ISTANBUL TECHNICAL UNIVERSITY GRADUATE SCHOOL OF SCIENCE ENGINEERING AND TECHNOLOGY
PhD. THESIS
INVESTIGATION OF THE EFFECT OF HEAT TREATMENTS ON THE FORMABILITY OF THE 6061 Al ALLOY
Raşid Ahmed YILDIZ
Department of Mechanical Engineering Mechanical Engineering Programme
DECEMBER 2019
ISTANBUL TECHNICAL UNIVERSITY GRADUATE SCHOOL OF SCIENCE ENGINEERING AND TECHNOLOGY
INVESTIGATION OF THE EFFECT OF HEAT TREATMENTS ON THE FORMABILITY OF THE 6061 Al ALLOY
PhD. THESIS Raşid Ahmed YILDIZ
(503112030)
Thesis Advisor: Prof. Dr. Şafak YILMAZ Department of Mechanical Engineering
ARALIK 2019
ISTANBUL TEKNİK ÜNİVERSİTESİ FEN BİLİMLERİ ENSTİTÜSÜ
ISIL İŞLEMLERİN 6061 Al ALAŞIMININ ŞEKİLLENDİRİLEBİLİRLİĞİNE ETKİSİNİN İNCELENMESİ
DOKTORA TEZİ Raşid Ahmed YILDIZ
(503112030)
Tez Danışmanı: Prof. Dr. Şafak YILMAZ Makina Mühendisliği Anabilim Dalı
Thesis Advisor : Prof. Dr. Şafak YILMAZ ... Istanbul Technical University
Jury Members : Prof. Dr. Paşa YAYLA ... Marmara University
Prof. Dr. Murat VURAL ... Istanbul Technical University
Prof. Dr. Ekrem Tüfekçi ... Istanbul Technical University
Prof. Dr. Hüsnü DİRİKOLU ... Istanbul University - Cerrahpasa
Raşid Ahmed YILDIZ, a Ph.D. student of ITU Graduate School of Science Engineering and Technology student ID 503112030, successfully defended the dissertation entitled “INVESTIGATION OF THE EFFECT OF HEAT TREATMENTS ON THE FORMABILITY OF THE 6061 Al ALLOY”, which he prepared after fulfilling the requirements specified in the associated legislations, before the jury whose signatures are below.
Date of Submission : 11 November 2019 Date of Defense : 09 December 2019
FOREWORD
I would like to express my special thanks of gratitude to my advisor, Prof. Dr. Şafak YILMAZ. His guidance, support and encouragement has led me through the challenging tasks. His valuable and constructive suggestions during the planning and development of this research work has been very much appreciated.
I would also like to thanks to Erdal Dinç, Osman Çelebi, Selçuk Kılıç, the technicians of the laboratory of the ITU Mechanical Engineering Department, for offering me the resources and contributions to the experiments.
My grateful thanks are also extended to Res. Asst. Tugba Tetik, for her enthusiastic encouragement, useful critiques and help in the MATLAB codes. I also would like to acknowledge Assoc. Prof. Dr. Turgut Gülmez handling the instruments and Asst. Prof. Dr. Canan Gamze Güleryüz for the editing of the manuscript. I thank Res. Asst. Vehbi Öztekin and the professors/research assistants in the manufacturing group of ITU Mechanical Engineering Department for their helps.
I finally want to extend my deepest gratitude to my parents, Muhterem and Aliye Yıldız, and my sister Afra Yıldız for their understanding, love and encouragement.
November 2019 Raşid Ahmed YILDIZ
TABLE OF CONTENTS Page FOREWORD ... ix TABLE OF CONTENTS ... xi ABBREVIATIONS ... xiii SYMBOLS ... xv
LIST OF TABLES ... xvii
LIST OF FIGURES ... xix
SUMMARY ... xxi
ÖZET ... xxiii
1. INTRODUCTION ... 1
1.1 Forming Limit Diagrams ... 2
1.2 Motivation ... 3
1.3 Thesis Overview ... 4
2. LITERATURE REVIEW ... 5
2.1 6061 Al Alloy: Microstructure and Deformation ... 5
2.2 GTN Damage Model ... 6
2.3 Formability ... 10
2.4 Grid Marking & Measurement ... 12
3. EXPERIMENTAL METHODS ... 13
3.1 Material ... 13
3.2 Heat Treatment Procedure ... 13
3.3 Microstructural Investigation ... 14
3.4 Tensile Testing & Anisotropy ... 15
3.5 Hardness Testing ... 16
3.6 Void Volume Fraction Measurements ... 17
3.7 Scanning Electron Microscopy ... 17
3.8 Grid Marking ... 17
3.9 Formability Testing ... 19
3.10 Measurement of Grid Geometry ... 22
4. MODELLING METHODS ... 23
4.1 GTN Damage Model ... 23
4.2 Finite Element Analysis Models ... 24
4.2.1 Simulation of tensile testing ... 25
4.2.2 Simulation of Nakajima deep drawing test ... 25
5. EXPERIMENTAL RESULTS ... 27
5.1 Anisotropy of the Sheet ... 27
5.2 Tensile Tests of 6061 Al Alloy After Different Heat Treatments ... 29
5.3 Hardness Measurements ... 33
5.4 Density Measurements ... 34
5.5 Results of Grid Measurements ... 38
5.6 FLC Experimental Results ... 40
6.2 Discussion on the Hardness Measurement Results ... 51
6.3 Grid Measurement Discussions ... 52
6.3.1 Verification of the strain measurements ... 52
6.3.2 Influence of error on the forming limit diagram ... 55
6.4 Discussion on the Experimental FLCs ... 56
6.4.1 Effect of sheet thickness on the forming limit ... 56
6.4.2 Effect of heat treatments on the forming limit ... 57
7. MODELLING RESULTS AND DISCUSSION ... 61
7.1 GTN Damage Model Parameters ... 61
7.1.1 Determination of initial void volume fraction (f0) ... 61
7.1.2 Determination of void volume fraction during deformation ... 62
7.1.3 Determination of critical (fc) and final (ff) void volume fractions... 62
7.1.4 Determination of parameters belonging to nucleated voids (fN, εN, SN) .... 63
7.1.4.1 Nucleation void volume fraction (fN) ... 64
7.1.4.2 Nucleation strain (εN) ... 66
7.1.4.3 Standard deviation for the distribution of nucleation (SN) ... 67
7.2 Verification of the GTN Damage Model Parameters ... 68
7.3 Verification of the Nakajima Test Simulations ... 71
7.3.1 Determination of the valid friction coefficient for the simulations ... 71
7.3.2 Verification of the simulations using experimentally measured dome height ... 73
7.3.3 Verification of the simulations using experimentally observed damage locations ... 74
7.4 Simulation Results of the FLC ... 75
7.5 Damage Evaluations using FLD Simulations... 77
8. CONCLUSION ... 81
REFERENCES ... 85
ABBREVIATIONS
FLD : Forming Limit Diagram FLC : Forming Limit Curve
TEM : Transmission Electron Microscopy GTN : Gurson-Tvergaard-Needleman
CT : Computed Tomography
SEM : Scanning Electron Microscopy DCPD : Direct Current Potential Drop FEM : Finite Element Method
EDX : Energy Dispersive X-Ray Spectroscopy RD : Rolling Direction ND : Normal Direction TD : Transverse Direction DC : Direct Current UV : Ultraviolet YS : Yield Strength
UTS : Ultraviolet Ultimate Tensile Strength HV : Hardness Vickers
MTM : Mori–Tanaka Method DIC : Digital Image Correlation FEA : Finite Element Analyses
SYMBOLS
f : Void volume fraction
𝜺𝒘, 𝜺𝒕 : Strain in width and thickness 𝒘𝟎, 𝒘𝒇 : Initial and final width
𝒕𝟎, 𝒕𝒇 : Initial and final thickness r : Plastic strain ratio
∆𝒓 : Planar anisotropy Rm : Normal anisotropy
f0, fc, ff : Initial, critical and final void volume fraction
f* : Effective void volume fraction q1, q2, q3 : GTN model coefficients
σm, σe, σY : Hydrostatic, equivalent Mises and flow stress in the metal matrix
fg, fN : Growth and nucleated void volume fraction
𝜺𝒑
̅̅̅̇ : Equivalent plastic tensile strain rate of the matrix SN : Standart deviation of the void nucleation distribution
εN : Nucleation strain
σ : Equivalent Mises stress
K : Strength coefficient of the material
n : Strain hardening coefficient of the material ε : Equivalent plastic strain
𝜺̅ : Effective strain
εl : Strain in the longitudinal direction
εw : Strain in the transverse direction
εt : Strain in the thickness direction
𝜺𝒎 : Equivalent plastic strain in the metal matrix 𝝈𝒓 : Rapture stress
A : Hardness coefficient
LIST OF TABLES
Page
Table 2.1: GTN model parameters in the literature. ... 9
Table 3.1: Chemical composition of the 6061 aluminum alloy. ... 13
Table 3.2: Etchants for 6061 Al alloy. . ... 15
Table 5.1: Grain sizes measured in different orientations. ... 28
