Crush Performance of Thin Walled Spot Welded and Weld ...

1

Crush Performance of Thin Walled Spot-Welded and Weld-Bonded Sections

Paul Davidson

AUTO503 Capstone Project

Submitted to

Donald E. Malen, project advisor Sponsored by:

Weld-bond group Auto-steel Partnership American Iron and Steel Institute Southfield, MI

2

Table of Contents

Abstract ...................................................................................................................................................................... 3

Nomenclature ............................................................................................................................................................. 3

1. Introduction .......................................................................................................................................................... 3

2. Design Parameters

2.1 Section Geometry .......................................................................................................................................... 4

2.2 Material –Steel .............................................................................................................................................. 5

2.3 Material – Adhesive ...................................................................................................................................... 5

3. Numerical Simulation

3.1 Design space .................................................................................................................................................. 5

3.2 Simulation set-up ........................................................................................................................................... 5

3.3 Finite Element Modeling ............................................................................................................................... 6

3.4 Measured response ......................................................................................................................................... 6

4. Results & Observations

4.1 Results ........................................................................................................................................................... 7

4.2 Qualitative Analysis ...................................................................................................................................... 8

4.3 Crush sequence ............................................................................................................................................ 11

5. Analysis

5.1 Critical slenderness ratio ............................................................................................................................. 12

5.2 Maximum load calculation & results .......................................................................................................... 13

5.3 Average crush force result ........................................................................................................................... 15

6. A qualitative model for crush behavior .............................................................................................................. 15

7. Conclusion ......................................................................................................................................................... 16

8. Future Work ....................................................................................................................................................... 16

Acknowledgements .................................................................................................................................................. 16

References ................................................................................................................................................................ 16

Appendix A .............................................................................................................................................................. 17

Appendix B ............................................................................................................................................................... 17

Appendix C ............................................................................................................................................................... 19

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Crush Performance of Thin Walled Spot-Welded and Weld-Bonded Sections

Paul Davidson, [email protected] Department of Automobile Engineering

University of Michigan, Ann Arbor, MI 48108, USA

Abstract With the focus on weight reduction of automotive body structure, the use of thinner sections made of Advanced

High Strength Steels has increased. These thin sections are prone to local buckling in the side walls and flanges, and it is

critical to design for this behavior. A means to improve the buckling performance of the flanges, even with increased spot

weld pitch is through the use of structural adhesives. The objective of this study was to simulate and analyze the influence of

several section design parameters on axial crush performance.

A numerical analysis on the crush performance of a hexagonal thin walled section under dynamic axial loading was

carried out using Finite Element Analysis. A designed experiment, DOE, was used to study the effect of varying steel grades,

material thickness, spot weld pitch, and the influence of adhesive on maximum and average crush forces. Sub-studies

addressing adhesive modeling methods and the influence of adhesive on axial spot weld loads were also conducted.

Keywords: Weld, Weld-bonded, Adhesive, AHSS, Spot Weld, Modeling, Dynamic Crash, Simulation.

NOMENCLATURE1

𝐸𝑎 Absorbed energy

𝐹𝑎𝑣𝑔 Average crush force

𝐹𝑒𝑓𝑓 Force on effective width.

𝐹𝑚𝑎𝑥 Maximum force

𝐿𝑓 Flange width = 17mm

𝐿𝑝 Plate width = 66.7mm

𝑏𝑒 Effective width

𝑡𝑎 Adhesive thickness = 0.66mm

𝑡𝑓𝑎 Assumed thickness of flange with adhesive

𝑣0 Impact initial velocity

𝛿𝑚 Maximum crush displacement

𝜎𝑐𝑟−𝑓 Flange critical stress

𝜎𝑐𝑟−𝑝 Plate critical stress

𝜎𝑦 Material yield stress

µ Poisson’s ratio

ℎ Column height = 400mm

M Impact Mass

β Slenderness ratio

λ Buckling wavelength

𝐸 Young’s modulus

𝐾 Plate buckling coefficient

𝑆𝑊 Spot weld spacing

𝑏 Width of plate

𝑡 Material thickness

1. INTRODUCTION

The automotive industry is challenged by three critical

issues; vehicular emissions, rising fuel prices, and rising

raw material cost. The car body is affected by all three

issues and is often the most expensive system in a car (1) .

The search for lighter and more efficient energy absorbing

components has led to an increased interest in thin-walled

high-strength steel sections. The use of thin walled sections

comes with its own set of issues. Thin walls are difficult to

weld and weld strength is low. To improve joint stiffness

and weld integrity, a combination of spot weld and

adhesive joining (weld-bonding) can be used. An important

concern in using weld-bond technology is the crash

performance.

While much research has been done on axial crush of

thin walled steel sections and on adhesive joints

individually, very few papers discuss the crush behavior of

weld-bonded high strength steel sections under axial

loading. In this paper, crush characteristics of a hexagonal

section were investigated under impact with a dropped

mass. The effect of material yield strength, section

thickness, spot weld spacing and adhesive on crush

performance was numerically studied using the explicit

non-linear finite element code LS-DYNA (2), (3).

In recent years there has been significant work done

on the study on thin walled structures, especially thin

walled impact energy absorbing members. White and Jones

(4) explored the collapse characteristics for top-hat and

double-hat sections made of mild steel when subjected to

axial crushing. They also provided analytical models for

thin-walled sections. Extensive work has been done by

Schneider, et al., on High Strength Steel and thin-walled

structures. In their research project (5), influence of

material thickness and material grade on the collapse

behavior of closed section thin-walled structures under

quasi-static and dynamic axial loads has been analyzed and

compared with theoretical models. Another study (6)

looked at the part and full failure of spot-welds during the

axial collapse of the thin walled structural sections and its

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4

influence on crushing of the sections. A study by

Tarigopula (7), uses high strength steel DP800 to assess the

crush behavior, the deformation force and energy

absorption. Their findings show a significant difference

between quasi-static and dynamic crushing tests in terms of

deformation force and impact energy absorption. Yan, et

al., (8) conducted testing on hat sections with various steel

grades ranging in strength from 410MPa to 1300MPa. The

effect of spot weld size was studied by Rusinski, et al., (9)

for thin walled structures.

Use of adhesive in automotive structures is motivated

by improvement in stiffness and crash resistance of a

structure by improving the weakest link – the joint.

Comparative studies of adhesive bonded, spot welded and

weld bonded joints using numerical and FE analysis were

carried out by Chang et al (10). Their results show stresses

in weld-bonded joints are more evenly spread than those in

spot welded joints. Adhesive material simulation is in itself

a challenge as the elasto-plastic material models and its

application their balance between computation time and

accuracy. A detailed explanation of the different types of

adhesive modeling methods, material models in LS Dyna

and their application is provided by Feucht (11). Specific

application of BETAMATE 1496V adhesive using LS

Dyna was presented by Droste (12). Matzenmiller, et al.,

(13) conducted numerical investigation with various modes

of failure of the adhesive layer under pure and combined

loading in normal and shear directions, with the using

continuum and interface elements. Ongoing research in the

field of stress analysis of adhesive bonded joints was

presented by Castagnetti et al (14).

The study reported here is a continuation of research

and physical testing conducted by Fickes, et al (15).

