finite element spot-weld modeling thesis (crash testing application)

INVESTIGATION OF GEOMETRIC EFFECTS IN SPOT-WELD MODELING AND A NEW SPOT-WELD MODEL FOR FINITE ELEMENT CRASH

SIMULATIONS

by

Yatin Anil Jayawant

A thesis submitted to the faculty of The University of North Carolina at Charlotte

in partial fulfillment of the requirements for the degree of Master of Science in

Mechanical Engineering

Charlotte

2009 Approved by: __________________________ Dr. Howie Fang __________________________ Dr. Harish Cherukuri __________________________ Dr. David C. Weggel

ii

© 2009

Yatin Anil Jayawant

ALL RIGHTS RESERVED

iii

ABSTRACT

YATIN ANIL JAYAWANT. Investigation of geometric effects in spot-weld modeling and a new spot-weld model for finite element crash simulations. (Under the direction of DR. HOWIE FANG) Vehicle crashworthiness is a critical issue to the automotive industry

because it is related to the human safety in the events of crashes. Physical crash

testing is expensive, time-consuming, and dangerous. In addition, crash testing is

limited by the number of scenarios that can be investigated. Recent

developments in computer hardware and parallel numerical methods have

enabled researchers to use finite element (FE) simulations on crashworthiness

research. One of the challenges to FE modeling and simulations of crash is spot-

weld modeling, because there are typically thousands of spot-welds in a vehicle.

Due to the complexity of spot-weld modeling as well as the high computational

costs, currently used spot-weld models use simplified geometries and may not

give realistic behaviors in crash simulations. In the work of this thesis, the

geometric effects of spot-weld models are investigated. Also, a new spot-weld

model is proposed with the intention of improving model accuracy and mesh

independency.

In this thesis, a spot-welded hat section is used for the investigation. The

new octagonal spot-weld model is compared with the current nine-node, rigid-link

model on deformation patterns, crushing forces, and energy absorption. The

comparisons are made on the hat sections with three different mesh sizes and

different number of spot-welds.

iv

ACKNOWLEDGEMENT

I would like to take this opportunity to express my sincere gratitude

towards my advisor, Dr. Howie Fang, for his encouragement, help, and organized

approach. Dr. Fang‟s guidance and timely input helped me to meet the

deadlines. I also want to thank my committee members, Dr. Cherukuri and Dr.

Weggel for reviewing my thesis. I appreciate the suggestions I received from

them.

I would like to express my gratitude to my parents, Dr. Anil Jayawant and

Mrs. Archana Jayawant, who always supported my vision, inspiration until now,

in all aspects of my education. I would like to thank them for their infinite faith

and love.

I am indebted to University of North Carolina at Charlotte for supporting

me financially throughout my master‟s degree. I would like to acknowledge the

help in proofreading gave by my friends, Ashwin and Aditi. Special thanks to

Aditya, Parthesh and Amol for giving valuable inputs and to Gurunath, Venkat

and Chaitanya for encouragement and suggestions from the first day I landed at

USA till now.

Last, but, not the least, my grateful thanks go out to all the teachers I met,

without whom, life would be an altogether different story.

v

TABLE OF CONTENTS

CHAPTER 1: INTRODUCTION 1

CHAPTER 2: LITERATURE REVIEW 4

CHAPTER 3: FINITE ELEMENT MODELLING 14

3.1 Theoretical Background 14

3.1.1 Nonlinear Finite Element Analysis 15

3.1.2 Explicit and Implicit Methods 18

3.1.3 Contact Analysis and Methods 20

3.2 Spot-weld Modeling 24

3.3 A New Spot-weld Model 27

CHAPTER 4: SIMULATION SETUP 28

CHAPTER 5: SIMULATION RESULTS AND ANALYSIS 35

5.1 Hat Sections with Six Spot-welds 35

5.2 Hat Sections with Seven Spot-welds 42

5.3 Hat Sections with Eight Spot-welds 50

5.4 Meshing Issues 57

CHAPTER 6: CONCLUSIONS 64

REFERENCES 66

CHAPTER 1: INTRODUCTION

Passenger safety is one of the most important aspects of vehicle designs.

Deaths caused by automobile accidents are the 3rd most reason in the year after

cancer and heart diseases [1]. Each year crash injuries result in approximately

$145 billion in economic losses or $340 billion in comprehensive costs including

the values of the pain and suffering [2]. To prevent and/or reduce crash injuries,

vehicles are assessed for safety using crashworthiness tests.

A structure is said to be crashworthy if it provides sufficient protection to

its occupants during an impact. White et al. defined crashworthiness as the ability

of a structure to absorb energy in a controlled manner during a collapse [3]. The

energy generated by the impact gets absorbed into the structure and the

structure crushes, preventing injuries to the occupants. One of the

measurements of crashworthiness is the total amount of energy that a structure

absorbs during an impact.

Typically, a vehicle consists of hundreds of components joined by spot-

welds. Depending upon how well a finite element (FE) spot-weld model can

represent the connection provided by real spot-welds, the structural behavior of

spot-welded components predicted by numerical analysis can be significantly

different from those of real spot-welds used in a vehicle. Therefore, spot-weld

modeling is important while considering safety criteria. A vehicle can be

2

assessed for crashworthiness by either physical testing or virtual simulation

models. A crash simulation provides results without an actual crash test, and

thus saves time and money in both design and manufacture.

A simulation is the imitative representation of the functioning of one

system or process by means of the functioning of another. It is the technique

used to represent a real world process with a computer program. One has to

restrict the use of approximations and assumptions on simulation models to

ensure simulations reflect the real world scenarios. A major advantage of

computer simulations is that design parameters can be modified before and after

the simulated crashes. Once the FE model is created, it can be used for an

infinite number of simulations.

Currently, there are spot-weld models available for simulations. The main

drawback of these models is that these models depend on the mesh sizes and/or

shapes. Secondly, a single point connection or quadrilateral shaped connection

does not adequately represent the actual circular weld nugget. Area connections

involve complex modeling techniques that increase the simulation time and cost.

For components with complex geometries, if their meshes do not match,

unrealistic spot-weld models may result.

The quality of a spot-weld model largely depends on the mesh generated

before developing the FE spot-weld model. It cannot be guaranteed that a

particular spot-weld will lie exactly on nodal points. So, the motivation behind

this research is to create mesh independent spot-weld models that can be placed

at the exact locations as in real situations.

3

The objectives of this research are to investigate the geometric effects of

existing spot-weld models and to develop a new mesh independent model with

zero or a minimal geometric effect. The remaining parts of this thesis are

organized as follows. A literature review is presented in Chapter 2, discussing

the recent research for spot-weld modeling. A theoretical background of finite

element analysis (FEA) is then provided in the third chapter. Chapter 4 gives a

detailed description of the FE models used for simulation. In Chapter 5,

comparisons are provided for the model designed in this study and the existing

model based on crush forces, total absorbed energy, and folding patterns. Issues

related to mesh quality are also discussed in this chapter. Finally, Chapter 6

gives several concluding remarks for this study.

CHAPTER 2: LITERATURE REVIEW

Spot welding is a process of joining sheet metals by passing high Ampere

current through them. Welding is a complex process that involves interactions of

thermal, mechanical, electrical, and metallurgical phenomena. The resulting

strength, residual stresses, and material properties in a spot-weld may be

different from those of the parent sheets. All these factors should be taken into

account while modeling a real spot-weld present in a vehicle. An FE model of a

spot-weld should represent and should be able to transmit the forces and

stresses generated, calculate the energy absorbed, and provide similar results to

those of an actual spot-weld. In addition, parameters involved in the FEA such as

material properties, geometric nonlinearities, boundary conditions, and loading

conditions should be taken into consideration. All these together make FE

modeling of spot-welds a complex study.