Table 5.2: Plastic strain ratios and degree of planar anisotropy because of rolling directions (sheet thickness: 2 mm). ... 29
Table 5.3: Yield and ultimate tensile strength of the 6061 aluminum alloy. ... 30
Table 5.4: Strength and strain hardening coefficient of the 6061 aluminum alloy. .. 32
Table 5.5: Void volume fraction percentage regarding effective plastic strain. ... 37
Table 5.6: Photographs of the grids obtained by various techniques. ... 39
Table 5.7: Measurements of the grids obtained by different marking methods. ... 40
Table 6.1: Uniform elongation and strain-hardening exponent. ... 45
Table 6.2: Comparison of hardness hardening and strain hardening coefficients. ... 51
Table 6.3: Measured dimensions and calculated maximum errors of the grid strain. ... 53
Table 7.1: Critical (fc) & final (ff) void volume fractions of the 6061 Al alloy for each heat treatment. ... 63
Table 7.2: EDX analysis result comparison in weight percentage. ... 65
Table 7.3: Nucleation strain (εN) values along with the heat treatments. ... 67
Table 7.4: GTN model parameters of 6061 Al alloy... 68
LIST OF FIGURES
Page
Figure 1.1: Illustration of a typical forming limit diagram. ... 2
Figure 3.1: Heat treatment procedure for the Al–Mg–Si alloy. ... 14
Figure 3.2: Schematic of the one-sided laser marked tensile specimen. ... 16
Figure 3.3: Commonly applied grid patterns. ... 18
Figure 3.4: Laser marked forming limit test piece geometries. ... 20
Figure 3.5: Nakajima test setup... 21
Figure 3.6: Dimensions of the Nakajima test setup. ... 21
Figure 3.7: Handheld microscope used to capture micrographs of the grids on (a) tensile specimen (b) FLD specimen. ... 22
Figure 4.1: Finite element model of the tensile specimen. ... 25
Figure 4.2: Boundary conditions of the model. ... 26
Figure 5.1: Tri-planar optical micrographs of the 6061-T6 Al alloy with x200 magnification. ... 27
Figure 5.2: Engineering stress-strain curve of 6061-T6 for different rolling directions (Sheet thickness: 2 mm). ... 28
Figure 5.3: Engineering stress–strain curves of the 6061 aluminum alloy specimens tested. ... 30
Figure 5.4: Duration of artificial aging with regard to a) Yield strength b) Ultimate tensile strength. ... 31
Figure 5.5: True stress–strain curve of the 6061 aluminum alloy. ... 32
Figure 5.6: Strain-hardening coefficient of the 6061 Al alloy regarding artificial aging duration. ... 33
Figure 5.7: True stress with regard to hardness for different heat treatment. ... 34
Figure 5.8: Density measurement zones on the necked region of tensile specimen. 35 Figure 5.9: Void volume fraction regard to effective plastic strain. ... 36
Figure 5.10: Nakajima test specimens after deep drawing tests. ... 41
Figure 5.11: Effect of the sheet thickness on the FLC for a) Naturally aged (T4) b) Artificially aged for 4 hours at 160 °C c) Artificially aged for 8 hours at 160 °C d) Artificially aged for 12 hours at 160 °C e) Artificially aged for 16 hours at 160 °C (Peak strength-T6). ... 42
Figure 5.12: Effect of the heat treatment on the FLCs... 43
Figure 6.1: SEM fractograph of the 6061 Al alloy tensile specimen. ... 47
Figure 6.2: Effective strain regarding hardness for different aging process. ... 47
Figure 6.3: Comparison of Holloman stress and true stress at fracture. ... 50
Figure 6.4: Hardness with regard to effective strain. ... 51
Figure 6.5: Error of grid-based strain regarding overall strain. ... 54
Figure 6.6: Maximum absolute error percentage of the grid strain versus overall strain. ... 55
Figure 6.8: Effect of the sheet thickness on the major strain for different heat treatments in the regions a) Uniaxial tension b) Plane strain c) Biaxial tension ... 57 Figure 6.9: Effects of the heat treatments on the major and minor strains for
different sheet thicknesses in the regions a) Uniaxial tension b) Plane strain c) Biaxial tension. ... 58 Figure 6.10: Effect of heat treatment duration on the major/minor strain ratios for
a) Uniaxial tension region b) Biaxial tension region. ... 58 Figure 7.1: Undeformed microstructure of the alloy. ... 61 Figure 7.2: SEM micrograph of the void nucleation originated from the
precipitate. ... 63 Figure 7.3: SEM micrograph showing EDX analysis regions of the undeformed
alloy. ... 64 Figure 7.4: EDX analysis results of a) Matrix metal b) Second-phase precipitate. .. 65 Figure 7.5: Digital image processed SEM micrograph to calculate second-phase
precipitates. ... 66 Figure 7.6: SEM micrograph a) x1000 b) x5000 of the fractured surface of
6061-T6. ... 67 Figure 7.7: The distribution of nucleated void volume fraction. ... 68 Figure 7.8: Load-displacement curves obtained experimentally vs FEM
simulations. ... 69 Figure 7.9: Final fracture region of 6061-T6 obtained by experimentally vs FEM. . 69 Figure 7.10: The distribution of the f in the finite element model. ... 70 Figure 7.11: Effect of the friction coefficient on the FLC simulations. ... 72 Figure 7.12: Fracture locations a) Simulation μ=0.05 b) Simulation μ=0.52
c) Simulation μ=0.75 d) Experiment. ... 73 Figure 7.13: Dome height comparison experiments vs simulations. ... 74 Figure 7.14: Fracture locations in the FEM vs experiment a) GL=25 mm
b) GL=50 mm c) GL=75 mm d) GL=100 mm e) GL=175 mm f) GL=200 mm... 75 Figure 7.15: Fracture zone of the FLC specimen. ... 75 Figure 7.16: Comparison of FLCs obtained by experiments and simulations. ... 76 Figure 7.17: Effect of sheet metal thickness on the void nucleation and growth
for 6061-T4. ... 78 Figure 7.18: Effect of heat treatments on the a) Void growth in uniaxial tension
b) Void nucleation in uniaxial tension c) Void growth in-plane strain d) Void nucleation in-plane strain e) Void growth in biaxial tension f) Void nucleation in biaxial tension. ... 79
INVESTIGATION THE EFFECT OF HEAT TREATMENTS ON THE FORMABILITY OF THE 6061 Al ALLOY
SUMMARY
This thesis examines the tensile deformation behavior and formability of Al–Mg–Si alloy (6061 Al alloy) subjected to various aging conditions. Five peculiar heat treatments were designed, including natural aging temper (T4) and peak-strength (T6) temper, to investigate the effect of heat treatments on the formability of 6061 Al alloy sheets. The temper conditions, were designed to investigate the effect of artificial aging on the mechanical behavior of the alloy. Tensile tests were performed to determine the stress–strain behavior of the material. Thus, mechanical properties including yield, ultimate and rapture strengths, uniform and total strains, hardness, strength coefficient, and strain-hardening exponent were obtained experimentally. The relationship between equivalent strain, equivalent stress, and hardness is also examined. The results of the hardness tests show that σ=2.98×HV for both the uniformly deformed region and the necked region is valid for all heat treatment conditions. The rapture strength of specimens were determined to be less than the Holloman model predictions for the corresponding rapture strains of specimens. Void development, which is dependent on the amount of plastic strain, is determined to be the main reason for this discrepancy between the Holloman model and rapture stress. The calculated average stress in the metal matrix shows good agreement with the Holloman equation predictions. Thus, it is concluded that the void development explains the interrupted strain hardening after necking.
