Ductile Fracture Behavior of a Nickel-Based Superalloy and Thermally

Ductile Fracture Behavior of a Nickel-Based Superalloy and Thermally-

Induced Strain Behavior of an Aluminum Alloy

THESIS

Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State University

Jarrod Lee Smith, B.S.

Graduate Program in Mechanical Engineering

The Ohio State University

2015

Master's Examination Committee:

Dr. Amos Gilat, Advisor

Dr. Brian Harper

Jarrod Lee Smith

2015

Abstract

The objective of this research is to generate experimental data that can be used to calibrate and validate constitutive models for plastic deformation and failure that are implemented in numerical simulations. In the first part of the research, tension tests are conducted at elevated temperatures on notched and unnotched thin flat specimens made of a nickel-based superalloy. The geometry of each sample is designed to induce various states of stress inherent in original jet engine components. Three-dimensional Digital

Image Coorelation (3D-DIC) is used to measure the full-field deformations. The results of these tests show the setup is successful in capturing displacements and strains on the surface of each sample at elevated temperatures for ductile materials. The force versus displacement curves reveal that the nickel-based superalloy being tested exhibits thermal softening and serrated flow due to strain localizations at elevated temperatures.

The second part of the research introduces a method to characterize the thermally induced strain behavior of a 6000 series aluminum alloy during the car manufacturing process. To simulate the stamping process, dogbone and rectangular strip specimens are subject to uniaxial and bending strains. A method for measuring strains on the surface of specimens during bend tests is established. Following deformation, specimens are subjected to thermal heating cycles that simulate the paint-bake cycle. The thermally ii induced strains during the heating cycle are measured for the each of the specimens. In addition, the material properties and thermal buckling behavior of the aluminum at various temperatures are investigated. The results show that specimens subject to different bending strains display elevated coefficients of thermal expansion and residual strain after being rendered to a heating cycle. The measurements from the material property and thermal buckling testing can be used to calibrate a thermally dependent material model.

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This document is dedicated to my closest friends, my family,

and the memory of my mother.

Acknowledgments

Several people have helped me during my life to get to this point and I would like to take the time to thank them now. First I’d like to thank my parents Mike and Marsha whose inspiration, love, and courage throughout my life and academic career has made this possible. To my sisters Shanna and Maryssa: your guidance, love, and resilience throughout all the pitfalls and peaks of our lives has been a beacon for me to follow. To my closest friends- Bryan Middlebrooks, Patrick Burr, Lucy Leard, Michael Heit, and

Jon Bentley- your friendship, support and advice has been exemplary.

My Advisor, Professor Amos Gilat has been both an inspiration and incribly supportive throughout my time here and it has been a pleasure to work with him. Dr.

Jeremy Seidt has been a tremendous mentor for me in and out of the laboratory and I’m eternally grateful for all of his help and guidance over the past few years. I would also like to thank Dr. Brian Harper for taking the time to serve as my thesis defense committee member.

This research was funded by Pratt and Whitney and the Honda Research and

Development Americas. Thanks to Mike Hribernik and Kon Haake at Pratt and Whitney for their advice and support over the completion of the research. Thanks to Ryan

Hahnlen for their support in this project as well. v

Lastly, I would like to thank my fellow students and colleagues from the Dynamic

Materials of Mechanics Laboratory: Jeremiah Hammer, Kevin Gardner, Tim Liutkus, and

Aaron Reesa. These researchers have been an important part in my experience not only through providing insight in our discussions but also through their friendship.

Vita

2008...... Xenia High School

2012...... B.S. Mechanical Engineering The Ohio State University

2012- present ...... Graduate Research Associate, Dynamic Mechanics of Materials Laboratory, Department of Mechanical and Aerospace Engineering, The Ohio State University

Fields of Study

Major Field: Mechanical Engineering

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Table of Contents

Abstract ...... ii

Acknowledgments...... v

Vita ...... vii

Fields of Study ...... vii

Table of Contents ...... viii

List of Tables ...... xi

List of Figures ...... xii

Chapter 1: Introduction ...... 1

Chapter 2: Ductile Behavior of a Nickel-based Superalloy at Elevated Temperature ... 5

2.1 Motivation & Objectives ...... 5

2.2 Literature Review ...... 7

2.2.1 Ductile Fracture ...... 7

2.2.2 Nickel-Based Superalloys ...... 11

2.2.3 Elevated Temperature 3D DIC ...... 12

2.3 Experimental Procedures and Techniques ...... 14

viii

2.3.1 Specimen Design ...... 14

2.3.2 Elevated Temperature Experiments ...... 15

2.3.3 3D-DIC Measurements ...... 20

2.4 Results & Discussion ...... 24

2.4.1 Smooth Uniaxial Test Series ...... 24

2.4.2 Varied Geometry Test Series ...... 25

2.4.3 Elevated Temperature Effects on Varied Geometry Test Series ...... 26

2.4.4 Serrated Flow Effects for Varied Geometry Test Series ...... 27

2.4.4 Fracture Locus for Varied Geometry Test Series ...... 32

2.5 Summary & Conclusions ...... 34

Chapter 3: Thermally Induced Strains of a 6000 Series Aluminum Alloy...... 36

3.1 Motivation & Objectives ...... 36

3.2 Literature Study ...... 37

3.2.1 Paint-Bake Response ...... 37

3.2.2 Thermal Buckling ...... 39

3.3 Experimental Procedures & Techniques ...... 41

3.3.1 Tension Tests ...... 41

3.3.2 Bend Testing ...... 45

3.3.3 Thermal Cycling ...... 49

3.4 Results & Discussion ...... 56

3.4.1 Initial Strain Testing ...... 56

3.4.2 Material Property Test Series ...... 58

3.4.3 Thermal Cycle Testing ...... 62

3.5 Summary & Conclusions ...... 72

Appendix A: Full Experimental Results - Ductile Fracture of Nickel-Based Superalloy 74

A.1 Force versus displacement curves ...... 75

A.2 True stress versus true strain curves ...... 80

A.3 Evolution of equivalent plastic strain versus stress triaxaility approximation plots

...... 81

Appendix B: Full Experimental Results – Thermally Induced Strains of a 6000 series

Aluminum Alloy ...... 86

B.1 Prestrain curves...... 87

B.2 Strain response to thermal cycles for various specimens ...... 89

B.3 Measured CTE values for various specimens...... 91

B.4 Strain offset measurements for various specimens ...... 93

Bibliography ...... 95

List of Tables

Table 3.1 Experimental test plan for uniaxial specimens ...... 41

Table 3.2 Overview of thermal profiles ...... 42

Table 3.3 Experimental test plan for bending experiments ...... 45

Table 3.4 Calculated coefficient of thermal expansion in different directions for a uniaxial specimen during an A-type thermal cycle...... 64

List of Figures

Figure 2.1 Geometries for (a)uniaxial, (b) 0.263” notch, and (c) hole specimens ...... 15

Figure 2.2 Furnace setup used with digital image correlation, (a) inside of furnace, (b)

DIC set up and furnace window, (c) thermocouple attachment to specimen ...... 18

Figure 2.3 Ceramic coating for ductile fracture specimens ...... 19

Figure 2.4 1” extensometer for uniaxial specimens ...... 21

Figure 2.5 Data point used for uniaxial specimens ...... 22

Figure 2.6 (a) 1” extensometer and (b) data point used for notched specimens ...... 22

Figure 2.7 (a) 1” extensometer and (b) data points used for hole specimens ...... 23

Figure 2.8 Comparison of true stress and strain for uniaxial tension experiments at 875°F and 1025°F ...... 25

Figure 2.9 Comparison of applied force versus displacement for different tension specimen geometries ...... 26

Figure 2.10 Force versus displacement curves for five separate tension experiments carried out on a Notch (0.394”) sample at 875°F and 1025°F ...... 27

Figure 2.11 Equivalent plastic strain versus displacement for each specimen geometry carried out at 875°F ...... 28

Figure 2.12 Evolution of strain between 25-50% versus a selected time period for a smooth uniaxial specimen tested at 875°F...... 29 xii

Figure 2.13 Evolution of strains in the x direction for a smooth uniaxial sample tested at

875°F. Each strain plot refers to a specific time in Figure 2.11...... 31

Figure 2.14 Equivalent strain and stress triaxiality approximation evolution for evolution for each geometry ...... 32

Figure 2.15 Equivalent plastic strain and stress triaxiality approximation at failure ...... 34

Figure 3.1 Uniaxial specimen geometry for thermal cycle testing ...... 43

Figure 3.2 Uniaxial prestrain experimental setup ...... 43

Figure 3.3 Bend specimen geometry for (a) original sample, (b) rolled direction sample,

Figure 3.4 Guided bend test fixture and plungers ...... 46

Figure 3.5 (a) Overview of bend test experimental setup (b) specimen placement (c) DIC setup ...... 48

Figure 3.6 (a) Furnace setup for thermal cycle testing (b)inside of furnace ...... 50

Figure 3.7 Overview of clamping mechanism, (a) clamped bend specimens, (b) exploded view with uniaxial specimens ...... 51

Figure 3.8 Clamped specimens for (a) thermal buckling, (b) combined, and (c) bend experiments ...... 52

Figure 3.9 Dimensions for thermal buckling boundary condition plate ...... 52

Figure 3.10 (a) Location of 1” Extensometer for a uniaxial specimen before mechanical testing. (b) Location of 1”extensometer and data point at maximum point of strain after a prestraining operation...... 53

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Figure 3.11 Location of data point before (a) and vertical displacement after (b) a 20% bending prestrain experiment ...... 54

Figure 3.12 (a) Data point on a 20% bending prestrain specimen and (b) Location of 1” extensometers and data point for a 0% bending prestrain specimen during a thermal cycle

...... 55

Figure 3.13 Location of a 1” extensometer before a thermal cycle (b) Location of a 1” extensometer and a data point placed on the point of maximum displacement during a thermal cycle ...... 55

Figure 3.14 Strain versus displacement for typical uniaxial prestrain experiments ...... 57

Figure 3.15 Strain versus vertical displacement for typical bending prestrain experiments

...... 58

Figure 3.16 True stress versus true strain data from uniaxial specimens in the unstrained and 20% prestrained conditions at 25°C ...... 59

