Modeling Of Material Response Research Articles

Testing and Modelling of Material Response to Deformation in Bulk Metal Forming

As the virtual prototyping of forming operations and systems becomes a real prospect for industries, reliable and versatile simulation software must be created to efficiently and accurately predict the events products and processes are subjected to. Useful and efficient models and tests able to evaluate the different aspects of the material response to plastic deformation are among the most critical prerequisites. The knowledge of how the material performs during and after deformation has, in fact, a great impact on product design and manufacturing decisions. This paper attempts to critically assess the modelling and testing approaches and techniques for predicting material response that are available today and then to discuss the latest developments in research labs and industrial applications in the fields of modelling and testing. The emphasis is on what is changing and must still change in order to provide industrial process designers with more useful models and efficient tests that can meet the increasing demand for accurate processes and product simulation.

Analysis of Heterogeneous Composites Based on Moving-Window Techniques

Moving-window micromechanics techniques are emerging as a useful tool for characterizing random composites, i.e., those with spatially random microstructures, in terms of local material property fields. These material property fields represent an approximate constitutive model for local material response. In this work, elastic property fields for randomly generated composite materials are estimated using a moving-window technique in combination with three micromechanical models, Mori-Tanaka, the generalized method of cells, and a brute-force finite element analysis. The first two methods make predictions of local properties based on small areas of the full sample. The brute-force finite element method performs its initial analysis on the full microstructure. Using the finite element results as the baseline solution, the fields developed from the methods are compared. Results illustrate the differences between the three methods and highlight the strong influence of window size on the analysis. Two criteria are suggested for further study of appropriate window size: A comparison of the correlation areas of the fields, which suggests an upper bound, and the analysis of a single fiber problem with known elasticity solution, which examines a potential lower bound. All of the techniques are demonstrated by application to numerically generated composite microstructures.

On nonlinear propagation of extremely short pulses in optically uniaxial media

Nonlinear wave equations describing the propagation of optical pulses of duration up to a period of electromagnetic oscillations in transparent media with uniaxial optical anisotropy are derived on the basis of a quantum-mechanical model of material response. The electron and electron-vibrational nonlinearities, electron and ion dispersion, and diffraction are taken into account. It is shown that the inclusion of the electron response alone leads to a system of two constitutive equations for the ordinary and extraordinary polarization components. When a pulse propagates across the optical axis, this system is reduced to an inhomogeneous model of the Henon-Heiles type and, hence, generalizes the Lorentz classical electron model. In order to take into account stimulated Raman scattering (SRS) processes, an anisotropic analog of the Bloembergen-Shen quantum-mechanical model taking into account the population dynamics of SRS sublevels is obtained. The generation of an extraordinary wave video pulse with the help of the high-frequency ordinary component in the Zakharov-Benney resonance mode is investigated. Some analytic soliton-like solutions in the form of propagating bound states of ordinary and extraordinary video pulses corresponding to different birefringence modes are considered and their stability to self-focusing is analyzed.

Three-Dimensional Finite Element Analysis of Doweled Joints for Airport Pavements

Various aspects of the structural behavior of doweled joints, including load transfer, in rigid airport pavement systems are investigated by using nonlinear three-dimensional finite element methods. The finite element models include two concrete slab segments connected by dowels. The concrete slab and supporting layers are simulated by continuum solid elements. Solid elements can capture the severe local deformation in the concrete slab in the vicinity of wheel loads. They allow the modeling of nonlinear material response of the supporting layers and of frictional contact between the concrete slabs and supporting layers. These features generally are not considered in classical analytical approaches. The structural behavior of the doweled joint is investigated for various design and loading conditions, including tire pressure, slab thickness, dowel looseness, and different landing gear configurations. An attempt is made to quantify the amount and efficiency of load transfer through the dowels. According to the finite element results, 15% to 30% of the applied wheel load is transferred to the adjacent slab segment by the dowels in an intact joint, depending on design and loading conditions. In addition, 95% of the transferred shear force is carried only by the 9 or 11 dowels that are closest to the applied load.

