Plastic behaviour of two-dimensional regular hexagonal structures with bilinear and uniaxial strength asymmetry in cellular materials

An elasto-plastic micromechanical model of the two-dimensional regular hexagonal structure was developed. General analytical expressions for the incremental constitutive relations were derived in terms of parameters defining the architecture and material of an internal beam. Non-linearity of the structure was introduced by considering the elastic—linear strain hardening behaviour of each internal beam, in which uniaxial strength asymmetry of the cellular material was accounted for. The plastic stress—strain relationship of the structure under any loading conditions can therefore be analysed by localized beam deformation. The results show that the bending deformation of the internal beam dominates under uniaxial stress loading conditions, however, the axial displacement dominates under the uniaxial strain conditions. The structure will present different behaviours under different loading conditions. The corresponding stresses under the uniaxial strain condition are greater than those under the uniaxial stress condition. The analyses also show that the volume fraction is highly correlated with the elastic constants and yield stresses of the structure. The denser the structure, the higher the moduli and yield stresses.

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Simulating Size and Volume Fraction-Dependent Strength and Ductility of Nanotwinned Composite Copper

Journal of Applied Mechanics ◽

10.1115/1.4033519 ◽

2016 ◽

Vol 83 (7) ◽

Cited By ~ 7

Author(s):

Linli Zhu ◽

Xiang Guo ◽

Haihui Ruan

Keyword(s):

Mechanical Properties ◽

Yield Strength ◽

Volume Fraction ◽

Constitutive Relations ◽

Micromechanical Model ◽

Mean Field ◽

Coarse Grained ◽

Proposed Model ◽

Strain Relationship ◽

Strength And Ductility

This work presents a micromechanical model to investigate mechanical properties of nanotwinned dual-phase copper, consisting of the coarse grained phase and the nanotwinned phase. Both strengthening mechanisms of nanotwinning and the contributions of nanovoids/microcracks have been taken into account in simulations. With the aid of modified mean-field approach, the stress–strain relationship is derived by combining the constitutive relations of the coarse grained phase and the nanotwinned phase. Numerical results show that the proposed model enables us to describe the mechanical properties of the nanotwinned composite copper, including both yield strength and ductility. The calculations based on the proposed model agree well with the results from finite element method (FEM). The predicted yield strength and ductility are sensitive to the twin spacing, grain size, as well as the volume fractions of phases in this composite copper. These results will benefit the optimization of both strength and ductility by controlling constituent fractions and the size of the microstructures in metallic materials.

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Instrumentation For Quantitative Microscopy

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100078584 ◽

1977 ◽

Vol 35 ◽

pp. 206-209

Author(s):

B. Ralph ◽

A.R. Jones

Keyword(s):

Volume Fraction ◽

Three Dimensional ◽

Two Dimensional ◽

Automatic Data ◽

Phase Volume Fraction ◽

Statistical Confidence ◽

Resultant Data ◽

Automatic Data Collection ◽

Third Dimension ◽

Evolution Of Microstructure

In all fields of microscopy there is an increasing interest in the quantification of microstructure. This interest may stem from a desire to establish quality control parameters or may have a more fundamental requirement involving the derivation of parameters which partially or completely define the three dimensional nature of the microstructure. This latter categorey of study may arise from an interest in the evolution of microstructure or from a desire to generate detailed property/microstructure relationships. In the more fundamental studies some convolution of two-dimensional data into the third dimension (stereological analysis) will be necessary.In some cases the two-dimensional data may be acquired relatively easily without recourse to automatic data collection and further, it may prove possible to perform the data reduction and analysis relatively easily. In such cases the only recourse to machines may well be in establishing the statistical confidence of the resultant data. Such relatively straightforward studies tend to result from acquiring data on the whole assemblage of features making up the microstructure. In this field data mode, when parameters such as phase volume fraction, mean size etc. are sought, the main case for resorting to automation is in order to perform repetitive analyses since each analysis is relatively easily performed.

