APPROVED:

Aleksandra Fortier, Major Professor Rajiv Mishra, Committee Member Kyle Horne, Committee Member Yong X. Tao, Chair of the Department of

Mechanical and Energy Engineering

Costas Tsatsoulis, Dean of the College of Engineering

Victor Prybutok, Vice Provost of the Toulouse Graduate School

MODELING OF FRACTURE TOUGHNESS OF MAGNESIUM ALLOY WE43

BEFORE AND AFTER FRICTION STIR PROCESSING

Celena Lipscomb

Thesis Prepared for the Degree of

MASTER OF SCIENCE

UNIVERSITY OF NORTH TEXAS

December 2016

Lipscomb, Celena. Modeling of Fracture Toughness of Magnesium Alloy WE43

Before and After Friction Stir Processing. Master of Science (Mechanical and Energy

Engineering), December 2016, 64 pp., 10 tables, 21 illustrations, reference list, 61

numbered references.

Magnesium alloys are a popular research topic for structural applications

because they have a lower density than conventional structural materials, including

steel, titanium, and aluminum; however, the reliability and safety of their mechanical

properties must be further proven. An important mechanical property for this purpose is

fracture toughness, which is the measure of the material’s resistance to crack

propagation. In this study, a model of an experiment to investigate the fracture

toughness of a magnesium alloy WE43 before and after friction stir processing (FSP) is

developed, and the results are compared to those produced by a digital image

correlation (DIC) system during an experiment from another paper. The model results of

the material before FSP matched well with the DIC results, but the model of the material

after FSP only partially matches the DIC results. In addition, a theoretical approach to

calculating the standard fracture toughness value, KIc, from the modeling results is

proposed, and is found to be a conservative approach.

ii

Copyright 2016

by

Celena Lipscomb

iii

ACKNOWLEDGEMENTS

I am most grateful to Dr. Aleksandra Fortier for the support and the many

opportunities she has provided.

Thanks to Dr. Rajiv Mishra and Dr. Nilesh Kumar for aiding in the direction of my

research, and Fanrong Kong for aiding in the development of the ANSYS model.

Thanks to Shamiparna Das for helping me understand the experiment I was

modeling and being patient with my constant questions.

Thanks to my fellow lab rats for helping me brainstorm about writing choices and

steps to take.

Thanks to my family and friends for staring blankly while I ramble about my work.

iv

TABLE OF CONTENTS

Page

ACKNOWLEDGEMENTS ............................................................................................... iii LIST OF TABLES ............................................................................................................ vi LIST OF FIGURES ......................................................................................................... vii CHAPTER 1 INTRODUCTION ........................................................................................ 1

1.1 Magnesium ................................................................................................ 1 1.1.1 Uses ................................................................................................ 1 1.1.2 Alloy Designation ............................................................................ 3 1.1.3 Alloy Categorization ........................................................................ 4 1.1.4 Properties ........................................................................................ 5

1.2 Processing of Magnesium Alloys ............................................................... 7 1.2.1 Friction Stir Processing and Welding .............................................. 8

1.3 Modeling .................................................................................................. 12 1.3.1 FSP ............................................................................................... 13 1.3.2 Fracture Toughness ...................................................................... 13

CHAPTER 2 MODELING APPROACH ......................................................................... 15

2.1 Fracture ................................................................................................... 15 2.1.1 Energy Criterion ............................................................................ 15 2.2.2 Stress Intensity.............................................................................. 15 2.2.3 Fracture Toughness Considerations ............................................. 16

2.2 Modeling Process .................................................................................... 17 2.2.1 Geometry ...................................................................................... 18 2.2.2 Materials ....................................................................................... 19 2.2.3 Load and Boundary Conditions ..................................................... 20 2.2.4 Crack ............................................................................................. 21 2.2.5 Mesh ............................................................................................. 22 2.2.6 Time Step and Other Considerations ............................................ 24

CHAPTER 3 MODELING RESULTS ............................................................................. 25

3.1 Abaqus Model .......................................................................................... 25

v

3.2 ANSYS Model .......................................................................................... 29 3.3 Digital Image Correlation ......................................................................... 32

CHAPTER 4 THEORETICAL APPROACH ................................................................... 35

4.1 ASTM Standard Test Method for Measurement of Fracture Toughness . 35 4.2 Calculation Attempt .................................................................................. 38

CHAPTER 5 FUTURE WORK ...................................................................................... 41

5.1 Conclusions ............................................................................................. 41 5.2 Future Work ............................................................................................. 41

APPENDIX: ANSYS CODE FOR WE43 FSP MATERIAL WITH CRACK PREDICTION ................................................................................................................ 43 REFERENCES .............................................................................................................. 57

LIST OF TABLES

Table 1 Composition limits of WE43 [7] ........................................................................... 4

Table 2 Tensile behavior of WE43-T6 at various temperatures [7] ................................. 5

Table 3 Tensile strength and percent elongation of commercially pure magnesium,

WE43A-T6, AZ31B-H24, and ZK61A-T6 [7] .................................................................... 6

Table 4 Dimensions of specimen for fracture toughness test according to ASTM B-871

[11] ................................................................................................................................ 18

Table 5 Material Properties of WE43 Base and FSP obtained from tensile and tear

tests, used as material inputs in the model [58] ............................................................ 20

Table 6 Finest Abaqus mesh details for WE43-Base and WE43-FSP .......................... 23

Table 7 Time step input data for the Abaqus model ...................................................... 24

Table 8 Abaqus meshes attempted for WE43-FSP model ............................................ 26

Table 9 ANSYS meshes attempted for WE43-FSP model ............................................ 29

Table 10 Values used in stress intensity calculation, and result .................................... 40

vi

LIST OF FIGURES

Figure 1 Explanation of designation of magnesium alloys [7] .......................................... 3

Figure 2 Four FSW tools ................................................................................................. 9

Figure 3 Typical FSP runs ............................................................................................. 10

Figure 4 Zones created during FSW/FSP [31] (a) stir zone, SZ (b) thermomechanically

affected zone, TMAZ (c) heat affected zone, HAZ (d) base material, BM ..................... 12

Figure 5 ASTM standard tear test specimen with labeled dimensions [11] ................... 18

Figure 6 Stress versus plastic strain of WE43-Base and WE43-FSP ............................ 19

Figure 7 Applied load and boundary conditions to Abaqus model ................................. 21

Figure 8 Crack applied to geometry .............................................................................. 22

Figure 9 Meshes in Abaqus model for a) WE43-Base material and b) WE43-FSP

material ......................................................................................................................... 23

