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공학박사 학위논문

Failure Analysis of Resistance Spot Welded Advanced High Strength Steel

Sheets

전기 저항 용접한 초고강도강판의 파손 거동 분석

2015년 2월

서울대학교 대학원

재료공학부

노 우 람

Failure Analysis of Resistance Spot Welded Advanced High Strength Steel

Sheets

전기 저항 용접한 초고강도강판의 파손 거동 분석

지도 교수 정 관 수

이 논문을 공학박사 학위논문으로 제출함 2015년 2월

서울대학교 대학원

재료공학부

노 우 람

노우람의 박사 학위논문을 인준함 2014년 12월

위 원 장 한 흥 남 (인)

부위원장 정 관 수 (인)

위 원 유 웅 렬 (인)

위 원 이 명 규 (인)

위 원 김 대 용 (인)

i

Abstract

Failure Analysis of Resistance Spot Welded Advanced High Strength Steel Sheets

Wooram Noh Department of Materials Science and Engineering

The Graduate School Seoul National University

A method to analyze the failure (fracture) behavior of resistance spot welded joints was

developed in this work, which was applied for the similar welds and the dissimilar

welds of advanced high strength steel sheets. As for the similar welds, TRIP980 and

DP980 sheets were analyzed along with a conventional mild steel sheet (GMW2) for

comparison purpose. Based on the TRIP980 sheet, as for the dissimilar welds, one was

fabricated with the DP980 sheet (DP980-TRIP980) and the other with a conventional

mild steel sheet GMW2 (GMW2-TRIP980). The method included the characterization

of base material sheets regarding hardening data and fracture criteria mainly based on

the inverse numerical analysis of uniaxial tension tests. Besides, hardness measurement

across the cross-section of the weld nugget along with optical microscopic observation

was utilized to identify the shapes and dimensions of the base, heat-affected zone, and

the fusion zone. Utilizing their geometric features, their fracture criteria as well as

mechanical properties were characterized based on the inverse numerical analysis of a

newly designed miniature tension test. Ultimately, the characterized properties of the

base materials and the weld zones were applied to analyze the failure (mode and

strength) in the coupon tests of lap-shear and U-shape tension tests for welded sheets

(also, as an effort to validate the calibrated properties). All analysis was performed

under the quasi-static condition in this work.

Keywords: Advanced high strength steel sheet, Resistance spot welding, Similar/Dissimilar welds, Fracture criterion, Hardening deterioration

Student Number: 2008-20642

ii

Contents

1. Introduction ................................................................................... 1

2. Property characterization of base material .................................... 8

2.1 Standard simple tension tests .............................................................. 8

2.2 Numerical inverse calibration of hardening curves and fracture criteria ..................................................................................................... 12

3. Property characterization of spot welded joint ............................ 25

3.1 Geometric features ............................................................................ 25

3.2 A newly designed miniature test ....................................................... 33

3.3 Numerical inverse calibration of hardening curves and fracture criteria ..................................................................................................... 43

4. Failure analysis of coupon tests ................................................... 59

4.1 Coupons with similar spot welded joints .......................................... 62

4.2 Coupons with dissimilar spot welded joints ..................................... 73

5. Conclusions ................................................................................. 83

Bibliography .................................................................................... 85

iii

List of Tables

Table 1: Mechanical properties of base sheets ................................................................ 9 Table 2: Parameters for the effective fracture strains of base sheets ............................. 19 Table 3: Electrical resistance spot welding process conditions ..................................... 26 Table 4: Dimensions of the axisymmetric barrel shape of spot welded joints .............. 32 Table 5: Parameters of the effective fracture strains for the weld nuggets in the similar welded joints (TRIP980, DP980, GMW2) and for the FZs of in the dissimilar welded joints (DP980-TRIP980, GMW2-TRIP980) ................................................................. 58

Equation Chapter 1 Section 1

iv

List of Figures

Figure 1: ASTM E 8M simple tension test specimen configuration for base sheets. ...... 9 Figure 2: Engineering stress-engineering strain curves for (a) TRIP980, (b) DP980, (c) GMW2. ......................................................................................................................... 11 Figure 3: Engineering and calibrated stress-strain curves for (a)~(b) TRIP980 (c)~(d) DP980 (e)~(f) GMW2. .................................................................................................. 16 Figure 4: Stress-triaxiality-dependent effective fracture strain for (a) the base sheet and (b) the weld nugget. ...................................................................................................... 18 Figure 5: The calibrated fracture criteria and effective plastic strain increment ratio between the critical element and neighboring elements for the standard simple tension test of (a)~(b) TRIP980, (c)~(d) DP980, (e)~(f) GMW2. ............................................. 23 Figure 6: Specimens failed after strain localization for (a) TRIP980, (b) DP980, (c) GMW2. ......................................................................................................................... 24 Figure 7: The optical microscopic observation and the Vickers hardness distribution for similar spot welded joints of TRIP980 with (a) 5.0 kA and (b) 6.0 kA, (c) DP980, (d) GMW2 and for dissimilar spot welded joints of (e) DP98-TRIP980, (f) GMW2-TRIP980. ....................................................................................................................... 30 Figure 8: Cross-section view of the assumed axisymmetric barrel shape of (a) similar spot weld nugget and (b) dissimilar spot weld nugget. ................................................. 31 Figure 9: Specimen configuration of the (a) as-received spot welded stack, (b) the top view, and (c) the side view of the newly designed miniature specimen and (d) the fixture with the specimen installed. .............................................................................. 35 Figure 10: The top view and the side view of the miniature specimen after failure for (a) DP980-TRIP980 (b) GMW2-TRIP980. ........................................................................ 36 Figure 11: Comparison of the simulated/measured engineering stress-strain and force-displacement curves for similar welds of (a)~(b) TRIP980, (c)~(d) DP980, (e)~(f) GMW2 and for dissimilar welds of (g)~(h) DP980-TRIP980, (i)~(j) GMW2-TRIP980........................................................................................................................................ 42 Figure 12. Finite element meshes of a newly designed miniature test: (a) the top view and (b) the side view. .................................................................................................... 44 Figure 13: Comparison of true stress-true strain curves and fracture criteria of base sheets and weld nuggets of similar spot welds for (a)~(b) TRIP980, (c)~(d) DP980, (e)~(f) GMW2, (g)~(h) all the weld nuggets, (i)~(j) all the base sheets. ...................... 51 Figure 14: True stress-true strain curves and the fracture criteria of the fusion zone of the dissimilar spot welded joints for (a)~(b) DP980-TRIP980, (c)~(d) GMW2-TRIP980 and comparison of base sheets, heat-affected zones and the fusion zone of the dissimilar joints for (e)~(f)DP980-TRIP980, (g)~(h) GMW2-TRIP980. ..................... 55

v

Figure 15: Specimen configurations and fixtures for (a) the lap-shear tension test and (b) the U-shape tension test. .......................................................................................... 60 Figure 16: Finite element meshes for simulation of (a) the lap-shear tension test and (b) the U-shape tension test. ............................................................................................... 61 Figure 17: Force–displacement curves and failure modes of the lap-shear tension test for the similar welded joints of (a) TRIP980-5kA, (b) TRIP980-6kA, (c) DP980, (d) GMW2. ......................................................................................................................... 66 Figure 18: Force–displacement curves and failure modes of the U-shape tension test for the similar welded joints of (a) TRIP980-5kA, (b) TRIP980-6kA, (c) DP980, (d) GMW2. ......................................................................................................................... 68 Figure 19: Comparison of experimental and simulated failure modes of the similar welded coupon tests: (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................................................................................ 72 Figure 20: Force–displacement curves and failure modes of the lap-shear test for the dissimilar spot welded joints of (a) DP980-TRIP980 and (b) GMW2-TRIP980. ......... 77 Figure 21: Force–displacement curves and failure modes of the U-shape tension test for the dissimilar welded joints of (a) DP980-TRIP980 and (b) GMW2-TRIP980. .......... 78 Figure 22: 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; (GMW2-TRIP980) the pull-out failure for both (c) lap-shear and (d) U-shape ............................................................................................................................. 80 Figure 23: Force–displacement curves of three finite element models with experimental results; (DP980-TRIP980) (a) lap-shear and (b) U-shape tension tests; (GMW2-TRIP980) (c) lap-shear and (d) U-shape tension tests. ................................................. 82

1

1. Introduction

Electrical resistance spot welding has been widely used to join sheet metal since it was

invented by Thomson in 1899 (Thomson, 1889). With rapid rate of production and

easy applicability to automation of its procedure, electrical resistance spot welding has

been widely employed in mass production process. In the automotive industry,

resistance spot welding has been especially utilized to assemble various parts and more

than three thousand spot welds are included to gather each part into one vehicle.

Recently, conforming to global environmental regulation, automotive industry have

ever increased usage of advanced high strength steel (AHSS) sheets for chassis of

automotive bodies in order to improve fuel efficiency by reducing weight of

automotive bodies as well as to enhance safety for passengers. Electrical resistance

spot welding is still effective and economic process to integrate each part into a full

automotive body, although AHSS sheets is much different from conventional mild

steels in various aspects such as chemical composition and tensile strength level (Kim

et al., 2011; Lee et al., 2009; Mahnken et al., 2009). Not only sheets of the same AHSS

but also different AHSS sheets or an AHSS sheet with a conventional mild steel sheet

can be combined to obtain the compromise among mechanical performance,

lightweight and material cost. Hence, many vehicle producers have made use of

dissimilar steel materials as well as similar steel materials in assemblies at the

component or subsystem level. For instance, an AHSS B-pillar is joined with a mild

steel side frame to achieve weight reduction and acceptable crashworthiness for side

2

impact protection. Therefore, it is very important to accurately characterize the

mechanical properties and evaluate the failure performance for spot welded joints

having significant effect on crashworthiness and durability of spot welded structures,

Attributed to inherently coupled problems of thermal-electrical, metallurgical, and

mechanical properties of materials, there have been several hurdles to overcome for

optimization of electrical resistance spot welding process. Much effort has been put

into achieving optimization of spot welding process to improve weldability of

automotive steel sheets. While analyzing their effects on weld nugget size and strength,

various combinations of weld process parameters have been empirically tried out.

Dynamic resistance proposed as an index for quality control of electrical resistance

spot welding process was monitored and related with nugget formation during welding

process for various automotive steel sheets (Dickinson et al., 1980; Savage et al., 1978).

