Chapter 6: Mechanical Properties 6.1. 서론 많은 재료들은 사용 중에 힘을 받게 된다. 재료의 특성을 이해하여 과도한 변형이나 파괴가 일어나지 않도록 설계 재료의 기계적 거동을 이해 필요 기계적 거동 : 외부 작용에 대한 재료의 반응 정도, 즉 외부의 힘(하중)과 이에 따른 재료의 변형 사이의 관계 (ex : 강도, 경도, 연성, 강성도 등) 하중의 형태 : 인장, 압축, 전단 하중의 시간 및 온도를 고려

탄성 변형(Elastic deformation) : Elastic means reversible! 1. Initial 2. Small load 3. Unload F d bonds stretch return to initial F d Linear- elastic Non-Linear-

eplastic eelastic + plastic s e eplastic 소성 변형(Plastic deformation) : Plastic means permanent 1. Initial 2. Small load 3. Unload planes still sheared bonds stretch & planes shear eplastic eelastic + plastic s e linear elastic eplastic F

응력-변형률 시험은 인장(tension)하중하에서 행함 6.2. 응력 및 변형률의 개념 응력-변형률 시험은 인장(tension)하중하에서 행함 인장(압축)시험 공칭응력 공칭변형률 전단시험 전단응력 전단변형률 (g) : tanq

• Typical tensile specimen • Typical tensile test machine gauge length specimen extensometer

6.3. 응력-변형률 거동 s = Ee 변형률은 가해지는 응력에 따라 변함 작은 인장 응력인 경우 아래의 식을 만족 E : modulus of elasticity or Young’s modulus : GPa 응력과 변형률이 비례하는 변형을 탄성변형 탄성계수 大 : 변형 難 응력을 제거하면 원래의 모양으로 돌아감

회주철이나 콘크리트는 응력-변형률 관계가 비선형 탄젠트 계수나 시컨트 계수 전단이나 비틀림도 탄성거동 낮은 응력에서는 같은 응력-변형률 특성 같은 탄성계수 t = Gg (G : 전단 계수)

6.4. 의탄성 6.5. 재료의 탄성 성질 탄성은 시간에 의존하지 않는다고 가정 응력을 제거한 후 변형을 회복하는데 시간이 걸림 : 의탄성 금속의 경우 무시 가능 폴리머는 매우 큼 : 점탄성 거동 6.5. 재료의 탄성 성질 z 방향 인장 →인장방향으로 변형률ez →x, y방향으로 수축→ex, ey Dlz 2 sz 수축량으로부터 압축변형률을 계산 응력이 z 방향으로 작용 → ex = ey 푸아송비(n) : 축방향 변형률에 대한 횡방향 변형률의 비 l0x Dlx 2 l0z z ex, ez : 반대부호, n : (+) 이론적으로 등방성 재료 :1/4 최대값 : 0.4 대부분 금속과 합금 : 0.25, 035 y sz x

전단계수, 탄성계수 및 푸아송 비의 관계 E = 2G(1 + n) 대부분의 금속 : 0.4E 많은 재료들의 탄성 거동은 비등방성 탄성 거동(E값)이 재료의 결정 방향에 따라 상이 탄성 성질은 여러 개의 탄성 상수로 표시 탄성 상수의 수는 재료의 결정 구조의 특성에 따라 결정 대부분의 다결정 재료는 결정립 방향이 다양→등방성으로 간주 기계적 거동은 등방성과 다결정을 가정하여 기술 예제)지름이 10mm인 실린더형의 황동막대에 장축 방향으로 인장 응력을 작용시겨 지름을 2.5 X 10-3mm만큼 수축시키는 데 필요한 하중을 구하여라. 변형을 완전 탄성으로 가정한다.

s e 6.6. 소성변형 : 탄성 변형 이상의 변형 시 영구변형 즉 소성변형 ep Elastic+Plastic at larger stress s Elastic initially ep e permanent (plastic) after load is removed plastic strain 대부분의 금속에서 탄성에서 소성의 전이는 점차적

6.6. 인장성질 항복현상

Yield Strength, sy y = yield strength sy • Stress at which noticeable plastic deformation has occurred. when ep = 0.002 tensile stress, s engineering strain, e sy p = 0.002 y = yield strength Note: for 2 inch sample  = 0.002 = z/z  z = 0.004 in Adapted from Fig. 6.10 (a), Callister 7e.

