Chapter 7: Dislocations & Strengthening Mech

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1 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? Chapter 7-1

2 전위와재료의종류 금속 (Cu, Al): 전위의이동이쉬움 - 방향성이없는결합 - 슬립을위한조밀충진방향 electron cloud ion cores 공유결합세라믹 (Si, diamond): 전위이동이어려움 - 방향성 (angular) 결합 이온결합세라믹 (NaCl): 이동이어려움 - 같은싸인 (- & +) 의이웃하는이온을회피 Chapter 7-2

3 전위의이동 & 소성변형 전위의이동 금속 슬립에의한소성변형 칼날전위 (extra halfplane of atoms) 는이웃하는반쪽원자면을따라이동 ( 슬립 ) 만약전위의이동이없다면소성변형도일어나지않는다! Adapted from Fig. 7.1, Callister & Rethwisch 8e. Chapter 7-3

4 전위의이동 전위는전위선에수직한슬립면상의슬립방향을따라움직인다. 슬립방향은버거스벡터의방향과일치한다. Edge dislocation 칼날전위의이동방향 - 전단응력에평행 Adapted from Fig. 7.2, Callister & Rethwisch 8e. Screw dislocation 나사전위의이동방향 - 전단응력에수직 Chapter 7-4

5 슬립계 (Slip System) 슬립면 (Slip plane) 전위가쉽게움직이는면 높은원자충진밀도를갖는면 ( 큰면간거리 ) 슬립방향 (Slip directions) 전위이동의방향 높은선밀도 변형기구 Adapted from Fig. 7.6, Callister & Rethwisch 8e. FCC 슬립은 {111} 면 (close-packed) 에서 <110> 방향 (close-packed) 으로일어남 => 총 12 개의슬립계가존재 BCC & HCP : 다른슬립계가존재 Chapter 7-5

6 응력과전위의이동 분해전단응력 (resolved shear stress, t R ) 작용인장응력의결과 Applied tensile stress: s = F/A A F F Resolved shear stress: t R = F s /A s slip plane normal, n s t R F S t R A S 상관관계 s and t R t R = F S /A S F cos l F l F S n S A / cos f f A S A f l t scoslcosf R 작용응력방향과슬립면의수직방향과의사이각 작용응력과슬립방향과의각도 Chapter 7-6

7 임계분해전단응력 (Critical Resolved Shear Stress) 전위이동조건 : 전위의움직임은결정의방향성에의존한다. t R s cos l cos f s s t R tcrss typically 10-4 GPa to 10-2 GPa s t R = 0 l = 90 t R = s /2 l = 45 f = 45 t R = 0 f = 90 l = f = 45º 일때 t 는최대 Chapter 7-7

8 Single Crystal Slip Adapted from Fig. 7.9, Callister & Rethwisch 8e. Adapted from Fig. 7.8, Callister & Rethwisch 8e. Chapter 7-8

9 f = 60 Ex: 단결정의소성변형 a) 단결정은항복이일어날까? b) 아니라면, 얼마의응력이필요할까? l = 35 t crss = 20.7 MPa t s cosl cosf s 45 MPa Adapted from Fig. 7.7, Callister & Rethwisch 8e. s = 45 MPa t (45MPa) (cos35 (45MPa) (0.41) t 18.4 MPa t crss 결과적으로, 45 Mpa의작용인장응력은단결정의항복을일으키지못함 )(cos MPa Chapter 7-9 )

10 Ex: 단결정의소성변형 얼마의작용인장하중이필요한가 (i.e., what is the yield stress, s y )? t crss 20.7 MPa sy cosl cosf sy(0.41) s y t crss coslcosf 20.7 MPa MPa 소성변형을일으키기위해서는작용인장하중이항복응력과같거나커야만한다. s s y 50.5 MPa Chapter 7-10

다결정재료의소성변형 다결정은단결정보다강하다. 결정입계는전위의이동에대한장벽으로작용 s 각각의결정립에서슬립면과방향 (l, f) 은다르다. t R 은각각의결정립에따라다르다. 가장큰 t R 이가장먼저항복 다른 ( 적절한방향에위치하지못한 ) 결정은늦게항복 Adapted from Fig. 7.

