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

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Section 2 conducted in the scanning electron microscope (SEM). The notch radius was 150 µm. The position and size of each particle was measured within a region of 500 µm around the notch and the extending crack tip. The chemical composition of the inclusions was determined by a SEM-EDX analysis. After each loading step, a micrograph was taken to detect the broken particles. From the value of the J-integral, J, the particle fracture stress was evaluated using the stress field approach proposed by Hutchinson [41], Rice, and Rosengren [42] (HRR- theory) and a mean field correction following Tanaka et al. [32]. The process zone where large deformations appear directly at the growing crack tip was excluded from the analysis. Toda et al. found values of the maximum normal stress of σ p max = 710 MPa for CuAl2 and Al2CuMg particles with diameters between 5 and 8 µm. Whereas the fracture strength of the CuAl2 particles did not change much with increasing particle size, larger Al2CuMg particles exhibited considerably smaller values, e.g., σ p max = 540 MPa for diameters between 14 and 18 µm. Al3Zr and Al3Ti particles did not fracture, thus a lower limit of their fracture strength could be determined: σ p max ≥ 1000 MPa and 910 MPa, respectively. The study of Toda et al. is remarkable, however, a few disadvantages has prevented the direct application of the procedure for our materials: (1.) The HRR-field is, strictly speaking, not applicable for a region around a notch, nor is it for a growing crack. Regarding the growing cracks, Toda et al. claim that the HRR- field should be still valid if a parameter Ω = Eεfr /σy is smaller than 34.5 (E is the Young modulus, εfr denotes the fracture strain in a uniaxial tensile test, and σy the yield stress). Hereby, Toda et al. refer to a paper by Chan [43] who used the parameter Ω to distinguish between stable and unstable crack growth regimes. As has been shown by Hutchinson and Paris [44], the conditions of J-controlled crack growth will be lost for any material, if the crack extension becomes too large. Moreover, it is demonstrated in [44] that a tough material, where dJ/da and the parameter Ω are large, will exhibit J-control for a longer regime of crack extension than a less tough material with a small Ω. (2.) The mean-field analysis was performed assuming an inclusion in a matrix under a uniaxial tensile stress. A particle near a crack tip will, however, experience a highly triaxial stress state. (3.) The measurement at the side surface of the specimen might be not representative for the bulk behavior. It is well known that, because of the lower constraint, void initiation and void growth are retarded near the side surface compared to the midsection region. 13
Section 2 (4.) The specimen preparation might pre-damage some of the particles so that they fail at a lower stress. As one can see, despite a large number of investigations dealing with the fracture behavior of MMCs, the local fracture properties in MMCs have not been investigated so far, probably, due to the absence of appropriate tools. But this topic is very important for inhomogeneous materials. As the void initiation is the first stage of the ductile fracture, the conditions for void nucleation call great interest, especially, near the crack front in the interior of the specimen. As shown in next section, an application of recently developed tools for fracture surface analysis could solve such a problem as the impossibility to investigate the fracture processes in the interior of the specimen and give a possibility to determine the local conditions for void initiation for individual particles near the crack tip. 14
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: Section 2 etched to mark the inclus
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 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
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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
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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
Page 101 and 102:
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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