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An Intrinsic Material Tailoring Approach for Functionally Graded Axisymmetric Hollow Bodies Under Plane Elasticity

Journal of Elasticity ◽

10.1007/s10659-021-09822-y ◽

2021 ◽

Author(s):

Hassan Mohamed Abdelalim Abdalla ◽

Daniele Casagrande

Keyword(s):

Optimization Problem ◽

Volume Fraction ◽

Minimum Principle ◽

Equivalent Stress ◽

Micromechanical Model ◽

Plane Elasticity ◽

Functionally Graded ◽

Pontryagin Minimum Principle ◽

Volume Fractions ◽

Material Tailoring

AbstractOne of the main requirements in the design of structures made of functionally graded materials is their best response when used in an actual environment. This optimum behaviour may be achieved by searching for the optimal variation of the mechanical and physical properties along which the material compositionally grades. In the works available in the literature, the solution of such an optimization problem usually is obtained by searching for the values of the so called heterogeneity factors (characterizing the expression of the property variations) such that an objective function is minimized. Results, however, do not necessarily guarantee realistic structures and may give rise to unfeasible volume fractions if mapped into a micromechanical model. This paper is motivated by the confidence that a more intrinsic optimization problem should a priori consist in the search for the constituents’ volume fractions rather than tuning parameters for prefixed classes of property variations. Obtaining a solution for such a class of problem requires tools borrowed from dynamic optimization theory. More precisely, herein the so-called Pontryagin Minimum Principle is used, which leads to unexpected results in terms of the derivative of constituents’ volume fractions, regardless of the involved micromechanical model. In particular, along this line of investigation, the optimization problem for axisymmetric bodies subject to internal pressure and for which plane elasticity holds is formulated and analytically solved. The material is assumed to be functionally graded in the radial direction and the goal is to find the gradation that minimizes the maximum equivalent stress. A numerical example on internally pressurized functionally graded cylinders is also performed. The corresponding solution is found to perform better than volume fraction profiles commonly employed in the literature.

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Characterization of the vibration, stability and static responses of graphene-reinforced sandwich plates under mechanical and thermal loadings using the refined shear deformation plate theory

Journal of Sandwich Structures & Materials ◽

10.1177/1099636221993865 ◽

2021 ◽

pp. 109963622199386

Author(s):

Hessameddin Yaghoobi ◽

Farid Taheri

Keyword(s):

Shear Deformation ◽

Volume Fraction ◽

Plate Theory ◽

Micromechanical Model ◽

Sheet Thickness ◽

Analytical Investigation ◽

Sandwich Plates ◽

Simply Supported ◽

Vibration Stability ◽

Shear Deformation Plate Theory

An analytical investigation was carried out to assess the free vibration, buckling and deformation responses of simply-supported sandwich plates. The plates constructed with graphene-reinforced polymer composite (GRPC) face sheets and are subjected to mechanical and thermal loadings while being simply-supported or resting on different types of elastic foundation. The temperature-dependent material properties of the face sheets are estimated by employing the modified Halpin-Tsai micromechanical model. The governing differential equations of the system are established based on the refined shear deformation plate theory and solved analytically using the Navier method. The validation of the formulation is carried out through comparisons of the calculated natural frequencies, thermal buckling capacities and maximum deflections of the sandwich plates with those evaluated by the available solutions in the literature. Numerical case studies are considered to examine the influences of the core to face sheet thickness ratio, temperature variation, Winkler- and Pasternak-types foundation, as well as the volume fraction of graphene on the response of the plates. It will be explicitly demonstrated that the vibration, stability and deflection responses of the sandwich plates become significantly affected by the aforementioned parameters.

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Deformation behavior of shape memory alloy under complex loading conditions (modeling and constitutive relations)

10.1117/12.316312 ◽

1998 ◽

Author(s):

Meng Ye ◽

Masataka Tokuda ◽

Petr Sittner ◽

B. Bundara

Keyword(s):

Shape Memory Alloy ◽

Shape Memory ◽

Deformation Behavior ◽

Constitutive Relations ◽

Complex Loading ◽

Loading Conditions

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Free vibration analysis of three-layer thin cylindrical shell with variable thickness two-dimensional FGM middle layer under arbitrary boundary conditions

Journal of Sandwich Structures & Materials ◽

10.1177/10996362211020429 ◽

2021 ◽

pp. 109963622110204

Author(s):

Xue-Yang Miao ◽

Chao-Feng Li ◽

Yu-Lin Jiang ◽

Zi-Xuan Zhang

Keyword(s):

