Isotropic Elastic-plastic Material Research Articles

Additively manufactured AlSi10Mg lattices – Potential and limits of modelling as-designed structures

Additive manufacturing overcomes the restrictions of classical manufacturing methods and enables the production of near-net-shaped, complex geometries. In that context, lattice structures are of high interest due to their superior weight reduction potential. AlSi10Mg is a well-known alloy for additive manufacturing and well suited for such applications due to its high strength to material density ratio. It has been selected in this study for producing bulk material and complex geometries of a strut-based lattice type (rhombic dodecahedron). A detailed characterisation of as-built and heat-treated specimens has been conducted including microstructural analyses, identification of imperfections and rigorous mechanical testing under different load conditions. An isotropic elastic–plastic material model is deduced on the basis of tension test results of bulk material test specimens. Performed experiments under compression, shear, torsion and tension load are compared to their virtual equivalents. With the help of numerical modelling, the overall structural behaviour was simulated using the detailed lattice geometry and was successfully predicted by the presented numerical models. The discussion of the limits of this approach aims to evaluate the potential of the numerical assessment in the modelling of the properties for novel lightweight structures.

Plane waves in anisotropic elastic–plastic material with voids

Dispersion equation is derived for the propagation of one-dimensional plane waves in a general linear anisotropic isothermal elastic–plastic material with voids. The plasticity of the considered material is defined through the dislocation of a single slip plane and direction. The derived dispersion equation is then reduced for the relevant wave propagation in particular media, namely, monoclinic, orthotropic, transversely isotropic, and isotropic elastic–plastic material with voids. In general, it is found that there exist four basic waves traveling with distinct speeds in these specific anisotropic elastic–plastic materials with voids. A new wave is found to appear because of the presence of plasticity in the material. Out of the four basic waves traveling in an orthotropic/transversely isotropic material with voids, a wave travels independent of plasticity and void parameters, whereas the remaining three waves depend on plasticity as well as on the presence of voids. The one which is traveling independent of plasticity and voids is nondispersive and nonattenuating, whereas the other waves are dispersive in nature. The speeds of all the existing waves are computed numerically for a specific model, displayed graphically, and discussed.

Influence of wear on the distribution of pressure and the state of tension at wheel-rail interface

Since no effective experimental approaches have been proposed to assess state of stress and distribution of pressures at the wheel and rail contact interface to date, numerical calculation methods are known as an alternative to approximate modelling of wheel-rail interaction. In this paper, a numerical procedure is proposed based on the finite element method of the complex tensions state on wheel-rail contact. This study includes the distribution of pressures and tensions on wheel-rail contact system with new and worn profiles, using a finite element modeling (FEM). Using a model of isotropic elastic-plastic material was obtained a FE model that can obtain the distribution of pressures and tensions at the wheel-rail interface for the real surfaces that are in contact, this model is necessary for any tribological study that requires data on the state of stress and pressure only by introducing input data: geometric characteristics, Young’s Modulus, Poisson’s Ratio, Tangent Modulus, Yield Strength, load on the wheel, lateral shift of wheelset.

Quasi-static compressive behaviour of aluminium cenosphere syntactic foams

ABSTRACTIn this paper, cenosphere particles embedded in AA2014 aluminium matrix are used to fabricate syntactic foam by stir casting method. The particle size is about 100 µm and foam density is about 1990 kg m−3. Compression tests at strain rate 0.001/s are performed on foam samples to characterise their mechanical properties which are then used in numerical analysis on commercial finite element analysis software ABAQUS/CAE with isotropic elastic-plastic material model. Experimental and numerical results show good conformity in deformation behaviour with elastic and plateau zones showing average deviations less than 5% and 20%, respectively. Foams showed high yield stress and energy absorption capabilities that can be useful in making blast and impact resistant structures.

Spinning Process Design Using Finite Element Analysis and Taguchi Method

Abstract Metal spinning process is widely used because of its low power requirement to producing complex symmetry components. Spinning process parameters influence the spinning force and wall breakage or wrinkling problems of finished parts. The experimental and numerical simulation of metal sheet spinning has been applied to investigate the effect of spinning process parameters in order to achieved lower force and large deformation without the wall breakage or wrinkling failure. In the study, Taguchi method is implemented in cooperate with finite element analysis to reduce the number of numerical simulation. The spinning experiments were carried out on a modified turning lathe to accommodate a Kreisler force transducer to measure spinning forces. The three dimensional finite element model of sheet metal spinning was developed using the same spinning experiment process parameters. The SPCC sheet metal workpiece is modelled as an isotropic elastic-plastic material. The average predicted spinning force was 853 N. There is an error of 6.25% in the FE model prediction. Furthermore, the predicted thicknesses of the deformed part were compared with the measured experimental parts thickness and the error was 6.06%. It is clear that the finite element model results agreed well with the spinning experimental results. The effect of eight process parameters, i.e. roller radius, spindle speed, feed rate and feed depth, friction coefficient, width of support roller, diameter of support roller and angel of mandrel slope, on spinning force and deformation were studied. Finite element analysis of Taguchi-L18 spinning experiment were carried out. Taguchi main effect analysis and ANOVA results show that the slope of mandrel, spinning depth and support roller width are the most important factors influencing the spinning force. The slopes of mandrel, spinning depth and roller radius are the most important factors influencing the thickness variation of deformed parts. The roller radius, spinning depth and support roller width are the most important factors influencing the severity of wrinkling failure.