Process optimization was carried out to endure external load to welded joints, while

diameters of weld nuggets were found to be affected by variation of heat input

corresponding to change of weld current and weld time (Jou, 2001). Mechanism of

nugget formation was also explored based on each frame of photographs captured by a

high-speed camera accompanying change of dynamic resistance (Cho and Rhee,

2003). Finite element simulation was also employed for process optimization of

electrical resistance spot welding. Under axial symmetric condition, temperature

distribution and associated stresses from difference of thermal expansion were taken

into account in order to predict size and shape of weld nugget (Nied, 1984). Contact

resistances between an electrode and a sheet as well as between two sheets should be

also considered in finite element simulation to clarify the effect of electrode force on

3

weld nugget formation by changing heat input (Na and Park, 1996).

As for performance evaluation of the spot welded joints in welded structures, the

several types of spot welded coupons were designed and subjected to either the

opening, shear or combined loading condition (Chao, 2003b; Zuniga and Sheppard,

1997). Their failure modes are typically categorized into two modes. One is the

interfacial failure where crack propagation though the weld nugget induces fracture

and the other is the pull-out failure where crack develops at the base sheet around the

weld nugget leaving the hole in the base sheet. In general, pull-out failure is more

preferred to interfacial failure because pull-out failure shows better load-carrying

capacity and absorbs larger amount of energy. Aslanlar (2006) and Oikawa et al. (2006)

observed that strength of spot welded joints of lap-shear and cross tension specimens

got stronger with increase of nugget diameter and sheet thickness. There also has been

the development of empirical force-based failure criteria of spot welded joints under

various combined axial and shear loading conditions, but without referring to any

specifics on mechanical properties of weld nuggets and predicting failure modes

(Wung et al., 2001).

There have been also substantial efforts to analytically and numerically predict failure

behavior in coupon tests. Fracture mechanics has been utilized to obtain analytical

solution to interfacial cracks in terms of stress intensity factor and J­integral around a

spot weld (Zhang, 1997, 1999). While its weld nugget has been assumed as a rigid

cylinder, pull out failure mode and failure strength of the spot weld was also

investigated by conducting lower bound limit load analysis where their failure strength

4

could be described in terms of sheet thickness, nugget diameter as well as combined

opening and shear static load level. (Lin et al., 2002; Lin et al., 2003). Those works on

both interfacial and pull-out failure have been combined in the work by (Chao, 2003a).

As for numerical works, the common practice has introduced the same properties into

the base sheet and the weld nugget while rigidity preventing interfacial failure has been

assumed on the faying surface in the welded joint. The properties commonly applied

both for the base and the weld nugget have been elastic in the early work (Deng et al.,

2000) or elasto-plastic (Radakovic and Tumuluru, 2008) and later the Gurson model

(Gurson, 1977), which accounts for hardening deterioration associated with micro-void

development. The method based on applying the common properties on the base and

the weld has been also utilized for the analysis of the impact test with coupon tests

(Chen and Deng, 2000).

The common practice in the numerical analysis to investigate the failure behavior of

the spot welded joint ignores the properties of the weld nugget by approximating its

properties same as the base sheet or assuming the rigid property on it. The practice

might be reasonably justifiable for mild steel sheets where pull-out failure mostly

happens from that strength of base sheets much weaker than that of their weld nugget.

However, for AHSS sheets which inherently have higher strength with lower ductility

compared to mild steel sheets, their spot welded joints have frequently failed with

unfavorable failure modes (Shi and Han, 2008) so that it has become necessary to

analyze failure considering weld properties. There have been several works to

investigate mechanical behavior of welded joints with AHSS sheets accompanying

apprehension of their microstructure. The Gleeble simulator has been utilized in order

5

to directly measure the mechanical properties of simulated microstructure (Adonyi and

Blodgett, 2006; Hernandez et al., 2010). Micro-indentation tests along with optical

microscopic observation have been also carried out to measure the toughness and the

diameter of fusion zone (FZ) (Marya et al., 2006; Sun et al., 2008). Tong et al. (2005)

and Tao et al. (2007) have developed a miniature fixture and have measured true stress-

strain curves of the heat-affected (HAZ) and FZ as well as the base material (BM),

utilizing the scanning electron microscopy (SEM) and the digital image correlation

(DIC) technique. At the level of coupon tests, furthermore, mechanical performance

have been evaluated considering influence of microstructure, especially for dissimilar

resistance spot welds between different steel sheets including AHSS sheets (Goodarzi

et al., 2009; Khan et al., 2009; Marashi et al., 2008). However, it has not been

attempted commonly in all the early efforts that the characterized properties of each

zone based on the measured results of the weld nugget would be applied to the analysis

of failure of welded joint in the coupon test, which was performed in this work for the

first time.

The main objective of this paper was to develop constructive procedure to analyze

failure behavior of electrical resistance spot welded joints by characterizing the

mechanical properties and failure properties of each zone generated in welding

processes, in particular for AHSS sheets in this research. Not only failure modes but

also failure strength was considered with the implementation of the characterized

properties into finite element simulation. As for the mechanical properties of the base

sheets, based on the standard uniaxial tension tests, hardening with strain rate

sensitivity as well as its deterioration (or softening) associated with micro-cracks

6

development (Gurson, 1977) was characterized along with the fracture criteria utilizing

the numerical inverse method (Chung et al., 2011) under the assumption of the isotropy

for the material properties. As for the fracture criterion, the effective fracture strain

with its dependence on the stress triaxiality was simplified in this work (ABAQUS,

2012; Bai and Wierzbicki, 2009).

As for the HAZ and the FZ, their dimensions were detailed based on hardness

distribution measurement along with optical microscopic observation. Based on the

resulting hardness distribution and dimensions of each zone, the FZ and the HAZ of

the similar spot welded joint were simultaneously regarded as a single zone (just

referred to as the weld nugget in this work), while the FZ and the HAZ of the

dissimilar spot welded joint were recognized as the distinct zones. As for each zone of

the welded joints, their fracture criteria and hardening curves were inversely

characterized with the finite element analysis based on the experimental results of a

miniature test newly designed. As for the case of the similar joints, mechanical

properties as well as fracture criteria of their weld nuggets were inversely calibrated

with the miniature test results. The FZs of the dissimilar joints could be similarly

characterized only with the assumption that hardening curves and fracture criteria of

the HAZs of the dissimilar joints are approximately identical to those of the weld

nuggets of the similar welded joint with the same base materials from which the HAZs

arose.

The characterized properties of the base sheets, the HAZs, and the FZs were applied to

the finite element analysis of failure mode and strength in the lap-shear and U-shape

7

tension tests for resistance spot welded sheets validating the calibration procedure

introduced here. Furthermore, the modeling of the welded joints in this work was

compared to the former modeling conventionally employed in early efforts, which

clarified the role of the welded zones to affect failure behavior of the coupon tests. All

works were performed under the quasi-static condition in this early effort. As the base

material, two AHSS sheets, TRIP980 (transformation Induced plasticity steel) with the

thickness of 1.2 mm and DP980 (dual phase steel) sheets with the thickness of 1.6 mm,

were considered, while a conventional mild steel, GMW2 with the thickness of 1.2 mm,

was also investigated. The analysis was executed for the similar welded joints of

TRIP980, DP980, and GMW2. Two dissimilar welded joints were also analyzed

successively, in which, based on TRIP980 sheets, one dissimilar welds was fabricated

with DP980 sheets (DP-TRIP) and the other with GMW2 sheets (GMW-TRIP).

8

2. Property characterization of base material

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

welded joints in this work: TRIP980 with the thickness of 1.2 mm and DP980 with the

thickness of 1.6 mm as well as GMW2 with the thickness of 1.2 mm. In order to

characterize the (assumed isotropic) mechanical properties of the base sheets (as for

their hardening behavior with strain rate sensitivity as well as hardening deterioration

observed after the ultimate tensile strength (UTS)) and their fracture criteria, standard

simple tension tests were performed for the base sheets and then the test results were

iteratively simulated following the inverse numerical procedure as detailed here.

2.1 Standard simple tension tests

The standard simple tension tests were performed using the Instron 8801 universal

tensile machine following the standard procedure ASTM E 8M with the specimen

prepared by EDM (electrical discharge machining) as shown in Figure 1. To evaluate

anisotropy, tensile tests were executed along 0, 45, and 90 degrees of the rolling

direction, respectively, with the constant cross head speed of 0.05 mm/s. Each test was

repeated three times and test results showed good duplication so that one representative

curve was plotted for each direction in Figure 2. The tests results confirmed that

directional difference is minimal for all three base sheets; therefore, the isotropy was

assumed for all base sheets for simplicity here. The basic properties such as Young’s

modulus (E), yield stress (YS), the uniform deformation limit strain corresponding to

the ultimate tensile strength (UTS) were obtained along the rolling direction as

9

summarized in Table 1, together with R-values (width-to-thickness plastic strain ratio

averaged for three directions per each base sheet).

Figure 1: ASTM E 8M simple tension test specimen configuration for base sheets.

Table 1: Mechanical properties of base sheets

Dir. E [GPa] YS [MPa] UTS [MPa]

Uniform def.

limit

TRIP 980 RD 205.3 767.3 999.0 14.8 %

DP 980 RD 198.3 791.8 1116 7.43%

GMW2 RD 116.8 156.2 289.0 26.6 %

Swift constants

m R K [MPa] 0 n

TRIP 980 1482.3 0.00468 0.119 0.00427 0.886

DP 980 1601.6 0.000193 0.101 0.00166 0.753

GMW2 570.52 0.0162 0.313 0.0203 2.16

10

(a)

(b)

Engineering strain (%)

0 5 10 15 20 25

En

gin

eeri

ng

str

ess

(MP

a)

0

200

400

600

800

1000

1200

RD45D TD

Engineering strain (%)

0 5 10 15 20 25

En

gin

eeri

ng

str

ess

(MP

a)

0

200

400

600

800

1000

1200

RD 45D TD

11

(c)

Figure 2: Engineering stress-engineering strain curves for (a) TRIP980, (b) DP980, (c)

GMW2.

Since the strain rate sensitivity significantly affects post-uniform deformation behavior,

the strain rate sensitivity was estimated by performing the simple tension test with

various cross head speeds along the rolling direction. For quasi-static loading

conditions, the simple tension tests were carried out with four constant cross head

speeds of 0.05, 0.5, 5.0, and 50 mm/s approximately corresponding to the engineering

strain rate of 0.001, 0.01, 0.1, and 1.0 /s, respectively, considering the gauge length of

50 mm.

