Elastic–plastic behavior of non-woven fibrous mats

Electrospinning is a novel method for creating non-woven polymer mats that have high surface area and high porosity. These attributes make them ideal candidates for multifunctional composites. Understanding the mechanical properties as a function of fiber properties and mat microstructure can aid in designing these composites. Further, a constitutive model which captures the membrane stress–strain behavior as a function of fiber properties and the geometry of the fibrous network would be a powerful design tool. Here, mats electrospun from amorphous polyamide are used as a model system. The elastic–plastic behavior of single fibers are obtained in tensile tests. Uniaxial monotonic and cyclic tensile tests are conducted on non-woven mats. The mat exhibits elastic–plastic stress–strain behavior. The transverse strain behavior provides important complementary data, showing a negligible initial Poisson's ratio followed by a transverse:axial strain ratio greater than ?1:1 after an axial strain of 0.02. A triangulated framework has been developed to emulate the fibrous network structure of the mat. The micromechanically based model incorporates the elastic–plastic behavior of single fibers into a macroscopic membrane model of the mat. This representative volume element based model is shown to capture the uniaxial elastic–plastic response of the mat under monotonic and cyclic loading. The initial modulus and yield stress of the mat are governed by the fiber properties, the network geometry, and the network density. The transverse strain behavior is linked to discrete deformation mechanisms of the fibrous mat structure including fiber alignment, fiber bending, and network consolidation. The model is further validated in comparison to experiments under different constrained axial loading conditions and found to capture the constraint effect on stiffness, yield, post-yield hardening, and post-yield transverse strain behavior. Due to the direct connection between microstructure and macroscopic behavior, this model should be extendable to other electrospun systems and other two dimensional random fibrous networks.     

Elastic–plastic and limit-state analyses of frames with softening plastic-hinge models by mathematical programming

Frames (and more general beam systems) subjected to monotonic loading are modelled by conventional finite elements with the traditional assumption of possible plastic deformations concentrated in pre-selected “critical sections”. The inelastic behaviour of these beam sections, i.e. the development of “plastic hinges”, is described by piece-wise-linear constitutive models allowing for hardening and/or softening, in terms of generalized stresses and conjugate kinematic variables.The following topics are discussed: step-by-step analysis methods, both “exact” and stepwise holonomic; path bifurcations and overall stability; limit and deformation analyses combined, as an optimization problem under complementarity constraints apt to compute the safety factor (with respect to global or local failures); numerical tests of nonconventional algorithms by means of simple representative applications.The objective of the paper is to provide a unified methodology and to propose novel procedures for inelastic analyses of frames up to failure, in the light of recent results in mathematical programming, particularly on complementarity theory.     

Elastic–plastic analysis of two-dimensional functionally graded materials under thermal loading

The two-dimensional functionally graded materials, (2D-FGMs) have been recently introduced in order to significantly reduce the thermal stresses in machine elements that subjected to sever thermal loading. To the author’s knowledge no work was found that investigates the elastic–plastic stress analysis for 2D-FGMs. In the current work, a 3D finite element model of 2D-FGM plates made of ZrO₂, 6061-T6 and Ti-6Al-4V with temperature dependent material properties has been proposed to perform such analysis. An elastic plastic stress–strain relation based on the rule of mixture of the 2D-FGM has been introduced in the model. Also, a 3D finite element model of conventional FGM plates, of ZrO₂/Ti-6Al-4V and ZrO₂/6061-T6, with temperature dependent material properties has been proposed for the investigation of these plates too. Then, elastic–plastic stress analysis of the considered four plates (two conventional FGMs and two 2D-FGMs) under the same transient cyclic heating and cooling was carried out. It was found that heat conductivity of the metallic constituents of FGM has great effect on the temperature distributions that resulting from the thermal loads. Minimum temperatures variation and minimum stresses can be obtained using ZrO₂/6061-T6/Ti-6Al-4V 2D-FGM. Also, the results indicate that only ZrO₂/6061-T6/Ti-6Al-4V 2D-FGM can stand with the adopted sever thermal loading without fracture or plastic deformations.     

