Chapter 9: Dislocations & Strengthening Mechanisms in Metals

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1 학습목표 Chapter 9: 전위와강화기구 (Dislocations & Strengthening Mechanisms) 왜금속에서전위의수가중요한가? 강도와전위운동은어떤관계를가지는것인가? 왜열처리는강도와다른기계적성질을변화시키는가? Chapter 9-1

2 전위와재료의종류 금속 ( 전자구름, Cu, Al): 전위운동이일어나기쉽다. - 방향성이없는 bonding 원자조밀방향에서 slip electron cloud ion cores 세라믹 ( 공유결합 ; Si, diamond): 전위운동이일어나기어렵다. - 방향성이있는 bonding 세라믹 ( 이온결함 ; NaCl): 전위운동이일어나기어렵다. - 같은전하를띠는이온은최인접으로존재하기어렵다 Chapter 9-2

3 전위운동 (Dislocation Motion) 의기본개념 전위운동과소성변형 금속 슬립 (slip) 에의해소성변형이일어난다. 칼날전위 (edge dislocation): 과잉반쪽원자면이전단응력에의해슬립면을따라미끄러지며같은쪽의면을순차적으로밀게된다. 전위가움직이지못하면, 소성변형이일어나지않는다. Fig. 9.1, Callister & Rethwisch 9e. (Adapted from A. G. Guy, Essentials of Materials Science, McGraw-Hill Book Company, New York, 1976, p. 153.) Chapter 9-3

4 칼날전위의운동 Motion of Edge Dislocation 전위운동은과잉반쪽원자면의연속적인범핑 (successive bumping) 이필요하다. 슬립면을가로지르는원자결합은끊어짐과연결됨을연속적으로반복한다. Chapter 9-4

전위운동 (Dislocation Motion) 전위는전위선에수직한미끄러짐방향 (slip direction) 의슬립면 ( slip plane) 을따라움직인다. 미끄러짐방향 (slip direction) 은버거스벡터방향 (Burgers vector direction) 과동일하다. Edge dislocation Fig. 9.

5 전위운동 (Dislocation Motion) 전위는전위선에수직한미끄러짐방향 (slip direction) 의슬립면 ( slip plane) 을따라움직인다. 미끄러짐방향 (slip direction) 은버거스벡터방향 (Burgers vector direction) 과동일하다. Edge dislocation Fig. 9.2, Callister & Rethwisch 9e. (Adapted from H. W. Hayden, W. G. Moffatt, and J. Wulff, The Structure and Properties of Materials, Vol. III, Mechanical Behavior, p. 70. Copyright 1965 by John Wiley & Sons, New York. Reprinted by permission of John Wiley & Sons, Inc.) Screw dislocation Chapter 9-5

변형기구 (Deformation Mechanisms) 슬립계 (Slip System) 슬립면 (Slip plane) 미끄러짐이일어나기쉬운면 가장조밀한원자충진밀도 ( 면간간격이크다 ) 슬립방향 (Slip directions) 미끄러짐이잘일어나는방향 최소선형원자밀도 Fig.

6 변형기구 (Deformation Mechanisms) 슬립계 (Slip System) 슬립면 (Slip plane) 미끄러짐이일어나기쉬운면 가장조밀한원자충진밀도 ( 면간간격이크다 ) 슬립방향 (Slip directions) 미끄러짐이잘일어나는방향 최소선형원자밀도 Fig. 9.6, Callister & Rethwisch 9e. FCC 의슬립은 {111} 면에서일어나고방향은 <110> 방향이다. (close-packed) => FCC 의슬립계는총 12 개이다. BCC & HCP 는다른슬립시스템이있다. ( 표 9.1) Chapter 9-6

7 단결정의슬립 - 응력과전위운동 분해전단응력 (Resolved shear stress, τ R ) 작용된인장응력 (tensile stress) 으로부터생긴다. Applied tensile stress: σ = F/A A F F Resolved shear stress: τ R = F s /A s slip plane normal, n s τ R F S τ R A S Relation between σ and τ R τ R = F S /A S F cos λ F λ F S n S A / cos ϕ ϕ A S A Chapter 9-7

8 임계전단응력 Critical Resolved Shear Stress 소성변형 ( 전위운동 ) 이시작조건 : 전위운동의용이성은결정방향에따라달라진다. 일반적으로 10-4 GPa to 10-2 GPa σ σ σ τ R = 0 λ = 90 τ R = σ /2 λ = 45 ϕ = 45 τ R = 0 ϕ = 90 τ maximum at λ = φ = 45º Chapter 9-8

