ANALYSIS OF WELDING DISTORTION USING QUALITATIVE AND SEMI-QUANTITATIVE TECHNIQUES

by

Y E Z H O U

B.A.Sc, Civil Engineering, University of British Columbia, 1995

A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF

THE REQUIREMENTS FOR THE DEGREE OF

MASTER OF APPLIED SCIENCE

in

THE FACULTY OF GRADUATE STUDIES

Department of Civil Engineering

We accept this thesis as conforming to the required standard

T H E U N I V E R S I T Y OFWITISH C O L U M B I A

September 1998

Y e Zhou, 1998

In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it

freely available for reference and study. I further agree that permission for extensive

copying of this thesis for scholarly purposes may be granted by the head of my

department or by his or her representatives. It is understood that copying or

publication of this thesis for financial gain shall not be allowed without my written

permission.

Department of C l V ' U &A/f/J &g-)*7

A B S T R A C T

In planning and design of engineering projects, engineers are often required to decide upon a course of action

irrespective of the completeness and accuracy of available information. With the fast development of computer

technology, many numerical analysis tools have arisen to assist engineering decision-making based on complete

design information, which is, however, rarely available at most design stages. Little has been done to help

engineers make sound decisions when complete design information is not available. Qualitative and Semi-

Quantitative Reasoning, a branch in the field of Artificial Intelligence, has the ability of analyzing "ill"-defined

problems using sound and clear arguments which are based on facts. This thesis is an attempt to tackle "ill"-

defined engineering problems with the above mentioned reasoning techniques.

This thesis revolves around the topic of shrinkage and distortion in welded structures. Steel fabrication

frequently involves the joining of components by welding. Each component must be fabricated to particular

dimensional tolerances. Distortion caused by welding is a frequently occurring problem that makes it difficult to

estimate the dimensions of the finished structures and thus increases the fabrication costs. Welding distortion is

a poorly quantified phenomenon controlled by many factors that are difficult to describe numerically. The

characteristics of the distortion problems make the traditional numerical analysis very arduous and expensive to

apply. Due its high complexity, for many years, welding distortion problems have been approached primarily

empirically or by trial and error, and uncertain design factors cannot be effectively considered. In this thesis, a

computer software tool was developed using qualitative and semi-quantitative techniques, attempting to solve

complex welding distortion problems with unclearly specified design factors. With the assistance of this

software tool, it is hoped to make the efforts of predicting and controlling welding distortion become more of a

science rather than an art.

11

C O N T E N T S

ABSTRACT II

CONTENTS Ill

TABLES VI

FIGURES VII

ACKNOWLEDGMENTS IX

1 INTRODUCTION 1

1.1 B A C K G R O U N D l

1.2 W E L D I N G DISTORTION 2

1.2.1 Development of Welding Distortion Analysis 3

1.2.2 Existing Approaches to Welding Distortion Analysis 4

1.3 QUALITATIVE A N D SEMI-QUANTITATIVE REASONING IN ENGINEERING 5

1.3.1 Applying Artificial Intelligence to Engineering 6

1.3.2 Qualitative and Semi-quantitative Analysis 8

1.4 INTRODUCTION TO QUALITATIVE ENGINEERING S Y S T E M FOR W E L D I N G DISTORTION 8

2 WELDING DISTORTION 10 2.1 W E L D E D STRUCTURES 10

2.1.1 Advantages of Welded Structures over Riveted Structures 10

2.1.2 Problems with welded structures 11

2.2 INSIGHTS INTO W E L D I N G DISTORTION P R O B L E M S 12

2.2.1 Residual Stresses 12

2.2.2 Cause of Welding Distortion 14

2.2.3 Types of Welding Distortion 15

2.2.4 Analysis of Distortion in Weldment 17

2.3 N U M E R I C A L A N A L Y S I S OF W E L D I N G DISTORTION 20

2.3.1 One-dimensional Numerical Analysis 20

2.3.2 Finite Element Analysis of Welding Distortion 23

2.4 A N A L Y T I C A L A N D EMPIRICAL F O R M U L A S 25

2.4.1 Transverse Shrinkage - Butt Welds 26

2.4.2 Transverse Shrinkage in Fillet Welds 34

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2.4.3 Angular Changes of Butt Welds 35

2.4.4 Angular Distortion of Fillet Welds 3 6

2.4.5 Longitudinal Shrinkage of Butt Welds 4 2

2.4.6 Longitudinal Shrinkage of Fillet Welds 4 2

2.4.7 Longitudinal Bending Distortion 4 3

2.4.8 Buckling Distortion 4 6

2.5 M E T H O D S OF DISTORTION R E D U C T I O N IN W E L D M E N T S 4 6

2.5.1 Commonly Use Distortion Reduction Methods 4 6

2.6 M E T H O D S OF R E M O V I N G DISTORTION 4 9

2.6.1 Straightening by Flame Heating 5 0

2.6.2 Vibratory stress-relieving and electromagnetic-hammer technique 51

3 Q U A L I T A T I V E A N D S E M I - Q U A N T I T A T I V E A N A L Y S I S IN E N G I N E E R I N G 53

3.1 D E V E L O P M E N T OF Q U A L I T A T I V E A N A L Y S IS 5 3

3.1.1 Qualitative Reasoning 5 3

3.1.2 Semi-quantitative Analysis 5 5

3.2 S O L V I N G PREDICTION P R O B L E M S WITH Q U A L I T A T I V E A N A L Y S I S 5 7

3.2.1 Prediction 58

3.2.2 Refinement 5 9

3.2.3 Discussion 5 9

3.3 THEORIES IN Q U A L I T A T I V E A N D SEMI-QUANTITATIVE A N A L Y S I S IN E N G I N E E R I N G 6 2

3.3.1 Components of Qualitative Calculus 62

3.3.2 Interval Analysis and Constraint-Satisfaction Methods 65

3.4 T H E Q U A L I T A T I V E E N G I N E E R I N G S Y S T E M QES 7 2

3.4.1 Structure of QES 7 3

3.4.2 Qualitative Analysis 7 4

3.4.3 Semi-Quantitative Reasoning 7 6

4 QES W D : A N A P P L I C A T I O N O F Q U A L I T A T I V E A N D S E M I - Q U A N T I T A T I V E A N A L Y S I S IN

W E L D I N G D I S T O R T I O N 78

4.1 INTRODUCTION 7 8

4 .2 S Y S T E M I M P L E M E N T A T I O N 7 9

4.2.1 System Structure 7 9

4.2.2 User Interface 83

4.2.3 Platform and Development Environment 85

4.3 S A M P L E A N A L Y S I S 86

5 C O N C L U S I O N 89

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BIBLIOGRAPHY

T A B L E S

T A B L E 2.1 F O R M U L A E FOR PREDICTION OF T R A N S V E R S E S H R I N K A G E 27

T A B L E 2.2. EFFECT OF VARIOUS PROCEDURES O N T R A N S V E R S E S H R I N K A G E IN BUTT W E L D S 32

T A B L E 2.3 M E T H O D S O F F L A M E - S T R A I G H T E N I N G 50

T A B L E 3.1 QUALITATIVE ADDITION, MULTIPLICATION, A N D N E G A T I O N 63

T A B L E 3.2: R U L E S USED TO G E N E R A T E QUALITATIVE EQUATIONS 64

T A B L E 3.3: B A C K T R A C K I N G E X A M P L E 69

T A B L E 4.1 INPUT P A R A M E T E R S OF S A M P L E P R O B L E M 87

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F I G U R E S

F IGURE 2.2 T Y P E S OF W E L D DISTORTION 16

F IGURE 2.3 P R O C E D U R E OF W E L D I N G DISTORTION A N A L Y S I S 17

F IGURE 2.4 STRIPPED E L E M E N T FOR ONE-DIMENSIONAL C A L C U L A T I O N 20

F IGURE 2.5 L O A D I N G A N D U N L O A D I N G 21

F IGURE 2.6 P R O C E D U R E OF C A L C U L A T I N G TRANSIENT DEFORMATION AT M I D - L E N G T H 22

F IGURE 2.7 C O M P A R I S O N OF DISTORTION - C A L C U L A T I O N VS. E X P E R I M E N T 24

F IGURE 2.8 C H A N G E S OF D E F L E C T I O N DURING W E L D I N G 25

F IGURE 2.9 S C H E M A T I C PRESENTATION OF A T R A N S V E R S E S H R I N K A G E OF A B U T T W E L D IN A S INGLE PASS 28

F IGURE 2.10 T E M P E R A T U R E DISTRIBUTION 31

F IGURE 2.11 I N C R E A S E OF T R A N S V E R S E S H R I N K A G E D U R I N G M U L T I - P A S S W E L D I N G OF A B U T T JOINT 32

F IGURE 2.12 DISTRIBUTION OF T R A N S V E R S E S H R I N K A G E O B T A I N E D IN SLIT-TYPE SPECIMENS WITH D I F F E R E N T