Wave-Like Solutions for a Class of Parabolic Models

A reduction aproach is developed for determining exact solutions of anonlinear second order parabolic PDE. The method in point makes acomplementary use of the leading ideas of the theory of quasilinearhyperbolic systems of first order endowed by differential constraintsand of the techniques providing multiple wave-like solutions ofnonlinear PDEs. The searched solutions exhibit a inherent wave featuresand they are obtained by solving a consistent overdetermined system ofPDEs. Remarkably, in the process it is possible to define nonlinearmodel equations which allow special classes of initial or boundary valueproblems to be solved in a closed form. Within the present reductionapproach exact solutions and model material response functions areobtained for an equation of widespread application in many fields ofinterest.

Response of Cross-Ply Composite to Off-Axis Loading

Polymer composites are known to exhibit nonlinear stress–strain response due to nonlinearly elastic or plastic deformation of the matrix and damage accumulation. Mechanistic modeling of material response explicitly accounting for these interacting factors often leads to complex theories. Plasticity theory formalism provides an alternative for nonlinear deformation description of composite material. We examine the applicability of an orthotropic plasticity model, developed by Sun et al. for unidirectionally reinforced composite, to composite laminate. The response of a symmetric and balanced cross-ply glass/epoxy laminate is studied under uniaxial tensile loading at different angles to the material orthotropy axis. It is found that the associated flow rule and a quadratic approximation of the orthotropic potential function provide satisfactory description for the nonlinear strain component under monotonic loading for 15–45° off-axis angle range. The nonlinearity in on-axis loading (modulus degradation)is well described by stiffness reduction due to the cracks in transverse plies. Meanwhile the change of elastic modulus due to intralaminar cracking can be neglected in off-axis loading, but the possible intensification of nonlinear deformation in off-axis loading caused by the presence of intralaminar cracks agrees well with orthotropic potential formalism.

Damage and rock-volatile mixture effects on impact crater formation

We explored simple geologic strength and material response models to determine which have the capability to simulate impact-induced faulting, complicated ejecta patterns and complex crater shapes. This led us to develop models for material damage, dilatancy, and inhomogeneous materials (mixtures). We found that a strength degradation (damage) model was necessary to produce faulting in homogeneous materials. Both normal and thrust ring faults may occur and extend relatively deeply into the planet during the transient cavity radial expansion. The maximum depth of fault development is about the depth of maximum penetration by the projectile. Dilatancy in geologic materials may reduce the final bulk density compared to the pristine state because of irreversible fracturing. When we include the effects of dilatancy, the radial position of faulting is displaced because of greater upward motions. In addition, the late time crater profile is shallower and the expression of features such as central peaks and rings may be more pronounced. Both damage and rock-ice mixtures effect the distribution of ejecta. The excavation flow field within the heavily damaged region is similar to flow fields in Mohr-Coulomb materials with no zero-pressure strength. In the outer, less damaged zone within the excavation cavity, the material trajectories collapse back into the crater. This effect creates a zone of reduced ejecta emplacement near the edge of the final crater. In the case of rock-ice mixtures, energy is preferentially deposited in the more compressible volatile component and the ejecta pattern is dependent upon the location of shock-induced phase changes in the volatile material.

A phenomenological plasticity model with non-normality effects representing observations in crystal plasticity

An abrupt strain path change has recently been used to determine the shape of the subsequent yield surface near a current loading point. Both polycrystal plasticity calculations and experiments have shown non-normality of plastic flow, with a vertex-type response on the apparently smooth yield surface. The physical reason for this observation is carefully discussed in the paper, with particular emphasis on the fact that the prediction appears in spite of the normality rule built into each slip system of the crystal plasticity model. To represent the observed non-linear material response, a phenomenological plasticity model is proposed, in which a smooth yield surface for an anisotropic solid is combined with a vertex-type plastic flow rule. As plastic instability results are particularly sensitive to accurate modeling of material response under abrupt stress path change, the material model is tested on predictions of the onset of necking in biaxially stretched metal sheets. It is shown that the phenomenological plasticity model gives a good approximation of critical strains predicted by direct application of the Taylor polycrystal plasticity model.

