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and vitrified wasteforms Russell J Hand ISL Department of - PowerPoint PPT Presentation

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Mechanical properties of glasses and vitrified wasteforms Russell J Hand ISL Department of Materials Science and Engineering University of Sheffield Acknowledgements Colleagues in the ISL, University of Sheffield Yordanos Bisrat, Andy

  1. Mechanical properties of glasses and vitrified wasteforms Russell J Hand ISL Department of Materials Science and Engineering University of Sheffield

  2. Acknowledgements • Colleagues in the ISL, University of Sheffield • Yordanos Bisrat, Andy Connolly, Norfadhilah Ibrahim, Erhan Kilinç, Owen McGann, Jesús González Rodríguez, Damir Tadjiev, Ben Whittle, Peng Zeng • IAEA-ICTP

  3. Background • Glasses are brittle (at RT) – Low toughness – Flaw sensitive – Low strains to failure – Usually low strength – Hard • Waste glasses are not usually annealed – Residual stresses – Cracking is expected in the canister • Handling strength supplied by the canister – Cracking increases the surface area available for attack by water once the canister is breached

  4. What can we measure? • Material properties – Modulus • Stiffness – Hardness Useful • Resistance to deformation – Fracture toughness • Resistance to crack growth – Brittleness • Hardness / fracture toughness • Sample property – Fracture strength • Depends on the defects present

  5. Moduli Normal stress E  Young's modulus, Normal strain Fractional lateral contraction   Poisson's ratio, Fractional longitudinal extension Shear stress G  Shear modulus, Shear strain Pressure K  Bulk modulus, Volumetric strain • Glasses are isotropic materials – Hence only 2 independent moduli E E   G K         2 1 3 1 2

  6. Modulus testing • Acoustic methods – Measure longitudinal, V l , and transverse (shear) velocities, V t  2 2 3 V 4 V     2 2 l t G V E V t  t 2 2 V V l t – Can also define a longitudinal modulus   2 M V l

  7. Modulus testing • Instrumented (nano-)indentation – Analysis of the unload curve gives reduced modulus     2 2 1 1 1   g i E E E – where r i g Load • i indicates properties of the indenter • g indicates properties of the glass Indentation depth – From this we can obtain the plane strain modulus       2 E 1 1 1         g 4 i E 1   1  8.721 10    2 1  E E   E  g r i r • For a diamond indenter and where E’ and E r are in GPa

  8. Young’s modulus 80 • Generally increases with T g Data from SciGlass database Shear modulus /GPa BUT atomic packing density 60 also important  40 i i • For a glass A B x y i 20     3 3 f xr yr  i i B 4 A i i 0  i C 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0  g 3 N fM T g / T 1 i i i 0.45 Rouxel Data from SciGlass database Data used by Rouxel Makashima & Mackenzie 0.35 Poisson's ratio 0.25 0.15 0.05 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Packing density

  9. Isomechanical groups • Originally used in analysis of crystalline bk T G  B m materials  – Different structures give different values of b bRT • For glasses  m G M V 40 35 Li borates (Kodama) 30 Na borates (Kodama) K borates (Kodama) G /GPa 25 Cs borates (Kodama) Rb borates (Kodama) 20 Sodium borosilicates SLS (Tille) 15 SLS (Kilinc & Hand) Ba titanosilicates 10 5 0.10 0.15 0.20 0.25 0.30 0.35 0.40 RT g / M v

  10. Moduli 80 Young's modulus /GPa • Data of Zheng et al. (2012) 75 – Nominal composition 70 15Na 2 O  x Al 2 O 3  5B 2 O 3  (80 – x )SiO 2 65 Increasing NBOs – x = 0, 1, 2.5, 5, 7.5, 10, 12.5, 15, Increasing NBOs due to Na 2 O due to Al 2 O 3 17.5, 20 60 -6 -4 -2 0 2 4 6 8 10 12 – Minimum in moduli when no [Na 2 O] [Al 2 O 3 ] N 4 x[B 2 O 3 ] NBOs 44 34 Shear modulus /GPa Bulk modulus /GPa Increasing NBOs Increasing NBOs due to Na 2 O due to Al 2 O 3 42 32 40 30 38 28 Increasing NBOs Increasing NBOs due to Na 2 O due to Al 2 O 3 36 26 -6 -4 -2 0 2 4 6 8 10 12 -6 -4 -2 0 2 4 6 8 10 12 [Na 2 O] [Al 2 O 3 ] N 4 x[B 2 O 3 ] [Na 2 O] [Al 2 O 3 ] N 4 x[B 2 O 3 ]

