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

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Section 3 The location of the particle center with respect to the crack tip, given in polar coordinates (r, θ), is also determined from the crack profile. The polar coordinates of the particle center shall be measured from the initial position of the tip of the fatigue pre-crack before the blunting process starts. This can be performed more accurately from the crack profiles depicting the moment of void initiation, Figure 3.3b. For many materials, the tip of the fatigue pre-crack can be found on the SEM micrographs as the beginning of the stretched zone. As follows from the procedure (parallel shifting of profiles), the method of determination of CODvi is based on the assumption that the void growth rate in a direction perpendicular to the crack plane, . R , is equal to the COD growth rate, y 19 . COD . An early numerical analysis of void growth near a crack tip, [55], suggests that the COD growth rate should be several times higher than the void growth rate. If this would be valid, we would get negative CODvi-values for most of the considered below particles, so that we conclude that this cannot be true. In [56], the growth of a single void near the crack tip was investigated for different specimen geometries by the finite element method. In Figure 3.4, the Fig. 3.4. Plots of the crack tip opening displacement, B, the dimension of the void size in two directions, Rx and Ry, and the size of the ligament between the crack tip and the void , D, in plane strain case (taken from [56]). i
Section 3 Fig. 3.5. The observations of the growth of an assemble of voids near the crack tip for plane strain conditions (taken from [57]). void size in two directions, Rx and Ry, the size of the ligament, D, the value of the crack tip opening displacement, B, are plotted as a function of the dimensionless loading parameter of the crack, J σ o o R , for different specimen geometries: the double-edge cracked (DEC), the center-cracked plain (CCP), three point bending (TPB), and the single-edge cracked (SEC). From Figure 3.4, the void and COD growth rates can be estimated for a TPB specimen (which has very similar constraint conditions as a compact tension specimen) and for plane strain conditions. The result is . . COD ≈ 1. 1⋅ D . It should be noted that results obtained for other specimen types differ: for instance, for the SEC specimen, 20 . CODi . ≈ 3⋅ D . In a recent study, [57], the growth of an assemble of voids in a polycrystalline microstructure near a crack tip has been modeled. An analysis of Figure 3.5 shows again that the void and COD growth rates are approximately equal. Thus, it can be concluded that the inaccuracy of determination of the CODvi-values related with the simple shifting of profiles is not high. 3.3. Estimate of the maximum principal stresses in both phases 3.3.1. Estimate of the HRR-stress tensor in the moment of void initiation The stress tensor at the moment of void initiation is estimated from the HRR-field solution (Eq. 3.1) which gives the stress field around a crack tip as a function of the global material properties and the polar coordinates with respect to the crack tip (Fig. 3.6) [41, 42],
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: height [µm] height [µm] 10 0 -10
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)
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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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