Experimental Study on the Elastic–plastic Transitions of the Hetero-structured High Pressure Die Casting Mg–Al-RE Alloy

Background

High pressure die casting (HPDC) Mg alloy has a hetero-structure in which the microstructures gradually coarsen from the casting surface to the interior, leading to the different elastic–plastic (E-P) transitional behaviors among the layers.

Objective

In this paper, we quantitively determined the diverse E-P transitions among the HPDC layers and related them to the microstructural evolution.

Methods

To investigate independently the E-P transitional behavior of the layer, the surface, middle, and central layers were deliberately sliced in sequence from the casting surface to the interior of the HPDC Mg-4Al-5.7RE (in wt.%) component. The onset and the end of E-P transition in each layer were quantitively determined by cyclic tensile test and Kocks-Mecking analysis, respectively.

Results

It was found that the plastic deformation for all layers occurred in the first unloading loop near zero strain, indicating the start of the E-P transition. With increasing strain, the E-P transition ended first in the middle layer at 0.0081 strain due to the lowest fraction of the second phases and ended last at the small-grained surface layer at 0.0090 strain. Excluding the twinning-dependent anelastic strain, the E-P transitions ended in advance at the strains of 0.0059 and 0.0062 in the middle and surface layer, respectively.

Conclusions

A combination of cyclic tensile test and Kocks-Mecking analysis provided a method to quantitively determine the diverse E-P transitions among the HPDC layers resulted from the hetero-structure regarding grains, the second phases, and twins.

     

Effect of large elastic strains on cavitation instability predictions for elastic–plastic solids

For an infinite solid containing a void, the cavitation instability limit is defined as the remote stress–and strain state, at which the void grows without bound, driven by the elastic energy stored in the surrounding material. Such cavitation limits have been analysed by a number of authors for metal plasticity as well as for nonlinear elastic solids. The analyses for elastic–plastic solids are here extended to consider the effect of a large initial yield strain, and it is shown how the critical stress value decays for increasing value of the yield strain. Analyses are carried out for remote hydrostatic tension as well as for more general axisymmetric remote stress field, with an initially spherical void. Different levels of strain hardening are considered.     

Effect of Evaporation of Liquid Droplets on the Distribution of Parameters in a Two–Species Laminar Flow

A calculation model was developed, and the heat– and mass–transfer characteristics in a laminar air—vapor—droplet flow moving in a round tube were studied numerically. The distributions of parameters of the two–phase flow over the tube radius were obtained for varied initial concentrations of the gas phase. The calculated heat and mass transfer is compared to experimental data and calculations of other authors. It is shown that evaporation of droplets in a vapor—gas flow leads to a more intense heat release as compared to a one–species vapor—droplet flow and one–phase vapor flow     

Spectral Properties of Schrödinger Operators on Domains with Varying Orders of Thinness

We consider the Schrödinger operator on two types of domains depending on a small parameter : dumbbell domains and thin domains with varying orders of thinness. In both situations we compare the eigenvalues and eigenvectors of the Schrödinger operator with the corresponding eigenvalues and eigenvectors of a limit operator defined on the limit domain.     

Elastic–plastic behavior of steel sheets under in-plane cyclic tension–compression at large strain

Elastic–plastic behavior of two types of steel sheets for press-forming (an aluminum-killed mild steel and a dual-phase high strength steel of 590 MPa ultimate tensile strength) under in-plane cyclic tension–compression at large strain (up to 25% strain for mild steel and 13% for high strength steel) have been investigated. From the experiments, it was found that the cyclic hardening is strongly influenced by cyclic strain range and mean strain. Transient softening and workhardening stagnation due to the Bauschinger effect, as well as the decrease in Young's moduli with increasing prestrain, were also observed during stress reversals. Some important points in constitutive modeling for such large-strain cyclic elasto-plasticity are discussed by comparing the stress–strain responses calculated by typical constitutive models of mixed isotropic–kinematic hardening with the corresponding experimental observations.     

