Interpretation of experimental data for Poisson's ratio of highly nonlinear materials

The salient features and concepts of a model developed in Part I of this paper are reviewed. The model is extended to include dilatancy and shear compaction which are determined from uniaxial stress-strain relationships. The parameters of the model are the peak stress, initial elastic modulus, and tangential Poisson’s ratio. The peak stress is assumed equal to the compressive strength of the concrete specimen, the initial elastic modulus and the Poisson’s ratio is calculated by proposed empirical formulas. Predictions of the model compare favorably with experimental data reported by various investigators. Responses of concrete specimens subjected to prescribed triaxial proportional stresses, triaxial proportional strains and stresses, hydrostatic plus stress combinations with loading paths on the deviatoric stress plane, biaxial compressive, biaxial tensile, and uniaxial tensile loadings are predicted and compared with test data. All predictions are satisfactory.

Download Full-text

Влияние микротрещин на коэффициент Пуассона при пластическом деформировании аустенитной стали

Журнал технической физики ◽

10.21883/jtf.2022.03.52135.277-21 ◽

2022 ◽

Vol 92 (3) ◽

pp. 405

Author(s):

С.В. Кириков ◽

В.В. Мишакин ◽

В.А. Клюшников

Keyword(s):

Experimental Data ◽

Plastic Deformation ◽

Poisson’S Ratio ◽

Damage Accumulation ◽

Theoretical Calculations ◽

Acoustic Method ◽

12Kh18n10t Steel ◽

Martensite Phase ◽

Poisson's Ratio ◽

Theoretical Dependence

We researched the influence of damage accumulation on the Poisson's ratio measured by echo-pulse acoustic method during plastic deformation of 12Kh18N10T steel. On the basis of the obtained experimental data we calculated the partial contributions to the change in the Poisson's ratio of damage accumulation and separation of the strain induced martensite phase. The characteristics of stable cracks forming near strain martensite particles at small degrees of plastic strain have been analyzed by computer simulation. The theoretical dependence of the change in the Poisson's ratio due to crack formation during plastic deformation has been constructed. A good agreement between the experimental data and theoretical calculations has been obtained.

Download Full-text

Extracting real-crack properties from nonlinear elastic behavior of rocks: abundance of cracks with dominating normal compliance and rocks with negative Poisson's ratio

10.5194/npg-2017-9 ◽

2017 ◽

Author(s):

Vladimir Y. Zaitsev ◽

Andrey V. Radostin ◽

Elena Pasternak ◽

Arcady Dyskin

Keyword(s):

Experimental Data ◽

Poisson’S Ratio ◽

A Priori ◽

Poisson's Ratio ◽

Elastic Behavior ◽

Crack Model ◽

Negative Poisson’S Ratio ◽

Normal Compliance ◽

S Wave ◽

Negative Poisson's Ratio

Abstract. Results of examination of experimental data on nonlinear elasticity of rocks using experimental pressure-dependences of P- and S-wave velocities from various literature sources are presented. Overall, over 90 rock samples are considered. Interpretation of the data is performed using an effective-medium description in which cracks are considered as compliant defects (cracks) with independent shear and normal compliances without specifying a particular crack model with an a priori given ratio of the compliances. Comparison with the experimental data indicated abundance of cracks (~ 80 %) with the normal-to-shear compliance ratios significantly exceeding the values typical of conventionally used crack models (such as penny-shape cuts or thin ellipsoidal cracks). Correspondingly, rocks with such cracks demonstrate strongly decreased Poisson's ratio including a significant portion of rocks (~ 45 %) exhibiting negative Poisson's ratios at lower pressures, for which the concentration of not yet closed cracks is maximal. The obtained results indicate the necessity of further development of crack models to account the revealed numerous examples of cracks with strong domination of normal compliance. Discovering such a significant number of naturally auxetic rocks is in contrast with the conventional viewpoint that occurrence of negative Poisson's ratio is an exotic fact that is mostly associated with specially engineered structures.

