Atomic-Level and Effective Elastic Moduli at Grain Boundaries

1991 ◽  
Vol 229 ◽  
Author(s):  
I. Alber ◽  
J. L. Bassani ◽  
M. Khantha ◽  
V. Vitek ◽  
G. J. Wang
Keyword(s):  
Grain Boundary ◽  
Grain Boundaries ◽  
Elastic Properties ◽  
Fourth Order ◽  
Continuum Model ◽  
Elastic Moduli ◽  
Atomic Level ◽  
Upper And Lower Bounds ◽  
Atomistic Model ◽  
The Continuum

AbstractThe relationship between atomic structure and elastic properties of grain boundaries is investigated from both discrete and continuum points of view. A heterogeneous continuum model of the boundary is introduced where distinct phases are associated with individual atoms and possess their atomic level elastic moduli determined from the atomistic model. The complete fourth-order tensors of both the atomic-level and the effective elastic moduli are determined, where the latter are defined for sub-blocks from an infinite bicrystal and are calculated here for a relatively small number of atom layers above and below the grain boundary. These effective moduli are determined exactly for the discrete atomistic model, while only estimates from upper and lower bounds can be determined for the continuum model. Comparison between the atomistic results and those for the continuum model establishes the validity of this definition of elastic properties for heterogeneous structures at these scales. Furthermore, these comparisons as well as algebraic properties of the fourth-order tensor of moduli lead to criteria to assess the stability of a given grain boundary structure.

Grain boundaries as heterogeneous systems: atomic and continuum elastic properties

1992 ◽  
Vol 339 (1655) ◽  
pp. 555-586 ◽  
Keyword(s):  
Grain Boundary ◽  
Grain Boundaries ◽  
Elastic Properties ◽  
Discrete Model ◽  
Continuum Model ◽  
Elastic Moduli ◽  
Atomic Level ◽  
Upper And Lower Bounds ◽  
Effective Moduli ◽  
The Continuum

The relation between atomic structure and elastic properties of grain boundaries is investigated theoretically from both atomistic and continuum points of view. A heterogeneous continuum model of the boundary is introduced where distinct phases are associated with individual atoms and possess their atomic level elastic moduli determined from the discrete model. The effective elastic moduli for sub-blocks from an infinite bicrystal are then calculated for a relatively small number of atom layers above and below the grain boundary. These effective moduli can be determined exactly for the discrete atomistic model, while estimates from upper and lower bounds are evaluated in the framework of the continuum model. The complete fourth-order elastic modulus tensor is calculated for both the local and the effective properties. Comparison between the discrete atomistic results and those for the continuum model establishes the validity of this model and leads to criteria to assess the stability of a given grain boundary structure. For stable structures the continuum estimates of the effective moduli agree well with the exact effective moduli for the discrete model. Metastable and unstable structures are associated with a significant fraction of atoms (phases) for which the atomic-level moduli lose positive definiteness or even strong ellipticity. In those cases, the agreement between the effective moduli of the discrete and continuum systems breaks down.

scholarly journals Equivalent plastic strain gradient plasticity with grain boundary hardening and comparison to discrete dislocation dynamics

2015 ◽  
Vol 471 (2184) ◽  
pp. 20150388 ◽  
Author(s):  
E. Bayerschen ◽  
M. Stricker ◽  
S. Wulfinghoff ◽  
D. Weygand ◽  
T. Böhlke
Keyword(s):  
Plastic Strain ◽  
Yield Strength ◽  
Grain Boundary ◽  
Continuum Model ◽  
Equivalent Plastic Strain ◽  
Elastic Interaction ◽  
Dislocation Dynamics ◽  
Discrete Dislocation Dynamics ◽  
Discrete Dislocation ◽  
The Continuum

The gradient crystal plasticity framework of Wulfinghoff et al. (Wulfinghoff et al. 2013 Int. J. Plasticity 51, 33–46. ( doi:10.1016/j.ijplas.2013.07.001 )), incorporating an equivalent plastic strain γ eq and grain boundary (GB) yielding, is extended with GB hardening. By comparison to averaged results from many discrete dislocation dynamics (DDD) simulations of an aluminium-type tricrystal under tensile loading, the new hardening parameter of the continuum model is calibrated. Although the GBs in the discrete simulations are impenetrable, an infinite GB yield strength, corresponding to microhard GB conditions, is not applicable in the continuum model. A combination of a finite GB yield strength with an isotropic bulk Voce hardening relation alone also fails to model the plastic strain profiles obtained by DDD. Instead, a finite GB yield strength in combination with GB hardening depending on the equivalent plastic strain at the GBs is shown to give a better agreement to DDD results. The differences in the plastic strain profiles obtained in DDD simulations by using different orientations of the central grain could not be captured. This indicates that the misorientation-dependent elastic interaction of dislocations reaching over the GBs should also be included in the continuum model.

