Validation of models for welding and post weld heat treatment in product development of aerospace components

n O P T O R AT T H F ^ K

Validation of Models for Welding and

Post Weld Heat Treatment in Product

Development of Aerospace Components

Daniel Berglund

Department of Applied Physics and Mechanical Engineering

Division of Computer Aided Design

Components

Daniel Berglund

2003

Division o f Computer Aided Design

Department of Applied Physics and Mechanical Engineering

Luleå University of Technology

SE-971 87 Luleå, Sweden

danielb@cadduth.se

Academic thesis for the degree of Doctor of Philosophy, which with the due permission o f the

Faculty Board at Luleå University of Technology w i l l be defended in public, in room E632,

Studion E-house, Wednesday the 10

of December 2003 at 09.00.

External Examiner: Associate Prof. P. Michaleris, Department of Mechanical and Nuclear

Engineering, Pennsylvania State University.

continued at Volvo Aero Corp the last three and an half years. I have been financed by Volvo Aero

and NFFP

during the whole time of my research which I am very grateful for. It has been a

fantastic opportunity to concentrate on a specific research area during such a long time and I have

many people to be thanked.

First of all I would like to thanks my supervisor, Lars-Erik Lindgren for all his advice, comments

and enthusiasm regarding my work. I would like to thank my colleagues at Computer Aided

Design and at the department of Advanced Manufacturing Process Development at Volvo Aero.

Peter Jonsson for his support in the beginning of the project and Henrik Runnemalm support

especially as a good friend.

A special thanks to my friend and college Henrik Alberg, who I have really enjoined working

with. We have had a lot of interesting discussions both regarding work and other important issues.

Finally, I would like to thank my fiancé Malin, you have been tremendous patient and supported

me, / love you.

achieved by finding a stable process-parameter window for each manufacturing operation and to

choose an order of manufacture, which gives an adequate result. Production planning has

traditionally been carried out from experience and experiments. However, in order to reduce

lead-time and cost, computer based numerical simulations using the finite element method is

increasingly being used. Simulations can give valuable information about component dimensions,

shape, and residual stresses after each manufacturing process. The generated stresses and

deformation at each individual manufacturing step affect the subsequent operation. One example is

welding where stresses are generated in the structure and the level of stress is dependent on the

type of fixture. I f the fixture does not allow the component to move during the operation, then

large residual stresses are generated but the deformations are small. Some of these stresses are

released when the component is taken out of the fixture and others are released when it is

heat-treated. This is one example why production must consider the whole manufacturing chain.

Using combined welding- and heat treatment simulation in the early stages of product

development require a tool, which give result of sufficient accuracy and simulations completed

within an acceptable time. The necessary conditions to f u l f i l the accuracy requirement are dealt

with in this thesis. Both geometrical- and material simplifications are investigated and conclusions

about the effect on full-scale components are drawn.

Before the simulation tool with its simplifications is used in product development, the models have

to be validated. Validation of tools used for manufacturing simulations on component level must

be minimised because of the cost and limited time. A two-stage validation strategy for welding and

post weld heat treatment models is presented. It can be performed in the pre-development stage or

even before a product is planned, and thereby reduces the time needed when simulations w i l l be

used in later stages. The material model is validated separately using a simple experiment

executing the relevant phenomena. In the second validation step, the models for welding and heat

treatment are validated on a test plate using the deformation and residual stress as validation

parameters.

This dissertation includes an introduction and the following papers:

I . D. Berglund, L.-E. Lindgren, A . Lundbäck, Three-Dimensional Finite Element

Simulation of Laser Welded Stainless Steel Plate, Proc: 7

Int. Conf. On Numerical

Methods in Industrial Forming (NUMIFORM), Japan (2001), 119-1123.

I I . D . Berglund, H. Runnemalm, Comparison of Deformation Pattern and Residual Stresses

in Finite Element Models of a TIG-welded Stainless Steel Plate, Proc: 6

Int. Conf.

Trends in Welding Research, USA (2002), 826-831.

III. D. Berglund, H . Alberg, A two-stage Approach for Validation of Welding- and Heat

Treatment Models used in Product Development, to be published.

IV. D. Berglund, H. Alberg, H . Runnemalm, Simulation of Welding and Stress Relief Heat

treatment of an Aero Engine Component, Finite Element in Analysis and Design, Vol 39

(2003), 865-881.

V. H . Alberg, D. Berglund, Comparison of Plastic, Viscoplastic, and Creep Models when

Modelling Welding and Stress Relief Heat Treatment, Accepted at Computer method in

P R E F A C E

A B S T R A C T

D I S S E R T A T I O N

1. I N T R O D U C T I O N 3

L I Background 3

1.2 A i m and Scope of present research 4

1.3 Approach 4

1.4 Manufacturing simulation in product development 4

1.5 Welding in the aerospace industry 5

1.6 Heat treating of metals 6

2. M A T E R I A L A S P E C T S IN W E L D I N G AND H E A T T R E A T M E N T S I M U L A T I O N S . . 9

2.1 Microstructure behaviour and thermal dilatation 9

2.2 Transformation Induced Plasticity (TRIP) 11

2.3 Rate dependent plasticity and creep 12

2.4 Material model in welding and quenching analysis 14

2.5 Material model during stress relief heat treatment 15

3. S I M U L A T I O N O F W E L D I N G 17

3.1 Simulation models in finite element analysis 17

3.2 Heat input model 19

3.3 Joining of material and treatment of filler material 19

3.4 Influence of initial geometry 20

4.2 Cooling sequence 23

5. V A L I D A T I O N O F S I M U L A T I O N M O D E L S 24

6. S U M M A R Y O F PAPERS 28

6.1 Three-Dimensional Finite Element Simulation of Laser Welded Stainless Steel Plate (Paper

I). 28

6.2 Comparison of Deformation Pattern and Residual Stresses in Finite Element Models of a

TIG-welded Stainless Steel Plate (Paper II) 28

6.3 A two-stage approach for validation of welding- and heat treatment models used in product

development (Paper III) 28

6.4 Simulation of Welding and Stress Relief Heat Treatment of an Aero Engine Component

(Paper I V ) 29

6.5 Comparison of plastic, viscoplastic, and creep models when modelling welding and stress

relief heat treatment (Paper V) 29

7. DISCUSSION AND C O N C L U S I O N S 30

8. S C I E N T I F I C C O N T R I B U T I O N 32

1. Introduction

1.1 Background

A large number o f the components in the aerospace industry are complex shaped and