Poisson's ratio, n eL e - n e n = - • Poisson's ratio, n: Units: metals: n ~ 0.33 ceramics: n ~ 0.25 polymers: n ~ 0.40 Units: E: [GPa] or [psi] n: dimensionless  > 0.50 density increases  < 0.50 density decreases (voids form)

Mechanical Properties Slope of stress strain plot (which is proportional to the elastic modulus) depends on bond strength of metal Adapted from Fig. 6.7, Callister 7e.

Other Elastic Properties simple torsion test M t G g • Elastic Shear modulus, G: t = G g • Elastic Bulk modulus, K: pressure test: Init. vol =Vo. Vol chg. = DV P P = - K D V o • Special relations for isotropic materials: 2(1 + n) E G = 3(1 - 2n) K

Young’s Moduli: Comparison Graphite Ceramics Semicond Metals Alloys Composites /fibers Polymers 0.2 8 0.6 1 Magnesium, Aluminum Platinum Silver, Gold Tantalum Zinc, Ti Steel, Ni Molybdenum G raphite Si crystal Glass - soda Concrete Si nitride Al oxide PC Wood( grain) AFRE( fibers) * CFRE GFRE* Glass fibers only Carbon fibers only A ramid fibers only Epoxy only 0.4 0.8 2 4 6 10 00 1200 Tin Cu alloys Tungsten <100> <111> Si carbide Diamond PTF E HDP LDPE PP Polyester PS PET C FRE( fibers) FRE( fibers)* FRE(|| fibers)* E(GPa) Based on data in Table B2, Callister 7e. Composite data based on reinforced epoxy with 60 vol% of aligned carbon (CFRE), aramid (AFRE), or glass (GFRE) fibers. 109 Pa

Useful Linear Elastic Relationships • Simple tension: • Simple torsion: a = 2 ML o p r 4 G M = moment = angle of twist 2ro Lo d = FL o E A d L = - n Fw o E A F A o d /2 L Lo w • Material, geometric, and loading parameters all contribute to deflection. • Larger elastic moduli minimize elastic deflection.

Yield Strength : Comparison Graphite/ Ceramics/ Semicond Metals/ Alloys Composites/ fibers Polymers Yield strength, s y (MPa) PVC Hard to measure , since in tension, fracture usually occurs before yield. Nylon 6,6 LDPE 70 20 40 60 50 100 10 30 2 00 3 4 5 6 7 Tin (pure) Al (6061) a ag Cu (71500) hr Ta (pure) Ti Steel (1020) cd (4140) qt (5Al-2.5Sn) W Mo (pure) cw Hard to measure, in ceramic matrix and epoxy matrix composites, since in tension, fracture usually occurs before yield. H DPE PP humid dry PC PET ¨ Room T values Based on data in Table B4, Callister 7e. a = annealed hr = hot rolled ag = aged cd = cold drawn cw = cold worked qt = quenched & tempered

Tensile Strength, TS TS engineering stress strain engineering strain • Maximum stress on engineering stress-strain curve. y strain Typical response of a metal F = fracture or ultimate strength Neck – acts as stress concentrator engineering TS stress engineering strain Adapted from Fig. 6.11, Callister 7e. • Metals: occurs when noticeable necking starts. • Polymers: occurs when polymer backbone chains are aligned and about to break.