In FE simulations, a spot-weld is modeled as either a point-to-point

connection [4-10] or an area connection [11-16]. In the point-to-point connection,

a single beam or spring element is used to model the link connecting two points

on the joining sheets. An area connection can have a set of beam elements, a

set of spring elements, a single brick element, or a hexa-element as a spot-weld

connection. The choice of the modeling technique depends on the analyst, the

goal, and the required accuracy. Single point connections are easy to model and

5

require less time for simulation but the accuracy of simulation results may not be

guaranteed. Area connections involve complex modeling but generally give

better results.

To model a spot-weld with a simple connection, Seeger et al. used a

single beam and single hexahedron element [4]. A beam element was used for

the ease of modeling, but after observing the contact forces and moments in the

vicinity of the welds, it was found that the overall stiffness was dependent on the

position of the nodes. A single hexahedron element was found inaccurate in most

of the cases, the issue being the placement of the weld element; as different

contact forces were developed at different locations which disturbed the internal

spot-weld forces.

A model with shell elements for the joining plates connected by a single

spring element was used by Combescure et al. to study the mechanical behavior

in the vicinity of a spot-weld [5]. The spot-weld was modeled in two ways, linear

elastic and elastic-plastic. The elastic-plastic model was proven to give better

results than the linear elastic model. Another type of single-point connections,

the CWELD element, was proposed by Fang et al. [6]. It was formulated with a

special shear flexible beam element with two nodes. It can join non coincident

meshes and accounts for a spot-weld area. The disadvantage of using this

element is that if the diameter is larger than the surface patch, it underestimates

the stiffness and if weld diameter to element length ratio is greater than one, the

prediction of force is not accurate with constraints from Kirchhoff shell theory.

6

Different types of sections were used to analyze the spot-welded joints.

Fyllingen et al. studied a thin-walled hat section, both experimentally and

analytically [7]. For numerical analysis, the specimen used in the experiment was

mapped by measuring the outer surface of a hat section by a 3D scanner. They

created different models and put them in batches differentiated based on material

types, and studied the effects of material variations, process histories, geometric

imperfections, and thickness variations. The numerical study was done in three

parts. The first part illustrated the influence of geometric imperfections on spot-

weld failures and mapping history (how well is a FE model represents the real

specimen). The second part analyzed material variation and spot-weld location.

In the third part, simulations were carried out to analyze the effects of geometric

and material variations. The mesh size of the FE model was 3 mm for shell

elements with a thickness of 1.5 mm. The spot-weld connection was modeled as

a massless rigid beam that connected the nodal points of the joining sheets. The

end nodes of the hat section were constrained for all the six degrees of freedom.

A sliding contact was defined between the impactor and the hat profile. The

members collapsed normally by folding and bending of the plate elements.

Fyllingen et al. observed a variation in the mean crushing force between models

of the same batch, which could be due to variations in geometry. They suggested

using a complex model (instead of single rigid connection) to study different

crushing patterns with different mean crush forces.

Simple connections with massless rigid beams were also studied by

Tarigopula et al. using simulations of a thin-walled section [8]. The model was

7

also validated by experiments but the mean crushing force was under-predicted.

Palmonella et al. reviewed a single beam model and observed that it

underestimates the stiffness [9]. Deng et al. studied four simplified FE spot-weld

models with refined meshes [10]. They used specimen with different lengths but

the weld diameter and sheet thickness were all the same. Structural stiffness of a

joint was taken as the basis for all of the comparisons. Various loading

conditions, namely in-plane and out-of-plane bending and torsions were taken

into account. The four models studied were the single bar, single-bar with spoke-

patterned radial bars on each sheet, multiple-bar connections, and solid-element

welds. A large number of elements with a variety of refinements were used for

analysis.

For more accurate analysis, area connections can be used. A detailed

modeling technique is employed in which a spot-weld is represented by elements

covering some area. Seeger et al. developed a complex model and compared it

to a connection with a single hexahedron element [5]. The spot-weld was

modeled with four hexahedron elements to form an area connection. The

problem of applying this technique lies in the element size. The small element

size decreases the time step too much and to counterbalance this small time

step, additional mass has to be used, which was not acceptable for their model

with area connection. Instead of multiple point connections, a single area

connection can be used. A spot-weld model with three dimensional brick element

with eight nodes was studied by Chang et al. [11]. The edges of the welded

region were divided into small elements for detailed analyses. Palmonella et al.

8

also studied a model in which a spot-weld was represented by a single brick

element [9]. The plate and brick elements were joined with pin jointed rigid bars

to transfer forces and moments. This model gave a good estimation of local

stiffness at the spot-weld, but required congruent meshes to use brick elements.

Since there are thousands of spot-welds present in a vehicle, a simple

model is preferred in order to save modeling time and computational cost. Zhang

developed a simplified spot-weld model for complex analysis in which a large

number of spot-welds were present in a structure [12]. This model was mainly

designed for linear elastic analysis. A nodal-force-based evaluation method was

used to predict the stresses in the spot-welds. This spot-weld model consisted of

a cylindrical beam element at the center with rigid bar elements connected in a

spoke pattern. Shell elements were inserted between the spokes that are formed

by the rigid bars. Rigid bar elements transfer three translational and one

rotational degree of freedom. The rigid bar elements in the spoke pattern are

multi-point constraints (MPC). The MPC forces were converted to line forces

(force per unit arc length) and line forces to structural stresses according to plate

theory. The MPC forces are less sensitive to FE meshes outside the periphery;

therefore, a coarse mesh can be used. For area connections, the umbrella model

(in Figure 2.1) proposed by Zhang and Taylor consists of two plates joined by a

Figure 2.1 The umbrella spot-weld model [13]

9

single beam [13]. Each sheet has a central node connected to eight

circumferential nodes lying on the same sheet in the radial direction.

Salvini et al. used FEA to study the structural behavior at the region

surrounding a spot-weld [14]. A spot-weld was modeled in two ways, rigid and

deformable link connecting two sheets. The deformable link is used to consider

varied stiffness to analyze fatigue damage. At both ends of the link, three-

dimensional beams were oriented in radial directions lying on each sheet. Beams

were assigned a particular stiffness (calculated by analytical method) to study the

surrounding region‟s behavior. The evaluation of load redistribution at each spot

was possible by the use of a deformable link.

Single point connections can also be modeled with a connecting element

whose diameter equals the diameter of the real spot-weld. Henrysson used a

beam element to model the spot-weld with diameter equal to nugget diameter.

Coarse meshes were employed to reduce the computational time. The two

joining sheets were modeled using four-node shell elements. The length of the

beam equaled the sum of half of the thickness of the two sheets.

To analyze the effect of spot-welds on the whole structure, the forces and

moments transferred between the spot-welds should be considered. Some

elements were specially developed to study this effect. The Rigid Body Elements

(RBE), RBE2 and RBE3 elements (available in NASTRAN) and hexahedral

elements were studied by Heiserer et al. [16]. In the RBE2 element, a single

node at the center (considered a master node) of the spot-weld connects multiple

nodes (slaves) along the periphery of the welded region. The peripheral nodes

10

can be constrained or set free depending on which DOF is to be fixed and which

DOF is to be set free. The RBE3 element also consists of a central node and

nodes on the edge. The difference between an RBE2 and RBE3 element is that

in RBE2 element, two nodes can have exact displacement and in RBE3 the

displacement is different. Heiserer et al. compared all the three elements types

and found that hexahedral elements provided good results and it can be used for

subsequent analysis by varying material properties. The diameter of a spot-weld

and the number of spot-welds also affect the simulation results. Rusinski et al.

studied the effect of weld diameter and pitch on the amount of absorbed energy

[17]. Energy absorption was a primary entity for comparisons between different

models. The built-in option (a single point connector element) available in

ABAQUS was used to model the spot-weld. It was observed that the weld size

was a significant factor and that the absorbed energy increased as the diameter

was increased and weld spacing was decreased. Spot-weld modeling with

ABAQUS is also is studied by Portillo et al. to investigate the crashworthiness

performance of spot-welded columns made from advanced high strength steels

[18]. Single and double hat columns with high strength steels and two types of

dual-phase steels were used in the analysis. A rigid plate was used as the

impactor to crush the columns. ABAQUS Explicit was used to perform the post-

buckling analysis. Two types of spot-weld models were developed using

ABAQUS meshing: independent spot-welds, fastener and element connection,

weld. Rigid constraints were used in the mesh independent fastener method so

spot-weld failure was not modeled while the weld was allowed to break in

11

element connection weld. Energy absorbed on impact was used to compare the

models. Numerical results for both types of spot-weld models were found in good

agreement with experimental data in terms of the collapse profile, deformed

column shape, final crush length, and peak impact force. The only limitation of

double hat section was that though the double hat section had an 8% larger

cross-sectional area, the peak load of the single hat column was slightly lower,

which is a desirable feature for crashworthiness.

