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MATERIALS SCIENCE Week 5 Fracture, Toughness, Fatigue, and Creep.

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Presentation on theme: "MATERIALS SCIENCE Week 5 Fracture, Toughness, Fatigue, and Creep."— Presentation transcript:

1 MATERIALS SCIENCE Week 5 Fracture, Toughness, Fatigue, and Creep

2 2 ISSUES TO ADDRESS... How do flaws in a material initiate failure? How is fracture resistance quantified; how do different material classes compare? How do we estimate the stress to fracture? How do loading rate, loading history, and temperature affect the failure stress? Ship-cyclic loading from waves. Computer chip-cyclic thermal loading. Hip implant-cyclic loading from walking. Mechanical Failure

3 What is a Fracture? Fracture is the separation of a body into two or more pieces in response to an imposed stress that is static and at temperatures that are low relative to the melting temperature of the material. The applied stress may be tensile, compressive, shear, or torsional Any fracture process involves two steps—crack formation and propagation—in response to an imposed stress.

4 4 Fracture mechanisms Ductile fracture  Occurs with plastic deformation Brittle fracture –Little or no plastic deformation –Catastrophic

5 5 Ductile vs Brittle Failure Very Ductile Moderately Ductile Brittle Fracture behavior: LargeModerate%AR or %EL Small Ductile fracture is usually desirable! Classification: Ductile: warning before fracture Brittle: No warning

6 6 Ductile failure: --one/two piece(s) --large deformation Example: Failure of a Pipe Brittle failure: --many pieces --small deformation

7 7 Evolution to failure: Resulting fracture surfaces (steel) 50 mm particles serve as void nucleation sites. 50 mm 100 mm Moderately Ductile Failure necking  void nucleation void growth and linkage shearing at surface fracture

8 8 Ductile vs. Brittle Failure cup-and-cone fracturebrittle fracture

9 Transgranular vs Intergranular Fracture Transgranular Fracture Intergranular Fracture

10 10 Intergranular (between grains) Transgranular (within grains) Al Oxide (ceramic) 316 S. Steel (metal) 304 S. Steel (metal) Polypropylene (polymer) 3 mm 4 mm 160 mm 1 mm Brittle Fracture Surfaces

11 11 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!

12 12 Flaws are Stress Concentrators! Results from crack propagation Griffith Crack where  t = radius of curvature  o = applied stress  m = stress at crack tip K t = Stress concentration factor tt

13 13 Concentration of Stress at Crack Tip

14 14 Engineering Fracture Design r/hr/h sharper fillet radius increasing w/hw/h Stress Conc. Factor, K t  max  o = Avoid sharp corners!  r, fillet radius w h o  max

15 15 Crack Propagation Cracks propagate due to sharpness of crack tip A plastic material deforms at the tip, “blunting” the crack. deformed region 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

16 16 When Does a Crack Propagate? Crack propagates if above critical stress where  E = modulus of elasticity   s = specific surface energy (J/m 2 )  a = one half length of internal crack For ductile => replace  s by  s +  p where  p is plastic deformation energy i.e.,  m >  c

17 17 Crack growth condition: Largest, most stressed cracks grow first! Fracture Toughness: Design Against Crack Growth K ≥ K c = --Result 1: Max. flaw size dictates design stress.  a max no fracture --Result 2: Design stress dictates max. flaw size. a max  no fracture

18 Fracture Toughness For relatively thin specimens, the value of Kc will depend on specimen thickness. However, when specimen thickness is much greater than the crack dimensions, Kc becomes independent of thickness. The Kc value for this thick-specimen situation is known as the plane strain fracture toughness K IC

19 19 Fracture Toughness K c =

20 20 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 c = 26 MPa-m 0.5 Design Example: Aircraft Wing Use... 9 mm112 MPa 4 mm --Result:

21 21 Loading Rate Increased loading rate increases  y and TS -- decreases %EL Why? An increased rate gives less time for dislocations to move past obstacles and form into a crack.   yy yy TS larger  smaller 

22 22 Impact Testing final heightinitial height Impact loading: -- severe testing case -- makes material more brittle -- decreases toughness (Charpy)

23 Impact Tests A material may have a high tensile strength and yet be unsuitable for shock loading conditions Impact testing is testing an object's ability to resist high-rate loading. An impact test is a test for determining the energy absorbed in fracturing a test piece at high velocity Types of Impact Tests -> Izod test and Charpy Impact test In these tests a load swings from a given height to strike the specimen, and the energy dissipated in the fracture is measured

24 A. Izod Test The Izod test is most commonly used to evaluate the relative toughness or impact toughness of materials Izod test sample usually have a V- notch cut into them Metallic samples tend to be square in cross section, while polymeric test specimens are often rectangular

25 Izod Test - Method It involves striking a suitable test piece with a striker, mounted at the end of a pendulum The test piece is clamped vertically with the notch facing the striker. The striker swings downwards impacting the test piece at the bottom of its swing.