Figure 3.17 True stress versus true strain data from uniaxial specimens in the unstrained and 20% prestrained conditions at 190°C ...... 60

Figure 3.18 True stress versus true strain data from uniaxial specimens in the 20% prestrained condition at 25 and 190°C ...... 61

Figure 3.19 True stress versus true strain data from uniaxial specimens in the unstrained conditions at 25 and 190°C ...... 62

Figure 3.20 Microstrains versus time for a uniaxial sample during an A-type thermal cycle ...... 63

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Figure 3.21 Microstrain in the X & Y directions versus specimen temperature with curve fits to determine CTE ...... 64

Figure 3.22 Comparison of strains in the X & Y directions with the estimated strains due to thermal expansion in samples with a bending prestrain of 10% and subjected to varying thermal cycles ...... 66

Figure 3.23 Comparison of strains in the X & Y directions with the estimated strains due to thermal expansion in samples with a bending prestrain of 20% and subjected to varying thermal cycles ...... 66

Figure 3.24 Comparison of strains in the X and Y directions for an undeformed bend specimen and a transverse bend specimen subjected to a C-type thermal cycle ...... 67

Figure 3.25 Comparison of strains in the X and Y directions for a combined strain specimen subjected to a C-type thermal cycle ...... 68

Figure 3.26 Comparison of average coefficient of thermal expansion values for all bend and combined tests ...... 70

Figure 3.27 Strain offsets in the X and Y directions during the first and second cooling sequences of A and C type heating cycles for all bending and combined tests ...... 71

Figure 3.28 Vertical displacement of the centerpoint of the gage section for dogbone specimens in the undeformed and 20% prestrained conditions during an A-type thermal cycle ...... 72

Figure A.1 Experimental results for 0.263" radius notch tests at 875°F……………………….75

Figure A.2 Experimental results for 0.263" radius notch tests at 1025°F ...... 75

Figure A.3 Experimental results for 0.394" radius notch tests at 875°F ...... 76

Figure A.4 Experimental results for 0.394" radius notch tests at 1025°F ...... 76

Figure A.5 Experimental results for 0.787" radius notch tests at 875°F ...... 77

Figure A.6 Experimental results for 0.787" radius notch tests at 1025°F ...... 77

Figure A.7 Experimental results for hole specimens at 875°F ...... 78

Figure A.8 Experimental results for hole specimens at 1025°F ...... 78

Figure A.9 Experimental results for uniaxial specimens at 875°F ...... 79

Figure A.10 Experimental results for uniaxial specimens at 1025°F ...... 79

Figure A.11 True stress versus strain for uniaxial specimens at 875°F ...... 80

Figure A.12 True stress versus strain for uniaxial specimens at 1025°F ...... 80

Figure A.13 Equivalent strain versus stress triaxility for 0.263" radius notched specimens

...... 81

Figure A.14 Equivalent strain versus stress triaxility for 0.394" radius notched specimens

...... 82

Figure A.15 Equivalent strain versus stress triaxility for 0.787" radius notched specimens

...... 83

Figure A.16 Equivalent strain versus stress triaxility for hole specimens ...... 84

Figure A.17 Equivalent strain versus stress triaxility for uniaxial specimens ...... 85

Figure B.1 Prestrains for transverse bend specimens ………………………………………………..87

Figure B. 2 Stress strain curves of prestraining operation for combined loading specimens

...... 88

Figure B. 3 Bending prestrains for combined loading specimens ...... 88

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Figure B. 4 Strains in the X-direction for transverse bend specimens during a C-type heat cycle ...... 89

Figure B. 5 Strains in the Y-direction for transverse bend specimens during a C-type heat cycle ...... 89

Figure B. 6 Strains in the X-direction for combined loading specimens during a C-type heat cycle ...... 90

Figure B. 7 Strains in the Y-direction for combined loading specimens during a C-type heat cycle ...... 90

Figure B. 8 CTE values for combined loading specimens during the first and second dwells ...... 91

Figure B. 9 CTE values for transverse bend specimens during the first and second dwells

...... 91

Figure B. 10 CTE values for each specimen during the first dwell of the specified heat cycle ...... 92

Figure B. 11 CTE values for each specimen during the second dwell of the specified heat cycle ...... 92

Figure B. 12 Strain offsets in the X and Y directions during the first and second heating dwells of A and C type heating cycles for all bending and combined tests ...... 93

Figure B. 13 Total strain offsets in the X and Y directions relative to normal estimated thermal expansion for all specimens after the first cooling period ...... 94

Figure B. 14 Total strain offsets in the X and Y directions relative to normal estimated thermal expansion for all specimens after the first cooling period ...... 94

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Chapter 1: Introduction

Finite Element Analysis (FEA) is the main tool employed by engineers and designers when designing new solid parts. FEA breaks down a component into simpler parts called finite elements that are used in conjunction with constitutive equations and boundary conditions to define a physical system. The constitutive equations and material parameters are determined from experimental data and are implemented in numerical codes like LS-DYNA [1] and ABAQUS [2] to simulate practical applicaitons. These simulations provide insight into the complex response of materials under various loading conditions without the monetary and time expense of full-scale prototyping. In order to effectively model material behavior both the elastic and plastic response must be understood. The linear elastic behavior of the material is considered in situations where the loading and deformation of the mechanical system is small. Material models used to predict behavior in the linear elastic range are calibrated using parameters such as the elastic modulus and the Poisson’s Ratio which are readily available for many materials.

During elastic deformation, the bonds between atoms in the material are strained but once the force is relieved the atoms return to their original positions. Past the yield point plastic deformation dominates within the material and more complex models are needed to determine the flow stress and defomration of the specimen.

In order for a material model to be reliable the parameters must be properly calibrated by consistent experimental data. New experimental techniques are necessary to accurately replicate the stress states and environments in which the material will operate. This thesis is composed of two experimental studies that involve the development of experimental techniques for measuring material properties and responses that will be used for the development of mathematical models and unification of material models. In the first study, the ductile behavior of a nickel-based superalloy at elevated temperatures is investigated. The objective of this work is to generate experimental data that can be used to calibrate plastic deformation and failure model for numerical simulations. Tension tests are conducted at strain rate of 1x10⁻³ s⁻¹ at temperatures of

875°F and 1025°F. Specimens are fabricated into five different geometries: dogbone, three notched specimens with cutouts of varying radii and a plate specimen with a central hole. The geometry of each sample is designed to induce various stress states during tension testing. Each specimen is tested to failure at elevated temperatures utilizing a custom-built furnace connected to a hydraulic load frame. Three-dimensional Digital

Image Coorelation (3D-DIC) is used to measure the full-field strains and displacements on the surface of each specimen by employing a sophisticated camera setup located outside the furnace. The results of these tests show that the camera setup is successful in capturing displacements and strains on the surface of each sample at elevated temperatures for ductile materials. The force versus displacement curves reveal that the nickel-based superalloy being tested exhibits thermal softening and serrated flow due to strain localizations.

The second experimental study aims to characterize the thermally-induced strain response of a 6000 series aluminum alloy during the stamping and paint-bake cycles of the car manufacturing process. To simulate the stamping process, dogbone and rectangular strip samples are punched from a rolled aluminum sheet and subjected to uniaxial strains ranging from 0% to 20%, bending strains ranging from 0% to 20%, combinations of uniaxial and bending strains, and bending strains transverse to the rolled direction of the sheet. A specially designed guided bend test apparatus allows for the measurements of displacements and strains on the surface of bend specimens during deformation by utilizing 3D-DIC. After each sample has been deformed they are placed in a furnace and subjected to thermal heating cycles that simulate the paint-bake cycle.

The thermally induced strains during the heating cycle are measured for each of the deformed dogbone and rectangular strip specimens by 3D-DIC. The material properties of the aluminum at various temperatures is investigated by testing unreformed and 20% uniaxially prestrained dogbone specimens to failure at 25°C and 190°C. Thermal buckling properties of the aluminum for similar dogbone specimens are analyzed by subjecting the specimens to a clamped boundary condition and a thermal loading cycle.

The results show that dogbone specimens subjected to 20% uniaxial strain and unreformed strip specimens exhibit typical strain behavior characterized by the coefficient of thermal expansion (CTE) of the aluminum. Specimens subject to bending strain, transverse bending strain, and a combination of uniaxial and bending strain display elevated CTE’s and residual strain after being rendered to a heating cycle. Dogbone specimens tested to failure exhibit strain hardening and thermal softening and increased

3 ductility at elevated temperatures. In thermal buckling testing the boundary conditions creates a force within the dogbone specimens resulting in a residual vertical displacement from the clamping plate regardless of the prestrain in the sample.

Chapter 2: Ductile Behavior of a Nickel-based Superalloy at Elevated

Temperature

2.1 Motivation & Objectives

Jet engines are designed to operate simultaneously at high speeds and elevated temperatures while exhibiting phenomenal reliability and maintaining an aerodynamic profile. Compromises during the design process must be made to accommodate for each attribute. However, the operators, passengers, and designers are ultimately concerned with minimizing the chance of catastrophic failure. Fan blades and turbine disks operate at high rotational speeds within the engine and failure of either part can lead to loss of the engine, damage to the fuselage and ultimately the loss of life. The Federal Aviation

Administration (FAA) has implemented the FAR/JAR 25.903(d)(1) regulation to ensure that design precautions are taken to decrease such risks [3]. In response to this regulation, fan blades and discs have been designed to reduce the frequency of blade-off failures and to reduce the energy of the fragments of these components should a failure occur. Engine shrouds have been specifically designed to contain the debris and mitigate any further damage to the aircraft. [4] Despite these regulations, catastrophes still have occurred. During the years, 1969-1997, 676 uncontained rotor failures occurred with 15 5 events that seriously damaged the airplane and 93 events where the airplane was capable of maintaining flight and making a safe landing [5] One of these events was LOT Flight

7 which crashed on approach to Warsaw Frederic Chopin Airport, Poland on March 14,

1980. During the plane’s descent, the crew experienced troubles with the landing gear and the landing was aborted. As the pilot increased thrust in the engines to return to flight, a low pressure turbine disc in one of the engines disintegrated and could not be contained by the engine shroud. The debris ejected from the engine damaging the controls and stabilizers of the aircraft. Unable to control the plane, the pilot attempted to perform a crash landing and all 87 passengers on board perished [6]. United Airlines

Flight 232 and LOT Polish Airlines Flight 5055 are similar examples of the catastrophes caused uncontained engine failures [6, 7]. With these disasters in mind it is important that great care is taken in the design of engine components to reduce the risk of failure and to also prevent catastrophe should a failure occur.