Moreover, this research experimentally determines the Gurson-Tvergaard-Needleman (GTN) damage mechanics model parameters for 6061 Al alloy. The GTN parameters considering different heat treatment conditions of the alloy were obtained by in-situ tensile tests. Scanning electron microscope (SEM) micrographs were used as inputs to determine initial and nucleated volume fractions. SEM and energy dispersive X-ray spectrography (EDX) analyses also revealed that the second-phase precipitates are the origin of the incipient voids. SEM analyses enabled the fractographic investigations where the primary and secondary voids were exhibited and thus showing nucleation strain. Density measurements were used to clarify the critical and final void volume fractions and the standard deviation of the nucleated void volume fraction distribution. The results show that the void volume fraction increases exponentially along with increasing effective tensile plastic strain. Hence, all of six different GTN parameters have been identified experimentally. Finite element method simulations based on GTN damage model were performed to verify the GTN model parameters.
The results show that the experimentally obtained GTN model parameters could be used when performing tensile deformation simulations of 6061 Al alloys fabricated with different heat treatment conditions.
Grid marking, which is applied before mechanical tests, is a crucial step in formability tests. In this study, four different grid marking methods, serigraphy, electro-chemical etching, photo-chemical etching and laser marking techniques, were investigated for the stability of grids and their measurement accuracy. After examining the performance of the grid marking methods, laser marking has been selected to obtain grids on the surface of aluminum alloy parts. To evaluate the efficiency of the strains calculation using grids, tensile tests were conducted that considered different levels of elongation. A forming limit diagram of the 6061-T6 Al alloy was constructed to demonstrate the influence of possible measurement errors. Verification of grid strain evaluation revealed that the error in size measurements is dependent on overall strain values and reduced with increasing overall strain as expected. The maximum error of the implemented method does not exceed 1% when 9% of overall uniform elongation is reached. The approach used in the study provides sufficient accuracy for evaluating strains in principal axis of deformed circular grids with minimalized costs.
The forming limit curves (FLCs) of the 6061 Al alloy subjected to heat treatments with various (1 mm, 1.6 mm, 2 mm, 2.5 mm) sheet metal thicknesses were obtained experimentally and computationally. Tensile tests were executed to determine the anisotropic behavior of the sheet, and the plastic strain ratio ‘r’ for sheet metal was determined. Laser- marked FLC specimens were waisted and deep drawn with the proposed spring-attached Nakajima deep drawing test setup. The degree of planar anisotropy based on the results indicates that the sheet was isotropic. Experimental FLC results revealed that the minor strain values remained stable with increased sheet metal thickness, while the major strain increased linearly. Moreover, increased artificial aging time exponentially decreased minor and major strain values. A finite element model (FEM) of the deep drawing test was constructed to investigate the effect of nucleation and growth mechanisms of the voids by using experimentally obtained GTN model parameters. The friction coefficients for the simulations were determined numerically with a trial and error method. The developed model was verified by comparing experimental FLC, fracture locations, and dome height. The effects of heat treatment conditions and the effects of sheet thicknesses on the FEM results differed simulations results from the experimental FLCs results by less than 5%. The results of the FEM were identified in regions of three different characteristic loading cases: uniaxial tension (Plane stress), plane strain, and equbiaxial stress (Two dimensional equal tensional stress state). The results indicate that sheet metal thickness has a positive effect on the effective strain up to failure. In contrast, increased artificial aging time reduced effective strain to failure, which is controlled by the nucleation and growth of voids.
ISIL İŞLEM KOŞULLARININ 6061 Al ALAŞIMININ ŞEKİLLENDİRİLEBİLİRLİĞİNE ETKİSİNİN İNCELENMESİ
ÖZET
Dünya çapındaki rekabet ve çevreyle ilgili standartların titizlikle uygulanmaya başlanması sonucunda hareketli yapıların hafifletilmesi ile enerji tasarrufu sağlanarak çevreye daha az zarar vermek aranan en önemli tasarım beklentilerinden biri olmuştur. Dolayısıyla hafifliklerinden dolayı uzun yıllardır uçak-uzay sanayinde kullanılmakta olan alüminyum alaşımları, son yıllarda, ülkemizde de hızla gelişmekte olan, otomotiv sanayi tarafından da yüksek özgül dayanım, korozyon direnci ve alışılmış imalat tekniklerine uygunluk avantajlarından dolayı, gittikçe artan oranda tercih edilir olmaktadır. Bu alaşımlar arasında 5xxx ve 6xxx serisi Al alaşımları korozyon direnci ile dikkat çekmektedir. Şekil verme sonrası gündeme gelen yaşlanma süreci şekillendirme sonrasında alüminyum mamul geometrilerinde; tasarım geometrisinden farklılaşmalara yol açmaktadır. Tasarım mühendisleri malzeme için yüksek mukavemet isterken, imalat mühendisleri için öncelik şekillendirilebilirlik dolayısıyla süneklik olmaktadır. Yapay yaşlandırılabilir alüminyum alaşımları için süneklik ve dayanım çökelme ile kontrol edilmektedir. Bu tez çalışması çerçevesinde farklı sıcaklık-zaman koşulları altında yaşlandırılmış 6061 Al alaşımının şekillendirme performansı incelenmiştir.
Öncelikle malzemenin mekanik özelliklerinin ısıl işlemlerden nasıl etkilendiğinin tespiti için 5 farklı ısıl işlem tasarlanmıştır. Bu ısıl işlemler T4 doğal yaşlandırma ve 160 0C’de 4, 8, 12 ve 16 saat (T6 en yüksek dayanım veren temper) yaşlandırma sürelerini de içermektedir. Farklı ısıl işlemler altındaki mekanik özelliklerinin belirlenmesi için sertlik ve çekme deneyleri gerçekleştirilmiştir. Gerçekleştirilen çekme deneylerinde malzemenin düzenli ve düzensiz uzama bölgelerindeki davranışı incelenmiştir. Malzemenin farklı ısıl işlem koşuları altındaki akma mukavemeti, çekme mukavemeti, kopma mukavemeti, dayanım sabiti, pekleşme üsteli, boyun verme öncesindeki ve sonrasındaki sertlik değerleri de deneysel olarak elde edilmiştir. Malzeme için eşdeğer birim şekil değişimi, eşdeğer gerilme ve sertlik değerleri arasındaki ilişki incelenmiş ve sonuçta düzenli ve düzensiz (Boyun verme bölgesinde) uzama bölgesi ve tüm ısıl işlem koşulları için σ=2.98×HV denkleminin geçerli olduğu görülmüştür. Malzemenin deformasyon davranışının düzgün uzama bölgesi içinde Holloman pekleşme modeli denklemine uygun olduğu görülmüştür. Ancak, boyun verme anındaki birim şekil değişimi değerinin pekleşme üsteline sayısal olarak eşit olmadığı ve kopma anındaki gerçek gerilme değerinin Holloman modeline uymayıp daha düşük olduğu tespit edilmiştir. İyi bilindiği üzere, bunun nedeni artan birim şekil değişiminden kaynaklanan, malzeme içerisindeki boşluk oluşumudur. Şekil değişimiyle gelişen boşluk oranını belirlemek amacıyla, düzgün uzamış ve boyun vermiş çekme deneyi numunesi kesitlerinde yoğunluk ölçümleri yapılmıştır. Boşluk hacim oranları küçük olduğundan, elde edilen boşluk oranları kullanılarak, boşluklu yapıya sahip metal matristeki gerilme değeri ortalama olarak hesaplanmıştır.
Hesaplanan gerilme değerlerinin Holloman modelindeki gerilme değeriyle uyumlu olduğu görülmüştür. Bu uyum tanıklığı, Al 6061 alaşımının çekme yükü altındaki şekil değiştirmesinde, şekil değişimi miktarına karşılık gelen Holloman denklemiyle hesaplanan çekme gerilmesiyle deneysel çekme gerilmesi arasındaki farkın matriste deformasyına bağlı olarak oluşan boşluk oranının tahmininde kullanılabileceğini ortaya konmuştur.