W E L D I N G S E Q U E N C E 34

F IGURE 2.13 T R A N S V E R S E S H R I N K A G E IN F I L L E T W E L D S 34

F IGURE 2 .14 E F F E C T OF S H A P E OF G R O O V E O N A N G U L A R C H A N G E 35

F IGURE 2.15 T H E M O S T S U I T A B L E G R O O V E S H A P E TO M INIMIZE A N G U L A R D ISTORTION IN B U T T W E L D 36

F IGURE 2 .16 P A N E L S T R U C T U R E WITH STIFFENERS 37

F IGURE 2.17 DISTORTION D U E TO F I L L E T W E L D S 38

F IGURE 2.18 PLASTIC P R E B E N D I N G A N D E L A S T I C PRESTRAINING 40

F IGURE 2 .19 E L A S T I C PRESTRAINING FOR R E D U C I N G A N G U L A R DISTORTION OF F I L L E T W E L D S 41

F IGURE 2.20 A N A L Y S I S OF L O N G I T U D I N A L DISORTION IN A F I L L E T - W E L D E D JOINT 43

F IGURE 2.21 I N C R E A S E OF LONGITUDINAL DISTORTION D U R I N G M U L T I - P A S S W E L D I N G 45

F IGURE 2.22 C A L C U L A T E D F I N A L C E N T E R D E F L E C T I O N VS. P R E H E A T I N G T E M P E R A T U R E O F T H E W E B 49

F IGURE 2.23 EFFECTS OF T R A V E L SPEED OF F L A M E O N A N G U L A R C H A N G E A N D T R A N S V E R S E S H R I N K A G E 51

F IGURE 3.1 A P O L Y G O N SOLUTION OF I N T E R V A L A N A L Y S I S 66

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F IGURE 3.2: A N IMPLEMENTATION OF T H E W A L T Z A L G O R I T H M [DAVIS , 1987] 71

F IGURE 3.4: A S A M P L E SOLUTION USING W A L T Z A L G O R I T H M [DAVIS , 1987] 72

F IGURE 3.3: G R A P H I C A L REPRESENTATION OF EXPRESSIONS 74

F IGURE 3 .3A S T R U C T U R E OF Q E S 74

F I G U R E 3.4: F I N A L CONSISTENCY NETWORK 7 6

F IGURE 3.5: A N E X A M P L E OF N U M E R I C A L CONSTRAINT SATISFACTION 77

F IGURE 4.2 S C R E E N C A P T U R E S OF Q E S W D 81

F IGURE 4.3 Q E S W D D A T A B A S E S T R U C T U R E 82

F IGURE 4.4 SECTIONAL PROPERTIES OF T H E S A M P L E GIRDER 86

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A C K N O W L E D G M E N T S

I would like to thank my thesis supervisor, Dr. Siegfried F. Stiemer, for his lucid advice and continual

encouragement throughout my student career at UBC. He helped me keep my standard high and provided me

with the opportunity to explore lots of interesting paths. Special appreciation goes to the engineers at Coast

Steel Fabricators: David J. Halliday, Adjunct Professor, David S. K. Lo and Michael Gedig, in particular, are

sincerely appreciated. I would like to thank my lovely wife, Jian, for putting up with the time I spent exploring

all of those interesting paths, and also my parents, for directing me onto the correct path of life.

The financial assistance from Coast Steel Fabricators, Ltd., National Science and Engineering Research Council

(NSERC), and the Science Council of British Columbia are gratefully acknowledged.

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

This thesis is concerned with an engineering software tool which, using sound logic techniques, can be used to

draw as many conclusions as possible from an ill-defined engineering problem. It is intended for such a tool to

be used by practicing engineers to make and collect guided design decisions, and by engineering students to

comprehend complex engineering problems. This thesis applies the techniques in qualitative and semi-

quantitative reasoning to the problems in welding distortion control.

1.1 BACKGROUND

Because of the incomplete information in most engineering design processes, in particular in the early stage of

design, numerical models are of limited value; instead, qualitative reasoning techniques, which have been

studied in depth in the field of artificial intelligence, are in a systematic way to practical engineering problems.

One of the objectives of this thesis is to incorporate these techniques within an accessible, expandable and

simple framework. Qualitative reasoning techniques are augmented with interval analysis methods, which are

sound procedures for reasoning with partially specified numerical information. In addition to qualitative

reasoning and interval methods, a number of other reasoning techniques are also used. The emphasis of this

thesis has been placed on the ability of the computer to use sound logic to gain insight into a welding distortion

problem rather than just on its ability to manipulate numbers.

The focus of interest lies on the topic of shrinkage and distortion in welded structures. Steel fabrication

frequently involves the joining of various components by welding. Each component must be fabricated to

particular dimensional tolerances. Distortion caused by welding is a frequently occurring problem that makes it

difficult to estimate the dimensions of the finished structure, and thus increases the fabrication costs. Welding

distortion is also a poorly quantified or ill-defined phenomenon controlled by factors that are difficult to

describe numerically. The characteristics of the distortion problems make the traditional numerical analysis

difficult and expensive to apply. Due to the high complexity of welding distortion, for many years, the

1

distortion problems in structural engineering have been approached primarily empirically or by trial and error.

Valuable knowledge from experienced technical staff is often lost because of changes of personnel, and

furthermore of the lack of an effective mechanism for knowledge collection. Therefore, it will be advantageous

to have a software system that is able to accept ill-defined numerical data as analysis input, having the ability of

integrating welding knowledge into a flexible information database. For this reason, qualitative and semi-

quantitative methods for engineering, developed earlier at University of British Columbia ^ ' s 1 9 9 5 ^ a r e used as

the main analysis tool; and a flexible knowledge database will be built to record engineering knowledge.

The focus of this research is to develop a computer software system which is able to provide information on

welding distortion, estimate the quantity of welding distortion, and give advice on welding distortion control.

The software system should also have the ability to gather engineering knowledge cognitively, and to construct a

knowledge database for the improvement of future decision making and also personnel training. The core of the

software system will consist of an analysis module, which will perform qualitative as well as semi-quantitative

reasoning. The software will organize such diverse sources of information as text, numerical data, equations, and

graphics into a coherent, expandable and easily accessible framework. With the development of this software

tool, it is attempted that the prediction and control of welding distortion in structural engineering will become

more of a science rather than an art.

1.2 WELDING DISTORTION

The welding process is used extensively in the fabrication of many structures, including buildings, bridges,

pressure vessels, ships, airplanes, etc. It provides significant advantages over other joining techniques such as

riveting, casting, and forging. Excellent mechanical properties, air and water tightness, and good joining

efficiency are among its outstanding qualities.

There might be, however, possible problems such as residual stresses and shape distortion associated with the

construction of welded structures. When a material is welded, it experiences local heat due to the welding heat

source. The temperature field inside the weldment is not uniform and changes as the welding progresses. The

2

welding heat cycle gives rise to a complex strain field in the weld metal and in the base metal regions near the

weld. These strains, along with the plastic upsetting, can create residual stresses that remain after the welding is

completed. Consequently, shrinkage and distortion can be also produced.

Residual stresses and distortion are highly undesirable effects in welding technology. Thermal stresses during

welding often cause cracking. High tensile residual stresses near the weld may lead to an immediate fracture or

fatigue of the weldment. Compressive residual stresses in the welded plate, often combined with distortion, may

reduce its buckling strength. If distortion occurs in the parts of complex structures that need to be joined, a

mismatch problem may happen. The mismatch increases the possibility of weld defects. Furthermore, if the

parts are forced into alignment and then joined, stresses are locked into the structures. This results in a strength

reduction of the joint under either static loads or cyclical loading. In some extreme cases it may be necessary to

remove any distortion completely before joining. However, correcting unacceptable distortion is often costly

and in some cases impossible.

1.2.1 Development of Welding Distortion Analysis

Since welding distortion is accompanied by many undesirable as well as expensive consequences, it is important

that design engineers can predict the amount of welding distortion before fabrication.

Studies of welding distortion have been conducted since the 1930s [ M a s u b u c h l 1 9 8 0 ] , Spraragen and others have

summarized the results of these early studies in a series of reviews. Naka pioneered in the analytical study of

shrinkage. In his work, most of which was carried out around 1940, he studied analytically and experimentally

how a butt weld shrinks. To avoid mathematical complication, the analysis was kept one-dimensional,

neglecting the change of shrinkage in the welding direction.

During the 1950s, several Japanese investigators, including Kihara, Watanabe, Masubuchi and Satoh, carried

out extensive study programmes on residual stresses and distortion. They concentrated on stress and distortion

in practical joints. In order to analyze their experimental data, they frequently used the concept of

3

incompatibility. A number of empirical formulae on various types of distortion were developed. Most of the

efforts during this period, however, concentrated on the distortion remaining after the welding is completed.

Most of the experiments were on weldments in low-carbon steel and covered electrodes. Since welding

distortion is produced by complex mechanisms, studies performed before approximately 1960 were based on

experiments and analyses of simple cases.

