Equivalent Poisson's Ratio Research Articles

Assessment of the Poisson Ratio Effect on Low Cycle Fatigue (LCF) Behavior of Shear-Cracking Mode Materials

Abstract This paper evaluates the effect of different Poisson's ratios and an equivalent Poisson's ratio formula on the crack initiation angle and life estimation by using the three shear-strain based fatigue damage models (Brown–Miller, Fatemi–Socie, and Liu's Virtual Energy) on strain-controlled biaxial cyclic loading tests of specific tubular material specimens. The four shear failure mode materials studied were Inconel 718, 304L stainless steel, normalized 1050, and quenched/tempered 1050 steels. This study was motivated by the fact that for all the strain-controlled fatigue testing, the induced transverse strain was not measured, but assumed to be a negative product of the axial strain and the Poisson ratio, where the axial strain was known and given, and the Poisson ratio was either assumed to be a constant or a variable represented by a function of elastic and plastic equivalent strains. Therefore, the assumption of a Poisson's ratio in the transverse strain calculation was assessed in this study. It is concluded that the use of different Poisson's ratios in the three fatigue damage models would have some effects on the crack angle prediction, depending on the material type, and little effect on the fatigue life estimation for all materials investigated in this study.

Investigation of underwater sound scattering on a cylindrical shell coated with anechoic coatings by the finite element method based on an equivalent parameter inversion

Anechoic coating attached to the surface of an underwater object is used for absorbing sound wave thereby reducing the reflection. The anechoic coating is often made of viscoelastic materials embedded with designed acoustic substructures, such as air cavities. The prediction of sound scattering on underwater object coated with such materials can be challenging due to the complex geometry of the anechoic coating, and it has been a research subject of interest in underwater acoustics. In this paper, we study the sound scattering on an infinite cylindrical shell coated with anechoic coating. Two types of coatings are considered: one is a layer of homogeneous isotropic material, and the other is a layer of homogeneous isotropic material with periodically embedded cylindrical air cavities. We use an equivalent method, in which the anechoic coating with air-filled cavities is regarded as a homogeneous isotropic material with equivalent material properties. The key point of the equivalent method is to ignore the internal structure of the anechoic coating, and the anechoic coating is considered as a homogeneous isotropic layer with the same complex reflection coefficient. These equivalent material properties are acquired based on the data of complex reflection coefficient obtained from either the physical experiment using water-filled impedance tube or the numerical experiment using the finite element method with COMSOL Mutiphysics software. Then a genetic algorithm is developed to inversely calculate the equivalent Young's modulus, Poisson's ratio, and damping loss factor of the coating which has the same reflection coefficient as the original coating. The results of the equivalent material properties show that 1) the three properties are all frequency dependent; 2) in general, equivalent Young's modulus increases with the increase of frequency, meanwhile the equivalent damping loss factor tends to decrease; 3) there is a wide variation in the results of equivalent Poisson's ratio. Despite that, the reflection coefficient of the equivalent homogeneous isotropic coating accords well with that of the original coating.Based on the above, the sound scattering on the infinite cylindrical shell coated with the equivalent coating is calculated by using the finite element method based on COMSOL Mutiphysics software. In order to verify the accuracy of the equivalent model, we use COMSOL Mutiphysics software to build up the full geometrical model of the coated shell to calculate the sound scattering. This can be considered as the benchmark. The results of morphic function show that the scattering calculated using equivalent material properties accords well with that obtained from the full finite element model with a mean error of about 1 dB in all frequency spectrum range.

A study of the scale effects on the flexural vibration of graphene sheets using REBO potential based atomistic structural and nonlocal couple stress thin plate models

The flexural vibration of nano-meter sized single layer graphene sheets is studied using a REBO potential based atomistic structural model for a wide range of graphene sheets sizes and chiralities, and with consideration for different boundary conditions, as well as the effects of in-plane forces and environmental stiffness. The scale effects on the vibration of graphene sheets are examined and discussed. A novel nonlocal couple stress thin plate model is then proposed for single layer graphene sheet and is iteratively fitted to the earlier obtained atomistic results to obtain estimations of the scale effect parameters. In addition to the nonlocal parameter, the equivalent Poisson's ratio of the plate model of graphene sheet in flexure is also shown to be a scale effect parameter having mostly negative values. This phenomenon is discussed to corroborate the use of couple stress theory in developing the current thin plate model for graphene sheets.

Prediction of Side Compression/Side Tension Elastic Modulus on Lattice Structure Sandwich Core Materials

In this paper, elastic modulus of core cell in x direction was built. Equivalent tensile/compressive modulus of core materials in y direction and equivalent Poisson ratio of core materials in yox plane were also built.

