Description Of Material Behavior Research Articles

Quantifying uncertainty in load–hardness relationships

This article presents methodology for constructing a probability space that quantifies the load–hardness relationship in ceramics. Aspects of this space are indicative of uncertainties introduced by variations in material microstructure, instrument repeatability, and technician skill. The developed method is general in nature, and can be made specific to particular types of hardness measurements or equations used to describe the load–hardness relationship such as Meyer’s law, the modified proportional specimen resistance model, and others. Construction of the probability space is accomplished by applying Bayesian hypothesis testing to determine the likelihood function of critical parameters of the chosen load–hardness equation. A demonstration of this methodology is presented for Vickers hardness measurements made at four applied loads on tungsten carbide. The utility of the technique in quantifying microstructural uncertainty is shown using Knoop hardness datasets for aluminum oxynitride and two types of silicon carbide. Analysis of the normality of hardness values was shown to provide an objective criterion for determining when enough measurements have been made to adequately describe material behavior. The probability spaces constructed for each material were used to quantify uncertainty in the load–hardness curve that would extend to predictions regarding microstructural features or performance based on this relationship.

A Study of Non-uniqueness During the Inverse Identification of Material Parameters

The Finite Element simulation of machining has been instrumental in developing a deeper understanding of the chip formation process. One of the problems in obtaining results which are valid over a large range of cutting conditions has been finding appropriate material parameters. The Johnson-Cook material model has been one of the most widely used models for machining simulations as it can describe material behaviour for different strains, strain-rates and temperatures. It has been challenging to obtain the Johnson-Cook parameters from experiments which are valid over the large range of conditions during machining. Whereas during machining strains larger than 200% and strain-rates of over 105 s-1 are observed, in experiments it is only possible to reasonably obtain a strain of 50% and strain-rate of 103 s-1 [1]. Inverse identification of the Johnson-Cook parameters from machining experiments has been proposed as an alternative method, so that the parameters are valid over large ranges [2–5]. One of the problems encountered in this technique is the non-uniqueness of parameter sets which give rise to similar chip shapes and cutting forces even if the material parameters are widely different. In this paper, the non-uniqueness of parameters has been studied with respect to varying strain-rates and temperatures. In order to do so, the Johnson-Cook parameter space is explored systematically to find parameter sets with closely matching stress-strain curves. The influence of plastic heat on the non-uniqueness is studied as well. A large pool of non-unique parameters can be reduced by widely changing the cutting conditions, for instance the rake angle.

Creep‐fatigue analysis of the steel AISI type 316 component failure

AbstractThe purpose of this work is to extend a typical creep‐damage model in order to describe material behavior under variable thermal and mechanical loading in wide stress range. The model basis is creep constitutive law in form of hyperbolic sine stress response function proposed by Nadai. The constitutive law is extended to assume the damage process under creep and fatigue by the introduction of scalar damage parameters and appropriate evolution equations according to Kachanov‐Rabotnov concept. The material constants for model are identified by fitting the experimental creep and low‐cycle fatigue data for the steel AISI type 316 at the range of temperatures 500°C – 750°C. The development of such model is motivated by the well described failure case study of high‐temperature components at unit 1 of Eddystone power plant, which have operated during 130520 hours under creep‐fatigue interaction conditions. The main steam piping (MSP) from this power plant is selected for thermo‐mechanical creep‐fatigue analysis applying the proposed material model. The estimated values of damage parameters comply with the real location of the component failure and a scatter of experimental data on creep‐fatigue interaction diagram. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Comparison of physically based constitutive models characterizing armor steel over wide temperature and strain rate ranges

Both descriptive and predictive capabilities of five physically based constitutive models (PB, NNL, ZA, VA, and RK) are investigated and compared systematically, in characterizing plastic behavior of the 603 steel at temperatures ranging from 288 to 873 K, and strain rates ranging from 0.001 to 4500 s−1. Determination of the constitutive parameters is introduced in detail for each model. Validities of the established models are checked by strain rate jump tests performed under different loading conditions. The results show that the RK and NNL models have better performance in the description of material behavior, especially the work-hardening effect, while the PB and VA models predict better. The inconsistency that is observed between the capabilities of description and prediction of the models indicates the existence of the minimum number of required fitting data, reflecting the degree of a model's requirement for basic data in parameter calibration. It is also found that the description capability of a model is dependent to a large extent on both its form and the number of its constitutive parameters, while the precision of prediction relies largely on the performance of description. In the selection of constitutive models, the experimental data and the constitutive models should be considered synthetically to obtain a better efficiency in material behavior characterization.