11 다결정재료의소성변형 다결정은단결정보다강하다. 결정입계는전위의이동에대한장벽으로작용 s 각각의결정립에서슬립면과방향 (l, f) 은다르다. t R 은각각의결정립에따라다르다. 가장큰 t R 이가장먼저항복 다른 ( 적절한방향에위치하지못한 ) 결정은늦게항복 Adapted from Fig. 7.10, Callister & Rethwisch 8e. (Fig is courtesy of C. Brady, National Bureau of Standards [now the National Institute of Standards and Technology, Gaithersburg, MD].) 300 mm Chapter 7-11

Wulff, The Structure and Properties of Materials, Vol. I, Structure, p.

12 항복점비등방성 (anisotropic) 다결정금속의압연에의한항복점비등방성야기 - before rolling - after rolling rolling direction Adapted from Fig. 7.11, Callister & Rethwisch 8e. (Fig is 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.) 235 mm - 등방성 (isotropic) 방향성이없는등축결정 (equiaxed & randomly oriented) - 비등방성 (anisotropic) 압연으로인한결정의방향과형태에변형 Chapter 7-12

13 rolling direction 1. 탄탈륨 (tantalum) 압연판재로부터가공된봉시편 : 비등방성소성변형 2. 봉시편을목표물에수직으로타격 3. 봉시편의변형 side view Photos courtesy of G.T. Gray III, Los Alamos National Labs. Used with permission. 변형된끝단의타원형은압연재의비등방성변형의예를보여줌 end view plate thickness direction Chapter 7-13

14 강화를위한 4 가지전략 : 1: 결정립미세화 (Reduce Grain Size) 결정립계는슬립에대한장벽 ( 전위의이동을방해 ) 장벽 ( 강화 ) 의효과는결정입계의불일치각도의증가와더불어증가 작은결정 : 슬립에대한많은장벽 Adapted from Fig. 7.14, Callister & Rethwisch 8e. (Fig is from A Textbook of Materials Technology, by Van Vlack, Pearson Education, Inc., Upper Saddle River, NJ.) Hall-Petch 관계식 : s yield s o k y d 1/ 2 d: 평균결정립지름 s 0 와 K y 는재료상수 Chapter 7-14

15 강화를위한 4 가지전략 : 2: 고용체강화 (solid solution strengthening) 이종원자는결정격자의변형을야기, 격자변형률부과 이종원자의격자변형장과전위의격자변형장의상호작용은결과적으로전위의움직임을제한 작은치환형이종원자 큰치환형이종원자 A C B D 이종원자는 A 와 B 에국부적인응력을야기하여전위의움직임을방해 이종원자는 C 와 D 에국부적인응력을야기하여전위의움직임을방해 Chapter 7-15

16 전위주위의격자변형 Adapted from Fig. 7.4, Callister & Rethwisch 8e. Chapter 7-16

17 합금에의한고용체강화 작은이종원자는압축응력이작용하는전위주위 (regions of compressive strains) 에집중 전위압축응력과이종원자의인장응력을부분적으로상쇄 전위의이동성을줄임으로써강도를증가 Adapted from Fig. 7.17, Callister & Rethwisch 8e. Chapter 7-17

18 합금에의한고용체강화 큰이종원자는인장응력이작용하는전위주위에집중 (regions of tensile strains) Adapted from Fig. 7.18, Callister & Rethwisch 8e. Chapter 7-18

19 VMSE Solid-Solution Strengthening Tutorial Chapter 7-19

20 Tensile strength (MPa) Yield strength (MPa) Ex: 동 (copper) 의고용체강화 Ni 의 wt% 에따른인장강도와항복강도의증가 Adapted from Fig. 7.16(a) and (b), Callister & Rethwisch 8e wt.% Ni, (Concentration C) wt.%ni, (Concentration C) 경험관계식 : 1/ s y ~ C 2 합금화는 s y 와 TS 를증가시킴 Chapter 7-20

