Mechanical Properties of Ceramics

Transcription

1 Materials Science & Technology Materials Science II , Ceramic Materials, Chapter 6, Part 2 Mechanical Properties of Ceramics or Mechanical Behavior of Brittle Materials Jakob Kübler Empa, Science & Technology Lab for High Performance Ceramics Überlandstrasse 129, CH-8600 Dübendorf jakob.kuebler@empa.ch & Prof. L.J. Gauckler ETH Zürich, Materials Department 1

2 Repetition learning targets part 1 What you already know and understand! Design relevant mechanical properties ( properties by technological tests) Fracture toughness, strength, creep, subcritical crack growth, All materials exhibit a natural defect population due to production. Defects differ in size, form and orientation. Mechanical stress at crack tip is by factors larger than stress calculated from macroscopically available cross section and average applied stress. σ max a = σ ρ σ max stress at crack tip σ 0 nominal stress ρ t radius of curvature at crack tip a ½ crack width Brittle materials like ceramics can t diminish stress superelevation at crack tip by plastic deformation. 2

3 Repetition learning targets part 1 Griffith s basic idea: Balance energy consumed in forming new surfaces as crack propagates against elastic energy released. Griffith s law: Failure occurs when rate at which energy is released is greater than rate at which it is consumed. (if defect related stress peak theoretical strength) σ π c 2 γ E σ, c applied stress, depth of crack 2, γ surfaces created, intrinsic surface energy of material E Young s modulus with help of Irwin s correlation: Failure occurs if Stress Intensity Factor Critical Stress Intensity Factor K Ic = σ c c Y Valid as long as only factor keeping crack from extending is creation of new surfaces. K Ic,σ c fracture toughness, critical applied stress c, Y depth of crack, Y-factor K Ic is material specific and indicates how well it withstands the extension of a crack under stress. The higher K Ic, the more difficult it is for a crack to advance. Y-factor predicts intensity and distribution of a stress field around a defect caused by an external load. 3

4 part 1 Crack tip Aim of chapter & Learning targets 1. Introduction Why mechanical testing 2. Stresses at a crack tip Higher than you d assume 3. Griffith law Conditions for failure 4. K I and K Ic Stress intensity & critical stress intensity learning targets 1 part 2 Strength 5. R-curve 6. Properties 7. Strength Improving toughness Knowing what you measure Just a value learning targets 2 part 3 Statistics 8. Statistic 9. Proof testing 10. Fractography Weibull, a name you ll never should forget Make it or Reading fracture surfaces learning targets 3 part 4 Time&Temp 11. Thermal shock 12. Slow crack growth 13. SPT diagrams 14. Creep 15. Failure maps Temperature, time and geometry After several years Combining strength, lifetime & statistics Temperature makes it move Finding your way learning targets 4 part 5 - Case Study: Lifetime of All-Ceramic Dental Bridges 4

5 Definition of crack dimensions for today s lecture last weeks definition ( just to stay flexible ) Attention: In literature c and a are often used vise versa. σ σ 2 c 2 c a a σ σ thin plate 5

6 R-curve behavior (1) Increasing resistance against crack propagation K IR K IR K IR = K Ic Crack growth Δa Fracture toughness of a polycrystalline ceramic is significantly higher than that of a single crystals of the same composition, e.g. K Ic of alumina single-crystal ~ 2.2 MPa m polycrystal ~ 4 MPa m 6

7 R-curve behavior (2) Example: R-curve behavior of Alumina Δa ~ 2 mm K tip = K Iapp ~ 6 MPa m Δa ~ 0 mm K tip = K Io ~ 3 MPa m Crack extension isn t characterized by a constant K Ic anymore but by a K IR - Δa curve. Why this increase? 7