Since the 1970s, with the accessibility of modern computers, interest in analytical simulation has been

revitalized. The analysis of thermal stress was the focus of the first computer-simulation projects on welding

distortion [ T a " i 9 6 4 \ Since then, the emphasis has been on transient metal movement and finite-element methods

for simulation. By using these computer-aided numerical analysis tools, it is now possible to analytically

determine distributions of residual stresses and distortions of weldments in various shapes with reasonable

accuracy.

1.2.2 Existing Approaches to Welding Distortion Analysis

Studies on transient welding distortion started in the 1930s. However, because the computation required for

analyzing transient phenomenon is complex and involving, very limited studies were done. Since modern

computers became accessible to researchers in the 1960s, more studies have been done to analyze welding

distortion numerically.

The first significant attempt to use a computer in the analysis of thermal stresses during welding was done

T a l l [ T a " 1 9 6 1 1 . Tall developed a simple programme on thermal stresses during bead-on-plate welding along the

centerline of a strip. In his analysis only the longitudinal stress was considered and was a function of lateral

distance only. This type of analysis was later designated as one-dimensional. In 1968, based upon Tail's

analysis, Masubuchi developed a F O R T R A N programme on the one-dimensional analysis of thermal stresses

during welding [ M a s u b u c h l l % 8 ^ T/ n j s programme was later modified and improved at Massachusetts Institute of

Technology. However, due to the complexities of welding problems, particularly the complex effects of

inelastic material response and material loading and unloading, this one-dimensional analysis could not be

4

further developed. The attention was the focused on numerical method, especially on the finite element method

that could be applied to the highly nonlinear inelastic behaviour of weld structures.

Hibbitt and Marcal did the first application of the F E M to welding problems [ H i b b i t t ' M a r c a l 1 9 7 2 ] . In their study a

thermo-mechanical model was developed to simulate the G M A W process. This model also accounted for

temperature dependent material properties. Several investigators including Nickell and Hibbitt later used this

model to investigate the welding phenomenon [ N , c k e " ' " , b b m l 9 7 5 ] . Fridman [ 1 9 7 7 ) developed finite element analysis

procedures for calculating stresses and distortion in longitudinal butt welds. Iwak i [ 1 9 7 1 1 developed a two-

dimensional finite element programme for the analysis of thermal stress during bead-on-plate welding.

Most of these analyses, however, share some common deficiencies:

Being very basic, they are all based on relatively simple setup of weldments, which is rarely the case in

actual engineering practice.

They require complete specifications of the welding material, setup, and ambient conditions, which are

seldom available at the design phase of a structure.

Although some of these numerical methods give good predictions on welding distortion, their strict requirements

on input make them less applicable in actual engineering design practice. Therefore, some other effective

approaches should be sought to make existing knowledge in welding distortion available to design engineers.

These new approaches, while adopting all current techniques in numerical analysis of welding distortion, should

also be able to generate prediction results based on partially specified input.

1.3 QUALITATIVE AND SEMI-QUANTITATIVE REASONING IN ENGINEERING

Recent advances in the field of artificial intelligence gradually make the conversion from theories in the

computer science to practical engineering application a reality. In the last two decades, the developments in

qualitative and semi-quantitative reasoning, expert systems, fuzzy logic and artificial neural networks have

created many exciting new areas for engineering applications, where traditional methods are difficult to apply.

5

1.3.1 Applying Artificial Intelligence to Engineering

In general, conventional engineering tools have a common weak area: they require a complete set of numerical

input data before any analysis can carry on. During most engineering design processes, many design parameters

are unknown at first and are gradually determined in the process of completing the design. Engineers are always

contented with the fact that they have to provide parameters based on their experience or intuition, which may

lead to some lengthen trial-and-error cycles and increase the design costs. The recent advances in artificial

intelligence provide many possible solutions to the above problems, and some of them are yet widely adopted in

the engineering applications. The following sections will give an introduction to some of these approaches:

1. Automated Reasoning: make a computer prove theorems in some domain, say, geometry. Qualitative

Reasoning and Semi-quantitative Reasoning are two branches in this area. In combination, these two

approaches can solve incompletely specified engineering problems, and simulate loosely defined

engineering processes.

2. Expert Systems: Expert Systems are the first commercially viable applications of artificial intelligence.

Expert systems have been implemented in many fields and make knowledge presentation more effective

than traditional numerical-only computing tools. Now many Expert Systems perform in day-to-day

operation throughout all areas of industry and government. They attempt to solve part, or perhaps all, of a

practical, significant problem that previously required scarce human expertise.

3. Learning: make a computer operating in areas such as the above learn to improve its performance over

time. The advances in this area have been concentrating on Artificial Neural Networks in the recent years.

By adopting Neural Networks, a computer programme can be trained to solve some engineering problems

which are difficult to describe with equations.

4. Natural Language Processing: make a computer communicate with humans in an everyday language, say,

English or Chinese.

5. Game Playing: make a computer play a game, say, chess.

6. Vision: make a computer, by looking at the photographic image of a scene, interpret what the scene depicts,

say, a kitchen with a running tap.

6

Among the above mentioned areas in Artificial Intelligence, automated thinking, expert systems and learning

can be applied to solve engineering problems.

In the recent years, expert systems are the most frequently used AI applications in the field of engineering.

However, expert systems typically rely on domain-specific heuristic knowledge, and tend to fail ungracefully

when confronted with problems that fall even slightly outside the domain for which the system is intended. The

key fault of most expert systems is their inability to reason using fundamental knowledge of the domain, such as

conservation laws.

The techniques of artificial neural networks (NN) have been progressing quickly in the recently years. An

artificial neural network simulates the mechanism of human brains in a very simplified way. It is a network

consisting of input nodes, output nodes and one or more layers of processing nodes. Through learning

processes, the processing nodes can be configured to direct input information to correct output, for which

explicit relations between input and output are not needed to be specified. In dealing with engineering

problems, N N techniques are most effective at analyzing problems for which equations or any other types of

explicit relationships between input and output are difficult or impossible to obtain. However, a N N

implementation requires a great amount of training before it becomes effectively functional, and its output is

generally unstable before it is adequately trained.

Welding distortion analysis, the focus of this thesis, involves numerical calculations and use of engineering

experience. It requires the adoption of fundamental knowledge and first principles, such as Hooke's Law, as

most engineering analysis. It demands the accountability of any analysis output. For these reasons, qualitative

and semi-quantitative reasoning is an ideal choice because of its ability to accept incompletely specified input,

and its accountability from solid and well developed reasoning techniques.

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1.3.2 Qualitative and Semi-quantitative Analysis

Qualitative analysis has been applied in diverse fields of the physical and social sciences, where precise

mathematical models are difficult to solve analytically or just not available. Qualitative techniques are also often

used in conjunction with precise mathematical models to determine bounds on the behaviour of the models.

Engineers often have to contend with complicated problems whereas only limit amount of information is

available. This makes qualitative analysis an effective tool for engineering designs. In many cases, the engineers

only need to know the bounds of certain behavioural properties instead of the complete, exact solution. In these

cases it is unnecessary to carry out expensive, detailed numerical calculations for such modest requirements.

When numerical analysis is necessary, it may not be warranted because of the amount of uncertainty within the

input data. In many situations, it may be beneficial to use qualitative analysis in the initial stages of analysis, and

to use quantitative analysis later when more detailed information is required. Qualitative analysis can also be

used as a guide for selecting input parameters so as to reduce the number of repetitions of the detailed analysis.

Because engineers are rarely confronted with a situation where purely qualitative information is available, it is

thus also necessary to be able to reason with partial numeric data. Semi-quantitative reasoning is the task of

combining incomplete quantitative and qualitative knowledge. Semi-quantitative reasoning is important to

model-based reasoning tasks such as design, monitoring and diagnosis. A l l of these tasks involve incomplete

knowledge in both qualitative and quantitative forms. There are a number of different representations available

for reasoning with incomplete knowledge of quantities, including bounding intervals, probability distribution

functions, fuzzy sets, and order-of-magnitude relations. This thesis uses bounding intervals to represent partial

knowledge of a real number.

1.4 INTRODUCTION TO QUALITATIVE ENGINEERING SYSTEM FOR WELDING DISTORTION

Qualitative Engineering System for Welding Distortion, or QESWD, is the software tool developed as part of

this thesis. QESWD is a prototype software programme targeted to engineers, technicians and students who

8

need to deal with problems of welding distortion. Using the qualitative reasoning engine, QESWD is able to

analyze welding distortion problems without complete or precise description of the input data. Due to the nature

of welding distortion that the phenomenon cannot be easily accessed numerically, a flexible information

database is set up and integrated into the software to assist users confine the problem and keep track of

knowledge on welding distortion.

The main functionality of QESWD is its ability to compute welding distortion when input parameters are not yet

available or cannot be accurately defined. At early stage of the design, engineers are often lack of such

information as actual welding procedure, welding environment, etc. To worsen the problem, many welding

parameters are impossible to precisely define at all. This scenario makes the conventional numerical analysis

tools difficult to apply. QESWD, on the other hand, has the ability to accept incomplete information at the

beginning of the design and derive all possible outcomes. When more information become available along with

the design progress, users may feed the newly available information into QESWD, which, in turn, will generate

more precise results from the better defined problem.

