Multiaxial yield surface of transversely isotropic foams: Part I—Modeling

A new yield criterion is proposed for transversely isotropic solid foams. Its derivation is based on the hypothesis that the yielding in foams is driven by the total strain energy density, rather than a completely phenomenological approach. This allows defining the yield surface with minimal number of parameters and does not require complex experiments. The general framework used leads to the introduction of new scalar measures of stress and strain (characteristic stress and strain) for transversely isotropic foams. Furthermore, the central hypothesis that the total strain energy density drives yielding in foams ascribes to the characteristic stress an analogous role of von Mises stress in metal plasticity. Unlike the overwhelming majority of yield models in literature the proposed model recognizes the tension–compression difference in yield behavior of foams through a linear mean stress term. Predictions of the proposed yield model are in excellent agreement with the results of uniaxial, biaxial and triaxial FE analyses implemented on both isotropic and transversely isotropic Kelvin foam models.     

Multiaxial yield surface of transversely isotropic foams: Part II—Experimental

A robust understanding and modeling of the yield behavior in solid foams under complex stress states is essential to design and analysis of optimal structures using these lightweight materials. In pursuit of this objective a new custom-built Multi-Axial Testing Apparatus (MATA) is developed to probe the yield surface of transversely isotropic Divinycell H-100 PVC foam under a multitude of uniaxial, biaxial and triaxial strain paths. Experimental yield data produced constitutes the most comprehensive data set ever produced for any foam as it covers the entire spectrum of stress paths from hydrostatic compression to hydrostatic tension. Experimental results reveal that yielding in foams exhibits not only a quadratic pressure dependence, which is widely recognized in literature, but also a significant linear pressure dependence, which has been largely overlooked in previous studies. A new energy-based yield criterion developed for transversely isotropic foams is also validated using the experimental yield data.     

Ultrasonic nondestructive evaluation of microstructural changes of solid materials under plastic deformation—Part I. Theory

In general, finite plastic deformation is accompanied by microstructural material property changes such as texture change and growth of localized slip bands. However, it is very difficult to evaluate these microstructural material property changes nondestructively by means of the usual methods used to date. The ultrasonic nondestructive evaluation method proposed by the author has been successfully applied to the evaluation of plastically deformed state. The purpose of the present paper is to formulate precisely a generalized acoustoelastic theory for plastically deformed solids with finite plastic deformation and, moreover, to provide a method of nondestructive evaluation of the plastically deformed state, i.e. yield surface, texture change and the occurrence of the instability associated with the microslip band.     

Biomechanical evaluation of heel elevation on load transfer — experimental measurement and finite element analysis

In spite of ill-effects of high heel shoes, they are widely used for women. Hence, it is essential to understand the load transfer biomechanics in order to design better fit and comfortable shoes. In this study, both experimental measurement and finite element analysis were used to evaluate the biomechanical effects of heel height on foot load transfer. A controlled experiment was conducted using custom-designed platforms. Under different weight-bearing conditions, peak plantar pressure, contact area and center of pressure were analyzed. A three-dimensional finite element foot model was used to simulate the high-heel support and to predict the internal stress distributions and deformations for different heel heights. Results from both experiment and model indicated that heel elevations had significant effects on all variables. When heel elevation increased, the center of pressure shifted from the midfoot region to the forefoot region, the contact area was reduced by 26% from 0 to 10.2 cm heel and the internal stress of foot bones increased. Prediction results also showed that the strain and total tension force of plantar fascia was minimum at 5.1 cm heel condition. This study helps to better understand the biomechanical behavior of foot, and to provide better suggestions for design parameters of high heeled shoes.     

Dynamic Separation of Resistance Spot Welded Joints: Part I—Experiments

An analysis for an impact system is presented. The results are then used to interpret the test data from dynamic separation of resistance spot welded joints. In this Part I of the investigation emphasis is placed on the design consideration, development of a test system and verification of the design from actual test data obtained from the test system. In addition, the inertia effect of a generic dynamic system is analyzed using the principle of rigid body dynamics. It is shown that the load recorded by a load cell could include both the load experienced by the test specimen and the inertia force generated from the mass and acceleration between the specimen and the load cell, when the load cell is placed on the fixed side of the test specimen. Impact fixtures designed for spot weld strength testing are then studied for the inertia effect.     

