1. Mechanical Engineering Department Alabama A&M University Fall 2014, Lecture 17 Mechanical Behavior: Part III Dr. Aaron L. Adams, Assistant Professor

2. What are modes of mechanical failure in materials? Why are flaws a critical feature of failure in ceramic based materials? What is K IC ? What is toughness? What is fatigue? Impact strength? Ch. 7, pp. 211-219; Ch. 9, pp. 308-348 Relevant Reading for this Lecture... Learning Objectives…. 2

3. Ductile Materials: – Undergo extensive plastic deformation prior to failure Brittle Materials: – Undergo little or no plastic deformation prior to failure. Figure 7.13 Schematic representations of tensile stress- strain behavior for brittle and ductile materials loaded to fracture. [Callister & Rethwisch, 4 th Ed.] Based on the definition of toughness from the previous lecture, do you believe ductile or brittle materials are more or less tough? Why? 3 Failure Modes for Materials

4. Failure: Ductile Fracture a)Necking b)Cavity formation c)Cavity coalescence to form cracks d)Crack propagation (growth) e)Fracture Crack grows 90° to applied stress Maximum shear stress Figure 8.2 Stages in the cup-and-cone fracture. (a) Initial necking. (b) Small cavity formation. (c) Coalescence of cavities to form a crack. (d) Crack propagation. (e) Final shear fracture at a 45° angle relative to the tensile direction. (From Ralls, Courtney and Wulff, Introduction to Materials Science and Engineering, p. 468, Copyright 1976, Wiley, New York). [Callister, 7 th Ed.] 4

5. DUCTILE FRACTURE ► Dimples on fracture surface correspond to microcavities that initiate crack formation. ► Picture at left is a typical “cup and cone” fracture. 5

6. BRITTLE FRACTURE No appreciable plastic deformation. Crack propagates very fast; nearly perpendicular to applied stress. Cracks often propagate along specific crystal planes or boundaries. Transgranular fracture Intergranular fracture 6

7. Transgranular Fracture Cracks pass through grains, often along specific crystal planes. Fracture surfaces have faceted texture because of different orientation of cleavage planes in grains. Transgranular fracture 7

8. Intergranular Fracture Cracks propagate along grain boundaries. Intergranular fracture 8

9. 9 Brittle Fracture of Ceramics ►Characteristic Fracture behavior in ceramics Origin point Initial region (mirror) is flat and smooth After reaches critical velocity crack branches –Mist region –Hackle region Adapted from Figs. 9.14 & 9.15, Callister & Rethwisch 4e.

10. 10 Mechanical Properties Ceramic materials are more brittle than metals. WHY? Consider mechanism of deformation In crystalline materials deformation occurs by dislocation motion In highly ionic solids, dislocation motion is difficult –few slip systems –resistance to motion of ions of like charge (e.g., anions) past one another In covalent solids, dislocation motion is restricted by directional bonding. As a result, behavior is elastic at room T. Can’t tensile test. Must test another way.

11. Strain Stress Brittle Ceramics ►S►Stress-strain behavior is not usually determined via tensile tests. WHY? ►M►Material fails before it yields. ►B►Bend/flexure tests are often used instead. Why is there little plasticity in ceramics at ambient temperatures? 11 YS

12. 12 3-point bend test to measure room-T flexural strength. Adapted from Fig. 7.18, Callister & Rethwisch 4e. Flexural Tests – Measurement of Flexural Strength F L/2  = midpoint deflection cross section R b d rect.circ. location of max tension Flexural strength: Typical values: Data from Table 7.2, Callister & Rethwisch 4e. Si nitride Si carbide Al oxide glass (soda-lime) 250-1000 100-820 275-700 69 304 345 393 69 Material  fs (MPa) E(GPa) (rect. cross section) (circ. cross section)

13. Why/How do Materials Fail? Are typical loading conditions severe enough to break all inter-atomic bonds? NO! Since we know the stress required to break bonds, why do materials fail in service at lower stresses than this? THEY CONTAIN FLAWS & DEFECTS! Flaws/defects concentrate stress locally to levels high enough to rupture bonds! What about materials that are perfect? NO MATERIAL IS PERFECT! There is ALWAYS some statistical distribution of defects, flaws, surface cracks, scratches, etc. Fracture plane  Simultaneous rupture of all atomic bonds Theoretical strength >> experimental measurements WHY? 1. Dislocations  slip 2. Flaws/cracks  fracture 13 