Cylindrical Shell ◽

Boundary Conditions ◽

Volume Fraction ◽

Ritz Method ◽

Admissible Function ◽

Free Vibration Analysis ◽

Middle Layer ◽

Two Dimensional ◽

Arbitrary Boundary ◽

Arbitrary Boundary Conditions

In this paper, a unified method is developed to analyze free vibrations of the three-layer functionally graded cylindrical shell with non-uniform thickness. The middle layer is composed of two-dimensional functionally gradient materials (2D-FGMs), whose thickness is set as a function of smooth continuity. Four sets of artificial springs are assigned at the ends of the shells to satisfy the arbitrary boundary conditions. The Sanders’ shell theory is used to obtain the strain and curvature-displacement relations. Furthermore, the Chebyshev polynomials are selected as the admissible function to improve computational efficiency, and the equation of motion is derived by the Rayleigh–Ritz method. The effects of spring stiffness, volume fraction indexes, configuration on of shell, and the change in thickness of the middle layer on the modal characteristics of the new structural shell are also analyzed.

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Effect of Fullerene Volume Fraction on Two-Dimensional Crystal-Constructed Supramolecular Liquid Crystals

Chemistry - An Asian Journal ◽

10.1002/asia.201801334 ◽

2018 ◽

Vol 14 (1) ◽

pp. 125-129 ◽

Cited By ~ 5

Author(s):

Peng Shen ◽

Xiaoyan Zhang ◽

Huanjun Lu ◽

Zebin Su ◽

Yi Zhou ◽

...

Keyword(s):

Liquid Crystals ◽

Volume Fraction ◽

Two Dimensional ◽

Dimensional Crystal

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Transformation Textures in Unstable Austenitic Steel

Journal of Engineering Materials and Technology ◽

10.1115/1.1525249 ◽

2002 ◽

Vol 125 (1) ◽

pp. 12-17 ◽

Cited By ~ 8

Author(s):

R. Kubler ◽

M. Berveiller ◽

M. Cherkaoui ◽

K. Inal

Keyword(s):

Martensitic Transformation ◽

Volume Fraction ◽

Micromechanical Model ◽

Slip Rate ◽

Transformation Strain ◽

Dislocation Motion ◽

Lattice Spin ◽

Two Phases ◽

The One ◽

Elastic Plastic Materials

During the martensitic transformation in elastic-plastic materials, the local transformation strain as well as the plastic flow inside austenite are strongly related with the crystallographic orientation of the austenitic lattice. Two mechanisms involved in these materials, i.e., plasticity by dislocation motion and martensitic phase formation are coupled through kinematical constraints so that the lattice spin of the austenitic grains is different from the one due to classical slip. In this work, the lattice spin ω˙eA of the austenitic grains is related with the slip rate on the slip systems of the two phases, γ˙A and γ˙M, the evolution of the martensite volume fraction f˙ and the overall rotation rate Ω˙ of the grains. This new relation is integrated in a micromechanical model developed for unstable austenite in order to predict the evolution of the austenite texture during TRansformation Induced Plasticity (TRIP). Results for the evolution of the lattice orientation during martensitic transformation are compared with experimental data obtained by X-ray diffraction on a 304 AISI steel.

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The Mechanical Analysis of the Composite Reinforced Circular Saw Blade

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.228-229.484 ◽

2011 ◽

Vol 228-229 ◽

pp. 484-489

Author(s):

Xiao Ling Wang ◽

Zhong Jun Yin ◽

Chao Zhang

Keyword(s):

Volume Fraction ◽

Mechanical Analysis ◽

Loading Conditions ◽

Circular Saw ◽

Model And Simulation ◽

Circular Saw Blade ◽

Saw Blade ◽

Reinforcement Model ◽

Circular Saws ◽

Composite Reinforcement

Thinner saw blades cannot resist large lateral cutting forces due to their lower stiffness. In this paper we propose a composite reinforcement method to improve the mechanical properties of circular saw blades. We analyze and simulate the stress and strain fields of our proposed reinforced circular saws by Finite element method. Our analytical results contain not only influences of reinforcing parameters but also loading conditions on the lateral stiffness and the natural frequency of composite saw blades. Here the reinforcing parameters include: 1) the reinforcement location on circular saw blades, 2) the volume fraction of the reinforcements, 3) the number of the reinforcements; and loading conditions include: 1) the cutting force, 2) the rotational speed. Our composite reinforcement model and simulation results can contribute to a better design of circular saw blades.

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