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

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 Connolly, Norfadhilah Ibrahim, Erhan Kilinç, Owen McGann, Jesús González Rodríguez, Damir Tadjiev, Ben Whittle, Peng Zeng • IAEA-ICTP

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

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

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

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

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

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

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

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 ]

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 ]

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 ]

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

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

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

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

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?

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

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