2. DESIGN PARAMETERS

2.1 Section Geometry

To perform an analysis which depends on many

parameters it is important to select those parameters to be

varied and those to be fixed throughout the experiment. In

this study, the section was fixed. A hexagonal shape was

selected as it has sides of equal length; hence each side will

have the same plate buckling stress.

A regular hexagonal column was made of two sections

assembled by two methods; spot welding without adhesive

and spot weld with adhesive (weld-bond). Sides were of

length 66.7mm and flange of 17mm shown in Figure 1. An

adhesive layer thickness was maintained at 0.66mm

(Figure 2).

The length of the section was fixed to 400mm. Spot

welds were equally placed along the flange length and

symmetrically located about the center in X and Z

directions. The spot weld is assumed to be at the center of

the flange.

Figure 1: Section Geometry

Figure 2: Flange details

Figure 3: Column geometry

SW

SW/2

h=4

00

5

For simulation, all dimensions apart from material

thickness, 𝑡, and spot weld spacing, 𝑆𝑊, were kept

constant.

2.2 Material – Steel

In this study four steel grades IFHS140, HSLA350,

DP590 and DP980 were used to cover a range of high and

low strength steels.

IFHS is an interstitial-free, rephosphorized steel, heat-

treated and double-sided surface coated in a combined

annealing and galvanizing process during manufacturing

(5). The Interstitial free (IF) steels are stabilized with Ti,

Cb, or Cb + Ti, and are normally ultra low carbon (0.005%

max). While most IF steels are produced as drawing

quality, solid solution strengthening with P, Mn, and Si can

be utilized to produce a higher strength formable steel (16).

The high strength low alloy steels (HSLA) contain the

addition of the carbide forming elements Cb, V, or Ti

singularly or in combination to a low carbon steel,

providing strength through precipitation of fine carbides or

carbonitrides of Cb, Ti, and/or V (16).

The dual phase (DP), ultra high strength steels rely on

a microstructure of ferrite and Martensite to provide a

unique combination of low yield strength and high tensile

strength. This combination results in a high level of

formability in the initial material and high strength due to

work hardening in the finished part (16).

Figure 4 shows stress strain curves for all materials

over a range of strain rates.

2.3 Material – Adhesive

BETAMATE 1496V grade adhesive, developed by

DOW Automotive, was used as the adhesive for this study.

The material is a single component epoxy treated with a

special multi-phase rubber technology to support high load

bearing capacity and decelerate the failure mechanism,

specifically designed for structures in crash (12). Figure 5

shows the stress-strain curve for BETAMATE 1496V for

different strain rates.

3. NUMERICAL SIMULATION

3.1 Design Space

The objective of this study was to assess the impact of

adhesive on crash performance of a spot welded thin

walled hexagonal column. For this study, parameters

covering material, design geometry and adhesive were

selected as variables in a DOE matrix. Four steel grades

(IF140, HSLA350, DP590 & DP980), three thicknesses

(0.7mm, 1.5mm & 2.2mm), three spot-weld pitches

(20mm, 60mm & 100mm) and two adhesive conditions

(with and without adhesive) were taken as design

variables.

Figure 6 is a graphical representation of these

combinations and was repeated for the two adhesive

conditions. In total 72 simulation points were run for this

study , Figure 7.

Figure 4: Steel Stress-Strain Curves

0

200

400

600

800

1000

1200

1400

1600

0 0.2 0.4 0.6 0.8 1

Tru

e St

ress

[M

Pa]

True Strain [-]

DP980

DP590

HSLA350

IF140

Figure 5: Adhesive Stress-Strain Curve

0

50

100

150

200

250

300

0.00 0.20 0.40 0.60 0.80 1.00 1.20

Tru

e St

ress

[MPa

]

True Strain [-]

BETAMATE

High strain rate

Low strain rate

Medium strain rate

Figure 6: Single DOE matrix

Pitc

h [m

m]

6

3.2 Simulation Setup The simulation setup was modeled after a physical

impact test, where a vertical column is crushed with an

impact body of mass, 𝑀 ,with initial velocity, 𝑣0. The test

set-up replicates a drop silo test Figure 8.

It was decided to fix the impact velocity at 11.15m/s

and mass at 130kg. The impact parameters were taken

from the physical test by Fickes et al (15).

3.3 Finite Element Modeling The Finite Element model was created and edited

using LS Pre/Post, and explicit non-linear finite element

code LS-DYNA was used for analysis. The complete

geometry, including adhesive, was meshed using

Belytschko-Lin-Tsay (2) shell element. Belytschko-

Bindeman assumed strain co-rotational stiffness type

hourglass control with 0.1 hourglass coefficient. The

choice of shell element adhesive modeling is important. To

decide between adhesive mesh options and material

models, a side study was conducted. A summary of this

study is provided in Appendix B. Mesh size of 4mm was

used for the steel hexagonal column, with sides having an

aspect ratio of 1.722 and flange having an aspect ratio of 1.

The corner curvature was disregarded for this study to

reduce simulation time. For adhesive a mesh size of 2mm x

2mm was used to ensure resolution. The impact mass was

modeled as a rigid wall with mesh size of 12mm x 12mm.

The steel material was modeled using

*MAT24_PIECEWISE-LINEAR-ELASTIC and the

impact wall was modeled with *MAT20_RIGID, both of

which are commonly used for modeling sheet metal. The

choice of adhesive material model has varied in literature,

*MAT120_GURSON is widely used to model

BETAMATE. However, application of other material

models like Arup or Johnson-Cook has also been reported.

To confirm the applicability of Gurson to the specific

adhesive used, a side study was conducted where different

modeling methods were compared, (Appendix B). This

study supported the use of the Gurson model.

The hexagonal column was assembled by LS-DYNA

spot weld option along the centerline of the flange. The

spot welds were constrained to avoid spot weld failure.

The base of the column was fixed by constraining all

six degrees of freedom, while the top of the specimen was

kept free. The impact wall and specimen contact was

modeled using “automatic surface-to-surface contact” with

a 0.25 friction coefficient. Contact between two halves of

the specimen was accounted using “automatic single

surface contact” with a 0.25 friction coefficient. The

contact between adhesive and flange was modeled as “Tied

surface to surface with offset” again with 0.25 friction

coefficient.

3.4 Measured responses

Three critical responses were measured; maximum

force (𝐹𝑚𝑎𝑥), average force (𝐹𝑎𝑣𝑔) and maximum

displacement (𝛿𝑚). The force displacement curve, Figure

9, provides graphical representation of all three.

Figure 7: Complete design space

No Adhesive

With Adhesive

t

(mm)

SW (mm)

0.7

2.2

10020 60

1.5

HSLA 350DP 590

IHS140 DP 980

t

(mm)

SW (mm)

0.7

2.2

10020 60

1.5

HSLA 350DP 590

IHS140 DP 980

Figure 8: Test setup

ν0M

Figure 9: Force Displacement curve

Fmax

Favg

0 25 255 δm

Forc

e

Displacement (mm)

7

𝐹𝑚𝑎𝑥is an indicator of the peak load, 𝐹𝑎𝑣𝑔 provides

information about crush energy dissipation. The absorbed

energy 𝐸𝑎 is obtained by integrating kinetic energy and

potential energy over the deformation 𝛿𝑚 of the section.

