dissertation global and local fracture properties of metal matrix ...

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Table 4.7. The detailed results of the calculation procedure for Particle 4 of Specimen Al2O3- 10-RT . The particle coordinates are r = 30.5 µm, θ = 30°, and the COD at void initiation is CODvi = 7 µm. The particle and matrix stress and strain tensors are evaluated via an iterative Stress tensor [MPa] procedure. The final value of the secant modulus of the matrix was Es m = 14.46 GPa. ⎛516 ⎜ ⎜ 37 ⎜ ⎝ 0 Mesoscopic Particle Matrix 37 735 0 0 ⎞ ⎟ 0 ⎟ 623⎟ ⎠ ⎛385 ⎜ ⎜ 79 ⎜ ⎝ 0 79 845 0 0 ⎞ ⎟ 0 ⎟ 609⎟ ⎠ ⎛531 33 0 ⎞ ⎜ ⎟ ⎜ 33 723 0 ⎟ ⎜ ⎟ ⎝ 0 0 624⎠ ⎛σ 1 ⎞ Principal stresses ⎜ ⎟ ⎜σ 2 ⎟ ⎜ ⎟ ⎝σ 3 ⎠ [MPa] ⎛ 741⎞ ⎜ ⎟ ⎜623⎟ ⎜ ⎟ ⎝510⎠ ⎛858⎞ ⎜ ⎟ ⎜609⎟ ⎜ ⎟ ⎝372⎠ ⎛728⎞ ⎜ ⎟ ⎜624⎟ ⎜ ⎟ ⎝525⎠ Maximal Shear Stress [MPa] 116 243 101 Equivalent stress [MPa] 200 421 176 Mean stress [MPa] 625 613 626 Stress triaxiality 3.1 1.5 3.6 Strain tensor ⎛− 0 . 0088 ⎜ ⎜ 0. 0031 ⎜ ⎝ 0 0. 0031 0. 0092 0 0 ⎞ ⎟ 0 ⎟ -8 - 7x10 ⎟ ⎠ ⎛ × ⎜ ⎜ ⎜ ⎝ −5 8 10 0. 00023 0 0. 00023 0. 00141 0 0 ⎞ ⎟ 0 ⎟ ⎟ 0. 00073⎠ ⎛−0. 0098 ⎜ ⎜ 0. 0034 ⎜ ⎝ 0 0. 0034 0. 0101 Maximal shear strain 0.0095 0.0007 0.0105 Equivalent strain 0.0106 0.0009 0.0117 0 0 ⎞ ⎟ 0 ⎟ −5 −8× 10 ⎟ ⎠
σ p max [MPa] σ p max [MPa] σ p max [MPa] 1600 1200 800 400 0 1600 1200 800 400 0 1600 1200 800 400 0 Section 4 0 20 40 60 80 θ [ o ] a) 0 20 40 60 80 θ [ o ] b) 0 20 40 60 80 θ [ o ] 58 10 % RT 8h 24h 200h 15 % RT 8h 24h 200h 20 % RT 8h 24h 200h c) Fig. 4.23. The σ p max-values vs. the distance between crack tip and particle, r, for different aging conditions of the cast MMCs: Specimens with (a) 10%, (b) 15%, (c) 20% Al2O3.
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MONTANUNIVERSITÄT MONTANUNIVERSIT
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TABLE OF CONTENTS 1. Introduction 5
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7.4.4. The effect of ECAP on the lo
Page 7 and 8: Section 1 The main results of this
Page 9 and 10: Section 2 2.2. The influence of the
Page 11 and 12: Section 2 high strength, fine reinf
Page 13 and 14: Section 2 etched to mark the inclus
Page 15 and 16: Section 2 (4.) The specimen prepara
Page 17 and 18: Section 3 Fig. 3.1. The digital ele
Page 19 and 20: height [µm] height [µm] 10 0 -10
Page 21 and 22: Section 3 Fig. 3.5. The observation
Page 23 and 24: Section 3 3.3.2. The determination
Page 25 and 26: Section 3 The Eshelby tensor does n
Page 27 and 28: equivalent stress Section 3 Fig. 3.