Gurson-Tveergaard-Needleman (GTN) hasar modeli sünek malzemelerin kırılma mekaniği çalışmalarında sıklıkla kullanılmaktadır. Literatürde GTN hasar modeli parametreleri çoğunlukla deneylerle ölçülmeden deneme yanılma yaklaşımına dayanan sayısal yöntemlerle tespit edilmeye çalışılmıştır. Bu çalışmada literatürden farklı olarak GTN hasar modeli paramtrelerinin deneysel olarak elde edilmesi amaçlanmıştır. GTN hasar modeli için dokuz farklı malzeme parametresinin bilinmesine ihtiyaç duyulmaktadır. Bunun için beş farklı ısıl işlem koşullarındaki 6061 Al alaşımı malzeme çekme testlerine tabi tutulmuştur. Taramalı elektron mikroskobu (SEM) yardımıyla başlangıç ve çekirdeklenen boşluk/hacim oranı tespit edilmiştir. SEM ve enerji saçılımlı X-ışını tayfölçüm analizleri ile ikincil fazların malzemede çekirdeklenen boşlukların kaynağı olduğu görülmüştür. Kırılma yüzeyleri incelendiğinde malzeme birincil ve ikincil boşlukların etkisinde tipik sünek kırılma örneği göstermektedir. Dolayısıyla, son kırılma bölgesindeki birim şekil değişimi değerinin kritik çekirdeklenme seviyesine ait birim şekil değişimi olduğu kabul edilmiştir. Malzeme içerisindeki boşluklar kritik bir değere ulaştığında birleşmeye başlamaktadır. Yoğunluk ölçümleri kullanılarak, çekirdeklenen boşluk/hacim oranındaki standart sapma da hesaplanmıştır. Yine yoğunluk ölçümleri ile, çekirdeklenen boşluk/hacim oranının standart sapması hesaplanmıştır. Ayrıca deneylerde boşluk/hacim oranının artan eşdeğer birim şekil değişimi ile birlikte eksponansiyel olarak arttığı gözlemlenmiştir. Bu tez çalışması, dokuz adet GTN hasar modeli parametresinden literatürden verilen üçü dışında, kalan altı adet katsayı deneysel olarak elde edilmiştir. Bu parametrelerin doğruluğunu kontrol edebilmek için çekme deneyini simüle edecek bir sonlu elemanlar modeli oluşturulmuştur. Bu modelde malzemenin elastik bölgedeki özellikleri literatürden alınmıştır. Plastik bölgedeki özellikleri ise gerçekleştirilen çekme deneylerinden elde edilmiştir. Son olarak deneysel olarak elde edilen GTN hasar modeli parametreleri sonlu elemanlar yazılımına veri olarak girilmiştir. Çekme deneylerinin sonuçları ve sonlu elemanlar modelinin gerilme-birim şekil değişimi grafikleri çıkartılmıştır. Tüm ısıl işlem durumları için, elde edilen GTN model parametreleriyle oluşturulan sonlu elemanlar modeli sonuçlarının, deneysel olarak elde edilen eğrilerle uyum içinde kaldığı tespit edilmiştir. Deneysel olarak elde edilen GTN model parametreleri, sonlu elemanlar simülasyonlarıyla doğrulanmıştır.
Sac malzemelerin şekil verilebilirlik sınırlarının belirlenmesinde şekillendirme sınırı diyagramları kullanılmaktadır. Şekillendirme sınır diyagramları genellikle Marciniak Deneyi ve Nakazima Deneyi olarak adlandırılan derin çekme şartlarında çalışan deney sistemlerinden elde edilmektedir. Bu deneylerin, malzeme üreticileri ve araştırmacılar tarafından aynı şekilde uygulanabilmesi amacıyla ASTM E2218-02 ve ISO 12004 standartları oluşturulmuştur. Tez çalışmasını gerçekleştirebilmek için öncelikle deney sistemi kurulmuştur. Derin çekme deneyinin (Nakajima deneyi) yapılabilmesi için İTÜ Makine Fakültesinde mevcut 150 ton kapasiteli hidrolik pres kullanılmıştır. Numunelerin hazırlanabilmesi için sac kesme kalıpları ve giyotinden yararlanılmıştır.
Malzemenin şekillendirilebilirliğinin incelenmesi için öncelikle uygun ölçülere getirilen numunelerin yüzeyine benek işlenmesi gereklidir. Benek kalitesi şekilllendirilebilirlik için önemli bir adımdır.
Tez çalışması kapsamında dört farklı benek işleme yöntemi (Serigrafi, elektro-kimyasal dağlama, foto-elektro-kimyasal dağlama ve lazer markalama) beneklerin test esnasındaki dayanıklılığı ve ölçüm doğruluğu açısından incelenmiştir. Gerçekleştirilen ön deneyler neticesinde yaygın olarak kullanılan tüm markalama yöntemleri denenmiş ve alüminyum malzeme için en uygun yöntemin lazer markalama olduğu görülmüştür. Lazer markalama ile işlenmiş beneklerin ölçüm amaçlı kullanılabilirliliğini değerlendirmek için doğrulama amaçlı çekme deneyleri yapılmıştır. Deneylerde önce lazer markalama ile benekler numune yüzeyine işlenmiştir. Deney sonrasında şekil değiştiren beneklerdeki birim şekil değişimi ölçmek için şekil değiştirmiş beneklerin tek tek fotoğrafları çekilmiştir. Çekilen fotoğraflar Matlab kodu yardımıyla dijital olarak işlenmiş ve major/minor birim şekil değişimleri hesaplanmıştır. Ek olarak, ölçüm yönteminin doğruluğunu değerlendirmek için çekme deneyleri farklı uzama seviyelerinde durdurulmuştur. Bu deneylerde ölçülen hata miktarının, beklendiği üzere toplam uzama ile ters orantılı olduğu görülmüştür. Çekme deneyinde %9 üniform uzama gerçekleştiğinde, uygulanan yöntemin hatasının %1’den az olduğu görülmüştür. Bunlara ilaveten ölçüm yöntemini değerlendirmek için 2 mm sac kalınlığına sahip T6 temperi kullanılarak bir adet şekillendirme sınır diyagramı oluşturulmuştur. Bu sınır diyagramına göre, sadece düşük birim şekil değişimi değerleri için hata oranı anlamlı seviyelere ulaşabilmektedir. Ancak ölçülen beneklerin diyagram üzerindeki normal dağılımına bağlı olarak bu hata oranı önemsenmeyecek bir seviyede kalmaktadır.
Beş farklı ısıl işlem koşulu altında (T4 doğal yaşlandırma ve 160 0C’de dört farklı sürede) yaşlandırılmış 6061 Al alaşımının şekillendirme sınır diyagramları oluşturulmuştur. Ayrıca kalınlığın 6061 Al alaşımının şekillendirilebilirliği üzerindeki etkisini incelemek için dört farklı kalınlıkta (1 mm, 1.6 mm, 2 mm ve 2.5 mm) sac levhanın şekillendirilebilirliği karşılaştırılmıştır. Temin edilen levhaların mekanik anizotropi gösterip göstermediğini tespit etmek için ASTM E517 standart testi yapılarak normal anizotropi ve düzlemsel anizotropi katsayıları belirlenmiştir. Ayrıca malzemenin mikroskopik incelemesinde tane boyutunun her üç düzlemde de benzer olduğu bulgusuna ulaşılmıştır. Levhanın haddeleme doğrultusuna göre 00, 450 ve 900 için gerçekleştirilen çekme testi sonuçları incelendiğinde eğrilerin birbirine çok yakın olduğu gözlemlenmiştir. Dolayısıyla malzemenin mekanik özelliklerinin yöne bağımlı olmadığının kabul edilebileceği belirlenmiştir. Isıl işlem koşullarına ve sac metal kalınlığına bağlı olarak şekillendirme sınır diyagramları hazırlanmıştır. Bu diyagramlar incelendiğinde sac metal kalınlığı arttıkça minor birim şekil değişimi değerleri sabit kalmasına karşın, major birim şekil değişimi değeri doğrusal olarak arttığı tespit edilmiştir. Öte yandan yapay yaşlandırma süresi arttıkça hem minor hem de major birim şekil değişimi değerleri eksponansiyel olarak artmaktadır.
