Lecture 04


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  • Lecture 04

    1. 1. Today’s objectives-Mechanical Properties <ul><li>How do mechanical characteristics (stress v strain) of metals and ceramics compare at room Temperature? </li></ul><ul><li>What are typical ceramic failure mechanisms? </li></ul><ul><li>Why are stress-strain characteristics of ceramic materials determined using transverse bending tests rather than tensile tests? </li></ul><ul><li>Be able to compute the flexural fracture strength of a ceramic from a flex test. </li></ul><ul><li>Be able to use fracture toughness to determine the max stress for a given ceramic with flaws of a known size and radius of curvature. </li></ul><ul><li>Why is there normally significant scatter in the fracture strength for specimens of the same ceramic material? </li></ul><ul><li>Why are crystalline ceramic materials so brittle? </li></ul>
    2. 2. Abrasives <ul><li>Ceramics are generally extremely hard </li></ul><ul><li>Applied as abrasives </li></ul><ul><ul><li>alumina </li></ul></ul><ul><ul><li>SiC </li></ul></ul><ul><ul><li>WC </li></ul></ul><ul><ul><li>sand </li></ul></ul><ul><ul><li>cubic BN, Diamond </li></ul></ul>http://www.abrasiveengineering.com/eurostus.pdf Almost 3000 tons a day! 700 Sand 550 Glass 600 Steel 80 Nickel 2500 Silicon carbide (SiC) 2100 Alumina (AL2O3) 2100 Tungsten carbide (WC) 800 Quartz (SiO2) 1 Graphite 7000 Diamond (C) Knoop Hardness (100g load) Material 60 1150 550 Super (no gems) 850k 310 580 Loose 70k 850 1600 Coatings 65k 860 450 Bonded tons Europe $ US $ Abrasive use, 2002 http://www.chm.bris.ac.uk/pt/diamond
    3. 3. Stress vs. Strain <ul><li>For many metals: </li></ul><ul><li>Elastic and significant plastic deformation </li></ul><ul><li>For most ceramics: </li></ul><ul><li>No appreciable plastic deformation </li></ul>Brass Brass strains to 35% = Fracture Strength (stress at failure) Ceramics strain to 0.1%
    4. 4. Fracture strength Callister, Appendix B Note that the fracture strength for ceramics is about 10* better in compression than in tension. Body armor 69 Soda lime glass 13.8-69 Graphite 230-825 SiC (sintered) 1050 Diamond (natural) 800-1400 Diamond (synthetic) 37.3-41.3 Concrete 130 Si [100] cleaved 282-551 Al 2 O 3 (99.9% pure) Strength (MPa) Ceramic
    5. 5. Failure Mechanisms-single xtals <ul><li>For single crystals, cleavage occurs </li></ul><ul><ul><li>Very rapid crack propagation along specific crystallographic planes. </li></ul></ul><ul><ul><li>Creates exceedingly flat surfaces (even atomically flat). </li></ul></ul><ul><ul><ul><li>Examples? </li></ul></ul></ul>http://www.theimage.com/crystalinfo/crystal_page2.htm
    6. 6. Failure Mechanisms-polycrystals <ul><li>Two possibilities: </li></ul><ul><ul><li>Transgranular (through grains) </li></ul></ul><ul><ul><ul><li>Rough surface everywhere </li></ul></ul></ul><ul><ul><li>Intergranular (along grain boundaries) </li></ul></ul><ul><ul><ul><li>Rough surface of many flat faces </li></ul></ul></ul><ul><li>In rare cases (usually nanoscale polycrystalline ceramics), there can be limited ductility at room temperature. </li></ul><ul><li>At higher temperatures, plastic deformation may occur. </li></ul>
    7. 7. Typical mechanical property measurements <ul><li>Standard tensile tests are problematic: </li></ul><ul><ul><li>Failure usually occurs at low strains (<0.1%), where bending stresses can be significant unless the sample is perfectly aligned in the tensile stage. </li></ul></ul><ul><ul><li>Gripping brittle materials like ceramics often leads to fracture at the grips. </li></ul></ul><ul><ul><li>Test geometry is difficult to prepare. </li></ul></ul>
    8. 8. Measuring ceramic mechanical properties <ul><li>We can’t use the standard tensile test, but we still need elastic modulus and fracture strength. </li></ul>Solution: bend test. Most appropriate for bars, rods, plates, and wafers. Where will cracks form? Which part is under tension and which is under compression?