Engineering strain (%)

0 10 20 30 40 50 60

En

gin

eeri

ng

str

ess

(MP

a)

0

50

100

150

200

250

300

350

RD 45D TD

12

2.2 Numerical inverse calibration of hardening curves and fracture criteria

As for the hardening behavior, the most common practice is to characterize hardening

only up to the UTS point corresponding to the uniform deformation limit and to

extrapolate the data in order to cover the range beyond its limit. Following the common

practice, the characterization of the hardening behavior was attempted up to the UTS

point first for all the test results, assuming that the distribution and the rate of strain are

homogeneous and constant within the gauge length for each test (such that algebraic

characterization was possible without numerical analysis). The hardening behavior of

the base sheet (up to UTS) was fitted to the following Swift hardening law with the

strain rate sensitivity of the power law type:

00

mn

K

(1)

in which the strain rate sensitivity exponent, m , was calculated as an average value

(for the effective strain) from hardening curves measured with various strain rates; i.e.,

0

0

ln

lnm

(2)

Here, and are the effective stress and the effective strain rate based on the von

Mises yield function, respectively, while 0 is the reference strain rate of 0.001 /s and

0 is the reference value for 0 . The Swift constants and the strain rate sensitivity

13

exponents are listed in Table 1.

Even though the common practice is to extrapolate the hardening behavior obtained up

to UTS to cover the range beyond UTS, the extrapolated hardening behavior does not

account for the hardening deterioration (softening) often observed to occur after UTS

for reasonably ductile sheets as micro-voids develop to form macro-crack as suggested

by the Gurson (1977). Therefore, the hardening behavior with softening after UTS was

characterized together with the fracture criterion utilizing the numerical inverse method

(Chung et al., 2011). For the numerical simulation of the standard simple tension test,

3D 8-node linear brick elements with reduced integration (C3D8R) were utilized along

with the ductile damage model offered by the commercial FE program,

ABAQUS/Explicit (ABAQUS, 2012). The mesh size to cover the gauge length of the

specimen was 0.10 0.20 0.20 mm3. The von Mises yield function (as well as the

isotropic elasticity with the assumed Poisson’s ratio of 0.333) was employed and the

strain rate sensitivity was accounted for utilizing the strain rate sensitivity listed in

Table 1. As for the numerical procedure, the hardening data extrapolated from data

obtained up to UTS was initially applied for the numerical simulation. Its simulation

result could not well predict the experimental one (as shown in Figure 3 for the

reference test data along the rolling direction with the constant cross head speed of

0.05 mm/s). Simulation was iteratively tried out with modified hardening data

considering softening until the simulated and experimental engineering data fit together

as shown in Figure 3. The calibrated (true stress-strain) hardening data as shown in

Figure 3 demonstrate that hardening softens for all the base sheets at deviation points

after UTS points before failure. The hardening data with softening were applied in a

14

tabular form as required by the commercial code for all the numerical simulation in this

work in the isotropic hardening formulation.

(a)

(b)

Engineering strain

0.00 0.05 0.10 0.15 0.20 0.25

En

gin

ee

rin

g s

tre

ss

(M

Pa

)

0

200

400

600

800

1000

1200

ExperimentSimulationSimulation with extrapolated hardeningCrack (=1.0)Deviation PointUTS

Equivalent plastic strain

0.0 0.2 0.4 0.6 0.8 1.0

Tru

e s

tre

ss

(MP

a)

0

400

800

1200

1600

2000

2400Hardening deterioration before =1.0Extraploated hardeningCrack (=1.0)Deviation PointUTS

15

(c)

(d)

Engineering strain

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16

En

gin

ee

rin

g s

tre

ss

(M

Pa

)

0

200

400

600

800

1000

1200

ExperimentSimulationSimulation with extrapolated hardeningCrack (=1.0)Deviation PointUTS

Equivalent plastic strain

0.0 0.2 0.4 0.6 0.8 1.0

Tru

e s

tre

ss

(MP

a)

0

400

800

1200

1600

2000

2400Hardening deterioration before =1.0Extraploated hardeningCrack (=1.0)Deviation PointUTS

16

(e)

(f)

Figure 3: Engineering and calibrated stress-strain curves for (a)~(b) TRIP980 (c)~(d)

DP980 (e)~(f) GMW2.

Engineering strain

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

En

gin

ee

rin

g s

tre

ss

(M

Pa

)

0

50

100

150

200

250

300

350

ExperimentSimulationSimulation with extrapolated hardeningCrack (=1.0)Deviation PointUTS

Equivalent plastic strain

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

Tru

e s

tre

ss

(MP

a)

0

200

400

600

800

1000Hardening deterioration before =1.0Extraploated hardeningCrack (=1.0)Deviation PointUTS

17

As for the fracture criterion, the effective fracture strain, F , dependent on the stress

triaxiality, (defined as the ratio of the hydrostatic stress to the yield stress,

trace( ) / (3σ)σ ), was utilized; the ductile damage model (ABAQUS, 2012). As for

the macro-crack formation, the following accumulative condition was applied;

1.0( )F

dd

(3)

in which is the damage (initiation) parameter. Note that ( )F

in Eq. (3) is the

value obtained under the proportional deformation condition defined by the stress

triaxiality and the accumulative form of this equation accounts for the deformation path

change (Chung et al., 2011). As for ( )F , its dependence on was simplified

considering three regions as schematically shown in Figure 4 (a). The following first-

order inverse function was assumed for the region beyond the simple tension mode

( 0.333 ):

F

C

(4)

with a constant C and a constant effective fracture strain was assumed for the

negative stress triaxiality region ( 0 ) with a constant D assumed as half of

0.333F

. In the transition zone ( 0 0.333 ), a second-order polynomial function

connecting the two zones was assumed such that 2

0.333 0 0( ) 9( )F F F F

.

Consequently, there was only one constant C to characterize in this simplified

fracture criterion (as determined for this work after various formulae have been tried

o

F

(

out for simpl

Figure 4: Str

(b) the weld n

licity).

(a)

(b)

ess-triaxialit

nugget.

)

)

ty-dependent

18

t effective fraacture strain

for (a) the bbase sheet annd

19

The constant C in Eq. (4) for the region beyond the simple tension mode was

calibrated based on the simple tension data. After the hardening data (with softening)

was characterized, the criterion was numerically tried out with various C values such

that failure occurred (with 1.0 ) at the assumed failure points (x-marked) in the

experimental engineering stress-strain curves as shown in Figure 3. The calibrated C

values of the base sheets are listed in Table 2, while the (apparent) effective fracture

strains accounting for the deformation mode change are shown in Figure 5. Since the

deformation mode changes from the mode of the high fracture strain to that of the low

fracture strain in the critical element due to strain localization during the simple tension

test, the apparent fracture strain in dotted lines becomes larger than that obtained

without any mode change (solid lines).

Table 2: Parameters for the effective fracture strains of base sheets

Steel type

Parameter TRIP980 DP980 GMW2

C 0.333 0.527 0.682

D 0.500 0.791 1.02

Severe strain localization was accompanied for all the base sheets before fracture

occurred as experimentally observed in Figure 6. Strain localization before fracture

was also confirmed by the simulation results shown in Figure 5. The simulated

effective strain development of the critical element (having the maximum effective

strain), cri , was compared with the average effective strain of its neighbors, avr , as

the critical element was located at the middle surface of the center of the specimen.

20

From that it was not feasible to identify the exact effective fracture strain due to the

severe strain localization before fracture, as shown in Figure 3, the fracture strain

should be calibrated only with x-mark which is not accurate measured point but

approximately lower bound point of fracture.

21

(a)

(b)

Triaxiality

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Fai

lure

str

ain

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6Fracture strainDeformation historyApparent fracture strainCrack (=1.0)

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

0

5

10

15

20

Effective plastic strain of critical elementSlopeUTSCrack (=1.0)

cri /cri aved d

ave

22

(c)

(d)

Triaxiality

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Fai

lure

str

ain

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6Fracture strainDeformation historyApparent fracture strainCrack (=1.0)

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

0

5

10

15

20

Effective plastic strain of critical elementSlopeUTSCrack (=1.0)

cri /cri aved d

ave

23

(e)

(f)

Figure 5: The calibrated fracture criteria and effective plastic strain increment ratio

between the critical element and neighboring elements for the standard simple tension

test of (a)~(b) TRIP980, (c)~(d) DP980, (e)~(f) GMW2.

Triaxiality

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Fai

lure

str

ain

0.0

0.5

1.0

1.5

2.0

2.5Fracture strainDeformation historyApparent fracture strainCrack (=1.0)

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.5

1.0

1.5

2.0

0

5

10

15

20Effective plastic strain of critical elementSlopeUTSCrack (0)

cri /cri aved d

ave

F

G

Figure 6: Sp

GMW2.

pecimens failed after stra

24

(a)

(b)

(c)

ain localizat

tion for (a) TTRIP980, (b

b) DP980, (cc)

25

3. Property characterization of spot welded joint

The welding process conditions applied to fabricate the spot welded joints were

summarized in Table 3. The similar spot welded joints were fabricated for each base

material, while two weld current conditions, 5.0 kA and 6.0 kA, were employed for

TRIP980 in order to distinctly compare different failure modes. Based on the TRIP980

sheet, meanwhile, two kinds of dissimilar spot welded joints were fabricated; one with

DP980 (DP980-TRIP980) and the other with GMW2 (GMW2-TRIP980).

As for the welded joints with AHSS sheets such as TRIP980 and DP980, the desirable

welding process conditions tend to take lower weld current or shorter welding time for

fabrication of the welded joints, compared to the welded joints including the mild steel

sheet such as GMW2. It is because an AHSS sheet usually has a larger amount of

carbon equivalents, which leads to larger electric resistance and more heat generation

requiring more electrode force to prevent expulsion (Oikawa et al., 2006).

3.1 Geometric features

The shape and dimensions of the base material (BM), the fusion zone (FZ) and the

heat-affected zone (HAZ) were determined based on optical microscopic observation

as well as the hardness distribution measurement on the cross-section of the welded

joint after they were prepared by grinding and polishing to obtain uniform roughness to

the extent of 1 µm. As for the optical microscopic observation, the micro polished

cross-section was etched with LePera’s reagent (Lepera, 1980). With the micro Vickers

26

hardness test machine, the hardness distribution was measured across the cross-section

of the welded joint with 0.2 mm interval by employing 100 gf of the indent force and

10 seconds of dwell time per one indent, as marked with dots in Figure 7.

Table 3: Electrical resistance spot welding process conditions

Weld

current [kA]Impulse

Impulse

welding time

[ms]

Electrode

force [kN]

Similar

spot weld

TRIP980 5.0 1 170 2.6

6.0 1 170 2.6

DP980 8.5 3 130 3.6

GMW2 7.5 1 170 2.6

Dissimilar

spot weld

DP980-

TRIP980 7.5 3 100 3.6

GMW2-

TRIP980 7.5 1 170 2.6

Based on the measured hardness distribution and optical microscopic observation, all

the similar spot welded joints were assumed to comprise two zones, i.e., the BMs and

the weld nuggets (simultaneously considering FZ and HAZ without distinction)

because the measured hardness values of HAZs were more or less in-between those of

BMs and FZs, while the sizes of HAZs were much smaller than those of BMs and FZs.