From an energy balance, we have the two relationships:

𝐹𝑎𝑣𝑔 = 𝐸𝑎

𝛿𝑚 (1)

𝐸𝑎 = 1

2 𝑀𝑣0

2 + 𝑀𝑔𝛿𝑚 (2)

Equation 1 is used to compute 𝐹𝑎𝑣𝑔.

(The low thickness and low strength column collapse

completely i.e.; 𝛿𝑚 ≈ 400𝑚𝑚. As this bottoming out is

unrepresentative of crush in a vehicle, the force was

averaged over the first 255mm of crush for this case.)

4. RESULTS & OBSERVATIONS 4.1 Results

The DOE matrix for this study contains 72 simulation

runs. The complete set of force displacement graphs are

provided in Appendix C.

In this paper we concentrate on the lowest (IF140) and

the highest strength (DP980) materials. The results for

IF140 and DP980 are given in Table 1.

In general both 𝐹𝑚𝑎𝑥 & 𝐹𝑎𝑣𝑔 increase in weld-bonded

columns compared with weld alone. There are exceptions,

IF140 with 0.7mm thickness and 100mm spot weld pitch,

where the reverse is observed. The percentage

improvement of 𝐹𝑚𝑎𝑥 & 𝐹𝑎𝑣𝑔 given by

(𝐹𝑤𝑒𝑙𝑑−𝑏𝑜𝑛𝑑 − 𝐹𝑠𝑝𝑜𝑡−𝑤𝑒𝑙𝑑)

𝐹𝑠𝑝𝑜𝑡−𝑤𝑒𝑙𝑑

100%

The percentage increase is shown in Figures 10- 13.

Figure 10: IF140 spot-welded and weld-bonded

𝐹𝑚𝑎𝑥 percentage improvement trend for different spot weld

pitches.

-20

0

20

40

60

0.7*mm 1.5mm 2.2mm

Perc

enta

ge Im

prov

emen

t [%

]

0.7mm1.5mm2.2mm

80

100

20mm

60mm

100mm

t

SW

Figure 11: IF140 spot-welded and weld-bonded 𝐹𝑎𝑣𝑔

percentage improvement trend for different spot weld pitches.

-20

0

20

40

60

80

100

0.7* mm 1.5mm 2.2mm

20mm

60mm

100mm

Perc

enta

ge Im

prov

emen

t [%

]

Figure 12: DP980 spot-welded and weld-bonded

𝐹𝑚𝑎𝑥 percentage improvement trend for different spot weld

pitch.

Perc

enta

ge Im

prov

emen

t [%

]

20mm

60mm

100mm

DP890

-20

0

20

40

60

80

100

0.7*mm 1.5mm 2.2mm

SW

t

Figure 13: DP980 spot-welded and weld-bonded 𝐹𝑎𝑣𝑔

percentage improvement trend for different spot weld pitch.

* Average force based on 255mm of crush.

20mm

60mm

100mm

0.7* mm 1.5mm 2.2mmPerc

enta

ge Im

prov

emen

t [%

]

-20

0

20

40

60

80

100

SW

t

𝐹𝑚𝑎𝑥 IF140 𝐹𝑎𝑣𝑔 IF140

𝐹𝑚𝑎𝑥 DP980

𝐹𝑎𝑣𝑔 DP980

8

The results are interesting because it challenges some

of the pre-conceived ideas associated with the use of

adhesives in columns. The use of adhesive is thought to be

most beneficial at low thicknesses and large spot weld

pitches. Also the adhesives are thought to have little effect

on the crush performance at high thicknesses. The results

show that these are not true in all cases. In an attempt to

understand these discrepancies, a qualitative analysis was

also done.

4.2 Qualitative Analysis In this section 𝐹𝑚𝑎𝑥 & 𝐹𝑎𝑣𝑔 results for IF140 and

DP980 are explained and then some of the inconsistent

results are analyzed. Four cases were analyzed;

1) IF140

- High thickness- low strength

- Low thickness- low strength

2) DP980:

- High thickness-high strength

- Low thickness-high strength

Case 1: IF140 Looking at the percentage improvement in 𝐹𝑚𝑎𝑥for

IF140 material, Figure 10, at different thicknesses and spot

weld spacing, the trend agrees with the idea that most

benefit of adhesive would be seen at low thickness.

However, one would expect the benefit would be higher at

higher spot weld pitch. This is not observed for IF140

material.

In case of 𝐹𝑎𝑣𝑔 ,Figure 11 , the percentage

improvement trend is almost reverse of that seen in 𝐹𝑚𝑎𝑥.

For 100mm of spot weld spacing the improvement due to

weld-bonding is in fact very slightly negative. The opposite

is seen with the same spot-weld spacing and higher

thickness where the improvement is high.

High Thickness – Low strength

IF140 material column with 2.2mm thickness

represents high thickness & low strength simulation point.

Figure 14 shows the column at 0.002s at the point of

maximum load. Inter-weld flange separation, due to flange

buckling is seen in the no adhesive case. This out of plane

Table 1: IF140 & DP590 Results

MAT t SW Fmax Favg Dmax Ea

mm mm N*105 N*104 mm J*104

IF1

40

Wel

ded

0.7 20 1.06 2.53 357.59 9.04

0.7 60 1.06 2.53 356.50 9.03

0.7 100 1.06 2.53 357.79 9.04

1.5 20 2.54 8.09 107.47 8.69

1.5 60 2.54 7.43 117.16 8.71

1.5 100 2.55 8.02 108.46 8.70

2.2 20 3.91 15.4 56.02 8.62

2.2 60 3.90 15.2 56.74 8.63

2.2 100 3.91 12.8 67.32 8.64

IF1

40

Wel

d-b

on

ded

0.7 20 1.31 3.11 287.07 8.94

0.7 60 1.26 2.84 316.68 8.98

0.7 100 1.26 2.50 361.07 9.04

1.5 20 2.71 9.97 86.89 8.67

1.5 60 2.76 9.63 90.07 8.67

1.5 100 2.76 9.82 88.25 8.67

2.2 20 4.14 20.7 41.75 8.65

2.2 60 4.14 21.5 40.31 8.65

2.2 100 4.14 21.5 40.16 8.65

DP

98

0 W

eld

ed

0.7 20 1.89 4.46 197.75 8.82

0.7 60 1.85 4.21 210.05 8.83

0.7 100 1.80 4.33 204.00 8.83

1.5 20 5.39 17.6 48.90 8.61

1.5 60 5.37 17.4 49.46 8.62

1.5 100 5.38 15.7 54.89 8.62

2.2 20 8.62 37.6 22.85 8.58

2.2 60 8.39 36.9 23.22 8.58

2.2 100 9.08 43.6 19.66 8.57

DP

98

0 W

eld

-bo

nd

ed

0.7 20 1.68 5.57 158.34 8.82

0.7 60 1.82 5.62 155.94 8.76

0.7 100 2.91 5.58 156.98 8.76

1.5 20 6.24 21.5 39.94 8.60

1.5 60 6.50 28.7 30.00 8.60

1.5 100 6.50 21.4 40.15 8.60

2.2 20 9.79 47.3 18.12 8.57

2.2 60 9.79 47.7 17.97 8.57

2.2 100 9.79 47.7 17.95 8.57

Figure 14: IF140 deformation spot-welded and weld-

bonded: t=2.2mm, SW=100mm, time=0.002s

Inter-weld flange separation

No Adhesive

With Adhesive

9

flange deformation now becomes a trigger for column

collapse. Note that the wavelength of deformation is equal

to the spot weld spacing.