21 강화를위한 4 가지전략 : 3: 석출강화 (Precipitation Strengthening) 단단한석출물은전단이어려움 Ex: Ceramics in metals (SiC in Iron or Aluminum). Side View precipitate Large shear stress needed to move dislocation toward precipitate and shear it. Top View Unslipped part of slip plane S Slipped part of slip plane Dislocation advances but precipitates act as pinning sites with spacing S. 결과 : s y ~ 1 S Chapter 7-21

) 알루미늄은합금화원소에따른석출상에의해강화됨 Adapted from Fig. 11.26, Callister & Rethwisch 8e. (Fig. 11.26 is courtesy of G.

22 Application: Precipitation Strengthening 내부날개구조 (Boeing 767) Adapted from chapteropening photograph, Chapter 11, Callister & Rethwisch 3e. (courtesy of G.H. Narayanan and A.G. Miller, Boeing Commercial Airplane Company.) 알루미늄은합금화원소에따른석출상에의해강화됨 Adapted from Fig , Callister & Rethwisch 8e. (Fig is courtesy of G.H. Narayanan and A.G. Miller, Boeing Commercial Airplane Company.) 1.5mm Chapter 7-22

23 강화를위한 4 가지전략 : 4: 냉간가공 [Cold Work ( 변형경화 Strain Hardening)] 대부분의금속은상온에서변형 일반적인성형공정에의한단면적의감소 : - 단조 (Forging) A o die blank force force - 인발 (Drawing) A o die die A d 냉간가공률 A d tensile force % CW Adapted from Fig. 11.8, Callister & Rethwisch 8e. A o force A o A A o d - 압연 (Rolling) A o - 압출 (Extrusion) ram x 100 container billet container roll roll A d die holder extrusion die Chapter 7-23 A d

24 냉간가공중전위의구조변화 Ti 의냉간가공후의전위의구조 냉간가공중전위는서로얽힌다. 결과적으로, 전위의이동은더욱어려워짐 Fig. 4.6, Callister & Rethwisch 8e. (Fig. 4.6 is courtesy of M.R. Plichta, Michigan Technological University.) Chapter 7-24

25 냉간가공중전위밀도증가 전위밀도 = 총전위길이단위체적 [mm/mm 3 (mm -2 )] 주위를기울여만든금속단결정의전위밀도 ca mm -2 소성변형은전위밀도증가 mm -2 열처리는전위밀도를감소 mm -2 전위밀도 (r d ) 의증가 - 항복응력증가 Chapter 7-25

26 전위사이의격자변형률상호작용 Adapted from Fig. 7.5, Callister & Rethwisch 8e. Chapter 7-26

27 냉간가공의영향 냉간가공 (cold work) 의증가 항복강도 [Yield strength (s y )] 증가 인장강도 [Tensile strength (TS)] 증가 연성 [Ductility (%EL or %AR)] 감소 Adapted from Fig. 7.20, Callister & Rethwisch 8e. low carbon steel Chapter 7-27

28 냉간가공에의한기계적특성의변화 실린더형 Cu 봉에대한냉간가공후항복강도, 인장강도및연성의변화는? D o = 15.2 mm Copper Cold Work D d = 12.2 mm %CW D 4 2 o 2 o D 4 D D D 2 o D 4 2 o 2 d 2 d x 100 x 100 %CW (15.2 mm) 2 (12.2 mm) (15.2 mm) 2 2 x % Chapter 7-28