Elastic–plastic behavior of a semicircular frame being pressed against a rigid plane

As a simplified structural model, a semicircular frame is used to study the crashworthiness behavior of an aircraft fuselage. The quasi-static large elastic-plastic deformation of a semicircular frame in the process of its being pressed against a rigid ground is analyzed. First, based on the linear elastic assumption, the quasi-static large deformation contact process of the frame can be divided into three phases, i.e., point contact, line contact and post-buckling. By means of a shooting method, the relations between the displacement and contact force as well as the distribution of bending moment in the three phases are obtained. Then, by assuming an elastic, perfectly-plastic moment-curvature relationship for the semi-circular frame, the contact process is analyzed in detail to reveal the plastic collapse mechanism, the traveling of plastic hinge and the force-displacement relationship. In order to verify the analysis, a preliminary experiment was conducted, in which two types of half rings with clamped ends were pressed by a rigid plate. In addition, a numerical simulation is also conducted by employing ABAQUS to analyze both rectangular cross-sectional beam and I-beam. Finally, the theoretical predictions are compared with the experimental results and numerical solutions, showing that the elastic-plastic analysis can predict the contact process very well.     

Spherical impression of thin elastic films on elastic–plastic substrates

The mechanical behavior of thin elastic films deposited onto structural alloys plays a critical role in determining film durability. This paper presents analysis of an impression experiment designed to evaluate some of the relevant properties of these films. The modeling provides quantitative strain information which can be used to estimate the fracture toughness of the film, the static friction coefficient of the surface and the constitutive behavior of the substrate. Results are presented for radial and circumferential strain distributions in the film relevant to the interpretation of cracking patterns. Additionally, load-displacement curves are provided that may be used to evaluate the plastic properties of the substrate. To facilitate estimates of the film cracking strain through correlation with experiments, the radial strain distributions are presented as functions of impression depth, yield strain and hardening exponent.     

On establishing elastic–plastic properties of a sphere by indentation testing

Instrumented indentation is a popular technique for determining mechanical properties of materials. Currently, the evaluation techniques of instrumented indentation are mostly limited to a flat substrate being indented by various shaped indenters (e.g., conical or spherical). This work investigates the possibility of extending instrumented indentation to non-flat surfaces. To this end, conical indentation of a sphere is investigated where two methodologies for establishing mechanical properties are explored. In the first approach, a semi-analytical approach is employed to determine the elastic modulus of the sphere utilizing the elastic unloading response (the “unloading slope”). In the second method, reverse analysis based on finite element analysis is used, where non-dimensional characteristic functions derived from the force–displacement response are utilized to determine the elastic modulus and yield strength. To investigate the accuracies of the proposed methodologies, selected numerical experiments have been performed and excellent agreement was obtained.     

Effect of Atwood number on convergent Richtmyer–Meshkov instability

Acta Mechanica Sinica - Developments of two-dimensional single-mode light/heavy interfaces driven by convergent shock waves are numerically investigated, focusing on the effect of the Atwood number...     

Study on magneto–elastic–plastic deformation characteristics of ferromagnetic rectangular plate with simple supports

In this paper, the magnetic-elastic-plastic deformation behavior is studied for a ferromagnetic plate with simple supports. The perturbation formula of magnetic force is first derived based on the perturbation technique, and is then applied to the analysis of deformation characteristics with emphasis laid on the analyses of modes, symmetry of deformation and influences of incident angle of applied magnetic field on the plate deformation. The theoretical analyses offer explanations why the configuration offer- romagnetic rectangular plate with simple supports under an oblique magnetic field is in-wavy type along the x-direction, and why the largest deformation of the ferromagnetic plate occurs at the incident angle of 45°for the magnetic field. A numerical code based on the finite element method is developed to simulate quantitatively behaviors of the nonlinearly coupled multi-field problem. Some characteristic curves are plotted to illustrate the magneto--elastic-plastic deflections, and to reveal how the deflections can be influenced by the incident angle of applied magnetic field. The deformation characteristics obtained from the numerical simulations are found in good agreement with the theoretical analyses.     

