Exam 2 Grade Distribution

Stress-strain behavior (Room T): Ideal vs Real Materials TS << TS engineering materials perfect materials   E/10 E/ perfect mat’l-no flaws carefully produced glass fiber typical ceramic typical strengthened metal typical polymer 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!

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

Mathematical Solution of Stress Concentration Where:  t = radius of curvature  o = applied stress  eff = stress at crack tip tt

Engineering Fracture Design r/hr/h sharper fillet radius increasingw/hw/h Stress Conc. Factor, K t  max  o = Avoid sharp corners!  r, fillet radius w h o  max

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

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

Plane Strain Fracture Toughness, K IC If you measure stress intensity you find: Source: T. L. Anderson, Fracture Mechanics Fundamentals and Applications, 3rd Edition, Taylor & Francis, That there is a critical value for a given geometry and material 2.That there is an effect of specimen thickness 3.That the critical values approaches a limit, K IC K IC 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, K IC

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

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 –K c =  c /  0 For ductile => replace  s by  s +  p where  p is plastic deformation energy i.e.,  m >  c or K t > K c Griffith Crack Criterion

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

Two designs to consider... Design A --largest flaw is 9 mm --failure stress = 112 MPa Design B --use same material --largest flaw is 4 mm --failure stress = ? Key point: Y and K c are the same in both designs. Answer: Reducing flaw size pays off! Material has K I c = 26 MPa-m 0.5 Design Example: Aircraft Wing Use... 9 mm112 MPa 4 mm --Result:

Loading Rate Increased loading rate increases  y and TS -- decreases %EL Why? An increased rate gives less time for dislocations to move past obstacles.   yy yy TS larger  smaller 

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

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

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

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.

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

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

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

Fatigue Fractography

Fatigue Striations Hardened Steel Sample tested in 3-point bending