Figure 10 Abaqus von Mises stress contour plots for a) WE43-Base and b) WE43-FSP

...................................................................................................................................... 25

Figure 11 Close up of cracked region of WE43-FSP model and contour legend for

Figure 10b ..................................................................................................................... 26

Figure 12 Stress contour plot of Abaqus WE43-FSP model with a global seed size of 1

a) stress plot legend, b) stress contour plot c) zoom in of notch area ........................... 27

vii

Figure 13 Stress contour plot of Abaqus WE43-FSP model with a global seed size of

0.7 a) stress plot legend, b) stress contour plot c) zoom in of notch area ..................... 27

Figure 14 Stress contour plot of Abaqus WE43-FSP model with a global seed size of

0.6 a) stress plot legend, b) stress contour plot c) zoom in of notch area ..................... 28

Figure 15 Stress contour plot of Abaqus WE43-FSP model with a global seed size of

0.4 a) stress plot legend, b) stress contour plot c) zoom in of notch area ..................... 28

Figure 16 ANSYS model of WE43-FSP model a) mesh with 1119 elements b) whole

stress plot and close-up of crack tip .............................................................................. 30

Figure 17 ANSYS model of WE43-FSP model a) mesh with 3697 elements b) whole

stress plot and close-up of crack tip .............................................................................. 31

Figure 18 ANSYS model of WE43-FSP model: mesh with 6023 elements, did not run 32

Figure 19 DIC image of plastic zone formation just before crack forms in a) WE3-Base

and b) WE43-FSP c) partially cracked domain of WE43 base d) cracked WE43 FSP

sample [58] .................................................................................................................... 33

Figure 20 Specimen shapes covered in ASTM E1820 [9] a) single edge bend [SE(B)] b)

compact [C(T)] c) disk-shaped compact [DC(T)] ........................................................... 36

Figure 21 ASTM E1820 notch shapes: a) chevron notch, b) straight through notch, c)

notch ending in drilled hole, and d) narrow notch .......................................................... 37

viii

CHAPTER 1

INTRODUCTION

Gas prices constantly fluctuate these days. Consumers are growing more concerned for

the environment and their carbon footprints. Laws about corporate average fuel

economy (CAFE) require a company’s average fleet miles per gallon to be a minimum

of 54.5 by 2025 [1, 2]. For these reasons and more, vehicles such as automobiles and

airplanes with a high gas mileage (miles per gallon, MPG) are in high demand. A quick

and relatively cheap way to increase the MPG of a vehicle is to decrease the weight,

which can be done by designing a smaller vehicle or by using a material with a lower

density that can still safely withstand the design stresses.

1.1 Magnesium

Magnesium alloys are a popular topic of research for this application for a number of

reasons: (1) magnesium is the lightest structural metal currently available; it is 75%

lighter than steel, 50% lighter than titanium, and 33% lighter than aluminum [3]; (2)

magnesium is very common, being the 8th most abundant element in the earth’s crust

[4]; (3) magnesium has a high strength-to-weight ratio [4]; (4) depending upon the alloy,

the cost of magnesium and of machining magnesium is generally comparable to that of

aluminum, and in many cases cheaper [5].

1.1.1 Uses As mentioned above, a lot of research is focused on replacing current

materials used in automobiles and airplanes with magnesium in order to make them

lighter; this application of making a product lighter extends to laptops, cell phones, and

1

bicycles [6]. Because of their low weight and low cost, magnesium alloys are used to

make many commercial products, including luggage, handheld tools, ladders, grain

shovels, and computer housings [7]. They are also good for small parts that have to

move at high speeds in textile and printing machines; these parts must be lightweight

because heavier parts would have a larger inertial effect [7].

Magnesium also has many non-structural applications [7]:

• Alloying element for other materials (Al, Zn, Pb, and other nonferrous metals)

• Manufacturing industry: oxygen scavenger, desulfurizer, and reducing agent

• Organic chemistry

• Pyrotechnics

• Batteries

• Foundries

• Photoengraving

2

Figure 1 Explanation of designation of magnesium alloys [7]

1.1.2 Alloy Designation The naming convention of magnesium alloys is explained in

Figure 1. There are four parts of an alloy’s name: The first two letters, which designate

the two principal alloying elements; the next two numbers, which specify the percent of

the first and second principal alloying elements, respectively; a third letter, not always

present, which differentiates between standard alloys with the same two principal

alloying elements; and a fourth alphanumeric sequence following a hyphen, also not

always present, which specifies the temper of the alloy. For example, the alloy WE43A-

T6: WE means the two principal alloying elements are yttrium and a rare earth metal, in

this case neodymium; the 43 means there is 4% yttrium and 3% neodymium in the

alloy; the A means this was the first alloy developed and standardized with these two

principal alloying elements and these percentages; and the T6 means the alloy was

3

solution heat treated and artificially aged [7]. Figure 1 lists possible choices for each of

these four parts of an alloy’s designation.

1.1.3 Alloy Categorization Magnesium alloys are categorized according to the type of

manufacturing process they are most suited for: casting or wrought alloys. Casting

alloys are used for high-pressure die casting and sand and permanent mold casting.

Common casting alloys include AZ91D and ZK61A. Wrought alloys are shaped by

extrusion, forging, rolling, and any other thermomechanical process.

WE43 is an uncommon cast alloy best used for sand and permanent mold casting. It is

relatively expensive because of the yttrium content. This alloy retains good properties

up to 250oC for long periods of time. Solution and aging treatments are necessary to

optimize the mechanical properties. It has high tensile and yield strengths, good

castability, high corrosion resistance, and good weldability. There is only one

standardized composition for WE43, so while the full designation would be WE43A, the

A is unnecessary since there is no other standard alloy from which to differentiate this

one. Table 1 shows the chemical composition of WE43. The rare earths used as the

second principal alloying element is primarily neodymium combined with a mixture of

heavy rare earths, including terbium, erbium, dysprosium, and gadolinium [7].

Table 1 Composition limits of WE43 [7]

Yttrium

(Y)

Rare Earths

(Nd, Tb, Er, Dy, Gd)

Zirconium

(Zr)

Other

(Mn, Zn, Cu, Ni, Si, Li)

3.7-4.3 2.4-4.4 0.4-1.0 0.595 max

4

This alloy is used primarily in the T6 condition, which means the alloy is solution-heat-

treated and then artificially aged. Table 2 shows the tensile properties of WE43 at

various temperatures [7]. The properties are not seriously affected by elevated

temperatures until around 250oC.

