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

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Section 4 4.3.2. The relation between the particle location with respect to the crack tip and the CODvi- values As seen from Figures 4.18 - 4.20, the scatter of the CODvi-values is still high in all investigated specimens, but less than those of the CODi-values. The maximum CODvi-values seem to decrease with increasing aging conditions and with increasing particle volume fraction, leading to a narrowing of the scatter. Only for the cast MMCs, the CODi-values for the Specimens 160°C-200h are slightly higher in comparison with Specimens 160°C-24h. Contrary to the CODi-values, a slight tendency to decreasing CODvi-values with increasing particle location angle, θ, can be noted for the cast MMCs (Fig. 4.18). Whereas small CODvi- values appear at large angles between θ = 50 and 70° in the RT-condition, they are more equally distributed for the materials aged at 160°C. Very interesting are the crack profiles through alumina particles in cast MMCs with large particle location angle θ. For such particles, a step appears on both fracture surfaces, and the CODvi- and CODi-values are measured as the height differences of the two steps. Figure 4.21 presents an example of the profiles through Particle 7 of the Specimen Al2O3-10-RT, located at θ = 47°. Here, void initiation and fracture initiation occur simultaneously at a very low value of CODvi ≈ CODi ≈ 0. One can conclude that Particle 7 fractures at a low external loading, and the crack immediately extends. No dependency of the CODvi-values on the distance to the crack tip, r, is observed in both the cast and PM MMCs. The CODvi vs. r curves show a scatter similar to those of Figures 4.16, 4.17a (Figs. 4.19, 4.20a). It should be noted that no near-zero CODvi-values are observed for the PM MMCs in comparison with the cast MMCs. What might be a reason for such different effect of the angle θ on the CODvi-values in different materials? It is plausible that the void initiation might be strongly influenced by plastic straining. Therefore, it can suggested that this finding has to do with the shape of the plastic zone which has its maximum extension at an angle of about θ = 70° with respect to the crack plane (Fig. 4.22). For plane strain conditions, the plastic zone size in that direction, ω70, is by a factor 4.4 larger than in the crack plane [73, 74]. As was shown in [74], ω70 can be determined directly from the COD as 2 K J E ω70 = 0. 157 ≈ 0. 16 ≈ σ σ 2 y 51 2 y 0. 16 d N E σ COD o 2 y σ (4.2)
COD vi [µm] COD vi [µm] CODvi [µm] 15 10 5 0 15 10 5 0 15 10 5 0 Section 4 0 20 40 60 80 θ [ o ] a) 0 20 40 60 80 θ [°] b) 0 20 40 60 80 θ [ o ] 52 10 % RT 8h 24h 200h 15 % RT 8h 24h 200h 20 % RT 8h 24h 200h c) Fig. 4.18. The CODvi-values vs. the angle between crack tip and particle, θ, for different aging conditions of the cast MMCs: Specimens with (a) 10%, (b) 15%, (c) 20% Al2O3.
Page 1 and 2: MONTANUNIVERSITÄT MONTANUNIVERSIT
Page 3 and 4: 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: Cast MMCs 10%-RT 10%-8h 10%-24h 10%
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 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
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Table 9.1. 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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