While safety is of utmost importance, manufacturers and researchers alike are currently attempting to increase the energy efficiency of jet turbine engines to reduce fuel costs and greenhouse gas emissions. The European Advisory Council for Aeronautical

Research has called for a 50% reduction in fuel burn per passenger mile by 2020 with 20-

25% of the reduction coming from the airframe and 15-20% from the specific fuel consumption of the aircraft. Simple solutions to increase the fuel efficiency such as increasing the turbine entry temperature or raising the overall pressure ratio of the engine have a small effect on the overall thermal efficiency [8]. One strategy currently being implemented by Pratt and Whitney in their new PurePower engine is reducing the fan

6 speed with the Geared Turbofan System while a low-pressure compressor and turbine operate at a different speed [9]. This new system has greatly improved the efficiency of the engine but the new gear box also adds undesired weight to the engine. 40-50% of the total weight of an aircraft engine comes from the nickel-based superalloy components of the turbine and combustor sections of the engine [10]. To offset the addition of weight to the airframe, super-nickel components such as turbine blades, engine shrouds, turbine disks, and combustion chambers need to be redesigned to use less material and reduce weight.

To ensure the safety of human life while also producing an economically viable engine, designers need access to accurate material models for the components within the engine. Because the operating conditions and geometries for these components are complex they need to be investigated experimentally to make the simulations more robust. The objective of this project is to investigate the ductile fracture of a nickel-based superalloy at elevated temperatures. A fracture locus is created by performing tension tests on thin, flat specimens. The specimens have varying geometries to induce different strain states and populate the fracture locus. 3D-DIC allows for full-field strain measurements to be made on the surface of each specimen.

2.2 Literature Review

2.2.1 Ductile Fracture

The physically based fracture models for ductile metals are based on the mechanism of void nucleation and growth that leads to the formation of cracks and failure of the material. McClintock [11] and Rice and Tracey [12] were the first to

7 investigate the growth and coalescence of pre-existing voids within a plastically deforming material. McClintock found fracture strain had a strong influence on the transverse principal stress rather than solely on the maximum principal stress. He also found that the history of stress and strain had a large bearing on the ductile fracture of a material. Rice and Tracey studied the growth of a spherical void in an infinite perfectly plastic material subjected to a remote strain field. Through their experiments the authors found that the expansion of the cavity was governed exponentially by the stress triaxiality, , which is defined as:

(1)

where is the mean stress and is the effective stress. The mean stress and effective stress defined as:

(2)

And

(3)

Where is the deviatoric stress tensor defined as:

(4)

Several material failure models have been built upon the effect of stress triaxiality on ductile fracture. The damage parameter governing the failure in this model is dependent on the equivalent plastic strain of the material which is a function of the stress triaxiality.

To better understand this phenomena, several researchers have investigated the 8 relationship between the equivalent plastic strain and stress triaxiality [13, 14]. Bau and

Wierzbicki conducted a series of tests on various specimens while conducting parallel simulations using finite element methods. By comparing the experimental results with those from the simulations a simple relation between the equivalent strain to fracture and the stress triaxiailty was developed. However, none of the models investigated were able to capture the behavior over the entire triaxiality range. To better characterize the material, Barsoum and Faleskog [15] implemented a deviatoric stress state parameter known as the Lode parameter or:

(5)

Where , , and are the principal stresses. The Lode parameter and stress triaxiality are used as independent variables to define the state of stress in more advanced failure models. One such model is the Modified Mohr-Coulomb (MMC) [16] criterion which provides a physically based model of ductile fracture. The MMC model is governed by the following equation:

(6)

Where is the equivalent failure strain, is the Lode parameter, is the stress triaxiality, and are parameters of the material strain hardening, and are basic

Mohr-Columb parameters and determines the Lode angle dependence of the model.

Each of the parameters can be determined from the experimental data or model simulations of the testing specimens and can be used to create a fracture locus. The

9 damage evolution is also an important part in predicting the failure of a material. The damage function is defined as:

(7)

Where the is the equivalent plastic strain and is a stress triaxiality and Lode parameter dependent failure strain. When the damage parameter is equal to 1 for any material element, failure of the material is imminent. If the stress triaxiality and Lode parameter are held constant, the equivalent plastic strain at failure can be found by integrating equation (7) and the resulting function represents the 3D failure locus. The best tests for calibration are the ones where the stress triaxiality and Lode parameter are held constant such as biaxial punch tests and notched specimen tests. To generate data points for the failure locus, the equivalent plastic failure strain can be determined thru 3D

Digital Image Correlation (DIC) measurements on the surface of the specimen at failure while the stress invariants are determined through simulations of the specimen.

Mohr and Eboenoether [17] and Mohr and Henn [18] developed another weighting function by studying the failure of a specially designed thin butterfly specimen under different loading conditions. Their research shows that the ratio of two principal strains can be correlated to the stress triaxiality under plane stress conditions as .

(8)

The Hencky strain tensor used to measure the strains on the surface of the specimen can be defined by:

(9)

where is the left Cauchy Green deformation tensor:

(10)

and is the deformation gradient tensor. If the material is incompressible, the deformation is isochoric, the trace of the Hencky strain rate is zero, and the third principal strain can be determined from:

(11) and the equivalent plastic strain is:

(12)

For thin specimens, the Hencky strain along with the ratio of the principal strains can be converted to a stress-state failure locus.

2.2.2 Nickel-Based Superalloys

Nickel-based superalloys exhibit high temperature strength, toughness and resistance to corrosion and oxidation in harsh environments. Because of these attributes, nickel-based superalloys are extensively used in jet engine turbines, rocket engines and power plants [11]. The study of these alloys at elevated temperatures has mainly focused on plastic deformation during compression and tension tests at different strain rates.

Agahaie-Khafri et al. [19] performed compression tests on Hastelloy X at strain rates of

1x10⁻³,1x10⁻² , 1x10⁻¹ and 5x10⁻¹ s⁻¹ at temperatures between 950°C-1050°C. Liutkus

[20] studied Inconel 718 tension specimens at strain rates from 1x10⁻⁴ s⁻¹ to 2000 s⁻¹ at room temperature and at a strain rate of 1 s⁻¹ at temperatures from 200°C-800°C using

DIC. Hrutkay et al. [21] studied the tensile deformation behavior of Haynes 230 at temperatures of 25-950C and strain rates of 1x10⁻³ , 1x10⁻⁴ and 1x10⁻⁵ s⁻¹. This study observed stress serrations at temperatures about 300C which were caused by dynamic strain aging, solute drag and dynamic recrystallization within the microstructure of the material. Sakthivel et al. [22] examined the serrated flow behavior in Hastelloy X by performing tensile tests over a temperature range of 27-754°C at strain rates of 3 x10⁻³ to

3x10⁻⁴ s⁻¹. These authors found that the type of stress serrations depend on temperature and strain rate. To further the study of serrated stresses, B. Swaminathan et al. [23] subjected Hastelloy X to a tensile, thermomechanical loading and investigated the propagation of Portevin-Le Chatelier band distribution in uniaxial and notched geometries utilizing 3-D DIC measurements.

2.2.3 Elevated Temperature 3D DIC

DIC techniques allow researchers to measure full-field strains and gather insight into the failure of materials in complex experimental setups and conditions. 3D-DIC at elevated temperatures is one technique that several researchers have successfully implemented in the past including: Turner et al. [24], Pan et al. [25], Grant et al. [26], and Hammer et al.

[27].

Turner et al. [24] used a single video camera with an infrared cut filter to take images of a mild steel specimen at 6 different temperatures from 20 to 600°C. The coeffiecient of thermal expansion was measured and compared to independent strain gage measurements. The system had limitations in the number of images that could be captured, infrared interference with the camera, and maximum test temperature.

Pan et al [25] captured high quality digital images of a chromium-nickel austenite stainless steel sample heated to 1200°C and calculated the full-field thermal deformation as well as the coefficient of thermal expansion using 2D-DIC. A single CMOS camera was used to capture the images in conjunction with an optical band pass filter that blocks any wavelength of light outside of the 428-470 nm range. Blue LED lights with a wavelength of 450nm were used to light the specimen and reduce the infrared signal interfering with the camera.

Grant et al. [26] investigated the thermo-mechanical loading of a RR1000 tension sample for strains up to 2% and 900°C. DIC was completed by tracking scratches on the surface of the specimen instead of applying a typical speckle pattern. Effects of blackbody radiation were reduced with the use of filters and LED lighting. The elastic modulus and coefficient of thermal expansion were determined from the data. Reference images had to be taken during each incremental heating step due to oxidation of the specimen surface thus different techniques need to be applied to future thermomechanical tests.

Hammer et al. [27] implemented a 3D-DIC system with linear polarizers and infrared mirrors to measure the full field strains of tension and compression specimens up to 600°C. Speckle pattern adhesion to the samples was an issue at temperatures over

600°C but the set-up is capable of temperatures up to 860°C with the utilization of different bonding agents for the speckle pattern. This experimental set-up was used in the completion of the current research and will be described in more detail herein.

2.3 Experimental Procedures and Techniques

The experimental program created to study the ductile fracture behavior of a nickel-based superalloy is presented in this section. The geometry of the thin, flat specimens designed to create various Lode parameters and stress triaxialities is described.

Techniques to perform tension tests at two elevated temperatures using a custom furnace and a servo-hydraulic load frame are discussed. Lastly, the method of utilizing 3D-DIC to measure full-field displacements and strains at elevated temperatures is introduced.

2.3.1 Specimen Design

In order to construct a strain-based failure locus for the superalloy a series of thin, flat specimens are tested to approximate the plane stress condition. The specimens are cut from a 0.060” thick sheet stock of the nickel-based superalloy with the use of

Electrical Discharge Machining (EDM). The specimens each have a different geometry: smooth, notched with cutouts of varying radii, and a flat specimen with a central hole.