manufactured in high strength material. The tolerance requirements on the dimension and the

shape are often rigorous. The manufacturing of such components is therefore limited to a number

of processes. One major choice is whether the components should be a casting or a fabrication. In

a fabricated structure, the individual parts can be castings but the main structure is created by

assembling different parts to a larger structure. A fabricated structure has a number of advantages

in comparison with large castings. It is for example possible to choose different material for

different parts o f the structure, the minimum thickness is not restricted. Furthermore, the design of

the component is more flexible and the number of potential subcontractors for incoming material

is not limited to only a few companies. The disadvantage is that the manufacturing processes

require a large number of operations and that joining operations such as welding generate

unwanted stresses and deformation.

The generated stresses and deformation at each individual manufacturing step affect the

subsequent operation. One example is welding where stresses are generated in the structure and the

level of stress is dependent on the type of fixture. I f the fixture does not allow the component to

move during the operation, then large residual stresses generated but the deformations are small.

Some of these stresses are released when the component is taken out of the fixture and others are

released when it is heattreated. The accompanying distortion may be so large that the tolerance

requirements after heat treatment are not fulfilled. However, i f the fixture is too loose, then the

deformations during welding will already be unacceptable large. This is one example why the

whole manufacturing chain has to be considered when designing an fabricated structure. More

planning is required for a fabricated stmcture than a large casting because of the larger number of

manufacturing operations involved. The decisions to be taken when a new product is going to be

manufactured are often based on knowledge from earlier projects and from experiments on

simplified components. This requires people with long experience and sufficient development

time. Reducing the lead-time in this process requires efficient simulation tools for prediction o f the

effects of the manufacturing chain. It is possible to use results from these simulations to estimate

the lifetime of a product and thereby also be used for design ofthe product.

1.2 Aim and Scope of present research

The objective of the work presented in this thesis is to find how to use the finite element method

for combined welding and heat treatment simulations in product development. The simulations

will be used for designing and planning the manufacturing processes in order to obtain an

acceptable final shape of the component and a robust manufacturing process. The research

question is formulated as:

How are models of combined welding- and heat treatment giving adequate accuracy created to

support design for manufacturing in the early stages of product development?

The term modelling is in this thesis the preparation of a symbolic device built to simulate and

predict certain aspects of the behavior of a system. Running the symbolic device, in this case a

FE-program is the definition of simulation. Large FE-models are computational demanding for

simulations o f the manufacture of components with complex shape. The result of the simulation

must be o f sufficient accuracy and completed within an acceptable time i f manufacturing

simulations are going to be used in product development. This requires geometrical

simplifications, correct modelling of the boundary conditions and a correct material behaviour in

each process. The validation of the simulation models is therefore another important issue

discussed in this work.

In this thesis, adequate accuracy is the level of result that gives qualitatively correct results and

makes it possible to compare different solutions and describe a general behaviour. Sudnik et al. [1]

have given the following definition of an adequate model. The necessary simulation accuracy must

be defined on the compromise between complexity and accuracy of the physical-mathematical

model. Such an optimised model is termed adequate model. The term acceptable time has a unique

meaning depending on industry and application. In the aerospace industry, a simulation time of

one to a number of days may be an acceptable simulation time.

The processes of interest in this work are arc/beam welding and stress relief heat treatment in gas

cooled vacuum furnaces. These are common in the aerospace industry. Only single pass welding is

studied and the global deformation during the processes is in focus. The material of the studied

objects is limited to one material, a martensitic stainless steel. An effort is made to support the

early stages of product development where different product and process concepts shall be

compared.

1.3 Approach

The work is carried out in close co-operation with participating industry and the research result is

used and evaluated in demonstration projects. The research is performed using both real

components and simplified stmctures. A commercial finite element program is the base tool and a

deductive research approach is used. Known technologies are tested and the limitations of these

models and techniques are investigated when used in welding and heat treatment applications.

1.4 Manufacturing simulation in product development

The finite element method (FEM) has frequently been used by design engineers to calculate

deformation and stresses for the functional analysis. This analysis gives for example stresses and

deformation due to in-service loads. The tools have been developed to support analysis of the

components performance but not for predicting the effect of manufacturing on components. To

develop efficient tools, supporting the evaluation of manufacturing effects, a number of research

issues have to be dealt with. The topics range from design and manufacturing methodology to

constitutive relations of materials and numerical algorithm for solution of equation systems. The

product development of a component, not only in the aerospace industry, can be divided in a

number of phases for both design and manufacturing, see Figure 1. Manufacturing simulations can

be used as a support tool in all phases of the product development. It works both as channel for

communication between design and manufacturing and as a tool for manufacturing engineers to

evaluate different manufacturing sequences (manufacturing planning).

Pre-development

Validation of

simulation tools

Product

Requirements

f

_{Tools for functional evaluation}

)

Concept

Design

Preliminary

Design

Detailed

Concept

Design

Preliminary

Design

Design

i r

Iff

i r

Tools for evaluation of manufacturing effects

1

J l

Inventorv of

Preliminary

_^

Detailed

known methods

preparation

Preparation

Tools for planning of manufac turing

17

Figure 1. Tools and preparation stages in product development.

Because of the requirements of low cost and effective product development, developing

manufacturing processes and simulation tools during product development is strictly limited due to

the short development time.

Validation of tools used for manufacturing simulations cannot be performed on component level

because o f the cost, time and the problem of finding model errors. Validation of simulation models

for manufacturing processes has to be done before the tool can be used as a qualified tool in

product development. The main objective in this thesis is to find suitable models to be used in the

concept design phase and to define a validation approach for thermo-mechanical models in

general.

1.5 Welding in the aerospace industry

The most common welding processes in the aerospace industry are Gas Tungsten Arc Welding

(GTAW), Electron Beam Welding (EB), Laser welding and Friction welding. In the

GTAW-process is the heat produced by an electric arc between a non-consumable tungsten electrode and

the workpiece. An inert gas, argon or helium is used as a shield for corrosion of the weld zone and

the electrode. Filler material can be used and is then added from the side, see Figure 2.