    9. 9. MEASURING FRACTURE STRENGTH • 3-point bend test to measure room T strength. Adapted from Fig. 12.29, Callister 6e. • Flexural strength: Flexural fracture strength is higher than the tensile fracture strength. Why? Test specimens undergo compressive and tensile loads instead of pure tension. Si carbide Al oxide glass (soda) 550-860 275-550 69 Data from Table 12.5, Callister 6e. circ.
    10. 10. MEASURING ELASTIC MODULUS • Room T behavior is usually elastic, with brittle failure. • Determine elastic (Young’s) modulus according to slope: Adapted from Fig. 12.29, Callister 6e. Si carbide Al oxide glass (soda) 430 390 69 Data from Table 12.5, Callister 6e.
    11. 11. Measured Fracture Strengths <ul><li>Practically, measured fracture strengths of ceramic materials are usually much lower than predicted. </li></ul><ul><ul><li>Is the strength equation wrong? </li></ul></ul><ul><li>NO. Omnipresent flaws concentrate stresses locally. </li></ul><ul><ul><li>Pores </li></ul></ul><ul><ul><li>Grain boundary grooves </li></ul></ul><ul><ul><li>Internal grain corners </li></ul></ul><ul><ul><li>Surface cracks / scratches </li></ul></ul><ul><ul><ul><li>Particularly enhanced by humidity and contaminants </li></ul></ul></ul><ul><li>So how can we ever apply ceramics structurally? </li></ul>
    12. 12. Fracture Toughness <ul><li>The mode I plane strain fracture toughness (K Ic ) guides engineers when trying to know whether a brittle material is applicable for a given tensile load. </li></ul><ul><ul><li>If the product of the applied stress ( σ ), crack length ( a), and geometric factor (Y ≈1 ) is greater than the fracture toughness, the part will fail . </li></ul></ul>Mode I a 2.7-5 Aluminum Oxide usually greater metals 0.7-1.1 Soda-lime glass 0.2-1.4 Concrete K Ic (MPa*m ½ ) Ceramic
    13. 13. <ul><li>An applied stress is amplified at crack tips and/or pores in ceramics (from σ o to σ m ) , depending on: </li></ul><ul><li>Crack tip radius (  t ). </li></ul><ul><li>Crack length (a) or length of a pore/2 (a/2). </li></ul><ul><li>Since fracture toughness related to max stress: </li></ul><ul><li>The resulting maximum tensile stress (ie. strength) applicable to the ceramic part before failure is: </li></ul>Fracture Toughness-stress concentration Note: no such stress concentration occurs for compression.
    14. 14. Journal of Irreproducible Results? <ul><li>Measurements of fracture strength for multiple specimens usually leads to a significant variation and scatter in the results. </li></ul><ul><li>Related to huge number of flaws, primarily pores (cracks). </li></ul><ul><ul><li>Fracture occurs when K Ic is surpassed. </li></ul></ul><ul><ul><li>K Ic depends on the maximum stress within the specimen, a function of flaw size and radius. </li></ul></ul><ul><ul><li>The flaw size and radius of curvature is governed by probability laws . </li></ul></ul><ul><ul><li>Thus, so must be the fracture strength for multiple specimens. </li></ul></ul>
    15. 15. Weibull statistics <ul><li>By controlling pore size, the flexural strength can be controlled (statistically). </li></ul><ul><li>With fewer flaws, strength is improved. </li></ul>130 MPa Si [100] cleaved 81.8 MPa Si [100] laser scribed
    16. 16. Minimizing Failures <ul><li>Take advantage of statistics and the behaviour of ceramics to minimize failures of parts you sell. </li></ul><ul><ul><li>There will be a few failures (statistically), but these can be replaced through customer service as long as there aren’t too many. </li></ul></ul><ul><ul><li>Limit the ‘rated load’ to somewhere low on the Weibull response curve. </li></ul></ul>rated load
