Engineering Elastic Constants Research Articles

The engineering elastic constants of bio-inspired sandwich cores with wavy cylinders

Beetle Elytron Plates (BEPs) represent a new class of biomimetic sandwich cores with excellent mechanical properties and inspired by the internal structure of the beetle elytra. The cores have a hexagonal centre-symmetric configuration with through-thickness cylinders in the unit cell. The present work describes the behaviour of the engineering elastic constants of an evolution of these BEP topologies that feature cylinders with waviness. These BEP core configurations are simulated using Finite Element models, with periodic boundary conditions for volumetric homogenization. The models are then used to perform a parametric analysis against the geometry characteristics of the new cellular configurations. This work further explores the potential design space of BEP cellular metamaterials by altering the geometry of the trabeculae and facilitates further investigation into the mechanical properties of these new BEP topologies with wave-shaped units. Although – and as expected - the specific nondimensional out-of-plane tensile modulus has values here close to unity, BEP topologies with out-of-plane wave-shaped cylinders show enhanced in-plane moduli values than classical straight cylinder configurations, except for the Young's modulus of MBEP cores with only one semi-wave. The same trend is observed for the nondimensional Young's modulus of EBEP configurations, whereas the situation is opposite for the MBEP topologies. The nondimensional out-of-plane shear modulus decreases for both EBEP and MBEP configurations compared to the straight cylinder cores.

Out-of-plane engineering constants of beetle elytra inspired sandwich cores

The Beetle Elytron Plate (BEP) is a new type of biomimetic sandwich core developed as a potential replacement of classical honeycomb cores in sandwich panels. This work investigates the out-of-plane engineering elastic constants, including Young's and pure shear moduli of parametric BEP cellular topologies. The BEP core configurations are simulated using Finite Element models, with both full-scale and representative unit cells for asymptotic homogenization. The numerical models are also validated by flatwise compression and out-of-plane pure shear loading experiments performed according to ASTM standards. The benchmarked models are then used to perform a parametric analysis of the beetle elytra cellular cores against their geometry characteristics. Results show that the out-of-plane Young's modulus E3/Esand the transverse pure shear modulus G31/Es of both BEP configurations are larger than those of the classic hexagonal honeycombs and increase when the size of the unit cell cylinders, or rib thickness become large. The specific shear moduli of the beetle-elytra inspired honeycombs are however lower than those of classical pure hexagonal honeycomb configurations, although the added presence of cylinders within the cell configuration offers opportunities for tailoring the design of multifunctional cores.

In-plane elasticity of beetle elytra inspired sandwich cores

The Beetle Elytron Plate (BEP) is a new class of biomimetic sandwich core that features excellent compressive strength, energy absorption capacity and flexural properties. These characteristics make BEPs suitable as potential replacements of classical honeycomb cores in sandwich panels. This work describes the behaviour of the in-plane engineering elastic constants of parametric BEP topologies for the first time. The beetle elytron cores configurations are simulated using Finite Element models, including full-scale models and representative unit cells with periodic boundary conditions for asymptotic homogenization. The models are also benchmarked against experimental results obtained from ASTM tensile tests related to the in-plane Young’s modulus, Poisson’s ratio and shear modulus. The benchmarked models are then used to perform a parametric analysis against the geometry characteristics of the cellular configurations. Results obtained from this work will provide a solid foundation for further research on BEP structures and expand their applications into wider engineering fields.

Homogenization of the macroscopic stiffness of 2D triaxially braided composites: Roles of the local stiffness model and undulating average scheme

This work investigates a two-level homogenization of the macroscopic stiffness of the 2DTBC with emphasizes on the roles of the local stiffness model and undulating average scheme. The effective elastic property of the braid yarn is rigorously derived by an energy method instead of intuitive mathematical average methods in the literature. General formulations of the compliance and stiffness undulating average schemes have been obtained, which are proven to be reduced to the simple mathematical average methods in certain cases. Validated with different experiments, it is unexpected to find out that the prediction combined with the simple rule of mixture and stiffness undulating average scheme yields the most consistent agreement with experimental results after the overall assessment of all the in-plane engineering elastic constants under various braiding conditions.

