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Chapter 6 - 1 DEĞİNELECEK KONULAR... Gerilme ve Genleme: What are they and why are they used instead of load and deformation? Elastik davranış: When loads.

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... konulu sunumlar: "Chapter 6 - 1 DEĞİNELECEK KONULAR... Gerilme ve Genleme: What are they and why are they used instead of load and deformation? Elastik davranış: When loads."— Sunum transkripti:

1 Chapter DEĞİNELECEK KONULAR... Gerilme ve Genleme: What are they and why are they used instead of load and deformation? Elastik davranış: When loads are small, how much deformation occurs? What materials deform least? Plastik davranış: At what point does permanent deformation occur? What materials are most resistant to permanent deformation? Tokluk ve Süneklik: What are they and how do we measure them? Bölüm 6: Mekanik Özellikler

2 Chapter Elastik geri dönebilen! anlamına gelir Elastik Deformasyon 1. İlk durum2. Küçük yük 3. Yükün kaldırılması F  bağlar geriniyor İlk duruma dönüş F  Doğrusal- elastik Doğrusal-Olmayan elastik

3 Chapter Plastik kalıcı! Anlamına gelir Plastik Deformasyon (Metaller) F  doğrusal elastik doğrusal elastik  plastik 1. İlk durum2. Küçük Yük3. Unload Düzlemler hala Kaymış durumda F  elastik + plastik Bağlar geriniyor & düzlemler kayıyor  plastik

4 Chapter  Gerilme birimleri: N/m 2 ya da lb f /in 2 Mühendislik Gerilmesi Kayma gerilmesi,  : Alan, A F t F t F s F F F s  = F s A o Çekme gerilmesi,  : Yüklemeden önceki İlk alan Alan, A F t F t  = F t A o 2 f 2 m N or in lb =

5 Chapter Basit çekme: kablo Not:  = M/A c R. Genel Gerilme Durumları A o = kesit alanı (yük kaldırıldıktan sonra) FF o   F A o   F s A  M M A o 2R2R F s A c Burma (kaymanın bir şekli): Tahrik Mili Kayak Telesiyeji (photo courtesy P.M. Anderson)

6 Chapter (photo courtesy P.M. Anderson) Canyon Bridge, Los Alamos, NM o   F A Basit basma: Not: basma Yapı elemanı (  < 0 here). (photo courtesy P.M. Anderson) DİĞER GENEL GERİLME DURUMLARI(1) A o Balanced Rock, Arches National Park

7 Chapter İki-eksenli çekme: Hydrostatik basma: Basınçlı tank   < 0 h (photo courtesy P.M. Anderson) (photo courtesy P.M. Anderson) DİĞER GERİLME DURUMLARI (2) Suyun içinde balık  z > 0  

8 Chapter Çekme genlemesi: Yatay genleme: Kayma genlemesi: Genleme her zaman boyutsuzdur. Mühendislik Genlemesi (Birim Şekil Değiştirmesi)  90º 90º -  y xx   =  x/y = tan   L o   L  L w o Adapted from Fig. 6.1 (a) and (c), Callister 7e.  /2  L L o w o

9 Chapter Gerime-Genleme Deneyleri Tipik bir çekme makinası Adapted from Fig. 6.3, Callister 7e. (Fig. 6.3 is taken from H.W. Hayden, W.G. Moffatt, and J. Wulff, The Structure and Properties of Materials, Vol. III, Mechanical Behavior, p. 2, John Wiley and Sons, New York, 1965.) specimen extensometer Tipik bir çekme numunesi Adapted from Fig. 6.2, Callister 7e. ölçü boyu

10 Chapter Doğrusal Elastik Özellikler Elastiklik Modülü, E: (Young modülü olarak ta bilinir) Hooke Kanunu:  = E   Doğrusal- elastik E  F F basit çekme deneyi

11 Chapter Poisson oranı, Poisson oranı, : Birimler: E: [GPa] ya da [psi] : boyutsuz – > 0.50 yoğunluk artar – < 0.50 yoğunluk azalır (boşluklar oluşur) LL  -   L  metaller: ~ 0.33 seramikler: ~ 0.25 polimerler: ~ 0.40

12 Chapter Mekanik Özellikler 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.

13 Chapter Elastik Kayma modülü, G:  G   = G  Diğer Elastik Özellikler simple torsion test M M İzotropik malzemeler için özel bağıntılar: 2(1  ) E G  3(1  2 ) E K  Elastik kütle (Bulk) modülü, K: pressure test: Init. vol =V o. Vol chg. =  V P PP P = -K  V V o P  V K V o

14 Chapter Metal Alaşımları Grafit Seramikler Yarıiletkenler Polimerler kompozitler /elyaflar (fiberler) 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. Young Modülü: Karşılaştırması 10 9 Pa

15 Chapter Simple tension:  FLFL o EA o  L  Fw o EA o Material, geometric, and loading parameters all contribute to deflection. Larger elastic moduli minimize elastic deflection. Useful Linear Elastic Relationships F A o  /2  L LoLo w o Simple torsion:  2ML o  r o 4 G M = moment  = angle of twist 2ro2ro LoLo

16 Chapter (at lower temperatures, i.e. T < T melt /3) Plastic (Permanent) Deformation Simple tension test: engineering stress,  engineering strain,  Elastic+Plastic at larger stress permanent (plastic) after load is removed pp plastic strain Elastic initially Adapted from Fig (a), Callister 7e.

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

18 Chapter 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 Yield Strength : Comparison

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

20 Chapter Tensile Strength : Comparison 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.

21 Chapter Plastic tensile strain at failure: Adapted from Fig. 6.13, Callister 7e. Ductility Another ductility measure: 100x A AA RA% o fo - = x 100 L LL EL% o of   Engineering tensile strain,  Engineering tensile stress,  smaller %EL larger %EL LfLf AoAo AfAf LoLo

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

23 Chapter Resilience, U r Ability of a material to store energy –Energy stored best in elastic region If we assume a linear stress-strain curve this simplifies to Adapted from Fig. 6.15, Callister 7e. yyr 2 1 U 

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

25 Chapter 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 steelsfile hard cutting tools nitrided steelsdiamond

26 Chapter Hardness: Measurement Rockwell –No major sample damage –Each scale runs to 130 but only useful in range –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

27 Chapter Hardness: Measurement Table 6.5

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

29 Chapter Hardening Curve fit to the stress-strain response:  T  K  T  n “true” stress (F/A) “true” strain: ln(L/L o ) hardening exponent: n =0.15 (some steels) to n =0.5 (some coppers) An increase in  y due to plastic deformation.   large hardening small hardening  y 0  y 1

30 Chapter 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 where n is the number of data points

31 Chapter 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. Design or Safety Factors plain carbon steel:  y = 310 MPa TS = 565 MPa F = 220,000N d L o d = m = 6.7 cm

32 Chapter 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). Toughness: The energy needed to break a unit volume of material. Ductility: The plastic strain at failure. Summary Plastic behavior: This permanent deformation behavior occurs when the tensile (or compressive) uniaxial stress reaches  y.

33 Chapter Core Problems: Self-help Problems: ANNOUNCEMENTS Reading:


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