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

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Section 6 6. Comparison of the local and global fracture properties In theoretical models to predict the fracture toughness in MMCs, the fracture toughness was estimated as a function of global material properties, such as average particle size, particle volume fraction, etc. (Eqs 2.1, 2.2) [2, 17, 54]. However, the results of our investigation clearly show that the local fracture properties significantly vary along the crack front. It can be assumed that the local fracture properties determine in some unknown way the global fracture properties. Therefore, it is interesting to compare the individual local values of the fracture initiation toughness along the crack front to the global fracture initiation toughness measured in the fracture mechanics experiments. In Figure 6.1, experimentally determined Ji- values (taken from Tables 4.2, 4.3) are compared to the Ji-values calculated from the average value of the CODi (including near-zero values) (Table 4.5) through the Eq. 3.2. In spite of the high scatter of the values of the local fracture toughness observed in our investigated materials, their average values correlate well with experimentally determined values of the global fracture toughness. A very good correlation is found for the cast MMCs with 10% and 20% Al2O3 particles in all aging conditions (Fig. 6.1c) and for the mild steel St37 (Fig. 6.2b). For the cast MMCs with 15%, a good correlation is observed for the specimen aged at room temperature; at other aging conditions the correlation becomes worse but still remains in the range of the standard deviation (Fig. 6.1a,b). For the PM MMC, Ji-values which are determined by the fracture mechanics experiment are close to the bottom boundary of the standard deviation of the Ji-values calculated from the average value of the CODi (Fig. 6.2a). This can be explained when it is assumed that the fracture of one particle might trigger the fracture of the neighboring particles within a certain region so that the area of local crack extension is larger than the resolution of the potential drop technique. The larger particle size (100 µm, compared to 10 µm for the cast MMC) facilitates this effect. So on, for the cast MMCs and the steel St37, it can be proposed that the global fracture toughness of any material can be estimated as J n ∑ global i = 1 75 J n local i , (6.1)
Section 6 where n is the number of considered local Ji-values. The Eq. 6.1. is not valid for the PM MMCs due to their brittleness. From these results it can be concluded, that the process of fracture in materials should be considered not only at the global level (as has been done so far), but at the local level, as well. Of course, in the first approach, the local fracture properties seem to be not so important for the fracture mechanics operating at the global level. But results obtained in current research can be very useful not only for improvement of application of damage mechanics at the local level, but they might have even industrial application for the cases where a high level of safety of structures is required. For instance, from results of this research, it can be advised to estimate the critical conditions for void initiation for such structures not in terms of the average particle size (as has been done so far), but in terms of the maximum particle size, since the largest particles are critical. 76
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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
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Section 1 The main results of this
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Section 2 2.2. The influence of the
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Section 2 high strength, fine reinf
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Section 2 etched to mark the inclus
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Section 2 (4.) The specimen prepara
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Section 3 Fig. 3.1. The digital ele
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height [µm] height [µm] 10 0 -10
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Section 3 Fig. 3.5. The observation
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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 and 58: Section 4 Table 4.6. The values of
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: σ interf [MPa] σ interf [MPa] σ
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 113 and 114: Table 9.11. Data on stress for Spec
Page 119 and 120: Table 9.17. Results of the stereoph
Page 121 and 122: 1 2 1 2 3 3 4 5 6 5 9 119 7 7 8 9 6
Page 123 and 124: 8 9 10 6 10 122 11 12 13 14 11 12 1
Page 125 and 126: 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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