An Investigation of Tensile Properties and a Simple Constitutive Model for a Random Continuous Fiber Thermoplastic Composite

The tensile properties of a commercially available, random continuousfiber thermoplastic composite material are investigated at various strain rates and elevated temperatures. The material utilizes polypropylene (PP) for the matrix material, with random continuous E-glass fiber reinforcement. Tensile modulus, tensile strength, strain to peak stress, and strain energy are experimentally determined at strain rates varying from 0.000167 sec-1 to 0.0334 sec-5 and temperatures varying from 20 to 120'C. The material properties are found to have large scatter caused by local variations in fiber content and orientation. The tensile properties are independent of the strain rate but depend on the temperature. A model for the material response based on a simple power law equation is presented.

Waterdrop impact modeling

The complete spatial and temporal interaction of a waterdrop impacting a deformable target can now be described using a three-dimensional finite element model. The advantage of the finite element formulation is that the stresses generated in structurally complex targets can be determined. The geometry of the target is also accurately represented in the model. A brief account of previous waterdrop impact modeling approaches is provided to illustrate the significance of what can be accomplished with the current model. A broad range of constitutive behavior and failure criteria are available within the finite element analysis, however implementation of the finite element analysis depends in many cases on how well the high rate of loading behavior of the components in the target is known. Experimentation to define the relevant material response models is being developed. Currently predictions for the onset of failure are based on the magnitude and duration of the stresses generated within the target. The finite element analysis is being extended to include the propagation of damage and the associated redistribution of stress around the failed elements. It will then be possible to predict the full extent of the damage produced by an arbitrary waterdrop impact.

Application of integral methods to ablation charring erosion - A review

To predict ablation, charring, and erosion of heat-shield materials, approximate heat balance integral (HBI) methods offer speed and versatility; however, traditional HBI articles treat only simple, idealized models of material response. This paper reviews application of HBI methods to more realistic models of material response, specifically, for carbon-carbon and carbon-phenolic heat shields on reentry vehicles. The review shows that HBI successfully extends to most such simulations of ablation, charring, and erosion in hypersonic flow, but unexpected problems can crop up and trade-offs exist. Pertinent material models are also summarized, including efficient expressions that fit material thermal properties and carbon-air thermochemical ablation functions.

Some Aspects of Erosion Prediction of Steam Turbine Blading

This paper deals with an issue of paramount importance for the turbine manufacturer today: the mathematical modeling of erosive wear at the inlet rotor blade edges by streams of coarsely dispersed liquid droplets. In the methodology of blade material wear an important element is the erosion model or material response Y = Y (τ) to the droplet impact intensity. On the background of this erosion model development the approaches of Szprengiel and Weigle (1983), Szprengiel (1985), and Shubenko and Kovalsky (1987) are presented and applied for erosion calculation of some real turbine blade profiles. There are, however, several factors that affect the erosion prediction quality as well as the field experimental data. Hence a procedure for verifying the methodology of the erosion prediction by experimental data is necessary. Krzyzanowski (1987, 1988, 1991) used for that purpose the calculated and measured erodet area of various turbine blade profiles. Here the comparison of the calculated and measured erosion width ηB ≡ z has been used to verify the prediction methodology of erosion. The use of ηB instead of erosion area looked promising since acquiring ηB experimental values seemed easier than any other geometric characteristics of the blade erosion wear. It has been shown, however, that the prediction of ηB underestimates the blade erosion wear for both material response models. To cope with the scatter of experimental data, statistics have been used. Reasons for this scatter and differences between the calculated (ηBcalc) and measured (ηBm) values of the erosion field width have been suggested. The list of factors that affect the erosion prediction quality may be looked upon as a list of promising topics of further research on the subject.