Other than the type of connections, spot-weld shape and size and mesh

size are also important parameters that can affect the simulation results. Coarse

meshes require less computation time than finer meshes but the results may be

less accurate. Donders et al. studied the spot-weld quality and spot-weld designs

and their impacts on vehicle‟s safety performance [19]. Experimental tests were

carried out to assess the FE modeling approach. They suggested a simple spot-

weld model for crashworthiness applications since complex modeling of each

spot-weld present in a vehicle was not possible. Song et al. studied energy

absorption in hat sections filled with metal foams using both FE modeling and

experiments [20]. The spot-weld was modeled with eight shell elements. The

shell elements were considered rigid, because the authors did not observe any

fracture or deformation during the experiments. They observed that the spot-weld

was one of the controlling factors that affect the overall model quality.

To summarize the current work on spot-weld modeling, it can be observed

that spot-weld is modeled in two basic types, a single point connection or an area

connection. Sometimes, single point connection can be modified with a set of

12

beam elements to have an area connection. All the techniques have their own

advantages and disadvantages. Figure 2.2 shows the basics of each technique,

a single bar model represents a point connection, multiple bars represent a

simplified area connection and solid elements represent a complex area

connection [21].

(a) (b) (c)

Figure 2.2 Three spot-weld modeling techniques (a) Single bar model (b) Multiple bar model (c) Solid nugget [21]

Single-point or quadrilateral connections do not give a good

representation of the circular-shaped spot-welds. Accurate results may not be

obtained even though single point connections require less modeling time. Area

connections such as brick elements increase the computation cost if they are

present in large numbers. For area connections, other than the simple modeling

technique, congruent mesh on the joining sheets is one of the requirements. But

for structures with complex geometries, mesh cannot be guaranteed to be

congruent and the mesh sizes and shapes on the joining sheets may not always

be the same. Therefore, to combine the advantages of all these techniques, a

new type of model is developed.

13

The new spot-weld model consists of 12 nodes on both the joining sheets

connected by rigid links. The nodes are connected in an octagonal shape. One of

the 12 nodes on the upper sheet is kept as master and joined to all other. This

spot-weld model can be placed at the exact location to achieve mesh

insensitivity. The region around the weld nugget is then remeshed. The details of

this model are described in the later chapters.

CHAPTER 3: FINITE ELEMENT MODELING

Although performing actual crash tests may address some of the design

issues related to crashworthiness, they are costly, time consuming, and limited

by the number of trials. To this end, numerical analysis, predominantly using the

finite element method (FEM), has become a viable means for crashworthiness

study.

3.1 Theoretical background

The FEM is a numerical procedure for obtaining approximate solutions to

many of the problems encountered in engineering analysis. In the FEM, a

complex region defining a continuum is discretized into simple geometric shapes

called elements. The properties and the governing relationships are assumed

over these elements and expressed mathematically in terms of unknown values

at specific points in the elements called nodes. The continuity and equilibrium

conditions are satisfied between neighboring elements at all times. By satisfying

boundary conditions, a solution in the terms of nodal displacements and element

stresses and strains is obtained for the entire system. One important thing that

affects the accuracy of FE solutions is the mesh quality. In general, a model with

fine and regular meshes gives more accurate results than a model with coarse

15

and irregular meshes. However, using fine meshes increases the complexity and

time of the modeling effort and incurs significant computational cost.

In linear FEA, the response of the structure is reversible, i.e. original

shape and size can be obtained after removing the load. But this is not the case

for crashworthiness problems. Typical features of crashworthiness problems

such as nonlinear behavior of materials, large displacements, changes in

boundary conditions caused by the contacts between different parts during

crashes, require the use of nonlinear FE code.

3.1.1 Nonlinear Finite Element Analysis

Nonlinearities in FEA can be classified into two types, material and

geometric nonlinearities. Material nonlinearities occur when the stress-strain

relationship is not linear and geometric nonlinearities arise due to large

deformations or displacements.

Figure 3.1 shows a bilinear elasto-plastic material model in reverse

loading condition with hardening behaviors. Hardening may be defined as the

increase in yield stress due to plastic deformation. Depending on how the yield

surface will evolve in a space, hardening is categorized by isotropic hardening,

kinematic hardening (shown in Figure 3.1 by I and K respectively) or mixed

hardening. In isotropic hardening, the yield strength changes due to plastic

deformation but the yield strengths in tension and compression are always equal.

As illustrated in Figure 3.1, where lengths BC and B‟C are equal, reversed

compressive yield stress σB‟ is equal to tensile yield stress σB before load

16

reversal. In the kinematic hardening model, the center of the yield surface moves

in the direction of plastic flow. As shown in Figure 3.1, the yield stress in tension

σB is greater than that in compression σA‟.

Figure 3.1 Elastic-plastic behavior [22]

Figure 3.2a shows the yield surface for isotropic hardening in which the

yield surface expands uniformly without changing the shape and position. In the

case of kinematic hardening, the yield surface translates in the direction of

outward normal without changing the shape and size (Figure 3.2b). For both

isotropic and kinematic hardenings, the orientations of the yield surfaces remain

unchanged. The hardening models can be written as [22]

( ) ( ) 0ij hijf h (3.1)

where σij are components of the symmetric stress tensor, βij denotes the

translation of initial yield surface, λk is a scalar function of plastic strain, and h(λk)

is a function quantifying the expansion of yield surface. In isotropic hardening, βij

is zero and in kinematic hardening, h(λk) is a constant.

O

A B

C

B‟ A‟

K I

ε

σy σmax

σ

2 σy

2σmax

17

(a) Expansion of yield surface (b) Translation of yield surface

Figure 3.2 Strain hardening [23] (a) Isotropic hardening; and (b) Kinematic hardening

Kinematic hardening is related to the Bauschinger Effect, an observation

on the metal yield strength that decreases upon changing the direction of the

strain. For example, an increase in tensile yield strength will result in a decrease

in compressive yield strength, as illustrated in Fig. 3.2b. In crashworthiness

problems cyclic loading is involved which diminishes the yield stress

(Bauschinger Effect). The kinematic hardening accounts for this effect by

assuming that the yield surface keeps the same form but is translated when

plastic deformation occurs. Hence kinematic hardening model is adopted in this

study.

Figure 3.3 Nonlinear contact problem

Nonlinear contact

behavior Area of contact

Displacement A

http://en.wikipedia.org/wiki/Yield_strength

18

Figure 3.3 shows the nonlinear contact behavior, a case of impact of rigid

wall with upper-hat section. Till point A, area of contact is directly proportional to

the displacement and varies linearly. But after that, area varies nonlinearly. The

reason behind this is that initially only the cross section of upper-hat is in contact

with the wall but after some time, due to number of folds, area increases

nonlinearly. The gap between mating parts changes as the contact force

changes and this can happen for materials with linear behavior and small

displacements. This is nonlinear contact behavior.

Geometric nonlinearity is the change in the load-displacement

characteristics of the structure caused by the change in the structural shape due

to large deformations or displacements. Since the area of contact is the function

of displacement or deformation, contact can also be classified as a type of

geometric nonlinearity.