Table 2 Tensile behavior of WE43-T6 at various temperatures [7]

Temperature, oC

Young’s

Modulus,

GPa

Yield

Strength,

MPa

Ultimate Tensile

Strength, MPa

Elongation,

%

22 44 165 250 2

150 47 170-180 240-250 4-8

200 39 160-180 240-260 8-14

250 36 150-170 210-230 15-20

300 36 110-130 150-170 30-50

1.1.4 Properties As with many metals, commercially pure magnesium is a very poor

choice for structural applications; the properties of magnesium improve greatly just by

alloying it with other elements.

One of the most important mechanical behaviors of any material is strength, which is

most commonly measured by two tensile properties: yield strength and ultimate tensile

strength. The yield strength is the point beyond which the material deforms plastically,

and the ultimate tensile strength is the absolute maximum amount of stress the material

can sustain [8]. Another tensile property investigated is percent elongation, which is a

quantitative measure of ductility. The percent elongation is the percentage of the

5

original length that the sample extends before it fractures [8]. Data from a tensile test

that is usually plotted is applied stress versus strain [8].

Table 3 compares the tensile properties of commercially pure magnesium to those of

some magnesium alloys: WE43A-T6, AZ31B-H24, and ZK61A-T6. The yield strength of

these alloys is at least eight times that of pure magnesium, and the ultimate tensile

strength is more than three times [7]. The elongation is also significantly improved in

two of the three alloys, all from simply alloying magnesium with other metals.

Table 3 Tensile strength and percent elongation of commercially pure magnesium, WE43A-T6, AZ31B-H24, and ZK61A-T6 [7]

Property Pure Mg WE43A-T6 AZ31B-H24 ZK61A-T6

Yield Strength,

MPa 20 165 220 195

Ultimate Tensile

Strength, MPa 80 250 290 310

Elongation, % 6 2 15 10

The mechanical property most relevant to this study is fracture toughness, which at its

simplest is a measure of how much energy a material absorbs before it fractures [8].

One measure of fracture toughness is tensile toughness, which is given by the area

under the stress-strain curve found from a standard tensile test.

6

The standard property used to measure the toughness of a material is the KIc value; this

value is the minimum value of the stress intensity factor at which the material fractures

[8].

ASTM standard E1820 [9] enumerates methods used to determine this value. The

loading can be either bending or tensile, depending on the type of specimen used. After

obtaining the load-displacement data from the experiment, it must be validated in order

to find the value of KIc; in order for the value to be valid, the test must have been

performed in the plane strain condition. This means that, in the tensile loading test,

there must be no strain in the direction of thickness in the sample, called the z direction;

in addition, the material must also only undergo elastic deformation prior to cracking, as

even a small amount of plastic deformation renders the assumptions of this theory

invalid [10].

The plane strain condition imposes a minimum thickness requirement on the sample,

which means that if an application of the material requires a smaller thickness, like

sheet metal, then the KIc value is not useful for design. For this reason, alternate tests

have been devised such as the one outlined in ASTM standard B871 [11] for aluminum

alloys in order to determine values more suitable for design.

1.2 Processing of Magnesium Alloys

Many processes are used in order to improve upon various mechanical properties of

alloys by altering the microstructure of the alloy, including extrusion, thermomechanical

processing, differential speed rolling, and friction stir processing [12].

7

Extrusion is a manufacturing process in which material is pushed through a die which is

the desired cross-sectional shape of the finished part [13]. A couple variations of the

process are used to refine the microstructure: some papers [14, 15, 16] investigated hot

extrusion in which the process is performed at an operating temperature above the

material’s recrystallization temperature which makes it easier to push through and

keeps the material from work hardening [13]; others [17, 18] investigated equal channel

angular extrusion in which the material is pushed around a corner before it goes through

the die, which cold works the material without any change in the cross sectional area

[13]. Kumar et al. [19] investigated thermomechanical processing, in which heat

treatment is combined with a mechanical manufacturing process such as forging or

rolling [13]. Kim et al. [20] found that high ratio differential speed rolling (HRDSR) works;

during this process, material is pushed between two rollers which are rolling at different

speeds, and the ratio of these speeds is high—in the paper, the ratio used was three.

The process studied in this thesis is friction stir processing.

1.2.1 Friction Stir Processing and Welding Friction stir welding (FSW) is a solid state

joining process developed in 1991 [21] in which the tool rotates and plunges into the

material, traverses, and then extracts and stops rotating. One important aspect of the

process is the geometry of the tool [22]. The large diameter face is called the shoulder,

and the smaller diameter piece on the shoulder is called the pin. Figure 2 shows four

tools with different pin geometries, features, and sizes, as well as different shoulder

geometries and sizes. Important measurements include the pin diameter, pin length,

and shoulder diameter. Possible pin shapes include cylindrical, square, and conical.

The shoulder of the tool can be flat, convex, concave, or scrolled.

8

Figure 2 Four FSW tools

During FSW, the shoulder is engaged with the material, and this contact combined with

the rotation of the tool provides frictional heat to the process [22]. The tool is submerged

into the material and stirs it. Features such as threads and flutes are placed on the pin

in order to improve the mixing of the material, as shown on the tools in Figure 2. These

changes to the pin geometry result in a variation in weld quality; many papers [23, 24,

and 25] focus on optimization of tool geometry for specific alloys.

The maximum temperature of this process never should exceed the melting

temperature of the material; many papers [26, 27, 28, 29, and 30] focus on recording

the thermal history of the process and finding an optimum operating temperature.

a)

9

b)

Figure 3 Typical FSP runs

Figure 3 shows a typical friction stir weld. In this figure, the tool path started on the left

and ended on the right for both welds. The weld ends with a circular hole, called a key.

This is where the tool extracts from the material, and is not filled in with material when

the tool extracts because the process operating temperature doesn’t reach melting point

so the material stays solid and retains its shape around the rotating pin. This key has no

effect on the weld strength; it is mainly aesthetically unappealing, and is usually cut off

[22]. The extra material on the edges of the weld is called flash, and is a result of the

material being displaced in the weld zone. More flash is produced when the shoulder is

not in contact with the surface, or too much in contact with it, and is a possible sign of a

defect in the weld [22]. Defects can be internal or external. The most common internal

defects are channel defects, which are long tunnel-like voids in the weld. They can

usually be seen in the key of the weld as a small hole, which is the end of the channel.

The same phenomenon can be large enough to be seen on the surface of the weld; in

this case it is more like a trough than a tunnel, and is considered an external defect [22].

