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

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Section 4 plane strain conditions, a similar stress triaxiality, σ c m/σ c eq, can be assumed for all specimens in front of the crack tip. Therefore, the composite mean stress, σm c , and, consequently, the mesoscopic maximum principal stress at void initiation, σ HRR max, will be proportional to σy. As the microscopic maximum principal particle stresses lie between 150 and 200 MPa higher than the meso-scale values (Tables 9.1-9.16), a linear relation between the σ p max-values and σy can be expected as is observed in Figure 4.29. What could be the physical reason for an increase of the maximum interfacial stresses? It is plausible that this finding has to do with the presence of the spinel phase MgAl2O4 at the particle/matrix interface. A spinel phase potentially can form strong chemical bonds with both metals and ceramics [71]. It has been suggested that this spinel phase may enhance the interfacial bonding. Thus, the interface bonding may be enhanced by a longer aging time, as the percentage of the interface covered by the spinel phase increases with increasing aging time [21]. Table 4.8. Conditions for void initiation in the cast MMCs (average values). Fractured particles Debonded particles Specimen Number average of particles σ max p average fr [MPa] σ max interf Number average fr [MPa] of particles σ max p dec [MPa] Al2O3-10-RT 13 867±84 823±89 3 984±88 943±66 65 average σ max interf dec [MPa] Al2O3-10-8h 10 993±53 947±55 4 977±37 935±25 Al2O3-10-24h 10 1090±78 1036±86 7 1173±41 1120±32 Al2O3-10-200h 3 1198±89 1115±97 12 1275±47 1195±47 Al2O3-15-RT 14 974±58 936±60 0 - - Al2O3-15-8h 11 1157±71 1107±73 5 1203±21 1151±21 Al2O3-15-24h 16 1331±31 1267±29 4 1367±36 1302±32 Al2O3-15-200h 3 1264±46 1209±14 13 1245±28 1214±48 Al2O3-20-RT 9 818±94 808±93 1 834 828 Al2O3-20-8h 12 1180±46 1147±47 0 - - Al2O3-20-24h 5 1175±125 1142±132 5 1265±25 1231±28 Al2O3-20-200h 8 1217±36 1185±41 7 1263±24 1245±25
Section 4 Table 4.9. Conditions for void initiation in the PM-MMCs. Specimen Number of particles σ max p fr [MPa] SiC-10-15min 15 803±86 730±80 66 σ max interf fr [MPa] SiC-10-8h 15 - - SiC-10-24h 15 - - SiC-10-200h 19 961±80 927±54 4.6. Application of Weibull distribution for fractured particles As the MMCs are reinforced by ceramic particles, a Weibull distribution can be assumed for the distributions of particle strengths. Such a distribution is often used for brittle materials [75-77]: F(σ) = 1-exp[-(σ /σ0) m ], (4.3) where F(σ) is the failure probability at the stress σ, σ0 is the characteristic stress, and m is the Weibull modulus which describes the distribution of the measured strengths. The higher the Weibull modulus, the smaller is the scatter of the strengths. The maximum principal stresses of the particles at the moment of void initiation are taken as σ. In Figures 4.30a and 4.31a, Weibull diagrams for alumina particles in the cast MMC with 10% of the Al2O3 particles and for SiC particles in some specimens of the PM-MMC are given. As seen, the Weibull modulus lies in the range 16..21 for Al2O3 and 9…10 for SiC particles. The high scatter of the Weibull modulus for the alumina particles can be explained by the small number of particles which has been available. As was shown in [75], the uncertainties of the calculated parameter strongly depend on the sample size, N. The uncertainties can be very high in the case of small sample size. For instance, the 95% confidence interval for the determined Weibull modulus m can lie for N = 10 between 70% and 230% of the real modulus. The accuracy of determination of m can be increased through increase of number of specimens (in our case, particles). Indeed, if all analysed Al2O3 particles are taken from all cast specimens (Fig. 4.30b), one gets the Weibull modulus m = 9, which is in a good accordance with experimentally determined values for Al2O3 [77].
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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
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 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: Section 4 4.5. The relation between
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 113 and 114: Table 9.11. Data on stress for Spec
Page 115 and 116: Table 9.13. Data on stress for Spec
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Table 9.15. 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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