Weld-bonded flange eliminates the inter-weld flange

separation, right side of Figure 14. However, plate

buckling is seen for the flange of double thickness, at the

top and bottom of the column. Low improvement in 𝐹𝑚𝑎𝑥

is explained by this flange buckling.

Figure 15 shows deformation of the same IF140

column at time 0.01s. This time is well into the energy

absorbing phase of the crush. For the no adhesive case, the

initial trigger due to inter-weld buckling described above

causes a large deformation failure at the bottom of the

column. The effect of such inter-weld buckling is to reduce

the load capacity as is seen in the force displacement curve

in Figure 16.

Using adhesive bonding in addition to spot welding,

inter-weld separation is avoided. The load for this case of

shows a secondary peak, Figure 16, which increases

average crush load.

The lack of inter-weld buckling failure mode with

adhesive explains the higher percentage improvement of

𝐹𝑎𝑣𝑔 in high thickness-low strength column.

Low thickness – Low strength

IF140 material column with 0.7mm thickness

represents low thickness & low strength simulation point.

Figure 17 shows the column at maximum crush force.

This condition shows similar inter weld separation to that

of high thickness-low strength column, Figure 14, for no

adhesive case. Difference is seen in the wavelength of the

flange buckling mode. In this case the wavelength is less

than the spot weld spacing (𝜆 < 𝑆𝑊).

Figure 18 shows the columns at a time during the


bonded: t=2.2mm, SW=100mm, time= 0.01s

No Adhesive With Adhesive

Fro

nt V

iew

Sid

e V

iew

Figure 16: Force Displacement graph: IF140 t=2.2mm,

SW=100mm

0

50,000

100,000

150,000

200,000

250,000

300,000

350,000

400,000

450,000

0 0.02 0.04 0.06 0.08

t=0.010s

Deformation (m)

Forc

e (N

)

no adhesive

with adhesive

t=0.0025s


bonded: t=0.7mm, SW=100mm, time=0.002s


Figure 18: IF140 deformation with and without adhesive:

t=0.7mm, SW=100mm, time= 0.016s


Fro

nt

Vie

wSi

de

Vie

w

Buckling

10

energy absorption phase of crush. For the with adhesive

case the bucklling mechanism is different from the thick

walled case. As the load increases the flange buckles by

folding about the constrained edge, Figure 19. After the

folding, the moment of inertia of the flange is reduced

which leads to global column failure Figure 20.

Figure 19: Flange folding mechanism

In the weld-bonded case the load is supported by the

flange, which is indicated by the high stress regions shown

as red, dark shaded, in Figure 18. The flange buckle

initiates deformation and the column tilts to one side ,

Figure 20. The global deformation explains the negative

improvement in 𝐹𝑎𝑣𝑔 for low strength-low thickness steel,

Figure 21.

Case 2: DP980

For DP980, the percentage improvement in 𝐹𝑚𝑎𝑥 is

positive for the thicker sections, Figure 12. For low

thicknesses, there is a negative to zero improvement in the

values.

Percentage improvement in 𝐹𝑎𝑣𝑔for DP980 is, in most

cases, around 20%, Figure 13. The exceptions are in

1.5mm and 2.2mm thicknesses, where the values are large

and small respectively. The almost constant improvement

is counter intuitive since one would expect differences due

to thickness and spot weld spacing.

High thickness – High strength

DP980 steel column with 2.2mm thickness represents

high thickness & high strength condition.

Figure 22 shows the column at the time of peak load.

The inter-weld separation is significantly less than the high

thickness low strength case. In the adhesive bonded

column the inter-weld separation is eliminated.

Figure 23 shows the column at a time near maximum

crush. The impact energy in this case is not sufficient to

Ivv

v

v

v

vIvv

v

v

Figure 21: Force Displacement graph: IF140 t=0.7mm,

SW=100mm

t=0.016s

0

20,000

40,000

60,000

80,000

100,000

120,000

140,000

0.00 0.10 0.20 0.30 0.40Deformation (m)

Forc

e (N

)

no adhesivewith adhesive

t=0.002s

t=0.034s

Figure 20: IF140 deformation with and without adhesive:

t=0.7mm, SW=100mm, time= 0.034s


Figure 22: DP980 deformation with and without

adhesive: t=2.2mm, SW=100mm, time=0.002s


Corner crippling




11

cause considerable crush. Therefore the average force is

determined by corner crippling. Since, corners take the

entire load, the difference between spot-weld and weld-

bonded case is small as seen from the force displacement

curve in Figure 24.

Low thickness – High strength

DP980 with 0.7m thickness represents the low

thickness - high strength condition. Figure 25 shows the

column at the time of peak load. The buckling and failure

is similar to the low thickness – low strength condition,

where the inter-weld flange separation is large. In this case

the inter-weld flange separation does not initiate the

column buckling. The column load is taken by the corners,

as seen in Figure 25.

As the load increases the collapse behavior of the

column is similar to that reported for low thickness low

strength condition, where the flange undergoes an in-plane

buckling. Again this results in asymmetric buckling of the

adhesive bonded flange, Figure 26.

Observation of these four conditions shows different

buckling modes are possible due to the different

parameters. The cases described in this section provide

four different failure mechanisms.

a) Failure due to inter-weld flange separation

b) Failure due to flange folding and buckling

c) Failure due to corner crippling

d) Failure due to in-plane buckling and asymmetric

flange buckling.

These failure modes may not be unique to a given

combination of parameters. However, it does indicate that

use of adhesive may not improve average crush force

significantly in all cases.

4.3 Crush Sequence

To understand the energy absorption of a thin walled

column consider the crush sequence, Figure 28. A thin

walled column undergoes four basic physical events prior

to peak loading:

Figure 24: DP980 Force Displacement comparison:

t=2.2mm, SW=100mm

t=0.004s

0

200,000

400,000

600,000

800,000

1,000,000

0 0.005 0.010 0.015 0.020 0.025

Forc

e (N

)

Deformation (m)

no adhesive with adhesive

t=0.001s

Figure 25:DP980 deformation with and without



Flange buckling

Flange inter-weld separation

Corner crippling




Fro

nt

Vie

wSi

de

Vie

w

Buckling

Figure 27: Force Displacement graph: DP980 t=0.7mm,

SW=100mm

0

50,000

100,000

150,000

200,000

250,000

300,000

0.00 0.05 0.10 0.15 0.20

Forc

e (N

)

Deformation (m)

t=0.015s

no adhesive

with adhesive

t=0.001s

12

1) As loading increase, across the section there will

be a uniform distribution of stress.

2) When stresses generated increases beyond critical

stress, plate members buckle.

3) Post buckling redistribution of stress to the

corners.

4) Corner failure due to crippling (peak load)

In thick walled sections events 2 and 3 are bypassed

and the section directly goes to corner crippling.