In addition to the tool geometry, process parameters like rotation and traverse speed, tilt

angle, and offset of the tool greatly affect the weld quality. Many papers [31, 32, and 33]

focus on optimization of these parameters in order to achieve the best weld properties.

10

The optimal parameters are specific to the material system being welded; there is no

one set of parameters that achieve the best possible results for all possible welds.

A particular area of interest for FSW is dissimilar metal joining. Traditional fusion

welding processes can only join two pieces of the same metal [13], and some metals

are simply unsuitable for fusion welding—dubbed “unweldable” alloys—like aluminum

2XXX series (Al-Cu) and 7XXX series (Al-Zn) [13]. FSW has been proven capable of

welding these alloys [30, 31, 32, and 33], and a large amount of research is focused on

friction stir welding various dissimilar material systems together [38] such as aluminum

and magnesium [39, 40], aluminum and steel [41, 42], and aluminum and titanium [43,

44].

In addition to joining two separate pieces of material, this process is used on a single

piece in order to improve the mechanical properties of the material. This is called friction

stir processing (FSP). Like during FSW, different parameters result in different

microstructures, which then have different effects on mechanical properties. Typically,

the stirring of the pin results in a finer microstructure [12, 26, and 27]; a finer

microstructure usually results in better mechanical properties (except for fatigue crack

resistance) [45].

The two sides of the weld zone are called the advancing side (AS) and the retreating

side (RS). The advancing side is so called because on this side, the direction of the

welding velocity and the direction of the tangent of the rotational velocity are the same

direction; on the retreating side, these two directions are in the opposite direction.

11

Different observations are generally found at each side, and so recorded in order to

possibly gain insight into how the material behaves during the process [22].

Figure 4 Zones created during FSW/FSP [31] (a) stir zone, SZ (b) thermomechanically affected zone, TMAZ (c) heat affected zone, HAZ (d) base material, BM

After one pass of FSW or FSP, there are four zones in the material, as shown in Figure

4: (a) the stir zone (SZ) or weld nugget, which is created by displacement by the actual

path of the tool; (b) the thermomechanically affected zone (TMAZ), affected by the heat

of the tool and incidentally mixed by the tool;(c) the heat affected zone (HAZ), affected

by the heat from the tool but not the motion of the tool; and (d) the base material (BM),

untouched by the tool or the heat produced by the tool. Generally, the weakest zone is

the HAZ, because the heat of the process causes the grains to grow, which results in a

decrease of tensile strength [33], and the grain refinement caused by the stirring of the

pin is absent from this zone.

1.3 Modeling

Compared to experimental literature, not much work has been done in modeling.

12

1.3.1 FSP There’s a large interest in modeling of the material behavior during friction stir

processing [46] because a better understanding of this behavior would help researchers

optimize the process parameters without actually consuming material.

One approach to modeling this process is a finite element method (FEM) approach in

which the material is discretized (cut up into pieces) and the heat input and residual

stresses on each element is calculated. Many papers use this approach [47, 48].

The material is solid during the process since the temperature never rises above the

melting point, but the behavior of the material around the pin is most likely similar to that

of a fluid; therefore, many papers take a computational fluid dynamics (CFD) approach

to modeling this behavior [49, 50, 51].

1.3.2 Fracture Toughness Some models have been developed to determine fracture

toughness. A few of these models were created to estimate fracture toughness from a

test that was not designed to find fracture toughness, like the scratch test [52, 53] or the

tensile test [54]. These models save the time it takes to perform a toughness test. Other

models predict the fracture toughness of a material based on the fracture surface [55]

and microstructural features such as grain size, degree of recrystallization, and

microstructural anisotropy [56, 57].

In the following thesis, chapter 2 outlines the process for developing a model to

investigate the effect of the friction stir process on the fracture toughness of WE43, and

chapter 3 presents the results of the model. Chapter 4 presents an alternate theoretical

13

approach for calculating the KIc value. Chapter 5 summarizes the conclusions and

proposes future work to be done.

14

CHAPTER 2

MODELING APPROACH

2.1 Fracture Mechanics Theories

There are two main approaches to defining fracture toughness: the energy criterion and

the stress intensity factor [10].

2.1.1 Energy Criterion The energy criterion defines the cause of fracture as “when the

energy available for crack growth is sufficient to overcome the resistance of the

material.” [10]. The important variable in this approach is the energy release rate, G. the

equation for calculating G is given in Equation 1.

Equation 1: 𝐺𝐺 = 𝜋𝜋𝜎𝜎2𝑎𝑎𝐸𝐸

E is Young’s modulus, a is half of the crack length, and σ is the applied stress. The

critical energy release rate is the value at which fracture occurs, and is the measure of

fracture toughness in this approach [10].

2.2.2 Stress Intensity The stress intensity factor is the ratio of the local stress

experienced by the material to the total applied stress to the material. Variations in local

stress are caused by many things, but the most considered cause in this approach is

the geometry of a crack tip. The cause of failure is viewed as a critical local stress,

which would have a corresponding critical stress intensity value, which is the definition

of fracture toughness in this approach.

The equation to calculate the stress intensity is given in Equation 2.

Equation 2: 𝐾𝐾𝐼𝐼 = 𝜎𝜎√𝜋𝜋𝜋𝜋

As in Equation 1, a is half of the crack length and σ is the applied stress [10].

15

2.2.3 Fracture Toughness Considerations An important assumption to consider is

similitude; the fracture toughness value in both approaches should be a material

property, which means it should be independent of size or geometry. This assumption is

valid as long as the material is largely linear elastic, with very little or no plasticity [10].

These are essentially equivalent approaches for linear elastic materials; combining

Equation 1 and Equation 2 gets Equation 3, which is a relationship between stress

intensity and energy release rate.

Equation 3: 𝐺𝐺 = 𝐾𝐾𝐼𝐼2

𝐸𝐸

Plasticity complicates these approaches because it is nonlinear behavior.

The two main branches of time-independent fracture mechanics are Linear Elastic

Fracture Mechanics (LEFM) and Elastic-Plastic Fracture Mechanics (EPFM). The

choice of which branch to apply depends on material behavior; at low fracture

toughness or low plasticity, LEFM is applicable.

LEFM uses the energy criterion and/or stress concentration approaches to define

fracture toughness; EPFM uses the parameters of crack tip opening displacement

(CTOD) and J contour integral [10].

A more recent alternative to these two models is the cohesive zone model (CZM). In

this model, a zone called the cohesive zone extends the crack tip, and the two surfaces

of the cohesive zone—called the cohesive surfaces—are held together by a cohesive

traction. As the load is applied, these cohesive surfaces are separated; various traction-

separation laws correlate the separation of the surfaces to the traction of those surfaces

[59, 60]. This is the theory chosen for damage definition in this Abaqus model.