3.1.2 Explicit and Implicit Methods

Nonlinear FE problems can be solved in two ways, explicitly or implicitly.

In the explicit methods, the new value is defined in terms of values that are

already known. In the implicit methods, new unknown value is also taken into

account and solution involves number of iterations to arrive at the final result. For

example, if we consider equation

2 3y x (3.2)

It can be written as

( )y f x (3.3)

19

where

( ) 2 3f x x (3.4)

This is the explicit form as „y’ can be found by putting values for „x’.

2 3x y (3.5)

Equation 3.5 describes the same function in the implicit form. This can be

treated as implicit definition of „y‟ as a function of „x’ and vice versa.

This can be explained by simple problem of wave propagation through a

pipe. If pressure is applied at one end of pipe, the pressure wave will move down

the pipe and be reflected from closed end. It will travel back and forth and settles

down to the constant value applied at the open end. If requirement is such that

steady conditions should be reached as soon as possible, damping is provided.

This is implicit solution scheme to have steady conditions be reached as quickly

as possible. If pressure waves are to be investigated, negligible or no damping

should be used so that the wave reflections can be accurately followed. This

situation can be treated with explicit solution method. The time-step size of

explicit method limits the advance of pressure steps to a unit cell per time. But

this affects accuracy as a pressure wave that propagates further than one cell in

one time step will move to the region that has no defined influence on the

pressure. This may lead to numerical instability. In implicit methods, all cells are

coupled together to allow pressure signals to be transmitted through a grid. But

for this damping of pressure waves, coupled equations need to be solved. Thus

more time is required to solve equations by implicit method but it is more stable

20

for solving stiff problems, i.e. larger step size can be used. Hence the choice of

whether to use implicit or explicit methods depends on accuracy and time.

3.1.3 Contact Analysis and Methods

Contact analysis is required when two bodies that are initially separate

apart come into contact. Contact can be defined between two bodies or for a

single surface of a deformable body. Figure 3.4 shows an impact simulation of a

hat-section in which the tube is fixed at one end and crushed by the rigid wall on

the other end. In this simulation, contact occurs between the tube and the wall

(deformable-to-rigid contact), between the hat and flat plate of the tube

(deformable-to-deformable contact), for the hat piece (single-surface contact),

and for the flat piece (single-surface contact).

(a) (b)

Figure 3.4 Nonlinear contact behavior (a) A hat section before impact; and (b) A hat section during impact

In contact analysis, the interacting surfaces on the two contact bodies are

termed as a master and a slave surface, respectively. Upon contact, nodes from

21

the slave surface are constrained to slide along the master surface. In case of

penalty based contact, when a penetration is found, a force proportional to

penetration depth is applied to resist and ultimately eliminate the penetration.

Initially for interaction, each node of the slave surface is associated with the

closest point on master surface (Figure 3.5a). This is determined by plotting a

normal between a slave node and a master surface [24].

(a) (b)

Figure 3.5 Contact analysis (a) Before contact (b) After contact [24]

One of the methods for detecting contacts is the standard penalty method.

In this method, penetrations of slave nodes into the master surface are checked

and if a penetration is found, (Figure 3.5b) a force proportional to the penetration

depth is applied to resist and eliminate the penetration. The interface stiffness

used in a contact algorithm is based on the stiffness values of the slave and

master surfaces, whichever is smaller. To calculate the contact stiffness, it is

A

B

C Master surface

Slave surface

Closest point to A

Penetration Gap

22

assumed that there is a linear spring between a slave node and a master

segment. The spring stiffness determines the force that will be applied to the

slave node and the master segment. The spring stiffness is calculated by [25]

min

sF A Kk

diagonal

(3.6)

where A is the area of the contact segment, K is the bulk modulus of the element

in contact and F is a scale factor that is defined as follows.

s d sF S S (3.7)

where Sd is a penalty scale factor and Ss is a scale factor on the slave/master

contact stiffness

Interior

shell edge

Exterior

shell edge

Slave

surfac

Master

surface

Projection

vectors

Mid-plane

Figure 3.6 Definition of contact thickness [26]

23

For contact of shells considering element thickness, the contact surface is

set with an offset from the mid-plane (Figure 3.6). The contact surface is

determined by normally projecting from the shell‟s mid-plane with a distance

equal to half of element thickness. At an exterior shell edge, the contact surface

forms a circular wrap around the edge with radius equal to half of the element

thickness [26]. Figure 3.7 shows the contact forces on the slave and master

bodies. Coulomb‟s formulation is used for frictional consideration. It is assumed

that an elastic spring is present between slave and master surface. As the

contact point moves along the master surface, a frictional force in a tangential

direction to the rigid surface resists the tangential relative movement.

Figure 3.7 Contact forces [24]

Initially, the frictional force is calculated by using the coefficient of friction µ

and the normal force Fn

y nF F (3.8)

24

3.2 Spot-Weld Modeling

Current spot-weld models are either simplified models used for analyzing

the overall behavior of the whole structure or detailed models used for studying

the stress/strain distributions and/or failures within or around a spot-weld. These

models can be either single-point or area connections between the two sheets of

materials.

In the study by Xiang et al. [27], the behavior of several spot-weld models

including both single-point and area connections is described. The mean

crushing force was used as one of the criteria for comparison. Figure 3.7 shows

six area-connected spot-weld models that are described as follows.

(a) Common element model - Two sheets are joined by common

elements. The same mesh size for both sheets around the spot-weld is

necessary to use this model.

(a) (b) (c)

(d) (e) (f)

Figure 3.7 Various spot-weld models (a) Common element model (b) Beam model (c) Spring model (d) Volume element model

(e) 9 rigid bar model (e) Shell element model [27]

25

(b) Beam model - Beams are used to transmit forces and moments from

one shell to another in the beam model. Material properties are assigned to

beam elements to calculate the forces based on the stress-strain relationship.

(c) Spring model - Elastic-plastic springs were used to connect shell

elements. Properties of the springs are determined from actual spot-weld

properties.

(d) Volume element model - Solid elements are used to connect shell

elements. The yield stress of spot-weld is calculated by

vw vu

sw su

H H

(3.9)

where Hvw and σsw are the Vickers hardness and yield stress of the spot-weld,

and Hvu and σsu are the Vickers hardness and yield stress of the flange.

(e) Nine bar rigid model - The nodes on joining flanges are connected by

rigid bars and translational and rotational degree of freedoms of nodes are

coupled.

(f) Shell element model - A shell element is embedded between the two

sheets with corresponding nodes rigidly connected.

Xiang et al. observed that the dimensions of spot-weld are important to

have accurate mean crush forces. Based on mean crush forces, numerical

results were compared with experimental data and Xiang found that mean crush

force values of a single beam and spring model were not comparable. The

volume and common element models gave satisfying results but more

computational modeling efforts were required. The nine rigid bar model required

26

less modeling efforts and analytical and experimental results were comparable.

Hence, it was selected for use in an optimization study.

Current spot-weld modeling techniques have some limitations. For

complex geometries, the meshes cannot be guaranteed to be congruent and

their sizes and shapes may not always be the same. Secondly, either single-

point or quadrilateral shapes do not represent well the circular spot-welds in

practice. Furthermore, volume-element connections using brick elements

increase the computational cost, if they are present in large numbers.

In crash analysis, hundreds of spot-welds are present in the structures

being analyzed, so a simple, accurate model is recommended. Simplified models

such as single point connections require less computation but reliable results

may not be guaranteed. Also, the diameter of single point connections is much

less than that of the real spot-welds which is about 5 to 6 mm. This can seriously

affect the accuracy of numerical analysis. Though area connections such as

those using brick elements have approximately equal diameter as that of the real

spot-weld, they are computationally expensive and generally challenging to

generate the spot-weld models. To this end, they are used mostly for fatigue

analysis in which a single spot-weld is studied instead of studying the overall

effects of spot-welds on a large system. Thus, to combine the advantages of

current modeling techniques, a new spot-weld model is developed in this study.