On the other hand, both kinds of dissimilar spot welded joints were assumed to consist

of five distinct zones, i.e., one FZ, two BMs and two HAZs (from two BMs) for each

dissimilar weld. As for the dissimilar spot welded joints (as shown in Figure 7), it was

27

found that the measured hardness values of their HAZs were not in-between those of

the FZs and BMs and the sizes of HAZs were not too narrow to ignore, unlike the case

of the similar spot welded joints. The shape of the weld nugget was considered as an

axisymmetric barrel shape, whose dimensions were schematically illustrated in Figure

8. The dimensions averaged from three measurements per each joint were summarized

in Table 4. As shown in Figure 7 (a) and (b), it was found that change of weld current

had no effect on the hardness values for the weld nuggets of the TRIP980 similar

welded joints. Therefore, it would be reasonable to suggest that both weld nuggets

from both weld currents with TRIP980 have the same material properties and keep

difference in dimensions. In the following section, a newly designed miniature

specimen from TRIP980 with 6.0 kA was utilized for the characterization of the weld

nugget of the TRIP980 similar joints.

(a)

(b)

28

(c)

(d)

29

F

s

G

T

Figure 7: The

similar spot w

GMW2 and

TRIP980.

e optical mic

welded joint

for dissimi

(e)

(f)

croscopic obs

ts of TRIP98

ilar spot we

30

servation and

80 with (a) 5

elded joints

d the Vickers

5.0 kA and (b

of (e) DP9

s hardness di

b) 6.0 kA, (c

98-TRIP980,

istribution fo

c) DP980, (d

, (f) GMW2

or

d)

2-

F

s

Figure 8: Cro

spot weld nu

T

oss-section v

gget and (b)

R2

(a)

(b)

view of the a

dissimilar sp

B

C

E

31

assumed axi

pot weld nug

isymmetric b

gget.

D

R1

barrel shape

of (a) similaar

32

Table 4: Dimensions of the axisymmetric barrel shape of spot welded joints

[mm]

Similar spot welds Dissimilar spot welds

TRIP980

(5.0 kA)

TRIP980

(6.0 kA) DP980 GMW2

DP980(U)-

TRIP980(L)

GMW2(U)-

TRIP980(L)

A 4.81 5.30 7.75 5.72

B 4.95 6.20 8.56 6.10

C 4.95 6.20 7.12 6.10 4.27 5.24

D 0.100 0.100 0.380 0.190 6.16 6.70

E 0.0900 0.0900 0.410 0.200 0.0630 0.0323

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

U-A 6.48 6.20

U-B 7.07 6.70

U-F 0.160 0.183

U-T 1.60 1.20

U-R1 4.42 3.01

U-R2 2.50 2.45

L-A 5.56 =U-A

L-B 6.16 =U-B

L-F 0.221 0.173

L-T 1.20 1.20

L-R1 2.55 =U-R1

L-R2 1.86 2.59

33

3.2 A newly designed miniature test

In order to analyze mechanical behavior of the welded joint, a miniature specimen was

newly designed. The new specimen was made with two base sheets spot welded

together in the middle, as shown in Figure 9. The new specimen was tapered around

the weld nugget so that major deformation was induced on the weld nugget and failure

occurred mainly near the middle of the specimen as a consequence of non-uniform

deformation. The size of the miniature specimen was intended to have tension test even

with a typical universal tensile machine such as Instron 8801 in this research.

Characteristic deformation of the specimen during the miniature test was attributed not

only to the featured geometry of the specimen but also to the difference of the material

properties corresponding to several zones of the weld joint. Therefore, it is essential to

analyze the mechanical behavior of each zone utilizing the inverse calibration method.

Deformation of the specimen was measured in two ways using the strain gauge and the

extensometer as shown in Figure 9 (c). The strain gauge (Tokyo Sokki kenkyujo Co.,

YFLA-2-1L) with the gauge length of 2 mm was attached on the top of the dented

surface of the weld nugget mainly to measure the deformation of the local region

confined in the weld nugget, while the extensometer with the gauge length of 25 mm

was hung up to assess combined deformation of the weld nugget and the base in the

mid-portion of the specimen. When attaching the strain gauge to dissimilar spot welded

joints, it should be on the top surface of the weld nugget in the side of the TRIP980

sheet to make probability of early detachment of the strain gauge much lower,

especially for the GMW2-TRIP980 specimen showing larger curvature after the test as

shown in Figure 10. As the larger curvature was due to the big difference of hardening

34

behaviors between two base sheets of the GMW2-TRIP980 welded specimen, the

TRIP980 side of GMW2-TRIP980 specimens was to be under tensile deformation

mode under which wide range of deformation was easily measurable, while its GMW2

side underwent compressive deformation.

Assuming that the weld nugget was more or less strain rate insensitive for simplicity

(Combescure et al., 2003), the miniature tests were carried out with one tensile speed,

0.05 mm/s. For the particular tensile speed, the engineering strain rate at the weld

nugget was approximately 0.017 /s calculated from the numerical simulation, which

was comparable to that of about 0.005 /s obtained for both quasi-static coupon tests

(the lap-shear and U-shape tension tests, which were to be analyzed later).

F

v

f

Figure 9: Spe

view, and (c

fixture with t

(a)

(d)

ecimen conf

c) the side v

the specimen

figuration of

view of the

n installed.

35

(b)

f the (a) as-re

newly desig

) (c)

eceived spot

gned miniatu

welded stac

ure specimen

ck, (b) the to

n and (d) th

op

he

F

D

T

e

d

T

G

D

s

w

T

d

m

d

m

b

Figure 10: Th

DP980-TRIP

The tests we

engineering

duplication

TRIP980 cas

GMW2 case

DP980 case,

strain gauge t

weld nugget

TRIP980 ca

detached be

measurement

detachment

measurement

but also from

he top view a

P980 (b) GM

ere repeated t

stress-strain

but their m

se, measurem

e stopped as

strain gaug

to the dented

surface incu

ases, among

fore the lim

t. As for the

of strain ga

t limit. Deta

m the high cu

and the side

MW2-TRIP98

two or three

n curves m

measurement

ment ended

it reached

es were deta

d surface was

urred by its l

three mini

mit of meas

dissimilar G

auges and on

achment of th

urvature indu

36

view of the

80.

e times for e

measured wit

ended wit

with (abrup

the limit of

ached before

s not so firm

large electro

iature test r

surement an

GMW2-TRIP

nly one firm

he strain gau

uced on the w

miniature sp

ach weld as

th the strai

th various r

pt) fracture,

f the strain g

e the limit b

m with the lar

ode force. As

results, only

nd the othe

P980 case, tw

mly stuck to

uge was not

weld nugget

pecimen after

shown in Fi

n gauges s

reasons. For

while that o

gauge. As fo

because attac

ge depth of t

s for the dis

one strain

ers showed

wo of three re

o the weld n

only from t

by large ben

r failure for (

igure 11. Th

showed goo

r the simila

of the simila

or the simila

chment of th

the dent at th

similar P980

n gauge wer

the limit o

esults showe

nugget up t

the deep den

nding momen

(a)

he

od

ar

ar

ar

he

he

0-

re

of

ed

to

nt

nt

37

from the boundary condition of the test and difference of hardening behavior between

materials, as shown in Figure 10. The force displacement curves measured with the

extensometer was also depicted in Figure 11 showing good duplication up to the

maximum force and ended with failure at different points. In addition, decreasing

tendency of force was somewhat different for every specimen. It might be from that

crack propagation has uncertainty in terms of its direction and speed affected by the

surface condition machined for each specimen even though it did not significantly

influence the deformation behavior before maximum force.

38

(a)

(b)

Engineering strain

0.00 0.01 0.02 0.03 0.04 0.05 0.06

En

gin

eeri

ng

str

ess

(MP

a)

0

200

400

600

800

1000

1200

1400

1600

1800

Experiment 1

Experiment 2

Simulation

Crack (=1.0)

Displacement (mm)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Fo

rce

(N)

0

2000

4000

6000

8000

10000

12000

14000Experiment 1

Experiment 2

Simulation

Termination point of straingauge measurement

Crack (=1.0)

39

(c)

(d)

Engineering strain

0.000 0.005 0.010 0.015 0.020

En

gin

eeri

ng

str

ess

(MP

a)

0

200

400

600

800

1000

1200

1400

1600

1800

Experiment 1

Experiment 2

Experiment 3

Simulation

Displacement (mm)

0.0 0.5 1.0 1.5 2.0 2.5

Fo

rce

(N)

0

2000

4000

6000

8000

10000

12000

14000Experiment 1

Experiment 2

Experiment 3

Simulation

Termination point of straingauge measurement

Crack (=1.0)

40

(e)

(f)

Engineering strain

0.00 0.02 0.04 0.06 0.08 0.10

En

gin

eeri

ng

str

ess

(MP

a)

0

200

400

600

800

1000

1200

1400

1600

1800Experiment 1

Experiment 2

Experiment 3

Simulation

Displacement (mm)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

Fo

rce

(N)

0

2000

4000

6000

8000

10000

12000

14000Experiment 1

Experiment 2

Experiment 3

Simulation

Termination point of straingauge measurement

Crack (

41

(g)

(h)

Engineering strain

0.00 0.02 0.04 0.06 0.08 0.10

En

gin

eeri

ng

str

ess

(MP

a)

0

200

400

600

800

1000

1200

1400

1600

1800

Experiment 1

Experiment 2Experiment 3

SimulationTermination point of straingauge measurement

Displacement (mm)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Fo

rce

(N)

0

2000

4000

6000

8000

10000

12000

14000

Experiment 1

Experiment 2Experiment 3

SimulationTermination point of straingauge measurement

Predicted failure point

42

(i)

(j)

Figure 11: Comparison of the simulated/measured engineering stress-strain and force-

displacement curves for similar welds of (a)~(b) TRIP980, (c)~(d) DP980, (e)~(f)

GMW2 and for dissimilar welds of (g)~(h) DP980-TRIP980, (i)~(j) GMW2-TRIP980.