The collapse of a column, beyond the peak load, is

also a series of events which depend on material, thickness,

flange, plate and corner buckling. Figure 29 shows some of

the various buckling modes that can occur in the post peak

load region.

Beam buckling is usually seen when the column is

extremely slender causing a global Euler buckling. These

forms of buckling were seen when there is a trigger, like a

flange which has folded inwards, Figure 19. All these

buckling modes depend on the relative slenderness of the

plate and the relation to yield stress.

5. ANALYSIS

5.1 Critical slenderness ratio

To investigate these buckling modes the hexagonal

section can be separated into discrete plates with boundary

conditions as shown in Figure 30. Here SS designates

simply supported condition and FR designates a free

boundary condition. The side of the hexagonal column can

be represented by a plate with all edgeds simply supported.

The flange can be represented by thin plate with three

edges simply supported and one edge free. By analyzing

the individual buckling characteristics of plates, one can

understand the behavior of the whole column.

A useful parameter in analyzing buckling behavior is

slenderness ratio β.

The slenderness ratio is defined as (17):

𝛽 =𝑏

𝑡√

𝜎𝑦

𝐸 (3)

The above equation can be manipulated to provide a

relationship between the buckling stress of the plates and

the material yield stress.

Squaring equation (3) and multiplying both sides by

12(1−𝜇2)

𝐾𝜋2 we get;

12(1 − 𝜇2)𝛽2

𝐾𝜋2=

𝜎𝑦

𝐾𝐸𝜋2

12(1 − 𝜇2) (𝑏𝑡)

2

(4)

Figure 28: Crush sequence

F

Δ

0mm ~

25m

m

>10

0mm

peak Oscillating about an

average value

Axial deformation

Axial force

Thick walled section

Thin walled section

Crush Sequence

Uniform stress across section

Buckling of section plates

Crippling failures of corners

Re-distribution of loads to corners

Progressive folding

of section

Figure 29: Various stability modes for a thin walled

column

Flange

buckling

Corner

buckling

Side wall

buckling

Interweld Flange

buckling

Beam

buckling

Figure 30: Exploded view of hexagonal section

showing discrete plate and boundary conditions

ssss

ssFR

ssFR

ss ss

ss

ssFR

Spot Welded Weld Bonded

Side wall Plate

FlangePlate

13

The denominator for RHS is the same as 𝜎𝑐𝑟 plate. So

the expression becomes:

12(1 − 𝜇2)𝛽2

𝐾𝜋2=

𝜎𝑦

𝜎𝑐𝑟 (5)

Substituting values for constants and rearranging we

can get a relationship between slenderness ratio, yield

stress and buckling stress for flange and sides of the

hexagonal column.

For flange:

𝐾 = 0.425

𝜎𝑐𝑟−𝑓 =𝜎𝑦

2.06𝛽𝑓2 (6)

∴ 𝜎𝑐𝑟−𝑓 = 𝜎𝑦 ∶ ∀ 𝛽𝑓 = 0.69

𝜎𝑐𝑟−𝑓 > 𝜎𝑦 ∶ ∀ 𝛽𝑓 < 0.69

𝜎𝑐𝑟−𝑓 < 𝜎𝑦 ∶ ∀ 𝛽𝑓 > 0.69

For plate:

𝐾 = 4

𝜎𝑐𝑟−𝑝 =𝜎𝑦

0.27𝛽𝑝2 (7)

∴ 𝜎𝑐𝑟−𝑓 = 𝜎𝑦 ∶ ∀ 𝛽𝑝 = 1.92

𝜎𝑐𝑟−𝑓 > 𝜎𝑦 ∶ ∀ 𝛽𝑝 < 1.92

𝜎𝑐𝑟−𝑓 < 𝜎𝑦 ∶ ∀ 𝛽𝑝 > 1.92

The critical slenderness ratios for the flange and side

plate are 0.619 and 1.92 respectively. The critical

slenderness ratio gives over indication of susceptibility of

the member to buckling. If, β, is greater than the critical

value then 𝜎𝑐𝑟 < 𝜎𝑦, and the member will buckle before

yielding. For 𝜎𝑐𝑟 > 𝜎𝑦, the member will to yielding

before buckling.

Figure 31 shows the variation of ( 𝜎𝑐𝑟/𝜎𝑦) with

respect to, β, for a) Side plate, b) Flange without adhesive

and c) Flange with adhesive. The two vertical dividing

lines represent the critical, β, value for flange and side

plate. To maintain the integrity of the model and have

consistency in design the spot weld is assumed not to fail.

In the case of a weld-bonded flange the adhesive is

assumed to join the flange without in-plane shear.

Therefore, the thickness of adhesively bonded flange is

taken as 𝑡𝑓𝑎 = (2𝑡 +𝑡𝑎

2) ≈ 𝑡 .

The area shaded in the figure represents the case in

which buckling critical stress is below yield stress. It is

also seen that in all cases, the flange has a higher

( 𝜎𝑐𝑟/𝜎𝑦) ratio than side plates, which indicates that

initial buckling is due to the plate buckling and not flange

buckling for this specific set of parameters. For low

thickness and high yield strength, β is not large for flange

or side wall plates, which means that neither flange nor

walls will be able to take on the load. This explains the

poor improvement due to weld bonding in low thickness

cases for DP980.

5.2 𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝑙𝑜𝑎𝑑 calculation & result

𝐹𝑚𝑎𝑥 is defined as the maximum load carrying

capacity of the plate and flange. One method to calculate

𝐹𝑚𝑎𝑥 is with the effective width concept (18). The failure

load is given by yield of the effective section.

∴ 𝐹𝑚𝑎𝑥 ≈ 𝐹𝑒𝑓𝑓 (8)

Effective width is given by the relation (several alternative

formulations are found in the literature):

𝑏𝑒 =1

2(1 +

𝜎𝑐𝑟

𝜎𝑦) 𝑏 (9)

∴ The load carried by this effective width for each plate is:

𝐹𝑒𝑓𝑓 = σybet (10)

The effective width of a simply supported plate

concept can be used to predict the maximum load carried

by the hexagonal section by calculating & adding up the

effective load of the side walls and the flange i.e;

For spot welded section:

𝐹𝑒𝑓𝑓 = σy ((6 be−pt) + (4 be−ft)) (11)

For weld bonded section:

Figure 31: Variation of ( 𝜎𝑐𝑟/𝜎𝑦) with respect to β for side

plate and flange (with and without adhesive) for DP980

0

1

2

3

4

5

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

σcr

/σy

ᵝ

Side Plate - DP980

Flange: No adhesive - DP980

Flange: With adhesive - DP980

0.62 1.92

Flan

ge(w

eld

ed &

sp

ot

wel

ded

)

Sid

e P

late

14

𝐹𝑒𝑓𝑓 = σy ((6 be−pt) + (4 be−f 𝑡𝑓𝑎)) (12)

The calculations may be done using the AISI CARS

software (16). Figure 32 shows this calculated value. The β

value is that of the side wall.