Figure 2. Schematic figure ofthe GTAW-process with external added filler material.

Gas tungsten welding is best suited for welding material with thickness between 0.5 and 3 mm.

Electron beam welding is a method where a concentrated electron beam with a high power

density is used to melt the material. Therefore, the fusion zone is small and the penetration depth is

large. EB has also the advantage o f giving small residual deformation o f the workpiece. It's a

method well suited for butt-welding in thick material, up to 250 mm. The welding operation has to

be done in a low-pressure environment to reduce the retardation of the electrons.

Laser welding is also a method that produces a high energy density beam but the energy source

is a light amplifier. The advantage of laser welding in comparison with EB-welding is that there is

no need for a low-pressure environment and the light can easily be transported from the light

source to the work piece by mirrors or by optical fibre. The most common types for welding is

C O 2 - and Nd:YAG-lasers where the light from the Nd:YAG can be "transported" in an optical

fibre. This is not the case for the C0

-lasers where mirrors have to be used but the method has the

advantage of producing a laser beam with a higher power than in the Nd: YAG-case. Laser welding

is most effective for thin plate applications.

Friction welding does not give a complete melted zone between the individual work pieces. Heat

is generated between the parts due to friction. The applied pressure is removed when the desirable

temperature has been reached. There are a number of procedures for this weld method. One

example is friction welding by using two rotational parts where one of the parts is put in contact

with the other by using a hydraulic cylinder. Friction stir welding is another method where a

consumable rotated tool is pressed onto the workpiece in the same time as the tool is moving along

the butt joint.

1.6 Heat treating of metals

The material in aerospace applications is often chosen because of their heat and corrosion

resistance, fatigue properties and low weight. Depending on the base material of the component,

the heat-treating is done at different temperatures and holding times. In order to describe a number

of common heat treating processes and their purpose, steels are used as an example. Steel is

defined as an alloy o f iron and carbon with the carbon content up to about 2 w t % [2]. Other alloy

elements can be up to 5 wt% in a low-alloy steel and more in a high-alloy steel. Heat treatment is a

general name of a large number of thermal processes where the goal is often to obtain a

satisfactory hardness. Figure 3 shows typical heating ranges in an Iron-Carbon diagram for

different heat treating processes. A\ is the eutectoid line, or the lower critical temperature for

austenite transformation and A

is the upper critical temperature. A

represent the upper critical

temperature for hypereutectoid steels (Steels with more than 0.77 w t % C). The most common

heat-treating processes for steels are described below.

Normalizing

912

727

400

Full Annealing

Tempering

Stress Relief Heat Treating

Figure 3. Iron-Iron Carbide phase diagram showing typical temperature ranges for different heat

treatment operations.

Annealing is a heat treatment process, refers to a material exposed to an elevated temperature

(above the A3 temperature) for an extended period of time, and thereafter cooled down. This is

primarily done in order to soften the material. Ferrite and pearlite are the dominating phases in the

material after the annealing process. I f the cooling rate is increased, then martensite w i l l be

created, this process is called quenching. The hardness of the material is controlled by the amount

of martensite created. The cooling rate and thereby the amount of martensite can be controlled by

the selection of quench medium. Common quench media is water, saltwater, oil, polymer solution

or some inert gas (helium, argon or nitrogen).

Tempering of steel is a process in which previously hardened or normalized steel is heated to a

temperature below the A]-temperature in order to increase ductility and toughness. The difference

between tempering and stress relief heat-treating is that the aim of the tempering operation is to

create a certain microstructure. In the other case, the primary aim is to relieve stresses, but both

procedures are performed in the same temperature interval. Post weld heat treatment is in this

thesis the definition of a process performed after welding and with the objective of reducing

welding residual stresses.

dependent of the required strength and hardness of the material. A t higher cooling rates, more

pearlite is formed and the lamellae are finer and more closely spaced. Larger amount of pearlite

and fine lamellae gives higher strength and hardness. Observe that the cooling rate should not be

as high as for the quenching process where martensite is created.

It is common in the aerospace industry to use vacuum furnaces cooled with gas when performing

quenching and stress relief heat treating of components. In a gas cooled furnace is both the

heating- and the cooling sequence of the heat treatment operation performed in the charge volume.

Gas cooling has therefore an advantage in comparison with liquid cooled furnaces where the

component is quenched in a separate liquid bath. The charge volume is the volume in which the

component is positioned, see Figure 4a.

The gas pressure in kept low during the heating- and holding sequence of the heat treatment

operation in order to reduce oxidation on the surface o f the component. In the heat-treating furnace

in Figure 4 is the cooling gas inlets positioned in the top and bottom of the furnace. The top and

bottom holes are used both as inlets and outlets and this is done by revert the flow every 10

seconds. During one period of time is the top holes used as inlets and the bottom holes as outlets,

and by using a flap is the gas flow direction changed in order to use the bottom holes as inlets. The

heating of the component is mainly due to radiation from the walls of the furnace. These radiators

can be seen in Figure 4.

a) b)

Figure 4. Gas cooled vacuum furnace at Volvo Aero Corp. a) Charge volume with the

2. Material aspects in welding and heat treatment

simulations

A major concern when simulating welding and heat treatment is being able to model the varying

material behaviour. This is further complicated by temperature and rate effects. Also, the evolution

of microstructure during the various processes changes the material properties in response to the

thermo-mechanical history of the material. This can also cause transformation plasticity. The

microstructure, strain rate dependence and non-elastic behaviour are briefly described in the

following sections. Depending on the process studied, a model reflecting the material behaviour is

chosen. The simplest model giving an acceptable result is preferred to reduce material testing and

increase the computational efficiency. The material in all the cases presented in this thesis is a

martensitic stainless steel. The effect of the microstructure behaviour, strain rate and time on the

mechanical response is discussed in the following sections. The models compared in this thesis for

each process is described in Section 2.4 and 2.5.