Engineering strain

0.00 0.02 0.04 0.06 0.08 0.10

En

gin

eeri

ng

str

ess

(MP

a)

0

200

400

600

800

1000

1200

1400

1600

1800

Experiment 1

Experiment 2Experiment 3

SimulationTermination point of straingauge measurement

Displacement (mm)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Fo

rce

(N)

0

2000

4000

6000

8000

10000

12000

14000

Experiment 1

Experiment 2Experiment 3

SimulationTermination point of straingauge measurement

Predicted failure point

43

3.3 Numerical inverse calibration of hardening curves and fracture criteria

During the miniature test, deformation was distributed non-uniformly throughout the

miniature specimen even though majority of deformation was concentrated at the weld

nugget. Therefore, the numerical inverse method was applied to characterize the

hardening behavior of the welded joint as similarly done for the base sheet while the

mechanical properties inversely calibrated were applied for the base sheet. The

ABAQUS/Explicit code was utilized for numerical simulations using the 3D 8-node

linear brick element with reduced integration (C3D8R) (ABAQUS, 2012), for which

mesh sizes were approximately 0.20 0.20 0.10 mm3 for the BM except for the

region for grip and 0.048 0.068 0.080 mm3 for fine meshes at the center of the

weld nugget as shown in Figure 12 (for the case of TRIP980 with 6.0 kA). The von

Mises yield function was also assumed for each weld zone (FZ and HAZ) along with

strain rate insensitivity for simplicity and the same isotropic elastic properties were

shared by the weld zones and the base sheet for simplicity. From the various simulation

results, it was found for the inversely calibrated hardening behavior to be sensitive to

weld nugget geometries, especially the dent size and depth, so that extra care should be

taken to provide accurate dimensions of the weld nuggets as listed in Table 4 with

Figure 8.

The fracture criterion as well as the hardening data of each welded joint was

characterized utilizing the inverse calibration method. As for the similar weld, various

hardening (true stress-strain) curves of its weld nugget (regarding FZ and HAZ as a

single zone) were iteratively tried out until the simulated curves simultaneously well

m

w

e

s

c

F

a

A

w

v

v

p

f

matched with

with the st

extensometer

similar weld

comparison.

Figure 12. Fi

and (b) the si

As for the dis

weld because

value not in-

value with

properties of

fracture crite

h the measur

train gauge

r as shown i

nuggets wer

inite elemen

ide view.

ssimilar weld

e measureme

-between tho

optical mic

f the HAZs w

eria for the

red ones bot

and the

n Figure 11.

re plotted in

t meshes of

d, its HAZs w

ent of harnde

ose on the BM

croscopic ob

were approxi

HAZs of T

(a

44

th in the eng

force-displa

. The resulti

Figure 13 a

a newly des

was to be co

eness value o

Ms and the F

bservation a

imiately assu

TRIP980, DP

a)

gineering stre

acement cur

ng calibrated

along with th

signed minia

onsidered in m

on some of th

FZs. Based o

as shown in

umed in that

P980, and G

ess-strain cu

rve measure

d hardening

hose of the b

ture test: (a)

modeling of

he HAZs sho

on the measu

n Figure 7

the hardenin

GMW2 in b

(b)

urve measure

ed with th

curves of th

ase sheets fo

) the top view

the dissimila

owed hardnes

ured hardnes

7, mechanica

ng curves an

both kinds o

ed

he

he

or

w

ar

ss

ss

al

nd

of

45

dissimilar spot welded joints were to be the same as those for the weld nuggets in the

similar spot welded joints of TRIP980, DP980, and GMW2, respectively, since the

hardeness values for HAZs of TRIP980, DP980, and GMW2 in both of the dissimilar

spot welded joints (DP980-TRIP980 and GMW2-TRIP980) were shown to be

comparable to those for the FZs in the similar spot welded joints with TRIP980, DP980,

and GMW2, respectively. Applying the properties characterized already to the HAZs as

well as the BMs, inverse calibration was iteratively carried out with various hardening

(true stress-strain) curves of the FZs until the simulated curves simultaneously matched

well with both of the engineering stress-strain curves measured with the strain gauge

and the force-displacement curve measured with the extensometer, as shown in Figure

11. The resulting calibrated hardening curves of the FZs for both dissimilar spot

welded joints were plotted along with those of the HAZs and the base sheets, as shown

in Figure 14.

As demonstrated in Figure 13 and Figure 14, the hardening curves were so distinct for

the base sheets and their weld zones. Except for the similar DP980 joints, the weld

nuggets of the similar TRIP980 and the similar GMW2 joints were much stronger than

their base sheets. The weld nugget of the similar TRIP980 joint was brittle and that of

the similar GMW2 joint was ductile enough as its base sheet was, while that of the

similar DP980 joint was not so brittle but less ductile than its base sheet. The strength

level of the characterized hardening curves of the FZs for each dissimilar spot welded

joint was positioned in-between those for its HAZs, like that the level of hardness

values of its FZ were found to be in-between those of its HAZs of each dissimilar spot

welded joint shown in Figure 7. Quite different from the base sheets, hardening

46

behavior of all the weld zones did not accompany hardening deterioration up to macro

crack formation.

47

(a)

(b)

Equivalent plastic strain

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Tru

e st

ress

(M

Pa)

0

200

400

600

800

1000

1200

1400

1600

1800

2000

WeldBaseCrack (=1.0)

Triaxiality

-0.5 0.0 0.5 1.0 1.5 2.0

Eq

uiv

alen

t p

last

ic s

trai

n

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Fracture strain of weldFracture strain of baseDeformation historyApparent fracture strainCrack (=1.0)

48

(c)

(d)

Equivalent plastic strain

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Tru

e st

ress

(M

Pa)

0

200

400

600

800

1000

1200

1400

1600

1800

2000

WeldBaseCrack (=1.0)

Triaxiality

-0.5 0.0 0.5 1.0 1.5 2.0

Eq

uiv

alen

t p

last

ic s

trai

n

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8Fracture strain of weldFracture strain of baseDeformation historyApparent fracture strainCrack (=1.0)

49

(e)

(f)

Equivalent plastic strain

0.0 0.5 1.0 1.5 2.0 2.5

Tru

e st

ress

(M

Pa)

0

200

400

600

800

1000

WeldBaseCrack (=1.0)

Triaxiality

-0.5 0.0 0.5 1.0 1.5 2.0

Eq

uiv

alen

t p

last

ic s

trai

n

0

1

2

3

4

5

6Fracture strain of weldFracture strain of baseDeformation historyApparent fracture strainCrack (=1.0)

50

(g)

(h)

Equivalent plastic strain

0.0 0.2 0.4 0.6 0.8 1.0

Tru

e st

ress

(M

Pa)

200

400

600

800

1000

1200

1400

1600

1800

Weld: TRIP980Weld: DP98Weld: GMW2

Triaxiality

-0.5 0.0 0.5 1.0 1.5 2.0

Fra

ctu

re s

tra

in

0

1

2

3

4

5

6Weld: TRIP980Weld: DP980Weld: GMW2

51

(i)

(j)

Figure 13: Comparison of true stress-true strain curves and fracture criteria of base

sheets and weld nuggets of similar spot welds for (a)~(b) TRIP980, (c)~(d) DP980,

(e)~(f) GMW2, (g)~(h) all the weld nuggets, (i)~(j) all the base sheets.

Equivalent plastic strain

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

Tru

e st

ress

(M

Pa)

0

200

400

600

800

1000

1200

1400

1600

1800

Base: TRIP980Base: DP980Base: GMW2

Triaxiality

-0.5 0.0 0.5 1.0 1.5 2.0

Fra

ctu

re s

tra

in

0.0

0.5

1.0

1.5

2.0

2.5

Base: TRIP980Base: DP980Base: GMW2

52

(a)

(b)

Equivalent plastic strain

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Tru

e s

tre

ss

(M

Pa

)

0

200

400

600

800

1000

1200

1400

1600

1800

2000FZ: DP980-TRIP980Crack (=1.0)

Triaxiality

-0.5 0.0 0.5 1.0 1.5 2.0

Eq

uiv

alen

t p

last

ic s

tra

in

0.0

0.2

0.4

0.6

0.8

1.0

1.2Fracture strainDeformation historyApparent fracture strainCrack (=1.0)

53

(c)

(d)

Equivalnet plastic strain

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Tru

e s

tre

ss

(M

Pa

)

0

200

400

600

800

1000

1200

1400

1600

1800

2000

FZ: GMW2-TRIP980Crack (=1.0)

Triaxiality

-0.5 0.0 0.5 1.0 1.5 2.0

Eq

uiv

alen

t p

last

ic s

trai

n

0.0

0.2

0.4

0.6

0.8

1.0

1.2Fracture strainDeformation historyApparent fracture strainCrack (=1.0)

54

(e)

(f)

Equivalent plastic strain

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Tru

e st

ress

(M

Pa)

0

200

400

600

800

1000

1200

1400

1600

1800

2000

FZ: DP980-TRIP980Crack (=1.0)Base: TRIP980Base: DP980HAZ: TRIP980HAZ: DP980

Triaxiality

-0.5 0.0 0.5 1.0 1.5 2.0

Fra

ctu

re s

trai

n

0.0

0.5

1.0

1.5

2.0

2.5

HAZ: TRIP980HAZ: DP980FZ: DP980-TRIP980Base: TRIP980Base: DP980

55

(g)

(h)

Figure 14: True stress-true strain curves and the fracture criteria of the fusion zone of

the dissimilar spot welded joints for (a)~(b) DP980-TRIP980, (c)~(d) GMW2-

TRIP980 and comparison of base sheets, heat-affected zones and the fusion zone of the

dissimilar joints for (e)~(f)DP980-TRIP980, (g)~(h) GMW2-TRIP980.

Equivalnet plastic strain

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Tru

e st

ress

(M

Pa)

0

200

400

600

800

1000

1200

1400

1600

1800

2000

FZ: GMW2-TRIP980Crack (=1.0)Base: TRIP 980Base: GMW2HAZ: TRIP980HAZ: GMW2

Triaxiality

-0.5 0.0 0.5 1.0 1.5 2.0

Fra

ctu

re s

trai

n

0

1

2

3

4

5

6HAZ: TRIP980HAZ: GMW2FZ: GMW2-TRIP980Base: TRIP980Base: GMW2

56

As for the fracture criterion of the weld zone, the same simplified dependence of the

effective fracture strain on the stress triaxiality was assumed similarly as done for the

base sheet only with one exception that there were two sets of ( )F for the region

beyond the simple tension mode ( 0.333 ). As for that region, Eq. (4) was

employed for the ductile weld zone (therefore, for the similar GMW2 weld nugget) and

Eq. (5) was suggested for the not-so-ductile weld zones (therefore, for the rest of spot

welded joints including TRIP980 or DP980), as shown in Figure 4:

/exp( )F n K

K

K

(5)

with 3.0n . Consequently, there was only one constant, C or K , to characterize

in this simplified fracture criterion for the weld zones of the similar and dissimilar

welded joints. As done for the base sheet, the simplified fracture criterion for the weld

nugget including Eq. (4) or Eq. (5) was also obtained after various formulae have

been tried out.

