Sim.

% error

13100 ± 300 16200 ± 129 21900 ± 536 5910 ± 13.0 2480 ± 343 2470 ± 362 7390 ± 451 6060 ± 70.0

14900

13.7

17500

8.02

22100

0.913

5970

1.02

2680

8.06

3250

31.6

7190

2.71

5360

11.6

5.92 (Av g.)

Exp.

Sim.

0.600 ± 0.0279 0.767 ± 0.0465 0.588 ± 0.0247 6.97 ± 0.0932 3.39 ± 0.463 3.39 ± 0.690 5.38 ± 0.140 20.3 ± 0.270

0.598

13.5 (Av g.)

EP

TE D

I – interfacial, P- pull-out failure modes

59

% error 0.333

RI PT

TRIP 980 with 5.0kA TRIP 980 with 6.0kA

Exp.

AC C

*

Sim.

Displacement (mm)

M AN U

Lapshear test

Exp.

Load (N)

SC

Failure mode*

0.656

14.5

0.580

1.36

4.43

36.4

2.24

33.9

2.48

26.8

3.20

40.5

16.7

17.7

13.2 (Av g.)

29.8 (Av g.)

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Research highlights + Failure behavior of welded structures for AHSS and mild steel sheets was analyzed.

RI PT

+ Origin of failure difference between AHSS and mild steel welded sheets was analyzed. + A simple but effective property characterization method was developed for welded joints.

AC C

EP

TE D

M AN U

SC

+ Mechanical properties of weld nuggets were analyzed in macro and micro scale levels.