2.1 Microstructure behaviour and thermal dilatation

The material consists initially of a ferritic and a pearlitic phase. The ferrite/pearlite mixture

changes to austenite when the temperature is increased above the A

-temperature, which is

approximately 850°C. The phase changes can be illustrated by the thermal dilatation shown in

Figure 5. Point 1 represent the A

temperature and Point 2, the start o f the martensite

transformation (M

) due to rapid cooling. Thermal dilation is the sum of the thermal expansion and

the volume changes due to phase changes. The cooling rate in the dilatation test was 0.3°C/s and

represents the lowest cooling rate in the temperature interval between 800°C and 400°C during

welding. Most of the austenite phase transforms to martensite during the cooling sequence of

welding due to the high cooling rate. The simulation of austenite transformation has been done

using two different approaches. In the simplified transformation model (ST-model), only the peak

temperature controls the amount of austenite. A peak temperature higher then the A j-temperature

generated a fully martensitic structure. The phase composition remains unchanged i f the peak

temperature is less then A j . The austenite transformation is diffusion controlled and thereby

dependent on the temperature and time. The nucleation and growth process has been studied by for

example Johnson and Mehl [3], Avrami [4] and Kirkaldy et al. [5].

Figure 5. Thermal dilatation, e'

vs. temperature

In the second transformatiotion model used in this thesis, the calculation o f austenite

transformation for an arbitrary thermal history is based on the theory presented by Kirkaldy et al.

[5]. The rate of transformation is described in Eq. 2.1, according to the expression proposed by

Oddy et al. [6] for low carbon steel. The model will be referred to as the extended microstructure

model (ET-model).

z

(t) = n

V

₍

(

eu(

)-

a

T(T)

(2.1)

-eu(T)-Z

(t)

The parameter z

is the austenite transformation rate, z„ is the volume fraction of austenite, z

the

equilibrium phase composition, and / the time. The material is fully austenised when z

is equal to

one. The material consists of a mixture of ferrite and pearlite at the beginning of the simulation

(z

=0). The parameter r i n Eq. 2.1 is temperature dependent. Oddy et al. [6] used the following

expression Eq. 2.2 for low carbon steel where T

, r

, and n are material constants.

r = T

(T-A

r-

(2.2)

The parameters used in Eq. 2.2 can be estimated from dilatometric tests. In this case, the

equilibrium phase composition z

varies linearly between the A

and ^-temperature. The

transformation rate equation is integrated explicitly and time step splitting is used i f the

temperature increment is too large. Austenite transformation only occurs during heating associated

with the weld operation and the fraction does not decrease until the material transforms to

martensite.

The calculation of martensite fraction is based on Koistinen-Marburger's equation and is

dependent on the maximum austenite fraction z™

created during heating, Eq. 2.3. The

martensite transformation occurs. The latter term is often referred to as the transformation induced

plasticity strain (TRIP) and will be further discussed in the next section.

(i -b'-(M-T)) max i \

zm

=V~

The major advantage of using the extended microstructure model is the smooth transition of the

martensite content in the heat-affected zone during welding. The phase content is used together

with a linear mixture of rule when calculating both the thermal dilatation and the mechanical

properties from the properties of the individual phases.

2.2 Transformation Induced Plasticity (TRIP)

The phase transformations do not only change the material's mechanical properties but also result

in volumetric and deviatoric transformation strains. Deviatoric transformation strains (TRIP) can

be orientated i f an applied stress is present during the phase transformation because the volume

differences between two phases generate microscopic internal stresses. At sufficiently high

stresses, plasticity is induced in the weaker phase; this is often referred to as the

Greenwood-Johnson mechanism, Leblond [7]. Any selective orientation (anisotropic orientation) in the created

martensite due to an external load is ignored, an assumption also used by Vincent et al. [8]. This

mechanism often referred to as the Magee mechanism. From experiments, it is known that

strain evolves in the direction o f the deviatoric stress Sy, Leblond [7]. The expression for

TRIP-strain rate according to Leblond [7] is;

q - l r - f r . . , ) . « ® . * . . , ,2.4)

Desalos [9] used an experimentally developed expression for 0(z);

<t>{z) = z{l-z) (2.5)

Equation 4 also includes a parameter K', an analytical expression for which has been proposed by

Leblond;

* • - - ! - £ (2.6)

Where AV/V (3 -é

) is the change of volume during austenite to martensite transformation and

Oyfpa is the yield limit of the austenite phase. According to Leblond, typical values for K' are

between 50-10"

and 100-10"

MPa"

. The function h in Eq. 2.4 describes the proportionality

between the applied von Mises stress and the transformation strain, it is given in Eq. 2.7.

1 "

cf<0.5-a

("

T,e

+Å£

,z)

"

ä>0.5-a

(

T,e

+Åe

,z)

h{a,a..) = \

1 + 3.5

"

c f 1^

c7

[

T,e

+Ae

,z) 2

In order to obtain an unconditionally stable algorithm, the transformation induced plasticity term

is evaluated implicitly. The deviatoric stress, s

and the function h are therefore evaluated at the

end of each time step. The transformation rate z is calculated in the middle of the increment but

the amount of the new phase z is calculated in the end of the time step.

The effect of TRIP is illustrated for an axial loaded rod in Figure 6. The compressive stress a has

been applied before the M

-temperature and the specimen is cooled with a rate of approximately

10 °C/s. The change of diameter d is registered, the combined transformation strain e

and

TRIP-strain d

represents the y-axis in Figure 6. An increased compression stress during the martensite

transformation generates an increased change in strain.

0,02 -i

Temp [°C]

Figure 6. Different applied compression stresses on a rod-specimen during martensitic

transformation.

2.3 Rate dependent plasticity and creep

In this section, the rate dependency and creep effects of the material are discussed. Plasticity and

creep are both non-elastic phenomena but are associated with different material mechanisms.

Strain-rate dependence is the expression of materials sensitivity to the strain rate. The elastic

properties are assumed to be rate-independent whereas the plastic deformation is rate dependent.

Strain rate dependence for metals results from the balance between strain hardening and dynamic

recovery. Dynamic recovery is the creation of low-energy dislocation structures (sub-grains)

during deformation. The rate of sub-grain development increases with temperature because of the

increase in mobility of vacancies and dislocations [10]. The strain rate dependence of a martensitic

stainless steel at 700 °C is illustrated in a strain rate jump test shown in Figure 7a). The strain rate

varies at three different levels e

, £

and , where £

represents the highest strain rate.