Determination of elastic and plastic characteristics of TiC–TiNi alloys by the ultrasonic resonance method

Elastic characteristics and propagation velocities of ultrasonic waves in a TiC–TiNi composite material are determined by the ultrasonic resonance method. The values of the elastic moduli of the solid composite obtained are used to estimate its plastic properties. The effect of various additives on the elastic and plastic properties of the composite is studied.     

Effect of process conditions on the synthesis of carbon nanotubes by catalytic decomposition of methane

A new dual-composition catalyst based on Ni-Mo/MgO with high efficiency of producing carbon nanotubes （CNTs） from methane was reported recently. In the present article, with this type of catalyst, the impact of such experimental parameters as reaction temperature, reaction time, concentration of H2, flow rate ratio of CH4 to H2 on yield and graphitization were investigated, leading to the following optimal growth conditions： reaction time 60min, reaction temperature 900℃, CH4：H2 about 100：20mL/min, under which high-yield multi-walled CNTs bundles were synthesized. Raman measurement indicated that the as-synthesized product was well-graphitized, and the purity was estimated over 95% by TG-DSC analysis. In terms of the above results, an explanation of high-efficiency formation of CNTs bundles and the co-catalysis mechanism of Ni-Mo/MgO were suggested. 2007 Chinese Societv of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V.     

A study on robust indentation techniques to evaluate elastic–plastic properties of metals

Spherical indentation is studied based on numerical analysis and experiment, to develop robust testing techniques to evaluate isotropic elastic–plastic material properties of metals. The representative stress and plastic strain concept is critically investigated via finite element analysis, and some conditions for the representative values are suggested. The representative values should also be a function of material properties, not only indenter angle for sharp indenter and indentation depth for spherical indenter. The pros and cons of shallow and deep spherical indentation techniques are also discussed. For an indentation depth of 20% of an indenter diameter, the relationships between normalized indentation parameters and load–depth data are characterized, and then numerical algorithm to estimate material elastic–plastic curve is presented. From the indentation load–depth curve, the new approach provides stress–strain curve and the values of elastic modulus, yield strength, and strain-hardening exponent with an average error of less than 5%. The method is confirmed to be valid for various elastic properties of indenter. Experimental validation of the approach then is performed by using developed micro-indentation system. For the material severely disobeying power law hardening, a modified method to reduce errors of predicted material properties is contrived. It is found that our method is robust enough to get ideal power law properties, and applicable to input of more complex physics.     

Effect of glycine–starch mixing ratio on the structural characteristics of MgAl2O4 nano-particles synthesized by sol–gel combustion

Sol–gel auto-ignition was used to prepare nano-scale magnesium aluminate spinel, using nitrate salts as an oxidizer and glycine–starch mixtures as the fuel. The glycine–starch mixture was varied to understand the effect of fuel mixing ratio on the structural characteristics of the resulting magnesium aluminate. The products were characterized by thermogravimetric-differential thermal analyses, Fourier-transform infrared spectroscopy, X-ray diffraction, Brunauer–Emmett–Teller surface area measurements, and transmission electron microscopy. The phase purity and crystallite size of the powder products depended on the fuel mixing ratio. The presence of starch in the fuel facilitated the preparation of pure nano-particles. To prepare nano-particles of uniform spherical morphology and diameter of <13 nm, the starch content should be optimized to avoid agglomeration.     

Effect of wall conditions on DDT in hydrogen–oxygen mixtures

Detonation in ducts is usually studied assuming adiabatic walls because of the high kinetic energy due to the incoming flow being supersonic. In the present work, numerical simulations of deflagration-to-detonation transition (DDT) using a detailed chemical reaction model are performed under adiabatic and isothermal boundary conditions in a tube with no-slip walls. The results show a local explosion driving DDT, which occurs near the tube wall in the case of an adiabatic wall, but close to the flame front in the case of an isothermal wall. Furthermore, to examine the effects of a turbulent boundary layer, a simulation using the Baldwin–Lomax turbulence model is carried out. In the case of the isothermal wall, there is again a local explosion near the tube wall, which leads to detonation. In summary, the present study confirms that the boundary conditions affect the transition to detonation and that the boundary layer is a key component of DDT.