Tensile Strength : Comparison Si crystal <100> Graphite/ Ceramics/ Semicond Metals/ Alloys Composites/ fibers Polymers Tensile strength, TS (MPa) PVC Nylon 6,6 10 100 200 300 1000 Al (6061) a ag Cu (71500) hr Ta (pure) Ti Steel (1020) (4140) qt (5Al-2.5Sn) W cw L DPE PP PC PET 20 30 40 2000 3000 5000 Graphite Al oxide Concrete Diamond Glass-soda Si nitride H wood ( fiber) wood(|| fiber) 1 GFRE (|| fiber) ( fiber) C FRE A FRE( fiber) E-glass fib Aramid fib Room Temp. values Based on data in Table B4, Callister 7e. a = annealed hr = hot rolled ag = aged cd = cold drawn cw = cold worked qt = quenched & tempered AFRE, GFRE, & CFRE = aramid, glass, & carbon fiber-reinforced epoxy composites, with 60 vol% fibers.

Ductility x 100 L EL % - = • Plastic tensile strain at failure: e s Lf o f - = • Plastic tensile strain at failure: Engineering tensile strain, e E ngineering tensile stress, s smaller %EL larger %EL Lf Ao Af Lo Adapted from Fig. 6.13, Callister 7e. • Another ductility measure: 100 x A RA % o f - =

Toughness • Energy to break a unit volume of material • Approximate by the area under the stress-strain curve. very small toughness (unreinforced polymers) Engineering tensile strain, e E ngineering tensile stress, s small toughness (ceramics) large toughness (metals) Adapted from Fig. 6.13, Callister 7e. Brittle fracture: elastic energy Ductile fracture: elastic + plastic energy

Resilience, Ur 2 1 U e s @ Ability of a material to store energy Energy stored best in elastic region If we assume a linear stress-strain curve this simplifies to y r 2 1 U e s @ Adapted from Fig. 6.15, Callister 7e.

Elastic Strain Recovery Adapted from Fig. 6.17, Callister 7e.

Hardness • Resistance to permanently indenting the surface. • Large hardness means: --resistance to plastic deformation or cracking in compression. --better wear properties. e.g., 10 mm sphere apply known force measure size of indent after removing load d D Smaller indents mean larger hardness. increasing hardness most plastics brasses Al alloys easy to machine steels file hard cutting tools nitrided diamond

Hardness: Measurement Rockwell No major sample damage Each scale runs to 130 but only useful in range 20-100. Minor load 10 kg Major load 60 (A), 100 (B) & 150 (C) kg A = diamond, B = 1/16 in. ball, C = diamond HB = Brinell Hardness TS (psia) = 500 x HB TS (MPa) = 3.45 x HB

Hardness: Measurement Table 6.5

True Stress & Strain Note: S.A. changes when sample stretched True Strain Adapted from Fig. 6.16, Callister 7e.

Hardening ( ) s e • An increase in sy due to plastic deformation. large hardening small hardening y 1 • Curve fit to the stress-strain response: s T = K e ( ) n “true” stress (F/A) “true” strain: ln(L/Lo) hardening exponent: n = 0.15 (some steels) to n = 0.5 (some coppers)

Variability in Material Properties Elastic modulus is material property Critical properties depend largely on sample flaws (defects, etc.). Large sample to sample variability. Statistics Mean Standard Deviation All samples have same value Because of large variability must have safety margin in engineering specifications where n is the number of data points

Design or Safety Factors • Design uncertainties mean we do not push the limit. • Factor of safety, N Often N is between 1.2 and 4 • Example: Calculate a diameter, d, to ensure that yield does not occur in the 1045 carbon steel rod below. Use a factor of safety of 5. 1045 plain carbon steel: s y = 310 MPa TS = 565 MPa F = 220,000N d L o 5 d = 0.067 m = 6.7 cm

Summary • Stress and strain: These are size-independent measures of load and displacement, respectively. • Elastic behavior: This reversible behavior often shows a linear relation between stress and strain. To minimize deformation, select a material with a large elastic modulus (E or G). • Plastic behavior: This permanent deformation behavior occurs when the tensile (or compressive) uniaxial stress reaches sy. • Toughness: The energy needed to break a unit volume of material. • Ductility: The plastic strain at failure.