14. Flaws concentrate applied stress onto a smaller area!  area = P/A P = load b/a  0,  local   A 1 >> A 2  1 >>  2 1 2 A 1 << A 2 σ 1 >> σ 2 14 Defect in solid

15. Figure 9.10 The three modes of crack surface displacement. (a)Mode I, opening; (b)Mode II, sliding; (c)Mode III, tearing Fundamental ways that forces can operate on cracks The mode of loading (state of stress) plays a role in how/when a material will fail. TENSILESLIDING (SHEAR) 15 TEARING

16. Griffith crack model: Stress concentration at a crack tip Max stress Applied stress Crack length* Radius of crack tip DEFECT! Stress (σ m ) at the tip of a Griffith crack. a 16 σ σ

17. Critical Stress Intensity Factor, K c Stress intensity, also K c (fixed) Critical Stress for crack propagation Crack Length, a Y is a geometric factor ~1 K c defines the ability of a material to resist fracture even when a flaw exists. When K > K c, cracks grow and the material fails. K c directly depends on the size of the flaw, material properties, and how stresses acts on a crack Using fracture mechanics, we can derive an equation that tells us how large of a crack can be tolerated for a given material and a given applied stress without failure 17 p. 317

18. General Expression ►Allows calculation of maximum allowable stress for a given flaw size. Depends on specimen and crack geometry Plane-strain fracture toughness (fixed) Critical crack length Mode I

19. Design Philosophy Design stressMaterial Property Materials selection (fixed) Allowable flaw size or NDT flaw detection K Ic is a fixed material parameter (can be found in handbooks)

20. a1a1 a2a2 a3a3 a4a4 K Ic1 K Ic2 K Ic3 K Ic4 <<< >>> === K Ic is a materials constant 20

21. general yielding occurs if flaw size a < a critical catastrophic fast fracture occurs if flaw size a > a critical Engineering Fracture Performance Re-arrange K IC equation 21 YS

22. Some Values of K IC MaterialK IC (MPa·m 1/2 ) Minerals0.5 – 1 Concrete0.35 SLS Glass1 Most Polymers1 – 3 Ceramics3 – 10 Cast Iron10 – 40 Aluminum Alloys20 – 50 Plane Carbon Steels30 – 100 Titanium Alloys30 – 120 TRIP Steel~200 Metals that exhibit high ductility, exhibit high toughness. Ceramics are very strong, but have low ductility and low toughness. Polymers are very ductile but are not generally very strong in shear (compared to metals and ceramics). They have low toughness. 22

23. ASTM E-399-09 1.Single-edge notched bend 2.Compact tension test. 23 Very sharp pre-crack How is fracture toughness measured? 1 2

24. In class problem: A structural component in the form of a wide plate is the be fabricated from a steel alloy that has a plane strain fracture toughness of 77.0 MPa√m and a yield strength of 1400 MPa. The flaw size resolution limit of the flaw detection apparatus is 4.0 mm. If the design stress is one-half the yield strength and the value of Y is 1.0, determine whether a critical flaw for this plate is subject to detection. a = [K Ic /(σ·Y)] 2 (1/π) 77.0 MPa√m 0.5 ·1400 MPa 1.0 a = 0.00385 m or 3.9 mm Below the detection limit! 24

25. Stress–strain curves for dense, polycrystalline Al 2 O 3. TensionCompression Why are ceramics so much stronger in compression than in tension? Video of chalk 25

26. Tension opens cracksCompression closes cracks 26

27. Engineering Fracture Performance Blunt the crack tip,  Volumetric change compresses the crack (closes it) 27 Some ways to improve the fracture toughness of brittle materials Stress initiated phase transformation  Transformation Toughening Microcracking can blunt crack tip. It can also change crack path.