8 R-curve behavior (3) Why is K IR increasing? a) Crack deflection at grain boundaries Polycrystalline material: as crack deflects along weak grain boundaries, K tip is reduced, because stress is no longer normal to crack plan ( 3 cos θ ) K app Ktip = 2 crack plan Barsoum, p380 assuming Θ avg = 45 K tip ~ 1.25 x single-crystal value crack deflection accounts for some of the enhanced toughness, but not all 8

9 R-curve behavior (4) Why is K IR increasing? b) Crack bridging 1 deflection of crack front along / around rod-shaped particles undeflected crack front ligament bridging mechanism with no interfacial debonding Toughening results from bridging of the crack surfaces behind crack tip by a strong reinforcing phase e.g. elongated grains continuous fibers whiskers particles (metal ) Bridging ligaments generate closure forces on crack face which reduce K tip. Name one of the most prominent materials using this mechanism to improve fracture toughness!?! 9

10 R-curve behavior (5) b) Crack bridging 3: example SiC whiskers in -glass - mullite -alumina lines: prediction points: experiments What s Mullite? Mineralogical name of only chemically stable intermediate phase in SiO 2 -Al 2 O 3 system. The natural mineral is rare, occurring on the Isle of Mull, west coast of Scotland. Si 3 N 4 F. Monteverde, A. Bellosi, S. Guicciardi, ISTEC-CNR Crack bridging and pullout can yield substantially increased fracture toughness. 10

11 R-curve behavior (6) b) Crack bridging 2: amount of increase Fracture toughness of a composite due to elastic stretching of a partially debonded reinforcing phase at crack tip with no interfacial friction: K Ic = E c G m + σ 2 f r V 12 f E E c f γ f γ i P. Becher, J.Am.Ceram.Soc., 74: (1991) where: c, m, f, i composite, matrix, reinforcement, interface E, V, r Young s modulus, volume fraction, radius of bridging ligament σ, G strength of reinforcement phase, toughness of unreinforced ligament γ f /γ i ratio of fracture energy of the bridging ligaments to that of the reinforcement/matrix interface i.e. fracture toughness is increased for high reinforcement content, weak reinforcement (increasing E c /E f ratio) and weak reinforcement / matrix interfaces (increasing γ f /γ i ratio) 11

12 Data for calculation m: matrix ; f : whisker E m 400 GPa K Ic Al 2 O 3 3 MPa m E w 580 GPa σ w MPa d f 1 μm l f 10 μm whisker direction random-3d interface γ f / γ i 1, 25, (1 = super strong) R-curve behavior (7) b) Crack bridging 4: amount of increase Al 2 O 3 & SiC-whisker composite composite KIc [MPa m] 'super strong' interface 'strong' interface 'weak' interface volume fraction of SiC-whisker 12

13 R-curve behavior (8) Why is K IR increasing? c) Transformation toughening t m in pure undoped ZrO2 during cooling is a reversible martensitic transformation, associated with a volume change (4 5%). Dopants (yttria, ceria, magnesia, calcia etc.) are usually added to stabilize the high temperature t and/or c-phase in the sintered microstructure. original metastable tetragonal zirconia particle martensitically transformed zirconia particle compressive stress field around crack tip if tetragonal particles are fine enough, then upon cooling from T process, they can be constrained from transformation by surrounding matrix. very large toughness due to stress-induced transformation of metastable phase (tetragonal monoclinic Zr) in vicinity of propagating crack. 13

14 R-curve behavior (9) Shielding factor K s K tip = K app K s if constrain is lost, transformation is induced (volume expansion ~4% shear strain up ~7%). Approaching crack front (= free surface) triggers transformation, which in turn places zone ahead of crack tip in compression. To extend crack into compressive zone extra energy is required K Ic and σ R.M.Mc. Meeking and A.G. Evans J.Amer.Ceram.Soc., 63: (1982) κ dimensionless constant (Δa/w = κ = depends on shape of zone ahead of crack tip) E V f ε T K w Δa s T = κ E V ε f w Young s modulus volume fraction of transformable phase transformation strain width of zone with transformed phase length of crack inside transformed zone Δ KIc = Ks [MPa m] Δa [μm] w = 10 μm ; E = 210 GPa ; V f =0.92 ; ε t =

