Effective properties of composite materials containing voids

1993 ◽  
Vol 440 (1909) ◽  
pp. 461-473 ◽  
Keyword(s):  
Young’S Modulus ◽  
Poisson’S Ratio ◽  
Effective Properties ◽  
Young's Modulus ◽  
Matrix Material ◽  
Practical Importance ◽  
Three Dimensional ◽  
Poisson's Ratio ◽  
Two Dimensional ◽  
Isotropic Composite

Recent results of theoretical and practical importance prove that the two-dimensional (in-plane) effective (average) Young’s modulus for an isotropic elastic material containing voids is independent of the Poisson’s ratio of the matrix material. This result is true regardless of the shape and morphology of the voids so long as isotropy is maintained. The present work uses this proof to obtain explicit analytical forms for the effective Young’s modulus property, forms which simplify greatly because of this characteristic. In some cases, the optimal morphology for the voids can be identified, giving the shapes of the voids, at fixed volume, that maximize the effective Young’s modulus in the two-dimensional situation. Recognizing that two-dimensional isotropy is a subset of three-dimensional transversely isotropic media, it is shown in this more general case that three of the five properties are independent of Poisson’s ratio, leaving only two that depend upon it. For three-dimensionally isotropic composite media containing voids, it is shown that a somewhat comparable situation exists whereby the three-dimensional Young’s modulus is insensitive to variations in Poisson’s ratio, v m , over the range 0 ≤ v m ≤ ½, although the same is not true for negative values of v m . This further extends the practical usefulness of the two-dimensional result to three-dimensional conditions for realistic values of v m .

On Effective Mechanical Properties of Two-Dimensional Porous Materials

2020 ◽  
Vol 12 (04) ◽  
pp. 2050040
Author(s):  
Zaoyang Guo ◽  
Lei Wang ◽  
Xiaojun Guo ◽  
Yang Chen ◽  
Leiting Dong
Keyword(s):  
Porous Materials ◽  
Young’S Modulus ◽  
Poisson’S Ratio ◽  
Young's Modulus ◽  
Full Range ◽  
Theoretical Models ◽  
Poisson's Ratio ◽  
Analytical Models ◽  
Two Dimensional ◽  
Effective Mechanical Properties

Two-dimensional (2D) representative volume element (RVE) has been widely used to simulate the effective behaviors of the materials with aligned pores. In this paper, the anisotropy indexes are defined for the 2D RVE model to quantitatively evaluate the extent of anisotropy of the model. A normalized procedure is then proposed to compute the effective moduli of the RVE models, which can further minimize the influence of anisotropy of the RVE models. The effective Poisson’s ratio of the porous materials is challengeable to be estimated well, and few analytical models can give good predictions. The theoretical models are proposed to approach the effective Young’s modulus and the effective Poisson’s ratio of the 2D porous materials covering the full range of porosity. It is numerically validated that the theoretical models give accurate predictions for the effective Young’s modulus and Poisson’s ratio of the 2D porous materials.

scholarly journals Research on Mechanical Properties of High-Pressure Anhydrite Based on First Principles

Crystals ◽  
2020 ◽  
Vol 10 (4) ◽  
pp. 240
Author(s):  
Xianren Zeng ◽  
Shihui You ◽  
Linmei Li ◽  
Zhangli Lai ◽  
Guangyan Hu ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Bulk Modulus ◽  
Young’S Modulus ◽  
First Principles ◽  
Poisson’S Ratio ◽  
Young's Modulus ◽  
Three Dimensional ◽  
Poisson's Ratio ◽  
Physical Parameters ◽  
Three Dimensional Model

This article focuses on the elucidation of a three-dimensional model of the structure of anhydrite crystal (CaSO4). The structure parameters of anhydrite crystal were obtained by means of first principles after structure optimization at 0~120 MPa. In comparison with previous experimental and theoretical calculation values, the results we obtained are strikingly similar to the previous data. The elastic constants and physical parameters of anhydrite crystal were also studied by the first-principles method. Based on this, we further studied the Young’s modulus and Poisson’s ratio of anhydrite crystal, the anisotropy factor, the speed of sound, the minimum thermal conductivity and the hardness of the material. It was shown that the bulk modulus and Poisson’s ratio of anhydrite crystal rose slowly with increasing pressure. The anisotropy characteristics of the Young’s modulus and shear modulus of anhydrite crystal were consistent under various pressure levels, while the difference in the anisotropy characteristics of the bulk modulus appeared. The acoustic velocities of anhydrite crystal tended to be stable with increasing pressure. The minimum thermal conductivity remained relatively unchanged with increasing pressure. However, the material hardness declined gradually with increasing pressure.

