The Directional Dependence of Elastic Stiffness and Compliance Shear Coefficients and Shear Moduli in Cubic Materials

Knowles, Kevin M.; Howie, Philip R.

doi:10.1007/s10659-014-9506-1

Cited by 80 publications

(28 citation statements)

References 23 publications

(50 reference statements)

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“…Elastic constants are created in the relationship between stress and strain and they are dependent on the configuration of crystal lattice, therefore elastic constants are derived from planes in the crystal lattice [ 5 , 6 , 7 , 8 ]. Furthermore, there are several studies on the correspondence of elastic constants and planes/directions such as Ref [ 9 , 10 , 11 ]. Crystallographic planes that are equivalent have similar atomic planar densities.…”

Section: Introductionmentioning

confidence: 99%

Measurement Modulus of Elasticity Related to the Atomic Density of Planes in Unit Cell of Crystal Lattices

et al. 2020

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Young’s modulus (E) is one of the most important parameters in the mechanical properties of solid materials. Young’s modulus is proportional to the stress and strain values. There are several experimental and theoretical methods for gaining Young’s modulus values, such as stress–strain curves in compression and tensile tests, electromagnetic-acoustic resonance, ultrasonic pulse echo and density functional theory (DFT) in different basis sets. Apparently, preparing specimens for measuring Young’s modulus through the experimental methods is not convenient and it is time-consuming. In addition, for calculating Young’s modulus values by software, presumptions of data and structures are needed. Therefore, this new method for gaining the Young’s modulus values of crystalline materials is presented. Herein, the new method for calculating Young’s modulus of crystalline materials is extracted by X-ray diffraction. In this study, Young’s modulus values were gained through the arbitrary planes such as random (hkl) in the research. In this study, calculation of Young’s modulus through the relationship between elastic compliances, geometry of the crystal lattice and the planar density of each plane is obtained by X-ray diffraction. Sodium chloride (NaCl) with crystal lattices of FCC was selected as the example. The X-ray diffraction, elastic stiffness constant and elastic compliances values have been chosen by the X’Pert software, literature and experimental measurements, respectively. The elastic stiffness constant and Young’s modulus of NaCl were measured by the ultrasonic technique and, finally, the results were in good agreement with the new method of this study. The aim of the modified Williamson–Hall (W–H) method in the uniform stress deformation model (USDM) utilized in this paper is to provide a new approach of using the W–H equation, so that a least squares technique can be applied to minimize the sources of errors.

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Section: Introductionmentioning

confidence: 99%

Measurement Modulus of Elasticity Related to the Atomic Density of Planes in Unit Cell of Crystal Lattices

et al. 2020

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“…The simulation results are compared with experimental data calculated using the temperature dependence of the elastic constants c ij . The relation between the elastic constants and the specific shear modulus for a 111 direction is G = (c 11 − c 12 + c 44 )/3 [31,32]. The experimental data for the temperature dependence of the elastic constants is taken from Ref.…”

Section: Discussionmentioning

confidence: 99%

Molecular dynamics simulations of thermally activated edge dislocation unpinning from voids inα-Fe

Byggmästar

Granberg

Nordlund

2017

Phys. Rev. Materials

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In this study, thermal unpinning of edge dislocations from voids in α-Fe is investigated by means of molecular dynamics simulations. The activation energy as a function of shear stress and temperature is systematically determined. Simulations with a constant applied stress are compared with dynamic simulations with a constant strain rate. We found that a constant applied stress results in a temperature dependent activation energy. The temperature dependence is attributed to the elastic softening of iron. If the stress is normalized with the softening of the specific shear modulus, the activation energy is shown to be temperature independent. From the dynamic simulations, the activation energy as a function of critical shear stress was determined using previously developed methods. The results from the dynamic simulations are in good agreement with the constant stress simulations, after the normalization. This indicates that the computationally more efficient dynamic method can be used to obtain the activation energy as a function of stress and temperature. The obtained relation between stress, temperature, and activation energy can be used to introduce a stochastic unpinning event in larger scale simulation methods, such as discrete dislocation dynamics.

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“…The model parameters for Al deformed under quasi-static loading conditions were identified in Rubio et al (2019) and are shown in Table 4. They include the elastic constants of the Al single crystals (Lefebvre, 2006;Knowles and Howie, 2015), the viscoplastic parametersγ 0 and m (Evers et al, 2004), and all the parameters that determine the interactions among dislocations and dislocations and GBs (Rubio et al, 2019). It should be noted that the grain boundaries are not modeled as a single row of elements in each crystal in the bicrystal model.…”

Section: Numerical Modelmentioning

confidence: 99%

Effect of slip transmission at grain boundaries in Al bicrystals

Haouala

Alizadeh

Bieler

et al. 2020

International Journal of Plasticity

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The effect of slip transfer on the deformation mechanisms of Al bicrystals was explored using a rate-dependent dislocation-based crystal plasticity model. Three different types of grain boundaries (GBs) were included in the model by modifying the rate of dislocation accumulation near the GB in the Kocks-Mecking law, leading to fully-opaque (dislocation blocking), fully-transparent and partially-transparent GBs. In the latter, slip transmission is only allowed in pairs of SS in neighbour grains that are suitably oriented for slip transfer according to the Luster-Morris parameter. Modifications of the GB character led to important changes in the deformation mechanisms at the GB. In general, bicrystals with fully-opaque boundaries showed an increase in the dislocation density near the GB, which was associated with an increase in the Von Mises stress. In contrast, the dislocation pile-ups and the stress concentration were less pronounced in the case of partially-transparent boundaries as the slip in one grain can progress into the next grain with some degree of continuity. No stress concentrations were found at these boundaries for fully-transparent boundaries, and there was continuity of strain across the boundary, which is not typical of most experimentally observed GBs (Hémery et al., 2018;Bieler et al., 2019). Simulations of ideal bicrystals oriented for favorable slip transfer on the most highly favored slip system in grains with high Schmid factors for slip transfer depends on the number of active SS in * Corresponding author. operation in the neighborhood and that most boundaries will lead to nearly opaque conditions while some boundaries will be transparent. Finally, the model was applied to a particular experimentally observed GB in which slip transfer was clearly operating indicating that the model predicted a nearly transparent GB.

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The Directional Dependence of Elastic Stiffness and Compliance Shear Coefficients and Shear Moduli in Cubic Materials

Cited by 80 publications

References 23 publications

Measurement Modulus of Elasticity Related to the Atomic Density of Planes in Unit Cell of Crystal Lattices

Measurement Modulus of Elasticity Related to the Atomic Density of Planes in Unit Cell of Crystal Lattices

Molecular dynamics simulations of thermally activated edge dislocation unpinning from voids inα-Fe

Effect of slip transmission at grain boundaries in Al bicrystals

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