15 R-curve behavior (10) Toughened zirconia-containing ceramics PSZ: partially stabilized zirconia Cubic phase is less than totally stabilized by the addition of MgO, CaO, or Y 2 O 3. Heat treatment needed to keep precipitates small enough so that they do not spontaneously transform within the cubic zirconia matrix. TZP: tetragonal zirconia polycristal 100% tetragonal phase and small amounts of yttria and other rare-earth additives. σ b up to MPa. ZTC: zirconia-toughened ceramic Tetragonal or monoclinic zirconia particles finely dispersed in other ceramic matrices such as alumina, mullite, and spinel. 15

16 R-curve behavior (11) Increasing resistance against crack propagation by design, e.g. compressive residual stresses in laminates Residual compressive stresses reduce actual stress in outer layer L1 σ Layer = σ Load - σ CRes L2 K Ic = ( σ σ C ) a Y L1 σ + σ - How can compressive stresses be introduced into surfaces, e.g. in glass and ceramics? Glass: Rapid cooling of outer surfaces. Ceramic: CTE gradient from surface to core. 16

17 6 R-curve behavior (12) Laminates (2): CTE mismatch to introduce residual stresses CTE 10-6 / o C Si3N4 + X% TiN Si 3 N 4 Si 3 N 4 +30% TiN Si 3 N Temperature C TiN particle addition in Si 3 N 4 increases the CTE. Si 3 N 4 gives layers under compressive residual stress. Si 3 N 4 +TiN gives layer under tensile residual stress. 17

18 R-curve behavior (13) Laminates (3): Design Strong boundary layer interfaces. External layers under compressive stress. Si3N4 Si3N % TiN 150 μm Si3N4 600 μm 1 mm Si3N4 +TiN 10 µm Remark: Joining temperature ~1 100 C 18

19 R-curve behavior (14) Laminates (4): Apparent Fracture Toughness = toughness you will measure but isn t solely material related a 0.5mm Si 3 N 4 Si 3 N 4 +TiN Notch length a [mm] K Ic-app increases with notch length towards interface in compressive layer K Ic-app decreases in tensile layer. K Ic-app more than three times K Ic of Si 3 N 4. 19

20 R-curve behavior (15) Prediction only with residual stresses. Laminates (5): improved design Micro-layered laminates (with external tensile layers) What s more? crack bridging 20

21 R-curve behavior (16) Laminates (6): further improved design Micro-layered laminates (with external compressive tensile layers) K Ic app as function of crack length of the 2 nd micro-laminate design with external compressive layers superimposed onto WFA model. Suggested design and K Ic app behaviour of micro-laminate design with layers of five different compositions. Kuebler J., et.al., KEM 333 (2007)

22 Properties (FT1) Test methods for determination of fracture toughness K Ic (K Ic resistance displayed by a material to propagation of crack through it) SEPB SEVNB CNB IF SCF IS Fracture toughness should be qualified with the conditions under which the test is performed (e.g. method, test conditions, crack size, geometry, stress field, crack velocity). 22

23 Properties (FT2) SEVNB (and SEPB, SENB) Single Edge V-Notched Beam (and Single Edge Precracked Beam, Single Edge Notched Beam) F K Ic with = ( σ a Y ) = F B max W S1 S W 2 3 Γ M 2(1 α) a 3/ 2 Γ M and α = = α a W 2 ( α α ) α(1 α) (1 + α) 2 W S1 S2 a NC Si 3 N 4 c b β a S 5 μm 23

24 Properties (FT3) CN Chevron Notched Beam F not valid d K = max ' Ic Y m B F W 2 Y' m ( a a 0 ) S 1 S 2 = W 2 24

25 Properties (FT4) SCF Surface Crack in Flexure 1 Knoop hardness indent 2 polished surface remove 4 x h 2c a improve visibility Y max : larger of Y s and Y d 25