16

ASTM standard B871 [11], entitled “Standard Test Method for Tear Testing of Aluminum

Alloy Products”, details the procedure for the tear test of aluminum alloy samples

between 0.04 in (1 mm) and 0.25 in (6.35 mm) thick.

This range of thickness does not satisfy the plane strain condition for KIc validity for

aluminum, but this test was not created to find the KIc value; instead, this test is for

ranking materials by fracture toughness or ruling them out for a design that they would

otherwise be equally suited for.

This test was specifically developed for aluminum alloys; however, aluminum and

magnesium are comparable in terms of density and plasticity [5], so the same test is

applicable to magnesium alloys.

The details of the performance of this experiment are outlined in another paper [58], the

results of which are used as model inputs in this study.

2.2 Modeling Process

The model was developed using both Abaqus and subsequently in ANSYS in order to

validate the results. The procedure followed was:

1. The geometry of the part was created

2. The WE43 base and friction stirred materials were created

3. The loads and boundary conditions were applied

4. The crack was imposed

5. The part was meshed

6. The time step and other model controls were determined/set

17

2.2.1 Geometry The geometry of the sample is specified in American Society for Testing

and Materials (ASTM) standard B-871 [11] and given in Figure 5 below. The dimensions

for this geometry are given in Table 4. The only difference between the specimen types

is the thickness of the sample; all other dimensions are the same. The model is a two

dimensional (2D) planar deformable shell, so it represents all five types of specimens.

The choice of 2D instead of 3D was made to simplify the geometry and ultimately

reduce the run time of the solution.

Figure 5 ASTM standard tear test specimen with labeled dimensions [11]

Table 4 Dimensions of specimen for fracture toughness test according to ASTM B-871 [11]

in mm in mm in mm in mm in mm1 0.064 1.6256 0.438 11.125 1.438 36.525 0.3125 7.9375 2.25 57.152 0.1 2.54 0.438 11.125 1.438 36.525 0.3125 7.9375 2.25 57.153 0.125 3.175 0.438 11.125 1.438 36.525 0.3125 7.9375 2.25 57.154 0.187 4.7498 0.438 11.125 1.438 36.525 0.3125 7.9375 2.25 57.155 0.25 6.35 0.438 11.125 1.438 36.525 0.3125 7.9375 2.25 57.15

Specimen Type T E W D L

18

2.2.2 Materials The mechanical material properties required for material definition in the

Abaqus model are: Young’s modulus, Poisson’s ratio, yield strength, ultimate tensile

strength, plasticity, and fracture energy.

Tensile tests were performed in order to obtain information about the plastic behavior of

WE43 before and after FSP, the details of which are reported in another paper [58];

Figure 6 shows the resulting plastic stress-strain curve used in the model. All other

mechanical property data is summarized in Table 5. The yield and ultimate tensile

strengths are taken from the tensile data in Figure 6, and the fracture energy is taken

from the tear test experiment reported in another paper [58].

Figure 6 Stress versus plastic strain of WE43-Base and WE43-FSP

0

50

100

150

200

250

300

0 0.1 0.2 0.3 0.4

Stre

ss (M

pa)

Plastic Strain

Stress vs Plastic Strain of Mg WE43 Base and FSP

WE43-Base

WE43-FSP

Poly. (WE43-Base)

Poly. (WE43-FSP)

19

Table 5 Material Properties of WE43 Base and FSP obtained from tensile and tear tests, used as material inputs in the model [58]

Parameter Unit Symbol Value for WE43-Base

Value for WE43-FSP

Young's Modulus MPa E 44200 57120

Poisson's Ratio N/A ν 0.27 0.27

Yield Stress MPa σy 195 252

Ultimate Tensile Stress

MPa σUTS 261 302

Fracture Energy J/mm2 Gf 0.048 0.056

2.2.3 Load and Boundary Conditions Figure 7 shows the application of the load and

boundary conditions in the model developed in Abaqus. The bottom hole was fixed and

the load was applied to the top hole, because in the experiment, the top grip moved and

the bottom grip stayed stationary. The magnitude of the load applied was varied from 10

MPa to 200 MPa to determine at which load the crack initiated and fully propagated.

20

Figure 7 Applied load and boundary conditions to Abaqus model

2.2.4 Crack The options in Abaqus for crack modeling are contour and extended finite

element method (XFEM). An XFEM crack was used in the current model because it

automatically predicts the path of the crack and propagates the crack in that direction,

whereas the contour crack requires the crack path as input. For an XFEM crack, only

the crack domain needs to be selected, which is the part. Figure 8 shows the XFEM

crack applied to the model; the software determined where the crack should start (at the

notch, marked by the red dot) and in which direction the crack should propagate

(horizontally to the left, marked by the red arrow).

21

Figure 8 Crack applied to geometry

In both software packages, an element is considered cracked when the stress exceeds

the ultimate tensile stress defined in the material model.

2.2.5 Mesh In Abaqus, the edges must be seeded before the part is meshed; the seeds

determine the size of the mesh. Then, the mesh controls including the element type and

shape must be selected; finally the part must be meshed. The mesh size was varied in

order to investigate the effect of the mesh on the results; Figure 9 shows the finest

meshes obtained for the Abaqus model, and Table 6 shows the selections made for

22

global seed size, element type, and element shape, as well as the number of nodes and

elements present for each mesh.

a) b)

Figure 9 Meshes in Abaqus model for a) WE43-Base material and b) WE43-FSP material

Table 6 Finest Abaqus mesh details for WE43-Base and WE43-FSP

WE43-Base WE43-FSP

Global Seed Size 0.5 0.5

Element Type CPS4R CPS4R

Element Shape Quadrilateral Quadrilateral

Number of Nodes 9,552 9,482

Number of Elements 9,303 9,233

23

2.2.6 Time Step and Other Considerations A load step is created in Abaqus and the

parameters defined are the time period, the minimum time increment size, the maximum

time increment size, the time increment to use first, and the maximum number of time

increments; Table 7 specifies the selections used in this Abaqus model for these

parameters. Abaqus automatically decides how big of a time step to use. If the solution

is converging, it increases the time step size until the maximum or until the solution is

not converging; if the solution is not converging, it decreases the step size until it starts

converging. If the step size required is less than the minimum step size, then the job is

aborted and the last converged solution is available.

