Plastic constitutive behavior of short-fiber/particle reinforced composites

A cylindrical cell model based on continuum theory for plastic constitutive behavior of short-fiber/particle reinforced composites is proposed. The composite is idealized as uniformly distributed periodic arrays of aligned cells, and each cell consists of a cylindrical inclusion surrounded by a plastically deforming matrix. In the analysis, the non-uniform deformation field of the cell is decomposed into the sum of the first order approximate field and the trial additional deformation field. The precise deformation field are determined based on the minimum strain energy principle. Systematic calculation results are presented for the influence of reinforcement volume fraction and shape on the overall mechanical behavior of the composites. The results are in good agreement with the existing finite element analyses and the experimental results. This paper attempts to stimulate the work to get the analytical constitutive relation of short-fiber/particle reinforced composites.

Nonlinear Constitutive Behavior Of Ferroelectric Materials

The ferroelectric specimen is considered as an aggregation of many randomly oriented domains. According to this mechanism, a multi-domain mechanical model is developed in this paper. Each domain is represented by one element. The applied stress and electric field are taken to be the stress and electric field in the formula of the driving force of domain switching for each element in the specimen. It means that the macroscopic switching criterion is used for calculating the volume fraction of domain switching for each element. By using the hardening relation between the driving force of domain switching and the volume fraction of domain switching calibrated, the volume fraction of domain switching for each element is calculated. Substituting the stress and electric field and the volume fraction of domain switching into the constitutive equation of ferroelectric material, one can easily get the strain and electric displacement for each element. The macroscopic behavior of the ferroelectric specimen is then directly calculated by volume averaging. Meanwhile, the nonlinear finite element analysis for the ferroelectric specimen is carried out. In the finite element simulation, the volume fraction of domain switching for each element is calculated by using the same method mentioned above. The interaction between different elements is taken into account in the finite element simulation and the local stress and electric field for each element is obtained. The macroscopic behavior of the specimen is then calculated by volume averaging. The computation results involve the electric butterfly shaped curves of axial strain versus the axial electric field and the hysteresis loops of electric displacement versus the electric field for ferroelectric specimens under the uniaxial coupled stress and electric field loading. The present theoretical prediction agrees reasonably with the experimental results.

Equivalent constitutive model-based design of wave-absorbing material system and controller

A design methodology for wave-absorbing active material system is reported. The design enforces equivalence between an assumed material model having wave-absorbing behavior and a set of target feedback controllers for an array of microelectro-mechanical transducers which are integral part of the active material system. The proposed methodology is applicable to problems involving the control of acoustic waves in passive-active material system with complex constitutive behavior at different length-scales. A stress relaxation type one-dimensional constitutive model involving viscous damping mechanism is considered, which shows asymmetric wave dispersion characteristics about the half-line. The acoustic power flow and asymptotic stability of such material system are studied. A single sensor non-collocated linear feedback control system in a one-dimensional finite waveguide, which is a representative volume element in an active material system, is considered. Equivalence between the exact dynamic equilibrium of these two systems is imposed. It results in the solution space of the design variables, namely the equivalent damping coefficient, the wavelength(s) to be controlled and the location of the sensor. The characteristics of the controller transfer functions and their pole-placement problem are studied. (c) 2005 Elsevier Ltd. All rights reserved.

Constitutive Response of Passivated Copper Films: Experiments and Analyses

The constitutive behavior of passivated copper films is studied. Stresses in copper films of thickness ranging from 1000 nm to 40 nm, passivated with silicon oxide on a quartz or silicon substrate, were measured using the curvature method. The thermal cycling spans a temperature range from - 196 to 600°C. It is seen that the strong relaxation at high temperatures normally found in unpassivated films is nonexistent for passivated films. The copper film did not show any rate-dependent effect over a range of heating/cooling rate from 5 to 25°C/min. Further analyses showed that significant strain hardening exists during the course of thermal loading. In particular, the measured stress- temperature response can only be fitted with a kinematic hardening model, if a simple constitutive law within the continuum plasticity framework is to be used. The analytic procedures for extracting the film properties are presented. Implications to stress modeling of copper interconnects in actual devices are discussed.

Energy Principle And Nonlinear Electric-Mechanical Behavior Of Ferroelectric Ceramics

Many experimental observations have shown that a single domain in a ferroelectric material switches by progressive movement of domain walls, driven by a combination of electric field and stress. The mechanism of the domain switch involves the following steps: initially, the domain has a uniform spontaneous polarization; new domains with the reverse polarization direction nucleate, mainly at the surface, and grow though the crystal thickness; the new domain expands sideways as a new domain continues to form; finally, the domain switch coalesces to complete the polarization reversal. According to this mechanism, the volume fraction of the domain switching is introduced in the constitutive law of the ferroelectric material and used to study the nonlinear constitutive behavior of a ferroelectric body in this paper. The principle of stationary total potential energy is put forward in which the basic unknown quantities are the displacement u(i), electric displacement D-i and volume fraction rho(I) of the domain switching for the variant I. The mechanical field equation and a new domain switching criterion are obtained from the principle of stationary total potential energy. The domain switching criterion proposed in this paper is an expansion and development of the energy criterion established by Hwang et al. [ 1]. Based on the domain switching criterion, a set of linear algebraic equations for determining the volume fraction rho(I) of domain switching is obtained, in which the coefficients of the linear algebraic equations only contain the unknown strain and electric fields. If the volume fraction rho(I) of domain switching for each domain is prescribed, the unknown displacement and electric potential can be obtained based on the conventional finite element procedure. It is assumed that a domain switches if the reduction in potential energy exceeds a critical energy barrier. According to the experimental results, the energy barrier will strengthen when the volume fraction of the domain switching increases. The external mechanical and electric loads are increased step by step. The volume fraction rho(I) of domain switching for each element obtained from the last loading step is used as input to the constitutive equations. Then the strain and electric fields are calculated based on the conventional finite element procedure. The finite element analysis is carried out on the specimens subjected to uniaxial coupling stress and electric field. Numerical results and available experimental data are compared and discussed. The present theoretic prediction agrees reasonably with the experimental results.