    17. 17. Guaranteeing No Failures <ul><li>Take advantage of statistics and the behaviour of ceramics to guarantee no failures : </li></ul><ul><ul><li>If the sample contains flaws that are too large, it will fail. No problem since this is in the factory, not the flying airplane. </li></ul></ul><ul><ul><li>All parts that survive are good to the rated load—but don’t surpass that load since then failures will begin to occur. </li></ul></ul><ul><ul><li>Load a particular critical component (e.g. airplane engine turbine blade) to a ‘rated load.’ </li></ul></ul>rated load
    18. 18. Where failures matter <ul><li>Ceramic Hips: “Modern medical grade ceramic is individually tested before use with weights 60 times greater than the patient body weight… </li></ul><ul><li>The Reported fracture rate = 0.004% or 4 in 100 000. </li></ul><ul><li>Not bad, except > 200,000 implants per year. </li></ul><ul><li>www.totaljoints.info/ceramic_total_hips.htm </li></ul>
    19. 19. Caveat for brittle materials: delayed fracture <ul><li>If a static load is applied, even if below K Ic , fracture may still eventually occur. </li></ul><ul><li>“ Delayed Fracture” is caused by slow crack propagation below fracture toughness (<K Ic ) </li></ul><ul><ul><li>Caused by “stress-corrosion cracking” </li></ul></ul><ul><ul><ul><li>Combination of crack tip, stress, and corrosion sharpens and elongates a crack. </li></ul></ul></ul><ul><ul><ul><li>Eventually, K IC is surpassed as crack size and radius changes. </li></ul></ul></ul><ul><ul><li>Very sensitive to chemical environment (esp. humidity). </li></ul></ul><ul><ul><li>A greater problem with increased porosity (more surface area for chemical reactions and thus crack growth). </li></ul></ul>
    20. 20. Ceramics at higher temperatures <ul><li>Dislocation motion (slip) is extremely difficult in ceramics due to their ionic nature. </li></ul><ul><ul><li>hardness and brittleness are extremely high. </li></ul></ul><ul><li>For covalent ceramics, the covalent bonds are also very strong and difficult to overcome. </li></ul><ul><li>Still, plastic deformation does occur in ceramics, but: </li></ul><ul><ul><li>less than for metals. </li></ul></ul><ul><ul><li>usually only near the melting point. </li></ul></ul>Ionic Bonding Slip is impossible: Too much electrostatic repulsion + - + - + - + - + - + -
    21. 21. Improvements for mechanical applications <ul><li>Use in compression </li></ul><ul><li>Decrease influence of internal flaws </li></ul><ul><ul><li>Decrease size by enhanced processing and optimal raw materials </li></ul></ul><ul><ul><li>Increase radius </li></ul></ul><ul><ul><li>Decrease number </li></ul></ul><ul><li>Decrease number of surface flaws </li></ul><ul><ul><li>Surface polishing </li></ul></ul><ul><li>Decrease influence of surface flaws </li></ul><ul><ul><li>Add a compressive layer at the surface </li></ul></ul><ul><li>Minimizing stress-corrosion cracking </li></ul><ul><ul><li>Protect the component from the environment </li></ul></ul><ul><li>Use below the Weibull ‘rated’ load </li></ul><ul><li>Decrease component size (fewer flaws) </li></ul><ul><li>Keep temperature as low as possible </li></ul>
    22. 22. SUMMARY Reading for next class Phase diagrams Chapter sections 12.6, 12.7 <ul><li>Room temperature mechanical response of ceramics is elastic, but fracture is brittle with negligible ductility. </li></ul><ul><li>Elastic modulus and fracture strength are determined differently than for metals. </li></ul><ul><li>Ceramic materials are stronger in compression than in tension. </li></ul><ul><li>Elevated temperature properties are generally superior to those of metals. </li></ul><ul><li>Viscosity is the mechanism for deformation for amorphous ceramics. </li></ul><ul><li>Porous ceramics exhibit a strong variation in properties—why, and how can this be overcome? </li></ul><ul><li>Many ceramics are extremely hard. Why? </li></ul>