Determination of Uniaxial Flow Stress Curve Using Aero-Bulge Test for Very Thin Copper Sheet

Determination of the flow stress curve is an important step for precisely describing material behavior in Finite Element simulations. The flow stress curve is generally determined by taking a uniaxial tensile test as a standard. In the case of very thin sheet, since the fracture is generated at a low strain, there is not enough uniaxial data obtained to be applied in the FE simulation. The reason for this is that charactering plastic deformation at a large strain values by extrapolating a flow stress curve which is based on insufficient measurement data is highly susceptible to error. Bulge test is useful method for determining the equivalent biaxial flow stress curve up to a large strain. In this paper, the biaxial flow stresses curve for very thin copper sheet with thickness 35 and 50 μm were determined using the aero-bulge test. A new empirical model was derived for the estimation of the sheet thickness at the pole. After the compatibility between uniaxial and biaxial flow stresses was verified, the uniaxial flow stress curve was determined from the aero-bulge test using reverse engineering. The methodology of extrapolation of the flow stress curve at a large strain was finally proposed for application in FE simulations.

Modeling of high velocity impact of spherical particles

Abstract A systematic analysis of a single copper particle impacting a semi-infinite copper substrate was carried out for initial impact velocities ranging between 100 m/s and 700 m/s by using the finite element method. Capability of and various issues related to: modeling in a Lagrangian reference frame; modeling using adaptive remeshing in an ALE reference frame; and, modeling considering material failure in a Lagrangian reference frame, are discussed. The Lagrangian approach with material failure is found effective in describing material behavior under high deformations and preventing excessive distortion of the mesh. It is found that at fast impact velocities the particle–substrate interface continuously undergoes shear failure as the particle penetrates into substrate. A lip which mostly contains failed material is formed as a result of localized deformation. Plastic deformation is confined to a small volume around the impact zone. Maximum strain is developed at the surface of particle and substrate. Compressive residual stresses are generated below the impact site after particle rebound, and higher impact velocities result in deeper compressive layers and somewhat larger stresses. A notable similarity in deformation patterns is observed between the impacts of 50 μm and 5 mm particles. Smaller particles are found to behave slightly stiffer than larger particles because of the strain-rate effects.

Experimental and numerical investigation on the deformation and failure behavior in the Taylor test

The present paper presents an experimental and numerical study concerning the deformation and failure behavior in the Taylor impact test. Projectiles manufactured from a commercial high strength and super-hard aluminum alloy 7A04-T6 with a nominal diameter of 12.6 mm and a length of 50.8 mm were fired against a hardened tool steel plate by a one- and two-stage compressed gas gun within the velocity range of 175–370 m/s. Three different deformation and failure modes were observed from the test: mushrooming, shear cracking and fragmentation. Individual velocity ranges and the transitions between the deformation/failure modes are identified by both experiments and numerical simulations. Slightly modified Johnson–Cook models of strength and accumulative damage failure are employed in 3D numerical simulations to describe material behavior of the striking cylinders. Good agreement between the numerical simulations and the experimental results was found. Detailed computational results of each scenario are offered to understand the deformation and failure mechanisms.