QESWD has the ability to cognitively store and present the knowledge on welding distortion. When QESWD is

initiated for a new analysis, related knowledge retrieved from a database is presented to help users define the

studied problem and select the methods for further analysis. After the analysis being carried out, users can get

access to all the information related to the programme output. The flexible setup of the information database

also enables the user to append the knowledge stored in QESWD by importing their own experience.

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2 W E L D I N G D I S T O R T I O N

This chapter provides the necessary background information on welding distortion and summarizes the current

methods for control and reduction of welding distortion. The software product QESWD of this thesis was built

upon the knowledge presented in this chapter.

2.1 WELDED STRUCTURES

Welded structures are superior in many aspects to riveted, castings, and forging structures. Therefore, welding

is widely used in the fabrication of buildings, bridges, ships, oil-drilling rigs, pipeline, spaceships, nuclear

reactors, and pressure vessels. Before World War II, most ships and other structures were riveted; today, almost

all of them are fabricated by welding. In fact, many of the structures presently being built, e.g., space rockets,

deep-diving submersibles, and very heavy containment vessels for nuclear reactors, could not have been

constructed without the proper application of welding technology.

2.1.1 Advantages of Welded Structures over Riveted Structures

Welded structures are superior to bolted (riveted) structures in the following aspects:

(1) High joint efficiency. The joint efficiency is defined as:

Fracture strength of a j oint ^ . Q Q Fracture strength of the base plate

Values of joint efficiency of welded joints are higher than those of most bolted joints. For example, the

joint efficiency of a normal, sound butt weld can be as high as 100%, while the joint efficiency of

bolted joints, depending on the bolt diameter, the spacing, etc., can never reach 100%.

(2) Water and air tightness. It is very difficult to maintain perfect water and air tightness in a bolted

structure during service. A welded structure is ideal of structures which require water and air tightness

such as submarine halls and storage tanks.

10

(3) Weight saving. The weight of a hull structure can be reduced as much as 10 and 20% if welding is

used.

(4) No limit on thickness. It is very difficult to efficiently rivet plates that are thicker than 2 inches. In

welded structures there is virtually no limit to the thickness that can be employed.

(5) Simple structural design. Joint designs in welded structures can be much simpler than those in riveted

structures. In welded structures, members can be simply butted together or fillet welded. In riveted

structures, complex joints are required.

(6) Reduction in fabrication time and cost. By utilizing module construction techniques in which many

assemblies are prefabricated in a plant and are assembled later on site, a welded structure can be

fabricated in a short period of time. In a modern ship year, a 200,000-ton welded tanker can be

launched in less than 3 months. If the same ship were fabricated with rivets and a similar effort in

labour and tools would be made, more than a year would be needed l M a s u b u c h l m o \

2.1.2 Problems with welded structures

Welded structures are by no means free from all problems. Some of the major difficulties with welded

structures are as follows:

(1) Difficult-to-arrest fracture. Once a crack starts to propagate in a welded structure, it is very difficult to

arrest it. Therefore, the study of fracture in welded structures is very important. If a crack occurs in a

bolted structure, the crack will propagate to the end of the plate and stop; and, though a new crack may

be initiated in the second plate, the fracture has been at least temporarily arrested. For this reason that

bolted joints are often used as crack arresters in welded structures.

(2) Possibility of defects. Welds are often plagued with various types of defects including porosity, cracks,

slag inclusion, etc.

(3) Sensitive to materials. Some materials are difficult to weld. For example, steels with high strength are

generally relatively difficult to weld without cracking and are very sensitive to even small defects.

Aluminum alloys are prone to porosity in the weld metal.

11

(4) Lack of reliable non-destructive-testing techniques. Although many non-destructive testing methods

have been developed and are in use today, none are completely satisfactory in terms of cost and

reliability.

(5) Residual stress and distortion. Due to local heating during welding, complex thermal stresses occur

during welding; and residual stress and distortion result after welding. Thermal stress, residual stress,

and distortion cause cracking and mismatching; high tensile residual stresses in areas near the weld may

cause fractures under certain conditions; distortion and compressive residual stress in the base plate

may reduce buckling strength of structural members.

Consequently, in order to design and fabricate a soundly welded structure, it is essential to have:

adequate design,

proper selection of materials,

adequate equipment and proper welding procedures,

good workmanship,

and strict quality control.

2.2 INSIGHTS INTO WELDING DISTORTION PROBLEMS

Welding is the process of joining two pieces of metal together by establishing a metallurgical bond between

them. Heating the weld till the liquid state is reached and then allowing the liquid to solidify produces a

continuous joint between the two metal pieces. Although the bond is seamless, the metallurgical properties of

the weld are not the same as those of the original plates. These properties are different near the joint between

the weld material and the host material. This area is called the heat-affected zone.

2.2.1 Residual Stresses

12

Residual stresses in metal structures occur during welding as well as in many manufacturing processes.

Mathematically, they are caused by some singularities in a continuous body, which may be called "dislocations".

Physically, they are those stresses that would exist in a body if all external loads were removed. Various

technical term have been used to refer to residual stresses, such as internal stresses, initial stresses, inherent

stresses, reaction stresses and lockup-in stresses. Residual stresses also occur when a body is subjected to a non-

uniform temperature change; these stresses are usually called thermal stresses.

-:o'c

\ \ \ \ \ \ \

Distortion Due to Heating by Solar Radioation

/

;nsi

o z 1 h

1 I

ress

ion

, Weld

a. E

E / , O

=

Residual Stresses Due to Grinding

Residual Stresses Due to Welding

Figure 2.1 Macroscopic residual stresses on various scales

A dislocation can be on a macroscopic or microscopic scale. Areas in which residual stresses exist vary greatly

in scale from a large portion of a metal structure down to areas measurable only on the atomic scale. Figure 2.1

shows macroscopic residual stresses on several different scales. Residual stresses also occur on a microscopic

scale. For example, residual stresses are produced in areas near martensitic structures in steel since the

martensite transformation that takes place at relatively low temperatures results in the expansion of the metal.

Residual stresses on the atomic scale exist in areas near dislocations. Welding distortion problems are

concerned with macroscopic residual stresses.

The magnitude and distribution of residual stresses in a weld are determined by:

13

Expansion and contraction characteristics of the base metal and weld metal during the welding thermal

cycle.

Temperature versus yield strength relationship of the base metal and weld metal.

Residual stresses in metal structures occur for many reasons during manufacturing. Residual stresses may be

produced:

In many materials including plates, bars, and sections during rolling, casting, forging, etc.

During forming and shaping of metal parts by such processes as shearing, bending, machining, and

grinding.

During fabrication processes, such as welding.

Heat treatments during manufacturing can also influence residual stresses residual stresses. For example,

quenching produces residual stresses while stress-relieving heat treatments reduce redisual stresses. Residual

stresses may be classified according to the mechanisms which produce them:

Those produced by structural mismatching.

Those produced by uneven distribution of non-elastic strains, including plastic and thermal strains.

The magnitude and distribution of residual stresses in a weld are determined by:

Expansion and contraction characteristics of the base metal and the weld metal during the welding thermal

cycle.

Temperature versus yield strength relationship of the base metal and the weld metal.

2.2.2 Cause of Welding Distortion

The temperatures required to melt the weld material cause a non-uniform heat distribution between the weld and

the original plate. When the weld begins to cool, different phases of steel are produced in the heat-affected zone

due to the different cooling rates across the section. The new phases are harder and more brittle than the 14

original plate material. This property of welded joints is a concern for engineers, but it is not the only property

that needs to be considered.

The large temperature differential between the weld material and the base material also produces residual

stresses near the heat-affected zone. When the weld begins to cool, the hot metal tries to contract, while the

surrounding, cooler parts of the base metal prevent it from shrinking. This causes the weld line to be in tension

and the base metal to be in compression. Residual stresses have two major effects: they produce distortion or

cause failure of the weld.

2.2.3 Types of Welding Distortion

Three fundamental dimensional changes that occur during the welding process cause distortion in fabricated

structures:

Transverse shrinkage perpendicular to the weld line.

Longitudinal shrinkage parallel to the weld line.

Angular distortion (rotation around the weld line).

15

(a) Transverse Shrinkage (b) Angular Change

I i J j J i l i i L L L J :

(c) Rotational Distortion

] 1 M )1 1 H 1 11 1 ] 11 ] 1 1 ] II 1 I (d) Longitudinal Shrinkage

(e) Longitudinal Bending (f) Buckling Distortion Distortion

Figure 2.2 Types of weld distortion

These dimensional changes are shown in Figure 2.2 and are classified by their appearance as follows:

Transverse shrinkage. Shrinkage perpendicular to the weld line.

Angular change (transverse distortion). A non-uniform thermal distribution in the thickness direction

causes distortion (angular change) close to the weld line.

Rotational distortion. Angular distortion in the plane of the plate due to thermal expansion.

