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

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z [µm] 30 20 10 0 -10 -20 COD vi 0 µm Θ r particle Section 4 -30 x [µm] -80 -40 0 40 80 Fig. 4.21. Crack profile through the Particle 7 of Specimen Al2O3-10-RT in the moment of void initiation: CODvi ≈ CODi ≈ 0. The values calculated by Eq. 4.2 for the specimens Al2O3-10-RT and SiC-10-24h in comparison with observed distances between particles and crack tip are given in Table 4.6. One can see that even for a very low COD of 0.2 µm, the maximum extension of the plastic zone for the cast MMC becomes comparable to the distances to nearest particles. As a result, the fracture of particles, that lie in the direction of the maximum extension of the plastic zone, can occur at very low COD. At the same time, for the PM MMC, the distance between the SiC particles and the crack tip, r, is significantly higher in comparison with ω70, i.e., the Fig. 4.22. The plastic zone shape for plane strain condition. 55
Section 4 Table 4.6. The values of the plastic zone size at angles θ =0°, 70° and the distance between particles and the crack tip at COD = 0.2 µm Material ω70 [µm] ω0 [µm] r[µm] cast Al2O3-10-RT 40 9.1 10…50 PM SiC-10-24h 12 2.7 50…300 maximum extension of the plastic zone at near-zero values is not comparable with the distance to the nearest SiC particle. So no near-zero CODvi-values can be observed for this material. 4.4. The maximum particle stresses at the moment of void initiation The stress tensors for both the particles and the matrix were calculated for investigated MMCs according to the procedure described in Section 4. In Table 4.7, the results of calculation for Particle 4 of Specimen Al2O3-10-RT (Fig. 9.1, Tab. 9.1) are presented as example. Figures 4.23-4.25, the maximum particle stresses at the moment of the void initiation are plotted against the angle to the crack plane, θ, and the distance to the crack tip, r, for the cast and PM MMCs. In comparison to the very large scatter of the CODi- and CODvi- values (Figs. 4.15- 4.20), the scatter of the σ p max-values is much lower. The stresses vary between 800 and 1400 MPa for the alumina particles in the cast MMCs and between 700 and 1100 MPa for SiC particles in the PM MMCs. The σ p max-values for alumina particles are nearly independent of the angle to the crack plane, θ, (Fig. 4.23). A slight decrease may be found for particles which lie at angles larger than θ ≈ 55°. A slight decrease of the σ p max-values with increasing r is observed for the cast MMCs in Figure 4.24. For the PM MMCs, the stress tensors were calculated only for specimens SiC-10%-15 min. and SiC-10%-200h. In other specimens, the particle fracture occurs in the elastic region, where the mean-field approach fails and cannot be used to determine the stress states in constituent phases. 56
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MONTANUNIVERSITÄT MONTANUNIVERSIT
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TABLE OF CONTENTS 1. Introduction 5
Page 5 and 6: 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: CODvi [µm] CODvi [µm] 80 60 40 20
Page 59 and 60: σ p max [MPa] σ p max [MPa] σ p
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
Page 105 and 106: Table 9.3. Data on stress for Speci
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Table 9.5. 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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