27

3.3 A New Spot-weld Model

Multiple point connections covering an area is a better option compared to

the single-point or complex area connections, though all of these models are

dependent on meshes generated before creating the spot-weld models. For

crash analysis, the minimum mesh size with which a vehicle can be modeled is

around 10 to 15 mm; however, the size of a spot-weld is only 5 to 6 mm in

diameter. So spot-welds cannot be placed at the exact locations as required. A

new FE spot-weld model is developed in this study. It has an octagonal shape

that resembles the circular shape of the real spot-weld and has rigid links among

nodes within the spot-weld model. This spot-weld model will be placed at the

exact location and remeshing is performed on existing meshes around the spot-

weld. Therefore, this model is mesh-independent and can be embedded in

meshes of any size. Figure 3.9 shows the schematic representation of the

octagonal mesh of new spot-weld model. Each octagonal mesh is embedded in

to the sheets and the two octagonal meshes are joined using rigid links among all

of the modes. In the next chapter, this new spot-weld model will be evaluated by

comparing simulation results with those using the nine rigid-bar model.

Figure 3.9 A new spot-weld model in octagonal shape

CHAPTER 4: SIMULATION SETUP

In this study, a 200 mm long hat-section is used to evaluate the new spot-

weld model. The hat-section consists of a flat plate and a hat column. They are

joined by spot-welds. Figure 4.1 shows the overall dimensions (in millimeter) of

the model. Eight equally spaced spot-welds are placed on each bottom flange of

the hat section. The hat section is crushed at one end by the rigid wall moving in

the longitudinal direction of the tube.

Figure 4.1 Overall dimensions of a spot-welded hat section.

29

The nodes on the other end of the hat section are fixed for all six degrees

of freedom. The rigid wall moves at a constant velocity that is defined by a linear

time-displacement curve. The rigid wall is to travel 100 mm in 10 ms. The FE

models are developed with the aid of Hypermesh [28], a general-purpose FE

preprocessor. All of the simulations were carried out using LS-DYNA explicit FE

code [25]. Table 4.1 gives a summary of models to be used for the analysis. A

total of eighteen models are created, nine with the new octagonal spot-weld

model and nine with the nine-node rigid-bar model. For each type of spot-weld

models, the number of spot-welds varies from six to eight and the mesh size

ranges from 2 to 4 mm.

Table 4.1 Matrix of simulation models

New Octagonal and Nine-Node Model

Mesh Size (mm)

2 3 4

Number of Spot-welds

6 7 8 6 7 8 6 7 8

Table 4.2 summarizes the material properties used in the simulation

models. The wall is defined by a rigid material while the tube is defined as an

elasto-plastic material with kinematic hardening.

Table 4.2 Material properties

Part

Materials Models

Mass Density * E-6

(kg/mm3)

Young's Modulus (kN/mm

2)

Poison's Ratio

Yield Stress

(kN/mm2)

Tangent Modulus (kN/mm

2)

Upper-hat and flat plate

Elastic plastic with kinematic hardening

27.8 200 0.3 0.2 0.63

Wall Rigid 57.8 200 0.3

30

The spot-welds are the rigid links joining two sheets. Figure 4.2 (a) shows

the different spot-weld models generated on 2, 3 and 4 mm meshes. Figure 4.2

(b) shows the constraints (end nodes fixed in all six degrees of freedom marked

with thick black lines) and direction of velocity.

(a)

(b)

Figure 4.2 FE spot-weld model (a) Meshes on 2, 3 and 4 mm models (b) 3- dimensional view showing direction of velocity and constrained nodes

The shell elements are formulated with Belytschko-Tsay formulation with

1.5 mm nodal thickness. For five through-thickness integration points, the

Belytschko-Tsay formulation requires only 725 mathematical operations

compared to 4,050 operations required by the Hughes-Liu formulation; hence it

consumes less CPU time. Initial mesh of quadrilateral elements and mesh sizes

31

of 2, 3 and 4 mm for the top-hat and flat plate are generated by automeshing

technique in Hypermesh. For the new octagonal spot-weld model, a computer

program is written in C programming language for generating spot-weld models

at given locations. By giving input as the number of spot-welds on each side, the

distance between two spot-welds (pitch) and the length of the sheet, the

octagonal shaped spot-weld models with their exact locations are obtained. The

output of the program then can be embedded in the LS-DYNA input file.

Compared to single point connections or quadrilateral shaped brick

elements, the octagonal shaped model is closer to the actual circular shape of

the real spot-weld nuggets. For the octagonal spot-weld model, remeshing is

required on the meshes of the two sheets around the spot-welds. The nine-node

model is created by taking spot-weld locations corresponding to new octagonal

model as the basis.

Figure 4.3 Aligning of centers for nine-node model

Actual spot-weld center

Nearest node taken as center

Rigid links

Mesh pattern

32

The centers of nine-node model are chosen as the closest node of the

respective centers of octagonal model. The nine-node spot-weld model is shown

in Figure 4.3.

(a)

(b)

Figure 4.4 Spot-weld models (a) nine-node model (b) New octagonal model

Figure 4.4 shows how the nodes of spot-welds of both the octagonal and

nine-node models are joined together by rigid links. For the nine-node model

33

(Figure 4.4a), the central node is selected and joined to eight nodes on the upper

sheet and nine nodes on bottom sheet. For the octagonal model (Figure 4.4b) a

node lying on upper sheet, closest to CG of spot-weld is selected and rigidly

joined to 11 upper nodes and 12 lower nodes. For octagonal model, nodes form

an octagon are compared to square shape of nine-node model.

Problems in automeshing technique are illustrated in Figure 4.5. The

model with 4 mm mesh is taken for analysis. Since the exact locations of spot-

welds are known, they are embedded such that the center of every spot-weld will

coincide with the exact center of the real spot-weld.

In this particular case, if the mesh around the spot-weld is removed, the

spot-weld may not lie at the center of remeshing zone. For the first and third

remeshing zone, the spot-weld lies on the right side while it lies on the left side

for second remeshing zone. So, symmetric mesh at alternate locations may be

possible. But for another model this cannot be guaranteed and the remeshing

results may be different.

Figure 4.5 Remeshing zone (nodes connected in octagonal shape)

1 2 3

34

For the 2 mm mesh, more elements are present in the remeshing zone

compared to the 4 mm mesh. This may also affect the simulation results. The

detailed discussion of the effects of mesh sizes and the number of spot-welds is

presented in the next chapter.

CHAPTER 5: SIMULATION RESULTS AND ANALYSIS

In this chapter, the octagonal and nine-node spot-weld models are

compared in tube crushing simulations on tube‟s folding patterns, crushing

forces, and absorbed energies. A detailed analysis is also provided at the end of

this chapter discussing the issues in meshing and the discrepancies in folding

patterns and crushing forces.

5.1 Hat Sections with Six Spot-welds

The time histories of crushing forces for hat sections with six spot-welds

are obtained for both the octagonal and nine-node spot-weld models. For each

type of the spot-weld models, 2, 3, and 4 mm meshes are used for the hat

sections.

In the case of 2 mm mesh, different folding patterns were observed

between the octagonal and nine-node models. In the octagonal model, folding

initiated and developed at the impacting end; while in the nine-node model,

folding initiated at one-third of tube length from the fixed end and subsequent

folds developed between the impacting end and the initiating location. Figure 5.1

shows the comparison of folding patterns of the octagonal and nine-node models

at 2, 6, and 10 ms.

36

t=2 ms

t=6 ms

t=10 ms Figure 5.1 Folding patterns of the hat section with 6 spot-welds and 2 mm mesh

(left: octagonal model, right: nine-node model)

Figure 5.2 shows the time history of crushing forces for both models. It

can be seen that the crushing force reached maximum at the beginning and

decreased significantly at 2 ms. Due to self impact of folds and development of a

37

new fold, the crushing forces started to go up at 4 ms and started to drop at 6

ms. It was also observed that the two models have similar trend on crushing-

force history.