Figure 7. a) Stress response during a tensile test at 700 °C with varying strain rates b) Strain rate

at different stress levels during a creep test at 700 °C.

A higher strain rate increases the resistance to plastic deformation and the stress in a tensile test

increases with an increasing strain rate. The plastic strain rate ejf can be described by a power law

Eq. 2.8 [11], where N and K are temperature dependent material parameters. In Eq. 2.8, a ,

o

represent the equivalent stress and the yield limit, respectively. The driving force for an

increased plastic strain rate is the difference between the stress state and the yield limit.

£

( ö - O >

;V

(2.8)

K

The evolution equation for isotropic hardening is shown in Eq. 2.9. The yield limit is assumed to

be dependent on the temperature T, accumulated equivalent plastic strain e

and the phase

composition z.

cr

(T, £

, z) = a

(T, z) + g , ( r , z)F

+ Q

{T, z)(l - ) (2,9)

The effect of including the strain rate dependence when simulating the welding process w i l l be

discussed in Section 2.4.

Creep is different from plasticity in the sense that the deformation is controlled by the diffusion of

atoms and vacancies, this is not the case for plasticity. The major driving force for creep is

temperature but the deformation is also influenced by the presence of stress [10]. The stress

dependence is shown in Figure 7b). Two different creep models have been used and compared in

this thesis, Norton's creep law [11] and a model referred to as the interpolation creep model.

Norton's law is a special case of Eq. 2.8 where the yield limit is set to zero. The creep strain rate in

the second model is dependent on the stress, temperature and the accumulated inelastic strain and

is not based on a specific equation, but on tabulated values. The creep rate is linearly interpolated

between two values tabulated for different temperatures, plastic strains and stresses. Uniaxel tests

are performed at three different stress levels at a number of temperatures. In Figure 7b), the strain

rate response is shown at three different stress levels at 700°C. The effect of the described models

2.4 Material model in welding and quenching analysis

The conditions during welding and quenching are similar in the respect o f temperature history and

load. The load rate (temperature increase) is higher during welding then during quenching where

the temperature is increased slowly up to the austenite temperature. The cooling rate from the high

temperature area can in some cases be higher during quenching then during welding. A welded

material is exposed to high temperature only for a short time and the creep effect is often ignored

[12]. The material effects and models used in welding analysis are described in this section.

An additive decomposition of the strain rate is used for all material models, Eq. 2.10. The total

strain rate is divided into elastic-, thermal-, plastic-, transformation- and TRIP strain rate

respectively.

£

<°< = e

+ e

+e

+ é"'

+ £

(2.10)

The plastic strain rate can be rate independent or rate dependent and the effect of including

different phenomena is illustrated in a Satoh-test. The test is performed by, heating and subsequent

cooling a specimen uniformly without allowing any movement of the specimen's ends in the axial

direction. The force response at one of the ends is registered and the average stress can be

calculated i f the diameter ofthe specimen is known.

X

F,£

T[°C]

t[s]

b)

Figure 8. a) Stress response during a modified Satoh-test. b) Temperature and strain rate history.

The stress response verses temperature in a modified Satoh-test is shown in Figure 8. The heating

rate was in this case 50°C/s and the cooling rate 20°C/s. The experiment is performed in a Gleeble

machine and the testing procedure is modified to obtain a stable force response. The Satoh-test is

modified in the sense that the axial strain e is controlled and given a negative value during the

heating sequence (compression) and a positive value during cooling.

In the simulations, three different material models have been compared. The Rl-model is a model

with Rate Independent plasticity, the RIT-model is the Rl-model plus transformation induced

plasticity and the RDT-model is based on Rate Dependent plasticity including

transformation-induced plasticity. Microstructure calculation is performed for all models. During the heating

sequence, all of the models show similar response but the maximum compression stress is

significant higher in the RDT-model. The largest difference between the models is observed

during cooling when martensite is created. The Rl-model does not capture the stress response

during the transformation but both the RIT- and RDT model is showing a similar behaviour as the

experiment.

2.5 Material model during stress relief heat treatment

The material is exposed to a temperature slightly below the austenite start temperature during

stress relief heat treatment. The material recovers during the process but no phase transformation

occurs. The heat treatment cycle can be divided into three sequences, heating, hold and the cooling

sequence, Figure 9. Three different combinations of material models are compared in the heat

treatment analysis and the acronyms C l , C2 and C3 are used. The models effect on the global

deformation is investigated in this section.

Holding

temperature

C I , 3-model

Temperature

•

•

- No creep active

- Creep active

C2-model

Temperature

Time

Heating Holding Cooling

sequence sequence sequence

Heating Holding Cooling

sequence sequence sequence

Figure 9. Different procedures for applying the interpolation creep model.

In all cases, a creep model is used in combination with rate independent plasticity, see Eq. 2.11

where e

is elastic strain-, é '

i s thennal-, £

plastic- and e

is the creep strain rate. A n additive

decomposition of these strain rates is assumed.

£

= £

+ £

+ £

+ £

(2.11)

This constitutive relation has earlier been used by Josefson [13] and the independent assumption

between the plastic- and creep strain increment is shown by Otterberg [14] for a 21/4 C r l M o steel.

He showed in his study that that the parameters in the creep law are almost independent o f the

magnitude of the applied plastic strain. The time dependent plasticity (creep), is simulated by the

use of Norton's law [10] and by using the interpolation model described in Section 2.3.

In model C1, the interpolation creep model is activated only during the holding sequence of the

heat treatment cycle, Figure 9 and no creep strain is generated during the heating and cooling

sequence. The only difference between model C I and C3 is that Norton's law replaces the

interpolation creep model. The interpolation creep model is active in all sequences when the

C2-C I - and C2-C3-model during the holding sequence. In Figure 10 is a part of a aerospace component

shown and the change of the axial distance a between the top side of the bearing house and the

flange is studied.

Time [s]

Figure 10. Change in distance a during the stress relief heat treatment using different ways to

apply the creep.