26 Determination of Izod Impact Energy At the point of impact, the striker has a known amount of kinetic energy. The impact energy is calculated based on the height to which the striker would have risen, if no test specimen was in place, and this compared to the height to which the striker actually rises. Tough materials absorb a lot of energy, whilst brittle materials tend to absorb very little energy prior to fracture

27 B. Charpy Test Charpy test specimens normally measure 55 x 10 x 10mm and have a notch machined across one of the larger faces The Charpy test involves striking a suitable test piece with a striker, mounted at the end of a pendulum. The test piece is fixed in place at both ends and the striker impacts the test piece immediately behind a machined notch.

28 Factors Affecting Impact Energy 1. For a given material the impact energy will be seen to decrease if the yield strength is increased 2. The notch serves as a stress concentration zone and some materials are more sensitive towards notches than others 3. Most of the impact energy is absorbed by means of plastic deformation during the yielding. Therefore, factors that affect the yield behavior (and hence ductility) of the material such as temperature and strain rate will affect the impact energy

29 29 Increasing temperature... --increases %EL and K c Ductile-to-Brittle Transition Temperature (DBTT)... Effect of Temperature on Toughness 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)

30 Fatigue Test Fatigue is concerned with the premature fracture of metals under repeatedly applied low stresses A specified mean load (which may be zero) and an alternating load are applied to a specimen and the number of cycles required to produce failure (fatigue life) is recorded. Generally, the test is repeated with identical specimens and various fluctuating loads. Data from fatigue testing often are presented in an S-N diagram which is a plot of the number of cycles required to cause failure in a specimen against the amplitude of the cyclical stress developed

31 Fatigue Testing Equipment

32 Fatigue Loading

33 Fatigue Test - S-N Curve This S–N diagram indicates that some metals can withstand indefinitely the application of a large number of stress reversals, provided the applied stress is below a limiting stress known as the endurance limit

34 34 Crack grows incrementally typ. 1 to 6 increase in crack length per loading cycle Failed rotating shaft --crack grew even though K max < K c --crack grows faster as  increases crack gets longer loading freq. increases. crack origin Fatigue Mechanism

35 35 Improving Fatigue Life 1. Impose a compressive surface stress (to suppress surface cracks from growing) N = Cycles to failure moderate tensile  m Larger tensile  m S = stress amplitude near zero or compressive  m Increasing  m --Method 1: shot peening put surface into compression shot --Method 2: carburizing C-rich gas 2. Remove stress concentrators. bad better

36 4. Creep Test Creep is defined as plastic (or irrevresible) flow under constant stress Creep is high temperature progressive deformation at constant stress A creep test involves a tensile specimen under a constant load maintained at a constant temperature. At relatively high temperatures creep appears to occur at all stress levels, but the creep rate increases with increasing stress at a given temperature.

37 Creep Test Creep occurs in three stages: Primary, or Stage I; Secondary, or Stage II, and Tertiary, or Stage III

38 Creep Test Stage I occurs at the beginning of the tests, and creep is mostly transient, not at a steady rate. In Stage II, the rate of creep becomes roughly steady In Stage III, the creep rate begins to accelerate as the cross sectional area of the specimen decreases due to necking decreases the effective area of the specimen

39 39 Occurs at elevated temperature, T > 0.4 T m Creep elastic primary secondary tertiary

40 40 Strain rate is constant at a given T,  stress exponent (material parameter) strain rate activation energy for creep (material parameter) applied stress material const. Secondary Creep

41 41 Creep Failure Estimate rupture time S-590 Iron, T = 800°C,  = 20 ksi Failure: along grain boundaries. time to failure (rupture) function of applied stress temperature applied stress g.b. cavities Time to rupture, t r 1073K Ans: t r = 233 hr 24x10 3 K-log hr L(10 3 K-log hr) Stress, ksi data for S-590 Iron 20

42 Numerical Problems Problems 8.1 – 8.10; 8.14 – 8.23; and 8.27

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