Figure 5.2 Crushing force histories of the hat section with 6 spot-welds and 2 mm mesh

Figure 5.3 shows the time histories of energy absorptions of both models.

Figure 5.3 Histories of absorbed energy for the hat section with 6 spot-welds and 2 mm mesh

38

The curves follow each other and are alternately above and below each

other which shows that the energy absorbed by both the models and the manner

in which it gets absorbed is similar, with more energy being absorbed by the

octagonal model.

t=2 ms

t=6 ms



39

For models with six spot-welds and 3 mm mesh (Figure 5.4), the folding

started at the crushing end for octagonal model and one-third of tube length from

the fixed end for nine-node model. This is similar to the case of the models with 2

mm mesh. Subsequent folding patterns of the 3 mm models are similar to those

of the 2 mm models up to 10 ms.

The crushing forces in Figure 5.5 for the nine-node model are slightly

higher than that for the octagonal model.



40

The reason is that when the mesh size is changed from 2 to 3 mm, the

locations of some spot-welds in the nine-node model are changed since they

have to occupy a square mesh of 2 × 2 elements. The increased crush forces in

the nine-node model resulted in an increase in the energy absorption as shown

in Figure 5.6.

t=2 ms

t=6 ms



41

Figure 5.7 shows the folding patterns of hat sections with 4 mm mesh and

6 spot-welds for the octagonal and nine-node spot-weld models. In both the

cases, folding started from the crushing end with a small bulge formed at the

one-third of the tube length from the fixed end. At every time step, both models

deform similarly, but their folding patterns are rough compared to those on the 2

mm and 3 mm models.

Although the folding patterns are similar, the crushing forces and energy

absorptions differ between the octagonal and nine-node model (Figure 5.8).


This is due to the locations and sizes of the two spot-weld models. For the

4 mm mesh, the mesh size of the octagonal spot-weld model remains 6 mm, but

the nine-node model has to take a square of 8 8 mm, which is formed by 2 2

elements.

The increased size on spot-welds increased the rigidity of the hat section.

Hence, the crushing forces required for deformation are increased.

42

Figure 5.9 shows the time history of energy absorption for both models.

There is more energy absorption by the nine-node model than the octagonal one

due to the increased crushing forces in the former.


5.2 Hat Sections with Seven Spot-welds

In this section, we examine the octagonal and nine-node models using a

hat section of seven spot-welds. Figure 5.10 shows the folding patterns of the

two models with 2 mm mesh.

Figure 5.10 shows the folding patterns for both models at three time

instances. Initially folds started to develop at the fixed ends; this is different from

the case of six spot-welds because of the changes on spot-weld locations. At the

end of the simulations, similar folding patterns were developed with most folds at

the rear fixed ends and small deformations at front, impacting ends.

43

t=2 ms

t=6 ms



Figure 5.11 shows the crushing force history and Figure 5.12 shows the

energy absorption of the two models. With small mesh size of the hat section, the

44

spot-welds in both models are nearly identical in size, which accounts for the

similarity in crushing force histories.



In addition, the increased number of spot-welds in the models further

reduced the differences between the two models. This can also be seen from the

histories of absorbed energy shown in Figure 5.12.

For models with 7 spot-welds and 3 mm mesh (Figure 5.13), the folding

started from the crushing end for both models. The folding patterns are similar

45

before 6 ms and different afterwards. Although folds were at the crushing end for

both models, folds for the octagonal model are not as smooth as those for the

nine-node model. The reason was due to the reduced spacing between spot

welds and the increased stiffness in the remeshing zone of the octagonal model.

t=2 ms

t=6 ms

t=10 ms

Figure 5.13 Folding patterns of the hat section with 7 spot-welds and 3 mm mesh (left: octagonal model, right: nine-node model)

Figure 5.14 shows the crushing force curves for both models. The

crushing forces are almost identical for the first 3 ms and differ slightly

46

afterwards. The energy absorption of the two models is almost the same during

the entire crushing period (Figure 5.15).



Figure 5.16 shows the folding patterns for the hat-section with 7 spot-

welds and 4 mm mesh. The deformation started in a different manner. Actually,

first spot-weld of nine-node model is located at 8 mm from the impacting end and

7.5 mm for octagonal model. Hence, for octagonal model, folding started from

47

area near the second spot weld from impacting end but for nine-node model, it

started from impacting end. Thereafter, the folding patterns are almost identical

till the end of the simulation.

t=2 ms

t=6 ms

t=10 ms

Figure 5.16 Folding patterns of the hat section with 7 spot-welds and 4 mm mesh


48

For this 4 mm mesh section, the crushing force histories are very different

between the two models as shown in Figure 5.17. The nine-node model has

larger crushing forces than the octagonal model.


The increase on crushing forces was due to the increased size of the spot-

welds in the nine-node model. In this case, the nine-node model was created

with 2 2 elements that resulted in an 8 8 mm spot-weld. The increased spot-

weld size increased the rigidity of the hat section. In addition, since the nine-node

spot-weld models used mesh on the hat section, their locations do not exactly

match the real spot-weld locations. This can be seen from the crushing forces in

Figure 5.17 whose second pick occurred at 4 ms, which is at 5 ms in the hat-

section with 2 mm mesh (as compared that in Figure 5.11). Due to frequent self

impact of lobes, fluctuations in nine-node model curve can be observed. Spot-

weld spacing also affects the simulation. For octagonal model, distance between

each spot-weld is maintained at 30.8 mm but for nine-node model, since exact

49

location is not available, the distance varies from 28 to 32 mm. Second and third

spot-welds from impacting end are spaced at 28 mm from each other, so at 4 ms,

crush force reaches at peak, and then 32 mm distance is maintained between

next four spot-welds so somewhat lower crush force is required for deformation.

Again, sixth and seventh spot-welds are spaced at 28 mm from each other, so

fluctuations can be seen around 8 ms. At the end, since there is just 8 mm

distance between last spot-weld and fixed end, crushing force reaches another

peak.

Figure 5.18 shows the histories of energy absorptions of the two models.

Both the models deformed in the same manner during 1 to 3 ms and 6 to 10 ms

interval hence energy curves almost coincide with each other. During 3 to 6 ms

interval, the deformation is through the second spot-weld from impacting end in

nine-node model which tries to resist it hence a small upward trend can be seen.

The deformation is between first and second, and second and third spot-weld in

octagonal model, hence not much resistance is provided and less energy gets

absorbed.


50

5.3 Hat Sections with Eight Spot-welds

For hat sections with 8 spot-welds and 2 mm mesh, the folding patterns of

octagonal and nine-node spot-weld models are shown in Figure 5.19.

t=2 ms

t=6 ms

t=10 ms



The folding in both models started at the fixed ends and continued to

develop in a similar way. Compared to the case with seven spot-welds, there are

fewer folds in the eight spot-weld models. The increased number of spot-welds

51

has increased the difficulty to fold between two spot-welds. Also, due to more

number of spot-welds and finer mesh, the folding patterns, crush force and

energy absorption histories of both the octagonal and nine-node model are

almost similar.

The crushing force histories of the two models are similar as shown in

Figure 5.20. For the nine-node model, there are slight fluctuations around 1 ms;

however, these are less severe than those found in the case of seven spot-

welds. The peaks in crush forces around 5 mm correspond to the deformation of

the lobes and formation of the second folds.



52

Figure 5.21 shows the histories of energy absorptions for both models.

There is no significant difference between the two models within the first 6 ms.

After that, the octagonal model started to absorb more energy than the nine-node

model.