29 yield strength (MPa) tensile strength (MPa) ductility (%EL) 냉간가공에의한기계적특성의변화 Cu 에대한 %CW = 35.6% 후항복강도, 인장강도및연성은? ( 그림 7.19 의 (a), (b), (c) 를참조 ) MPa % Cold Work Cu MPa Cu % Cold Work % 0 0 Cu % Cold Work s y = 300 MPa TS = 340 MPa %EL = 7% Adapted from Fig. 7.19, Callister & Rethwisch 8e. (Fig is adapted from Metals Handbook: Properties and Selection: Iron and Steels, Vol. 1, 9th ed., B. Bardes (Ed.), American Society for Metals, 1978, p. 226; and Metals Handbook: Properties and Selection: Nonferrous Alloys and Pure Metals, Vol. 2, 9th ed., H. Baker (Managing Ed.), American Society for Metals, 1979, p. 276 and 327.) Chapter 7-29

30 tensile strength (MPa) ductility (%EL) 냉간가공후열처리의영향 T anneal 에서 1 hour 열처리 TS 는감소하고, %EL 은증가 냉간가공의효과가감쇄! 500 annealing temperature (ºC) 세가지열처리단계 : tensile strength 회복 (Recovery) 2. 재결정 (Recrystallization) 3. 결정립성장 (Grain Growth) ductility 20 Adapted from Fig. 7.22, Callister & Rethwisch 8e. (Fig is adapted from G. Sachs and K.R. van Horn, Practical Metallurgy, Applied Metallurgy, and the Industrial Processing of Ferrous and Nonferrous Metals and Alloys, American Society for Metals, 1940, p. 139.) Chapter 7-30

31 Scenario 1 확산의결과 Scenario 2 열처리중 3단계 : 1. 회복 (Recovery) 전위의소멸에의한전위밀도의감소 extra half-plane of atoms atoms diffuse to regions of tension extra half-plane of atoms 3. 상승한 ( Climbed ) 전위는새로운슬립면으로이동 2. 공공의확산에의한회색원자의이동은전위의상승 ( climb ) 1. 고정전위 ; 오른쪽으로이동불가 4. 상반된전위들이서로만나서소멸 Dislocations annihilate and form a perfect atomic plane. Obstacle dislocation t R Chapter 7-31

32 열처리중 3 단계 : 2. 재결정 (Recrystallization) 새로운결정의생성 : -- 재결정의구동력은냉간가공에의해축적된내부에너지 -- 낮은전위밀도 -- 작은결정크기 -- 모상의냉간가공된결정립의소멸과대체 0.6 mm 0.6 mm Adapted from Fig. 7.21(a),(b), Callister & Rethwisch 8e. (Fig. 7.21(a),(b) are courtesy of J.E. Burke, General Electric Company.) 33% cold worked brass New crystals nucleate after 3 sec. at 580C. Chapter 7-32

33 모든냉간가공된결정립들은열처리에의하여소멸 / 대체된다. 0.6 mm 재결정의연속 0.6 mm Adapted from Fig. 7.21(c),(d), Callister & Rethwisch 8e. (Fig. 7.21(c),(d) are courtesy of J.E. Burke, General Electric Company.) After 4 seconds After 8 seconds Chapter 7-33

34 열처리중 3 단계 : 3. 결정립성장 (Grain Growth) 보다긴열처리시간에따라, 평균결정립의크기증가 -- 작은결정립은축소 ( 최종적으로소멸 ) -- 큰결정립은계속성장 -- 결정립성장의구동력 : 입계의면적감소 총에너지감소 After 8 s, 580ºC 0.6 mm 0.6 mm After 15 min, 580ºC 시간에따른결정립크기 ( 경험식 ): exponent typ. ~ 2 grain diam. at time t. d n d n o Kt Adapted from Fig. 7.21(d),(e), Callister & Rethwisch 8e. (Fig. 7.21(d),(e) are courtesy of J.E. Burke, General Electric Company.) coefficient dependent on material and T. elapsed time Chapter 7-34

35 T R T R = recrystallization temperature :1 시간안에재결정이완결된온도 Adapted from Fig. 7.22, Callister & Rethwisch 8e. º Chapter 7-35