  11. Moduli 80 Young's modulus /GPa • Data of Potuzak et al (2014) 75 – Nominal composition 70 12Na 2 O  6MO  x Al 2 O 3  6B 2 O 3  MgO (76 – x )SiO 2 65 Increasing NBOs Increasing NBOs CaO due to Al 2 O 3 due to Na 2 O + RO SrO – M = Mg, Ca, Sr and Ba BaO 60 -15 -10 -5 0 5 10 15 – x = 0, 3, 6, 9, 12, 15, 18, 21, [Na 2 O]+[MO] [Al 2 O 3 ] [B 2 O 3 ] and 24 – Position of minima in E and 50 48 G depends on alkaline earth Bulk modulus /GPa 46 • Larger alkaline earths are less 44 capable of creating B 4 units 42 – But no clear minima for 40 MgO Increasing NBOs Increasing NBOs bulk moduli or Poisson’s 38 CaO due to Al 2 O 3 due to Na 2 O + RO SrO ratio 36 BaO -15 -10 -5 0 5 10 15 [Na 2 O]+[MO] [Al 2 O 3 ] [B 2 O 3 ]

  12. 80 Moduli N 7.6 M 1.1 C 3 B 7.6 A x S 79 x Young's modulus /GPa N 15 C 5 A x B 10 x S 70 75 N 15 C 5 A x B 20 x S 60 N 15 C x A 15 x B 10 S 60 • However this sort N 15 Ba x A 15 x B 10 S 60 70 N 10 C x A 20 x B 10 S 60 N 10 Ba x A 20 x B 10 S 60 of relationship is N 10 C x A 2 B 10 S 78 x 65 N 15 C x A 2 B 10 S 73 x N 10 C x Ba 2 A y B 10 S 78 x y not always seen 60 -20 -15 -10 -5 0 5 10 15 20 – Ibrahim & Hand [M 2 O+M'O] [Al 2 O 3 ] [B 2 O 3 ] (unpublished data) 35 N 7.6 M 1.1 C 3 B 7.6 A x S 79 x Shear modulus /GPa N 15 C 5 A x B 10 x S 70 N 15 C 5 A x B 20 x S 60 30 N 15 C x A 15 x B 10 S 60 N 15 Ba x A 15 x B 10 S 60 N 10 C x A 20 x B 10 S 60 N 10 Ba x A 20 x B 10 S 60 25 N 10 C x A 2 B 10 S 78 x N 15 C x A 2 B 10 S 73 x N 10 C x Ba 2 A y B 10 S 78 x y 20 -20 -15 -10 -5 0 5 10 15 20 [M 2 O+M'O] [Al 2 O 3 ] [B 2 O 3 ]

  13. Hardness • Resistance of a material to permanent penetration by another harder material • Usually measured via indentation • indentation load Projected area H  or actual surface area indentation area 12 • Exact form depends on 9 indenter geometry Hardness /GPa • May be expressed as a 6 hardness number or in GPa 3 – The latter is more common when dealing with glass 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 T g / T 1 Data from SciGlass database

  14. Hardness • Vicker’s indentation • Berkovich – Pyramid shaped 68 ᵒ indentation indenter – Surface area of – Used in indentation nanoindentation • Instrumented tests 0.4635 P  H 2 a • Measure H and E V 2 a – Surface area of • Knoop indentation indentation – Elongated pyramid – Has the same b indenter area/depth a dependence as – Projected area Vickers indentation 14.2 P  • Standard H K 2 a Berkovich – same 65.3  – Some authors claim actual area on unloading b  b ’ P • Modified  max H ( a is little changed) Berkovich – same A projected area 0.45 Ha  E   b b

  15. Hardness • Nuclear borosilicates relatively high hardnesses and Young’s moduli 9.5 14 Indentation hardness /GPa Nuclear borosils 9.0 UK HLW glass 12 SciGlass E Novel ILW glasses Other silicates 8.5 Other nuclear glasses Hardness /GPa 10 8.0 8 7.5 6 7.0 4 6.5 2 6.0 5.5 0 78 80 82 84 86 88 90 0 20 40 60 80 100 120 140 160 E /GPa Plane strain modulus /GPa

  16. Fracture toughness • Intrinsic resistance of a T = Fracture toughness K Ic = Critical stress intensity factor material to crack growth for failure     K T C a Ic Normally report mode I – – σ is strength opening mode – a is crack depth Mode 1 Mode 2 Mode 3 – C is a “geometric” constant y x y x x y • Material property z z z – Residual stresses will Diagram taken from J Lemaitre & J-L affect results Chaboche Mechanics of Solid Materials             K C a C a T C a Ic r r

  17. Fracture toughness testing • General procedure is to introduce a controlled defect and measure stress at which failure occurs – Plane strain fracture toughness – Related to initiation of crack growth • Controlled defect – Metals • Notch and then fatigue pre-crack. – Brittle materials • Notch and then?

  18. Single edge notched bend (SENB) test • ASTM C1421-10 • Crack “popped - in” from pre -sawn notch or line of   a indents  W  1/2 K f   a I max       2       a a a a         1.99  1  2.15 3.93   2.7            W W W W        a  f W     3/2    a a    1 2  1  F    W W b 3 FL   max 2 2 bW W a a   0.35 0.6 L W

  19. Single edge notched bend (SENB) test • Can use indents as the strength controlling defect 1/8     E 3/4    1/3 T   F – Vicker’s indent f   H – Knoop indent • Newman and Raju solution for SIF • In this case ASTM standard specifies grinding back much of the indent to leave sub-surface crack • Also recommends no annealing • But residual stresses arises from – Indentation of glass – Grinding and polishing of glass • These will affect crack initiation

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