Design of a New Arcan Fixture for In-plane Pure Shear and Combined Normal/Shear Stress Characterization of Fiber Reinforced Polymer Composites

Engineering elastic constants and strength parameters shall be known to the designer in order to predict the structural response of composite materials. These properties shall be determined in various directions as per the designated standards. Testing of composite materials under the combined effect of in-plane shear and normal stress is of great importance. In this work, a new Arcan fixture has been designed, and then manufactured from aluminum alloy AA7075-T73. This test fixture can be used for uniaxial as well as biaxial testing of fiber reinforced polymers (FRPs) laminates in pure shear, and combined normal/shear stress states. Nevertheless, the fixture can be used for other materials where combined in-plane testing is required including metals and polymers. The special butterfly shape Arcan specimen was optimized based on the parametric study in ABAQUS environment by a Python scripting. The objective of the parametric study was to get a uniform shear stress field in the notch section of the specimen which is the cross-sectional area between the two opposite V-notch roots. The domain of the uniform shear stress-strain distribution in the notch section must be greater enough than the size of the strain gauge rosettes where these can be effectively installed for strain acquisition. The experimental set-ups for the realization of pure shear stress, normal stress, and combined normal/shear stress scenarios are schematically elaborated. The pure shear stress-strain response based on the Arcan test was compared with the tensile testing of ±450 symmetric laminate.

Elastic properties of diamond-like phases based on carbon nanotubes

Eight diamond-like structures (tubulanes) of different morphology based on carbon nanotubes are studied by the combination of molecular dynamics simulation and analytical calculations. Molecular dynamics is used for the structure relaxation, stability analysis, and calculation of the stiffness and compliance coefficients of stable tubulanes. Six stable tubulanes which can be elastically deformed are distinguished among the considered structures. Engineering elastic constants such as Young's modulus, Poisson's ratio, shear modulus, and bulk modulus are found by analytical methods. Two of the studied structures, TA6 and TB, are found to be partial auxetics having negative Poisson's ratio with the minimum values of −0.01 and −0.8, respectively. The maximum Young's modulus for tubulanes TA6, TA8, and TB is found to be >1 TPa. In combination with hardness close to that of diamond, considered phases with their outstanding mechanical properties can be potentially used as protective coatings.

Design on the driveshaft of 3D 4-Directional carbon fiber braided composites

In this paper, the method of designing a drive shaft with a 3D 4-Directional braided composite structure is proposed. First, the tubular unit cell model of 3D 4-Directional braided composite is established for obtaining the engineering elastic constants and the strength values of the tubular braided composite. Also, the relationship among the shear modulus, the braided angles and the fiber volume fraction is analyzed. Second, an orthogonal anisotropic tubular model with a fiber volume fraction of 50% and a braided angle of 45° is established to predict the torsional strength, torsional stiffness and virbration modes of the 3D braided composite drive shaft. Finally, the parameterized design with the thickness of the tubular is used to calculate the ultimate torque of the drive shaft, also the optimal drive shaft size is given and the 60.18% weight loss is achieved. This work will play an important role in the lightweight design of the 3D 4-Directional braided composite drive shaft.

Equilibrium diamond‐like carbon nanostructures with cubic anisotropy: Elastic properties

AbstractDiamond‐like carbon nanostructures with cubic anisotropy made by joining fullerene‐like molecules of different types via valence bonds are studied by means of molecular dynamics simulations. The considered structures are interesting because they include both‐ and‐hybridized carbon atoms, which lead to their distinct properties compared to the structures with one type of hybridization. Seven diamond‐like carbon phases having different shapes of structural units and/or different ways of their connection are studied in the present work. For the relaxed equilibrium structures, the engineering elastic constants (Poisson's ratio, Young's modulus, and shear modulus) are calculated as the functions of the crystal orientation angles. Extreme values of the elastic constants are reported. It is shown that two of the considered diamond‐like structures have negative Poisson's ratio and can be regarded as the partial auxetics. According to the results of the present study, elastic properties of the bulk diamond‐like carbon structures can vary considerably depending on their structure.Diamond‐like carbon nanostructures

A two-scale method for predicting the mechanical properties of 3D braided composites with internal defects

Pore defects have significant effect on the mechanical properties of 3D braided composites. Two-scale finite element models of the fiber tows and the braided composites are developed to predict the elastic properties and the micro stress of 3D braided composites. Two basic types of pore defects, the voids in resin matrix and the dry patches in fiber tows, have been taken into account. Periodical boundary conditions are applied on the two-scale FE models by the coupling and constraint equation defining commands in ANSYS. The predicted effective elastic constants agree well with the available experimental data, demonstrating the validity of the two-scale FE models. The effects of braiding angle and fiber volume fraction on the engineering elastic constants are discussed. Furthermore, the effects of two types of defects on the effective elastic properties of 3D braided composites are also discussed in detail. Some useful conclusions are drawn herein. From simulation, dry patches in fiber tows have more significant effect on the elastic properties than voids in matrix.