Effect of Anisotropy and Direction of Magnetization on Complex Permeability of Ferromagnetic Rectangular Thin Slabs

Ultrasoft magnetic materials, such as amorphous, nanocrystalline, and polycrystalline alloys, have been successfully used for power electronic applications during recent years. However, enhancements are needed for the integration of power electronic features, which involves high power densities and operating frequencies up to a few megahertz. Complex permeability spectra, which are used to describe material behavior in these applications, depend mainly on domain-wall motions and coherent magnetization rotation mechanisms. In this paper, we present a model describing these mechanisms, in terms of magnetic anisotropies and domain structure of the material. To validate the model, we measured permeability spectra of polycrystalline Ni-Fe alloys under mechanical stress using a specific setup. These measurements are suitable for comparing the physical model according to different magnetoelastic anisotropies. Results are useful for correlating high-frequency magnetic behavior and the annealing process of materials.

New methods for more accurate material characterization

In order to ensure better process design and tool optimization, it makes sense to describe material behavior in the context of phenomenological plasto-mechanics. To achieve this, it will be necessary to determine material behavior comprehensively and also to a high level of precision, in order to determine accurately the start of flow and to put forward specific variables relative to the forming process. At Fraunhofer IWU these endeavors have been expanded to form a main research area, with the aim, for example, of making the necessary material variables available under actual process conditions, detailed and accurate, for a range of different simulation programs.

Multiscale modeling of elasto-viscoplastic polycrystals subjected to finite deformations

In the present work, the elasto-viscoplastic behavior, interactions between grains, and the texture evolution in polycrystalline materials subjected to finite deformations are modeled using a multiscale analysis procedure within a finite element framework. Computational homogenization is used to relate the grain (meso) scale to the macroscale. Specifically, a polycrystal is modeled by a material representative volume element (RVE) consisting of an aggregate of grains, and a periodic distribution of such unit cells is considered to describe material behavior locally on the macroscale. The elastic behavior is defined by a hyperelastic potential, and the viscoplastic response is modeled by a simple power law complemented by a work hardening equation. The finite element framework is based on a Lagrangian formulation, where a kinematic split of the deformation gradient into volume preserving and volumetric parts together with a three-field form of the Hu-Washizu variational principle is adopted to create a stable finite element method. Examples involving simple deformations of an aluminum alloy are modeled to predict inhomogeneous fields on the grain scale, and the macroscopic effective stress-strain curve and texture evolution are compared to those obtained using both upper and lower bound models.

Inverse parameter identification of sheet metals utilizing the distribution of field variables

The accurate simulation of sheet metal forming processes requires the accurate description of material behaviour. This is accomplished by utilization of sophisticated constitutive models that use several parameters. This work proposes a procedure which makes use of the distribution of field variables to identify the material parameters by the help of inverse analysis. In this procedure, the distribution of the field variables on a sheet surface is captured by an optical measurement system during a process, which is capable of computing the displacement and strain distribution. The finite element simulation of the same process is also performed. However, it is not possible to compare the experimental data directly with the simulation results because of the differences regarding the coordinate systems and discretizations in space and time domain. These problems are solved by coordinate transformations and parameter mapping. The procedure is applied to simple tension test as an application example, in which the flow curves of two materials are calculated successfully.

Features of the development of extrusion granulation of biofuel based on wood and plant waste products

The problem is considered of using granulated fuel from sawdust as a replacement for traditional energy sources, and the advantages of wood granules over other types of fuel are demonstrated. Results are provided for a study of the behavior of sawdust in a channel during continuous compaction. Results are given for a study of the effect of temperature on the change in plastic strength of the original raw material. It is shown that use of heating leads to a reduction in the specific compaction pressure, and this makes it possible to reduce energy expenditure and to increase the efficiency of preparing the final product. Operating principles are considered for rotary presses and also forces that operate on the compacted mass at a deformation site. A series of equations is provided describing material behavior in an extrusion compaction channel, and also the connection of channel geometric parameters and reprocessed material properties.