36 재결정온도 (Recrystallization Temperature) T R = recrystallization temperature = 1 시간안에재결정이완결된온도 0.3T m < T R < 0.6T m 특정금속 / 합금에서, T R 은 : %CW -- %CW 의증가는 T R 감소 금속의순도 순도의증가는 T R 감소 Chapter 7-36

37 지름감소절차 - 문제 초기지름이 10 mm 인실린더형황동을냉간인발가공하여단면적을감소시켰다. 가공동안실린더형의단면은유지된다. 냉간가공후의인장강도는 380 Mpa 이상, 연성은최소한 15%EL 이요구된다. 최종지름은 7.5 mm 이다. 이에대한인발가공절차를설명하라. Chapter 7-37

38 Chapter 7-38 지름감소절차 - 문제최종지름으로직접인발가공한결과는? 43.8% x x x 100 %CW o f o f o f o D D x A A A A A D o = 10 mm Brass Cold Work D f = 7.5 mm

39 지름감소절차 Solution ( 그림 7.19 참조 ) %CW = 43.8% s y = 420 MPa TS = 540 MPa > 380 MPa %EL = 6 < 15 조건에만족하지않음 다른가능한옵션은? Adapted from Fig. 7.19, Callister & Rethwisch 8e. Chapter 7-39

40 지름감소절차 Solution ( 그림 7.19 참조 ) TS > 380 MPa %EL > 15 > 12 %CW < 27 %CW Adapted from Fig. 7.19, Callister & Rethwisch 8e. 냉간가공의제한된범위는 12 < %CW < 27 Chapter 7-40

41 지름감소절차 Solution ( 그림 7.19 참조 ) 냉간가공, 열처리, 그리고다시냉간가공 목적달성을위하여 12 < %CW < 27의냉간가공 20 %CW 최초냉간가공후의지름 : %CW D 1 D f D x f D02 02 %CW 100 D 0.5 D f 2 %CW D f 0. D %CW 차인발후지름 = Df 1 D mm mm Chapter 7-41

42 지름감소절차 Summary Stage 1: 냉간가공 10 mm 에서 8.39 mm 로지름감소 mm %CW 1 1 x mm Stage 2: 열처리 ( 재결정 ) 29.6 Stage 3: 냉간가공 8.39 mm 에서 7.5 mm 로지름감소 %CW 결과적으로모든조건을만족 2 20 Fig 7.19 sy 340MPa TS 400MPa % EL 24 Chapter 7-42

43 냉간가공 vs. 열간가공 열간가공 (Hot working) T R 이상에서변형 - 변형경화무 - 재료는대체로무르고연하여, 많은양의변형이가능 냉간가공 (Cold working) T R 이하에서변형 Chapter 7-43

44 결정립의크기에따른특성의영향 작은결정립크기를갖는금속 낮은온도에서비교적강하고인성이있음 큰결정립크기를갖는금속 비교적높은온도에서크립 (creep) 저항성이우수 Chapter 7 -

45 Summary Dislocations are observed primarily in metals and alloys. Strength is increased by making dislocation motion difficult. Strength of metals may be increased by: -- decreasing grain size -- solid solution strengthening -- precipitate hardening -- cold working A cold-worked metal that is heat treated may experience recovery, recrystallization, and grain growth its properties will be altered. Chapter 7-45

46 ANNOUNCEMENTS Reading: Core Problems: Self-help Problems: Chapter 7-46

Chapter 9: Dislocations & Strengthening Mechanisms in Metals

Chapter 9: Dislocations & Strengthening Mechanisms in Metals 학습목표 Chapter 9: 전위와강화기구 (Dislocations & Strengthening Mechanisms) 왜금속에서전위의수가중요한가? 강도와전위운동은어떤관계를가지는것인가? 왜열처리는강도와다른기계적성질을변화시키는가? Chapter 9-1 전위와재료의종류 금속 ( 전자구름, Cu, Al): 전위운동이일어나기쉽다. - 방향성이없는 bonding + +