Microstructure and mechanical properties of 3D surface-core 4-directional braided composites

This paper first presents an analytical model for a new kind of braided composite called 3D surface-core 4-directional braided composite. Taking into account the braiding process, three types of microstructural unit-cell models are established with respect to the interior, surface, and corner regions. According to the spatial paths and squeezing deformation of yarns in the material, different braiding angles and cross-section shapes are adopted. By using the volume averaging method, the total stiffness is calculated and the engineering elastic constants are obtained. The effect of braiding angle and fiber volume fraction on the stiffness is addressed. The theoretical predictions are in good agreement with the experimental data. The effects of edge cuttings on the longitudinal tensile properties of the new material and 3D 4-directional braided composites are experimentally compared. The proposed structure has obvious advantage to restrain the degradation of mechanical properties caused by cuttings.

Stiffness prediction of multilayer-connected biaxial weft-knitted fabric-reinforced composites

Based on the representative volume element (RVE) model of single layer in multilayer-connected biaxial weft-knitted (MBWK) fabric-reinforced composites, the elastic properties of multilayer-connected biaxial weft-knitted fabric-reinforced composites have been developed and presented hereafter. The average stiffness matrix of the multilayer-connected biaxial weft-knitted fabric-reinforced composites, taking into account the contribution the final geometrical of the knitting loops, can be obtained by the volume average stiffness of the unidirectional composites with different local coordinate system, and the engineering elastic constants of this kind of composites have been figured out. Numerical predictions have compared to the results of tensile tests performed on composite samples. The percentage error of the numerical prediction results and the experimental results is less than 10%.

A New Geometric Model for Three-Dimensional Braided Composites

According to the structural features of 3-D braided composites, the whole structure is divided into three types of sub-unit cells, these are the interior unit cell, the surface unit cell and the corner unit cell. Considering the bending of fiber bundle and the deformation of cross-section which are caused by the space fiber extrusion and twist together, the corresponding geometric analysis models for every type of sub-unit cell are established, and the engineering elastic constants of the 3-D braided composites are predicted. The results show that the calculated results well agree with the experimental results, and the effectiveness of the model is verified.

Analysis of Micro Structure and Elastic Property on 3-D Tubular Woven Carbon Fiber Composite

For the further research of 3D tubular woven carbon fiber composite, a unit cell division method and a mechanical model were put forward to predict the engineering elastic constants. The model adopted raceway shape as the yarns cross-section, and prediction methods of volume fractions and elastic modulus were established based on the micro structure and geometric parameters of the yarn. Then the finite element method was used to analysis the mechanical behavior under the circumstances of axial-tensile load, and the stress state was revealed. The results shows that the predicted values using finite element method agree well with the theoretical calculation values, thus the model and analysis method of elastic constants is verified.

Group Analysis Method of 3D Braided Composites Elastic Properties

The matrix representation of space point group is used in transferring the elastic matrix of the braided yarn based on the symmetries of braided composites representative volume element (RVE) meso-geometrical structure. The off-axis elastic matrixes of the whole braided yarns of the RVE are deduced. With a use of meso-mechanical model based on the mixture rule, the yarn segments off-axis elastic matrixes in the RVE and matrixs one are summed with weight; Equivalent elastic matrix of 3D braided composites was deduced. Equivalent engineering elastic constants are achieved in the end. The model can be applied in 2D braided composites mechanical analysis if its geometry is satisfied to the symmetries corresponding to plain point group.