Deformation and Failure Modes of Soft Steel Projectiles Impacting Harder Steel Targets at Increasing Velocity

The present paper describes an experimental and numerical study concerning the impact of blunt steel projectiles against harder steel plates, at impact velocities between 200 and 800 m/s. In contrast with previously published observations, three modes of deformation and failure of the soft steel projectiles were observed in the present study. These included: Taylor cylinder mushrooming, sunflower-like petalling and plugging perforation. Individual velocity ranges and the transitions between the deformation/failure modes are identified by both experiments and numerical simulations. Complex material failure mechanisms of projectile and target play conflicting roles in the various penetration stages. Johnson–Cook models of strength and accumulative damage failure are employed in 3D numerical simulation to describe material behavior of both projectile and target. Computational evolutions of each scenario are offered in detail to understand the deformation and failure of projectile and target plate.

Rate dependence of crack-tip processes predicts twinning trends in f.c.c. metals

Crack-tip behaviour in metals is among the most basic problems in mechanics of materials. Yet, long-standing experimental evidence suggests that crack-tip twinning in face-centred-cubic (f.c.c.) metals is highly dependent on the material, temperature and loading rate, and previous simulations and models predict twinning in aluminium, where it has never been observed. Here, this discrepancy between theory and experiment is resolved through a new model guided and validated by extensive multiscale simulations. Both the analytic model and simulations reveal a transition from crack-tip twinning at short times to full dislocation formation at long times. Applied to a host of f.c.c. metals, the model agrees with experimental trends as it predicts large differences in the thermal activation needed for full dislocation emission to dominate. More broadly, this work demonstrates the necessity of multiscale modelling and attention to rate dependence for accurate description of material behaviour and computationally guided material design.

GALERKIN LEAST-SQUARES APPROXIMATIONS FOR FLOWS OF CASSON FLUIDS THROUGH AN EXPANSION

Among non-Newtonian fluid models, purely viscous constitutive equations play an important role in industrial applications regardless their lack of accuracy in non-viscometric flows. In this work we are concerned with the flow of viscoplastic shear-thinning fluids in complex geometry. Viscoplastic fluids are those that behave as extremely high viscosity materials when submitted to low stresses and that flow when submitted to stresses higher than a yield stress value. Usually, they also present shearthinning behavior. Fluids such as molten chocolate, xanthan gum solutions, blood, wastewater sludges, muds, and polymer solutions present viscoplastic shear-thinning features. In order to approximate numerically viscoplastic shear-thinning flows we first describe a mechanical model based on continuum mechanics conservation laws of mass and momentum. The description of material behavior is such as to respect certain principles of objectivity and generality in continuum mechanics. The Generalized Newtonian Liquid constitutive equation with Casson viscosity function is able to predict viscoplasticity and shear-thinning. The numerical approximation of the equations is performed by a finite element method. To prevent the model from pathologies known for the classic Galerkin method, we employ a stabilized method based on a Galerkin least-squares (GLS) scheme, which is designed to circumvent Babuška-Brezzi condition and deal with the asymmetry of the advective operator. We present approximations for the flow through a planar 4:1 sudden expansion. We investigate the influence of Reynolds and Casson numbers on the flow dynamics.

Stochastic Characterization and Models to Predict Performance Uncertainty in Photonic Packages

There is considerable uncertainty in the prediction of performance of a system, due mainly to idealizations in geometry, material behavior, and loading history. Uncertainties in geometry can be predicted and controlled using tighter tolerances. However, the models currently used to describe material behavior are mostly deterministic. To predict the coupling efficiency of a photonic system to a greater degree of confidence, stochastic analysis procedures are necessary. As part of such an analysis, the behavior of materials must be stochastically characterized. In this paper, we present extensive experimental data on thermally and UV-cured epoxies, typically used in photonic packages to enable stochastic analysis. We perform dynamic mechanical analysis over a wide frequency and temperature range to determine the viscoelastic behavior of the epoxies. We next derive an analytical description of the time-dependent behavior of a vertical cavity surface emitting laser (VCSEL) array bonded to a substrate. We further characterize the variation in the displacement of the VCSEL array due to the stochastic, viscoelastic behavior of the bond epoxy. We carry out Monte Carlo simulation to predict the uncertainty in the coupling efficiency of a generic photonic package. We finally relate the size of the VCSEL laser array to its ability to achieve the required coupling efficiency.