Download Full-text

Velocity‐porosity relationships, 1: Accurate velocity model for clean consolidated sandstones

Geophysics ◽

10.1190/1.1635035 ◽

2003 ◽

Vol 68 (6) ◽

pp. 1822-1834 ◽

Cited By ~ 22

Author(s):

Mark A. Knackstedt ◽

Christoph H. Arns ◽

W. Val Pinczewski

Keyword(s):

Experimental Data ◽

Shear Modulus ◽

Elastic Properties ◽

Poisson’S Ratio ◽

Empirical Relationship ◽

Numerical Data ◽

Empirical Method ◽

Poisson's Ratio ◽

Mineral Phase ◽

Water Saturated

We use numerical simulations to derive the elastic properties of model monomineralic consolidated sandstones. The model morphology is based on overlapping spheres of a mineral phase. We consider model quartzose and feldspathic sands. We generate moduli‐porosity relationships for both the dry and water‐saturated states. The ability to control pore space structure and mineralogy results in numerical data sets which exhibit much less noise than corresponding experimental data. The numerical data allows us to quantitatively analyze the effects of porosity and the properties of the mineral phase on the elastic properties of porous rocks. The agreement between the numerical results and available experimental data for clean consolidated sandstones is encouraging. We compare our numerical data to commonly used theoretical and empirical moduli‐porosity relationships. The self‐consistent method gives the best theoretical fit to the numerical data. We find that the empirical relationship of Krief et al. is successful at describing the numerical data for dry shear modulus and that the recent empirical method of Arns et al. gives a good match to the numerical data for Poisson's ratio or Vp/Vs ratio of dry rock. The Raymer equation is the best of the velocity‐porosity models for the water‐saturated systems. Gassmann's relations are shown to accurately map between the dry and fluid‐saturated states. Based on these results, we propose a new empirical method, based solely on a knowledge of the mineral modulus, to estimate the full velocity‐porosity relationship for monomineralic consolidated sands under dry and fluid‐saturated states. The method uses the equation of Krief et al. for the dry shear modulus and the empirical equation of Arns et al. for the dry Poisson's ratio. Gassmann's relations are applied to obtain the fluid‐saturated states. The agreement between the new empirical method, the numerical data and available experimental data for dry and water‐saturated states is encouraging.

Download Full-text

Comments on “Hardness, elasticity, and fracture toughness of polycrystalline spinel germanium nitride and tin nitride,” by M.P. Shemkunas, W.T. Petuskey, A.V.G. Chizmeshya, K. Leinenweber, and G.H. Wolf [J. Mater. Res. 19, 1392 (2004)]: Reestablishing of elastic moduli for γ-Ge3N4

Journal of Materials Research ◽

10.1557/jmr.2008.0405 ◽

2008 ◽

Vol 23 (12) ◽

pp. 3273-3274

Author(s):

Andreas Zerr

Keyword(s):

Experimental Data ◽

Fracture Toughness ◽

Shear Modulus ◽

Young’S Modulus ◽

Poisson’S Ratio ◽

Spinel Structure ◽

Elastic Moduli ◽

Young's Modulus ◽

Poisson's Ratio ◽

Tin Nitride

It will be shown that in the considered paper, a mistake occurred by handling or editing of experimental data for one of two investigated materials, namely, for cubic germanium nitride having spinel structure (γ-Ge3N4). This mistake led to incorrect values of the shear modulus G0, Young’s modulus E0, and Poisson’s ratio ν0 of this compound. My effort to recover the elastic moduli of γ-Ge3N4 from the available data gave the following results: G0 = 124 GPa, E0 = 326 GPa, and ν0 = 0.32.

Download Full-text

Применение эмпирических потенциалов для расчета упругих свойств графена

Письма в журнал технической физики ◽

10.21883/pjtf.2019.03.47275.17239 ◽

2019 ◽

Vol 45 (3) ◽

pp. 52

Author(s):

А.С. Минкин ◽

И.В. Лебедева ◽

А.М. Попов ◽

А.А. Книжник

Keyword(s):

Experimental Data ◽

Ab Initio Calculations ◽

Ab Initio ◽

Elastic Properties ◽

Poisson’S Ratio ◽

Graphene Layer ◽

Poisson's Ratio ◽

Account System ◽

Potential Parameters ◽

Mechanical Phenomena

AbstractThe elastic properties of a flat graphene layer calculated using the classical empirical Tersoff, Brenner, AIREBO, PPBE-G, and LCBOP potentials have been compared. It is shown that, although the popular Brenner and AIREBO potentials have been developed formally taking into account the elastic properties of graphene, they give significant discrepancies in the values of Young’s modulus and Poisson’s ratio. Among the potentials under consideration, the LCBOP potential yields the values of these parameters that are closest to experimental data and results of ab initio calculations in the limit of zero elongation. For the quantitative simulation of mechanical phenomena in graphene-based systems, the potential parameters should be fitted to reproduce elastic properties of graphene completely taking into account system deformations and dependences of these constants on the elongation.

Download Full-text