Page 29 and 30: Assume σ m eq Calculate matrix sec
Page 31 and 32: Section 4 Table 4.1. Chemical compo
Page 33 and 34: 4.1.1.3. Fracture mechanics tests S
Page 35 and 36: Section 4 Fig. 4.4. A view of a com
Page 37 and 38: Section 4 Table 4.3. Mechanical pro
Page 39 and 40: εfr [%] εfr [%] N 16 12 8 4 0 150
Page 41 and 42: Section 4 4.2. The effect of the he
Page 43 and 44: Section 4 It should be noted that n
Page 45 and 46: CODi [µm] 40 30 20 10 0 Section 4
Page 47 and 48: Section 4 Table 4.4. Results of the
Page 49 and 50: CODi [µm] COD i [µm] CODi [µm] 2
Page 51 and 52: Cast MMCs 10%-RT 10%-8h 10%-24h 10%
Page 53 and 54: COD vi [µm] COD vi [µm] CODvi [µ
Page 55 and 56: CODvi [µm] CODvi [µm] 80 60 40 20
Page 57: Section 4 Table 4.6. The values of
Page 61 and 62: σ p max [MPa] σ p max [MPa] 1200
Page 63 and 64: σ interf max [MPa] σ interf max [
Page 65 and 66: Section 4 4.5. The relation between
Page 67 and 68: Section 4 Table 4.9. Conditions for
Page 69 and 70: Ln(Ln(1/(1-F σ))) Ln(Ln(1/(1-F σ)
Page 71 and 72: Section 5 diameter of 2…8 µm and
Page 73 and 74: MnS-inclusion r θ MnS-inclusion Se
Page 75 and 76: σ interf [MPa] σ interf [MPa] σ
Page 77 and 78: Section 6 where n is the number of
Page 79 and 80: Ji [kN/m] J i [kN/m] 25 20 15 10 5
Page 81 and 82: Section 7 7.2. A model by Tan and Z
Page 83 and 84: Section 7 its initial length, li. O
Page 85 and 86: 1 µm Section 7 5 µm Fig. 7.3. A s
Page 87 and 88: Section 7 a) b) c) Fig. 7.4. Micros
Page 89 and 90: Section 7 It is important that no p
Page 91 and 92: Section 7 between the Rtot and the
Page 93 and 94: Section 7 Fig. 7.8. The fracture su
Page 95 and 96: 10 z [mm] 5 -10 -15 Section 7 0 -20
Page 97 and 98: Section 7 Table 7.3. Data on measur
Page 99 and 100: 8. Summary Section 8 This work deal
Page 101 and 102: Section 8 The effect of the homogen
Page 103 and 104: Table 9.1. Data on stress for Speci
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Table 9.7. Data on stress for Speci
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Table 9.9. Data on stress for Speci
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Table 9.11. Data on stress for Spec
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Table 9.17. Results of the stereoph
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1 2 1 2 3 3 4 5 6 5 9 119 7 7 8 9 6
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8 9 10 6 10 122 11 12 13 14 11 12 1
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9 10 11 12 13 124 50 µm Fig. 9.6.
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1 2 1 2 3 3 4 4 126 5 5 6 9 7 50 µ
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1 1 2 2 3 4 3 4 5 5 128 6 7 6 7 50
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Fig. 9.12. Fracture surface with ma
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1 2 3 1 2 3 4 5 6 7 8 9 10 4 5 132
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Fig. 12.36. Fracture surface of the
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[14] Lewandowski JJ, Liu C, Hunt WH
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[42] Rice JR, Rosengren GF. Plane s
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[70] ASTM E1820-01, “Standard Tes
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