Each of these geometries was designed to provide various triaxialities and Lode parameters. For the smooth sample and large radii specimens the stress state near the area of failure corresponds to uniaxial tension while a plain strain condition is achieved for small notch radii. The smooth sample has a gage length of 1.5” and a width of

0.316”. All notched samples are 0.787” wide and feature a 0.394” wide gage section.

Three different notch radii are considered in this test: 0.263”, 0.394”, and 0.787”. The plate specimen has a gage width of 0.787” and a hole with a diameter of 0.316” in the center of the specimen. Each specimen has a 1.5”x15/16” tab with a 0.5” diameter hole located in the center which is used to attach the specimens to the loading assembly of the

14 servo-hydraulic load frame. An overview of the specimen geometries can be found in

Figure 2.1. The minimum gage width and plate thickness were measured before each test to insure accurate data analysis.

a b

c Figure 2.1 Geometries for (a)uniaxial, (b) 0.263” notch, and (c) hole specimens

2.3.2 Elevated Temperature Experiments

Tension tests are completed on the thin, flat superalloy specimens at a single strain rate of 1x10⁻³ s⁻¹ and two elevated temperatures of 875°F and 1025°F. These temperatures are achieved with the use of a custom designed furnace attached to a 20 kip

Instron Load Frame. The front of the furnace is mounted to the load frame so that the rear of the furnace is free to open for specimen manipulation while maintaining a

15 constant optical path to the cameras located in front of the furnace. A PID controller maintains a constant temperature through a feedback loop with the use of two thermocouples located within the insulation wall of the furnace. An Inconel 718 fan is located at the rear of the furnace to stir the air and remove thermal gradients that could disrupt DIC measurements on the surface of the specimens. The circulation also allows for the specimens to be heated rapidly and uniformly.

Each tension specimen is placed in between two slotted Inconel 718 adapters and attached via an Inconel 718 0.5” diameter pin. The adapters are joined to two separate push rods which are attached to a 20 kip load cell attached to the vertical cross head and a hydraulic actuator. MTS 793 control software directs the motion of the hydraulic actuator with the use of an MTS FlexTest SE. To prevent heating of the load cell a heat shield is placed between the furnace and the load cell. The push rods are cooled with a circulating water system to further prevent heating of the measurement devices.

Temperature rise in the measurement system could lead to drift and inaccurate measurements.

Point Grey Grasshopper cameras are mounted outside the furnace to allow for

DIC measurements to be recorded on the surface of each specimen. The cameras operate at a 1624x1224 resolution at 2 frames per second (FPS) for notched and hole specimens and 0.5 FPS for smooth uniaxial specimens. Two separate filters are used in front of the

Schneider 35mm optical lens in each camera to eliminate noise in the images collected by the cameras. The first filter is a hot mirror or near-infrared dichroic block filter that reflects wavelengths of 700 nanometers and is used to reduce the infrared signal observed

16 by the cameras. Infrared signals can create a lensing effect which can lead to higher correlation errors during DIC analysis. A linear polarizer is used between the lens of the camera and the hot mirror to remove image glare from the heated specimen and the surroundings. The cameras view each specimen though an optical quartz window encased in a ceramic holder in the front of the furnace. Optical quartz has a low thermal conductivity and thermal expansion coefficient which makes it an obvious choice for high temperature operations. The window is also free to expand within its casing, eliminating the optical lensing effects that occur when images are taken through a curved surface. An overview of the experimental setup is presented in Figure 2.2 Furnace setup used with digital image correlation, (a) inside of furnace, (b) DIC set up and furnace window, (c) thermocouple attachment to specimen

c Figure 2.2 Furnace setup used with digital image correlation, (a) inside of furnace, (b) DIC set up and furnace window, (c) thermocouple attachment to specimen

A thermal coating is necessary to take DIC measurements on the surface of each specimen. In this experiment, strains near 50% are expected at the prescribed temperatures during failure. The coating of each sample needs to be uniform, possess high ductility to endure deformation of the specimen, and must retain optical qualities at elevated temperatures. A ceramic-based plasma coating was used for the coating due to its ability to withstand large deformations and elevated temperatures while also providing contrast to the black speckle pattern. The speckle pattern was applied using Rust-Oleum

18 heat resistant paint black spray paint rated up to 1093°C. The ceramic coating applied to each sample along with a typical speckle pattern on a uniaxial specimen is displayed in

Figure 2.3.

Figure 2.3 Ceramic coating for ductile fracture specimens

The ductile fracture experiments are carried out by placing the load frame under load control with a 10 lb. tensile load on the specimen. The preload allows for the sample to thermally expand during heating under constant load without plastically deforming the specimen. Two thermocouples are attached to the back of each sample on opposite sides of the gage section and temperature measurements are taken at 1 Hz. Once the average specimen temperature reaches the specified temperature the load frame is placed in displacement control and the actuator is displaced at a constant velocity of

1.25x10⁻³ft/

2.3.3 3D-DIC Measurements

The advancement of 3D-DIC technology has allowed researchers to gain insight into the full-field strains and displacements of deformed specimens. A review of several of these techniques can be found in [28]. 3D-DIC is completed by capturing images using two digitally aligned and time synchronized cameras. Many software platforms are available to complete the DIC measurements including the Correlated Solutions VIC-3D

2009 used for these experiments [29].

The cameras are initially calibrated by capturing images of a calibration panel with a number of black circles in a grid pattern. The pattern and the distance between each circle is known and allows the software to determine a center point for each camera along with its rotation and focal length. Using these parameters the software can create a three-dimensional world coordinate system. Once calibrated, the cameras take time synchronized photographs of the speckle pattern on each specimen. The first image taken is used as a reference image and broken down into small, square reference subsets of

pixels. The grayscale intensity is recorded in all reference subsets and used for comparison to all subsequent deformed subset thereafter to find a displacement parameter. Using the displacement parameter, the shape and position of each subset can be found which the software utilizes to determine the strains on the surface of the specimen.

The strains can be measured in a number of ways in VIC-3D 2009: a virtual extensometer, a singular data point, an averaged rectangular region, and a line consisting of multiple data points. The virtual extensometer averages the strain and displacement in

20 the direction of the line over the gage length of the specimen. Data at the failure point of the specimen is collected using a singular data point. Lines with multiple data points describe the displacement and strain across a specimen on a single deformed image. Data from points and averaged areas include five strain components – , , , , and three displacement measurements – x-displacement ( ), y-displacement ( ), and z- displacement ( ).

Displacement and strain for all ductile fracture tests are recorded using a 1” extensometer and a data point at the location of ductile fracture. Figure 2.4 shows the 1” extensometer for a smooth uniaxial specimen before deformation and Figure 2.5 shows the virtual extensometer and data point at the moment of failure

Figure 2.4 1” extensometer for uniaxial specimens

Figure 2.5 Data point used for uniaxial specimens A 1” extensometer spans the gage section for all notched specimens as shown in

Figure 2.6a. Similar to the smooth uniaxial test, a data point is taken at the center of the sample before ductile failure occurs as shown in Figure 2.6b.

b Figure 2.6 (a) 1” extensometer and (b) data point used for notched specimens

Figure 2.7a displays a 1” extensometer that spans the hole over the gage section of each hole specimen. Two different data points are also used to track the strains on opposite sides of the hole in the plate specimen as shown in Figure 2.7b.

b Figure 2.7 (a) 1” extensometer and (b) data points used for hole specimens

Engineering stress and strain are calculated for the smooth uniaxial specimens using the recorded measurements of each sample before testing and the results of the 3D-

DIC. The engineering strain is calculated by:

(14)

Where is the displacement measured using DIC and is the original length of the gage section. The engineering stress is calculated with the formula: 23

(15)

Where is the width of the specimen, is the thickness and is the recorded force.

These values are converted into true stress and stain using the following equations:

(16)

(17)

2.4 Results & Discussion

Experimental results for the various geometries tested at a strain rate of 1x10⁻³ s⁻¹ and two elevated temperatures of 875°F and 1025°F are presented. The data was generated using the methods prescribed in the previous section. Characteristic trends of the data, including load, yield, ultimate stress, displacement, equivalent plastic strain, and stress triaxiality are discussed.

2.4.1 Smooth Uniaxial Test Series

Typical true stress and strain curves for tension experiments conducted at 875°F and 1025°F on the smooth uniaxial specimens are shown in Figure 2.8. The specimens yield near 28 ksi regardless of temperature. Considerable strain hardening is exhibited by both specimens as the ultimate stress is a 100 ksi increase from the yield point. At 875°F the average ultimate stress of the specimen is 134 ksi with an average failure strain of

44%. At 1025°F the average ultimate stress of the specimen is 128 ksi with an average failure strain of 44%. This corresponds to a -4.55% drop in ultimate stress and no increase in failure strain between the two temperatures. Serrated flow manifests in each

24 curve as an abrupt rise in stress followed by an immediate drop in stress and subsequent rise in stress with increasing strain.

Figure 2.8 Comparison of true stress and strain for uniaxial tension experiments at 875°F and 1025°F

2.4.2 Varied Geometry Test Series

The general trend for the force and displacement curves of each specimen geometry at 875°F is presented in Figure 2.9. Uniaxial data features the largest average displacement of 0.556” and the lowest average peak load of 1700.2 lb. The data generated for the 0.787” notch specimen resulted in an average load of 2138.9 and an average displacement of 0.275”. Three experiments for the 0.394” notch specimen resulted in an average peak load of 2176.8 lb and an average displacement of 0.221”.

The 0.263” notch experienced an average load of 2123.9 lb and an average displacement of 0.198”. Finally, the plate specimen with a hole reported the largest average peak load

25 of 2284.3 lb and the smallest average displacement of 0.139”. The results of these experiments show that the varying geometries have a substantial effect on the force and displacement incurred in each test specimen.

Figure 2.9 Comparison of applied force versus displacement for different tension specimen geometries

2.4.3 Elevated Temperature Effects on Varied Geometry Test Series

Figure 2.10 shows the force and displacement curves for 3 tests at 875°F and 2 tests at 1025°F for the 0.394” notch. The average peak load at 1025°F is 2085.6lb while the average displacement is 0.218”. These values correspond to a 4.19% drop in peak load and a 1.33% reduction of displacement in comparison to the curves at 875°F. This reduction in peak load and displacement at 1025°F is a general trend for each of the notched samples. The 0.263” notch sample experiences a 2.69% reduction in peak load

26 and a 0.64% reduction in displacement while the 0.787” specimen has a 3.14% and

3.81% reduction in peak force and displacement respectively. The hole sample also follows this behavior and experiences a 3.66% drop in peak load and a 0.39% decline in displacement.