Macro-performance evaluation of friction stir welded automotive tailor-welded blank sheets: Part I – Material properties

In order to evaluate the macroscopic performance of friction stir welded automotive tailor-welded blank (TWB) sheets, the hardening behavior, anisotropic yielding properties and forming limit diagram were characterized both for base (material) and weld zones. In order to describe the Bauschinger and transient hardening behaviors as well as permanent softening during reverse loading, the modified Chaboche type combined isotropic–kinematic hardening law was applied. As for anisotropic yielding, the non-quadratic anisotropic yield function, Yld2000-2d, was utilized for base material zones, while isotropy was assumed for weld zones for simplicity. As for weld zones, hardening properties were obtained using the rule of mixture and selectively by direct measurement using sub-sized specimens. Forming limit diagrams were measured for base materials but calculated for weld zones based on Hill’s bifurcation and M–K theories. In this work, four automotive sheets were considered: aluminum alloy 6111-T4, 5083-H18, 5083-O and dual-phase steel DP590 sheets, each having one or two thicknesses. Base sheets with the same and different thicknesses were friction-stir welded for tailor-welded blank (TWB) samples.     

Modeling and waveform optimization of stick–slip micro-drives using the method of dimensionality reduction

In this paper, the dynamics of piezo-actuated stick–slip micro-drives are studied experimentally and theoretically. First, the stick–slip-based force-generating test stand is introduced, and experimental results are presented. Then, a numerical model is formulated which explicitly includes the dynamics of normal and tangential properties of the contact areas in the frictional driving elements of the drive. The contact forces are simulated using the method of dimensionality reduction. We show that the experimentally observed behavior can be described without using any fitting parameters or assuming any generalized laws of friction if the explicit contact mechanics of the frictional contacts is taken into account. Furthermore, an even simpler model of the drive is developed to get a qualitative understanding of the system. It is employed to gain a new actuation method, which reduces the vibrations of the drive’s runner and therefore enhances its performance.     

Hidden components of 3D-DIC: Triangulation and post-processing—Part 3

Experimental Techniques -     

Ultrasonic nondestructive evaluation of microstructural changes of solid materials under plastic deformation—Part II. Experiment and simulation

The microstructure of materials introduced by rolling, drawing, heat treatment or other methods of material processing relates to the macroscopic mechanical properties of the materials, such as the strength and anisotropy. The velocity and attenuation of the ultrasonic waves propagating in the materials are known to be dependent upon such microstructural material properties. The author has proposed a theoretical modeling of an ultrasonic nondestructive method to evaluate the microstructural property changes of materials in Part I of this work. In the present paper, annealed effects on plastically deformed states of an aluminium alloy were studied using the proposed ultrasonic nondestructive evaluation method and it was found that close agreement between the simulated results and experimental data was possible.     

Dynamic crushing of aluminum foams: Part I – Experiments

The two-part series of papers presents the results of a study of the crushing behavior of open-cell Al foams under impact. In Part I, direct and stationary impact tests are performed on cylindrical foam specimens at impacts speeds in the range of 20–160 m/s using a gas gun. The stress at one end is recorded using a pressure bar, while the deformation of the entire foam specimen is monitored with high-speed photography. Specimens impacted at velocities of 60 m/s and above developed nearly planar shocks that propagated at well-defined velocities crushing the specimen. The shock speed vs. impact speed, and the strain behind the shock vs. impact speed representations of the Hugoniot were both extracted directly from the high-speed images. The former follows a linear relationship and the latter asymptotically approaches a strain of about 90% at higher velocities. The Hugoniot enables calculation of all problem variables without resorting to an assumed constitutive model. The compaction energy dissipation across the shock is shown to increase with impact velocity and to be significantly greater than the corresponding quasi-static value. Specimens impacted at velocities lower than 40 m/s exhibited response and deformation patterns that are very similar to those observed under quasi-static crushing. Apparently, in this impact speed regime inertia increases the energy absorption capacity very modestly.     

