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

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Section 7 Fig. 7.2. The principle of the equal channel angular pressing. For this reason, a deformation method would be advantageous which induces intense strains into the sample without any change of the sample size. The equal channel angular pressing (ECAP) might be an effective tool to solve this problem. In this method, intense plastic strains are induced into massive billets without changing their cross section [79]. The ECAP facility consists of two channels which are equal in cross section (Fig. 7.2). The channels are intersected at a certain angle, ϕ. Another important parameter describing the ECAP facility is the angle subtended by the arc curvature, ψ. A sample is usually subjected to a multiple pressing through a die. An analysis performed in [80] has shown that the strains introduced into a sample during ECAP are a function of the angles ϕ and ψ, and the number of ECAP passes, N, ε Die ECAP = Plunger N ⎡ ⎛ ϕ ψ ⎞ ⎛ ϕ ψ ⎞⎤ ⎢2cot⎜ + ⎟ + ψ ⋅ csc⎜ + ⎟⎥ . (7.4) 3 ⎣ ⎝ 2 2 ⎠ ⎝ 2 2 ⎠⎦ The extrusion ratio, R, in Eq (7.1) is considered as a measure of strain induced into the sample. Actually, it is equal to the ratio of the final length of the sample after extrusion, lf, to 81 Sample
Section 7 its initial length, li. On the other hand, this ratio can be also presented as a function of the true strain induced into the sample by extrusion (Eq. 7.5) which follows from the general determination of the true strain, ε = ln (lf / li), R = exp (ε ). (7.5) In the case of two step extrusion with extrusion ratios R1 and R2, a total extrusion ratio can be determined as R = R1⋅ R2. So, if we combine extrusion and ECAP, a total extrusion ratio can be presented as R = Rext ⋅ RECAP . (7.6) According to Eq. 7.5, RECAP can be determined as RECAP = exp (εECAP) or, taking into account Eq. 7.4, as R ECAP ⎡ N ⎡ ⎛ ϕ ψ ⎞ ⎛ ϕ ψ ⎞⎤⎤ = exp⎢ ⎢2cot⎜ + ⎟ + ψ ⋅ csc⎜ + ⎟⎥⎥ . (7.7) ⎣ 3 ⎣ ⎝ 2 2 ⎠ ⎝ 2 2 ⎠⎦⎦ Inserting Eq. 7.7 into Eq. 7.6, and obtained result into Eq. 7.1, we get the model for the case of combination of extrusion with ECAP d c d m = . (7.8) 1/ 3 ⎡⎛ π ⎞ ⎤ ⎡ N ⎡ ⎛ ϕ ψ ⎞ ⎛ ϕ ψ ⎞⎤⎤ ⎢⎜ ⎟ −1⎥ Rext exp⎢ ⋅ ⎢2cot⎜ + ⎟ + ψ ⋅ csc⎜ + ⎟⎥⎥ ⎢⎣ ⎝ 6 f ⎠ ⎥⎦ ⎣ 3 ⎣ ⎝ 2 2 ⎠ ⎝ 2 2 ⎠⎦⎦ Here, both the strains introduced during extrusion and ECAP are taken into account. It should be noted that ECAP has been used so far just for processing of the bulk nanostructured materials [79]. There have been already attempts to subject MMCs to ECAP in order to refine grains. In [81], a cast Al6061 MMC reinforced by 10% Al2O3 particles having a size in the range of 6…13 µm was subjected to ECAP. The samples were pressed for 8 passes at 400°C plus additional 2 passes at 200°C in order to give a total strain of ∼10. Detailed measurements indicated that there was little or no breaking of the Al2O3 particles during the ECAP. Significant grain refinement and increase of the composite strength by almost a factor of 2 was observed. But the material did not have any particle clusters initially. Therefore, the evolution of uniformity of particle distribution was not investigated. 82
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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
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Section 3 The Eshelby tensor does n
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equivalent stress Section 3 Fig. 3.
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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 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: Section 7 7.2. A model by Tan and Z
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.
Page 127 and 128: 1 2 1 2 3 3 4 4 126 5 5 6 9 7 50 µ
Page 129 and 130: 1 1 2 2 3 4 3 4 5 5 128 6 7 6 7 50
Page 131 and 132: 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. 9.16. Fracture surface with ma
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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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