Figure 2.10 Force versus displacement curves for five separate tension experiments carried out on a Notch (0.394”) sample at 875°F and 1025°F

2.4.4 Serrated Flow Effects for Varied Geometry Test Series

Figure 2.11 displays representative curves for equivalent plastic strain measured at the point of fracture versus the average displacement across the gage section of each specimen at 875°F. The serrated flow represented in these curves can be explained by the formation of shear bands which cause an abrupt increase in strain in the material and then

27 propagate throughout the material until a uniform strain is reached throughout the gage section.

Figure 2.11 Equivalent plastic strain versus displacement for each specimen geometry carried out at 875°F

Figure 2.12 presents the evolution of the equivalent plastic strain presented in equation 12 for a 1” extensometer placed over the gage section, the average strain over the entire data region and data points placed at the failure point and a strain localization that appears at 422 seconds into the test. The effects of strain localization and serrated flow are evident in these graphs. The failure point and localization point show the most extreme cases of strain localization as strains jump 3-5% followed by periods of strain constant strain. During these periods of constant strain for the data points, the levels of strain throughout the rest of the specimen’s gage section is increasing as the strain localizations flow through the material and is shown by the graphs of the average of the 28 entire specimen and the 1” extensometer. The extensometer measurements exhibit periods of constant strain as the strains increase outside of the measured area while the average of the entire plot displays an almost linear relationship between strain and time.

Figure 2.12 Evolution of strain between 25-50% versus a selected time period for a smooth uniaxial specimen tested at 875°F.

Each of the times labeled on the x-axis of Figure 2.12 correspond to a contour plot of strain in Figure 2.13. In the first image for time 422s, the emergence of a strain band is captured and shows the location of the two data points and the 1” extensometer. At time 440s, the formation of a second strain band close to the failure point is captured.

Each of the strain bands flow through the gage section and increase the overall level of strain in the specimen until the two strain bands experience increases in strain at times of

448s, 464s, 502s, 520s, 568s and 596s. After the strain concentrations originate near the failure point and the original strain localization, the areas of localized strain increase in size until they coalesce and create a uniform strain throughout the gage section as shown in the contour plots for 554-612 seconds.

422

440

448

456

464

482

502

510

520

530

554

568

580

596

612

Figure 2.13 Evolution of strains in the x direction for a smooth uniaxial sample tested at 875°F. Each strain plot refers to a specific time in Figure 2.12. 31

2.4.4 Fracture Locus for Varied Geometry Test Series

Figure 2.14 presents the strain data from the uniaxial, notch, and hole specimens.

The evolution of the equivalent plastic strain is plotted versus the ratio of the two principal strains and at the point of fracture initiation in each specimen. At small equivalent strains the principal strain ratios of each geometry vary. Once an equivalent strain of 0.05 is reached the strain states do not evolve much until failure. The evolution plots for all test specimens can be found in Appendix A.

Figure 2.14 Equivalent strain and stress triaxiality approximation evolution for evolution for each geometry

The equivalent plastic strain and ratio of the two principal strains at failure for each geometry is shown in Figure 2.15. The equivalent strain at failure for the uniaxial specimens ranged from 49.1% to 57.4% and the ratio between the two principal strains

( ) ranged from -0.309 to -0.354. The notch 0.263”, 0.394”, and 0.787” specimens had an equivalent strain range of 43.7% to 47.5%, 47.8% to 49.3%, and 51.1% to 53.5% with a ( ) range of -.114 to-0.144, -0.156 to -0.185, and -0.243 to -0.275 respectively at failure. Lastly, the plate specimen with a hole had a fracture strain range of 39.5% to

48.9% and a principal strain ratio of -0.178 to -0.214 at failure. No temperature dependence could be discerned from the strain data due to the relatively small difference in experimental temperatures. However, the strain states created by the varying geometries created repeatable results at different principal strain ratios. These data points can be used to determine a stress-state based failure assuming the stress state in each specimen is plane stress.

Figure 2.15 Equivalent plastic strain and stress triaxiality approximation at failure

2.5 Summary & Conclusions

The ductile fracture behavior of a nickel-based superalloy is studied in tension for five different plane stress geometries at a strain rate of 1x10⁻³ s⁻¹ at temperatures of

875°F and 1025°F. An experimental set up employing a custom furnace with an optical quartz window and an Inconel 718 fan in conjunction with a camera set up including special optical filters is utilized to capture 3D-DIC measurements on the surface of each sample during testing at elevated temperatures. The geometry for each specimen is selected to induce a different stress triaxiality and Lode parameter. Generally, as the stress concentration in the specimen geometry increased the failure displacement decreased and the failure load increased. The equivalent plastic strain to failure decreases with increase in stress concentration. The increase in temperature from 875 to 1025°F

34 led to a modest decrease in force and displacement of failure due to thermal softening of the material. The strain states illustrated by the approximation of the stress triaxiality do not evolve at failure for each geometry that was tested. The band propogation of strains is evident in DIC and force measurements and is justified by the serrated flows seen in other nickel-based superalloys investigated by several other researchers [21,22,23].

Stress triaxiality approximations and the calculated equivalent plastic strain at failure for each geometry are used to investigate the beginning stages of a strain-based failure locus.

Chapter 3: Thermally Induced Strains of a 6000 Series Aluminum Alloy

This study aims to observe the thermally induced deformation of an exterior grade

Aluminum 6000 series alloy. Uniaxial and bending strains of 0-20% are induced in uniaxial and bending specimens to observe the changes in strain during heat cycles that replicate the paint-bake cycle of production. In addition to strain type, the initial strain level, soak temperature, and deformation direction is investigated. Uniaxial samples are tested to failure in tension to find the failure load and strain for different initial strains and temperatures. A fixture is designed to create a thermal buckling state in uniaxial test specimens under thermal load of the paint-bake cycle. 3D-DIC is used in each test to measure the surface strains and displacements on each test specimen. This experimental test plan was completed in conjunction with Honda R&D Americas (HRA).

3.1 Motivation & Objectives

Competition throughout the automotive industry has been a driving force for research and modification of manufacturing processes. Recently the focus of the industry has been centered on reducing the weight of each vehicle to increase the fuel efficiency, improve driving performance, and meet the meet the strict requirements of energy saving and environmental protection outlined by governing bodies [30]. To accomplish these goals considerable efforts were taken to replace the steel body panels of cars with 36 aluminum. An estimated 50% total energy savings from production to end of service life was obtained for every 20 tons of steel replaced by 1 ton of aluminum [31]. Initially, several car manufacturers selected 2000 series aluminum-copper alloys for the outer body of the car while Magnesium-based 5000 series aluminum alloys is used for the inner body elements of each vehicle [32]. However, the 2000 series alloys were incompatible with the 5000 series alloys in recycling processes due to their differences in composition.

Also, the 2000 series alloys strain hardened during paint-bake heating cycle of 180°C for

30 minutes while the 5000 series alloys experienced softening effects. A new

Magnesium-Silicon based Aluminum 6000 series alloy with was developed to assist in recycling compatibility while retaining paint-bake strengthening properties [30]. As the need for weight reduction has increased, the thickness of the 6000 series alloys sheets has decreased dramatically creating a need for better understanding the response of the sheet to prestrained conditions, differences in paint-bake cycle, and the boundary conditions emplaced on the sheet during assembly. The goal of the current study is to relate the amount of permanent thermally-induced strain to the test variables to improve modeling efforts and to avoid excessive deformation during production.

3.2 Literature Study

3.2.1 Paint-Bake Response

The behavior of several 6000 series aluminum alloy sheets during the paint-bake cycle has been simulated by several researchers to better understand the mechanical property changes of the material. Balderach et al. [33] cold rolled three different Al-Mg-

Zn alloys to a sheet thickness 4.1mm and subjected the tension and disk samples to four

37 different types of aging treatments combining natural and artificial aging. After heat treatment the samples were subjected to Vicker’s hardness, tension, and differential scanning calorimetry tests. Samples subjected to the paint-bake cycle of 175°C for 30 minutes were found to have an increase in ultimate tensile strength and hardness when compared with the solution-treated condition. Natural aging of the samples for one year after the simulated paint-bake cycle increased the hardness and ultimate tensile strength by 41-78%. Zhen and Kang [34] studied the effects of pre-aging on two Al-Mg-Si alloys under a paint-bake condition. After cold rolling the specimens were solution treated and then quenched at room temperature. Each set of specimens was then subject to either a natural aging for three months, a pre-aged condition at 150°C for 5 minutes or a combination of the two and then half were subjected to the 180°C simulated paint-bake cycle for 30 minutes. The yield strength of each alloy was increased by the paint-bake cycle but the greatest increase came from samples that were pre-aged due to the increase in density of precipitates. Birol [35] prepared uniaxial samples and subjected them to a uniaxial strain between 0-5%. A paint-bake treatment of 180°C for 30 minutes was then applied to each specimen and the microhardness of each sample was recorded. It was discovered that as the amount of prestrain increased, the hardness of the sample increased as well. Lastly, Ratchev et al. [36] recrystallized tension and disk specimens of Al-Cu-

Mg alloy by means of a 550°C salt bath treatment to study the effects of 4 different cooling rates from 2°C/s to 500°C/s on the strength and precipitation behavior of the material. Several of the tension samples were baked at 180°C for 30 mins to compare to the recrystalized samples. Baking each sample increased the strength of the material,

38 however the yield stress after baking was nearly constant and did not depend on the cooling rate. Interrupted tensile tests were also performed on uniaxial specimens to give a uniaxial prestrain between 0% to 10%. In general, the strength of the material increased with increasing prestrain due to work hardening of the material while specimens subjected to a paint-bake cycle displayed greater strength due to the nucleation of precipitates along dislocations.