Overspeed burst of elastoviscoplastic rotating disks – Part I: Analytical and numerical stability analyses

Burst of rotating disks in case of overspeed is investigated. The certification of turbo-engines requires to demonstrate the integrity of disks at higher rotation speeds than the maximum rotation speed reachable in service. The determination of the burst speed by analysis can help to reduce the number of tests required for the certification. This prediction can be established by non-linear stability analyses of finite element simulations. Non-linearities originate from (i) the material behaviour described by elastoviscoplastic constitutive equations, (ii) geometric changes accounted for by the finite strain formulation. In this work, loss of uniqueness and loss of stability criteria from [Hill, R., 1958. A general theory of uniqueness and stability in elastic-plastic solids. J. Mech. Phys. Solids 6, 236–249] are applied. The loss of stability criterion is restricted to the case of rotating disks and compared to several simple widely used material based failure criteria. 3D simulations of rotating metal disks are performed for a given elastoviscoplastic behaviour and the stability criteria are evaluated. The sensitivity of disk stability to material parameters, such as yield criterion, hardening and viscosity is evaluated in the case of a nickel based superalloy.     

Biaxial crushing of honeycombs: —Part 1: Experiments

The in-plane compression and crushing of honeycombs is known to be closely related to the crushing behavior of the broader class of space filling cellular solids. Previously, the authors conducted an extensive study of uniaxial crushing of a polycarbonate honeycomb with circular cells. In this paper the same honeycomb is crushed biaxially. The crushing was performed in a custom testing facility between rigid platens which can be moved independently in two orthogonal directions. The facility allows testing at various biaxiality ratios and volume reductions as high as 95%. The facility was used to conduct several series of biaxial crushing experiments on nearly square honeycomb specimens (18×21 cells) . In each experiment we recorded the true stress–displacement responses in the x- and y-directions as well as full field views of the deformation using a video camera. Biaxial crushing is quite complex and the prevalent mechanisms of collapse depend on the biaxiality ratio (γ) . As is the case in uniaxial crushing, the onset of collapse involves localized instabilities, however, the extent of localized deformation varies with γ. The energy absorption capacity of the material depends on γ. The highest energy is required when the specimen is crushed at the same rates in the two directions.     

Modeling of the catalytic properties of high-temperature surface insulation in a dissociated carbon dioxide — Nitrogen mixture

A model of the heterogeneous catalysis of a dissociated carbon dioxide — nitrogen mixture on high-temperature heat-shield coatings is developed; the model takes into account nonequilibrium adsorption-desorption reactions of nitrogen and oxygen atoms and carbon dioxide molecules and their recombination in the Eley-Rideal reactions. On the basis of a comparison of the calculated heat fluxes in dissociated carbon dioxide with those measured on the VGU-4 plasma generator of the Institute for Problems in Mechanics of the RAS, the parameters of the catalysis model in question are chosen for three modern oxidant-resistant coating materials. The performances of these coatings are compared for the conditions of Mars Miniprobe entry into the Martian atmosphere. Their usability for the entry path considered is shown. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 106–116, January–February, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 99-01-00259) and the “Integratisya“ Federal Program (project No. 2.1–414).     

An enhanced beam-theory model of the mixed-mode bending (MMB) test—Part I: Literature review and mechanical model

The paper presents a mechanical model of the mixed-mode bending (MMB) test used to assess the mixed-mode interlaminar fracture toughness of composite laminates. The laminated specimen is considered as an assemblage of two sublaminates partly connected by an elastic–brittle interface. The problem is formulated through a set of 36 differential equations, accompanied by suitable boundary conditions. Solution of the problem is achieved by separately considering the two subproblems related to the symmetric and antisymmetric parts of the loads, which for symmetric specimens correspond to fracture modes I and II, respectively. Explicit expressions are determined for the interfacial stresses, internal forces, and displacements.     