26 Properties (FT5) Fracture toughness values measured with various test methods in comparison with SEVNB values Frac. Toughness [MPa m] Alumina-999 SEPB (25/4) SEPB (26/5) Why those differences? CN (8/5) SCF (9/4) SCF (10/5) other methods, indiv. avg. SEVNB; G.P.Avg. SEVNB; G.P.Std.Dev. SCF+halo (10/5) SCF-N 2 (10/5) SEVNB-N 2 (1/5) SEVNB-H 2 O (1/5) Method (Participant / Number of Specimens) J. Kübler, ASTM STP 1409,

27 Properties (FT6) Vickers - IF Indentation Fracture K Ic = 0.032H a E H c - a 1-2 Development of Vickers indentation cracks What the V-IF actually measures in terms of fracture resistance cannot be readily defined. It is recommended that the V-IF technique no longer be acceptable for the fracture toughness testing of ceramic materials. H = F/2a (hardness) only valid if c/a > 2.5 F deformation zone crack starts G.D.Quinn, R.C.Bradt: J.Am.Ceram.Soc., 90 [3] (2007) 2c crack advances till surface 2a crack enlarges while deloading 27

28 Properties (FT7) Example: Micro-Hardness ( plasticity ) plastic deformation!! Si 3 N 4 05 Optical Glass BK7, HV-1N Scanning Probe Microscope 28

29 Strength (1) Determination of design relevant strength properties Fracture toughness Strength Crack growth / Lifetime Creep Relation between defect size and strength. Relation between strength and probability of failure. static dynamic Relation between crack growth speed and stress intensity factor. Relation between creep rate and load. K Ic 29

30 Strength (2) Strength of ceramics; evolution 30

31 Strength (3) Bend test Advantage simple (fixation of sample, simulation of environment, ) cheap (sample, jig, ) universal (strength, fracture toughness, Young s modulus, fatigue, ) sensitive to surface defects Disadvantage small volume tested stress gradient therefore not valid by plastic deformation σ B = M B W 31

32 Strength (4) 3- vs. 4-pt-bending 32

33 Strength (5) Measurement uncertainty Example: 4-Pt-bending elevated temperature σ 3 P d ( P, b, h, d ): = 2 b h P: load at failure r ΔP = 0.2 % b, h: size (3x4 mm) r Δb, r Δh = 0.07 % d: o/i rolls (10 mm) r Δd = 1.0 % (calculated from tolerances of test jig) Δy = n n= 1 d dx i f ( x1... xn ) 2 Δx i + m Δe m= 1 j law of failure propagation Relative measurement uncertainty: Δσ% 1.2 % Relevant factors, e.g.: σf 100 MPa / MPa Δe 1 > ± 2.7 % / < ± 0.3 % Δl jig (T related) Δe 2 ~ ± 3.0 % chem. surface Δe 3 ~ ± 5.0 % Remark: Considering uncertainty of TC ± 2.0 C, registration equipment Not considered: test speed variation, surface quality, rel. humidity Bending strength "Real" relative measurement uncertainty 100 MPa ± 1.2 % % % % = 11.9 % 1000 MPa ± 1.2 % % % % = 9.5 % 33

34 Strength (6) Scatter of mechanical strength f(σ c ) Dispersion density of the strength measured on a series of components σ c σ c1 σ c2 σ c ( σ ) f d = 1 0 c σ c P( σ c1 < σ c < σ c2 ) = σ c2 f σ c1 ( σ ) c dσ c σ ( σ ) F( σ = c c ) f c dσ c 0 34

35 Strength (7) Dispersion of the largest (failure relevant) defects and failure strengths h(a) f(σ c ) 1-F(σ c ) H(a) a σ c large largest defect low strength small largest defect high strength 35