Table 7 Time step input data for the Abaqus model

Time Period Minimum Time Increment

Maximum Time Increment

Initial Time Increment

Maximum number of increments

1 1E-35 0.01 0.01 10,000

24

CHAPTER 3

MODELING RESULTS

3.1 Abaqus Model

The Abaqus model was developed first, as described in chapter 2; Figure 10a is the

strain plot obtained from the Abaqus model of the base material, and Figure 10b is the

same thing for the FSP material.

a) b)

Figure 10 Abaqus von Mises stress contour plots for a) WE43-Base and b) WE43-FSP

Figure 11 shows the contour legend for Figure 10b as well as a close up of the cracked

notch region for Figure 10b. The job that gave these results actually aborted before fully

completing the solution; Figure 11 shows that only two elements cracked before the job

completed. Various parameters changed in order to hopefully allow the job to be

25

completed include the load magnitude, the time step inputs, and the mesh size, all with

limited to no success.

Figure 11 Close up of cracked region of WE43-FSP model and contour legend for Figure 10b

Table 8 shows the different global seed sizes tried and the number of elements in the

resulting mesh; the figure with the resulting contour plots is also identified, and the

number of cracked elements before the job aborted is noted. A finer mesh certainly

affects the results, but the changes are not promising. Therefore, a subsequent model

was developed in ANSYS.

Table 8 Abaqus meshes attempted for WE43-FSP model

Global Seed Size

Mesh Elements

Contour Plot Number of Elements Cracked

Maximum Stress, MPa

1 2,369 Figure 12 6 270.7

0.7 4,406 Figure 13 2 264.1

0.6 6,313 Figure 14 3 266.5

0.5 9,233 Figure 10b/Figure 11

2 264

0.4 14,151 Figure 15 2 269.7

26

a) b) c)

Figure 12 Stress contour plot of Abaqus WE43-FSP model with a global seed size of 1 a) stress plot legend, b) stress contour plot c) zoom in of notch area

a) b) c)

Figure 13 Stress contour plot of Abaqus WE43-FSP model with a global seed size of 0.7 a) stress plot legend, b) stress contour plot c) zoom in of notch area

27

a) b) c)

Figure 14 Stress contour plot of Abaqus WE43-FSP model with a global seed size of 0.6 a) stress plot legend, b) stress contour plot c) zoom in of notch area

a) b) c)

Figure 15 Stress contour plot of Abaqus WE43-FSP model with a global seed size of 0.4 a) stress plot legend, b) stress contour plot c) zoom in of notch area

28

3.2 ANSYS Model

The ANSYS Parametric Design Language (APDL) code developed is given in Appendix

1. The mesh was altered by refining the mesh only in the middle FSP region of the

sample. Table 9 compares the three mesh sizes developed in this model. It lists the

element size given for the FSP region, the number of elements in each mesh, the figure

number of each stress contour plot, and the maximum stress obtained in each stress

plot.

Table 9 ANSYS meshes attempted for WE43-FSP model

Element Size Mesh Elements Contour Plot Maximum Stress, MPa

0.0005 1119 Figure 16

366

0.0004 3697 Figure 17 371

0.0003 6023 Figure 18 N/A

29

a)

b)

Figure 16 ANSYS model of WE43-FSP model a) mesh with 1119 elements b) whole stress plot and close-up of crack tip

30

a)

b)

Figure 17 ANSYS model of WE43-FSP model a) mesh with 3697 elements b) whole stress plot and close-up of crack tip

31

Figure 18 ANSYS model of WE43-FSP model: mesh with 6023 elements, did not run

In this model, the most coarse mesh with 1119 elements (mesh 1) propagated the crack

the farthest; the mesh with 3697 elements (mesh 2) would not propagate the crack

further than as shown in Figure 17, and the mesh with 6023 elements (mesh 3) would

not generate any results at all. Mesh 2 shows a large developing plastic zone when

compared to the plastic zone of mesh 1.

3.3 Digital Image Correlation

The tear test experiment is outlined in another paper [58]. The samples were tested

along with a digital image correlation (DIC) setup. The DIC results are a strain map of

32

the middle strip of the experimental samples tested, where the crack should

theoretically propagate from the machined notch.

Figure 19a is a screenshot of the experimental digital image correlation result of the

WE43 base sample [58], which is a video. Figure 19b is the same screenshot for the

WE43 FSP sample. These screenshots were taken right before the crack started to

develop, showing the full plastic zone development just before cracking. Figure 19c is

the WE43 base sample partway through cracking; the full crack goes out of frame.

Figure 19d shows the FSP crack

a) b)

c) d)

Figure 19 DIC image of plastic zone formation just before crack forms in a) WE3-Base and b) WE43-FSP c) partially cracked domain of WE43 base d) cracked WE43 FSP sample [58]

As seen in Figure 19d, the crack in the experimental FSP sample doesn’t crack straight

across the sample; instead, it propagates towards the border between the stronger FSP

material and the weaker base material. The ANSYS model crack, however, propagates

straight across the part. This obvious discrepancy is because the material in the model

33

doesn’t truly plasticize in the way that the material plasticizes during the tear test. This

could also be partially due to the coarse mesh and the fact that the model is 2D instead

of 3D.

The Abaqus model for the base material ran and produced good results, but the FSP

model in the same modeling software did not produce satisfactory results. Refining the

mesh produced different results, but they were not any better. Therefore, a model for

the FSP sample was developed in ANSYS; this model did produce good results. When

the mesh was refined, however, the crack became smaller until at a certain mesh the

simulation produced no results at all. The digital image correlation (DIC) results

produced during the experiment in another paper [58] show similar qualitative results to

the model results for the base material, but the crack in the FSP sample did not take the

same path as that in the model of the FSP sample.

34

CHAPTER 4

THEORETICAL APPROACH

4.1 ASTM Standard Test Method for Measurement of Fracture Toughness

ASTM standard E1820 [9] enumerates the method for measuring fracture toughness

from the calculated stress intensity factor (K), J-integral (J), or crack tip opening

displacement (CTOD). All methods to specifically determine the KIc value are in another

standard, ASTM E399 [61].

The standard covers 3 specimen shapes, as shown in Figure 20: single-edge bend

[SE(B)], compact [C(T)], and disk-shaped compact [DC(T)]. For all three shapes, the

loading is mode I, or opening.

35

a)

b)

c)

Figure 20 Specimen shapes covered in ASTM E1820 [9] a) single edge bend [SE(B)] b) compact [C(T)] c) disk-shaped compact [DC(T)]

The sample must have a fatigue crack prior to this test, in order to sharpen the notch on

a microstructural scale. Various fatigue crack starter notch shapes are used, as shown

in Figure 21: a chevron notch, a straight through notch, a notch ending in a drilled hole,

and a narrow notch.