Numerical modeling for underground nuclear test monitoring

The symposium for Numerical Modeling for Underground Nuclear Test Monitoring was held March 23–25 in Durango, Colo. Funded by the DOE Office of Arms Control and Nonproliferation (OACN) and hosted by the Source Region Program at Los Alamos National Laboratory (LANL), the meetings's purpose was to discuss the state‐of‐the‐art in numerical simulations of nuclear explosion phenomenology with applications to test‐ban monitoring. In particular, we wished to focus on the uniqueness of model fits to data, the measurement and characterization of material response models, advanced modeling techniques, and applications of modeling to monitoring problems.The concept for the meeting arose through discussions with Marv Denny, who was on assignment at Department of Energy Headquarters from Lawrence Livermore National Laboratory (LLNL). In these conversations, the following question was discussed: how are numerical modeling techniques being used to understand the effects of explosion‐ source phenomenology on test‐ban treaty monitoring? Numerical studies are becoming increasingly important in the evaluation of capabilities for proliferation monitoring; this trend has accelerated with the curtailment of the nuclear testing program. During these discussions, the issue of the uniqueness and limitations of numerical models arose. It was decided to address these questions by convening a group of experts to present and discuss the problems associated with modeling of close‐in data from explosions.

Analysis of RC Membrane Elements With Anisotropic Reinforcement

The internal load resisting mechanisms in anisotropically reinforced concrete membrane elements is studied, and a suitable time independent material response model for finite element analysis of such elements up to failure is formulated. Appropriate consitituive models to simulate the pre-cracked responses of concrete and reinforcement are employed. The postcracking model is based on the smeared crack approach, and takes into account the bond forces between concrete and reinforcement and is capable of simulating multiple non-orthogonal cracks at a sampling point. An hypothetical RC panel analysis is presented to identify the internal load resisting mechanisms after cracking and upon partial yielding of the panel reinforcement. The constitutive models are then implemented in a finite element program and two highly anisotropically reinforced test panels are then analyzed. The merits of the numerical models are then explored. The sensitivity of the results to variations in post-cracking parameter is also investigated.

Thermodynamic Characterization of Microcrack Dependent Material Response Properties

Available experimental data from uniaxial tests are analyzed to estimate values for parameters of a microcrack dependent model of material response. The experimental data on microcrack density evolution during uniaxial deformation were obtained with small-angle X-ray scattering techniques on polymer specimens. The parameters of the microcrack dependent model are the opening and size of the microcracks, a thermodynamic potential for microcrack kinetics that describes energy conditions for microcrack creation, and coefficients in a nonlinear Onsager type relationship to describe rate kinetics of microcrack creation. The Onsager relationship contains a nonequilibrium thermodynamic measure that is the work done per microcrack created minus the thermodynamic energy per microcrack created. Deformation stability concepts of microcrack dependent material response are discussed in terms of mechanical stability, thermodynamic stability, and global or system stability of the uniaxial test.

Disintegration behavior of metal rods subjected to hypervelocity impact

The disintegration behavior of projectile rods when impacting plates at velocities above 10 km/s is largely unexplored. Possible material responses include vaporization, melting, solid state phase changes, plastic flow, shear localization, and ductile and brittle tensile fracture. Two primary difficulties have prevented experimental studies of projectile response in this velocity regime, namely the lack of a technique for accelerating a projectile to velocities above 10 km/s, and the lack of a procedure for recovering the projectile remains after impact for examination. These difficulties were overcome recently by using an exploding foil technique to drive an impactor plate and by using a reverse ballistics test arrangement to allow projectile recovery. This paper describes this experimental procedure for investigating the disintegration behavior of projectile rods under hypervelocity impact conditions, presents preliminary results for steel, aluminum and lead, and discusses requirements for computational material response models.