Employing the hardening curves and the fracture criteria of the base sheets and their

weld zones previously characterized, the fracture criteria of the weld zones could be

inversely calibrated such that failure occurred with 1.0 at the assumed failure

points as x-marked in the measured force-displacement curves as shown in Figure 11.

The calibrated values of the each weld zone were listed in Table 5, while the (apparent)

effective fracture strains accounting for the change of the deformation mode were

depicted in Figure 13 and Figure 14. As for the TRIP980 similar joints, the miniature

test showed brittle fracture, as shown in Figure 11 (a)~(b), so that it was easy to

57

identify the failure point. As for the rest of the spot welded joints, however, the

measured force-displacement curves did not show good duplication after the maximum

force point so that it was reasonable to assume failure points to be the point right

before divergence of experimental curves as shown in Figure 11 (c)~(j).

As for comparison of the ways the spot welded joints were modeled, furthermore, the

dissimilar welded joints were also considered as the sole weld nugget, in which there

was no distinction between the HAZ and the FZ and regarded as a single zone. Based

on the miniature test results, hardening curves and fracture criteria of the sole weld

nugget for two dissimilar spot welded joints, DP980-TRIP980 and GMW2-TRIP980,

was inversely calibrated with finite element simulation as similarly done in above. The

resulting calibrated properties were not shown in this because the calibrated hardening

curves and fracture criteria of the sole weld nugget did not show noticeable gap but

almost same properties as those of the FZ in the modeling with five distinct zones. The

ignorable gap of calibrated properties between two modeling ways might be from that

the characteristic geometry of the miniature specimen configuration enabled majority

of deformation to occur only in the common region between two modeling, i.e., the

region FZ occupied in the five distinct zone modeling.

58

Table 5: Parameters of the effective fracture strains for the weld nuggets in the similar

welded joints (TRIP980, DP980, GMW2) and for the FZs of in the dissimilar welded

joints (DP980-TRIP980, GMW2-TRIP980)

Steel type

Parameter TRIP980 DP980 GMW2

DP980-

TRIP980

GMW2-

TRIP980

K 5.90 3.25 4.76 4.36

C 1.71

D 0.103 0.505 2.57 0.223 0.285

59

4. Failure analysis of coupon tests

Utilizing the calibrated mechanical properties such as the hardening behavior as well as

the fracture criteria of the base sheet and each weld zone, the failure behavior of the

resistance spot welded joints in the coupon tests was analyzed. As for the coupon tests,

the lap-shear and the U-shape tension tests were executed with the specimen

configuration and fixtures shown in Figure 15, while extensometers with the gauge

lengths of 81 mm and 12.5 mm were used to measure the displacement of the lap-shear

and the U-shape tensile tests, respectively.

Since the relative difference of strength and ductility between the base sheets and the

weld zones directly affected the failure mode as well as peak load in the coupon tests,

the experimental results of the lap-shear and U-shape tests were informative to validate

the previously calibrated properties of the base sheets and the weld zones. The two

coupon tests were simulated utilizing the ABAQUS/Explicit code and the 3D 8-node

linear brick element with reduced integration (C3D8R) (ABAQUS, 2012), while the

mesh size was 0.03 0.03 0.10 mm3 near the center of the welded joint as shown in

Figure 16.

F

(

Figure 15: Sp

(b) the U-sha

pecimen con

ape tension te

nfigurations

est.

60

(a)

(b)

and fixtures

for (a) the lap-shear ten

nsion test annd

F

t

Figure 16: Fi

the U-shape t

inite element

tension test.

t meshes for

61

(a)

(b)

simulation oof (a) the lap

-shear tensioon test and (b

b)

62

4.1 Coupons with similar spot welded joints

All the tests were repeated five times under the quasi-static loading condition with the

tensile speed of 0.02 mm/s. The force-displacement test data and the failure modes are

summarized in Figure 17 and Figure 18 for the lap-shear and U-shape tension tests,

respectively. The repeated tests showed good duplication for the failure mode of each

type of samples and each type had distinct failure mode. The GMW2 and DP980

welded samples showed all pull-out and interfacial modes, respectively, for both

coupon tests. However, the TRIP980 welded samples showed mixed results, in which

the interfacial mode occurred for both coupon tests with 5.0 kA and the pull-out mode

for the lap-shear test and the interfacial mode for the U-shape test arose for the case of

6.0 kA.

As for the GMW2 sheet, the simulation results properly predicted pull-out failure

modes for both coupon tests, complying with the experiments as shown in Figure 19

(g)~(h), which were mainly incurred by deformation concentration at the base sheet

(with minimal deformation at the weld nugget) associated with the much lower

strength of the base sheet compared to that of the weld nugget. The simulated force-

displacement curves also agreed reasonably well, especially for failure strength, with

the experimental ones for both coupon tests as shown in Figure 17 (d) and Figure 18

(d), respectively. The results suggested that, for the GMW2 case as a conventional mild

steel sheet, ductility was good both for the base and the weld nugget so that detailed

fracture criteria did not play an important role and the softer hardening of the base

sheet was supposed to lead the coupons to pull-out failure. It could support the

common practice employed in the earlier analysis to assume the rigidity on the weld

63

nugget only to induce pull-out failure (Chao, 2003b; Lin et al., 2003).

As for the GMW2 coupon, the early interfacial failure was averted with a large enough

constant D (assumed value, 50% of 0.333F

) in the negative stress traxiality region

so that the pull-out failure was achieved. In order to simulate the gradual decline with

the pull-out failure mode, the resistance to the macro-crack propagation was considered

in simulation by adding the linear gradual decline of the stress (in addition to the

vertical decline) in the base sheet data after the macro-crack formation (with 1.0

in Eq. (3)) as shown in Figure 3 (f). The added resistance to the macro-crack

propagation improved the simulation result (with gradual decline of force) as shown in

Figure 17 (d). However, the added resistance did not affect the results for the standard

simple tension test and the U-shape test, for which the crack propagation was minimal.

As for the similar joints of the DP980 sheets, the numerical analysis well predicted the

interfacial failure mode and the force-displacement curves, especially the peak loads,

for both coupon tests as shown in Figure 19 (e)~(f), Figure 17 (c) and Figure 18 (c).

Unlike the GMW2 case (as one extreme), for which the softer base sheet and

comparably good ductility for the base and the weld drove all pull-out failure for both

tests, the significantly lower ductility of the weld nugget (while strength is similar), as

shown in Figure 13 (d), led to all interfacial failure in both tests for the DP980 case (as

another extreme).

As for the TRIP980 case, as mentioned earlier, the same simulation conditions were

applied to simulation of both cases of 5.0 kA and 6.0 kA, except for only dimensional

64

difference of the weld nuggets as listed in Table 4. Unlike the two extremes above, for

which ductility or strength is similar or distinct, the weld nugget was much stronger

with much lower ductility (compared to the base sheet) for the TRIP980 case (therefore,

an interim of two extremes) as shown in Figure 13 (b) and the failure mode was mixed.

However, the mixed failure modes and the force-displacement curves of both coupon

tests with 5.0 kA and 6.0 kA cases were well numerically predicted as shown in Figure

19 (a)~(d), Figure 17 (a)~(b) and Figure 18 (a)~(b), respectively. As for the force-

displacement curves of the U-shape tension tests, experimental duplication was not so

good but the simulation results matched reasonably well with the peak loads in Figure

19 (a)~(b). As for the force-displacement curve of the lap-shear test with the 6.0 kA

case, which failed in the pull-out mode both for the simulation and the experiment

(with a bigger nugget size compared to that of the 5.0 kA case), the force decline after

the maximum point was gradual with the pull-out failure as occurred in the GMW2

case. The linear gradual decline of the stress in the base sheet data after the macro-

crack formation (with 1.0 in Eq. (3)), as shown in Figure 3 (b), was added to

emulate the resistance to the macro-crack propagation, which improved the simulation

result as shown in Figure 17 (b).

65

(a)

(b)

TRIP980-TRIP980 (5.0 kA)

Failure mode

01 Interfacial

02 Interfacial

03 Interfacial

04 Interfacial

05 Interfacial

Displacement (mm)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Fo

rce

(N)

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

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24000Experiment 1Experiment 2Experiment 3Experiment 4Experiment 5Simulation

TRIP980-TRIP980 (6.0 kA)

Failure mode

01 Pull-out

02 Pull-out

03 Pull-out

04 Pull-out

05 Pull-out

Displacement (mm)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Fo

rce

(N)

0

2000

4000

6000

8000

10000

12000

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20000

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24000Experiment 1Experiment 2Experiment 3Experiment 4Experiment 5

Simulation

66

(c)

(d)

Figure 17: Force–displacement curves and failure modes of the lap-shear tension test

for the similar welded joints of (a) TRIP980-5kA, (b) TRIP980-6kA, (c) DP980, (d)

GMW2.

Displacement (mm)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Fo

rce

(N)

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

22000

24000Experiment 1Experiment 2Experiment 3Experiment 4Experiment 5Simulation

DP980-DP980

Failure mode

01 Interfacial

02 Interfacial

03 Interfacial

04 Interfacial

05 Interfacial

GMW2-GMW2 Failure mode

01 Pull-out

02 Pull-out

03 Pull-out

04 Pull-out

05 Pull-out

Displacement (mm)

0 2 4 6 8 10 12 14 16 18 20 22

Fo

rce

(N)

0

2000

4000

6000

8000

10000

12000

14000

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18000

20000

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24000Experiment 1Experiment 2Experiment 3Experiment 4Experiment 5

Simulation

67

(a)

(b)

TRIP980-TRIP980(5.0 kA)

Failure mode

01 Interfacial

02 Interfacial

03 Interfacial

04 Interfacial

05 Interfacial

Displacement (mm)

0 1 2 3 4 5 6 7 8 9 10 11 12

Fo

rce

(N

)

0

1000

2000

3000

4000

5000

6000

7000

8000

9000Experiment 1Experiment 2Experiment 3Experiment 4Experiment 5Simulation

TRIP980-TRIP980(6.0 kA)

Failure mode

01 Interfacial

02 Interfacial

03 Interfacial

04 Interfacial

05 Interfacial

Displacement (mm)

0 1 2 3 4 5 6 7 8 9 10 11 12

Fo

rce

(N

)

0

1000

2000

3000

4000

5000

6000

7000

8000

9000Experiment 1Experiment 2Experiment 3Experiment 4Experiment 5Simulation

68

(c)

(d)

Figure 18: Force–displacement curves and failure modes of the U-shape tension test for

the similar welded joints of (a) TRIP980-5kA, (b) TRIP980-6kA, (c) DP980, (d)

GMW2.