Deneysel olarak elde edilen GTN model parametreleri kullanılarak Nakajima deney sisteminin sonlu elemanlar modeli hazırlanmıştır. Sonlu elemanlar modelinde sürtünme katsayısının çözüme ciddi biçimde etki ettiği bilinmektedir. Farklı sürtünme katsayıları kullanılarak sürtünme katsayısının şekillendirme sınır diyagramı üzerindeki etkisi incelenmiştir. Kalıplar ile alüminyum levha arasındaki uygun sürtünme katsayısının 0.52 olduğu tespit edilmiştir.
Oluşturulan sonlu elemanlar modeli sonuçlarıyla, deney numunelerindeki kırılma bölgesinin konumu, kubbe yüksekliği ve deneysel şekillendirme sınırı diyagramları karşılaştırılarak GTN hasar modeli parametreleri doğrulanmıştır. Sonlu elemanlar çözümü, deneysel sonuçlarla karşılaştırıldığında tüm ısıl işlem durumları ve sac metal kalınlıkları için en fazla %5 oranında farklılık olduğu görülmüştür.
Sac metal kalınlığı arttıkça hasara kadar olan eşdeğer birim şekil değişiminin artmış olduğu tespit edilmiştir. Ayrıca yapay yaşlandırma süresi ile de sünekliğin azaldığı ve dolayısıyla hasara kadar olan eşdeğer birim şekil değişiminin azaldığı gözlemlenmiştir. Gerilme hali boşluk çekirdeklenmesi ve büyümesini etkilediği için sonlu elemanlar modeline ait sonuçlardan karakteristik üç farklı duruma ait sonuçlar dikkate alınarak incelenmiştir: Tek eksenli gerilme (Düzlem gerilme), düzlem genleme ve iki eksenli eşit gerilmeli germe durumları. İki eksenli eşit gerilmeli germe durumundaki sınırın, hidrostatik gerilme değerinin düşük olmasının boşluk çekirdeklenmesini ve büyümesini geciktirmesi dolayısıyla, diyagramın düzlem genleme haline ait olan en düşük şekilledirme sınırının üzerinde kalabildiği tespit edilmiştir.
Bilindiği üzere Al 6061 alaşımlarından yapılan mamüller en sünek oldukları, ısıl işlem görmemiş haliyle şekillendirilirler ve sonrasında yaşlandırılarak mukavemetli hale getirilirler. Şekil verme imalatı sonrası doğal ya da yapay yaşladırma sürecinde mamül geometrisinde yaşlanmaya bağlı olarak çarpıklaşma meydana gelmesi tekniğin bilinen bir problemidir. Değişik seviyelerde yaşlandırılarak çökelti oluşumunu kısmen tamamlamış içyapıların deformasyon işleminden sonra çarpıklaşmasının, yaşlandırma işlemi uygulanmamış durumuyla şekillendirilmesinden sonraki çarpıklaşmasından daha az olacağı açıktır. Bu yararlı durumun bedeli, metalin yaşlandırılmamış halindeki başlangıç sünekliğinden yani, şekil verilebilirlikten taviz verilmesidir. Sunulan tez çalışması kapsamında, ısıl işlem koşulları ile şekil verilebilirlik arasındaki ilişki şekillendirme sınırı diyagramları aracılığıyla incelenmiş ve şekillendirilebilirlik sınırındaki değişimin kuramsal mekanizmaları deneylerle ve simülasyon analizleriyle elde dilen bulugularla açığa çıkartılmıştır. Tez çalışmasıyla, bir yandan bilimsel ve teknik literatürdeki igili boşlukları dolduracak bulgular, diğer yandan da sanayide bu yöntemin verimli kullanılmasını sağlayacak ısıl işlem parametrelerinin belirlenmesine yönelik çıktılar elde edilmiştir. Çalışma sonuçlarının, ülkemizde ve dünyada hızla gelişen otomotiv, havacılık/uzay sanayine ve alüminyum alaşımı levhaların (soğuk şekil verilerek) yoğun olarak kullanıldığı tüm imalat dünyasına katkı sağlaması beklenmektedir.
1. INTRODUCTION
The fuel economy and the regulations on the CO2 emissions force the manufacturers to weight reduction. The increasing demand for lightweight concerns has led to aluminum alloys being used in a wide range of areas because of their high strength/weight ratio and corrosion resistance [1]. Alternative materials as a substitute for steel have been investigated by the design engineers and researchers such as composites, polymers and magnesium and aluminum alloys. Aluminum alloys have been used by the automotive and aerospace/aircraft manufacturers due to their lower density, higher strength/weight, corrosion resistance and recyclability. Among the aluminum alloys, age hardenable or precipitation-hardenable Al alloys provide high strength through precipitation. The precipitation process affects the strength and the ductility, or in other words, the formability of the alloy. Al-Mg-Si alloys are the preferred precipitation hardened Al alloys in the aerospace and automotive industry because they have medium/high strength, good formability, corrosion resistance, weldability, and low cost [2]. After precipitation hardening, the alloy possesses high strength at the expense of formability [3]. The 6061 Al alloy is one of the most extensively used Al-Mg-Si alloys.
The plastic deformation of metals, commonly referred to as metal forming is of utmost technological importance. The metal forming includes the well-known processes of forging, extrusion, wire-drawing, rolling and sheet metal forming operations. Sheet metal forming is widely used in every sector of industrial production: automotive, aircraft, home appliance and food industries, providing high strength, good surface, and accurate tolerances. The complexity of manufacturing processes leads to several methods to evaluate the formability of the sheet metals [4, 5]. The forming limit diagrams (FLDs) are generally evaluated as a useful testing technique in formability. The effect of aging time on the formability of the 6061 Al alloy has been investigated within the scope of the thesis.
1.1 Forming Limit Diagrams
Formability is the capability of sheet metal to undergo plastic deformation to a predetermined shape without defects [6]. Formability is evaluated through different methods: mechanical tests [7], simulations [8, 9], limiting dome height [10, 11] and forming limit diagrams [12].
Keeler was the first pioneered the studies on the forming limit diagrams [13]. Forming limit diagrams (FLDs) are constituted by using the principal strains (Major & minor) at failure. The major strain is the largest strain, developed at the deep drawn surface of sheet metal. On the other hand, minor strain is the strain in sheet metal surface in a direction perpendicular to the major strain. Before the forming operation the sheet metal is covered with grids which are mostly circular. During the forming, the initial circular grids become ellipses along with the stress state.
Figure 1.1 shows a typical forming limit diagram for a sheet metal. The blue solid line represents the forming limit. Although most of the researchers/engineers plot the diagram only with the marginal strains, the diagram may include good (no localized necking), marginal (localized necking), and fracture areas.
Figure 1.1: Illustration of a typical forming limit diagram [14].
Formability limit or forming limit curve (FLC) of a sheet metal can be influenced by many factors: Sheet metal thickness, grid size, strain path, mechanical properties of the material, punch curvature, working temperature, strain rate.
FLD describes the forming limit or in other words formability of a sheet metal. To avoid manufacturing defects FLD method enables both the range of safety for deep-drawing and the critical zones for localized necking. In the industrial practice, manufacturing engineer compare the maximum strains in the designed sheet metal parts with the FLD. If the maximum strains are beyond the forming limit curve, the manufacturing design have to be modificated.
The comparasion between the FLD and the designed parts can be difficult for the complex parts since the analytical methods cannot be applicable. Numerical solution methods, in particular the finite element method, has become more and more the method of choice.
