3D DISCRETE DISLOCATION DYNAMICS APPLIED TO ... - NUMODIS

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122 Dislocation-precipitate interactions Strength of particle Initial strength, τ ∗ facet τ facet τfacet Slope= 2ri/b Number of dislocation passage Figure 4.20: Evolution of facet’s strength with dislocation passages Particles of radius 160 nm are assumed to be easily shearable, and the initial strength of facets is defined as 292 MP a and the final strength τ ∗ facet being 162 MP a. Particle of radius 400 nm are assumed to be non-shearable or difficult to be sheared by using the initial strength being 7310 MP a. The initial configuration The initial dislocation microstructure of all the simulations is composed of four Frank-Read sources, in the form of pinned dislocation segments. All the Frank-Read sources are of the edge-type with the Burgers vector a 2 [¯1¯10] on the slip plane (¯11¯1) (system 7 in Table 2.1). It should be noted that there is no dislocation nucleation around the particles and also that no dislocations are punched in from the free surface. The loading conditions Fatigue simulations are performed under a plastic strain control with a fully symmetrical push- pull loading ratio (ɛmax p /ɛmin p = −1), and an applied plastic strain amplitude △ɛp = 1 × 10−3 . In DDD simulations, only stresses can be applied. Imposed plastic strain conditions are achieved by monitoring the total slip accumulated in all the active slip systems. The applied stresses then are increased or decreased by comparing the resulting plastic strain to the pre-selected strain level. In the fatigue simulations, the plastic strain rate is monitored at each time step. The applied stress is stepwise increased by 1 MP a if the plastic strain rate is lower than the pre-selected minimum plastic strain rate, 10 −7 ((1) in Fig. 4.21). The load is kept constant in the case that the plastic
4.3 Fatigue simulations of materials hardened by particles 123 dλ λ k εp VM εp VM εp max εp min 1 2 3 4 Figure 4.21: Quasi-static loading condition: stepwise increment and decrement of the applied stresses strain rate is between the minimum and the maximum strain rate ((2) in Fig. 4.21), until the dislocation microstructure is in equilibrium with the external loading. This condition is achieved by keeping the load constant while performing discrete time steps until the resulting plastic strain rate becomes lower than the pre-selected minimum strain rate ((3) in Fig. 4.21). The applied stress is decreased by 1 MP a if the plastic strain rate is higher than the pre-selected maximum plastic strain rate, 10 −4 ((4) in Fig. 4.21). 4.3.3 Evolution of the dislocation microstructure during the fatigue tests Pas k Pas k Pas k General features of the formation of the dislocation microstructure The initial Frank-Read sources begin to expand and generate dislocation loops as the applied stresses are increased during the first quarter cycle. Parts of the loops are leaving the simulation volume through the free surface, which prints steps on the free surface as will be detailed in Sec. 4.3.5. The other parts are piled up along the strong grain boundaries. The screw part of dislocation lines tends to cross slip owing to the back stresses from the stored dislocations. The cross slip mechanism spreads slip lines over the whole simulation volume. Particles affect both the dislocation mobility and the cross slip probabilities which result in quite different microstructures as compared with the single-phased material case.
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INSTITUT NATIONAL POLYTECHNIQUE DE
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Acknowledgements First of all, I ex
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Résumé La dynamique des dislocati
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viii CONTENTS 2.3.5 Plastic strain
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Chapter 1 Introduction 1.1 Computat
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1.2 Dislocation dynamics 3 (a) Weak
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1.3 Scope of Thesis 5 Recently the
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1.3 Scope of Thesis 7 coupling meth
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10 Description of the simulation me
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Chapter 3 Parallelization of the Di
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3.1 An introduction to Supercomputi
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3.2 Towards a parallel DDD code 61
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3.3 Parallelization of the serial D
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3.3 Parallelization of the serial D
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Page 163 and 164: Bibliography [Abraham 97] Abraham F
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Page 169 and 170: BIBLIOGRAPHY 159 [Risbet et al. 03]
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3D DISCRETE DISLOCATION DYNAMICS APPLIED TO ... - NUMODIS

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