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

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Section 3 3. A method to estimate the local conditions for void initiation in materials with inclusions This section describes the proposed procedure to estimate the local conditions for void initiation near the crack tip. The procedure consists of: 1) For individual particles lying in the midsection region near the crack tip, the values of the crack tip opening displacement at the moment of void initiation, CODvi, are determined. This is done by using stereophotogrammetry and a digital image analysis system. 2) The mesoscopic stress tensor at the position of each considered particle is estimated by the HRR-theory from the determined CODvi-value. 3) The stress tensors in both the particle and in the matrix are calculated by a non-linear Mori-Tanaka secant approach. Below, each step is outlined in detail. 3.1. An automatic fracture surface analysis system To determine the values of the crack tip opening displacement at the moment of void initiation, CODvi, and at the moment of fracture initiation, CODi, as well as the polar coordinates of the particle location with respect to the crack plane, an automatic fracture surface analysis system is used [45, 46]. The key part of this system is a matching algorithm which is able to find automatically homologue points in a stereo image pair which is taken in a scanning electron microscope (SEM). Homologue points are points in the two images which belong to the same physical point on the specimen. The stereo image pair is produced by tilting the specimen in the SEM. Each image consists of 1024 x 768 pixels at 256 gray levels. On average, between 20000 to 30000 homologue points are found. It should be noted that images with a resolution of up to 4000x3200 pixels can be taken in new SEMs. For such pictures, the number of homologue points may increase by a factor 10 or more. From the homologue points and the three image parameters, magnification, working distance, and tilt angle, a three-dimensional model of the depicted fracture surface region is generated, called “digital elevation model” (DEM). In Figure 3.1, a DEM for a cast Al6061-10%Al2O3 MMC is given as an example. The DEM can be cut arbitrarily to extract fracture surface 15
Section 3 Fig. 3.1. The digital elevation model of a cast Al6061-10%Al2O3 MMC. profiles. Further important capabilities of the automatic fracture surface analysis system are the automatic evaluation of profile and surface roughness parameters and the determination of fractal dimensions [47]. The first version of the automatic fracture surface analysis system used a simple matching algorithm, based on the evaluation of a cross-correlation coefficient [48]. Later, the system has been completely modified with respect to the matching algorithm and the user interface [46]. A comprehensive description of the principles of the new matching algorithm is given in [49]. Both systems have been applied successfully to analyze ductile and cleavage fracture surfaces of metals [50, 51], metallic glasses [52], and intermetallic alloys [53], but it has been also proven valuable for the inspection of the surface structure of many classes of materials, from metals to biological materials. In the following section, it is described how the automatic fracture surface analysis system is applied to determine the local CODi- and CODvi-values in materials with inclusions. 3.2. The determination of the CODi- and CODvi –values The SEM-micrographs of Figure 3.2 show corresponding regions near the midsection on the two halves of a broken compact tension (CT) specimen made of a cast Al6061-10%Al2O3 16
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: Section 2 (4.) The specimen prepara
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 and 66: Section 4 4.5. The relation between
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Section 4 Table 4.9. Conditions for
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Ln(Ln(1/(1-F σ))) Ln(Ln(1/(1-F σ)
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Section 5 diameter of 2…8 µm and
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MnS-inclusion r θ MnS-inclusion Se
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σ interf [MPa] σ interf [MPa] σ
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Section 6 where n is the number of
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Ji [kN/m] J i [kN/m] 25 20 15 10 5
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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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