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

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Section 7 Table 7.1. Data on the critical particle size for the PM-MMC Al6061-20%Al2O3 before and after different number of ECAP passes. Number of ECAP passes 0 4 7 dc [µm] 33.4 4.1 0.9 The rod of investigated material is cut into samples with a length of 100 mm. These samples are heated to 370°C and pressed repeatedly through the ECAP die. The parameters of the ECAP die are ϕ = 90° and ψ = 20°. The material is subjected to 4 and 7 ECAP passes. The choice of these numbers of the ECAP passes can by explained by results of calculations given in Table 8.1. Here, the critical values of the particle size determined by Eq. 7.8 are presented for the as-fabricated MMC, and the MMC after 4 and 7 ECAP passes. It is seen that the increase of number of ECAP passes significantly decreases the dc-value. dc = 33.4 µm for the as-fabricated MMCs, thus, the strongly clustered particle distribution is expected for this material. After 4 ECAP passes, the dc-value decreases up to 4.1 µm. Taking into account that the particle size in investigated material is in the range of 1…5 µm, particle clusters should start to scatter. After 7 ECAP passes, the dc = 0.9 µm. Since this value is less than the lowest bound of the particle size, a homogeneous particle distribution after 7 ECAP passes can be expected. 7.3. A quadrat method to estimate the homogeneity of the particle distribution in the metal matrix composites Different methods to estimate the homogeneity of the particle distribution in the MMCs have been proposed: the mean free path, the nearest neighbour distance, the radial distribution function, and the quadrat method [82]. As was found in [82], for the MMCs with strongly clustered particle distribution, the quadrat method is more effective to detect pronounced changes in the MMC microstructure in comparison to other methods. With the quadrat method, the image to be studied is divided into a grid of square cells and the number of particles in each cell is counted [83]. In general, an ordered particle distribution would be expected to generate a large number of quadrats containing approximately the same number of particles, whereas a clustered distribution would be expected to produce a combination of empty quadrats, quadrats with a small number of particles, and quadrats with many particles. 83
1 µm Section 7 5 µm Fig. 7.3. A schematic view of the quadrat method for the PM-MMC Al6061-20%Al2O3. The major problem of the quadrat method is to determine the optimum quadrat size. Non- randomness is highly dependent on the size of the sample quadrat. In this study, the problem becomes more complicated due to the difference in the size of the reinforcements. According to [82], the optimum quadrat size is twice the size of the mean area per particle. If for our material the particle size is set to 3 µm (which lies in the middle of the range of observed particle sizes), the quadrat size becomes a = 8.5 µm. Qualitative analysis of the microstructures shows that this quadrat size seems to be the optimum value for this investigation. In Figure 7.3, a schematic view of the quadrat method for our case is presented. The particles that belong to different quadrats are painted in different colours. One can see that a lower a-value could artificially decrease the number of particles in the quadrats corresponding to clusters containing large particles (5 µm). At the same time, higher a-values could significantly decrease the number of empty quadrats and tend to give the same number of particles in each quadrat, irrespective of the presence of clusters. For the microstructural investigation, the rods are sectioned in the longitudinal direction, grinded, polished, and investigated in the SEM. 9 micrographs from the center region of the specimens are taken in the SEM, each covering an area of 130×100 µm. Each image is divided into 140 quadrats. The histograms of the particle per quadrat distribution for each material condition are plotted. These histograms are compared with theoretical distributions: 84 a =8.5 µm
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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
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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 and 82: Section 7 7.2. A model by Tan and Z
Page 83: Section 7 its initial length, li. O
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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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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