Identification of Material Damage Model Parameters: an Inverse Approach Using Digital Image Processing

A reliable prediction of ductile failure in metals is still a wide-open matter of research. Several models are available in the literature, ranging from empirical criteria, porosity-based models and continuum damage mechanics (CDM). One major issue is the accurate identification of parameters which describe material behavior. For some damage models, parameter identification is more or less straightforward, being possible to perform experiments for their evaluation. For the others, direct calibration from laboratory tests is not possible, so that the approach of inverse methods is required for a proper identification. In material model calibration, the inverse approach consists in a non-linear iterative fitting of a parameter-dependent load–displacement curve (coming from a FEM simulation) on the experimental specimen response. The test is usually a tensile test on a round-notched cylindrical bar. The present paper shows a novel inverse procedure aimed to estimate the material parameters of the Gurson–Tvergaard–Needleman (GTN) porosity-based plastic damage model by means of experimental data collected using image analysis. The use of digital image processing allows to substitute the load–displacement curve with other global quantities resulting from the measuring of specimen profile during loading. The advantage of this analysis is that more data are available for calibration thus allowing a greater level of confidence and accuracy in model parameter evaluation.

Two-step procedure for identification of metal behavior from dynamic compression tests

Simulation of forming processes requires accurate constitutive models describing material behavior at large strains up to 150% and intermediate strain rates up to 10 3 s −1, and taking into account adiabatic heating. The choice of a rheological model and the determination of its parameters should be made from tests generating such conditions. The major difficulty encountered is that few experimental tests satisfy these criteria. The uniaxial compressive test seems well adapted and is frequently used to characterize the rheological behavior at operating conditions corresponding to forming applications. However, for high strain rate tests, the load measurement is disturbed by the elastic response of the experimental set-up. Therefore, the difficulty is to identify the behavior of the material studied independently of the experimental set-up. This paper proposes to improve the analysis of the dynamic compression test and presents a method to convert experimental data into true stress–strain relationships. A specific experimental set-up is used to realize compression tests at high velocities and at elevated temperatures. The dynamic response of the experimental set-up is analyzed and a finite-element (FE) model taking into account the elastic and inertia effects of the whole experimental structure is defined. A two-step sequential identification method of the material behavior based on inverse analysis is presented. Finally, behavior of a 27MnCr5 steel, submitted to different compression velocities and heated to different temperatures is identified.

An efficient implicit approach for the thermomechanical behavior of materials submitted to high strain rates

In the present paper, three solutions are proposed to simulate fast phenomena with finite element method at best. At first, material constitutive laws of Johnson-Cook and Zerilli-Armstrong types are implemented. These well-known laws are efficient for the description of material behavior at high velocities, especially for material used in automotive or aeronautics industry. The second contribution of this paper is the coupling of an implicit Chung-Hulbert algorithm taking into account the inertial effects with a staggered scheme for solving the thermal problem. The last input of this paper is the use of EAS (Enhanced Assumed Strain) finite elements to better capture complex strain modes, especially bending that is not accurately evaluated with classical finite elements. These EAS finite elements are used in the scope of thermomechanical dynamic phenomena implemented in a modular C++ environment at the University of Liege in the home made software METAFOR.

The mechanical behavior of conductors exposed to short-duration thermal loading

The current-carrying conductors in an electromagnetic (EM) launcher are exposed to high thermal loads that last for a few milliseconds. In some instances, the temperature increases range up to the melting point of the materials. Even though the equilibrium and creep behavior of materials at high temperature at long time scales is well characterized, such characterization is generally not available for thermal loads lasting for very short durations. Here, we study the mechanical properties, such as elastic modulus and yield strength, of commonly used conductors such as aluminum and copper alloys under millisecond-duration thermal loads. A pulser circuit is designed and used in conjunction with a tensile-testing machine to study property degradation concurrent with and subsequent to the application of the thermal load at different strain rates. The results of our study shall be used for generating constitutive descriptions of material behavior and in designing various components of the EM launchers.