In-plane biaxial crushing of honeycombs—: Part II: Analysis

The in-plane biaxial crushing experiments on polycarbonate honeycomb presented in Part I are simulated using large scale finite element models. The models account for nonlinearities in geometry and due to contact while the polycarbonate is modeled as an elastic-powerlaw viscoplastic solid. Full-scale simulations of the uniaxial crushing of this honeycomb were shown in the past to reproduce experiments with accuracy. In biaxial crushing, it was not practical to model specimens the same size as those in the experiments due to computational limitations; instead, a smaller model with 10×11 cells was adopted. Results from simulations of seven of the crushing experiments in Part I with various biaxiality ratios are presented. Through parametric studies it is demonstrated that the size of the specimen and friction between the specimen and the loading surfaces affect the initial elastic parts of the stress–displacement responses and the onset of instability. By contrast, for average crushing strains higher than approximately 10%, their effect was relatively small and the calculated responses were in good agreement with the experimental ones. As a consequence, the energy absorption capacity was predicted to good accuracy for all biaxiality ratios. In addition, many of the modes of cell collapse seen in the experiment are reproduced in the simulations.     

Analytical study of the nonlinear behavior of a shape memory oscillator: Part I—primary resonance and free response at low temperatures

In this work, the response of a single-degree-of-freedom shape memory oscillator subjected to the excitation harmonic has been investigated. Equation of motion is formulated assuming a polynomial constitutive model to describe the restitution force of the oscillator. Here the method of multiple scales is used to obtain an approximate solution to the equations of the motion describing the modulation equations of amplitude and phase, and to investigate theoretically its stability. This work is presented in two parts. In Part I of this study we showed the modeling of the problem where the free vibration of the oscillator at low temperature is analyzed, where martensitic phase is stable. Part I also presents the investigation dynamics of the primary resonance of the pseudoelastic oscillator. Part II of the work is focused on the study in the secondary resonance of a pseudoelastic oscillator using the model developed in Part I. The analysis of the system in Part I as well as in Part II is accomplished numerically by means of phase portraits, Lyapunov exponents, power spectrum and Poincare maps. Frequency-response curves are constructed for shape memory oscillators for various excitation levels and detuning parameter. A rich class of solutions and bifurcations, including jump phenomena and saddle-node bifurcations, is found.     

Mathematical and numerical modeling of the non-associated plasticity of soils—Part 2: Finite element analysis

The method of the implicit standard material has allowed the formulation of a consistent mathematical model of the boundary value problem for the non-associated plasticity of soil. The mean accomplished steps are the achievement of the bipotential function, the recovering of the stress–strain relationship under a normality rule, introduction of the bifunctional and the proof of the solution existence. Here the mathematical model is discretized by the finite element method. First, the stress update scheme was formulated, the tangent matrix is explicitly derived and then the non-linear system is solved by the Newton–Raphson method where a new algorithm using a symmetrical tangent matrix is improved. This is in opposition to conventional non-associated plasticity, which uses a non-symmetric tangent matrix. Through the numerical examples we show the feasibility and the efficiency of the algorithm. It is also seen that we perform some studies of the numerical solutions, particularly the comparison between associated and non-associated limit load.     

A comparative study on design standards of screw conveyors in China,Germany and the USA — Part I: Theoretical calculation and quantitative analysis

Screw conveyors, widely used devices for transporting bulk materials, play an irreplaceable role in the modern industrial system. Despite of their traditional advantages, designers of screw conveyors still heavily rely on their own country’s experiments and standards, which are closely related to empirical data. Therefore, the same conveying task often results in different designs. This work aims to compare the design standards of screw conveyors in China, Germany and the USA. Based on related standards acquired from renowned associations in the three countries, the similarities and particularities of these design guidances are compared. With preforming the geometrical and operational designs for horizontal, slightly inclined and vertical conveyance of three representative bulk solids (barley, lignite, sand), the advantages and disadvantages of these semi-empirical designs are comprehensively presented. Furthermore, the potential influence of empirical coefficients, which are not explicitly documented, are extensively discussed. By analysing all outcomes, the compatibility and applicability of each standard are qualitatively assessed.