Parenchymal stability

1992 ◽  
Vol 73 (2) ◽  
pp. 596-602 ◽  
Author(s):  
D. Stamenovic ◽  
T. A. Wilson
Keyword(s):  
Surface Tension ◽  
Surface Density ◽  
Continuum Model ◽  
Elastic Moduli ◽  
Micromechanical Model ◽  
Volume Ratio ◽  
Transpulmonary Pressure ◽  
Lung Parenchyma ◽  
Micromechanical Modeling ◽  
The Continuum

Both continuum and micromechanical models have been used to describe the mechanics of lung parenchyma. Different authors, using different models, have come to different conclusions about parenchymal stability. We show that the continuum model, augmented by bounds on the elastic moduli obtained from recent micromechanical modeling, yields the same conclusions about stability that have been obtained from purely micromechanical modeling: if the lung were homogeneous, it would be stable; local atelectasis would not occur at positive transpulmonary pressure. However, the same analysis yields the prediction that if the surface-to-volume ratio is not uniform throughout the lung, regions of higher surface density collapse if surface tension is large and insensitive to surface area. A micromechanical model that illustrates regional collapse is described.

scholarly journals Single Crystal Elastic Properties of Hemimorphite, a Novel Hydrous Silicate

Minerals ◽  
2020 ◽  
Vol 10 (5) ◽  
pp. 425
Author(s):  
Yingzhe Li ◽  
Jay D. Bass
Keyword(s):  
Single Crystal ◽  
Elastic Properties ◽  
Wave Velocity ◽  
Elastic Moduli ◽  
Elastic Anisotropy ◽  
Pure Shear ◽  
P Wave ◽  
Upper And Lower Bounds ◽  
Molecular Water ◽  
High Degree

Hemimorphite, with the chemical formula Zn4Si2O7(OH)2·H2O, contains two different types of structurally bound hydrogen: molecular water and hydroxyl. The elastic properties of single-crystal hemimorphite have been determined by Brillouin spectroscopy at ambient conditions, yielding tight constraints on all nine single-crystal elastic moduli (Cij). The Voigt–Reuss–Hill (VRH) averaged isotropic aggregate elastic moduli are KS (VRH) = 74(3) GPa and μ (VRH) = 27(2) GPa, for the adiabatic bulk modulus and shear modulus, respectively. The average of the Hashin–Shtrickman (HS) bounds are Ks (HS) = 74.2(7) GPa and and μ (HS) = 26.5(6) GPa. Hemimorphite displays a high degree of velocity anisotropy. As a result, differences between upper and lower bounds on aggregate properties are large and the main source of uncertainty in Ks and μ. The HS average P wave velocity is VP = 5.61(4) km/s, and the HS S-wave velocity is VS = 2.77(3) km/s. The high degree of elastic anisotropy among the on-diagonal longitudinal and pure shear moduli of hemimorphite are largely explained by its distinctive crystal structure.

Enhanced ionic conductivity in electroceramics by nanoscale enrichment of grain boundaries with high solute concentration

Nanoscale ◽  
2017 ◽  
Vol 9 (44) ◽  
pp. 17293-17302 ◽  
Author(s):  
William J. Bowman ◽  
Madeleine N. Kelly ◽  
Gregory S. Rohrer ◽  
Cruz A. Hernandez ◽  
Peter A. Crozier
Keyword(s):  
Ionic Conductivity ◽  
Grain Boundary ◽  
Grain Boundaries ◽  
Solute Concentration ◽  
Atomic Level ◽  
Oxygen Ionic Conductivity ◽  
Boundary Composition ◽  
High Solute Concentration

The enhancement of grain boundary oxygen ionic conductivity by four orders of magnitude in an electroceramic is explicitly shown to result from modulation of local grain boundary composition at the atomic level.