Correlation of spherical nanoindentation stress-strain curves to simple compression stress-strain curves for elastic-plastic isotropic materials using finite element models

The stress-strain fields realized in spherical indentation tests are highly heterogeneous, and present a significant challenge to the recovery of bulk stress-strain responses such as those measured in simple compression tests performed on samples with a uniform cross section in the gauge section. In this paper, we critically explore the correlations between indentation stress-strain curves and the simple compression stress-strain curves using the finite element model of indentation as a surrogate for the actual experiment. The central advantage of using a finite element model is that it allows us to critically explore the sensitivity of various assumptions or values of parameters or other choices made in the analyses protocols on the extracted results. Based on this study, a general protocol has been established to reliably recover the uniaxial stress-strain response directly from the indentation stress-strain curve for isotropic elastic-plastic materials. The protocols developed are validated for a range of hardening behaviors.

Effective plastic properties of laminates made of isotropic elastic plastic materials

The effective elastic behavior of laminates is well understood. In this contribution, we make use of the fact that the elastic homogenization can be extended relatively easy to the plastic case (He and Feng, 2012), which is interesting for bilayer metallic structures. With the aid of stress concentration tensors, the effective yield limit is calculated, and its properties are examined. It turns out to be anisotropic, pressure-dependent, non-smooth, and evolves with the plastic deformation. Using the constitutive equations of von Mises elastic plastic materials, the effective plastic flow behavior is obtained as a set of coupled nonlinear ordinary differential equations with algebraic conditions. A general solution can hardly be given, but it can be integrated numerically. Further, it is possible to examine some properties of its solution without explicitly stating it, such as its poles. The latter allow to extract closed form-expressions for the ultimate loading stress in monotonic stress-driven tests. All analytical results are compared to representative volume element simulations, and found to match very well.

Elastic-Plastic Analysis for Functionally Graded Thick-Walled Tube Subjected to Internal Pressure

AbstractThe elastic-plastic response of the functionally graded thick-walled tube subjected to internal pressure is investigated by using the relation of the volume average stresses of constituents and the macroscopic stress of composite material in micromechanics. The tube consists of two idealized isotropic elastic-plastic materials whose volume fractions are power functions of the radius. As the internal pressure increases, the deformations of one phase and two phases from elastic to plastic are analyzed. In order to simplify the calculations we assume both materials with the same Poisson's ratio. By using the assumption of a uniform strain field within the representative volume element and the Tresca yield criterion, the theoretical solutions are obtained for the case of two elastic phases and the case of two plastic phases, and the function of the radial displacement is presented for the case with both elastic and plastic phases. The yield criterion of functionally graded material is given in terms of the yield stresses and volume fractions of constituents rather than Young's modulus and yield stress with different unknown parameters of the whole material in the existing papers. Finally we also discuss the position where the plastic deformation first occurs and the conditions for which material first yields in the tube.

Numerical Modelling of Deformation of Soil Foundations

The algorithm for investigation of soil foundations under its own weight and surface loading is considered. A soil is presented as a continuous medium, which has specific physical and mechanical properties. Structurally, there are three groups of soils, the first – sand, the second – clay and the third – rocks. The main difference is a bonding strength between the individual crystal grains and the medium continuum.Kinematics of a medium continuum is described by the spatial gradient of rate tensor, the deformation rate tensor and the rate of rotation tensor. The state of stress is described by the Cauchy stress tensor and objective Jaumann rate of Cauchy stress. An isotropic elastic-plastic material is considered. The linearized constitutive equations of elastic deformation are obtained as a function of objective Jaumann rate of Cauchy stress in the current state. The theory of a flow and an additive representation of the total deformation rate on elastic and plastic parts are used. The Drucker-Prager yield criterion is applied.The research algorithm is based on the incremental method. The principle of virtual work in terms of the virtual velocity is used. After linearization, the system of linear equations is obtained, where an increment of displacement in the current state is unknown. The radial return method with an iterative refinement of the current mode of deformation is applied. This procedure is based on the introduction into constitutive equations a work of the additional stresses in virtual deformation of the rate.The numerical implementation is based on the finite element method. An eight-node isoparametric hexahedron element is used. The calculation of the soil foundation is considered as an example. The fields of displacements and stresses are obtained. The intensity of stresses and plastic deformations are shown.