9 Single Crystal Slip Fig. 9.9, Callister & Rethwisch 9e. (From C. F. Elam, The Distortion of Metal Crystals, Oxford University Press, London, 1935.) Fig. 9.8, Callister & Rethwisch 9e. Chapter 9-9

10 Ex: Deformation of single crystal φ = 60 a) 단결정을변형될까? b) 소성변형에필요한응력은? λ = 30 τ crss = 20.7 MPa Adapted from Fig. 9.7, Callister & Rethwisch 9e. σ = 42 MPa τ = (42 MPa) (cos 30 = (42 MPa) (0.433) τ = 18.2 MPa < τ crss = )(cos60 ) 20.7 MPa 42 MPa 의작용응력은이단결정을변형시킬수없다. Chapter 9-10

11 Ex: Deformation of single crystal 소성변형에필요한응력은얼마인가? ( 또는, 항복응력 (σ y ) 이얼마인가?) τ = 20.7 MPa = σ cosλ cosϕ = σ crss y y (0.433) σ y = τ = cosλ cosϕ 20.7 MPa crss = 47.8 MPa 따라서작용응력이항복강도이상일때변형이일어난다. σ σ y = 47.8 MPa Chapter 9-11

다결정에슬립운동 Slip Motion in Polycrystals σ 다결정은단결정보다단단하다. - 결정립계는전위운동의방해물 결정립들사이에슬립면 & 방향 (λ, ϕ) 이변한다. τ R 는결정립들사이에달라진다. τ R 이가장큰결정립에서항복이일어난다. Adapted from Fig. 9.10, Callister & Rethwisch 9e.

12 다결정에슬립운동 Slip Motion in Polycrystals σ 다결정은단결정보다단단하다. - 결정립계는전위운동의방해물 결정립들사이에슬립면 & 방향 (λ, ϕ) 이변한다. τ R 는결정립들사이에달라진다. τ R 이가장큰결정립에서항복이일어난다. Adapted from Fig. 9.10, Callister & Rethwisch 9e. (Photomicrograph courtesy of C. Brady, National Bureau of Standards [now the National Institute of Standards and Technology, Gaithersburg, MD].) 결정방향이불리한결정립은항복이나중에일어난다. 300 μm Chapter 9-12

13 강화기구 (Strengthening mechanism): 1: 결정립미세화 결정립계는슬립의방해물 작은결정립 : 입계의수의증가 결정립간결정배열의각도가증가하면방해물의 강도 증가한다. Fig. 9.14, Callister & Rethwisch 9e. (From L. H. Van Vlack, A Textbook of Materials Technology, Addison-Wesley Publishing Co., Reproduced with the permission of the Estate of Lawrence H. Van Vlack.) Hall-Petch Equation: Chapter 9-13

14 강화기구 (Strengthening mechanism): 2: 고용체 (Solid Solutions) 강화 불순물은격자를뒤틀고격자변형을일으킨다. 이런변형은전위운동의방해물로작용한다. Smaller substitutional impurity Larger substitutional impurity A C B D Impurity generates local stress at A and B that opposes dislocation motion to the right. Impurity generates local stress at C and D that opposes dislocation motion to the right. Chapter 9-14

15 Lattice Strains Around Dislocations Fig. 9.4, Callister & Rethwisch 9e. (Adapted from W.G. Moffatt, G.W. Pearsall, and J. Wulff, The Structure and Properties of Materials, Vol. I, Structure, p. 140, John Wiley and Sons, New York, 1964.) Chapter 9-15

16 고용체강화 (Strengthening by Solid Solutions) 작은불순물은전위의압축영역에집중하는경향이있다. 전위의압축변형과불순물의인장변형의감쇄된다. 전위의이동성을감소시키고강도를증가시킨다. Fig. 9.17, Callister & Rethwisch 9e. Chapter 9-16

17 Strengthening by Solid Solution Alloying 불순물이클경우전위의인장변형에집중하는경향이있다 Fig. 9.18, Callister & Rethwisch 9e. Chapter 9-17

18 Ex: Cu 의고용체강화 Ni 함유량과함께인장강도 & 항복강도가증가한다. Tensile strength (MPa) wt.% Ni, (Concentration C) Yield strength (MPa) wt.%ni, (Concentration C) Adapted from Fig (a) and (b), Callister & Rethwisch 9e. 합금의이종원자는 σ y 와 TS 를증가시킴. Chapter 9-18