Elastic Properties of Grain Boundaries in Copper

1989 ◽  
Vol 153 ◽  
Author(s):  
James B. Adams ◽  
Wilhelm G. Wolfer ◽  
Stephen M. Foiles
Keyword(s):  
Grain Boundary ◽  
Grain Boundaries ◽  
Elastic Properties ◽  
Elastic Constants ◽  
Elastic Behavior ◽  
Order Of Magnitude

AbstractThe elastic constants of a Σ5 (100) twist grain boundary are calculated on a monolayer-by-monolayer basis, and the elastic behavior is shown to differ by up to an order of magnitude from bulk-like behavior. This unusual elastic behavior is found to be similar to that of uniaxiallystrained crystals, since the grain boundaries themselves are regions which are strained (expanded) in one direction.

Elastic moduli of grain boundaries in nanocrystalline MgO ceramics

2005 ◽  
Vol 20 (3) ◽  
pp. 719-725 ◽  
Author(s):  
Ori Yeheskel ◽  
Rachman Chaim ◽  
Zhijian Shen ◽  
Mats Nygren
Keyword(s):  
Grain Size ◽  
Grain Boundaries ◽  
Elastic Properties ◽  
Elastic Moduli ◽  
Hot Isostatic Pressing ◽  
Velocity Measurements ◽  
Shear Moduli ◽  
Plasma Sintering ◽  
Spark Plasma ◽  
Nanocrystalline Mgo

Dense MgO ceramics with nanometer to submicrometer grain size were fabricated by high-temperature hot-isostatic pressing, low-temperature hot-pressing, and spark plasma sintering. The elastic properties were determined by sound wave velocity measurements. Young's and shear moduli of nanocrystalline MgO were lower by 13% than those with submicrometer grain size. Softening of the elastic properties was analyzed and related to the lower density and lower elastic moduli of the grain boundaries compared to the crystal interior. Young's and shear moduli of the grain boundaries were evaluated as 90 and 34 GPa, respectively. This leads to a more than 3-fold decrease in the effective elastic moduli with the decrease of grain size into the nanometer range.

Measurement of the Displacement Across a Coincidence Grain Boundary

1977 ◽  
Vol 35 ◽  
pp. 124-125
Author(s):  
J. W. Matthews ◽  
W. M. Stobbs
Keyword(s):  
Grain Boundary ◽  
Grain Boundaries ◽  
Stacking Fault ◽  
The Other ◽  
Measuring Technique ◽  
High Angle ◽  
Twin Boundaries ◽  
Rigid Displacement ◽  
Cubic Crystals ◽  
Lattice Displacement

Many high-angle grain boundaries in cubic crystals are thought to be either coincidence boundaries (1) or coincidence boundaries to which grain boundary dislocations have been added (1,2). Calculations of the arrangement of atoms inside coincidence boundaries suggest that the coincidence lattice will usually not be continuous across a coincidence boundary (3). There will usually be a rigid displacement of the lattice on one side of the boundary relative to that on the other. This displacement gives rise to a stacking fault in the coincidence lattice.Recently, Pond (4) and Smith (5) have measured the lattice displacement at coincidence boundaries in aluminum. We have developed (6) an alternative to the measuring technique used by them, and have used it to find two of the three components of the displacement at {112} lateral twin boundaries in gold. This paper describes our method and presents a brief account of the results we have obtained.

Observations of dislocation interactions with recrystallized grain boundaries

1988 ◽  
Vol 46 ◽  
pp. 628-629
Author(s):  
C. W. Price
Keyword(s):  
Dislocation Density ◽  
Grain Boundary ◽  
Strain Rate ◽  
Grain Boundaries ◽  
Dislocation Structure ◽  
Hot Deformation ◽  
Static Recrystallization ◽  
High Dislocation Density ◽  
High Angle ◽  
Dislocation Interactions

Little evidence exists on the interaction of individual dislocations with recrystallized grain boundaries, primarily because of the severely overlapping contrast of the high dislocation density usually present during recrystallization. Interesting evidence of such interaction, Fig. 1, was discovered during examination of some old work on the hot deformation of Al-4.64 Cu. The specimen was deformed in a programmable thermomechanical instrument at 527 C and a strain rate of 25 cm/cm/s to a strain of 0.7. Static recrystallization occurred during a post anneal of 23 s also at 527 C. The figure shows evidence of dissociation of a subboundary at an intersection with a recrystallized high-angle grain boundary. At least one set of dislocations appears to be out of contrast in Fig. 1, and a grainboundary precipitate also is visible. Unfortunately, only subgrain sizes were of interest at the time the micrograph was recorded, and no attempt was made to analyze the dislocation structure.

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