It is seen that for a particular material, maximum load

always decreases with increase in slenderness ratio. For the

same thickness, the maximum load carried always

increases with increase in slenderness ratio. The interesting

result is in the rate of increase of 𝐹𝑒𝑓𝑓 with respect to

different thicknesses. The trend lines for different

thicknesses fan out as the slenderness ratio increases with

Figure 32: Carpet plot of theoretical 𝐹𝑒𝑓𝑓 against 𝛽𝑝 for different material yield and thicknesses (with and without adhesive)

0.0E+00

2.0E+05

4.0E+05

6.0E+05

8.0E+05

1.0E+06

1.2E+06

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

Feff

[N

]

ᵝp

IF140 X HSLA350 X DP590 X DP980 X IF140 A HSLA350 A DP590 A DP980 A

DP590

HSLA350

IF140

1.5mm

0.7mm

σcr-p>σy σcr-p<σy

----- : With adhesive ___ : No adhesive----- : With adhesive ___ : No adhesive----- : With adhesive ___ : No adhesive

DP980

2.2mm

Figure 33: Carpet plot of simulation 𝐹max against 𝛽𝑝 for different material yield and thicknesses (with and without adhesive)

0.00E+00

2.00E+05

4.00E+05

6.00E+05

8.00E+05

1.00E+06

1.20E+06

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

Fmax

[N]

ᵝ p


----- : With adhesive ___ : No adhesive

DP980

HSLA350

IF140

2.2mm

1.5mm

0.7mm


15

0.7mm thickness having the lowest slope and 2.2mm with

the highest slope. The fanning out means that a relative

increase in 𝐹𝑒𝑓𝑓 is significantly higher as steel thickness

increase.

The plot of 𝐹𝑒𝑓𝑓 for weld-bonded column is seen as an

offset of that the spot-welded column. For the same

thickness the difference in 𝐹𝑒𝑓𝑓 with increasing β starts out

small but increases with increasing material yield strength.

Figure 33 shows the carpet plot of FEA results for

𝐹𝑚𝑎𝑥 against 𝛽𝑝for different material yield and thicknesses.

Similar trends are seen with the calculated 𝐹𝑒𝑓𝑓 are seen.

5.3 Average crush force result

Figure 34 shows the carpet plot of 𝐹𝑎𝑣𝑔 against 𝛽𝑝 for

different material yield and thicknesses. From the result

and analysis we see that Fmax& Favg do show similar

trends with theory. It may be possible to explain the crush

mechanism of a column using 𝛽 and ( 𝜎𝑐𝑟/𝜎𝑦) ratio.

6. A QUALITATIVE MODEL FOR CRUSH BEHAVIOR

The load-deformation curve may be viewed as a series

of peaks and valleys, Figure 35.

Each peak in the curve occurs at an incipient stability

event—some portion of the section is about to buckle. The

stability event results in diminished load as deformation

increases. The load continues to diminish until there is a

bottoming out in the column geometry and a new axial

load path is formed. With the new load path, the load again

increases until the next peak is found. In this way the load

oscillates between peaks and valleys. It is desirable that

this oscillation occur at a high average level as this will

result in higher energy absorbed during the crush process.

The average force level is largely determined by the

geometry resulting after the stability event: if the geometry

promotes continuing axial deformation, the force will be

high; if the geometry promotes an overall bending

deformation, the force will be low.

Figure 35: Stability Event model for axial crush of thin

walled column

Flange

buckling 1

Corner

buckling,

crippling

Side wall

buckling

Interweld

Flange

buckling 1

Beam

buckling

Uniform

elastic

stress

Flange

buckling 2

Interweld

Flange

buckling 2

1

23 4

5Stability events

Figure 34: Carpet plot of simulation 𝐹avg against 𝛽𝑝 for different material yield and thicknesses (with and without adhesive)

0.00E+00

5.00E+04

1.00E+05

1.50E+05

2.00E+05

2.50E+05

3.00E+05

3.50E+05

4.00E+05

4.50E+05

5.00E+05

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

Favg

[N]

ᵝp


----- : With adhesive ___ : No adhesive

DP980

HSLA350

IF140

2.2mm

1.5mm

0.7mm


DP590

16

At each stability event, there are a multitude of

possible buckling modes, Figure 35 bottom. The mode

realized will be the one having the lowest bifurcation load.

Once realized, the particular mode will then set the

geometry for the following column deformation. Thus a

desirable buckling mode will have both a high bifurcation

load and also set a desirable geometry for the following

deformation. For example, Figure 19 described the flange

buckling mode realized for the low strength-low stiffness

column. Although occurring at a high bifurcation load, it

set up undesirable column geometry for the next event

(Euler buckling of the column).

Viewed in this way, the most desirable path through

this tree is a path which oscillates between corner crippling

setting the geometry for an accordion type folding, Figure

35. This occurs for sections with a relatively low

slenderness ratio, , i.e. thicker sections.

For sections with a high slenderness ratio, thin

sections, the potential number of stability modes (modal

density) is very high. This increases the opportunity for a

buckling event to limit the peak force.

This model offers an explanation of why the addition

of adhesive does not provide a greater percentage increase

in average crush force for very thin sections (0.7 mm in

this study). With many more potential buckling modes in

this high slender case, even though presence of adhesive

may increase the critical load for some modes, there exist

so many other possible paths that little improvement is

seen.

7. CONCLUSION

This paper has studied the influence of design,

material and adhesive influence on crush performance of a

thin-walled column. The results show that:

Presence of adhesive (weld-bond) can increase

average crush force by 20% over the no adhesive case.

However, smaller increases are observed in some

cases.

Spot weld pitch does not have a strong, consistent

influence on mean crush force improvement with

adhesive.

Plate slenderness is an important indicator for peak

and mean crush force. The benefit of adhesive bonding

is greater for less slender plates.

An adhesive bonded flange can precipitate an unstable

crush mode particularly for sections with slender

plates

For the fixed energy level used in this DOE, the mean

crush force for the thicker and higher strength

conditions was dominated by corner crippling

behavior.

8. FUTURE WORK

In this paper, we have fixed levels for all parameters

other than those under study—material strength, thickness,

weld pitch, and adhesive presence. In automotive

applications of energy absorbing structure, there are

several uncontrollable parameters which will also affect

crush behavior—flange out-of-plane imperfections,

irregular spot weld spacing, offset loading, varying section

shape along beam length, etc.

It is very possible that the presence of adhesive will

enhance the crush performance robustness in the presence

of these uncontrollable noise factors. There are existing

techniques, for example Taguchi methods, to assess this

robustness problem and it is recommended that this be

done.

ACKNOWLEDGMENTS

The author would like to acknowledge the American

Iron & Steel Institute (AISI) and Auto-Steel Partnership

(AS-P) for sponsoring this study. The author is indebted to

Mr. J.D. Fickes (GM) for the base study data and FEA

model, and would also like to thank members of Weld

Bond Project Team (ASP070) especially Mr. M. Bzdok

(AS-P), Mr. J. Hill (Ford), Mr. D Biernat (Chrysler), Mr M.

Mirdamadi (Dow) for their valuable inputs and discussion

throughout the project.

REFERENCES

1. Gerth, Richard and Brueckner, Sven A. The Digital

Body Development. Ann Arbor : Center for Automotive

Reseach.

2. Hallquist J.O.,. LS DYNA Theoretical Maual. s.l. :

Livemore Software Technology Corp, May 1998.