Consolidation under an isotropic total stress increase: part II, experimental results for marine clay

Deformation and internal pressure changes have been measured in a large sample (of the order of 1 m3) of remoulded, reconsolidated marine sediment subjected to a series of step-like, 6·9 MPa changes in hydrostatic pressure. Undrained surface displacements of 0·2–0·4 mm were observed in response to each increment in external pressure. The surface then slowly rebounded with a characteristic time of about 106 s. The excess pore pressure induced by each step in pressure at the boundary was of the order of from −1 kPa to −2 kPa (suction) and likewise relaxed as external fluid diffused into the sample. Predictions based on a poroelastic material response model agree qualitatively with these observations when values of material properties are estimated from independent measurements. The experimental data can also be used to determine parameter values. Such a procedure yields very good fits to the data and indicates permeability, drained bulk modulus and solid bulk moduli of the order of 10−16 m2, 10 MPa and 10 GPa respectively, in reasonable agreement with independent measurements. Des changements de déformation et de pression interne ont été measurés dans un grand échantillon (de l'ordre de 1 m3) de sédiment marin remanié et reconsolidé soumis à une série de modification de pression hydraulique par paliers de 6, 9 MPa. Des déplacements non-drainés superficiels compris entre 0, 2 et 0, 4 mm ont été observés en réponse à chaque augmentation de pression externe. Puis la surface s'est lentement restaurée au cours d'un temps caractéristique d'environ 106 s. Les surpressions induites à la limite lors de chaque palier de pression étaient de l'ordre de −1 kPa à −2 kPa (succion) et se relâchaient de façon analogue au fur et à mesure que du fluide externe se diffusait dans l'échantillon. Des prévisions basées sur un modèle de réponse d'une matière poroélastique s'accordent de façon qualitative lorsque les valeurs des propriétés des matières sont estimées à partir de mesures indépendantes. Les données expérimentales peuvent s'employer aussi pour déterminer les valeurs des paramètres. Une telle procédure donne des résultats très compatibles avec les données et indique une perméabilité, un module de masse drainée et des modules de masse solide de l'ordre de 10−16 m2, 10 MPa et 10 GPa respectivement. Ceci s'accorde assez bien avec les mesures indépendantes.

Geotechnical Materials Considerations for Conceptual Repository Design in the Palo Duro Basin, Texas

ABSTRACTThe Palo Duro Basin is only one of numerous potential repository locations for placement of a nuclear waste repository. Conceptual designs in the Palo Duro Basin involve considerations of the character and properties of the geologic materials found on several sites throughout the Basin. The first consideration presented includes current basin exploration results and interpretations of engineering properties for the basin geologic sequences.The next consideration presented includes identification of the characteristics of rock taken from the geologic sequence of interest through laboratory and field testing. Values for materials properties of representative samples are obtained for input into modeling of the material response to repository placement. Conceptual designs which respond to these geotechnical considerations are discussed.

A viscoelastic wave propagation model for tungsten at near-melt conditions (3000K)

Analysis of dynamic response data for tungsten at 3000 K has confirmed the suitability of a linear viscoelastic constitutive relationship which can be used to model material response due to high-strain-rate loadings. Such uniaxial strain loadings are produced by planar impact energy deposition due to electrons or photons.

Stress Waves Generated by Heat Addition in an Elastic Solid

The problem of stress-wave generation in a linear thermoelastic solid by internal heat addition is investigated on the basis of a one-dimensional model of material response. A method of integration of the governing equations is given for the case of power deposition with arbitrary time and space variation. Closed-form results are presented for the half-space and the finite slab for power deposition which is a step function in time and exponential with distance from one surface, assuming negligible heat conduction. The influence of thermal diffusion on the stress field is estimated in terms of a dimensionless parameter representing the ratio of characteristic times of stress-wave propagation and thermal diffusion.