Longitudinal shrinkage. Shrinkage in the direction of the weld line.

Longitudinal bending distortion. Distortion in a plane through the weld line and perpendicular to the plate.

Buckling distortion. Thermal compressive stresses cause instability when the plates are thin.

Shrinkage and distortion that occur during the fabrication of actual structures are far more complex than those

shown in Figure 2.2. For example, when a long butt joint is welded by the step-back sequence, the transverse

shrinkage is not uniform along the weld as shown in Figure 2.2 (a). When longitudinal shrinkage occurs in a

16

fillet-welded joint, the joint will bend longitudinally unless the weld line is located along the neutral axis of the

joint. Whether or not a joint is restrained externally will also affect the magnitude and form of distortion.

2.2.4 Analysis of Distortion in Weldment

There are many factors that contribute to the total distortion in a weldment. These factors, their interaction, and

their effect on the total distortion are shown in Figure 2.3. This figure depicts that distortion in a welded

structure is a function of the structural parameters, the material parameters and the fabrication parameters.

Structural parameters

Geomet ry , of Structure

Plate Thickness

Joint Type

Material parameters

Base-Plate Mater ia l

FilierrMetal mater ial

Fabr icat ion pa ramete rs

Weld ing p rocesses

Procedure pa ramete rs

Assembty parameters

(1 ] Determine Dimensional C h a n g e s ih E a c h We ld

a . analysis of Heat Flow

Extremely Difficult

Y b. Analysis of Thermal

Stresses a n d Incompat ib le Strains

c : Analysis of Residual Stress a n d Distortion

Angular . C h a n g e

Transverse Shrinkage

Longitudinal Shrinkage

C o m p l e x We ldment

(2) Determine.Distortion I nduced in the Weldment

(3)' C o m b i n e All D imensional C h a n g e s a n d I nduced Distortion

Simple We ldment

Total Distortion 1 Figure 2.3 Procedure of welding distortion analysis [Masubuchi 1980]

The structural parameters include the geometry of the structure (whether it is a panel stiffened with frames, a

cylinder, a spherical structure, etc.), plate thickness and joint type (whether it is a butt joint, fillet joint, etc.).

17

The material parameters include types and conditions of base plate and filler-metal materials.

Among the fabrication parameters are the welding processes, including shielding metal-arc, submerged arc,

G M A , GTA, and others; the procedure parameters: welding current, voltage, arc travel speed, preheat and inter-

pass temperature, etc.; and the assembly parameters: welding sequence and degree of constraint, among others.

To determine residual stresses and distortion analytically, it is necessary to establish analytic relationships

among these three sets of parameters and distortion. This can be done by:

1. Determining dimensional changes produced in the structure by each weld.

2. Determining distortion induced in the structure by these dimensional changes.

3. Combining all dimensional changes and induced distortions.

For a simple weld, the second and third steps are not necessary.

The first step, the determination of dimensional change in each weld, can be further divided into the following:

Analysis of heat flow.

Analysis of thermal stresses during welding to determine incompatible strains that do not satisfy the

condition of compatibility of the theory of elasticity.

Determination of dimensional changes, including transverse shrinkage, longitudinal shrinkage, and angular

change, induced by the incompatible strains.

In fusion welding a weldment is locally heated by the welding heat source. During the thermal cycle, the

weldment is subjected to thermal stresses. When the weld is completed, incompatible strains remain in regions

near the weld. Incompatible strains, which include dimensional changes associated with solidification of the

weld metal, metallurgical transformations, and plastic deformation, are the sources of residual stresses and

distortion. When welding processes and parameters are changed, the heat flow patterns are also changed. The

18

change in heat-flow pattern causes a change in the distribution of incompatible strains, and this causes changes

in shrinkage and distortion. A number of articles have been published on the subject of heat flow, and, although

not an easy problem, it can be handled analytically.

It is difficult to determine the distribution of incompatible strain. When a material undergoes plastic

deformation, the stress-strain relationship is not linear and the plastic properties of the material change with the

temperature. Even with the use of the computer, however, no complex geometric analysis has ever been made

for practical weldments.

When the incompatible strains are determined, analytically or experimentally, the third stage in determining

dimensional changes can be handled analytically. Moriguchi 1 1 9 4 8 1 has developed a fundamental theory

concerning stress caused by incompatible strains, and Masubuchi has applied Moriguchi's theory to the study of

residual stress and distortion due to welding.

Assuming that the dimensional changes in the welds are found either analytically or experimentally, the second

step is to determine the distortion induced in the structure by these dimensional changes. The solution to this

problem is rather straightforward. Although plastic deformation is produced in small areas near the weld, most

of the remaining material in the structure is elastic. Consequently, the induced distortion can be analyzed by

elastic theory. Solutions for a large number of boundary conditions are already available. The elastic theory

equations used to determine the induced distortion are independent of fabrication parameters and involve only

well-established material parameters. Thus, after the first experiments, the induced distortions can be readily

calculated for all types of materials.

19

2.3 NUMERICAL ANALYSIS OF WELDING DISTORTION

2.3.1 One-dimensional Numerical Analysis

One-dimensional analysis employs the method of successive elastic solutions to calculate the transient strains,

transient stresses, distortion, and residual stresses during welding. This method was first developed by Tall and

later improved by Masubuchi.

X+AX

Figure 2.4 Stripped element for one-dimensional calculation

A simple model for a one-dimensional analysis is illustrated in Figure 2.4. To analyze the stress state of the

plate cross section, a narrow strip element perpendicular to the weld line is cut out as shown. Both edges of the

strip at x and x + Ax remain straight, the same as the assumption used in the simple beam theory.

A basic assumption inherent in the on-dimensional stress analysis is that a y = x x y = 0. The stress equilibrium

equation in the absence of any external forces is thereby reduced to a single equation:

3 a r 3 x

= 0 (Formula 2.1)

20

This indicates that o~x cannot vary in the direction of the weld. It should be pointed out here, however, that the

temperature distribution does vary in this direction and consequently so does o~x. Hence, the one-dimensional

model does not satisfy the equilibrium conditions. It is further assumed that at time t, the strip is a part of an

infinitely long plate subject to the same temperature over its entire length.

If a single longitudinal position is considered, the entire welding process may be divided into a number of time

steps. During each time step, the transverse temperature distribution is assumed to remain constant at the

observed longitudinal position. At each new time step, the temperature is changed and a new stress distribution

is obtained. Each time step is the fixed system corresponded to a given transverse strip in the moving system.

The width of each strip is the product of the length of time step and the speed of the arc. The stress at each time

step is calculated using the method of successive elastic solutions.

e e

Figure 2.5 Loading and unloading

During the calculation of the total strains at each time step, the accumulated plastic strains from previous time

steps are included to account for possible elastic loading and unloading (Figure 2.5). This is important in the

case of welding, where the complex uneven temperature distribution present in the plate gives rise to complex

stress histories.

21

2.4 @ x = mid length

Once the transient strains are calculated, it is possible to calculate the transient distortion of the weld plates.

Figure 2.6 illustrates the procedure for determining transient distortion.

Computer programmes have been developed by Vitooraporn [ l 9 9 0 1 and other researchers. These computer

programmes can take into account the temperature dependence of all material properties and any type of strain

hardening, and can solve all bead-on-plate, bead-on-edge, and butt welds of flate plates with finite width. The

output of each time step consists of the total strain, mechanical strain, plastic strain, and stress at each of the

predetermined points located at various transverse distances from the weld line.

22

2.3.2 Finite Element Analysis of Welding Distortion

In order to improve the accuracy of the distortion prediction, the existence of the transverse stress, a y near the

weld line cannot be neglected. Thus, a two-dimensional model should be considered. In the plastic-elastic

region, the only possible mean is the use of finite element method.

The governing incremental finite element equation for the problem can be written as:

K(M) [t + At] AU(0 = R[t + At] - F ( M ) [t + At] (Formula 2.2)

where

AT(M)[f + Af] = tangent stiffness matrix at time t + At which includes the linear and nonlinear

strain stiffness matrices.

R[t + At] = vector of externally applied force at time t + At.

F ( M ) [ f + At] = vector of nodal point force due to element internal stress at time t.

= increment in nodal point displacement in iteration i : U(,) [t + At] - U(' l)[t + At].

The term F ( M ) [ f + Af] can be evaluated for the materially nonlinear as follows:

(Formula 2.3)

where

BTL[t] = Constant strain-displacement transformation matrix.

0.02

-0.02 1 1 1 1 1 1 0 100 200 300 400 500

Time, sec

Figure 2.7 Comparison of Distortion - Calculation vs. Experiment ( V i t o o r a P r n 1 9 91

Figure 2.7 shows an example of calculated distortion compared with the experimental results. The 1-D

analytical analysis tends to shift the peak distortion further away from the one predicted by finite element

method and experiment. Furthermore, the 1-D analytical analysis tends to overestimate the peak distortion.