3. LSTC. LS Dyna Keywork User Manual . s.l. : Livemore

Software Technology Corp, July 2006.

4. White M.D, Jones N. Experimental quasi-static axial

crushing of top-hat and double-hat thin walled sections.

s.l. : International Journal of Mechanical Science, 1999.

5. F Schneider, N Jones. Impact of thin-walled high-

strength steel structual sections. s.l. : Institute of

Mechanical Engineers, 2004.

6. F Schneider, F Jones. Inflence of spot-weld failure on

crushing of thin walled strucutal sections. s.l. : Internatioal

Journal of Mechanical Sciences, 2003. 2061-2081.

7. V. Tarigopula, M Langseth, O S Hopperstad, A H Clausen. Axial Crushing of thin-walled high strength steel

sections. s.l. : International Journal of Impact Engineering,

2006. 847-882.

8. B Yan, C Kantner, H Zhu, G Nandkarni. Evaluation

of Crush Performance of A Hat section component using

dual phase and martensitic steel. s.l. : SAE International,

2005. 2005-01-0837.

17

9. E Rusinski, A Kopczynski, J Czmochowski. Test of

thin-walled beams joined by spot welding. s.l. : Journal of

Materail Processing Technology, 2004. 405-409.

10. B Chang, Y Shi, S Dong. Comparative studies on

stresses in weld-bonded, spot-welded and adhesive-bonded

joints. s.l. : Journal of Material Processing Technology,

1999. 230-236.

11. Feucht M., Haufe A., Pietsch G. Modeling of

Adhesive Bonding in Crash Simulation. s.l. : LS Dyna

Anwenderforum, Keynote, DYNAmore , 2007.

12. A, Droste. Crash Stalble Adhesive in Application and

Simulation. s.l. : LS Dyna Anwenderforum, DYNAmore

GmbH, 2006.

13. Matzenmiller A, Gerlach S, Fiolka M. Progressive

Failure Analysis of Adhesivley Bonded Joints in Crash

Simulations. s.l. : LS-DYNA Anvenderforum, DYNAmore,

GmbH, 2006.

14. Castagnetti D., Dragoni E. Standard finite element

techniques for efficient stress analysis of adhesive joints.

s.l. : International Journal of Adhesion & Adhesives,

Elsevier Ltd, 2008.

15. Fickes J, Schroeder J, Nandkarni G, Agarwal R. AHSS Weld Bond energy management: Drop tower

investigation - Presentation. Detroit : AISI Great Designs

in Steel, 2007.

16. AISI. Automotive Steel Design Manual . s.l. : American

Iron and Steel Institute - Auto Steel Partnership, June 2004.

17. Mateus A.F, Witz J.A. A parametric study of the post-

buckling behavious of steel plates. s.l. : Elsevier Science

Ltd - Journal of Engineering Structures , 2001. 23, P172-

185.

18. Malen D, Kikuchi N. Fundamentals of Auto body

strucutres. s.l. : Course pack ME513, 2007.

APPENDIX A: MODEL CALIBRATION

The calibration of the FEA was done by comparing the

maximum deformation to that of the physical test

conducted by Fickes et al (15).

In their experiment a mass of 276.5kg and impact

velocity of 10.7m/s was used on a hexagonal section of

thickness 1.5mm, spot-weld pitch of 60mm and HSLA350

steel material. Figure 36 shows the results of their

experiment and Figure 37 shows the force displacement

graph obtained by simulation. The maximum crush

distance result was almost same (184mm for physical test

v/s 183.33mm for simulation).

Figure 36: Physical test results. Courtesy: J.Fickes

Figure 37: Simulation force displacement graph

APPENDIX B: ADHESIVE MODEL SELECTION

Two modeling methods and five adhesive models were

benchmarked with a physical test conducted by Fickes, et

al., (15). The adhesive can be modeled as a shell element,

where the adhesive is represented as a surface with shell

elements of uniform thickness used to mesh the surface,

Figure 38. Using a shell model the computation time can

be reduced.

Another modeling method is to model the adhesive

layer as a solid with brick elements used to mesh the layer.

This method will be computationally intensive as number

of nodes increases.

The five material models were built in LS DYNA and

compared, Figure 39. Material models can be classified as

continuum models, Cohesive models and tie-break models.

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0 50 100 150 200

Change in length (mm)

Forc

e [1

06N

] Crush Distance = 183.337 mm

18

In a continuum models the adhesive layer is constructed

with finite brick of material with the physical properties of

adhesive. In cohesive modeling the adhesive element is

modeled using four spring elements; two for tension,

compression and two for shear.

Figure 40 shows the resulting force displacement plots

comparing the various modeling methods and material

models.

From the simulations, it was clear that Gurson Shell

model was the closest to the physical test maximum

deformation. Hence it was decided to use Gurson shell

model for this DOE.

The spot weld tensile loads were compared for all the

adhesive models. Figure 41 shows the tensile load on each

spot-weld in the column during the entire crush. Here also

the Gurson model showed better adhesive capabilities of

reducing spot weld tension below 2kN. This level is the

maximum load that a spot weld can withstand before

failure for this material thickness.

Figure 41: Adhesive comparison using spot-weld failure as a response; Material = HSLA350, Thickness = 1.5mm, Spot

weld pitch = 60mm

Reference – no adh

Arup

Johnson

Gurson

-202468

0 0.01 0.02 0.03 0.04 0.05 0.06

A

B

C

D

E

F

G

Figure 40: Force displacement plot for various adhesive models

- Gurson – Fickes Data Shell element

- Gurson – DOW Data Shell element- Gurson – DOW Data Solid element

- Johnson – Fickes Data Solid element

- Arup – Fickes Data Solid element

Fo

rce

[N] (E

+6

)

Physical testing Dmax = 147 mmDisplacement [mm]

Material = HSLA350

Thickness = 1.5mm

Spot weld pitch = 60mm

Figure 38: Adhesive modeling methods

Figure 39: Adhesive material models

Solid Model

Metal Mid Plane

Metal Mid Plane

Adhesive Mid Plane

Shell ModelPhysical section

Cohesive model

Continuum model

Tie Break

Contact

1. Arup solid model2. Johnson-Cook solid

model

1. Gurson shell model2. Gurson solid model

Spot

wel

d a

xia

l fo

rce

(KN

)

Time (s)

19

APPENDIX C: FORCE DISPLACEMENT GRAPHS 1. IF140: Spot Welded

Fma

xFa

tota

lD

ma

x

10

.62

.53

35

7.5

9

Fma

xFa

tota

lD

ma

x1

0.6

2.5

33

56

.5Fm

ax

Fato

tal

Dm

ax

10

.62

.53

35

7.7

Fma

xFa

tota

lD

ma

x2

5.4

8.0

91

07

.4Fm

ax

Fato

talD

ma

x2

5.4

7.4

31

17

.1

Fma

xFa

tota

lD

ma

x2

5.5

8.0

21

08

.4

Fma

xFa

tota

lD

ma

x3

9.1

15

.45

6.0

1Fm

ax

Fato

talD

ma

x3

9.0

15

.25

6.7

4

Fma

xFa

tota

lD

ma

x3

9.1

12

.86

7.3

1

SW

= 2

0m

m60m

m100m

m

0.7mm 1.5mm t = 2.2mm

All

forc

es in x

10

4N

20

2. IF140: Weld Bonded

Fma

xFa

vgD

max

13

.15

3.1

128

7.07

Fmax

Favg

Dm

ax12

.62

.84

316.