Analysis of failure modes in three-dimensional woven composites subjected to quasi-static indentation

Finite element models are developed to predict potential failure initiation sites and associated failure modes in S2-Glass/SC15 three-dimensional (3D) woven composites under quasi-static indentation. As part of this modeling effort, experimental micrographs of the composite specimen obtained from a previous experimental study1,2 are analyzed. In conjunction with these micrographs, model outcomes demonstrate the ability of warp weavers or through-thickness Z-yarns to shield inter-laminar cracks. Quasi-static indentation is modeled as a contact interaction between a rigid cylindrical indenter and a deformable S2-Glass/SC15 3D woven composite laminate using ABAQUS®. Tow elements are modeled as transversely isotropic elastic-plastic material entities, whereas the inter-tow matrix is modeled as an isotropic elastic-plastic material. Through-thickness failure modes are predicted based on the Tsai-Hill criterion. Contour maps of these failure modes point to the location and corresponding damage initiation mode within the material. Experimentally obtained micrographs1,2 are then analyzed on the basis of these contour maps, thereby serving to validate the modeling methodology. The effect of Z-yarns is demonstrated with the aid of two-dimensional plane strain linear elastic fracture mechanics analysis. Crack shielding abilities of the Z-yarns manifest as the variation of strain energy release rate as a function of crack length and location. In the vicinity of a Z-yarn, the energy release rate decreases precipitously, indicating the inability of the crack to penetrate the Z-yarns.

Determination of Burst Pressure of API Steel Pipes using Stress Modified Critical Strain Model

This paper presents a technique which can be used to determine the burst pressure of defective steel pipes using non-linear finite element (FE) analysis. The technique uses stress modified critical strain (SMCS) failure criterion to study the effect of gouge defects on maximum working pressure of API X65 steel pipes. The procedures in determining the model parameters using 3-D, homogeneous isotropic elastic-plastic material model with large deformation finite element analyses from notched tensile bars were systematically discussed. The relationship between burst pressure and gouge depth was proposed. The burst pressure estimated then was compared to experimental data from the literature for validation showing overall good agreements.

A large-deformation gradient theory for elastic–plastic materials: Strain softening and regularization of shear bands

We present a large deformation gradient theory for rate-independent, isotropic elastic–plastic materials in which in addition to the standard equivalent tensile plastic strain ϵ¯p, a variable ep is introduced for the purpose of regularization of numerical simulations of shear band formation under strain softening conditions. Specifically, in contrast to traditional gradient theories which are based on ϵ¯p and ∇ϵ¯p, here we develop a theory which depends on ϵ¯p,ep, and the gradient ∇ep, with the latter chosen to represent a measure of the inhomogeneity of the microscale plasticity. We have numerically implemented a two-dimensional plane strain version of our theory in a commercial finite element program by writing a user-element subroutine. Representative examples which demonstrate the ability of the theory and its numerical implementation to satisfactorily model large-deformation strain-softening response accompanied by intense localized shear bands — with no pathological mesh-dependence — are provided.

MACHINING OF CORTICAL BONE: SIMULATIONS OF CHIP FORMATION MECHANICS USING METAL MACHINING MODELS

This paper investigates chip formation in the machining of cortical bone and the application of isotropic elastic-plastic material models with a pressure dependent yield stress and a strain path dependent failure strain law to finite element calculations to predict observed behaviour. It is shown that a range of models can be created that result in segmented chip formations and a range of specific cutting forces similar to those observed experimentally. Results from the simulations provide an explanation for differences in the ratio of thrust to cutting forces observed between previous experimental studies, namely that the cutting tools used may have had different edge sharpness or degree of damage induced by the material removal process. Measurements of edge profiles from one of these studies support that explanation and emphasize the importance of tool toughness in maintaining efficient cutting of bone.

Limit analysis of narrow support elements in W7-X considering the serration effect of the stress–strain relation at 4 K

The magnet support system of the Wendelstein 7-X (W7-X) fusion stellarator includes challenging components, called Narrow Support Elements (NSEs), placed between the Non Planar Coils (NPCs) at the inboard side and aimed at reducing deformation of the coils. NSEs are small contact elements, with special coating to reduce friction, that have to withstand high compressive and shear forces. The objective of this article is to demonstrate the structural reliability of the NSEs under electromagnetic loading (EML), taking into account in a conservative way the relevant material properties at cryogenic temperatures. To this purpose, an appropriate parametric local Finite Element (FE) model of one highly loaded NSE with its components (pad, pad frame and counter pad) and of a portion of the coils has been developed with ABAQUS code and isotropic elastic–plastic material model with hardening/softening has been used, in order to include the serration effect at 4 K. Different mechanical limit analyses have been performed including consecutive steps of shrink fitting the NSEs in the coils, cooling down to 4 K and gradual increasing of the coil displacements induced by the EML.