This result can be attributed to the higher temperature as well as slower cooling rate calculated from the

analytical analysis. A good correlation can be obtained between the results from finite element calculation and

experimental data. The degree of good correlation, however, varies with different materials. This can be

attributed to the accuracy of the material property data obtained at elevated temperatures for each material.

In summation, the same physical behaviour of the specimen in experiments can be obtained from the numerical

analysis. The discrepancy between the calculated results and the experimental data can be attributed to the

accuracy of the input data such as material properties, heat source distribution, finite element mesh, assumptions

made in the analysis, etc. It should be mentioned that the phase transformation does not include in both one-

dimension analysis and finite element analysis for this investigation. This will be the case, however, when poor

agreement is observed between experimental data and calculated results. Nevertheless, this is another source of

error.

24

2.4 A N A L Y T I C A L AND EMPIRICAL FORMULAS

There are several ways to analyze residual stresses and distortion. The orthodox method is analytical

simulation. This approach makes it possible to study not only distortion after welding is completed, but also

transient metal movement as well, which is desirable. It is important to follow the metal movement, because

distortion during welding and distortion after welding is completed are quite different. For example, Figure 2.8

shows change of deflection during welding along the longitudinal edge of rectangular plate. Distortion during

welding is opposite to the distortion after welding is completed.

However, analytical simulation is too complex a method to be useful in very many situations. Computer

programmes with strict input requirements are needed to calculate the transient distortion, even in simple cases,

such as a weld along the edge of a rectangular plate. The determination of the incompatible strains produced

during welding in regions near the weld is the step that makes the analysis so complex.

25

If one is concerned only with the distortion that remains after the welding is completed, analytical simulation is

unnecessary. In this case the distortion is treated as an elastic stress field containing incompatible strains. The

mathematics involved is relatively simple, which makes this approach useful in analyzing actual practical joints.

In the following sections, analytical or empirical formulas for distortion calculation of all types of weld details

are discussed.

2.4.1 Transverse Shrinkage - Butt Welds

The mechanisms of transverse shrinkage have been studied by several investigators including Naka and Matsui

[1964] j j i e m o s t j m p 0 r t a n t f m c ] i n g 0 f their mathematical analyses is as follows: The major portion of transverse

shrinkage of a butt weld is due to contraction of the base plate. The base plate expands during welding. When

the weld metal solidifies the expand base metal must shrink, and this shrinkage accounts for the major part of

transverse shrinkage. Shrinkage of the weld metal itself is only about 10% of the actual shrinkage.

The major factors that cause this non-uniform transverse shrinkage in butt welds are:

Rotational distortion. When welding is conducted progressively from one end of a joint to the other, the

unwelded portion of the joint moves, causing a rotational distortion, as shown in Figure 2.2 (c). The

rotational distortion is affected by the welding heat input and the location of tack welds.

Restraint. The amount of transverse shrinkage that occurs in welds is affected by the degree of restraint

applied to the weld joint. The amount of shrinkage decreases as the degree of restraint increases.

The welding sequence has a complex effect on the rotational distortion and the distribution of restrain along the

weld.

26

Empirical and Analytical Formulas

Many investigators have proposed formulas for the estimation of transverse shrinkage of butt welds, which by

and large are based on empirical information. These formulae are listed in Table 2.1.

Table 2.1 Formulae for prediction of transverse shrinkage

Malisius's formula 1 1 9 3 6 1

S=LK + X-yb S,

S: axial shrinkage perpendicular to the weld, mm.

X\ \ linear thermal expansion of the bar from T0 to (T\-TQ)/2, about 0.004.

T0: initial temperature of the bar T\. temperature above which the material is no longer elastic

(Ti>7b) Xq,: linear thermal expansion of the weld from To to Ti, about

0.0093 Q: cross-section of weld including reinforcement, mm 2, Si: average thickness of bars, mm. B: average breadth of weld, mm. K: a constant depending on the thermal output of the welding

process and the thermal conductivity. 43 for arc welding, bare electrodes (S=1.0 mm), 45 to 55 for coated electrodes (S=1.4 mm average), 64 for atomic-hydrogen welding (S=1.4 mm), 75 for oxyacetylene welding (S=1.7 mm).

Capel's formula 1 1 9 6 2 1

. . K x W x l O 3 Al =

sxu

Al: transverse shrinkage, mm. s: thickness of layer of weld metal, mm. u: welding speed, cm/min.

W: electric power of welding arc, 7xV I: welding current, amperes. V: arc voltage, volts. K: constant dependent on materials,

20.4 for aluminum,

22.7 for stainless steel, 17.4 for carbon steel.

Cline's formula 1 1 9 6 5 1

Al = 0.1(77-0.230)

Al: transverse shrinkage, in. t: plate thickness in.

27

Analytical Analysis

Figure 2.9 is a schematic presentation that shows the changes of transverse shrinkage in a single-pass butt weld

in a free joint after welding. Shortly after welding, the heat of the weld metal is transmitted into the base metal.

This causes the base metal to expand, with a consequent contraction of the weld metal. During this period the

points of sections A and A ' do not move. When the weld metal begins to resist the additional thermal

deformation of the base metal, parts of sections A and A ' , begin to move in response. The starting time of the

movement of A and A ' is indicated by ts.

(a) t = 0

(b) t - tc

(c) t > te

(d) t =

A x * - A '

m m w *-L/2

i n *-L w /2 nsw/2

i n A 1 :i"

1 * 1 ^ (

T i i

J-8,/2 i

i I A S S/2- -(L.S5*Sr-lj

2 i \ !* S/2-J L / 2

Figure 2.9 Schematic Presentation of a Transverse Shrinkage of a Butt Weld in a Single Pass ' M a s u b u c h i 1 9 8 0 '

Based on the above illustration, the transverse shrinkage can be calculated as followed:

28

/ 2 , ^ s , l , &: Thermal expansion of the base metal at t = ts. a(T) T(ts, x) - a(T0 )-T0\-dx 8: Additional thermal deformation fo the base

Sx=2j\

8 = 2J\a(T) T(t, x)-a(T0)- T(ts, x)] dx

Sw = [a(TM )-TM-a(T0)-T0\Lw S- Transverse shrinkage. a{T): Thermal expansion coefficient.

metal caused in A A ' at t > ts.

5 W : Thermal contraction of the weld metal at t > ts.

0, for0

From the equation 2.5, it can be seen that the final shrinkage decreases with an increasing thickness, which was

verified by Matsui's experimental data. But it should be emphasized that this is true only if the same amount of

heat input is used, regardless of the joint thickness. Welding thicker plates may require more than one pass,

which introduces more heat input.

Effect of Materials

The amount of transverse shrinkage is different for the various materials. For example, compared to steel,

aluminum alloys, because of their higher heat conductivity and thermal expansion coefficients, shrink more. It is

well known that transverse shrinkage in aluminum welds is greater that that in steel welds.

Phase transformation of ferrous materials also plays an important role. Ma t su i [ 1 9 6 4 ! has proposed that the

expansion due to phase transformation should be subtracted from the estimated shrinkage in order to predict the

real shrinkage.

Effects of Restraint and Forced Chilling

It is known that transverse shrinkage decreases when a joint is restrained. Iwamura [ 1 9 7 4 1 investigated how

restraint and forced chilling affects the transverse shrinkage of butt welds in aluminum alloy. Both computer

analysis and experiments showed that the restraint reduced the amount of shrinkage by about 30%. Chilling,

however, were not proven to be a effective way to reduce shrinkage.

30

800

DISTANCE FROM CENTERLINE (mm) 0 10 20 30

1

r 6oou

H 400^ < tr. Ul a.

5 200h

T" T

0 \ t 10 sec.

t = 60 sec. N N

^ CHILLED ZONE _|o

400

300"

rr 200< tr ui a.

ioo l

0 0.5 1.0 DISTANCE FROM CENTERLINE (in.)

Fee Joint

Figure 2.10 Temperature Distribution

Iwamura's tests were carried out on plated as illustrated in Figure 2.10. The chilling had little effect on the

temperature distribution in the early stages of welding, e.g. the first 9 seconds, but lowered the temperatures at a

later stage, e.g., after 60 seconds. The mathematical analysis indicates that the temperature distribution in the

joint after the weld metal solidifies has a critical affect on transverse shrinkage. In order for the chilling to be

effective, it is therefore important to alter the temperature distribution before the weld metal solidifies. But

although this was possible, it was too late to effectively reduce transverse shrinkage.

Effects of Welding Procedures

Table 2.2 shows the effects of various procedures on transverse shrinkage in butt welds.

31

0 5 10 15 20 25 0 0.5 1.0 1.5 Weight of Weld Metal perUnit Log ! 0 w

Weld Length (w),gr/cm

a. Increase of Tronsverse Shrinkage in b. Relationship Between' log w and u Multipass Welding

w: Weight of weld metal per unit weld length (H>), gr/cm. t u: Transverse shrinkage (u), mm.

Figure 2.11 Increase of Transverse Shrinkage During Multi-pass Welding of a Butt J o i n t [ M a s u b u c h i 1 9 7 0 1

Figure 2.11 shows schematically how the transverse shrinkage increases during multi-pass welding. Because the

resistance against shrinkage increases as the weld gets larger, shrinkage was pronounced during the early weld

passes but diminished during later passes.