3.2.2 Thermal Buckling

During the paint-bake cycle the outer panels of the exterior of the car are normally constrained to the car body by welds, bolts, rivets, epoxies, or other means. Due to these constraints the thin sheet metals may experience thermal buckling. The theoretical critical buckling temperatures and mode for thin isotropic plates have been investigated using classical theory of elastic stability and has been summarized in Timoshenko &

Gere’s Theory of Elastic Stability [37]. Issues such as temperature distribution across the thin sheet, plane stress assumption errors, lack of experimental strain data and imperfection of materials invalidate the theoretical equations when applying them to real- world situations [38, 39]. Several techniques have been attempted by researchers to experimentally determine the buckling load of different materials.

Southwell [39] developed a relationship between the applied load ( ), critical load ( ), column deflection ( ), and the initial imperfection ( ) as shown in equation

(17):

(18)

This equation is based on the assumption that the deformation of the material is linear as buckling is approached. Test results showed that the relationship between the deflections or strains and the corresponding levels of loading are rarely linear and severely limited the capabilities of determining the true critical load.

According to small-deflection theory, the square root of the natural frequency for a structure is linearly related to the load applied on the structure. When the load on the structure is equal to the critical load, theoretically the natural frequency of the structure should also be zero [39]. Researchers [40] considered this method to find the buckling load of a pinned, shallow, elastic arch. The compressive loads that could be measured in this method are small and limit the amount of data that could be obtained during experiments to find a reliable critical load for the structures.

Murphy and Ferreria [41] measured the deformation at the center of a plate using an LVDT to try and determine the critical buckling temperature of a rectangular plate.

The investigators sought to incorporate nonlinear effects by measuring the temperature of the plate and the out of plate deformation under different buckling modes. The LVDT presented certain limitations because of predicting the location of true maximum deflection on the bar was difficult to ascertain before testing and therefore was rarely measured by the LVDT.

Jin and Goo [42] investigated thermal buckling of an aluminum plate using 3D-

DIC technology. The aluminum plate was cut into circular specimens and then placed inside an oversized titanium ring. Due to the differences in thermal expansion, the aluminum disks expanded at a faster rate than the titanium ring resulting in a compressive

40 load on the disk. The DIC technique measured the out of plane deformation as well as the surface strain on the aluminum disk. An ABAQUS model was developed in coordination with the results of the experiment to approximate the critical buckling load and temperature.

3.3 Experimental Procedures & Techniques

3.3.1 Tension Tests

Tension tests are performed on an aluminum 6000 series alloy to study the material response to various prestrains, loadings, thermal cycles, and boundary conditions. The experimental test plan for the tension tests is shown in Table 3.1

Experimental test plan for uniaxial specimens.

Test No. Test Type Axial Prestrain Heat Cycle Temperature at Failure(°C) 1 Uniaxial 20% A 2 Combined 10% C N/A 3 Thermal 0% A 4 Buckling 20% 5 25 0% 6 Material 190 N/A 7 Property 25 20% 8 190 Table 3.1 Experimental test plan for uniaxial specimens

Testing consists of two soak periods at a specified temperature followed by a return to 30°C during two cooling periods. A summary of the thermal profiles is displayed in Table 3.2 Overview of thermal profiles.

Thermal Cycle 1st Dwell Temperature (°C) 2nd Dwell Temperature (°C) Cooling Temperature (°C) Dwell Hold Time (min) A 190 160 30 20 C 160 160 30 20 Table 3.2 Overview of thermal profiles

A 20% uniaxial prestrain is induced in a uniaxial tension specimen subjected to an

A-type heat cycle. Tension specimens subjected to a prestrain of 0 or 20% and tested to failure at temperatures of 25°C and 190°C. Finally, thermal buckling tests are completed by prestraining a specimen from 0-20% and constraining the sample using a specially designed plate before exposure to a C-type thermal heat cycle.

3.3.1.1 Tension Specimen Design and Fabrication

The uniaxial test specimen is designed according to the Japanese Industrial

Standard JIS-Z-2241. The standard outlines the test piece dimensions and preparation, testing machine requirements and methods of determining the properties of metallic materials such as yield strength, proof strength, elongation and reduction of area. The specimens were obtained from HRA. A schematic of the tensile specimen dimensions is shown in Figure 3.1 Uniaxial specimen geometry for thermal cycle testing. Each specimen is stamped out of a 0.40” thick sheet of a 6000 series aluminum alloy. The length and width of the gage section is 1.339” and 0.241” respectively which allows the

DIC system sufficient area to take measurements on the surface of the specimen. The overall length of the specimen is 3.15” and features two 0.236” through holes located

0.236” from the each end of the specimen. Hastelloy-X pins and bushings fit into the slotted fixture to hold the specimen in place during testing described in the following section.

Figure 3.1 Uniaxial specimen geometry for thermal cycle testing

3.3.1.2 Uniaxial Deformation

The uniaxial samples for the uniaxial expansion, failure behavior, thermal buckling, and combined strain tests are predeformed to strains of 0-20% using the set-up in Figure 3.2 Uniaxial prestrain experimental setup.

Figure 3.2 Uniaxial prestrain experimental setup

Tests are conducted using a 20 kip servo-hydraulic load frame at a strain rate of

1x10⁻³s⁻¹. The specimen is placed in two slotted adapters and pinned in place by passing two pin through the holes on the front of the adapters and placing two bushings in the opposite holes. The slotted adapters are connected to two Inconel 718 push rods which are mounted to the LVDT and 20 kip load cell. The LVDT measures the displacement of the actuator and the load cell records the force for each experiment. Two Point Gray

Research 20S4M-C cameras equipped with a Schneider 30mm lens are positioned 1.5 ft away from the sample to capture images at 2 frames per second while fiber optic lamps provide illumination on the specimen surface. Approximately 430 images are taken of each deformation event and are processed by Correlated Solutions VIC-3D 7 software to calculate the displacements on the specimen. For each prestraining operation the load frame is placed in load control with a 10 lb tensile load on the specimen to insure the sample is in contact with both pins. The specimen is then loaded by placing the controller in stroke control and displacing the actuator at a rate of 1.2 x10⁻³ ft/s a pre- determined distance of 0.170” or 0.317” depending on the desired prestrain of 10% or

20% respectively. Once the specimen has been prestrained the controller is placed back in load control and the specimen is unloaded and removed from the setup.

Failure testing and DIC is conducted on prestrained and unstrained uniaxial samples at room temperature and 190°C using a furnace attached to the load frame as described in Section 2.2.2. Rust-oleum High Heat paint is used to provide a base coat and speckle pattern on each specimen. Digital image correlation is used to measure and

44 record displacements and strains. The engineering and true stress and strain to failure are calculated for each specimen using the collected data from the load cell and DIC analysis.

3.3.2 Bend Testing

Bend tests are completed on uniaxial and bend specimens to observe the behavior of combined and bending strain states in an aluminum 6000 series alloy under thermal cycle loading. A summary of the bending experiment plan is shown in Table 3.3.

Samples undergo bending strains of 0, 10, and 20% before being exposed to A and C type thermal cycles. Samples are also bent in the transverse direction to study the effect of material anisotropy on thermal expansion. Lastly, samples that were previously prestrained with a uniaxial strain of 10% are subject to a bending strain of 20% to observe the effects of combined loading.

Test No. Test Type Bending Prestrain Heat Cycle 1 A 10% 2 C Bending 3 A 4 20% C 5 Combined C

Table 3.3 Experimental test plan for bending experiments

3.3.2.1 Bend Specimen Design

Aluminum 6000 series bend specimens were received from HRA in the form of strips with the dimensions shown in Figure 3.3a. The specimens were then cut using a

45 sheet metal shear to the dimensions shown in Figure 3.3b while transverse specimens were created by cutting the sample in the direction and dimensions shown in Figure 3.3c.

Figure 3.3 Bend specimen geometry for (a) original sample, (b) rolled direction sample, (c) transverse direction sample

3.3.2.2 Bend Apparatus

Applying the prestrain for bending specimens is accomplished using a guided bend test apparatus shown in Figure 3.4 Guided bend test fixture and plungers.

Figure 3.4 Guided bend test fixture and plungers

The apparatus is based upon the ASTM 190 and 290 standards for guided bend tests

[42,43] and was designed in collaboration with HRA then fabricated by Wyoming

Testing Fixtures to allow DIC measurements on the surface of the bend specimen during mechanical testing. Two hardened shoulders with a radius of 1/8” are attached to a steel plate to support each bend specimen near its ends while a male plunger applies a force midway between the two supports until the desired bend is formed. The shoulder plate is attached to two 3” x 4” vertical steel plates and a 1” thick base plate with eight 3/8-16 screws. The base plate provides a platform for a mirror fixture that sits 45° from the shoulder plates and allows DIC measurements on the outer surface of each specimen during deformation. Two different plungers were designed with radii of 0.177” and

0.079” to create bending strains of 10 and 20% in the aluminum strips.

3.3.2.3 Bend Testing

Bend testing is carried out by attaching the entire bend apparatus to an Inconel

718 push rod and the load cell of the servo-hydraulic load fram. Next, the plunger with the appropriate bending radius for the desired strain is attached to the actuator with a 1” steel rod. An overview of the setup is presented in Figure 3.5. The surfaces of the plunger and the shoulders are greased using a high pressure resistant G-N Metal

Assembly Paste to ensure the sample can bend without seizing. The specimen is then placed in contact with the plunger and the shoulders which are separated by a distance equal determined by the equation:

(19)

Where is the radius of the plunger and is the thickness of the bend specimen. Once the specimen is in contact with all three surfaces the controller is placed in displacement control and the actuator is displaced until the specified bending strain for the fixture is reached. As deformation occurs, two cameras collect DIC information through the mirror below the shoulder plate as demonstrated in Figure 3.5. These cameras are calibrated by focusing the cameras on the speckle pattern of the sample through the mirror and then taking images of a calibration panel without the mirror in place. With this method the cameras are appropriately calibrated in space and not just to the image on the mirror.

a b

c Figure 3.5 (a) Overview of bend test experimental setup (b) specimen placement (c) DIC setup

3.3.3 Thermal Cycling

3.3.3.1 Testing Methods

Each specimen is subjected to a specific temperature profile meant to replicate the the paint-bake cycle of manufacturing. Thermal cycle profiles remain within ±5°C of the prescribed temperature as measured by a K-type thermocouple while soak times are to be

+1/-0 minutes from the specified times. The thermal cycles are applied to the specimens by a modified split-box furnace as shown in Figure 3.6. The oven has a 4x5” optical quartz window in the door to allow DIC measurements to be taken from cameras outside the furnace.

b Figure 3.6 (a) Furnace setup for thermal cycle testing (b)inside of furnace

A heat cycle fixture is designed to provide a consistent basis for DIC image capture and to allow unrestrained thermal expansion during the simulated paint-bake cycles. A diagram of the fixture and its clamping mechanism is shown in Figure 3.7.

a b Figure 3.7 Overview of clamping mechanism, (a) clamped bend specimens, (b) exploded view with uniaxial specimens

The fixture is designed to hold 3 separate uniaxial or bend specimens for each heat cycle.