DP980-DP980

Failure mode

01 Interfacial

02 Interfacial

03 Interfacial

04 Interfacial

05 Interfacial

Displacement (mm)

0 1 2 3 4 5 6 7 8 9 10 11 12

Fo

rce

(N

)

0

1000

2000

3000

4000

5000

6000

7000

8000

9000Experiment 1Experiment 2Experiment 3Experiment 4Experiment 5Simulation

GMW2-GMW2

Failure mode

01 Pull-out

02 Pull-out

03 Pull-out

04 Pull-out

05 Pull-out

Displacement (mm)

0 2 4 6 8 10 12 14 16 18 20 22

Fo

rce

(N)

0

1000

2000

3000

4000

5000

6000

7000

8000

9000Experiment 1Experiment 2Experiment 3Experiment 4Experiment 5Simulation

69

(a)

(b)

70

(c)

(d)

71

(e)

(f)

F

w

s

(

b

Figure 19: C

welded coup

shape; (TRIP

(DP980) the

both (g) lap-s

Comparison

pon tests: (TR

P980-6kA) (c

interfacial fo

shear and (h)

of experime

RIP980-5kA

c) the pull-ou

or both (e) la

) U-shape.

72

(g)

(h)

ental and sim

A) the interfa

ut for lap-she

ap-shear and

mulated failu

acial for both

ear and (d) th

(f) U-shape;

ure modes o

h (a) lap-she

he interfacial

(GMW2) th

of the simila

ear and (b) U

l for U-shape

he pull-out fo

ar

U-

e;

or

73

4.2 Coupons with dissimilar spot welded joints

Under the quasi-static loading condition with the tensile speed of 0.02 mm/s, both

coupon tests were repeated three times and two times for the dissimilar welded joints

of DP980-TRIP980 and GMW2-TRIP980, respectively. The resulting force-

displacement data and the failure modes were summarized in Figure 20 and Figure 21

for the lap-shear and U-shape tension tests, respectively. The repeated tests showed

good duplication for the failure mode as well as the force-displacement curves. All the

samples showed the pull-out failure mode for both coupon tests. For evaluation of

finite element modeling for dissimilar spot welded joints, modeling with five distinct

zones was carried out with the characterized properties of each zone in advance. The

numerical simulation results well predicted the experimental failure modes for both

coupon tests as shown in Figure 22 and matched well with the measured force-

displacement curves as shown in Figure 21.

Furthermore, other two approaches to modeling of dissimilar spot welded joints were

also introduced for comparison. One was the sole weld nugget modeling proposed in

the similar case of the welded joint and the other was the rigid modeling in which the

faying surface region was assumed to be rigid (not allowing deformation) and base

material properties were applied to the whole of the sample except on the faying

surface region. The numerical simulation results were plotted with experimental ones

as shown in Figure 23.

As for the dissimilar welded joint of DP980-TRIP980, finite element simulation

considering five distinct zones for the welded joint showed the best match with

74

experimental results of the lap-shear and the U-shape tension tests as shown in Figure

23 (a)~(b), respectively, in which the pull-out failure mode as well as the maximum

force level of the tests were well predicted. The TRIP980 sheet of the lap-shear and the

U-shape tension specimens undergone major deformation, while the DP980 sheet of

the specimens withstood better against the external load since the DP980 sheet had

much larger thickness and comparable strength compared to the TRIP980 sheet. It was

inferred that crack initiated at the TRIP980 sheet near to the weld nugget rather than

the DP980 sheet, as shown in Figure 22 (a)~(b).

Compared to the modeling with the five distinct zones for the dissimilar welded joint,

the other two ways of modeling the welded joint, the sole weld nugget and the rigid

modeling, were determined not to be suitable for application. As for the lap-shear

tension test of the TRIP980-DP980 joint, as shown in Figure 23 (a), the rigid modeling

more or less deviation of the maximum force. The deviation was attributed to

difference of mechanical properties applied to the welded joint. As for the rigid

modeling, the mechanical properties of the base sheets were implemented into the weld

zones except on the faying surface, which resulted in weaker than the original strength

of the FZ. This made the maximum force a little bit lower for the simulation of the lap-

shear test with the rigid modeling. As for the U-shape tension test, simulation results

with three ways of modeling had totally different response, as shown in Figure 23 (b).

Finite element simulation concerning five distinct zones well predicted the pull-out

failure mode as well as the force-displacement curve. However, the sole weld nugget

modeling for the welded joint showed a little bit higher maximum force compared to

the experimental result and gave a rise to the interfacial failure mode, while a rigid

75

modeling bore much higher maximum force keeping the pull-out failure mode. As for

the modeling concerning five distinct zones, the material properties applied to the HAZ

of the TRIP980 sheet had the least ductility in spite of the highest strength, as shown in

Figure 14 (e), which led early failure to occur initially in the HAZ of the TRIP980

sheet resulting in the pull-out failure mode. As for the sole weld nugget modeling, its

mechanical properties (the same as those of the FZ in the modeling with the five

distinct zones) applied to the sole weld nugget showed better ductility compared to the

HAZ of TRIP980 so that failure did not arise initially until high triaxiality on the

faying surface region was reached and failed. Meanwhile, simulation result with the

rigid modeling for the welded joint overestimated the maximum force because of

superior ductility of the base sheet, as shown in Figure 14 (a), applied to the welded

joint.

As for the dissimilar welded joint of GMW2-TRIP980, experimental results and all the

simulation results with three ways of modeling for the welded joint showed the almost

same force-displacement curves along with the pull-out failure mode for the lap-shear

and U-shape tension tests, as shown in Figure 22 (c)~(d) and Figure 23 (c)~(d). Since

the GMW2 sheet was confirmed to be very ductile and much weaker than the other

materials, as shown in Figure 14 (h), most deformation during both coupon tests was

concentrated on the region of the base sheet of the GMW2 close to the weld nugget,

which got to make no difference between three ways of modeling for the welded joint.

Only for the rigid modeling, failure initiation was found to be a little bit earlier during

simulations of both coupon tests, which was caused by faster concentration of

deformation in the base sheet promoted by large difference of strength between the

76

base sheet and the rigid faying surface. Consequently, as for the resistance spot

welding of a conventional mild steel sheet with an AHSS sheet (GMW2-TRIP980 in

this paper), conventional way of modeling the welded joint was validated to be useful.

Rigidity would be assumed on the faying surface and the properties of the weld nugget

could not be characterized by sharing the common properties with the base sheet.

77

(a)

(b)

Figure 20: Force–displacement curves and failure modes of the lap-shear test for the

dissimilar spot welded joints of (a) DP980-TRIP980 and (b) GMW2-TRIP980.

DP980-TRIP980

Failure mode

01 Pull-out

02 Pull-out

03 Pull-out

Extension (mm)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Fo

rce

(N

)

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

22000

24000Experiment 1Experiment 2Experiment 3Simulation

GMW2-TRIP980

Failure mode

01 Pull-out

02 Pull-out

Displacement (mm)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5

Fo

rce

(N)

0

2000

4000

6000

8000

10000

12000

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16000

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20000

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24000Experiment 1Experiment 2Simulation

78

(a)

(b)

Figure 21: Force–displacement curves and failure modes of the U-shape tension test for

the dissimilar welded joints of (a) DP980-TRIP980 and (b) GMW2-TRIP980.

DP980-TRIP980

Failure mode

01 Pull-out

02 Pull-out

03 Pull-out

Displacement (mm)

0 1 2 3 4 5 6 7 8 9 10 11 12

Fo

rce

(N)

0

1000

2000

3000

4000

5000

6000

7000

8000

9000Experiment 1Experiment 2Experiment 3Simulation

Extension (mm)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Fo

rce

(N)

0

1000

2000

3000

4000

5000

6000

7000

8000

9000Experiment 1Experiment 2Simulation GMW2-

TRIP980Failure mode

01 Pull-out

02 Pull-out

79

(a)

(b)

F

w

(

s

Figure 22: C

welded coup

(b) U-shape;

shape.

Comparison o

on tests; (DP

(GMW2-TR

of experimen

P980-TRIP9

RIP980) the

80

(c)

(d)

ntal and simu

980) the pull-

pull-out fail

ulated failur

-out failure f

lure for both

e modes of t

for both (a)

h (c) lap-she

the dissimila

lap-shear an

ear and (d) U

ar

nd

U-

81

(a)

(b)

DP980-TRIP980:Lap-shear test

Failure mode

Experiment Pull-out

FE model:Five zones

Pull-out

FE model: Sole weld nugget

Pull-out

FE model: Rigidity assumed

Pull-out

Dismplacement (mm)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Fo

rce

(N)

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

22000

24000ExperimentFive zones Sole weld nuggetRigidity assumed forthe faying surface

DP980-TRIP980:U-shape test Failure mode

Experiment Pull-out

FE model:Five zones

Pull-out

FE model: Sole weld nugget Interfacial

FE model: Rigidity assumed Pull-out

Dismplacement (mm)

0 1 2 3 4 5 6 7 8 9 10 11 12

Fo

rce

(N)

0

1000

2000

3000

4000

5000

6000

7000

8000

9000ExperimentFive zones Sole weld nuggetRigidity assumed forthe faying surface

82

(c)

(d)

Figure 23: Force–displacement curves of three finite element models with experimental

results; (DP980-TRIP980) (a) lap-shear and (b) U-shape tension tests; (GMW2-

TRIP980) (c) lap-shear and (d) U-shape tension tests.