36

a) b) c) d)

Figure 21 ASTM E1820 notch shapes: a) chevron notch, b) straight through notch, c) notch ending in drilled hole, and d) narrow notch

The objective of the test method described in this standard is to load a precracked

specimen until crack growth occurs. This crack growth will either be unstable, called

fracture instability, or stable, called stable tearing. If fracture instability happens, the

fracture toughness will be a single point-value from the point of instability; if stable

tearing happens, a graph is obtained that plots the fracture toughness versus the crack-

extension (R-curve), and key points of interest may be determined from the R-curve.

The resulting fracture toughness data characterizes the material’s resistance to: fracture

of a stationary crack, fracture after some stable tearing, stable tearing onset, and

sustained stable tearing.

There are two possible procedures: the basic procedure and the resistance curve

procedure. In the basic procedure, the specimen is loaded to a certain displacement

level and the amount of crack extension that occurred is determined. This procedure

does not require crack extension measurement equipment, and determines only a

single K, J, or CTOD value. The purpose of this experiment is to develop a force-

displacement curve that can be used to evaluate K, J, or CTOD.

There are 17 annexes in this standard and 2 appendixes. Annexes 1 through 3 specify

requirements for testing single-edge bending, compact, and disk-shaped compact

specimens, respectively. Annex 4 specifies the methods for evaluating fracture

37

instability and pop-in. Annex 5 has been moved to ASTM standard E399 [61] because it

gives the method for determining the KIc value. Annexes 6 and 7 specify the methods

for determining the fracture toughness from fracture instability using J in annex 6 and

CTOD in annex 7. Annex 8 gives how to determine the J-R curve. Annex 9 gives how to

evaluate the JIc and KJIc values, which are the values obtained near the start of crack

growth. Annex 10 explains how to determine the δ-R curve. Annex 11 explains how to

evaluate the δIc value. Annex 12 covers miscellaneous information, including how to

calculate the stress intensity factor and compliance from crack size for all three

specimen shapes. Annex 13 has been moved to ASTM standard E399 [61] because it

gives the method for determining the KIc value from rapid loading. Annex 14 gives

special requirements for rapid-load J-integral fracture toughness testing. Annex 15

describes the technique for obtaining a J-R curve from a force-displacement curve and

initial and final crack size measurements. Annex 16 explains how to correct the J-

integral values. Annex 17 describes how to perform impact testing on Charpy-type

specimens and how to determine the fracture toughness from the results using a

fracture mechanics approach. Appendix 1 explains how to fit the J and crack size data

to an equation using the method of least squares, and appendix 2 gives guidelines for

measuring the fracture toughness of materials with shallow cracks.

4.2 Calculation Attempt

In this chapter, observations from the model are used as inputs to the calculations in

this standard instead of using the experimental results as the inputs.

38

This approach is based on the stress intensity definition of fracture toughness, and

enumerated in annexes 2 and 12 of ASTM standard E1820 [9]. The equation for the K

value from annex 2 is given in Equation 4.

Equation 4: 𝐾𝐾(𝑖𝑖) = 𝑃𝑃(𝑖𝑖)

(𝐵𝐵𝐵𝐵𝑁𝑁𝑊𝑊)1/2 𝑓𝑓 �𝑎𝑎𝑖𝑖𝑊𝑊�

Where K is the stress intensity factor, P is the applied load, W is the width of the

specimen, a is crack length, and B is specimen thickness. The function of the ratio of

crack length to specimen width is dependent on the specimen type; the model most

closely resembles a compact specimen, so the function for a compact specimen from

annex 2 is defined in Equation 5.

Equation 5: 𝑓𝑓 �𝑎𝑎𝑖𝑖𝑊𝑊� =

��2+𝑎𝑎𝑖𝑖𝑊𝑊��0.886+4.64�

𝑎𝑎𝑖𝑖𝑊𝑊�−13.32�

𝑎𝑎𝑖𝑖𝑊𝑊�

2+14.72�

𝑎𝑎𝑖𝑖𝑊𝑊�

3−5.6�

𝑎𝑎𝑖𝑖𝑊𝑊�

4��

�1−𝑎𝑎𝑖𝑖𝑊𝑊�

3/2

The crack length can be measured from the model, and all other variables are actually

inputs to the model. In the base material Abaqus model, the crack initiated at a

minimum load value of 200 MPa, so that is used for P in the equation in order to get the

stress intensity value at this point; annex 9 explains that the JIc value “characterizes the

toughness of a material near the onset of crack extension” [9], so the value of K

obtained closest to the start of the crack should be closest to the KIc value. Table 10

shows the values used for the calculation, as well as the result.

39

Table 10 Values used in stress intensity calculation, and result

Symbol Variable Name Value

E Elastic Modulus 44200 MPa

B Specimen Thickness 1.6 mm

BN Net Thickness 1.6 mm

P Applied Force 200 N

W Specimen Width 25.4 mm

a Crack Length 15.24 mm

K Stress Intensity Factor 338.66 N/mm3/2

The typical unit for the stress intensity definition of fracture toughness is MPa*m1/2. A

simple unit conversion shows that the answer given in Table 10 is equivalent to 10.7

MPa*m1/2.

Literature values of this value for various magnesium alloys [14, 15, 16, 17, 18] report a

range from 16.5 MPa*m1/2 to 34.8 MPa*m1/2. The estimate obtained from the calculation

is below this range, and so is most likely a conservative approach.

40

CHAPTER 5

FUTURE WORK

5.1 Conclusions

The model of the base material of WE43 created in Abaqus correlated well with the

experimental results; however, the FSP material model made in Abaqus aborted before

it could fully develop the results, and so a crack did not propagate in the same way that

it did in the base material model. The mesh was refined but no better results were

generated.

The FSP material model developed in ANSYS generated results. Mesh refinement did

not help the ANSYS results either. When compared to the experimental DIC results, the

crack in the model did not propagate in the same way as the crack in the experimental

FSP sample; this is due to an imperfect theory of plasticity upon which the modeling

software is based.

The selection of a two dimensional model could have been an oversimplification that

caused error in the results of the models.

The proposed approach to calculating the KIc fracture toughness in chapter 4 yields a

value lower than literature values for other magnesium alloys, and so is a conservative

approach.

5.2 Future Work

Further study of why the two models gave vastly different results despite similar inputs

is required.

