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

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Section 4 Fig 4.2. A view of a tensile test specimen of the cast Al6061 MMC fixed in the holders for Material E tensile test. Table 4.2. Mechanical properties of the cast Al6061 MMCs. [GPa] σy [MPa] σUTS [MPa] εfr [%] N α dn Ji 31 [kN/m] J0.2 / Bl [kN/m] Al2O3-0-RT 71 167 290 16.0 0.26 4.34 0.36 42.4 150.4 Al2O3-0-8h 71 218 300 13.3 0.19 4.39 0.47 28.2 63.5 Al2O3-0-24h 71 260 288 8.0 0.07 1.43 0.61 14.0 28.8 Al2O3-0-200h 71 303 309 4.0 0.03 1.76 0.73 9.8 25.2 Jic (HR) [kN/m] Al2O3-10-RT 86 185 318 14.8 0.20 2.21 0.37 5.0 10.4 10.5 3.2 Al2O3-10-8h 86 281 334 9.4 0.12 3.39 0.56 4.1 6.5 16.0 3.2 Al2O3-10-24h 86 320 354 3.5 0.07 1.58 0.63 4.8 6.4 18.2 3.2 Al2O3-10-200h 86 342 361 2.8 0.03 0.79 0.69 2.5 4.5 19.4 3.2 Al2O3-15-RT 95 224 333 7.5 0.15 1.22 0.43 2.9 6.5 11.1 2.9 Al2O3-15-8h 95 318 368 4.0 0.07 0.79 0.59 3.0 6.4 15.8 3.0 Al2O3-15-24h 95 351 388 1.1 0.04 0.18 0.65 1.2 5.7 17.4 3.0 Al2O3-15-200h 95 351 373 1.1 0.03 0.39 0.70 1.7 4.4 17.4 2.8 Al2O3-20-RT 104 228 324 6.3 0.14 1.44 0.45 2.7 6.5 10.3 2.6 Al2O3-20-8h 104 329 372 1.5 0.06 0.57 0.60 1.8 3.7 14.8 2.8 Al2O3-20-24h 104 349 379 1.1 0.05 0.79 0.64 1.2 3.6 15.7 2.8 Al2O3-20-200h 104 365 381 1.0 0.03 0.65 0.71 1.3 2.5 16.5 2.6 Jic (P) [kN/m]
4.1.1.3. Fracture mechanics tests Section 4 Compact tension (CT) specimens with a thickness of B = 12.5 mm, a width of W = 40 mm, and an initial crack length of a0 ≈ 20 mm are machined for the fracture mechanics tests of the cast MMCs (Fig. 4.4). The specimens have a longitudinal-transverse (LT) crack plane orientation. To insert the pre-crack in the CT specimens, they are subjected to cyclic compression loading with ∆K = 10 MPa m and further to cyclic tensile loading with ∆K = 5 MPa m . Fracture mechanics tests are conducted using the “ZWICK” testing machine which is equipped by a special computer program for fracture mechanics tests. The cross-head velocity is of 0.02 mm/min for the reinforced materials, and 0.08 mm/min for unreinforced materials. A potential drop method is employed to determine the crack extension during the fracture mechanics tests. In this method, a constant electric current is sent through the specimen. An increase of the crack length changes the electric resistance of the system and the measured potential. From the change of the potential, the crack extension can be calculated by the Johnson equation (4.1) [69], ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ π cosh ⎥ 2W ⎢ ⎥ a = ⋅ arccos 2W ⎢ ⎥ , (4.1) π ⎢ ⎡ πy ⎤ ⎥ ⎢ ⎢ cosh U ⎥ cosh ⎥ ⎢ ⎢ ⋅ arccos 2W ⎥ ⎥ ⎢ ⎢U πa o o cos ⎥ ⎥ ⎣ ⎢⎣ 2W ⎥⎦ ⎦ where 2y is the distance between the points of the potential measurement, U is the current potential value, and Uo is the initial potential value. A schematic view of the potential drop method is presented in Figure 4.5. The electrical current intensity, I, is 10 A. The potential, U, is determined by a nanovoltmeter with an accuracy of ± 100 nV, which corresponds to an accuracy of the crack length of ± 0.01 mm. A clip-gage is used to determine the load line displacement of the specimen during the fracture tests of the cast MMCs. The data on the load, load line displacement, and potential are saved in a file by the computer program every 10 s. The J-integral resistance curves were determined according to [73]. The J0.2/Bl -, Ji-values determined from these curves are given in Table 4.2, as well. 32
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: Section 4 Table 4.1. Chemical compo
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
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Section 7 its initial length, li. O
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1 µm Section 7 5 µm Fig. 7.3. A s
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Section 7 a) b) c) Fig. 7.4. Micros
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Section 7 It is important that no p
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Section 7 between the Rtot and the
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Section 7 Fig. 7.8. The fracture su
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10 z [mm] 5 -10 -15 Section 7 0 -20
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Section 7 Table 7.3. Data on measur
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8. Summary Section 8 This work deal
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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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