GMW2-TRIP980:Lap-shear test

Failure mode

Experiment Pull-out

FE model:Five zones

Pull-out

FE model: Sole weld nugget Pull-out

FE model: Rigidity assumed Pull-out

Dismplacement (mm)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

Fo

rce

(N)

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

22000

24000ExperimentFive zones G HAZ baseSole weld nuggetRigidity assumed forthe faying surface

GMW2-TRIP980:U-shape test Failure mode

Experiment Pull-out

FE model:Five zones

Pull-out

FE model: Sole weld nugget

Pull-out

FE model: Rigidity assumed Pull-out

Dismplacement (mm)

0 1 2 3 4 5 6 7 8 9 10 11 12

Fo

rce

(N)

0

1000

2000

3000

4000

5000

6000

7000

8000

9000ExperimentFive zones G HAZ baseSole weld nuggetRigidity assumed forthe faying surface

83

5. Conclusions

A practical procedure to analyze the failure of resistance spot welded joints was

developed and the procedure was applied for especially for the similar and dissimilar

welded joints of advanced high strength steel (AHSS) sheets. Three similar welds were

fabricated with two AHSS sheets, TRIP980 with the thickness of 1.2 mm and DP980

with the thickness of 1.6 mm, and with a conventional mild steel sheet, GMW2 with

the thickness of 1.2mm, for comparison purpose. Based on the TRIP980, there were

also two dissimilar welds introduced, in which one were fabricated with the DP980

(DP980-TRIP980) and the other with the GMW2 (GMW2-TRIP980). The method

included the characterization of the base material sheet regarding their mechanical

properties (as for hardening with strain rate sensitivity as well as its deterioration) and

fracture criteria (stress-triaxiality-dependent effective fracture strains) mainly based on

the inverse numerical analysis of the standard simple tension test. As for the

characterization of the weld zones, hardness measurement across the weld nugget

along with optical microscopic observation was utilized to identify the shapes and the

dimensions of the base material zones (BM), the heat-affected zones (HAZs), and the

fusion zones (FZs). Their mechanical properties as well as fracture criteria were also

characterized based on the inverse numerical analysis of the miniature tension test

newly designed in this work. The characterized properties of the base sheets, the HAZs,

and the FZs were applied to analyze failure (mode and strength) in the coupon tests of

the lap-shear and the U-shape tension tests for the similar and dissimilar welded joints,

validating the characterized properties in advance. Analysis was done under the quasi-

static condition in this early effort. The efforts were also focused on utilizing simplified

84

plasticity (based on the isotropic hardening formulation of the von Mesis yield function)

and fracture criterion (only dependent on the stress triaxiality) as well as commonly

available experimental tools (for the standard tension test, the miniature tension test,

and two coupon tests of lap-shear and U-shape tension tests), even though more

sophisticated formulations and experiments might improve the accuracy (with

significantly added costs). The simulation results based on the calibrated properties

reasonably well complied with experimental results of the coupon tests as well as the

modified miniature and the standard simple tension tests. Furthermore, in order to

evaluate the finite element modeling devised here for the dissimilar welded joints (with

five distinct zones), other two ways of modeling were also introduced, in which one

was the modeling of the welded joint as the sole weld nugget considering the HAZ and

the FZ without distinction and the other was a conventional modeling assume rigidity

on the faying surface of the welded joint. From the simulation results for the lap-shear

and the U-shape tension tests with above three ways of modeling, the following

conclusion was reached. As for the DP980-TRIP980 samples, the modeling with five

distinct zones proposed in this research was confirmed to be the best since the

mechanical properties of the HAZs surrounding the FZ were found to be crucial to

determination of the failure mode and strength of both coupon tests. As for the GMW2-

TRIP980 samples, meanwhile, the rigid modeling on the faying surface was proved to

be enough for prediction of mechanical response of the welded joints during both

coupon tests because major deformation was concentrated on the mild steel sheet,

GMW2.

85

Bibliography

ABAQUS, 2012. User's Manual (version 6.12). Dassault Systèmes Simulia Corp.,

Providence, RI, USA.

Adonyi, Y., Blodgett, O., 2006. Heat-affected zone characterization by physical

simulations. Welding journal 85, 42-47.

Aslanlar, S., 2006. The effect of nucleus size on mechanical properties in electrical

resistance spot welding of sheets used in automotive industry. Materials & Design 27,

125-131.

Bai, Y., Wierzbicki, T., 2009. Application of extended Mohr–Coulomb criterion to

ductile fracture. International Journal of Fracture 161, 1-20.

Chao, Y.J., 2003a. Failure mode of spot welds: interfacial versus pullout. Science and

technology of welding and joining 8, 133-137.

Chao, Y.J., 2003b. Ultimate strength and failure mechanism of resistance spot weld

subjected to tensile, shear, or combined tensile/shear loads. Journal of Engineering

Materials and Technology 125, 125-132.

Chen, W., Deng, X., 2000. Performance of shell elements in modeling spot-welded

joints. Finite elements in analysis and design 35, 41-57.

Cho, Y., Rhee, S., 2003. Experimental study of nugget formation in resistance spot

welding. Welding journal 82, 195-201.

Chung, K., Ma, N., Park, T., Kim, D., Yoo, D., Kim, C., 2011. A modified damage

model for advanced high strength steel sheets. International Journal of Plasticity 27,

1485-1511.

Combescure, A., Delcroix, F., Caplain, L., Espanol, S., Eliot, P., 2003. A finite

element to simulate the failure of weld points on impact. International Journal of

Impact Engineering 28, 783-802.

Deng, X., Chen, W., Shi, G., 2000. Three-dimensional finite element analysis of the

mechanical behavior of spot welds. Finite Elements in Analysis and Design 35, 17-39.

Dickinson, D., Franklin, J., Stanya, A., 1980. Characterization of spot welding

86

behavior by dynamic electrical parameter monitoring. Welding Journal 59, 170.

Goodarzi, M., Marashi, S., Pouranvari, M., 2009. Dependence of overload

performance on weld attributes for resistance spot welded galvanized low carbon steel.

Journal of Materials Processing Technology 209, 4379-4384.

Gurson, A.L., 1977. Continuum theory of ductile rupture by void nucleation and

growth: Part I—Yield criteria and flow rules for porous ductile media. Journal of

engineering materials and technology 99, 2-15.

Hernandez, V.H.B., Panda, S.K., Okita, Y., Zhou, N.Y., 2010. A study on heat affected

zone softening in resistance spot welded dual phase steel by nanoindentation. Journal

of materials science 45, 1638-1647.

Jou, M., 2001. Experimental investigation of resistance spot welding for sheet metals

used in automotive industry. Jsme International Journal Series C-Mechanical Systems

Machine Elements and Manufacturing 44, 544-552.

Khan, M., Bhole, S., Chen, D., Biro, E., Boudreau, G., Van Deventer, J., 2009.

Welding behaviour, microstructure and mechanical properties of dissimilar resistance

spot welds between galvannealed HSLA350 and DP600 steels. Science and

Technology of Welding & Joining 14, 616-625.

Kim, J.H., Sung, J.H., Piao, K., Wagoner, R.H., 2011. The shear fracture of dual-

phase steel. International Journal of Plasticity 27, 1658-1676.

Lee, W., Chung, K.-H., Kim, D., Kim, J., Kim, C., Okamoto, K., Wagoner, R.H.,

Chung, K., 2009. Experimental and numerical study on formability of friction stir

welded TWB sheets based on hemispherical dome stretch tests. International Journal

of Plasticity 25, 1626-1654.

Lepera, F.S., 1980. Improved etching technique to emphasize martensite and bainite

in high-strength dual-phase steel. J. Met. 32, 38-39.

Lin, S.-H., Pan, J., Wu, S.-R., Tyan, T., Wung, P., 2002. Failure loads of spot welds

under combined opening and shear static loading conditions. International Journal of

Solids and Structures 39, 19-39.

Lin, S.H., Pan, J., Tyan, T., Prasad, P., 2003. A general failure criterion for spot welds

under combined loading conditions. International Journal of Solids and Structures 40,

87

5539-5564.

Mahnken, R., Schneidt, A., Antretter, T., 2009. Macro modelling and homogenization

for transformation induced plasticity of a low-alloy steel. International Journal of

Plasticity 25, 183-204.

Marashi, P., Pouranvari, M., Amirabdollahian, S., Abedi, A., Goodarzi, M., 2008.

Microstructure and failure behavior of dissimilar resistance spot welds between low

carbon galvanized and austenitic stainless steels. Materials Science and Engineering:

A 480, 175-180.

Marya, M., Wang, K., Hector, L.G., Gayden, X., 2006. Tensile-Shear Forces and

Fracture Modes in Single and Multiple Weld Specimens in Dual-Phase Steels. Journal

of Manufacturing Science and Engineering 128, 287.

Na, S., Park, S., 1996. A theoretical study on electrical and thermal response in

resistance spot welding. Welding Journal-Including Welding Research Supplement 75,

233-242.

Nied, H., 1984. The finite element modeling of the resistance spot welding process.

Weld. J. 63, 123.

Oikawa, H., Murayama, G., Sakiyama, T., Takahashi, Y., Ishikawa, T., 2006.

Resistance Spot Weldability of High Strength Steel (HSS) Sheets for Automobile.

Shinnittetsu Giho 385, 36.

Radakovic, D., Tumuluru, M., 2008. Predicting resistance spot weld failure modes in

shear tension tests of advanced high-strength automotive steels. WELDING

JOURNAL-NEW YORK- 87, 96.

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.

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.

88

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.

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.

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.

89

Korean abstract (국문 초록)

초고강도강판 TRIP980, DP980 의 전기 저항 용접부에서 발생하는

파손거동을 분석하기 위한 방법을 개발하고 일반 상용강판 GMW2 의

거동과 비교 분석하였다. 세 종류의 동종 용접부 (TRIP-TRIP, DP-DP, GMW2-

GMW2) 와 두 종류의 이종 용접부 (GMW2-TRIP980 과 DP980-TRIP980) 를

분석하였다. 모재의 기본 역학적 물성을 얻기 위한 일축인장시험을

수행하였다. 실험결과에 유한요소해석을 이용한 역보정 방법을 적용하여

연화 현상을 고려한 등방 경화 곡선, 경화 곡선의 변형률 속도 의존도,

삼축응력과 변형이력을 고려한 유효 파손 변형률 모델의 지표를 수치화

하였다. 또한, 용접부 단면에 대한 경도분포 를 측정과 미세조직을

분석하였으며, 그 결과를 바탕으로 용접부를 이산화하였다. 개발한 소형

인장 시편의 시험 결과와 유한 요소 해석을 이용하여 이산화된 용접부의

등방 경화곡선과 파손 변형률 모델의 지표를 수치화였다. 파손 거동 분석과

수치화된 물성의 검증을 위하여, 대표적인 두 가지의 용접부 인장시험 (U-

shape 인장시험, lap-shear 인장시험) 을 수행하고 수치화된 물성들을

유한요소해석에 적용하여 파손을 예측하고 분석하였다. 파손 시점의

외력뿐만 아니라 그 형태까지 예측함을 확인함으로써 파손 거동 분석을

위해 개발된 모델의 효용성을 검증할 수 있었다.

주요어: 초고강도강판, 전기저항용접, 이종/동종 용접, 파손 모델, 연화거동

학 번: 2008-20642