41

Three dimensional models will be more descriptive and true to the assumptions made

for fracture mechanics specified in section 2.1 than the two dimensional models

developed here. The ASTM standard B871 outlining the experiment states that the

relevant result value depends on the thickness of the sample [11], but the dependence

of the plastic zone development on the thickness could be investigated.

The plastic zone development in other materials could be investigated and compared to

these results.

In this paper, the experiment outlined in ASTM standard B871 [11] was modeled, and

then the calculations for fracture toughness described in ASTM standard E1820 [9]

were applied to the results of that experiment; in the future, a model of the experiment

from E1820 could be used to generate the inputs for the calculation instead.

42

APPENDIX

ANSYS CODE FOR WE43 FSP MATERIAL WITH CRACK PREDICTION

43

*SET,W,0.0365

*SET,L,0.0286

*SET,E1,0.0111

*SET,E2,0.0064

/PREP7

ET,1,PLANE182

MPTEMP,,,,,,,,

MPTEMP,1,0

MPDATA,EX,1,,4.42E10

MPDATA,PRXY,1,,0.27

TB,BISO,1,1,2,

TBTEMP,0

TBDATA,,1.95E8,2E9,,,,

MPTEMP,,,,,,,,

MPTEMP,1,0

44

MPDATA,EX,2,,4.42E10

MPDATA,PRXY,2,,0.27

TB,BISO,2,1,2,

TBTEMP,0

TBDATA,,2.61E8,2E9,,,,

K, ,,,,

K, ,W,L,,

K, ,,L,,

K, ,(W-E1),,,

K, ,W,E2,,

*SET,WE,(W-E1)

CYL4,WE,L/2,0.004

K, ,,E2,,

LSTR, 10, 3

LSTR, 3, 2

LSTR, 2, 5

LSTR, 10, 5

45

LSTR, 4, 1

LSTR, 1, 10

LSTR, 4, 5

FLST,2,4,4

FITEM,2,5

FITEM,2,8

FITEM,2,7

FITEM,2,6

AL,P51X

FLST,2,4,4

FITEM,2,10

FITEM,2,8

FITEM,2,9

FITEM,2,11

AL,P51X

ASBA, 2, 1

FLST,3,2,5,ORDE,2

46

FITEM,3,3

FITEM,3,-4

ARSYM,Y,P51X, , , ,0,0

FLST,2,4,5,ORDE,2

FITEM,2,1

FITEM,2,-4

AGLUE,P51X

FLST,5,2,5,ORDE,2

FITEM,5,1

FITEM,5,5

CM,_Y,AREA

ASEL, , , ,P51X

CM,_Y1,AREA

CMSEL,S,_Y

!*

CMSEL,S,_Y1

AATT, 2, , 1, 0,

47

CMSEL,S,_Y

CMDELE,_Y

CMDELE,_Y1

!*

FLST,5,2,5,ORDE,2

FITEM,5,2

FITEM,5,4

CM,_Y,AREA

ASEL, , , ,P51X

CM,_Y1,AREA

CMSEL,S,_Y

!*

CMSEL,S,_Y1

AATT, 1, , 1, 0,

CMSEL,S,_Y

CMDELE,_Y

CMDELE,_Y1

48

!*

ESIZE,0.0005,0,

MSHAPE,0,2D

MSHKEY,0

!*

FLST,5,2,5,ORDE,2

FITEM,5,1

FITEM,5,5

CM,_Y,AREA

ASEL, , , ,P51X

CM,_Y1,AREA

CHKMSH,'AREA'

CMSEL,S,_Y

!*

AMESH,_Y1

!*

CMDELE,_Y

49

CMDELE,_Y1

CMDELE,_Y2

!*

ESIZE,0.002,0,

FLST,5,2,5,ORDE,2

FITEM,5,2

FITEM,5,4

CM,_Y,AREA

ASEL, , , ,P51X

CM,_Y1,AREA

CHKMSH,'AREA'

CMSEL,S,_Y

!*

AMESH,_Y1

!*

CMDELE,_Y

CMDELE,_Y1

50

CMDELE,_Y2

!*

FINISH

/SOL

!*

ANTYPE,4

!*

TRNOPT,FULL

LUMPM,0

!*

ANTYPE,4

NLGEOM,1

FLST,2,4,4,ORDE,2

FITEM,2,19

FITEM,2,-2

!*

/GO

51

DL,P51X, ,ALL,

FLST,2,4,4,ORDE,2

FITEM,2,1

FITEM,2,-4

!*

/GO

DL,P51X, ,UX,

!!!MMM=7949

MMM=2776

FLST,2,4,4,ORDE,2

FITEM,2,1

FITEM,2,-4

DL,P51X, ,UY,0.001/60*1

ESEL,S,LIVE

CM,K%1%,ELEM

CMSEL,S,K%1%

52

ALLSEL,ALL

OUTPR,BASIC,ALL,

ANTYPE,4

NLGEOM,1

NSUBST,20,20,12

TIME,1

SOLVE

*DO,J,1,MMM

*GET,A1,NODE,J,S,EQV

*IF,A1,GT,302E6,THEN

NSEL,S, , ,J

ESEL,ALL

ESLN,S

NROPT,FULL,,ON

EKILL,ALL

ALLSEL,ALL

*ENDIF

53

*ENDDO

*DO,I,2,14

FLST,2,4,4,ORDE,2

FITEM,2,1

FITEM,2,-4

DL,P51X, ,UY,0.001/60*I

ESEL,S,LIVE

CM,K%I%,ELEM

CMSEL,R,K%I%

ALLSEL,ALL

OUTPR,BASIC,ALL,

ANTYPE,4

NLGEOM,1

NSUBST,20,20,12

TIME,I

SOLVE

*DO,J,1,MMM

54

*GET,A1,NODE,J,S,EQV

*IF,A1,GT,340E6,THEN

NSEL,S, , ,J

ESEL,ALL

ESLN,S

NROPT,FULL,,ON

EKILL,ALL

ALLSEL,ALL

*ENDIF

*ENDDO

*ENDDO

CMSEL,NONE

ESEL,NONE

/SEG,DELETE

/SEG,MULTI,,0.5

/POST1

SET,I,LAST,1

55

! SET,1,LAST,1

CMSEL,S,K%1%

PLNSOL,S,EQV,0,

*DO,I,2,14

SET,I,LAST,1

CMSEL,R,K%I%

PLNSOL,S,EQV,0,

*ENDDO

FINI

/SEG,OFF

/ANFILE,SAVE,'video','avi',' '

ANIM,1,1

56

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