Determination of Poisson's Ratio of Thin low-k Films using Bidirectional Thermal Expansion Measurement

2006 ◽  
Vol 914 ◽  
Author(s):  
Jiping Ye ◽  
Satoshi Shimizu ◽  
Shigeo Sato ◽  
Nobuo Kojima ◽  
Junnji Noro
Keyword(s):  
Thermal Expansion ◽  
Temperature Gradient ◽  
Young’S Modulus ◽  
Poisson’S Ratio ◽  
Silicon Oxide ◽  
Young's Modulus ◽  
Polymer Materials ◽  
Poisson's Ratio ◽  
Thermal Expansion Measurement ◽  
Low K

AbstractA recently developed bidirectional thermal expansion measurement (BTEM) method was applied to different types of low-k films to substantiate the reliability of the Poisson's ratio found with this technique and thereby to corroborate its practical utility. In this work, the Poisson's ratio was determined by obtaining the temperature gradient of the biaxial thermal stress from substrate curvature measurements, the temperature gradient of the whole thermal expansion strain along the film thickness from x-ray reflectivity (XRR) measurements, and reduced modulus of the film from nanoindentation measurements. For silicon oxide-based SiOC film having a thickness of 382.5 nm, the Poisson's ratio, Young's modulus and thermal extension coefficient (TEC) were determined to be Vf = 0.26, αf =21 ppm/K and Ef =9,7 GPa. These data are close to the levels of metals and polymers rather than the levels of fused silicon oxide, which is characterized by Vf = 0.17 and Er = 69.6 GPa. The alkyl component in the silicon oxide-based framework is thought to act as an agent in reducing the modulus and elevating the Poisson's ratio in SiOC low-k materials. In the case of an organic polymer SiLK film with a thickness of 501.5 nm, the Poisson's ratio, Young's modulus and TEC were determined to be Vf = 0.39, αf =74 ppm/K and Er =3.1 GPa, which are in the typical range of V= 0.34~0.47 with E =1.0~10 GPa for polymer materials. From the viewpoint of the relationship between the Poisson's ratio and Young's modulus as classified by different material types, the Poisson's ratios found for the silicon oxide-based SiOC and organic SiLK films are reasonable values, thereby confirming that BTEM is a reliable and effective method for evaluating the Poisson's ratio of thin films.

Measurement of Young's Modulus and Poisson's Ratio of Thin Film by Combination of Bulge Test and Nano-Indentation

2008 ◽  
Vol 33-37 ◽  
pp. 969-974 ◽  
Author(s):  
Bong Bu Jung ◽  
Seong Hyun Ko ◽  
Hun Kee Lee ◽  
Hyun Chul Park
Keyword(s):  
Thin Film ◽  
Mechanical Properties ◽  
Young’S Modulus ◽  
Poisson’S Ratio ◽  
Young's Modulus ◽  
Applied Pressure ◽  
Indentation Test ◽  
Poisson's Ratio ◽  
Bulge Test ◽  
Nano Indentation

This paper will discuss two different techniques to measure mechanical properties of thin film, bulge test and nano-indentation test. In the bulge test, uniform pressure applies to one side of thin film. Measurement of the membrane deflection as a function of the applied pressure allows one to determine the mechanical properties such as the elastic modulus and the residual stress. Nano-indentation measurements are accomplished by pushing the indenter tip into a sample and then withdrawing it, recording the force required as a function of position. . In this study, modified King’s model can be used to estimate the mechanical properties of the thin film in order to avoid the effect of substrates. Both techniques can be used to determine Young’s modulus or Poisson’s ratio, but in both cases knowledge of the other variables is needed. However, the mathematical relationship between the modulus and Poisson's ratio is different for the two experimental techniques. Hence, achieving agreement between the techniques means that the modulus and Poisson’s ratio and Young’s modulus of thin films can be determined with no a priori knowledge of either.

Multi-Parameter Optimization to Improve the Erosion Resistance of Coating by Fe Simulation

2021 ◽  
Author(s):  
Fang Li ◽  
Liuxi Cai ◽  
Shun-sen Wang ◽  
Zhenping Feng
Keyword(s):  
Tensile Stress ◽  
Young’S Modulus ◽  
Impact Velocity ◽  
Coating Thickness ◽  
Poisson’S Ratio ◽  
Erosion Resistance ◽  
Young's Modulus ◽  
Tio2 Coating ◽  
Poisson's Ratio ◽  
Stress Peak

Abstract Finite element method (FEM) was used to study the stress peak of stress S11 (Radial stress component in X-axis) on the steam turbine blade surface of four typical erosion-resistant coatings (Fe2B, CrN, Cr3C2-NiCr and Al2O3-13%TiO2). The effect of four parameters, such as impact velocity, coating thickness, Young's modulus and Poisson's ratio on the stress peak of stress S11 were analyzed. Results show that: the position of tensile stress peak and compressive stress peak of stress S11 are far away from the impact center point with the increase of impact velocity. When coating thickness is equal to or greater than 10μm, the magnitude of tensile stress peak of stress S11 on the four coating surfaces does not change with the coating thickness at different impact velocities. When coating thickness is equal to or greater than 2μm, the magnitude of tensile stress peak of stress S11 of four coatings show a trend of increasing first and then decreasing with the increase of Young's modulus. Meanwhile, the larger the Poisson's ratio, the smaller the tensile stress peak of stress S11. After optimization, When coating thickness is 2μm, Poisson's ratio is 0.35 and Young's modulus is 800 GPa, the Fe2B coating has the strongest erosion resistance under the same impact conditions, followed by Cr3C2-NiCr, CrN, and the Al2O3- 13%TiO2 coating, Al2O3-13%TiO2 coating has the worst erosion resistance.