67Fm

axFa

vgD

ma

x12

.62.

503

61

.07

Fma

xFa

vgD

max

27

.19.

9786

.88

Fmax

Favg

Dm

ax

27.6

9.6

39

0.0

7

Fma

xFa

vgD

max

27

.69.

8288

.24

Fmax

Favg

Dm

ax

41.4

20.7

41

.74

Fmax

Favg

Dm

ax

41.4

21

.54

0.3

1

Fma

xFa

vgD

max

41

.421

.540

.15

20m

m60m

m100m

m

0.7mm 1.5mm 2.2mm

All

forc

es in x

10

4N

21

3. HSLA30: Spot-Weld

Fm

ax

Fa

vgD

ma

x

1.4

6E

+0

52

.72

E+0

43

30

.62

Fmax

Favg

Dm

ax

1.4

5E+

05

2.6

9E

+0

43

35

.19

Fm

ax

Fa

vgD

ma

x

1.4

5E

+0

52

.74

E+0

43

28

.09

Fm

ax

Fa

vgD

ma

x

3.2

3E

+0

51

.00

E+0

58

6.5

1

Fm

ax

Fa

vgD

ma

x

3.2

3E

+05

9.8

2E

+0

48

8.3

0

Fm

ax

Fa

vgD

ma

x

3.2

7E

+0

51

.10

E+0

57

8.7

8

Fm

ax

Fa

vgD

ma

x

4.9

5E

+05

2.1

6E

+05

39

.90

Fmax

Favg

Dm

ax

4.9

5E+

05

2.1

1E

+0

54

0.6

9

Fm

ax

Fa

vgD

ma

x

4.9

6E

+0

51

.97

E+0

54

3.6

7

20

mm

60

mm

10

0m

m

0.7mm 1.5mm 2.2mm

22

4. HSLA30: Weld-Bonded

Fm

ax

Fa

vgD

ma

x

1.5

6E

+0

53

.35

E+

04

26

6.3

5

Fm

ax

Fa

vgD

ma

x

1.5

6E

+0

52

.84

E+

04

31

6.4

5

Fm

ax

Fa

vgD

ma

x

1.5

5E

+0

52

.71

E+

04

33

1.6

7

Fm

ax

Fa

vgD

ma

x

3.4

0E

+0

51

.26

E+

05

68

.45

Fm

ax

Fa

vgD

ma

x

3.3

8E

+0

51

.26

E+

05

68

.58

Fm

ax

Fa

vgD

ma

x

3.3

8E

+0

51

.25

E+

05

69

.38

Fm

ax

Fa

vgD

ma

x

4.9

7E

+0

52

.85

E+

05

30

.22

Fm

ax

Fa

vgD

ma

x

4.9

8E

+0

52

.88

E+

05

29

.85

Fm

ax

Fa

vgD

ma

x

4.9

8E

+0

52

.90

E+

05

29

.59

20

mm

60

mm

10

0m

m

0.7mm 1.5mm 2.2mm

23

5. DP590: Spot- Weld

Fm

ax

Fa

vgD

ma

x

2.8

0E

+0

53

.52

E+0

42

52

.53

Fmax

Favg

Dm

ax

2.8

0E+

05

2.9

5E

+0

43

03

.64

Fm

ax

Fa

vgD

ma

x

2.7

7E

+0

52

.87

E+0

43

12

.79

Fm

ax

Fa

vgD

ma

x

7.1

8E

+0

51

.59

E+0

55

4.2

1

Fm

ax

Fa

vgD

ma

x

7.1

2E

+05

1.5

2E

+0

55

6.6

8

Fm

ax

Fa

vgD

ma

x

7.0

7E

+0

51

.52

E+0

55

6.9

0

Fm

ax

Fa

vgD

ma

x

1.0

4E

+06

3.6

5E

+05

23

.52

Fmax

Favg

Dm

ax

1.0

3E+

06

3.5

4E

+0

52

4.2

2

Fm

ax

Fa

vgD

ma

x

1.0

3E

+0

63

.55

E+0

52

4.1

7

20

mm

60

mm

10

0m

m

0.7mm 1.5mm 2.2mm

24

6. DP590: Weld-Bonded

Fm

ax

Fa

vgD

ma

x

2.6

8E

+0

53

.78

E+

04

23

4.4

7

Fm

ax

Fa

vgD

ma

x

2.8

8E

+0

54

.31

E+

04

20

4.9

5

Fm

ax

Fa

vgD

ma

x

2.9

1E

+0

55

.62

E+

04

15

6.9

8

Fm

ax

Fa

vgD

ma

x

7.1

2E

+0

51

.77

E+

05

49

.92

Fm

ax

Fa

vgD

ma

x

7.1

9E

+0

51

.77

E+

05

49

.77

Fm

ax

Fa

vgD

ma

x

7.1

9E

+0

51

.69

E+

05

52

.14

Fm

ax

Fa

vgD

ma

x

1.1

0E

+0

64

.23

E+

05

20

.83

Fm

ax

Fa

vgD

ma

x

1.1

0E

+0

63

.87

E+

05

22

.80

Fm

ax

Fa

vgD

ma

x

1.1

1E

+0

64

.00

E+

05

22

.04

20

mm

60

mm

10

0m

m

0.7mm 1.5mm 2.2mm

25

7. DP980: Spot-Welded

20m

m60m

m100m

m

0.7mm 1.5mm 2.2mm

Fma

xFa

tota

lD

ma

x

18

.94

.46

197.

75

Fmax

Fato

talD

ma

x18

.54.

212

10

.0Fm

axFa

tota

lD

ma

x18

.64

.33

20

4

Fmax

Fato

tal

Dm

ax53

.917

.648

.9Fm

axFa

tota

lD

ma

x53

.71

7.4

49

.46

Fma

xFa

tota

lD

max

53

.815

.754

.88

Fmax

Fato

talD

ma

x86

.237

.62

2.8

4Fm

axFa

tota

lD

ma

x83

.93

6.9

23

.22

Fma

xFa

tota

lD

max

90

.843

.619

.66

All

forc

es in x

10

4N

26

8. DP980: Weld-Bonded

20m

m60m

m100m

m

0.7mm 1.5mm 2.2mm

Fmax

Fato

tal

Dm

ax

16

.85

.57

158.

34

Fmax

Fato

talD

max

18.2

5.62

15

5.9

Fmax

Fato

tal

Dm

ax29

.15.

581

56

.9

Fmax

Fato

tal

Dm

ax62

.421

.539

.94

Fmax

Fato

talD

ma

x65

.02

8.7

30

Fma

xFa

tota

lD

max

65

.021

.440

.15

Fmax

Fato

talD

ma

x97

.947

.31

8.1

2Fm

axFa

tota

lD

ma

x97

.94

7.7

17

.97

Fma

xFa

tota

lD

max

97

.947

.717

.95

All

forc

es in x

10

4N

Crush Performance of Thin Walled Spot Welded and Weld ...

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