In Figure 10 is the change in a during the heat treatment process shown. Observe that the initial

value of the result parameter a is negative due to the distortion during welding. The result shows

only minor differences in residual deformation when different creep models are used.

3. Simulation of welding

The finite element method has been used since early 1970's in order to predict stresses and

deformations as a result of welding [15-17]. The method has become more commonly used in the

aerospace during the last decade. For example Roberts et al. [18] used welding simulations to

develop a process model for electron beam welding that predict residual stresses and distortion on

compressor assemblies. Simulations of large fabricated components have earlier been done by for

example Rick et al. [19] and Andersen [20]. Large simulation models are computational

demanding and often require long modelling time. This is a problem when performing

manufacturing simulations in the early stage of the product development. Andersen used a

local/global approach where simulations results on a detailed solid model were mapped on a global

shell model. Simplified models may be used to keep the modelling time short when making

preliminary preparation in the manufacturing planning. These models must describe the

deformation behaviour qualitatively correct so that it can be used to indicate whether changes in

the manufacturing are an improvement or not. In the following chapters are different simulation

models discussed, and methods for simulating the heat input and filler material during welding are

shown.

3.1 Simulation models in finite element analysis

Simulations are based on choice of finite element formulation and a corresponding finite element

model. Modelling the welding process includes the representation of thermal- and mechanical

loads, the material behaviour and the choice of geometric model. The type of finite element

formulation and geometric model for welding simulation is discussed in this section. The choice of

geometric model depends on the geometry of the component, the nature of the boundary

conditions and the desirable accuracy of the result. Lindgren [21] has categorised and named the

different accuracy levels. They depend on the scope of the analysis to be performed. A simulation

where the transient strains and stresses are wanted is called an accurate simulation, according to

his definitions.

a) b) c)

Figure 11. Geometrical models in welding analysis, a) 2D-plane strain model, b) 3D-shell model,

c) 3D-solid model.

Geometrical models are shown in Figure 11, a is a plane strain model where the heat source is

moving through the plane, b is a 3D-shell model where the stresses in the thickness direction is

neglected and c is a model with solid elements. The different geometrical models give different

transient deformation behaviour. It is of great importance not only to choose accuracy level but

also to decide what type of deformation mode to be studied as they determine the choice of

geometric model to a subset of the general 3D-solid model. The different deformation modes are

exemplified in Figure 12.

2 )

4

3.2 Heat input model

There are different methods to introduce the thermal load in a welding analysis. One way is to

prescribe the temperature in certain volume of material and adjust the temperature level in order to

obtain an acceptable dimension of the fusion zone (FZ). A more sophisticated method is to use a

double ellipsoid heat source first recommended by Goldak [22] et al. The heat flux is in this case

distributed as a double ellipsoid Different welding processes can be simulated by adjusting a

limited number of parameters.

The double ellipsoid heat source is used for all geometrical models. In the 2D-model, the heat

source is passing through the cross section, as illustrated in Figure 11a. When using a shell model

is the heat input on the top and bottom of the shell. The volumetric heat source is replaced by a

surface heat source and the fraction of energy applied on the top- and bottom side is obtained by

integrating the volumetric heat source and lump the energy on the shell's surface.

3.3 Joining of material and treatment offiller material

Welding can be done with or without filler material depending on the process and requirements

on the weld geometry. Filler material is commonly used in GTA- and laser welding. The

modelling of addition of filler material poses some extra complications in simulation of welding.

Lindgren et al. [23] have compared two different approaches, the quiet element- and the inactive

element technique when performing multipass welding simulations. In the quiet element technique

is the filler material already included in the model in the beginning of the analysis but the

corresponding elements are given low conductivity and stiffness so they do not affect the rest of

the model. The elements corresponding to the filler material are not included at all in the model

until the weld is laid, when using the inactive element approach. Lindgren et al. [23] showed that

both techniques can give the same result but the computational effort was reduced and the

condition number of the stiffness matrix was improved by using the inactive element technique.

In this thesis, only single pass welds are considered and the inactive element technique is used

when modelling the joining of material. One row of elements is deactivated at the start of the

analysis to simulate the gap between the welded plates. The volume of the inactivated element

corresponds to the amount of filler material added during the welding sequence. These inactivated

elements do not contribute to the stiffness matrix but they are active in the thermal part of the

calculation. In Paper I , the elements are activated when the centre of the heat source is one heat

source length from the element edge. This method has been improved to reduce the influence of

the molten material on the global deformation. In Paper I I I , the elements are activated when the

temperature in the beginning of the increment is larger then the melting temperature and when the

temperature increment is less then 0.

The molten material is treated as a soft solid The stiffness or yield limit of the material can only

be decreased to a certain level until numerical problems occurs in the solution procedure. The

value of the lowest yield limit does affect the deformation result. One example is the gap

behaviour when no tack-welds are present. The deformation behaviour o f a point during

GTA-welding is shown in Figure 13 with different minimum yield limit. The measured result is

significant lower then the calculated.

Time [s]

a) b)

Figure 13. a) Position of sampling point, b) Deformation history in the y-direction for a single

point.

3.4 Influence of initial geometry

Depending on weld conditions, instability phenomena can occur during welding. One example is

a welded T-plate shown by Deo and Michaleris [24], where the welding process induces buckling.

Another example is the effect of the initial geometry on the deformation behaviour. The plate

illustrated in Figure 13 a) has been welded using GTAW and with one of the ends clamped in a

fixture. The out of plane deformation behaviour during welding is in this case dependent on the

initial shape of the test plate. By giving the simulated plate an initial positive "butterfly" angle of

1° results in a movement downwards and the opposite behaviour is observed i f the angle is

negative. The out of plane deformation of the sampling point and the definition of the "butterfly"

angle is shown in Figure 14.

e=-i°

6,0

-a) b)

Figure 14. a) Definition o f "butterfly" angle, b) Out of plane deformation of sampling point

4. Simulation of stress relief heat treatment

Detailed heat treatment simulations have earlier been done by for example Donzella et al. [25]

who predicted the residual stresses and microstructure in a solid rail wheel. Thuvander [26]

obtained good correlation between simulated and measured distortion due to quenching of a tool

steel. Combined welding and heat treatment analysis have been done by Josefson [13] who

calculated the residual stresses after post weld heat treatment of a thin wall pipe.

