Exam 2 Grade Distribution

1. Exam 2 Grade Distribution

2. Ideal vs Real Materials s TS << TS perfect mat’l-no flaws perfect materials engineering materials E/10 carefully produced glass fiber typical ceramic typical strengthened metal E/100 typical polymer e 0.1 • Stress-strain behavior (Room T): • DaVinci (500 yrs ago!) observed... -- the longer the wire, the smaller the load for failure. • Reasons: -- flaws cause premature failure. -- Larger samples contain more flaws!

3. Concentration of Stress at a Flaw • First solved mathematically by Inglis in 1913 • Solved the elasticity problem of an elliptical hole • in an otherwise uniformly loaded plate

4. Mathematical Solution of Stress Concentration Where: t = radius of curvature so = applied stress seff = stress at crack tip t

5. s o max Stress Conc. Factor, Kt = s o w s 2.5 max h r , 2.0 increasing w/h fillet radius 1.5 r/h 1.0 0 0.5 1.0 sharper fillet radius Engineering Fracture Design Avoid sharp corners! s

6. Fracture Toughness Stress Intensity Factor: Define Stress Intensity: [Units: ksi√in] Geometrically determined factor Typically defined as: f (a/w)

7. Examples Source: T. L. Anderson, Fracture Mechanics Fundamentals and Applications, 3rd Edition, Taylor & Francis, 2005.

8. Plane Strain Fracture Toughness, KIC If you measure stress intensity you find: • That there is a critical value for a given geometry and material • That there is an effect of specimen thickness • That the critical values approaches a limit, KIC KIC is a material constant In fracture mechanics theory, a crack will not propagate unless the applied stress intensity is greater than the critical stress intensity, KIC Source: T. L. Anderson, Fracture Mechanics Fundamentals and Applications, 3rd Edition, Taylor & Francis, 2005.

9. Crack Propagation Cracks propagate due to sharpness of crack tip • A plastic material deforms at the tip, “blunting” the crack. brittle Energy balance on the crack • Elastic strain energy- • energy stored in material as it is elastically deformed • this energy is released when the crack propagates • creation of new surfaces requires energy plastic

10. When Does a Crack Propagate? Crack propagates if above critical stress where • E = modulus of elasticity • s= specific surface energy • a = one half length of internal crack • Kc = sc/s0 For ductile => replace gs by gs + gp where gp is plastic deformation energy i.e., sm>sc orKt> Kc Griffith Crack Criterion

11. Design Against Crack Growth K ≥ KIC= --Result 2: Design stress dictates max. flaw size. --Result 1: Max. flaw size dictates design stress. amax s fracture fracture no no amax s fracture fracture • Crack growth condition: • Largest, most stressed cracks grow first!

12. Design Example: Aircraft Wing • Use... --Result: 112 MPa 9 mm 4 mm Answer: • Material has KIc = 26 MPa-m0.5 • Two designs to consider... Design B --use same material --largest flaw is 4 mm --failure stress = ? Design A --largest flaw is 9 mm --failure stress = 112 MPa • Key point: Y and Kc are the same in both designs. • Reducing flaw size pays off!

13. TS sy larger e TS smaller sy e e Loading Rate • Increased loading rate... -- increases sy and TS -- decreases %EL • Why? An increased rate gives less time for dislocations to move past obstacles. s

14. (Charpy) final height initial height Charpy (or Izod) Impact Testing • Impact loading: -- severe testing case -- makes material more brittle -- decreases toughness

15. Temperature • Increasing temperature... --increases %EL and Kc • Ductile-to-Brittle Transition Temperature (DBTT)... FCC metals (e.g., Cu, Ni) BCC metals (e.g., iron at T < 914°C) polymers Impact Energy Brittle More Ductile s High strength materials ( > E/150) y Temperature Ductile-to-brittle transition temperature

16. specimen compression on top motor counter bearing bearing flex coupling tension on bottom s s max S s m s time min Fatigue • Fatigue = failure under cyclic stresses • Stress varies with time. -- key parameters are S, sm, and frequency • Key points: Fatigue... --can cause part failure, even though smax < sc. --causes ~ 90% of mechanical engineering failures.

17. Bauschinger Effect • In most metals there is a hysteresis in stress-strain behavior • Leads to accumulative damage to the microstructure under cyclic loading • Think of a paper clip… Source: Reed-Hill, Abbaschian, Physical Metallurgy Principles, 3rd Edition, PWS Publishing Company, 1994.

18. Micromechanisms of Fatigue Source: T. L. Anderson, Fracture Mechanics Fundamentals and Applications, 3rd Edition, Taylor & Francis, 2005.

19. Formation of Slip Bands During Cyclic Loading Copper single crystals – persistent slip bands Source: Reed-Hill, Abbaschian, Physical Metallurgy Principles, 3rd Edition, PWS Publishing Company, 1994.

20. Fatigue Fractography Microscopic Fatigue Striations (SEM) Source: T. L. Anderson, Fracture Mechanics Fundamentals and Applications, 3rd Edition, Taylor & Francis, 2005. Source: Reed-Hill, Abbaschian, Physical Metallurgy Principles, 3rd Edition, PWS Publishing Company, 1994.

21. Fatigue Fractography

22. Fatigue Striations Hardened Steel Sample tested in 3-point bending