The apparatus consists of a 3 x 3”, 0.5” thick steel base connected to a 10.5” steel rod with a 0.5” screw connection. The rod features a 5.25” x 1” flat surface machined 0.5” into the rod and a steel plate is used to clamp the uniaxial and bend specimens on one end. The steel plate is attached to the rod using 3-4 #13-20 screws depending on the sample being tested. Each sample was individually clamped to the fixture as shown in

Figure 3.8.

a b c Figure 3.8 Clamped specimens for (a) thermal buckling, (b) combined, and (c) bend experiments

For the thermal buckling experiments a 3.5” x 1.25” plate was steel fabricated to apply a fixed boundary conditions to the ends of the uniaxial specimens that are unstrained or strained to 20%. The dimensions of the plate and its features are displayed in Figure 3.9.

Figure 3.9 Dimensions for thermal buckling boundary condition plate

Two #12 clearance holes in the center of the plate allows for two #12-24 cap screws to pass through the plate and connect to the rod from the heat cycle apparatus. Each uniaxial specimen is fixed to the plate by two #12-24 screws placed through the pin holes of each specimen and threaded through the tapped holes in the center of the plate.

Temperature measurements are taken at 0.1 Hz by attaching a K-type thermocouple to each specimen using Omega CC high temperature cement.

3.3.3.2 3D-DIC Measurements

The displacements and strains for each specimen during deformation and the thermal cycles are recorded using a combination of 1” extensometers and data points.

For each uniaxial tension test an extensometer was placed over the gage section and a data point was located at the point of maximum strain for prestraining operations or the failure point for mechanical tests to failure. An overview of these locations is shown in

Figure 3.10.

X a b Figure 3.10 (a) Location of 1” Extensometer for a uniaxial specimen before mechanical testing. (b) Location of 1”extensometer and data point at maximum point of strain after a prestraining operation

During bending prestrain experiments a data point was used to capture the strain along the bend axis and the vertical displacement of the specimen during deformation.

Figure 3.12 shows the location of the data point before and after deformation of the specimen.

X a b Figure 3.11 Location of data point before (a) and vertical displacement after (b) a 20% bending prestrain experiment

Throughout thermal cycle testing a single data point was placed in the center of the bend for samples prestrained to 10% and 20% bending strain as shown in Figure

3.12a while a data point and two 1” extensometers in the x and y directions were used to calculated the displacements and strains for unstrained bending specimens as shown in

Figure 3.12b. Extensometers were not used for prestrained bending specimens because of the inaccuracies caused by the curvature of the bend.

X a b Figure 3.12 (a) Data point on a 20% bending prestrain specimen and (b) Location of 1” extensometers and data point for a 0% bending prestrain specimen during a thermal cycle

Figure 3.13a presents the location of 1” extensometer over the gage section of uniaxial specimens during thermal buckling experiments to capture strains and horizontal displacement. The vertical displacement and the strains during a thermal buckling experiment for an unstrained uniaxial sample are captured by a data point placed at the point of maximum deflection as shown in Figure 3.13b.

X a b Figure 3.13 Location of a 1” extensometer before a thermal cycle (b) Location of a 1” extensometer and a data point placed on the point of maximum displacement during a thermal cycle

3.4 Results & Discussion

Results for the study of an aluminum 6000 series alloy subject to thermally induced strains of a paint bake cycle and thermal buckling tests are presented. Data from each test is presented followed by a discussion of the effect of prestrain, temperature, strain type and boundary conditions on various parameters such as yield stress, flow stress, coefficient of thermal expansion, residual strain and buckling load. Each set of data is representative of a single, multiple iterations of the same test, or an average of several iterations. Additional data for individual tests can be found in Appendix B.

3.4.1 Initial Strain Testing

The initial engineering strains induced in uniaxial specimens via tension experiments are shown in Figure 3.14. The strains and displacement of the gage section were measured using a 1” extensometer over the length of the gage section and a data point placed in the area of maximum deformation at the end of the test. The specimens reached a strain of 9.7% and 19.7% at actuator displacements of displacements of 0.17” and 0.31” respectively.

Figure 3.14 Strain versus displacement for typical uniaxial prestrain experiments

The initial bending strains for the 10% and 20% rolled direction bend specimens as well as the 20% transverse and 20% combined specimens can be seen in Figure 3.15.

The maximum strain for each specimen occurs around 0.225” vertical displacement.

Each sample was displaced into the punch shoulders past its point of maximum bending strain which shows that the bending strain is determined by shoulder separation and specimen geometry. The combined and transverse specimens reached a bending strain of

22.3% and the 20% and 10% bend specimens incurred strains of 17.3% and 9.6% respectively.

Figure 3.15 Strain versus vertical displacement for typical bending prestrain experiments

3.4.2 Material Property Test Series

Experimental data from the material property study on the behavior of the material under prestrained and elevated temperature conditions is presented in this section. Figure 3.16 displays the true stress and true strain of 20% prestrained and undeformed uniaxial samples tested to failure at 25°C. The prestrained data has an average yield stress of 34.1 ksi, average ultimate stress of 34.8 ksi and ultimately fails at approximately 5.5% strain. The three unstrained specimens tested at room temperature have an average yield stress of 18.5 ksi, average ultimate stress of 41.7 ksi and fail at a strain between 21.7 and 22.3%. The prestrained material exhibits an increase in yield

58 strength and a large decrease in flow stress compared to the unstrained specimens and can be accounted for by the strain hardening present in the prestrained samples.

Figure 3.16 True stress versus true strain data from uniaxial specimens in the unstrained and 20% prestrained conditions at 25°C

A comparison of the true stress versus true strain curves for prestrained and unstrained samples at a temperature of 190°C is shown in Figure 3.17. The prestrained samples have an average yield stress of 21 ksi, average ultimate stress of 23.1 ksi and fail at a strain between 10-15%. The previously unstrained samples exhibit a lower yield point near 16 ksi but a higher ultimate stress of 25.8 ksi. The unstrained samples also possess more ductility as evidenced by the average failure strain of 20%.

Figure 3.17 True stress versus true strain data from uniaxial specimens in the unstrained and 20% prestrained conditions at 190°C

Figure 3.18 displays the true stress and true strain for the prestraining experiment for each specimen and the subsequent test to failure at 25°C and 190°C. Each prestraining operation is represented by the solid lines in the figure and resulted in a true strain near

17.8% and a true stress of 41 ksi. Thermal softening is displayed by the 38% decrease in yield stress and 127 % increase in ductility shown by the samples tested to failure at

190°C as compared to the samples at 25°C.

Figure 3.18 True stress versus true strain data from uniaxial specimens in the 20% prestrained condition at 25 and 190°C

The true stress and strain curves for unstrained uniaxial specimens tested to failure are shown in Figure 3.19. Thermal softening is displayed by the degradation of strength in the specimens tested at 190°C. The tests at elevated temperature also revealed an unusual decrease in overall ductility. Typically metals present increased ductility with increased temperature. In this aluminum alloy the decrease in ductility may can be attributed to the increase in strain localization in the necking region and a decrease in total elongation of the sample.

Figure 3.19 True stress versus true strain data from uniaxial specimens in the unstrained conditions at 25 and 190°C

3.4.3 Thermal Cycle Testing

3.4.3.1 Uniaxial Thermal Cycle

Strain data for a 20% prestrained uniaxial specimen during an A-type thermal cycle is displayed in Figure 3.20. The specimen is shown to expand and contract as the temperatures increase and decrease during the heating cycle. At 190°C and 160°C the strains measured by the data point, the 1” extensometer over the gage section and the estimated strain sustain strains of 4000μϵ and 3000μϵ. Similarly, after cooling to 30°C the strains are measured within 200μϵ of equilibrium. For uniaxial tests it is observed

62 that the strain has no effect on the residual strains inherent in the specimen after a paint bake cycle.

Figure 3.20 Microstrains versus time for a uniaxial sample during an A-type thermal cycle

Figure 3.21 plots the linear fit of the microstrain versus temperature for the strain data in the X during Y directions during the initial temperature rise to 190°C and the return to 30°C for an A-type thermal cycle. The slope of each of the linear fits is estimated as the coefficients of thermal expansion (CTE) in the X and Y directions. The

CTE is calculated using the strain data from the data point and the 1” extensometer for each of the two heating and cooling periods during the thermal cycle. A summary of the calculated CTE values can be found in Table 3.4. The CTEs were at a maximum during the first heating to 190°C and the strains in the Y direction resulted in the largest average 63

CTE. The strain in the uniaxial direction did not affect the residual strains in the specimen during thermal cycling nor did it greatly affect the directionality of the CTE.

Figure 3.21 Microstrain in the X & Y directions versus specimen temperature with curve fits to determine CTE

Overall First Heating Cycle Second Heating Cycle Reference CTE xx (μϵ/⁰C) 21.06 21.59 20.16 CTE yy (μϵ/⁰C) 22.97 23.03 22.77 23.2 CTE gage (μϵ/⁰C) 20.77 20.95 20.44

Table 3.4 Calculated coefficient of thermal expansion in different directions for a uniaxial specimen during an A-type thermal cycle

3.4.3.2 Bend Testing Thermal Cycles

Figure 3.22 and Figure 3.23 represent the strain response in the X and Y directions for samples prestrained to a 10% and 20% bending strain and subjected to A and C type heating cycles. The strains in the X direction are perpendicular to the bend axis while the strains are parallel to the bend axis. The 60°C difference in temperature for the first dwells in each of the heating cycles is evident in the strain responses for both the 10% and 20 % prestrained samples. The 10 and 20% samples subjected to the C type heating cycle incurred strains in the X direction of 1500 and 2500 μϵ respectively during the first dwell while the samples subjected to the A type heating cycle reached strains near 3000 and 4000 μϵ. In the Y direction the strains for each specimen plateaued at levels above the estimated strains due to thermal expansion but then returned close to the estimated thermal expansion after cooling. In each of the tests a residual strain in the X direction remained in the specimen after cooling as shown by the differences between the estimated strains due to thermal expansion and the measured strains for each sample.