36 Strength (8) Strength of a ceramic component single largest, but not failure relevant defect is defined by a combination of critical stress intensity factor size of critical defect position of critical defect stress and stress direction the crack sees failure relevant defect A large number of small defects present in a component are loaded too, but aren t responsible for catastrophic failure σ = f ( σ, K, ca,, σ, ac ) component Ic direction position therefore it s difficult to predict the strength of a component! single 36

37 Strength (9) Sources for defects during fabrication of component: always: powder agglomerates friction when pressing powder sedimentation when casting (slurry) always: cracks and pores from sintering during usage of component: corrosion, pitting subcritical crack growth, creep friction, scratches stress peaks (impact, ) (in ductile materials, e.g. in fcc-metals, stress peaks can be reduced by plastic deformation at RT due to 5 independent plains for sliding) ceramic materials are very brittle - they fail without warning even at elevated temperatures (K Ic is between 1 MPa m and 20 MPa m) increase of toughness in ceramics has to happen in a different way than over sliding and plastic deformation 37

38 Strength (10) Toughness defect size strength Tough metal Brittle metal Typical ceramic Brittle ceramic Good steel Cast iron Al 2 O 3 ; SiC glass, SiO 2 K Ic (MPa m) Defect dimension a for 100 MPa 320 mm 13 mm 510 µm 32 µm Defect dimension a for 500 MPa 13 mm 510 µm 20 µm 1.2 µm ~ 1 : (!!) 38

39 Strength (11) Two strategies 1) increase σ c by reducing a c, e.g. by improved processing to improve σ c and K Ic 2) increase K Ic by increasing fracture energy, e.g. by crack bridging, transformation toughening K Ic = 50 logσ c = 1 2 log a c + (log K Ic logy ) σ c (MPa) K Ic = 20 K Ic = 15 K Ic = 10 K Ic = 5 K Ic = 0.75 TZP+Al 2 O 3 Al 2 O 3 +ZrO 2 Y-TZP PSZ - glass Al2O3 2 O critical defect size (μm) 39

40 Strength (12) in ceramics strength controlling defects have a size of a few μm up to a few 100 μm failure relevant is the largest volume or surface defect under stress ceramic materials don t have a single strength value Summary identical components will not fail at one reproducible strength value (= strength value distribution) When is the density of defects small enough so that we can be absolutely sure that no defect with a critical size is present? density of defects defect size Never Statistical data is needed! The strength of ceramics is described by the Weibull statistics - see part 3. 40

41 Learning targets part 2 What you should know and understand, now! Improving toughness Fracture toughness is related to the work required to extend a crack and is determined by the details of the crack propagation process. It can be enhanced by increasing the energy required to extend the crack. Ceramics with R-curve behavior: - degradation in strength with increasing flaw size is less severe - reliability increases (some recent evidence shows that thermal shock resistance increases) Only for the fracture of the most brittle solids is the fracture toughness simply related to surface energy. Crack deflection, crack bridging, martensitic transformation (next to others) (and design) are mechanisms that enhance K Ic app. Know what you measure Fracture toughness values measured with different test methods may differ. Bend test: - universal (e.g. strength, fracture toughness) - sensitive to surface defects - only a small volume is tested - value σ 3Pt test > value σ 4PT test - specimen sees stress gradient (not valid by plastic deformation) 41

42 Learning targets part 2 Strength is just a value All components have defects due to fabrication and usage The strength controlling defects in ceramic components have a size of a few μm up to a few 100 μm The strength of a component is defined by a combination of - critical stress intensity factor - size of critical defect - position of critical defect - stress and stress direction the crack sees Identical components will not fail at one reproducible strength value = strength value distribution Ceramic materials fail without warning even at elevated temperatures K Ic is between 1 MPa m and 20 MPa m The aim is always to improve both - σ c by reducing a c, e.g. by improved processing -K Ic by increasing fracture energy, e.g. crack bridging, transformation toughening The strength of ceramics must be described by statistics 42