19 강화기구 (Strengthening mechanism): 3: 냉간가공 ( 변형경화 ) 일반적으로실온에서의변형. 일반적인성형작업은단면적을감소시킨다. : - 단조 (Forging) A o die blank - 인발 (Drawing) A o die die force force A d A d tensile force Adapted from Fig. 17.2, Callister & Rethwisch 9e. - 롤링 (Rolling) - 압출 (Extrusion) A o force A o ram container billet container roll roll A d die holder extrusion die A d Chapter 9-19

20 Impact of Cold Work 냉간가공 (cold work) 이증가할수록 항복강도 (σ y ) 증가. 인장강도 (TS) 증가. 연성 (%EL or %AR) 감소. Adapted from Fig. 9.20, Callister & Rethwisch 9e. low carbon steel Chapter 9-20

21 냉간가공으로인한기계적성질의개선 - 냉간가공률 냉간가공후 Cu 의항복강도, 인장강도및연성의값은얼마? Copper Cold Work D o = 15.2 mm D d = 12.2 mm Chapter 9-21

22 냉간가공으로인한기계적성질의개선 What are the values of yield strength, tensile strength & ductility for Cu for %CW = 35.6%? yield strength (MPa) MPa % Cold Work Cu tensile strength (MPa) MPa Cu % Cold Work ductility (%EL) % 0 0 Cu % Cold Work σ y = 300 MPa TS = 340 MPa %EL = 7% Fig. 9.19, Callister & Rethwisch 9e. [Adapted from Metals Handbook: Properties and Selection: Irons and Steels, Vol. 1, 9th edition, B. Bardes (Editor), 1978; and Metals Handbook: Properties and Selection: Nonferrous Alloys and Pure Metals, Vol. 2, 9th edition, H. Baker (Managing Editor), Reproduced by permission of ASM International, Materials Park, OH.] Chapter 9-22

23 냉간가공후열처리의효과 어느온도에서열처리를하면인장강도 (TS) 는감소연성 (%EL) 은증가. 냉간가공의효과는무효화된다! tensile strength (MPa) annealing temperature ( C) Three Annealing stages: tensile strength ductility ductility (%EL) 1. Recovery 2. Recrystallization 3. Grain Growth Fig. 9.22, Callister & Rethwisch 9e. (Adapted from G. Sachs and K. R. Van Horn, Practical Metallurgy, Applied Metallurgy and the Industrial Processing of Ferrous and Nonferrous Metals and Alloys, Reproduced by permission of ASM International, Materials Park, OH.) Chapter 9-23

24 Three Stages During Heat Treatment: 1. 회복 (Recovery) 전위가소멸하여밀도가감소. Scenario 1 원자확산에의해서 extra half-plane of atoms 원자가인장영역에확산 전위가소멸하고완벽한원자면이생성 extra half-plane of atoms Chapter 9-24

6 mm 0.6 mm Adapted from Fig. 9.21 (a),(b), Callister & Rethwisch 9e.

25 Three Stages During Heat Treatment: 2. 재결정 (Recrystallization) 새결정의생성으로 : -- 전위밀도가감소 -- 결정립의크기가감소 -- 냉간가공된결정립의소멸과대체된다. 0.6 mm 0.6 mm Adapted from Fig (a),(b), Callister & Rethwisch 9e. (Photomicrographs courtesy of J.E. Burke, General Electric Company.) 33% cold worked brass New crystals nucleate after 3 sec. at 580 C. Chapter 9-25

As Recrystallization Continues All cold-worked grains are eventually consumed/replaced. 0.6 mm 0.6 mm Adapted from Fig. 9.

26 As Recrystallization Continues All cold-worked grains are eventually consumed/replaced. 0.6 mm 0.6 mm Adapted from Fig (c),(d), Callister & Rethwisch 9e. (Photomicrographs courtesy of J.E. Burke, General Electric Company.) After 4 seconds After 8 seconds Chapter 9-26

(Photomicrographs courtesy of J.E. Burke, General Electric Company.