The presence of a negative residual strain indicates the specimen relieving the tension in the outermost curved surface of each specimen.

Figure 3.22 Comparison of strains in the X & Y directions with the estimated strains due to thermal expansion in samples with a bending prestrain of 10% and subjected to varying thermal cycles

Figure 3.23 Comparison of strains in the X & Y directions with the estimated strains due to thermal expansion in samples with a bending prestrain of 20% and subjected to varying thermal cycles

The strains in the X and Y directions for an undeformed bend specimen and a combined transverse bend specimen during an A-type thermal cycle are shown in Figure

3.24. Similar to the 10% and 20% bend specimens, the undeformed and specimen

66 demonstrates limited deviation from expected thermal expansion behavior while the transverse specimen displays a residual strain in both directions after the cooling sequences of the thermal cycle. The residual strain in the X direction is large than the residual strain present in Y direction. The X direction strain during the first dwell also decreases by approximately 750 μϵ while at a constant temperature of 130°C and then remains nearly constant during the second dwell of 160°C. The small residual strain in the Y direction shown in the transverse bend tests but not the undeformed, 10% and 20% bend tests could be due to the differences in small differences in CTE between the rolled direction and 90° to the rolled direction.

Figure 3.24 Comparison of strains in the X and Y directions for an undeformed bend specimen and a transverse bend specimen subjected to a C-type thermal cycle

Figure 3.25 displays the strains in the X and Y directions for a combined strain specimen.

Similar to the undeformed, 10% and 20% bend specimens, the strains in the X direction along the bend axis of the specimen follow typical thermal expansion. The strains in the

Y direction, perpendicular to the bend axis, resemble the strains from the transverse bend specimen where a 750 μϵ decrease is evident during the temperature dwell at 130°C. The decrease in strain during the first dwell in the transverse bend and combined tests is due to the differences in bend direction between the transverse tests and the original bend tests and the different types of strain inherent in the combined specimen. At the temperature dwells the specimens unwraps to relieve the stress caused by the bending prestrain. As the specimen unwraps top surface of the specimen are compressed leading to a residual negative strain.

Figure 3.25 Comparison of strains in the X and Y directions for a combined strain specimen subjected to a C-type thermal cycle

A comparison of the calculated coefficient of thermal expansion values over an entire thermal cycle for all tests is presented with the average coefficient of thermal expansion and a 95% confidence interval in Figure 3.26. Each CTE was calculated using by finding the best fit line for the measured strains at each temperature as previously

68 shown in Figure 3.21. The CTEs in the X direction vary from the lower bound of the confidence interval of 25.77 μϵ/°C to approximately 33 μϵ/°C. Meanwhile the CTEs in the Y direction land between 23 μϵ/°C to the overall average CTE of 27.12 μϵ/°C. The increased CTE values in the X direction for the combined specimens as well as the 10%,

20% and transverse bend specimens illustrate the effect of the strain relaxation and springback on the samples. The largest CTE values are displayed by the transverse and combined specimen and helps describe the strain response during the initial heating sequence of each thermal cycle. The CTEs in the Y direction for each of the tests and the

X direction for the undeformed bend tests portrays the adherence of samples in the unstrained direction to normal thermal expansion.

Figure 3.26 Comparison of average coefficient of thermal expansion values for all bend and combined tests

Figure 3.27 displays the difference between the estimated strains due to thermal expansion and the measured strains in the X and Y directions from experiments after cooling to 30°C for each of the heating cycles. The average strain offset for all of the experiments is -617.90 μϵ/°C and the 95% confidence interval lies between -312.71 μϵ/°C and -923.10 μϵ/°C. The plot displays that for unstrained specimens or unstrained specimen directions residual strains are held to a minimum. Once the strain offset occurs after the initial cooling sequence the subsequent reheating of the sample to 160°C has a minimal effect on the residual strains in each specimen. This plot also suggests that the 70 residual strain is not sensitive to level of non-zero strain, prestrain type, nor the heating profile.

Figure 3.27 Strain offsets in the X and Y directions during the first and second cooling sequences of A and C type heating cycles for all bending and combined tests

3.4.3.3 Boundary Condition Thermal Experiments

The vertical displacement at the center of the gage section for a dogbone specimen subjected to uniaxial prestrains of 0 and 20% then bolted to a steel plate and subjected to an A type thermal cycle is displayed in Figure 3.28. The displacements after the two cooling periods show little deviation. The amount of prestrain also has little effect on the residual displacements as each experiment lands between 0.1-0.2mm.

Figure 3.28 Vertical displacement of the centerpoint of the gage section for dogbone specimens in the undeformed and 20% prestrained conditions during an A-type thermal cycle

3.5 Summary & Conclusions

The thermal strain behavior of a 6000 series aluminum alloy is studied under a variety of different prestrains, specimen orientations and temperatures. Uniaxial dogbone specimens were tested to failure in tension under different prestrains and different temperatures. The material exhibits thermal softening characteristics at elevated temperatures with decreasing failure load and failure strain. The specimens also exhibit strain hardening at room temperature and elevated temperatures alike when subjected to a

20% uniaxial strain.

Bend specimens were subjected to bending strains of 0-20% while uniaxial specimens were subject to 20% axial strains and a combination of 10% axial strain and

20% bending strain then placed in a furnace and exposed to a thermal cycles that

72 replicate the conditions of a paint-bake cycle during manufacturing. The CTE’s were determined from the strains along the bend axis and perpendicular to the bend axis. It was found that the CTEs were higher perpendicular to the bend axis and relatively stable in the direction of the bend axis. The strains were also compared to the expected levels of strain due to thermal expansion and the strain difference was not sensitive to level of non-zero strain, prestrain type, nor the heating profile. The observed behavior can be attributed to the proclivity of the samples to return to their original shape and remove the effects of the bending prestrain.

Uniaxial samples were bolted to a steel plate to observe the effects of thermal buckling. After each thermal cycle a residual strain and vertical displacement was seen in the gage section of the sample. The amount of displacement and strain was not sensitive to the prestrain in each sample. The recorded displacements and strains will be used in conjunction with the material property study to create an LS-DYNA model for the effects of thermal cycles on 6000 series aluminum alloys.

Appendix A: Full Experimental Results - Ductile Fracture of Nickel- Based Superalloy

The full experimental results for the ductile fracture behavior of a nickel-based superalloy are discussed here. The results include, stress versus strain curves, force versus displacement curves, and strain histories. The results of these tests are discussed in Chapter 2 along with a presentation of representative data curves.

A.1 Force versus displacement curves

Figure A.1 Experimental results for 0.263" radius notch tests at 875°F

Figure A.2 Experimental results for 0.263" radius notch tests at 1025°F

Figure A.3 Experimental results for 0.394" radius notch tests at 875°F

Figure A.4 Experimental results for 0.394" radius notch tests at 1025°F

Figure A.5 Experimental results for 0.787" radius notch tests at 875°F

Figure A.6 Experimental results for 0.787" radius notch tests at 1025°F

Figure A.7 Experimental results for hole specimens at 875°F

Figure A.8 Experimental results for hole specimens at 1025°F

Figure A.9 Experimental results for uniaxial specimens at 875°F

Figure A.10 Experimental results for uniaxial specimens at 1025°F

A.2 True stress versus true strain curves

Figure A.11 True stress versus strain for uniaxial specimens at 875°F

Figure A.12 True stress versus strain for uniaxial specimens at 1025°F

A.3 Evolution of equivalent plastic strain versus stress triaxaility approximation plots

Figure A.13 Equivalent strain versus stress triaxility for 0.263" radius notched specimens

Figure A.14 Equivalent strain versus stress triaxility for 0.394" radius notched specimens

Figure A.15 Equivalent strain versus stress triaxility for 0.787" radius notched specimens

Figure A.16 Equivalent strain versus stress triaxility for hole specimens

Figure A.17 Equivalent strain versus stress triaxility for uniaxial specimens

Appendix B: Full Experimental Results – Thermally Induced Strains of a 6000 series Aluminum Alloy

The full experimental results for the prestraining operations and thermal cycle experiments for a 6000 series aluminum alloy are presented here. The results include, initially induced strains, calculations of CTE values, strain offset values and the evolution of strain versus time for each test. The results of these tests are discussed in Chapter 3 along with a presentation of representative data curves.

B.1 Prestrain curves

Figure B.1 Prestrains for transverse bend specimens

Figure B. 2 Stress strain curves of prestraining operation for combined loading specimens

Figure B. 3 Bending prestrains for combined loading specimens

B.2 Strain response to thermal cycles for various specimens

Figure B. 4 Strains in the X-direction for transverse bend specimens during a C-type heat cycle

Figure B. 5 Strains in the Y-direction for transverse bend specimens during a C-type heat cycle

Figure B. 6 Strains in the X-direction for combined loading specimens during a C-type heat cycle

Figure B. 7 Strains in the Y-direction for combined loading specimens during a C-type heat cycle

B.3 Measured CTE values for various specimens

Figure B. 8 CTE values for combined loading specimens during the first and second dwells

Figure B. 9 CTE values for transverse bend specimens during the first and second dwells

Figure B. 10 CTE values for each specimen during the first dwell of the specified heat cycle

Figure B. 11 CTE values for each specimen during the second dwell of the specified heat cycle

B.4 Strain offset measurements for various specimens

Figure B. 12 Strain offsets in the X and Y directions during the first and second heating dwells of A and C type heating cycles for all bending and combined tests

Figure B. 13 Total strain offsets in the X and Y directions relative to normal estimated thermal expansion for all specimens after the first cooling period

Figure B. 14 Total strain offsets in the X and Y directions relative to normal estimated thermal expansion for all specimens after the first cooling period 94

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