Generic stiffness model for 3D woven orthogonal hybrid composites

Due to developments in the advanced 3D textile composite materials, it has become possible to tailor their mechanical properties by either placing the reinforcing fibers in a particular direction or mixing the fibers of superior mechanical properties with fibers of nominal mechanical properties in a certain ratio. The latter process is well known as reinforcing material hybridization. The mixing of reinforcing materials incurs cost due to fibers of superior mechanical properties and adds complexities in determining the macroscopic mechanical properties. The present paper proposes a methodology named as Generic Stiffness Model (GS-Model) to predict the engineering elastic constants of hybrid composites, taking 3D woven orthogonal hybrid composite as a baseline. A sensitivity study about reinforcing material hybridization has also been conducted in order to determine the net effect on the elastic properties of 3D woven orthogonal hybrid composite. The GS-Model and material hybridization study can be a useful tool for designers and manufacturers of composite materials to help them in the designing and selection of appropriate material for a specific application.

Applications of a New Element Model of Solid Bodies in Plasticity

Based on the deformations under the equivalent external forces are the same, a new element model of elastic perfectly-plastic and orthotropic solid bodies is presented, and the elastic perfectly-plastic and isotropic materials is a special subclass. Furthermore, the method for determining the displacements, the stresses and the strains of a body under the action of applied forces has been given. A new method for predicting the engineering elastic constants of a fiber-reinforced composite material is also presented. It can be found that the precision by using the new element method is good, and the limit analysis has the highest precision in all methods.

Temperature Dependent Elastic Constants of Directionally Solidified Superalloys

Directionally solidified superalloys have been extensively used as turbine blade materials to improve creep-rupture and thermal fatigue performances. Turbine blades are subjected to fluctuant temperature changes. Precise knowledge of material behavior at various temperatures is essential in design and service life evaluation of turbine blades. In this study, coaxial model is extended to consider temperature dependent engineering elastic constants. Although no existing theory predicts the temperature dependence engineering elastic constants over large range of temperature, these constants could be estimated based upon very limited experimental data of direction solidification specimens and other temperature dependent materials data. Excellent agreement is observed between estimations and experimental data of 45 deg and 90 deg off directionally solidified direction specimens.

Research on Constitutive Equation for Steel Wire Wound Reinforced High-Pressure Hose

According to the features of reinforced layer of steel wire wound reinforced high-pressure hose (hereinafter referred to as SRH), 9 classical models for predicting the engineering elastic modulus of reinforced layer of continuous filament reinforced composite material were contrastively analyzed. As a result, Chinese engineering empirical formula should be conformable for predicting the engineering elastic constants of SRH reinforced layer in material normal coordinates. Based on composite microscopic theory and tensor theory, constitutive equation of SRH reinforced layer in structural cylindrical coordinates in three-dimensional case was obtained.

Research on Constitutive Equation for Steel Wire Wound Reinforced High-Pressure Hose

According to the features of reinforced layer of steel wire wound reinforced high-pressure hose (hereinafter referred to as SRH), 9 classical models for predicting the engineering elastic modulus of reinforced layer of continuous filament reinforced composite material were contrastively analyzed. As a result, Chinese engineering empirical formula should be conformable for predicting the engineering elastic constants of SRH reinforced layer in material normal coordinates. Based on composite microscopic theory and tensor theory, constitutive equation of SRH reinforced layer in structural cylindrical coordinates in three-dimensional case was obtained.

Elastic analysis of 3D woven orthogonal composites

PurposeThe purpose of this paper is to present an analytical modelling approach to predict engineering elastic constants of 3D woven orthogonal composites (3DWOCs) at representative volume element (RVE) level using a volume averaging method.Design/methodology/approachThe present analytical modeling approach uses a more realistic internal geometry representation of the 3DWOC. A RVE which is a repeating element at macroscopic level is first identified and volume proportions and engineering elastic constants of various constituents (matrix and family of constituent tows; warp, weft and z‐fibers) which contribute to the global stiffness of RVE/composite are next determined. For accurate predictions, emphasis is given to accurate measurements of micro‐structural data such as fiber volume fraction and fiber volume proportion of constituent tows and internal geometry of the 3DWOC structure‐in particular, undulation of z‐fibers. Microscopic study has been conducted in this regard.FindingsThe predicted engineering elastic constants are compared against experimental data, showing a strong correlation between predicted and experimental values.Practical implicationsThe methodology presented in the paper can be used for accurate computation of the engineering elastic constants of 3DWOCs. The method can also be used for other types of 2D or 3D textile composites such as 2D woven composites, 2D braided composites, 3D woven angle interlock composites and 3D braided composites.Originality/valueThe paper succeeds in relating the micro‐structural properties and analytical model for the accurate prediction of engineering elastic constants.