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

Recommendations

Info

126 Dislocation-precipitate interactions ρ[m -2 ] 1.8e+13 1.6e+13 1.4e+13 1.2e+13 1e+13 8e+12 6e+12 4e+12 2e+12 0 0.0e0 2.0e-3 4.0e-3 6.0e-3 8.0e-3 1.0e-2 1.2e-2 ε VM * r p =160nm r p =400nm No particle Figure 4.23: Evolution of the total dislocation density of the volume containing rp = 160 nm, rp = 400 nm and no particles left around the particles from the forwarding glide. Thus the irreversibility of slip is significantly reduced in the case of non-shearable particles. Strain localization kinematics In the preceding section, it is shown that the shearable particles favor high ρtot. The next question to address is whether the simulation can reproduce the localization of the plastic deformation or strain. Fig. 4.24 shows the dislocation microstructure formed after 3 cycles in the rp = 160 nm case and after 5 cycles in the rp = 400 nm case, along [110] direction. The figures illustrate clearly that the dislocation structures are highly heterogenous and intense slip bands are formed on the primary slip plane due to the cyclic loading. This result is consistent with experimental observations ([Calabrese & Laird 74]). Plastic strain localization is believed to cause fatigue damage, since the local plastic strain has to be high enough to accommodate all the applied plastic strain. This process can eventually lead to fatigue crack nucleation. To demonstrate the statistics of the PSBs formation quantitatively, the spatial distribution of the dislocation densities is computed as follows at each time step k. The cylindrical simulation volume
4.3 Fatigue simulations of materials hardened by particles 127 (a) Particles with rp = 160 nm (b) Particles with rp = 400 nm Figure 4.24: Localization of slip by forming intense slip bands is sliced into finite layers along the slip planes normal [¯11¯1]. Dislocation densities are then computed in each layer . The heterogeneity of the dislocation density can be shown by plotting the calculated dislocation densities of each layer along the reference axis [¯11¯1]. Fig. 4.25 shows the evolution of such spatial dislocation density distributions. Three axis of the coordinate system correspond to the dislocation density, the position of each layer and the cycle number. From the figure, the general features of the formation of dislocation microstructure can be confirmed, i.e. the first increase of the applied plastic strain spreads dislocations over the simulation volume in all the cases. In the next cycles, the heterogeneous dislocation structure forms and certain zones accumulate a high dislocation density. The detailed observation of Fig. 4.25 reveals that the particles affect the slip localization in several ways : 1. The width wdisl of the dislocation distributions over the simulation volume is the largest in the case rp = 400 nm (non-shearable particles) and the smallest in the case rp = 160 nm rp=400 nm (shearable particles), i.e. wd No particle > wd > w rp=160 nm d rp=160 nm 2. The maximum local dislocation densities (ρmax) are in the following order, ρmax ρ rp=400 nm max > ρ No particle max . rp=400 nm 3. The intense slip band width is smaller in the case of shearable particles, i.e. db d rp=160 nm b . . > >
Page 1 and 2:
INSTITUT NATIONAL POLYTECHNIQUE DE
Page 3:
Acknowledgements First of all, I ex
Page 6 and 7:
Résumé La dynamique des dislocati
Page 8 and 9:
viii CONTENTS 2.3.5 Plastic strain
Page 11 and 12:
Chapter 1 Introduction 1.1 Computat
Page 13 and 14:
1.2 Dislocation dynamics 3 (a) Weak
Page 15 and 16:
1.3 Scope of Thesis 5 Recently the
Page 17:
1.3 Scope of Thesis 7 coupling meth
Page 20 and 21:
10 Description of the simulation me
Page 22 and 23:
Page 24 and 25:
Page 26 and 27:
Page 28 and 29:
Page 30 and 31:
Page 32 and 33:
Page 34 and 35:
Page 36 and 37:
Page 38 and 39:
Page 40 and 41:
Page 42 and 43:
Page 44 and 45:
Page 46 and 47:
Page 48 and 49:
Page 50 and 51:
Page 52 and 53:
Page 54 and 55:
Page 56 and 57:
Page 58 and 59:
Page 61 and 62:
Chapter 3 Parallelization of the Di
Page 63 and 64:
3.1 An introduction to Supercomputi
Page 65 and 66:
Page 67 and 68:
Page 69 and 70:
Page 71 and 72:
3.2 Towards a parallel DDD code 61
Page 73 and 74:
Page 75 and 76:
Page 77 and 78:
3.3 Parallelization of the serial D
Page 79 and 80:
Page 81 and 82:
Page 83 and 84:
Page 85 and 86: 3.3 Parallelization of the serial D
Page 91 and 92: 3.4 Performance improvment 81 Speed
Page 97 and 98: 3.4 Performance improvment 87 Y Z I
Page 99 and 100: 3.5 Application to Stage I-II trans
Page 105 and 106: Chapter 4 Dislocation-precipitate i
Page 107 and 108: 4.1 Image stresses due to a 3D part
Page 115 and 116: 4.2 A simple case of dislocation-pa
Page 127 and 128: 4.3 Fatigue simulations of material
Page 135: 4.3 Fatigue simulations of material
Page 159 and 160: Chapter 5 Conclusions and perspecti
Page 161 and 162: namics codes into a parallel versio
Page 163 and 164: Bibliography [Abraham 97] Abraham F
Page 165 and 166: BIBLIOGRAPHY 155 [Devincre & Robert
Page 167 and 168: BIBLIOGRAPHY 157 [Khraishi et al. 0
Page 169 and 170: BIBLIOGRAPHY 159 [Risbet et al. 03]
show all

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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?