Figure 5.22 shows the comparison between the octagonal and nine-node

model with 8 spot-welds and 3 mm mesh.

t=2 ms

t=6 ms

t=10 ms



53

For the octagonal model, the folding started from the fixed end and the

folds continued to develop in the same direction. In the nine-node model, folding

started from the impacting end along with a bulge formed at one-third of the tube

length from the fixed end. Folds were then developed at both locations. The

difference in folding patterns is due to the different locations of the spot-welds in

the nine-node model to accommodate the existing mesh. Compared to the

models with 2 mm mesh, it can be seen that the octagonal model with 3 mm

mesh gives more consistent behavior than the nine-node model.

For the two models with 3 mm mesh, the time histories of crushing forces

are shown in Figure 5.23. Both curves follow a similar trend during the entire

history but with slight difference in the locations of peak loads.


The total energy absorption of the two models is shown in Figure 5.24.

Similar trend was observed for the first 6 ms and then there is a slight difference

between the two models. The nine-node model was slightly stiffer and thus

54

absorbed less energy than the octagonal model. This increased stiffness in the

nine-node model was due to the occurrence of the folds at one-third tube length

that turned the initial long crushing tube into two shorter sections.


Figure 5.25 shows development of folding in the two hat section models

with 8 spot-welds and 4 mm meshes. For the octagonal model, folding started

from the impacting end, and continued to develop till the end of crushing. For the

nine-node model, folding started in the middle and successive folding was

developed in both directions from midway.

The center of first spot-weld in nine-node model is closer to the impacting

end than that in the octagonal model; this made it difficult to fold at this end.

Consequently, the initial folding started at the mid section. Because of this

difference in spot-weld locations, it required less force to initiate folding for the

nine-node model than for the octagonal models.

55

t=2 ms

t=6 ms

t=10 ms



This can be seen from the crushing force histories shown in Figure 5.26.

The fluctuations of crushing forces around 2 ms for the nine-node model are due

to self-impact of lobes. After the initial peak loads, the crushing forces for both

models do not significantly differ from each other in magnitude, but differ in the

locations of peak loads.

56


The energy absorption histories of both models are similar, as shown in

Figure 5.27.


Comparing the results in Figure 5.9 for 6 spot-welds and in Figure 5.18 for

7 spot-welds, all with 4 mm meshes, it can be seen that the differences between

the two models becomes less significant when more spot-welds are used for the

57

hat section. Despite this, it is observed that the mesh sizes do affect the

simulation results of both models.

5.4 Meshing Issues

This section addresses the issues involved while modeling spot-weld with

the new technique. Table 5.1 shows the locations of the spot-welds in each of the

hat-section models discussed in Section 5.3. The spot-weld locations in Table

5.1 are measured from their centers to the impacting end, and the exact locations

are given by those of the octagonal models.

Table 5.1 Comparison of spot-weld locations

Spot- Mesh 1 2 3 4 5 6 7 8

welds size Locations of centers of spot-weld

models

6

OCT (mm) 7.5 44.5 81.5 118.5 155.5 192.5

9 N 2 8 44 82 118 156 192

3 8.95 44.77 80.59 119.4 155.2 194

4 8 44 80 120 156 192

7

OCT (mm) 7.5 37.5 67.5 97.5 127.5 157.5 187.5

9 N 2 8 38 70 100 130 162 192

3 5.97 38.8 68.65 98.5 131.3 161.2 194

4 8 40 68 100 132 164 192

8

OCT (mm) 8 34 60 86 112 138 164 190

9 N 2 8 34 60 86 112 138 166 192

3 5.97 32.83 59.7 86.56 113.4 140.3 167.2 194

4 8 36 60 88 112 140 168 192

For each hat-section, the locations of spot-welds in the octagonal and

nine-node models with 2 mm meshes almost coincide with each other due to the

small meshes. For the models with 3 and 4 mm meshes, the differences in spot-

58

weld locations become larger. It was observed from the simulation results that

folds were developed between two spot-welds. Therefore, folding patterns are

affected by the distances between neighboring spot-welds that are in turn

affected by the locations of the spot-welds.

For the hat section with 8 spot-welds, and 3 mm mesh, the center of the

first spot-weld in the nine-node model is closer to the impacting wall compared to

the octagonal model. Hence folding started from one-third tube length from the

fixed end in the nine-node model but started at the impacting end in the

octagonal model. In the case of hat sections with 7 spot-welds and 3 mm mesh,

the distance between the first two spot-welds is 30 mm for the octagonal model

and 32.83 mm for the nine-node model. Hence, more folds were formed between

these two spot-welds in the nine-node model than octagonal model. In the hat

sections of 8 spot-welds and 7 spot-welds with 2 mm meshes, the spot-weld

locations in both the octagonal and nine-node models closely matched each

other and thus resulted in similar folding patterns. These findings are consistent

with those of Fyllingen et al. [7] who reported that variations in mean crushing

force were due to geometric imperfections.

The mean crushing forces and total energy absorptions for all of the

models are summarized in Table 5.2. The mean crushing forces for both models

are almost identical for 2 mm mesh. When the mesh sizes are increased, the

mean crushing forces decrease for the octagonal models and slightly increase for

the nine-node model.

59

Table 5.2 Summary of the results

6 spot-welds 7 spot-welds 8 spot-welds

Mesh size (mm) Mesh size (mm) Mesh size (mm)

2 3 4 2 3 4 2 3 4

Crush OCT 22 19.2 18.4 22.4 23 23.5 25.1 24.4 25

Force (kN) 9 N 21.4 21.4 22.2 22.3 23.4 25.3 24.9 25.3 25.8

Energy OCT 1.3 1.24 1.34 1.33 1.41 1.49 1.43 1.39 1.48

(*103 kN-mm) 9 N 1.24 1.24 1.45 1.32 1.4 1.46 1.4 1.46 1.45

For the hat section with 6 spot-welds, a comparison of the mean crushing

forces is shown in Figure 5.28 between the octagonal and nine-node models with

different mesh sizes.

Figure 5.28 Comparison of mean crushing force for Octagonal and nine-node model with 6 spot-welds

The octagonal model appears to be less effective in this case than the

nine-node model for large mesh sizes. The reason is that when the mesh size

increases, the element sizes in the re-meshing zone are also increased based on

60

the current remeshing method in this study (by automesh in Hypermesh). This

problem can be resolved with a new mesher that can provide a smoother

transition from the surrounding large mesh to the small spot-weld meshes. Figure

5.29 shows the comparison between the octagonal and nine-node models for the

hat section of seven spot-welds. In this case, the two models give similar results

with 2 mm meshes. However, the octagonal models are less sensitive than the

nine-node models with respect to changes on mesh sizes. Compared to the case

with six spot-welds, the octagonal model becomes less sensitive for more spot-

welds in a section with a given length.


Figure 5.30 shows the comparison between the octagonal and nine-node

model with eight spot-welds. Both models become less sensitive to changes on

mesh sizes, with the octagonal models being more consistent than the nine-node

model.

61


The octagonal and nine-node models are also compared on total energy

absorptions for the hat sections with six, seven, and eight spot-welds as shown in

Figures 5.31, 5.32, and 5.33, respectively. Both the octagonal and nine-node

models become less sensitive to changes on mesh sizes when the number of

spot-welds is increased

Figure 5.31 Comparison of energy absorption for Octagonal and nine-node model with 6 spot-welds

62



Although the octagonal models are more consistent than the nine-node

models in the case of hat sections with eight spot-welds, relatively large

inconsistency was still found in the models for hat sections of six and seven spot-

welds. This is related to both the folding patterns and re-meshing around the

spot-welds.

Figure 5.34 shows the remeshing zones for the hat section with 7 spot-

welds and all mesh sizes. In the remeshing process, 1 mm element size was

63

initially used. Since the sizes of the elements outside the remeshing zone are

larger than 1 mm, they affect the meshing around the spot-weld. The remeshing

can be done with more elements for the 2 mm mesh compared to the 4 mm

mesh. Additionally, the center of a spot-weld does not coincide with the center of

the remeshing zone; hence symmetry cannot be maintained.