27 Three Stages During Heat Treatment: 3. 결정립성장 (Grain Growth) 열처리시간이길어지며평균결정립의크기가증가. -- 작은결정립은축소 ( 궁극적으로사라짐 ). -- 큰결정립은계속성장. 0.6 mm 0.6 mm Adapted from Fig (d),(e), Callister & Rethwisch 9e. (Photomicrographs courtesy of J.E. Burke, General Electric Company.) After 8 s, 580 C Empirical Relation: exponent typ. ~ 2 grain diam. at time t. After 15 min, 580 C coefficient dependent on material and T. elapsed time Chapter 9-27

28 T R = recrystallization temperature 재결정온도 T R Fig. 9.22, Callister & Rethwisch 9e. (Adapted from G. Sachs and K. R. Van Horn, Practical Metallurgy, Applied Metallurgy and the Industrial Processing of Ferrous and Nonferrous Metals and Alloys, Reproduced by permission of ASM International, Materials Park, OH.) º Chapter 9-28

29 재결정온도 Recrystallization Temperature T R = recrystallization temperature = 1 시간내에재결정화가끝나는온도 0.3T m < T R < 0.6T m 특정금속 / 함급에대해 T R 의의존성 : %CW -- %CW의증가와함께 T R 감소 금속의순도 (Purity) 순도의증가와함께 T R 감소 Chapter 9-29

30 Diameter Reduction Procedure - Solution 인발 (drawing) 을이용한생산품의직경은? TS = 380 Mpa %EL = 15 Brass Cold Work D o = 10 mm D f = 7.5 mm Chapter 9-30

31 Diameter Reduction Procedure Solution (Cont.) For %CW = 43.8% σ y = 420 MPa TS = 540 MPa > 380 MPa %EL = 6 < 15 Fig. 9.19, Callister & Rethwisch 9e. [Adapted from Metals Handbook: Properties and Selection: Irons and Steels, Vol. 1, 9th edition, B. Bardes (Editor), 1978; and Metals Handbook: Properties and Selection: Nonferrous Alloys and Pure Metals, Vol. 2, 9th edition, H. Baker (Managing Editor), Reproduced by permission of ASM International, Materials Park, OH.] 이기준을만족하지않는다. 어떻게하면될까? Chapter 9-31

32 Diameter Reduction Procedure Solution (cont.) For TS > 380 MPa For %EL > 15 > 12 %CW < 27 %CW Fig. 9.19, Callister & Rethwisch 9e. [Adapted from Metals Handbook: Properties and Selection: Irons and Steels, Vol. 1, 9th edition, B. Bardes (Editor), 1978; and Metals Handbook: Properties and Selection: Nonferrous Alloys and Pure Metals, Vol. 2, 9th edition, H. Baker (Managing Editor), Reproduced by permission of ASM International, Materials Park, OH.] our working range is limited to 12 < %CW < 27 Chapter 9-32

33 Diameter Reduction Procedure Solution (cont.) 냉간가공후, 어닐링후냉간가공다시 12 < %CW < 27 범위내로냉간가공률을설정 - 20 %CW 로설정 다음과같이냉간가공후의직경 ( 두번째냉간가공전 ) 은계산된다 : Intermediate diameter = Chapter 9-33

34 Diameter Reduction Procedure Summary Stage 1: 냉간가공 - 10 mm 에서 8.39 mm 로직경을감소 Stage 2: 열처리 ( 재결정화 ) Stage 3: 냉간가공 8.39 mm에서 7.5 mm로직경을감소 %CW Fig 9.19 = = 모든조건은만족한다. Chapter 9-34

35 Cold Working vs. Hot Working 열간가공 (Hot working) T R 보다높은온도에서변형 냉간가공 (Cold working) T R 보다낮은온도에서변형 Chapter 9-35

36 Summary 전위는주로금속및합금에서발견된다. 전위운동을어렵게만드는것이강도를증가시킨다. 금속의강도증가방법 : -- 결정립크기를줄임 -- 고용체강화 (solid solution strengthening) -- 냉간가공 (cold working) 냉간가공된금속은열처리를통해회복, 재결정및결정립성장을거치고기계적성질이변한다. Chapter 9-36

Chapter 7: Dislocations & Strengthening Mech

Chapter 7: Dislocations & Strengthening Mech Chapter 7: 전위와강화기구 ISSUES TO ADDRESS... Why are the number of dislocations present greatest in metals? How are strength and dislocation motion related? Why does heating alter strength and other properties?