Proper Orthogonal Decomposition and Radial Basis Functions in material characterization based on instrumented indentation

For the mechanical characterization of structural materials non-destructive tests combined with computer simulations and inverse analyses are more and more frequently and advantageously employed in various engineering fields. The contribution to such development presented in this paper can be outlined as follows. With reference to isotropic elastic–plastic material models, indentation test simulations are done preliminarily, once-for-all, by a conventional finite element forward operator. Results of these simulations are employed in a procedure which is centered on Proper Orthogonal Decomposition and Radial Basis Functions approximation and is used for fast interpolations which replace further finite element analyses in the parameter identification process. Comparative computational exercises are presented in order to point out the consequent significant reduction of computing times in test simulations and, hence, in the minimization of the discrepancy function by the Trust Region Algorithm, namely by a traditional first-order mathematical programming method. Such a parameter identification procedure may be carried out routinely and economically on small computers for in situ structural diagnoses. Both the force–penetration relationship (provided by an instrumented indenter) and the average imprint profile (achievable by laser profilometer) are considered as sources of measurable response quantities or experimental data.

A numerical performance comparison of a dual-phase steel and aluminium alloy bumper bar system

Bumper bar systems are important automotive structures to help protect passengers during frontal and rear collisions. This paper presents the outcomes of a numerical modelling study of a simple rectangular cross section bumper bar system using the explicit finite element code LS Dyna for a low velocity (16 km/h) centre pole frontal impact. The study utilises and compares a dual-phase steel (DP600) and two aluminium alloys (A16061T6 and A17108T6). A simple material model using isotropic elastic plastic material behaviour is utilised together with a failure criterion. When the bumper system weight is held constant by reducing the wall thickness of the steel bumper system, both aluminium alloy bumpers outperform the high-strength dual-phase steel.

FEM and ANN Analysis in Fine-Blanking Process

Fine-blanking (FB) is an effective and economical shearing process that offers a precise and clean cutting-edge finish, eliminates unnecessary secondary operations, and increases quality. In the traditional blanking product development paradigm, the design of the formed product and tooling is usually based on know-how and experience, which are generally obtained through long years of apprenticeship and skilled craftsmanship. In this study, the possibility of using finite element method (FEM) together with artificial neural networks (ANN) was investigated to analysis the fine-blanking process. Finite element analysis was used to simulate the process with an isotropic elastic–plastic material model. The results compare well with experimental results available in the literature; after confirming the validity of the model with experimental data, a number of parameters such as V-ring height effect, punch and holder force on die-roll, hydrostatic pressure status as an important factor in increasing burnish zone, and accuracy of part and radial stress status as a factor in increasing die erosion, which were also used for training the ANN, were considered. Finally, numerical data were used to train neural networks. The Levenberg–Marquardt (LM) algorithm with three neurons in the hidden layer (LM-3) appeared to be the most optimal topology and gives the best results. It was found that the coefficient of multiple determinations (R 2 value) between the FEM and ANN predicted data is equal to about 0.999 for the size of die-roll, therefore indicating the possibility of FEM and ANN as a powerful design tool for the fine-blanking process.

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.

Analysis of the Parameters Affecting Warping In Radial Forging Process

Radial forging is a process in which one or two punches move axially causing a radial flow into a die cavity by means of which a flange is formed. During forging, warping, in which the lower face of thin flange rises from the die face may occur. To better understand the effect of parameters affecting the warping in radial forging a Finite Element analysis was used to simulate the process with isotropic elastic-plastic material model. Parameters such as die corner Radius (r) or shape and ring gap Height (H), on the warping, were investigated and results were compared with experimental work. It has been shown that increasing ring gap height and die corner radius will lead to warping reduction. Also it has been shown that special profile such as chamfered die, tapered ring gap, cosine profile and polynomial function may be used to reduce the warping.

Indenter tip radius and load frame compliance calibration using nanoindentation loading curves

The finite-element method has been used to simulate the indentation process of a variety of isotropic elastic-plastic materials indented by a rigid conical indenter with a perfectly sharp tip and round tips of various radii. Analyses of the obtained loading curves showed that the load frame compliance Cf of the nanoindentation instrument and the tip roundness r of the indenter can be determined from the loading curve. In a real indentation experiment, the obtained raw load-depth data during the loading stage can be described by the second-order polynomial dependence of depth on the square root of load, from which the Cf and r values are determined. An experimental procedure has thus been proposed for Cf and r calibration using the loading curves of a hard and isotropic material. Nanoindentation experiments on fused silica demonstrate the reliability of the proposed technique for accurate and quick Cf and r calibration.