New Constitutive Model for Two-Dimensional Jointed Rock Mass

Mechanical analysis for jointed rock mass is very significant in geotechnical engineering. In particular, the mechanical characteristics of jointed rock mass can result in nonlinear response of geotechnical engineering and in consequence mechanical analysis for the engineering is difficult. In order to simulate jointed rock mass, a new equivalent model is proposed for two-dimensional jointed rock mass based on strain energy equivalence principle. Firstly, the equivalent elastic modulus and Poisson's ratio for a horizontal joint in unit square is deduced. Then, the equivalent flexibility matrix for a joint of specified angle in unit square is given. Moreover, the equivalent flexibility matrix for multiple joints, which have different angles in unit square, is obtained. Finally, a numerical simulation is given to verify the model. Compared with other conventional algorithm, the proposed approach has some strong points: it is easy to implement in the finite element program. Furthermore, it provides a new model to compute the deformation of joints and rock and the precision is high.

Non-linear analysis of cable networks by FEM and experimental validation

This work studies the analysis of the resistant capacity of cable nets for the stabilization of slopes. Two tests have been carried out, one with a distributed longitudinal load and the other with distributed transversal load, in order to simulate in situ the working conditions of these systems. Tensile tests were also carried out on the cable elements of the network in order to obtain the non-linear mechanical properties. On the one hand, the proposed numerical procedure uses the finite element method (FEM) and it takes into account the material and geometrical non-linearities due to the geometrical change in the cable net substructure. On the other hand, the contour (boundary) beam is modelled by linear beam elements with contact between them. The numerical results of the longitudinal and cross tests were simulated for different geometrical configurations, generating convergent results with respect to strain and resistance, which permit the extrapolation from tested cable nets to untested simulated cable nets, maintaining a basic configuration of constant parameters. The laboratory tests only provide information about the strain and maximum resistance, but they do not establish a relationship between the values of stresses of each net element. These data have been obtained through the computational simulation by FEM. A reliable model of the interaction of the flexible contour beam with the cable network enables the achievement of more efficient solutions in the design analysis. Finally, we compare the structural behaviour of the numerical and experimental results by means of the equivalent elastic modulus and the equivalent Poisson ratio. Excellent agreement between the predicted results by FEM and test observations was found. Besides, conclusions and suggested procedures of calculation applied on the cable networks are given and numerical models to evaluate the stability of the slope protection systems are presented.

Resonant vibration investigations for piezoceramic disks and annuli by using the equivalent constant method

This paper presents the equivalent constant method to investigate the transverse vibration of piezoceramic disks and annuli. By comparing the characteristic equations of resonant frequencies between isotropic and piezoceramic disks, the named equivalent Poisson's ratio v is derived, then the transverse vibration characteristic equation can be expressed as a single formulation for these two materials. To verify this method, characteristic equations of transverse vibration for piezoceramic disks and annuli with many different boundary conditions are discussed and calculated for resonant frequencies. Numerical calculations based on the finite-element method (FEM) also are performed, and the results agree rather well with the theoretical predictions. With the aid of the relations between frequency parameter and equivalent Poisson's ratio in explicit form, the other application of equivalent Poisson's ratio is the inverse evaluation of material constants. The laser Doppler vibrometer (LDV) and impedance analyzer are used to experimentally obtain the resonant frequencies of transverse and radial extensional vibrations, respectively. By the experimental results for the traction-free piezoceramic disk, the planar Poisson's ratio v(p) and planar electromechanical coupling coefficient k(p) are determined.

Effects of perfusion on the mechanical behavior of the brain exposed to hypergravity

In certain flight configurations, fighter pilots are exposed to high Gz acceleration which may induce inflight loss of consciousness (G-LOC). In order to study the mechanical effects induced by these accelerations on the cerebral structures, an experimental model has been developed in vitro. Fresh bovine brains were excised and placed in a transparent mold modeling the inside of the skull. Half of these brains were perfused during the experiment. This assembly was placed into the gondola of a centrifuge, in front of a camera lens. Displacements and deformations of the brains were filmed and recorded at different onset rates. Measurements were made after off-line digitalization of images. Experimental data were incorporated into a finite element calculation code whose mesh represented the brain. The applied behavior law was elastic, the structure being considered as homogeneous and isotropic. The first results concerned the elastic properties of the brains under hypergravity. The mean value of the Young's modulus of the nonperfused brain was 46.8 kPa, which corresponded to the values published in reference literature. For the perfused brains, the mean value of the Young's modulus was higher. The mean value of the equivalent Poisson's ratio was 0.35. In fact, contrary to impacts, the mechanical stimulation is long enough to allow fluid displacements. The mean value of the equivalent Poisson's ratio calculated in the present study should probably be increased since this study was performed post mortem.