Table 2.2. Effect of various procedures on transverse shrinkage in butt welds

Procedures Effects

Root opening Shrinkage increases as root opening increase. Effect is large. Joint design A single-vee joint produces more shrinkage than a double-vee joint. Effect is

large.

Electrode diameter Shrinkage decreases by using larger-seized electrodes.. Effect is medium. Degree of constraint Shrinkage decreases as the degree of constraint increases. Effect is medium. Electrode type Effect is minor. Peening Shrinkage decreases by peening. Effect is minor.

Rotational distortion of Butt Welds

Rotational distortion is affected by both heat input and welding speed. When Vi-in. thick mild steel plates are

welded using covered electrodes at a low welding speed, the unwelded portion of the joint tends to close. When

32

steel plates are welded using the submerged-arc process, the unwelded portion of the joint tends to open. This

means that the tack welds used must be large enough to withstand the stresses caused by the rotational distortion.

Rotational distortion causes two problems:

Rotational distortion is one component involved in the transverse shrinkage of a butt joint, especially in a

long butt weld. When studying how the welding sequence affects the transverse shrinkage in a long butt

weld, the effects of rotational distortion must be considered. The largest amount of rotational distortion

occurs during the first pass, when the unwelded portions of the joint are relatively free.

The separating force produced by the rotational distortion can be large enough to fracture the tack welds

and crack portions of the weld metal.

How Welding Sequence Affects Transverse Shrinkage

Several steps are involved in the welding of a long butt joint. A variety of welding sequences may be used.

These welding sequences are of two types:

The block-welding sequence. The joint is divided into several blocks. Each block is welded separately, in

turn.

The multi-layer welding sequence. Each layer is welded along the entire joint length before any of the next

layer is begun.

Both types have many variations.

It is often found that rather uneven transverse-shrinkage distributions were obtained with block-welding

sequence whereas the shrinkage distribution obtained with the multi-layer sequence was much more even.

Welding using different arrangement of block sequencing often gives approximately the same distortion. Figure

2.12 shows an example of influence of weld sequencing.

33

Welding Blocks

1.0

0.8

0.6

0.4

0.2

- - -

/ ^

// | Left .

T^W I Block

V

\ / - - y - ( i K i H 2 )

[-100 i

\ . Center .

Block Right Block

Figure 2.12 Distribution of Transverse Shrinkage Obtained in Slit-type Specimens with Different Welding

Sequence

Shrinkage Shrinkage

Figure 2.13 Transverse Shrinkage in Fillet Welds

2.4.2 Transverse Shrinkage in Fillet Welds

A fillet weld undergoes less transverse shrinkage than a butt weld (Figure 2.13). Only a limited amount of study

has been done on transverse shrinkage in fillet welds. Spraragen and Ettinger [ 1 9 5 0 1 suggested the following

simple formula:

For tee-joints with two continuous fillets:

, leg of fillet Shrinkage x 1.016 mm thickness of plate

(Formula 2.6)

34

For intermittent welds, use correcting factor of proportional length of fillet to total length.

For fillets in lap joint (two fillet welds):

Shrinkage leg of fillet

xl.0\6mm (Formula 2.7) thickness of plate

2.4.3 Angular Changes of Butt Welds

Angular change often occurs in a butt weld when the transverse shrinkage is not uniform in the thickness

direction. A thorough investigation has been made of how various welding-procedure parameters, including the

shape of the groove and the degree of restraint, affect the angular change in butt welds.

During a groove welding, a mild increase of angular change was observed in the earliest stage of welding on the

first side. The increase of angular change became greater in the intermediate stage, and then mild again in the

final stage. The back chipping did not affect the angular change. Angular change in the reverse direction was

produced during the welding of the second side. The angular change that remained after the welding was

completed depended on the ratio of the weld metal deposited on the two sides of the plate. Since the angular

change increased more rapidly during the welding of the second side, the minimum angular change was obtained

in the specimen that had a little larger groove in the first side. Some researchers proposed that the angular

change could be minimized for a butt joint having a (hi+1/2h3) to h ratio of approximately 0.6 (Figure 2.14).

.60.

Figure 2.14 Effect of Shape of Groove on Angular Change

35

An extensive programme was conducted by the Shipbuilding Research Association of Japan on angular change

in butt welds. Figure 2.15 shows the groove shape that most successfully minimized angular change in butt

welds of various thickness. Curves are shown for situations with and without strongbacks. For example, when

the plate thickness is 20 mm, the ratio of hi and h 2 that gives the minimum distortion when the joint is free is 7

to 3. In terms of the weight of the deposited metal, the Wi / w 2 ratio is approximately 49 to 9.

2.4.4 Angular Distortion of Fillet Welds

The panel structure, a flat plate with longitudinal and transverse stiffeners fillet welded to the bottom, is a typical

structural component in ships, aerospace vehicles, and other structures. An example of such panel structures is

shown in Figure 2.16.

36

Figure 2.16 Panel Structure with Stiffeners

The major distortion problem in the fabrication of panel structures is related to out-of-plane distortion caused by

angular changes along the fillet welds. Corrugation failures of bottom shell plating in some welded cargo

vessels are believed to be caused when excessive initial distortion reduces the buckling strength of the plating.

When longitudinal and transverse stiffeners are fillet welded as shown in Figure 2.16, the deflection of the panel,

8, changes in both the x-direction and y-direction. Because of the mathematical difficulties involved in two-

dimensional analysis, most studies conducted so far have been one-dimensional.

Distortion Calculation

Figure 2.17 shows the typical out-of-plane distortion found in two types of simple fillet-welded structures. In

both cases, the distortion is one-dimensional. When a fillet joint is free from external constraint, the structure

bends at each joint and forms a polygon. But if the joint is constrained by some means, a different type of

distortion is produced. For example, if the stiffeners are welded to a rigid beam, the angular changes at the fillet

welds will cause a wavy, or arc-form, distortion of the bottom plate.

37

A. Free joint

RIGID BEAM ///////////////////////////////////a

BOTTOM PLATE

B. Constrained joint (framed structure )

Figure 2.17 Distortion Due to Fillet Welds

Masubuchi et al i m t ' 1 found that the wavy distortion and resulting stresses could be analyzed as a rigid-frame

stress problem. In the simplest case in which the sizes of all welds are the same, the distortion of all spans are

equal and distortion, 5, can be expressed as follows:

angular change at a fillet weld, radians,

angular change of a free fillet weld (ref.0.280)

length of span

rigidity of bottom plate

coefficient of rigidity for angular changes

(Formula 2.8)

5 = a . [ I_ (_O. 5 ) 2 ] .0 4 a

0=-1 +

0o 2D aC

0: fo-ci: D: C:

Out-of-plane Distortion

Out-of-plane distortion reduces the buckling strength of a panel. It is believed that the initial distortion and the

residual stresses are the major reasons for the corrugation damage in the bottom plates of a number of

transversely framed welded cargo ships.

38

Structural designs and welding procedures have rarely been considered at the same time, although both need to

deal with out-of-plane distortion. This can be understood because normally they are conducted by different

specialists, structural and welding engineers. In addition, each subject is rather complicated and an integrated

study has to involve complicated computations that might not be possible to be handled manually. In practice,

however, it is desirable to combine the two analyses. For example, a simple way to reduce the amount of

distortion is to reduce the size of the fillet welds. But if the fillet size is too small, the welds may fail and floors

may be ripped from the plating during service. On the other hand, if the fillet size is increased too much,

distortion of the plate will become excessive and the plate may buckle during service. In order to achieve the

optimum design, it is important to analyze both weld distortion and its effects on the service behaviour of the

structure.

A design procedure to satisfy the above requirements may consist two parts. The first part calculates values of

allowable initial distortion, for a given set of structural parameters, including plate thickness, frame spacing,

aspect ratio of panel, and compressive in-plane stresses, while the second part calculates the amount of weld

allowed to produce the maximum distortion at panel centre.

Parameters Affecting Angular Distortion

The parameters affecting the angular distortion of fillet welds is discussed as follows:

(1) Welding current, speed and plate thickness.

Watanabe and Satoh 1 1 9 6 1 1 proposed the following formula:

/: welding current, amperes,

V: welding speed, cm/sec, Iv. plate thickness, cm.

C\, C 2 and m: coefficients determined by the type of electrodes. For an ilmenite electrode: C,=0.0885xl0"6, C 2=6.0xl0" 3, m=1.5.

(2) Preheating. Preheating can reduce the angular distortion. Preheating the back of the plate proves more

effective in reducing angular distortion than preheating the front. It is an additional expense during fabrication.

0o = c i | \ m + l

Mvh

1 h^fvh

(Formula 2.9)

39

(3) Prestraining. The angular distortion of a fillet weld can be reduced if an initial angular distortion is

provided in the negative direction. There are basically two methods for this: (1) plastic prebending and, (2)

elastic prestraining (See Figure 2.18).