1.2 Motivation
In the literature and industry, the knowledge and experience is already available for steel sheets. On the other hand, there is limited knowledge on the formability of aluminum alloy sheets which constrains the use of aluminum alloys. The formability of aluminum alloy sheets should be better understood to be used more extensively. The complex mechanism of sheet metal forming inhibits prediction of failure during forming operations. 6061 Al alloy have more complex formability characteristics due to precipitation hardening process. Heat treatments highly affect the deformation behavior of the 6061 Al alloy. Defining the mechanical properties of the 6061 Al alloy regarding the aging time is essential to predict the outcome of metal forming operation. FLDs have been used as a predictive tool in sheet metal forming. The FLD of 6061 Al alloy is crucial for numerical modelling since it depicts the limit strains experimentally. The heat treatments also affect the formability of 6061 Al alloy and distortion of the part after forming operation.
Target of this thesis is to obtain the forming limit diagrams of 6061 Al alloy subjected to different heat treatment conditions. A micro-mechanical damage model coupled to finite element model is used to understand the mechanism beyond the fracture.
1.3 Thesis Overview
Formability of 6061 Al alloy was investigated through forming limit diagrams within this research after obtaining the deformation behavior of the 6061 Al alloy.
In the present work, the mechanical properties of 6061 Al alloy were investigated under various artificial aging conditions. Stress–strain behavior of the alloy including yield, ultimate, and rapture tensile strengths as well as uniform and rapture strains were examined in this research. The relationships between strain, stress, and hardness were also investigated. The stress–strain behavior of the 6061 Al alloy beyond the necking strains of the tensile test specimen was determined via hardness measurement. Thus, the stress–strain behaviors of 6061 Al alloys having different aging conditions while eliminating the strain localization effects were plotted up to the rapture.
The GTN damage model parameters of 6061 Al alloy is obtained experimentally through various artificial aging conditions. Also, the mechanical response of the alloy during the tensile tests was investigated along with porous material ductile fracture mechanics based on the GTN damage model.
A method combining a digital image processing system with a handheld microscope was proposed for the measurement of deformed circular grids in a cost-effective way. The error range of grid size measurements for different strain levels was also discussed. Not only operation procedures to obtain sufficient image quality by grid marking but also the accuracy of this technique were presented. A sample FLD was also produced to investigate the effect of grid-based strain evaluation using a digital image processing technique on the FLD.
In the thesis, forming limit curves of the 6061 Al alloy are subjected through various artificial aging conditions. Nakajima deep drawing tests and FE simulations were performed to determine experimental forming limit curves for the sheet metal thickness of 1 mm to 2.5 mm under various aging conditions. The GTN damage model was implemented to simulate the ductile damage of sheets subjected to Nakajima tests.
2. LITERATURE REVIEW
2.1 6061 Al Alloy: Microstructure and Deformation
Aluminum alloys constitute a wide range of application for aerospace, aircraft, and automotive industries through their high strength-to-weight ratio. Miller et al. determined that one obvious and significant difference between aluminum and steel is the outstanding bare metal corrosion of the 5xxx and 6xxx aluminum materials. Steel must have a coating comprising zinc, nickel, hard chromium, and other components in a coating to achieve acceptable corrosion resistance, and this coating is not necessary for aluminum [15]. Design engineers usually demand high strength in the materials as a design requirement, while manufacturing engineers mostly prefer high ductility for the metal-forming applications. The age-hardenable or precipitation-hardenable aluminum alloys are useful for engineering applications. Thus, ductility and strength properties of aluminum alloy are controlled by precipitation during the age hardening of aluminum alloys to optimize the design and manufacturing requirements in same metal alloys. Nevertheless, precipitation process of age hardaneble alloys can cause the distortion of the part shape in case of continuous aging after forming operations.
Precipitation hardening is a heat treatment process used to improve the strength of the age-hardenable alloys [16]. Mechanical/manufacturing engineers prefer Al–Mg–Si alloy systems in extruded products and automotive body sheets because they have medium strength, good corrosion resistance, formability, weldability, and low cost [2]. The 6061 aluminum alloy is one of the most extensively used Al–Mg–Si alloys and is commonly preferred in the peak-strength condition that is designated by the temper designation-T6 [17]. In contrast, engineers prefer 6061-T4, which is the natural-aged temper condition, in applications where ductility is required such as in forming operations. The natural aging condition is obtained through three steps: first, solution treatment is executed at 527 C. Second, quenching is implemented immediately after the solution heat treatment.
Lastly, the alloys remained in the room temperature at least two days [18]. Nevertheless, peak-strength is achieved by artificial aging at 160-180 °C for 10-20 hours after the quenching [19].
Many researchers have been studying the complex mechanism in the precipitation sequence [20–26]. Maisonette et al. studied the variations in the mechanical properties in the microstructure of 6061 Al alloy samples. They revealed that the precipitates evolve into β’ phases, as observed by transmission electron microscopy (TEM) [27]. Ozturk et al. researched the effect of aging duration on the mechanical properties (strength and hardness) of the 6061 Al alloy based on the paint-baking process [28]. In addition, Xu and colleagues investigated the effect of quenching temperature on precipitation behavior. The effect of the quenching temperature on the precipitation behavior and hardness of precipitation strengthened Al–Mg–Si–Cu 6061 alloy was investigated by means of hardness testing, precipitate microstructure observation, and real-time electrical resistivity monitoring during the artificial aging process [29]. In manufacturing applications, materials are generally formed under compressive-stress states. The mechanical behavior data given in the literature is mainly determined by uniaxial tensile tests since they are very practical to perform. In the tensile testing of metals, stress states have uniaxial tension characteristics until necking begins. The necking, or in other words strain localization, in the uniaxial tensile test is the major factor that determines the true stress-true strain behavior of metals. True stress–strain behavior of the material beyond necking to failure is vital because of the plastic-deformation-based manufacturing processes or finite-element-method simulations. Thus, true stress–true strain curves including strain levels beyond necking strain is required for metal forming engineering. After the initiation of necking, the uniaxial stress state transforms to a multiaxial stress state. However, uniaxial tensile testing can still permit stress–strain data beyond necking strain. In the literature, there are few studies on the mechanical behavior of 6061 Al alloys beyond the necking zone.
2.2 GTN Damage Model
As commonly known, ductile fracture is a mechanical response of nucleation, growth and coalescence of voids in porous materials. The voids in the as-received material are called initial or original voids.
Moreover, new voids can nucleate from inclusions and/or second-phase precipitates during deformation [30]. Therefore, the metals contain voids after deformation based manufacturing processes. In other words, plastic deformation also yields void growth once the voids have nucleated. Finally, the voids coalescence and result in ductile fracture [31].
Gurson proposed a model for void-related damage in porous domains including voids [32]. Later, Tvergaard and Needleman make contributions to the original theory of porous metal plasticity [33, 34]. Thus, Gurson-Tvergaard-Needleman (GTN) damage model has been widely used for the prediction of deformation and fracture behavior of metals.
To predict ductile damage in metals, scholars have conducted various studies via the GTN model [35–38]. GTN damage model considers the void evolution during the plastic deformation. Researchers have identified the stages of the void evolution through in-situ X-ray laminography or computed tomography (CT) [39–41]. Cao and colleagues characterized the ductile damage of high carbon steel by X-ray microtomography in addition to mechanical tests [42]. They reported that the void density which characterizes the void nucleation process and void size increased exponentially with the effective plastic strain. Moreover, Yuenyong and coworkers performed a practical approach to determine the void nucleation related GTN model parameters: Direct current potential drop (DCPD). They correlated the void density with the change in the resistance of the inspected region [43].
Al-Mg-Si alloys have a wide range of usage area including aerospace, aircraft and automotive industries as a result of their high strength/weight ratio, good corrosion resistance, formability, weldability, medium strength and low cost [2]. Therefore, GTN model of Al alloys were studied by the researchers and they have numerically identified GTN model parameters for various manufacturing applications of aluminum alloys [44–47]. Microstructural analysis and simulations of tensile testing have revealed the GTN model parameters to compare the experimental results with the finite element solver [48, 49].
Furthermore, Abbasi et al. used an artificial neural network and tensile testing results to identify the GTN model parameters [50]. However, there are few studies that have experimentally obtained GTN model parameters of metals.