28. Adapted from Fig. 9.24, Callister & Rethwisch 4e. (Fig. 9.24 is from Materials Science in Engineering, 4/E by Carl. A. Keyser, Pearson Education, Inc., Upper Saddle River, NJ.) Fatigue = failure under applied cyclic stress. Stress varies with time. -- key parameters are S,  m, and cycling frequency  max  min  time mm S Key points: Fatigue... --can cause part failure, even though  max <  ys. --responsible for ~ 90% of mechanical engineering failures. tension on bottom compression on top counter motor flex coupling specimen bearing FATIGUE – it’s important http://deicinginnovations.com/wp- content/uploads/2012/07/Aloha.jpg 28 Aloha Airlines Flight 243

29. Examples of Fatigue in “Everyday Engineering” AircraftRailroad Travel 29 The cause for lots of death and destruction in the 19 th and 20 th centuries. No end in sight. Can’t stop it. Can only design to mitigate it.

30. Adapted from Fig. 9.25(a), Callister & Rethwisch 4e. FATIGUE DESIGN PARAMETERS Fatigue limit, S fat : --no fatigue if S < S fat S fat case for steel (typ.) N = Cycles to failure 10 3 5 7 9 unsafe safe S = stress amplitude For some materials, there is no fatigue limit! Adapted from Fig. 9.25(b), Callister & Rethwisch 4e. case for Al (typ.) N = Cycles to failure 10 3 5 7 9 unsafe safe S = stress amplitude Note log scale (goes by decades) Endurance limit 30

31. 1. Fatigue cracks must INITIATE. almost always from a surface at a stress concentrator 2. Fatigue cracks then GROW 31

32. Crack grows incrementally typically 1 to 6 increase in crack length per loading cycle Failed rotating shaft --crack grew even though K max < K c --crack grows faster if  increases crack gets longer loading freq. increases. crack origin Adapted from Fig. 9.28, Callister & Rethwisch 4e. (Fig. 9.28 is from D.J. Wulpi, Understanding How Components Fail, American Society for Metals, Materials Park, OH, 1985.) FATIGUE MECHANISM Change in stress intensity factor,  K Small crack lengths or low stress, pre-existing cracks do not grow 32

33. Fatigue Failure in Heart Values accelerated by pre-existing crack flaw  During the initial use of heart valve replacements, surgeons inadvertently scratched the metal rings during surgery.  These scratches were initiation sites for fatigue failures where cracks could grow under cyclic loading (e.g., heart beating) and leading to early failure! 33

34. Some Ways to Improve Fatigue Life 2. Remove stress concentrators. Adapted from Fig. 9.32, Callister & Rethwisch 4e. bad better Adapted from Fig. 9.31, Callister & Rethwisch 4e. 1. Impose compressive surface stresses (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 puts surface into compression shot --Method 2: case hardening C-rich gas steel alloy 34 Reduce σ m, increase fatigue life Surface Effects:

35. Impact Strength Short term dynamic stressing – Car collisions – Bullets – Athletic equipment – Etc… Ability of the material to absorb energy prior to fracture; energy necessary to push a crack (flaw) through a material. – Fracture toughness is the resistance of a crack to growing (K IC ).  Impact strength, sometimes called impact toughness, is not the same as fracture toughness! Useful in quality control. 35

36. Figure 8.12 (a) Specimen used for Charpy and Izod impact tests. (b) A schematic drawing of an impact testing machine. The hammer is released from a fixed height and strikes the specimen; the energy expended to break the specimen is reflected in the difference between the initial height of the hammer and the swing height. Charpy or Izod test Strike a notched sample with an anvil. Measure how far the anvil travels following impact. Distance traveled is related to energy required to break the sample. Very high rate of loading. Makes materials more “brittle.” Impact energy is analogous to toughness. High impact energy means high toughness; material resist crack propagation Impact Energy 36

37. Griffith crack model. 1 2 Flaws concentrate applied stress! ToughnessStress Crack Length Materials fail when K IC is exceeded Depends on size of flawSummary 37 Most brittle materials tested in compression or via flexure testing – why? Fatigue – s applied < s max under cycling can result in material failure Impact strength – is determined from a Charpy impact test.