Q. PLASTIC PREBENDING

b. ELASTIC PRESTRAINING

Figure 2.18 Plastic Prebending and Elastic Prestraining

If an exact amount of plastic prebending could be used, a fillet weld with no angular distortion whatsoever

would be the result. In elastic pre-straining a restraining jig is used. Often this is simply a bar of a certain size

placed under the weld and the plate clamped in a jig. If the proper amount of prestraining is used, the fillet weld

will have no angular distortion after release.

There are advantages and disadvantages with both methods. It is generally believed that in practice elastic

prestraining is more reliable than plastic prebending. Since the weldment is clamped, the angular distortion is

always much less than it would be if it were free. Even if an error is made in the amount of prestraining used,

40

the angular distortion is always reduced. If plastic prebending is used, the amount of prebending used must be

exact if a joint without distortion is to be produced. The amount of adequate prebending changes with the plate

thickness, the welding conditions, and other parameters, and the bending-line must exactly match the weld line.

A. Experimental set-up used

z 6

{ft / A-' to

{ft / A-' to

c LEG LENGTH 10 "SFAN 380 X LEG LENGTH 75 SFttN 380 LEG LENGTH 6 SPAN 380 LEG LENGTH 75 SPAN 760

,

E' = E

D: diameter of the bar placed under the bottom of the plate, t: plate thickness, L: length of free span,

E: Young's modulus, v: Poisson's ratio.

(Formula 2.10)

2.4.5 Longitudinal Shrinkage of Butt Welds

The longitudinal shrinkage in a butt weld is approximately 1/1000* the weld length, much less than the

transverse shrinkage. Only limited studies have been made of longitudinal shrinkage in a butt weld. King

proposed the following formula:

For example, when t = XA in . (6.4mm) and I = 250 amperes, A L / L = 1.2 x 10"3.

2.4.6 Longitudinal Shrinkage of Fillet Welds

Guyot [b716] conducted an extensive study on the longitudinal shrinkage of fillet welds in carbon steel. We

found that longitudinal shrinkage is primarily a function of the total cross-section of the joints involved.

Restraint is more effective when the plates are thicker and wider. The total cross-section of the welded plates in

the transverse section is called the resisting cross-section. The following formula may be used to predict the

longitudinal shrinkage of fillet welds: /

AL = 0 . 1 2 / L 100,000?

/: welding current, amps, L: length of weld, in., t: plate thickness, in.

(Formula 2.11)

42

x25 8: longitudinal shrinkage (mm) per 1 m of weld. A w : area of the weld metal. Ap: resisting cross-sectional area.

(Formula 2.12)

2.4.7 Longitudinal Bending Distortion

When the weld line does not coincide with the neutral axis of a weld structure, the longitudinal shrinkage of the

weld metal induces bending moments, resulting in longitudinal distortion of the structure. This type of

distortion is of special importance when fabricating T-bars and I-beams.

Take the welding of an I beam as an example (Figure 2.20). When the welding proceeds, the deformation

increases with the welding of the underside fillet, and decreases with the welding of the upper side. The

deformation due to the welding of this second fillet is generally smaller than that of the first, causing some

residual deformation to remain, even when the weight of the deposit metal of both fillet welds is equal and the

geometry of the joint is symmetric. This occurs because the effective resisting area of the joint differs between

the two; the upper flange does not effectively constrain the deformation during the welding of the underside of

the fillet, since the upper flange is only tack welded to the web plate, but both flanges effectively constrain the

welding of the upper side fillet, since the lower flange has already been welded to the web.

x

Figure 2.20 Longitudinal Distortion in a Fillet-welded joint

43

Sasayama et al y m i i analyzed some experimental results and developed a theory similar to the bending-beam

theory. In the case of the bending distortion of a long, slender beam, longitudinal residual stress (ax) and the

curvature of longitudinal distortion (\/R) are given by the following equation:

ex": incompatible strain,

A: sectional area of the joint,

/ y : moment of inertia of the joint around the neutral axis,

P x *: apparent shrinkage force, Px -^Eex dydz

My*: apparent shrinkage moment,

M " = ^Eex"zdydz = Px*l*

L*: distance between the neutral axis and the acting axis of apparent shrinkage force

Formula 2.13 shows that it is necessary to know the distribution of incompatible strain (e x") in order to know

the distribution of residual stress (ox) but the information about moment (My*) is sufficient only for determining

the amount of distortion (l/R). The moment (My*) can be determined when the magnitude of the apparent

shrinkage force (Px*) and the location of its acting axis are known. Through experiments, it was found that the

acting axis of "x' is located somewhere in the weld metal. It is believed that the apparent shrinkage force (Px*)

causes residual stress and distortion. More information can be obtained when the P%* value rather than the

distortion value itself is used in the analysis of experimental results. With this it is possible to separate the

various factors that affect the magnitude of distortion into those caused by changes in geometry (A, Iy, or L*)

and those caused by changes in the value of P** itself.

" M * p * o=-Eer + z + -^

Iy A

l _ My * _ Ely ~ Ely

(Formula 2.13)

44

150

0- 100 r -

.c IS)

o a Q. < 50 r-

T-Bar

I - Beam

0 0.5 1.0 1.5 2.0 2. Weight of Electrode Consumed Per Unit Weld Length , g r / m m I l i i i i i I 0 6 8 10 12 14

Length of Leg , mm

Figure 2.21 Increase of Longitudinal distortion During Multi-pass Welding ^ y " 1 9 5 5 ]

The increase of longitudinal distortion, i.e. the apparent shrinkage force P x *, during multi-pass welding is as

shown in Figure 2.21. A l l of the plate specimens were made from mild steel 1200 mm long and 12 to 13 mm

thick. The P x * values increased proportionally with the weight of the electrode consumed per weld length,

except for the first layer. The large amount of distortion obtained in the first layer was due to the lack of

resisting-area during that stage of welding; the flange plate was not yet attached firmly to the web plate.

Practically no distortion was produced during the intermittent welding (Specimen 1-4). This is due to the fact

that longitudinal residual stress does not reach a high value in a short intermittent weld.

45

2.4.8 Buckling Distortion

When thin plates are connected by welding, residual tensile stresses occur in the weld and compressive stresses

occur in areas away from the weld which cause buckling. Buckling distortion occurs when the specimen length

exceeds the critical length for a given thickness in a given size specimen. In studying weld distortion in thin-

plated structures, it is important to first determine whether the distortion is being produced by buckling or by

bending. Buckling distortion differs from bending distortion in that:

There is possibly more than one stable deformed shape.

The amount of deformation in buckling distortion is much greater than bending distortion.

Since the amount of buckling distortion is large, the best way to avoid it is to select appropriate plate thickness,

stiffener spacing, and welding parameters. Any plate has a critical buckling load. In order to avoid failure, the

welding stresses must remain below this level. This can be achieved by less welding, using less heat, or

removing the heat. One way to reduce the amount of weld is to use intermittent welding; by halving the amount

of welding, the critical load is approximately doubled. Another way is to decrease the weld-bead size, which

results in smaller heat requirements during welding and hence in lower stress levels. The alternate way to

reduce the stress levels is to remove the welding heat from the plate using chill bars, water-cooled backing

plates, etc.

2.5 METHODS OF DISTORTION REDUCTION IN WELDMENTS

This section presents several methods of reducing distortion in weldments.

2.5.1 Commonly Use Distortion Reduction Methods

The common methods of reducing weld distortion are reviewed as follows:

Weldment Dimension

The length, the width, and the thickness of a weldment all influence the amount of distortion. The plate

thickness greatly influences the angular distortion in a fillet weld. Since the angular change of a fillet weld is

46

caused by temperature differences between the top and bottom surfaces of the plate, at a certain plate thickness

(about 3/8 in.for steel and XA in. for aluminum respectively) the angular change is maximum. When the

thickness is greater than this, the angular change is less because of the rigidity of the plate and also because the

temperature differential between the top and bottom surfaces is less. However, this does not mean that when

engineers fabricate thin-plated structures they will have fewer distortion problems. Buckling governs and since

buckling distortion, if present, is always serious. It is best to avoid it by a careful selection of structural

parameters, e.g. plate thickness, stiffener spacing, and welding parameters.

Joint Design

Distortion is affected by joint design. As a general rule, distortion can be reduced by keeping the amount of

weld metal used at a minimum. Sections 2.4.3 shows the groove shape that gives a zero angular distortion in butt

welds.

Welding Processes and Welding Conditions

Since residual stresses and distortion are the result of uneven heating during welding, it is generally true that the

less total heat a process uses in joining, the less distortion will be produced. Weldments produced using narrow-

gap welding, electron beam welding, and laser welding all exhibit less distortion than those produced using arc

welding. Generally, a weld made using a low heat input generally exhibits less distortion than a weld made

using a high heat input.

It must also be recognized that the influence of the temperature distribution and the heat input on various types

of distortion can be rather complex. For example, the transverse shrinkage of a butt weld is greatly affected by

the temperature distribution in the base