Wcislik stated that the final fracture scanning electron microscopy (SEM) photograph and quantitative image analysis could be used to determine the final void volume fraction [51]. He et al. also proposed to determine GTN model parameters of 5052-0 Al alloy via tensile tests and SEM micrographs. However, their experimental methodologies are not practical because they proposed digital image processing to obtain the final void volume fraction using fractographs. Also, the standard deviation of the void nucleation distribution is based on values from literature [52]. In the literature, researchers obtained GTN model parameters for various metallic materials. These parameters are tabulated in Table 2.1 to show the range of each parameter based on previous works. In addition, the method for each study is given in Table 2.1. Most of the studies executed computational convergence via finite element method (FEM) and compared the results with the tensile testing. Some researchers tried to predict ductile damage by using the GTN parameters given in the literature. However, some researchers did not match materials used in the study with the literature GTN model parameters. In addition, collaborators utilize SEM investigations with digital image processing tools.
Table 2.1: GTN model parameters in the literature.
Material Method q1 q2 q3 f0 fc ff fN εN SN Ref.
Mild Steel FEM 1.5 1 2.15 0.001 0.0601 - 0.039 0.21 0.1 [53]
Mild Steel FEM and Biaxial Tensile Tests 1.5 1 2.25 - 0.08 0.12 0.04 0.3 0.22 [54]
Silicon Steel FEM, SEM 1.55 0.9 - 0.0025 0.101 0.155 0.04 0.24 0.01 [55]
IF-Steel FEM, Tensile Tests and Deep Drawing 1.5 1 2.25 0.0002 0.0134 0.0216 0.0106 0.1 0.1 [56] Monolithic Blank FEM and Deep drawing - - - 0.005 0.02 0.05 0.01 0.08 0.06 [57] BR1500HS FEM, Tensile Tests and Literature 1.5 1 2.25 0.005 0.2324 0.3071 0.04 0.3 0.1 [58] 22MnB5 FEM, Tensile Tests and Literature, 1.5 1 2.25 0.002 0.05 0.13 0.0155 0.3 0.1 [59] 3Cr1MoV FEM and Tensile Tests 0.608 0.562 0.369 0 0.240 0.261 0.179 0.124 0.083 [60] S235JR Steel Calculation and SEM 1.5 1 2.25 0.0017 0.06 0.667 0.04 0.3 0.05 [61] DC06 Steel FEM and Tensile Tests 1.5 1 2.25 0.001 0.04 0.06 0.004 0.3 0.1 [62] DP 600 Steel Literature, Tensile Tests and SEM 1.5 1 2.25 0.0008 0.028 0.09 0.02 0.2 0.1 [63] DP780 FEM and Tensile Test 1.5 1 2.25 0.003 0.013 0.207 0.018 0.102 0.206 [64]
SUS304 Sheet FEM and SEM 1.5 1 2.25 0.002 0.11 0.156 0.032 0.54 0.09 [65]
SS304 SEM and DCPD 1.5 1 2.25 0.00183 0.0135 0.2628 0.0056 0.3 0.1 [43]
SS304LN FEM and Literature 1.5 1 2.25 0.00001 0.11 0.25 0.006 0.3 0.1 [66]
Pure Ti SEM, Tensile Testing, Literature 1.5 1 2.25 0.00138 0.2593 0.3025 0.017 0.3 0.1 [67] AZ61 Mg alloy FEM and Tensile Tests 1.5 1 2.25 - 0.18 0.2 0.078 0.2 0.0064 [68]
AA2024-T351 FEM and Literature 1.2 1 - 0.1 0.25 0.5 - - - [69]
AA2219-T6 FEM and Tensile Testing 1.5 1.25 2.25 0.00328 0.011 0.015 0.01 0.12 0.3 [70]
AA5A02 FEM 1.5 1 2.25 0.001 0.02 0.0363 0.0242 0.1 0.1 [71]
AA5A06 FEM and Tensile Tests 1.5 1 2.25 0.0012 0.034 0.042 0.032 0.25 0.08 [72] AA5182-O FEM, Tensile Tests and Literature, 1.5 1 2.25 0.01 0.021 0.04 0.001 0.3 0.1 [73]
AA6016-T4 FEM and Literature 1.5 1 2.25 0.00035 0.05 0.15 0.05 0.3 0.1 [74]
AA6061-T6 Literature 1.5 1.0 2.25 0.000125 0.013 0.04 0.0008 0.3 0.1 [75]
2.3 Formability
The forming limit is the capacity of the sheet to undergo deformation without fracture or excessive thinning [77]. Thus, FLCs can be used to evaluate the formability of sheet metal. Keeler and Backofen [78] and Goodwin [79] were the first to propose to determine FLC by measuring the major and minor strains in the sheet plane for a wide range of strain paths. Nakajima out-of-plane and Marciniak in-plane stretching tests are the most widely used approaches to obtain the formability limits of the sheet metals [80].
Mohammed and colleagues executed Nakajima tests to define the material response for macroscopic scale based on the constituent phase distribution and properties of the advanced high strength steels (AHSS)[81, 82]. In addition, Panich et al. performed the Nakajima test to obtain forming limit diagram (FLD) of AHSS and compared experimental data with the theoretical yield criteria, namely, von Mises, Hill’s 48, and Barlat 2000 [83]. They reported that the FLCs calculated by the combination of Barlat 2000 and Swift hardening law showed better agreement with the experimental data. Bong et al. compared the FLCs obtained by modified Marciniak test and ASTM E2218-15 test [84]. They claimed that both test methods could be used for sheet metals having thickness below 1 mm. In addition, they reported that the ASTM E2218-15 test could result in undesired fractures in the specimens [85]. Saxena et al. evaluated the FLC and bending limit curve (BLC) of the 6014-T4 Al alloy by using the Nakajima test setup, and BLC were found to be at a higher level than FLC [7]. The researchers have indicated that the FLCs are affected by various factors: strain path dependency [86–88], sheet metal thickness [89–91], strain rate [92, 93], anisotropy [94–96], and microstructure [97].
Because finite element analysis has become widely used, both academic and industrial researchers have performed these methods to simulate the formability and predict the FLCs of the sheets. Lumelskyj et al. constructed FLCs numerically and developed a thickness thinning method to predict formability limits [98]. Continuum damage mechanics coupled with the FEM is a useful and practical tool to reduce the number of experiments in sheet metal forming.
To evaluate the ability for predicting fracture, researchers compared the ductile damage models. They compared the Lemaitre [99], Gurson–Tvergaard–Needleman (GTN) [32], and Johnson–Cook [100] damage models and concluded that the GTN and Lemaitre damage models agree with the experimental damage location [73]. Li et al. simulated the incremental sheet forming by using a GTN damage model and numerically calibrated the GTN damage model coefficients. They declared that the critical void volume fractions—a GTN damage model parameter—plays an important role to incrementally evaluate the performance of sheet metal forming [62]. Kami et al. determined FLC of 6016-T4 Al alloy sheet by using an Abaqus/explicit solver. They implement the GTN damage model to simulate the Nakajima test, and the numerical FLC showed good agreement with the experimental results. They reported that GTN model based FEM results were more accurate than those from the theoretical Marciniak–Kuczynski model [74].
Nguyen et al. studied to predict the ductile fracture and formability of the 6061-T6 Al alloy by using a user-defined material subroutine (VUMAT) in commercially available Abaqus/explicit FEM software. They used the GTN damage model to investigate ductile fracture in the material. They calibrated the GTN damage model coefficients by tensile testing executed through R-notched specimens. They reported that the forming limits were consistent with the developed equivalent plastic strain and stress triaxiality relation [76].
Haltom et al. asserted that the 6061 Al alloy exhibits a typical ductile fracture and that micromechanics based ductile damage models could be applied [101]. Sarraf et al. implemented the Rousselier damage model [102] as an alternative to GTN damage model to predict the strain localization and failure [103].
Researchers also used commercial FEM software Abaqus through a Matlab terminal to determine the correlation between simulations and experiments of electro-hydraulic forming of commercial 5082-O sheets by a coupled Eulerian–Lagrangian model [104].
2.4 Grid Marking & Measurement
Grid marking, advocated by Keeler, is usually practiced in sheet metal formability tests to calculate strain in principal axis [105].