All heat treatment processes can be divided in a number of sequences, Figure 9. The heating

sequence is defined as the time where the furnace temperature is increasing at a certain rate in a

regular- or a low-pressure environment. During the holding sequence is the temperature held at a

constant level in a specific time. The component is then cooled down to room temperature by

using a gas or a liquid.

An important issue in heat treatment analysis is how well the boundary condition of the model

represents the actual process. The heat transfer from the surrounding should give the correct

temperature gradients in the component. The modelling of the heat transfer is described in the

following chapters for each sequence of the heat treatment process.

4.1 Heating sequence

Thermal radiation from the radiating elements on the walls of the furnace provides the heat input

to the component. Heat transfer by convection can be ignored due to the low operating pressure in

the evacuated chamber. The temperature of the furnace is measured by a number of temperature

gauges positioned in the top and bottom of the charge volume. The temperature of the gauges,

which are following a prescribed temperature curve, controls the power input to the heating

elements. A closed-loop control system adjusts the input power to obtain the desired temperature

profile. The gauges are protected by a ceramic envelope shown in Figure 15a), which result in a

lower heating- and cooling rate then on the surface of the inner walls. In the numerical model, the

temperature of the walls is used as a boundary condition.

Figure 15. a) Temperature gauge with protecting envelope, b) Temperature history of furnace

wall and temperature gauge.

In Figure 15b) is the simulated gauge- and wall temperature shown as a function of time. The

gauge temperature is representing the control temperature in the furnace and is determined

depending on heat treatment cycle. It can be observed in Figure 15b) the large difference in

temperature between the wall and the gauge, which is due to the nature of radiate heat transfer and

the thermal inertia ofthe gauge.

The shape of the furnace and components are taken into account when calculating the radiation

view factors in the beginning of the analysis. Figure 16 shows a schematic picture of the heat

treatment model used when simulating the heat treatment cycle for an aerospace component. The

size of the furnace model does not represent the actual size of the furnace, however this

simplification can be done because ofthe properties of radiation for a completely surrounded body

[27]. The heat transfer during the holding sequence is the same, as during heating but the wall

temperature is kept constant.

4.2 Cooling sequence

The cooling of the component is controlled by blowing gas into the charge volume. The gas flow

is changing direction every 10 seconds to produce a uniform cooling of the component. The gas

flow is highly turbulent giving a non-uniform velocity field around the components, which affect

the heat transfer between the gas and the components.

The amount of energy transferred from the components to the gas during cooling is dependent

on two major parameters, the temperature difference between the component surface and the

surrounding, and the heat transfer coefficient h. Lind et al. [28] used Computational Fluid

Dynamic (CFD) simulations to obtain an approximate distribution of the surface heat transfer

coefficient when quenching a steel cylinder in a gas cooled furnace. In this thesis, the heat transfer

coefficient on a components surface calculated using CFD and the result is exported to a finite

element program where the temperature distribution, stress and deformation of the component was

calculated for each time step. It was assumed that the time to reach stationary flow was short, and

therefore h is assumed independent of time for each flow direction.

5 . Validation of simulation models

The question whether a model would be considered validated or not depends on the scope of the

analysis and the required accuracy. Whether a model give results with adequate accuracy [1]

depends on the application and at what stage in product development the result shall be used.

When doing the detailed preparation, the magnitude of the deformation can be important to assure

that the tolerance requirements are fulfilled. In the conceptual design stage, different design and

manufacturing concepts are compared and evaluated. The requirements on the simulation tool

result are then less demanding. The simulation result used in the early stages of product

development is adequate i f it can be used to compare different, design concepts qualitatively to

choose better candidates for further evaluation.

The quality of the result that can be obtained is also coupled to the type of problem studied.

Belytschko et al. [29] have defined an expression called computability, which refers to how well a

physical process can be computed. Belytschko et al. address three major barriers for computability

in a solid mechanics simulation, material model and data, smoothness and stability. Smoothness

includes both smoothness in material data and in the model. A typical example of roughness in a

model is contact-impact phenomena where the load and boundary condition changes abruptly. In

welding and heat treatment models, a thermo-elastic-plastic material is commonly used and

represent the material behaviour with acceptable accuracy at temperature lower then 0.8 o f the

melting temperature. Although, large differences in material data between different batches of the

same material can occur. Welding- and heat treatment models can be defined as smooth problems

i f no contact-impact occurs during the process but stability problems may exist. Buckling

phenomena is one example of instability during welding and heat treatment analysis. Deo et al.

[24] shows an example of buckling distortion of a T-joint configuration because o f the generated

residual stresses due to welding. Predicting the final shape of a structure is difficult i f buckling

occurs. A small perturbation of the boundary condition, load or initial geometry can have large

influence on the deformation behaviour and final shape, this makes the validation process more

complex.

Validation of a thermo-mechanical simulation models for welding and heat treatment can be

performed in a number of ways depending on the chosen result parameters. Oberkampf et al. [30]

give a guideline for validation experiments. "The main issue is to capture the essential physics of

interest, including all relevant physical modelling data, initial and boundary conditions required

by the code". In general, the deformation of the component and reaction forces in fixtures are of

stresses and strains are of interest i f the risk for cracking due to the process is of concern or i f the

lifetime o f the component should be estimated.

Validation on full-scale components is costly and is not possible to carry out during the later

phases of product development because of time constraint. Using different validation techniques to

isolate certain phenomena can be successful when validating simulation models. Oberkampf et al.

[30] describe a validation process for computer fluid dynamics problem where the validation is

decomposed into three steps, subsystem cases, benchmark cases and unit problems. It is of great

importance that the chosen cases can represent relevant phenomena so they can effectively reveal

weaknesses in the model.

Subsystem is the first decomposition of the complete system and can represent part o f the

complete system or a case where only a limited number of the physical processes are involved. In

a mechanical analysis, this can be a geometrical part of the system experiencing the conditions of

the complete model. An example of a subsystem case for validation o f welding is shown in Figure

13a). For benchmark problems, special hardware is fabricated to represent the main features of

each subsystem. Evaluation of mathematical models of a single or few physical phenomena is the

purpose with the unit problems.