Analysis of stress singularities at the corner point of lozenge hole and rigid lozenge inclusion in elastic plates by conformal mapping

The plane elastostatic problems of a lozenge hole and a rigid lozenge inclusion in the infinite plate under tension loading condition are examined by the conformal mapping and Goursat stress functions. A new method is developed for the calculation of the orders of singularity and the stress intensity factors of a singular point, such as the corners of a lozenge hole and rigid lozenge inclusion in the elastic plates submitted to an overall tension at infinity. The rotation of rigid lozenge inclusion by the overall tension at infinity is also considered. Coefficients of Goursat stress functions are determined respectively, for the number m of terms of the finite series of the function for the conformal mapping. Then, the two types of the orders of stress singularities λ I and λ II which correspond to Mode I (opening mode) and Mode II (in-plane shear mode) deformations, respectively, are determined and their numerical results are in good agreement with the exact solutions by Williams for various corner angles of a lozenge. Also the stress intensity factors K 1 and K II of the singular stress field of the corner are determined for arbitrary equivalent Poisson's ratio k , and it is confirmed that K I and K II converge the exact solutions of crack and rigid line inclusion problems when a corner angle of a lozenge tends to zero. Moreover, the angle of the rotation ϵ converges the exact solutions of a rigid line inclusion problems when a corner angle of a lozenge becomes zero. Singular stress and displacement fields corresponding to Mode I and II deformations around the vicinity of the corner of a lozenge hole and a rigid lozenge inclusion are also obtained.

Analysis of stress singularities at the corner point of square hole and rigid square inclusion in elastic plates by conformal mapping

The plane elastostatic problems of a square hole and a rigid square inclusion in the infinite plate under tension loading are examined by the conformal mapping and Goursat stress functions. A new method is developed for the calculation of the orders of singularity and the stress intensity factors of a singular point, such as the corners of a square hole and square inclusion (non-rotation) in the elastic plates submitted to an overall tension at infinity. Coefficients of Goursat stress functions are determined, respectively, for the number m of terms of the finite series of the function for the conformal mapping. Then, the two types of the orders of stress singularities λ i and λ II which correspond to Mode I (opening mode) and Mode II (in-plane shear mode) deformations, respectively, are determined and their numerical results are in good agreement with the exact solutions by Williams. Also the stress intensity factors K I and K II are determined for arbitrary equivalent Poisson's ratio κ. Singular stress and displacement fields corresponding to Mode I and Mode II deformations around a corner point of a square hole and a rigid square inclusion are also obtained.

Singular stress and displacement fields around the corner point of a fiber end in short fiber reinforced composites

Singular elastic stress and displacement fields around the comer point of a fiber end are examined. Using the eigenfunction expansion method, the elastic fields are determined for the three fundamental problems, which are (I) the stress-free edges of the corner, (II) the fixed displacement edges, and (III) the stress-free edge and fixed displacement edge. On the fundamental problems (I) and (II), singular stress and displacement fields are determined with two kinds of singularity order, λ = λ + and λ = λ −, respectively; also, it is found that, for λ = λ +, the stress field is symmetrical with respect to the bisector angle of the corner point of the fiber end and, for λ = λ −, the stress field is antisymmetrical. For the fundamental problem (III), the stress field without symmetry with respect to the bisector angle of the corner point of the fiber end is determined. Also, the singular stress and displacement fields around the corner point of the fiber end are obtained for equivalent Poisson's ratio, K.

Analysis of stress singularities at the corner point of square hole and square inclusion in elastic plates submitted to tension at infinity.

The plane stress elastostatic problems of a square hole and a square inclusion in the infinite plate are examined. A new method was developed for the calculation of the order of singularity and the stress intensity of a singular point, such as the corners of a square hole and a square inclusion in the elastic plates submitted to an overall tension at infinity. Coefficients of Goursat stress function Φ'(ζ), Ψ(ζ) were determined, respectively, for the number m of terms of the finite series of the mapping function. Then, the stress concentration factors at the corner point of the square hole and the rigid square inclusion were determined. Using the stress concentration factors, the orders of stress singularities were determined and their calculation results were in good agreement with one of the exact solutions by Williams(6). Also the stress intensities were determined for each equivalent Poisson's ratio x.

Biaxial cyclic high-strain fatigue of aluminum alloy RR58

In the régime of biaxial high-strain fatigue there is a scarcity of data and consequently of information regarding methods of predicting such behaviour from simpler uniaxial tests. An investigation was carried out on the aluminum alloy RR58 in the form of cylindrical specimens subjected to axial tensile/compressive load and internal/external pressures at room temperature and 140°C. Additional tests were also conducted in separate cyclic torsion and uniaxial machines. The results in the range 100–5000 c indicated that the biaxial strain ratio 1/1 was the most severe case, the effect being less severe as the ratio changed to 1/-1. Of the correlation techniques examined the most successful was a von Mises strain function using the concept of a equivalent Poisson's ratio; the method of maximum shear strain showed promise. Comparative tests on the different cyclic test rigs on the same batch of material indicated the need for care when such aspects as specimen shape and definition of failure are considered, as well as the more obvious effects of material variation and anisotropy.