(a) (b) (c)

Figure 5.34 Remeshing zones for 7spot-welds with (a) 2 mm (b) 3 mm and (c) 4 mm mesh

All of the above mentioned issues affect the simulation results of the new,

octagonal spot-weld model. A more sophisticated remesher should be adopted to

help improve the consistency of the new spot-weld model for use in meshes of

different sizes.

CHAPTER 6: CONCLUSIONS

FE modeling of spot-welds is one of the most important issues in

crashworthiness analysis. This study provides a new FE spot-weld model for

use in crash simulations. The new spot-weld model represents the real spot-

welds in vehicles more closely than existing models.

The difficulty in generating spot-weld models for FE analysis lies in the

geometric difference between spot-welds and the residing structure. Current

spot-weld models are created on existing meshes in an FE model. Therefore, the

geometric shape, size, and location of a spot-weld will depend on the existing

mesh. Consequently, the quality of the spot-weld model cannot be guaranteed

and its behavior in crash analysis will be affected. The new spot-weld model is

introduced to eliminate the dependency of spot-welds on existing meshes while

maintaining realistic shapes, sizes, and locations. A computer program is

developed in this study to ease the effort in generating the spot-weld models.

This study focuses on investigating the geometric effect of spot-weld

models and evaluating the performance of the new spot-weld model without

remeshing the entire existing mesh. Using hat sections of different mesh sizes

and a different numbers of spot-welds, the new octagonal spot-weld model is

compared with the commonly used nine-node model for folding patterns,

crushing forces, and energy absorptions.

65

With the same number of spot-welds on fine meshes (e.g., 2 mm), both

the octagonal and nine-node models show similar results. On coarse meshes

(e.g., 3 or 4 mm), the new octagonal model outperforms the nine-node model.

The reason behind this is that the octagonal model is less sensitive to existing

meshes and has a constant spot-weld size. It is also observed that the spot-weld

locations and remeshing around the spot-welds affect the behavior of the new

spot-weld model and deserve further investigation. There are several advantages

of the new spot-weld model:

1. No effect of the component‟s meshes on the size and location of a spot-

weld

2. Better geometric representation compared to the single-point connections

and area connections using quadratic or hexagonal elements

3. Less computational costs by employing coarser meshes on the

components than using more-refined meshes in the current models.

To conclude, the new spot-weld model has advantages of both the single-

point and area-connected spot-weld models in which the former has less

computational cost and the later is more realistic.

As a future scope, the joining sheets with different mesh patterns/sizes

can be analyzed. Also, the remeshing zone can be created automatically using

computer code of better remeshing algorithms.

REFERENCES 1. NCSA, National Centre for Statistics and Analysis, “Traffic safety facts, research note”, http://www-nrd.nhtsa.dot.gov/pdf/nrd-30/NCSA/RNotes/2006/810568.pdf

2. NHTSA, CIREN Program Report 2002, U.S. Department of Transportation, National Highway Traffic Safety Administration, DOT HS 809 564.

3. White M, Jones N, "Experimental study into the energy absorbing characteristics of top hat and double hat sections subjected to dynamic axial crushing", Proc Instn Mech Engrs, Vol. 213(D), 1999, pp. 259-278.

4. Seeger F, Feucht M, Frank Th, Keding B, Haufe A, "An investigation on Spot-weld Modeling for crash simulations with LS-DYNA", 4th LS-DYNA Anwenderforum, Bamberg, 2005.

5. Combescure A, Delcroix F, Caplain L, Espanol S, Eliot P, "A finite element to simulate the failure of weld points on impact", International Journal of Impact Engineering, Vol. 28(7), 2005, pp. 783-802.

6. Fang J, Hoff C, Holman B, Mueller F, Wallerstein D, “Weld modeling with MSC Nastran”, 2nd MSC worldwide automotive user conf, Dearborn, MI, 2000.

7. Fyllingen Ø, Hopperstad O, Langseth M, “Simulations of a top-hat section subjected to axial crushing taking into account material and geometry variations”, International Journal of Solids and Structures, Vol. 45, 2008, pp. 6205-6219.

8. Tarigopula V, Langseth M, Hopperstad O, Clausen A, “Axial crushing of thin walled, high-strength, steel sections”, International journal of Impact Engineering, Vol. 32 (5), 2006, pp. 847-882.

9. Palmonella M, Friswell M, Mottershead J, Lees A, “Finite element models of spot-welds in structure dynamics: review and updating”, Computers and Structures, Vol. 83(8-9), 2005, pp. 648-661.

http://www-nrd.nhtsa.dot.gov/pdf/nrd-30/NCSA/RNotes/2006/810568.pdf

67

10. Deng X, Xu S, “An evaluation of simplified spot-weld models for spot-welded joints”, Finite Element in Analysis and Design, Vol. 40(9-10), 2004, pp. 1175-1194.

11. Chang B, Shi Y, Dong S, “Studies on a computational model and the stresses field characteristics of weld bonded joints for a car body steel sheet”, J Mater Process Technol, Vol. 100, 2000, pp. 171-178.

12. Zhang S, “A simplified spot-weld model for finite element analysis”, SAE World congress, Vol.113, 2004, pp. 375-381.

13. Zhang Y, Taylor d, “Optimization of spot-welded structures”, Finite Element in Analysis and Design, Vol. 37(12), 2001, pp. 1013-1022.

14. Salvini P, Vivio F, Vullo V, “A spot weld finite element for structural modeling”, International Journal of Fatigue, Vol. 22, 2000, pp. 645-656.

15. Henrysson H, “Fatige life predictions of spot welds using coarse FE meshes”, Fatigue Fract Engng Mater Struct, Vol. 23(9), 2000, pp. 737-746.

16. Heiserer D, Charging M, Sielaft J, “High performance, process oriented, weld spot approach”, 1st MSC worldwide automotive user conf, Munich, Germany, 1999.

17. Rusinski E, Kopczynski A, Czzmochowski J, "Test of thin walled beams joined by spot-welding", Materials Processing Technology, 2004, pp. 405-409.

18. Portillo O, Nemes J, “Impact modeling of spot-welded columns fabricated with advanced high strength steels”, JSAE FISITA World Automotive Congress F2006SC39.

19. Donders S, Brughmans M, Hermans L, Liefooghe C, H Van der Auweraer, Desmet W, "The robustness of dynamic vehicle performance to spot-weld failures", Finite Elements in Analysis and Design, Vol. 42(8-9), 2005, pp. 670-682.

20. Song H, Fan Z, Gang Y, Wang Q, Tobota A, "Partition energy absorption of axially crushed aluminum foam-filled hat sections", International Journal of Solids and Structures, Vol.42(9-10), 2005, pp. 2575-2600.

68

21. Stone Donald, “Kinematic Vs Isotropic Hardening”, University of Wisconsin-Madison, MS&EE441, Lecture No #20, Spring 2005

22. Subra Suresh, “Fatigue of materials”, Cambridge University Press, Cambridge, UK, 1998.

23. Becker A.A., “An introductory guide to finite element analysis”, ASME Press, NY, 2004.

24. ABAQUS documentation, http://www.engr.mun.ca/docs/abaqus

25. LS-DYNA Theory Manual, Livermore Software Technology Corp., 2006

26. LS-DYNA User‟s Guide, CAD-FEM GmbH, PWS, Rev. 1.19, 2001

27. Xiang Y, Wang Q, Fan Z, Fang H, “Optimal crashworthiness design of a spot-welded thin-walled hat section”, Finite Element in Analysis and Design, Vol. 42(10), 2006, pp. 846-855.

28. Altair Corporate, http://www.altair.com/Default.aspx

http://www.dynasupport.com/support-1/tutorials/users.guide/contact.modeling/

http://www.altair.com/Default.aspx

finite element spot-weld modeling thesis (crash testing application)

Documents