scholarly journals Finite Element Analysis of Tibial Bone-Implant Load Transfer and Bone Strains with a Modern Fixed-bearing Total Ankle Replacement

2018 ◽  
Vol 3 (3) ◽  
pp. 2473011418S0011
Author(s):  
Daniel Sturnick ◽  
Guilherme Saito ◽  
Jonathan Deland ◽  
Constantine Demetracopoulos ◽  
Xiang Chen ◽  
...  
Keyword(s):  
Young’S Modulus ◽  
Poisson’S Ratio ◽  
Tibial Component ◽  
Load Transfer ◽  
Young's Modulus ◽  
Stress Shielding ◽  
Poisson's Ratio ◽  
Bone Implant ◽  
Tibial Tray ◽  
Tibial Bone

Category: Ankle Arthritis Introduction/Purpose: Loosening of the tibial component is the primary failure mode in total ankle arthroplasty (TAA). The mechanics of the tibial component loosening has not been fully elucidated. Clinically observed radiolucency and cyst formation in the periprosthetic bone may be associated with unfavorable load sharing at and adjacent to the tibial bone-implant interface contributory to implant loosening. However, no study has fully investigated the load transfer from the tibial component to the bone under multiaxial loads in the ankle. The objective of this study was to utilize subject-specific finite element (FE) models to investigate the load transfer through tibial bone-implant interface, as well as periprosthetic bone strains under simulated multiaxial loads. Methods: Bone-implant FE models were developed from CT datasets of three cadaveric specimens that underwent TAA using a modern fixed-bearing tibial implant (a cobalt-chrome tray with a polyethylene bearing, Salto Talaris, Integra LifeSciences). Implant placement was estimated from the post-operative CT scans. Bone was modeled as isotropic elastic material with inhomogeneous Young’s modulus (determined from CT Hounsfield units) and a uniform Poisson’s ratio of 0.3. The tibial tray (Young’s modulus: 200,000 MPa, Poisson’s ratio: 0.3) and the polyethylene bearing (Young’s modulus: 600 MPa, Poisson’s ratio: 0.4) were modeled as isotropic elastic. A 100-N compressive force, a 300-N anterior force, and a 3-Nm moment were applied to two literature based loading regions on the surface of the polyethylene bearing. The proximal tibia was fixed in all directions. The bone-implant contact was modeled as frictional with a coefficient of 0.7, whereas the polyethylene bearing was bonded to the tray. Results: Along the long axis of the tibia, load was transferred to the bone primarily through the flat bone-contacting base of the tibial tray and the cylindrical top of the keel, little amount of load was transferred to the bone between those two features (Fig. 1A). Low strain was observed in bone regions medial and lateral to the keel of the tibial tray, where bone cysts were often observed clinically (Fig. 1A). On average, approximated 70% of load was transferred through the anterior aspect of the tibial tray at the flat bone-contacting base, which corresponded to the relatively high bone strain adjacent to the implant edge in the anterior bone-implant interface (Fig. 1B). Conclusion: Our results demonstrated a two-step load transfer pattern along the long axis of the tibia, revealing regions with low bone strain peripheral to the keel indicative to stress shielding. Those regions were consistent with the locations of bone cysts observed clinically, which may be explained by the stress shielding associated remodeling of bone. These findings could also describe the mechanism of implant loosening and failure. Future studies may use our model to simulate more loading scenarios, as well as different implant placement and design, to identify means to optimize load transfer to the bone and prevent stress shielding.

The Effect of Design Changes on Sound Transmission through a Building

1996 ◽  
Vol 3 (3) ◽  
pp. 145-185
Author(s):  
Robert J.M. Craik
Keyword(s):  
Young’S Modulus ◽  
Poisson’S Ratio ◽  
Young's Modulus ◽  
Sound Transmission ◽  
Poisson's Ratio ◽  
Analysis Model ◽  
Room Size ◽  
Design Changes ◽  
Small Change ◽  
The Individual

A statistical energy analysis model of a building was used to assess the effect of design changes on sound transmission. Systematic changes were made to the material properties (density, Young's modulus, Poisson's ratio and internal loss factor) and to the dimensions (thickness and room size). These changes resulted in a redistribution of the energy throughout the building causing the noise level to go up in some rooms and to go down in others. For each case examined it was found that the effect of several changes could be estimated from the sum of the individual changes. Thus a change of 20% in the density resulted in approximately double the change in DnTw that was obtained from a 10% change in density. The same additive effect was also found to apply if more than one variable was changed at the same time. Thus the change in DnTw resulting from a small change in Young's modulus for the floors and a small change in the density of the walls can be estimated from the sum of the two individual effects. Changes to the thickness and density of the walls and floors have the greatest effect on sound transmission whilst changes to Young's modulus and Poisson's ratio have a much smaller effect. Damping can also have a significant effect on transmission particularly far from the source.

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