A number of different measurements techniques have been used in validation of welding and heat

treatment. Lindgren [12] lists a large number of papers including validation of welding

simulations. Measuring the forces in the fixtures can be done in the case o f welding, but not for

heat treatment where fixtures are seldom used. Using the deformation patterns at certain points or

measuring the shape of the component after each process step is one way o f comparing the result

from the computational model with the real component. Comparing the transient deformations

between the computational model and the measured deformation give information about the

quality of the simulation result. Although, the result does not give any helpful information where

the error occur i f the result of the model is unsatisfactory. Measuring the transient strain field give

better information than the transient deformation because the rigid body motion is not measured,

but the tools and methods for performing this type of measurements on welding and heat treatment

applications are under development and therefore not commonly used.

Another technique is comparing the measured and calculated residual stress. The residual stresses

of welded or heat treated structures can be measured for example by hole drilling, surface contour

measurement, neutron diffraction or X-ray diffraction. Note that acceptable agreement of the

residual stresses does not guarantee adequate deformation result. One example of this is Stone et

al. [31].

Figure 17 and 18 show the proposed strategy for validation of simulation models for welding and

stress relief heat treatment that can be used already in the pre-development phase. The definition

of calibration is the adjustment of a parameter in the model to match a measurement. One example

is the determination of material parameters by matching with tensile tests. The validation process

strategy for welding and heat treatment is divided in two steps, material model and process

validation. The material model is validated using a simple geometry and by using well-known

boundary conditions (benchmark case). In the second step, the thermal boundary conditions and

process parameters are validated. This step is referred to as the process validation step or the

Calibration/

Input data

Validation of

material model

Validation of

process

Unit Case

Benchmark case

Sub system model

Material

Tensile tests

Dilatation test

DSC test

Sub system model

Welding

Heat source cal.

Satoh-test

Stress Response

Cantilever plate

Residual stress

Transient def.

Residual def.

Figure 17. Strategy for validation during the pre-delopment phase of simulation models used for

welding.

The welding validation in Figure 17 has two calibration steps. The first one is the use of material

tests for determining the material parameters of the chosen material model. The other is the

calibration of the heat input in the subsystem case where measured temperatures or profile of the

fusion zone are used as calibration parameters. A thermal model is used for this purpose. The

material model is validated in the benchmark case where the temperature-strain cycle of the

welding is imitated in the Satoh test. The validation of the material is done by comparing the force

response (stress response) at one end of the specimen when exposed to a thermal cycle. The

process model is validated by comparing measured and computed transient deformations on a

certain point or area in the subsystem case. The residual shape and residual stresses in also

compared and used as validation parameters.

Calibration/

Input data

Validation of

material model

Validation of

process

Unit Case

Benchmark case

Sub system model

Material

Tensile tests

Dilatation test

Creep tests

DSC test

Sub system model

Heat Treatment

Wall temp cal.

Relaxation-test

Change of diameter

Cantilever plate

Residual def.

Figure 18. Strategy for validation during the pre-development phase of simulation models used

for stress relief heat treatment.

The heat treatment validation in Figure 18 has also two calibration steps. The first one is the use

of material tests for determining the material parameters of the chosen material model as in the

welding case but the material model is different.

The other is the calibration of the wall furnace temperature, which is modelled as the heat input in

the model. The wall temperature is adjusted until the simulated thermo-couple shows a correct

temperature history. The latter is used by the control system that controls the thermal cycle in the

fumace. The material model is validated in a relaxation test with a thermal cycle similar to the

conditions for a full-scale component and exposed to a varying load. The change of diameter is

used as the validation parameter. The geometry used in the sub system model is the same as during

welding but only the residual deformations are compared with measurements. The validation of

the heat transfer model for heat treatment is not performed during pre-development because the

geometrical aspects o f the component have to be taken into account. The heating rate in a vacuum

fumace is assumed not to affect the final shape of the test plate.

Decomposing the validation process has one major advantage, the material model is "qualified"

before the process is validated. This reduces the uncertainties when running the subsystem cases

and the efforts lies in validating the loads and boundary conditions during the process step.

Both the material and process validation have to be performed i f a new material shall be qualified

because there exist no physical coupling between the heat input during welding and dimension of

fusion zone. The weld process model becomes valid for a particular material, weld groove and

process parameters. The density of a mesh and the time stepping in the subsystem case has to be

similar for the full-scale component to be analysed subsequently as the validation also includes the

control of discretisation errors. Using a coarser mesh and longer time steps for the f u l l system will

introduce more errors and then reduce the value of the validation done.

6. Summary of papers

In the following sections is a review of the appended papers presented. The papers have been

jointly planned and written with corresponding co-authors.

6.1 Three-Dimensional Finite Element Simulation of Laser Welded Stainless Steel

Plate (Paper I).

A three-dimensional model was used to simulate laser welding of two stainless steel plates. The

heat input was simulated as a moving heat source. Elements where activated along the welding

path in order to account for the joining of the material. Large deformations, temperature dependent

material properties, volume changes due to phase changes are included in the model. Experiments

have been performed in order to evaluate the accuracy of the model.

The present author has designed the experimental set-up and carried out the finite element

simulation of the model using parallel computing. The author has also implemented the method of

deactivating/activation elements in the welding model.

6.2 Comparison of Deformation Pattern and Residual Stresses in Finite Element

Models of a TIG-welded Stainless Steel Plate (Paper II).

Comparison between results from 2D, 3D-shell and 3D-solid models are compared in this study.

Both the residual stresses, transient deformation and simulation time are compared on a plate of a

martensitic stainless steel. The test plate is restraint with different degrees of freedom for all

geometrical models.

The present author has performed the modelling and simulations.

6.3 A two-stage approach for validation of welding- and heat treatment models

used in product development (Paper III).

An approach where the validation is separated into two sub-steps to be done before simulating

large-scale components is presented. The material model is validated using a simple geometry and

by using well-known boundary conditions (benchmark case). In the second step, the thermal

boundary conditions and process parameters are validated. A three-dimensional shell model was

used to demonstrate the validation procedure and conclusions are drawn about the applicability on

a large scale-component.