Before a forming operation, a grid pattern is imprinted on the surface of sheet metal and then after the test, the dimensions of deformed grids are measured, thereby acquiring a strain measurement. Measuring maximum and minimum diameters of the grids determines the critical combinations of major and minor strains scribed on the sheet metal surface to determine forming limit curves. Manual strain measurement methods including Mylar tapes, microscopes and rulers, but all are either time-consuming or yield low resolution. Therefore, many researchers have developed automated dimension measurements to calculate strains [106–109]. Tan et al. recorded two or more images with various angles and read the image coordinates automatically, thus calculating the spatial coordinates [110]. An algorithm of pattern recognition system for automatically constructing the forming limit curve of sheet metal was also offered in the literature [111]. In addition, the implementation of an optical digitizer that uses 3D topometry and digital image processing to achieve the 3D coordinates of sheet metal has been reported in the work of Canal et al. [112]. Others suggested a new grid dimension measuring scheme that relies on close-range photogrammetry technology [113]. Moreover, Berger and Zussman proposed a method to measure thinning in the deep drawing process based on an ultrasonic transducer, which was located under the die [114].
On the other hand, companies including GOM, FMTI, ASAME, and ViaLux sell systems to measure strains that offer not only high accuracy but also ease of use. These systems have a major drawback—high cost, which prevents smaller research/development organizations from entering this challenging area.
3. EXPERIMENTAL METHODS
3.1 Material
In this study, commercial standard 6061 aluminum alloy with the chemical composition represented in Table 3.1 was used. The sheets were received in artificially aged condition-T6. To determine the aging behavior of the aluminum alloy, 25 mm x 25 mm specimens having a thickness of 2 mm were consumed.
Table 3.1: Chemical composition of the 6061 aluminum alloy.
Element Al Mg Si Fe Cu Zn Ti Mn Cr Others Weight % Balance 1.02 0.61 0.28 0.23 0.14 0.08 0.07 0.06 - 3.2 Heat Treatment Procedure
In the present study, five different heat treatments were designed to determine the mechanical behavior of 6061 Al alloy with regard to aging time. All the tensile specimens first were subjected to solution heat treatment, which was conducted at 527
C for 1 hour. Immediately after the solution heat treatment, the quenching process was executed. Banhart et al. claimed that the natural aging process consists of three regions: fast hardening, transitioning, and slow hardening [115]. Hardness measurements demonstrated a transition range for natural aging no longer than 48 hours. To eliminate the transition range of the precipitation, the specimens were kept at room temperature for two days.
According to the ASM Metals Handbook, peak strength is achieved when the specimen is heat treated at 160 C after quenching for 18h [19]. Nonetheless, natural aging applied for 48 hours reduced the time to reach peak strength; thereby, the T6 aging condition was obtained by aging for 16 hours at 160 C. To determine the effect of aging, heat treatments depicted in Figure 3.1 were designed.
Figure 3.1: Heat treatment procedure for the Al–Mg–Si alloy. 3.3 Microstructural Investigation
To investigate the microstructure of the 6061 Al alloy with the light microscope, the alloy was cut via the rolling, normal, and transverse directions. Then, the specimens were mounted using Bakelite thermoplastic. After the mounting process, the specimens were ground on 240, 400, 600 and 1000 sieve size papers. The grinding process was executed with water cooling, and the specimen was washed after each grinding. After grinding, the specimen was polished with 1 μm diamond paste. Lastly, the specimens were polished with the colloidal silica (spherical silica particles in a liquid phase).
There are numerous etchants proposed in the literature that can be used to reveal the grain boundaries and precipitates in the 6061 Al alloy. Polished specimens were then etched with the etchants given in Table 3.2. The etchants given in Table 3.2 were tested to obtain grain boundaries and precipitates in the microstructure.
Table 3.2: Etchants for 6061 Al alloy [116].
Keller 1 Weck’s Poulton’s Keller 2 95 mL water 100 mL water 30 mL HCl 25 mL Methanol 2.5 mL HNO3 4 g KMnO4 40 mL HNO3 25 mL HCl
1.5 mL HCl 1 g NaOH 2.5 mL HF 25 mL HNO3
1 mL HF 2.5 mL H2O 1 drop HF
40 mL Chromic Acid
The grain boundaries and precipitates were optimally achieved by the Keller 2 solution with an etching time of 20 s. To obtain the grain sizes, at least five different micrographs were used.
3.4 Tensile Testing & Anisotropy
Tensile tests were accomplished through ASTM E8-09: Standard test methods for tension testing of metallic materials [117]. The velocity of the tensile testing was maintained at a deformation of 2 mm/min that corresponds to an initial strain rate of 4.76x10-4 s-1. Tensile tests were performed by using Shimadzu Autograph 50 kN tensile tester with two CCD cameras. At least three different transverse oriented tensile testing specimen having a width of 12.5 mm and a gauge length of 75 mm were consumed for each heat treatment procedure.
To verify the grid measurement accuracy three tensile testing specimens were made for each elongation levels. Strain evaluations were conducted by using the deformed grid geometry on the surface of the tensile specimen. Figure 3.2 shows the one-sided laser marked tensile testing specimens used in the experiments with the magnified view of grids.
During heat treatments and deformation processes of the sheet metals, crystallographic textures were developed. Previous research indicates that the textures affect the forming behavior of aluminum alloy sheets [118].
Barnwal et al. found that that plastic anisotropy considerably affects the formability and crack direction of 6061 Al alloy [119]. Hence, an experimental study is required to reveal the crystallographic orientations of the material. Furthermore, r-bar tests were performed to determine the plastic anisotropy (‘r’ value) of the alloy in all three directions (0°, 45°, and 90°).
Figure 3.2: Schematic of the one-sided laser marked tensile specimen.
Tensile test specimens were prepared in three different orientations at 0°, 45°, and 90° for the peak-strength condition: 6061-T6. A minimum of three different samples were consumed in each direction. The r-bar test specimens were prepared having laser marking according to ASTM E517: Standard Test Method for Plastic Strain Ratio ‘r’ for Sheet Metal [120]. Then, the plastic anisotropy ratio of the sheet was calculated using Equation (3.1). r = Strain in width (εw) Strain in thickness (εt)= ln (wf w0 ⁄ ) ln (tf t0 ⁄ ) (3.1)
These ‘r’ values were further used to obtain the normal anisotropy of the sheet metal, as expressed in Equation (3.2), and the earing tendency, as expressed in Equation (3.3).
r =R0+ 2 × R45+ R90 4 (3.2) ∆r =R0+ R90 − 2 × R45 2 (3.3) 3.5 Hardness Testing
The microhardness tests were performed using the Shimadzu HMV2 under an applied load of 200 gf according to ASTM E 384-11 standard [121]. More than three hardness measurements were performed to determine hardness measurements.
3.6 Void Volume Fraction Measurements
To obtain the void volume fraction (f) in the tensile testing specimen, density measurements were conducted. The density measurements were executed by a Precisa XB 220A analytical balance with a density measurement kit. The necked regions of the tensile specimens were sliced into four pieces by using a precision cutter.
3.7 Scanning Electron Microscopy
Fractographic investigations were performed via Tescan Vega 3 versatile tungsten thermionic emission SEM. Furthermore, cross-sectional observations of the alloy have been conducted by Hitachi TM3030Plus SEM linked to an Oxford Instruments x-stream-2 energy dispersive X-ray spectroscopy (EDX) analyser to determine elemental weight percentage.
3.8 Grid Marking
Various grid marking techniques have been developed for different applications. Within this study, four different grid marking techniques-serigraphy, electro-chemical etching, photo-chemical etching and laser marking were investigated for stability, accuracy and ease of application. These methods are widely used techniques to mark the formability specimens. After marking the specimens by using appropriate technique, the dimensional change in the grid were then measured. Thus, the grid pattern should also be selected before the marking process. Various grid patterns have been used by the researchers and Figure 3.3 shows commonly applied grid patterns. For this study, the pattern was selected as solid circle grids since the geometry is non-directional for a direct reading of maximum strain in principal axis and point-to-point changes in strain distribution can be detected. The diameter of the circular grids should be large enough to scan dimensional changes and small enough to indicate local strain alterations. Diameters of the grids are generally between 2 mm and 3 mm in experimental studies [106, 111, 122, 123]. For this work, the diameter of the grids was defined as 2.5 mm. Distance between two-neighbor circles centers was set at 6 mm in an array.
