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

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Section 2 An energy criterion and a stress criterion have been suggested to characterize the particle/matrix interface separation [32]. A detailed analysis by Tanaka et al. [32] has shown that for particles having a size smaller than 250 Å, the particle/matrix separation is primarily controlled by the energy criterion. In this case, the particle/matrix separation will occur when the elastic strain energy which is released upon decohesion becomes equal to the newly created surface energy. When an inclusion is larger than 250 Å, the energy criterion is always fulfilled and the particle/matrix separation is primarily controlled by the stress criterion [32]. Void nucleation occurs at the attainment of a critical normal stress at the particle/matrix interface. Some models based on a dislocation theory were developed. Ashby proposed a model where primary deformation incompatibilities do not produce cavities directly, but initiate highly organized secondary dislocation loops from the interface of the inclusion with the matrix to reduce the local shear stresses [33]. These loops can form reverse pile-ups and can build up increasing interfacial stresses until they reach the interfacial strength. In [31], the local stress on the particle interface has been estimated as a function of the local dislocation density around a particle. It was demonstrated that the rate of dislocation storage around a particle, in a plastically deforming matrix, decreases with an increase in particle size and, above a critical particle size of 1 µm, a continuum plasticity model can be applied to describe the microvoid nucleation process, since the local strain hardening effect around the particle is of the same magnitude as that in the matrix. Argon et al. [34] used a continuum mechanics theory to estimate the maximum interfacial stresses. They considered a rigid cylindrical inclusion embedded into an incompressible power-law hardening material subjected to a pure shear deformation. The actual behavior of the material is bounded by two limiting idealizations: a rigid ideally plastic behavior and a linear behavior. The stress concentrations obtained for these two extreme idealizations were compared to estimate the actual interfacial stresses. It was shown that the maximum interfacial stresses can be calculated as a sum of the von Mises equivalent stress, σeq, and the hydrostatic stress, σm, σ interf max = σeq + σm. (2.3) In [35], Argon and Im investigated the behavior of equiaxed Fe3C particles in a 1045 Steel, Cu-Cr particles in a Cu-0.6%Cr alloy, and TiC particles in a maraging steel. Cylindrical tensile specimens with and without machined notches were tested up to failure. The broken specimen halves were sectioned along the axis, metallographically polished, and lightly 11
Section 2 etched to mark the inclusions. The inclusions which have initiated voids were detected, and the number of voids was plotted as a function of the distance from the fracture surface. The point along the axis where the void density drops to zero was taken as characterizing the critical conditions for interface separation. A finite element analysis was performed, [36], to compute the stress conditions at this point. The critical interfacial stresses were then calculated according to Eq. (2.3). The maximum interfacial stresses were 1670 MPa, 990 MPa, and 1820 MPa for Fe3C, Cu-Cr, and TiC particles, respectively. Arsenault and Flom evaluated the interfacial strength between particles and the matrix in an Al6061 based MMC with 1% SiC particles [37]. Specimens similar to that used in [35] were machined and procedure used in [35] was applied to the specimens. The interfacial strength was calculated by Eq (2.3), taking into account the stress triaxiality for the tip of the notch, where the triaxiality reaches its maximum. The interfacial strength was determined as 1690 MPa. This result does not seem to be correct, since the number of voids associated with the debonding of SiC particles was much smaller than the total number of voids related to the fracture. A few examples of the areas where debonded SiC particles are located were observed, but they were distant from the tip of the notch. Beremin [38] studied the conditions for void initiation for elongated MnS inclusions in a low alloy steel A508. Notched tensile specimens were loaded to different global deformations and subsequently sectioned and polished to determine the outer boundary of the region within which voids have been initiated. The local stresses at this boundary were computed with a finite element analysis, and the maximum principal stress in the inclusion at the moment of void initiation evaluated by the equation σ p max =σm + (2/3+λ)σeq. (2.4) This equation was deduced from a non-linear Eshelby-type approach, following [39]. The parameter λ is a function of the particle shape; λ = 1 for a spherical particle. Beremin found that the σ p max-values for the MnS-inclusions in the steel A508 are temperature independent, but depend on the specimen orientation: σ p max = 1120±60 MPa in the longitudinal direction, where MnS-inclusions are fractured, and σ p max = 810±50 MPa in the short transverse direction, where MnS-inclusion/matrix decohesion prevails. Toda et al. [40] determined the fracture strength of second-phase particles in a notched 3- point bend specimen made of a wrought Al-Li alloy. A side-surface of the specimen was polished and etched before the testing. An interrupted in-situ loading experiment was 12
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: Section 2 high strength, fine reinf
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 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
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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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