Multiscale constitutive modeling of polymer materials

Materials are inherently multi-scale in nature consisting of distinct characteristics at various length scales from atoms to bulk material. There are no widely accepted predictive multi-scale modeling techniques that span from atomic level to bulk relating the effects of the structure at the nanometer (10-9 meter) on macro-scale properties. Traditional engineering deals with treating matter as continuous with no internal structure. In contrast to engineers, physicists have dealt with matter in its discrete structure at small length scales to understand fundamental behavior of materials. Multiscale modeling is of great scientific and technical importance as it can aid in designing novel materials that will enable us to tailor properties specific to an application like multi-functional materials. Polymer nanocomposite materials have the potential to provide significant increases in mechanical properties relative to current polymers used for structural applications. The nanoscale reinforcements have the potential to increase the effective interface between the reinforcement and the matrix by orders of magnitude for a given reinforcement volume fraction as relative to traditional micro- or macro-scale reinforcements. To facilitate the development of polymer nanocomposite materials, constitutive relationships must be established that predict the bulk mechanical properties of the materials as a function of the molecular structure. A computational hierarchical multiscale modeling technique is developed to study the bulk-level constitutive behavior of polymeric materials as a function of its molecular chemistry. Various parameters and modeling techniques from computational chemistry to continuum mechanics are utilized for the current modeling method. The cause and effect relationship of the parameters are studied to establish an efficient modeling framework. The proposed methodology is applied to three different polymers and validated using experimental data available in literature.

Characterization of a strong, constitutive mung bean (Vigna radiata L.) promoter with a complex mode of regulation in planta

We report the cloning and characterization in tobacco and Arabidopsis of a Vigna radiata L. (mung bean) promoter that controls the expression of VR-ACS1, an auxin-inducible ACC synthase gene. The VR-ACS1 promoter exhibits a very unusual behavior when studied in plants different from its original host, mung bean. GUS and luciferase in situ assays of transgenic plants containing VR-ACS1 promoter fusions show strong constitutive reporter gene expression throughout tobacco and Arabidopsis development. In vitro quantitative analyses show that transgenic plants harboring VR-ACS1 promoter-reporter constructs have on average 4-6 fold higher protein and activity levels of both reporter genes than plants transformed with comparable CaMV 35S promoter fusions. Similar transcript levels are present in VR-ACS1 and CaMV 35S promoter lines, suggesting that the high levels of gene product observed for the VR-ACS1 promoter are the combined result of transcriptional and translational activation. All tested deletion constructs retaining the core promoter region can drive strong constitutive promoter activity in transgenic plants. This is in contrast to mung bean, where expression of the native VR-ACS1 gene is almost undetectable in plants grown under normal conditions, but is rapidly and highly induced by a variety of stimuli. The constitutive behavior of the VR-ACS1 promoter in heterologous hosts is surprising, suggesting that the control mechanisms active in mung bean are impaired in tobacco and Arabidopsis. The 'aberrant' behavior of the VR-ACS1 promoter is further emphasized by its failure to respond to auxin and cycloheximide in heterologous hosts. VR-ACS1 promoter regulatory mechanisms seem to be different from all previously characterized auxin-inducible promoters.

Entropic bounds for multi-scale and multi-physics coupling in earth sciences

The ability to understand and predict how thermal, hydrological,mechanical and chemical (THMC) processes interact is fundamental to many research initiatives and industrial applications. We present (1) a new Thermal– Hydrological–Mechanical–Chemical (THMC) coupling formulation, based on non-equilibrium thermodynamics; (2) show how THMC feedback is incorporated in the thermodynamic approach; (3) suggest a unifying thermodynamic framework for multi-scaling; and (4) formulate a new rationale for assessing upper and lower bounds of dissipation for THMC processes. The technique is based on deducing time and length scales suitable for separating processes using a macroscopic finite time thermodynamic approach. We show that if the time and length scales are suitably chosen, the calculation of entropic bounds can be used to describe three different types of material and process uncertainties: geometric uncertainties,stemming from the microstructure; process uncertainty, stemming from the correct derivation of the constitutive behavior; and uncertainties in time evolution, stemming from the path dependence of the time integration of the irreversible entropy production. Although the approach is specifically formulated here for THMC coupling we suggest that it has a much broader applicability. In a general sense it consists of finding the entropic bounds of the dissipation defined by the product of thermodynamic force times thermodynamic flux which in material sciences corresponds to generalized stress and generalized strain rates, respectively.

Effect of Zirconium on the Processing MAPS For Hot-Working of Alpha-Beta Brass

The effect of zirconium on the hot working characteristics of alpha and alpha-beta brass was studied in the temperature range of 500 to 850-degrees-C and the strain rate range of 0.001 to 100 s-1. On the basis of the flow stress data, processing maps showing the variation of the efficiency of power dissipation (given by [2m/(m+1)] where m is the strain rate sensitivity) with temperature and strain rate were obtained. The addition of zirconium to alpha brass decreased the maximum efficiency of power dissipation from 53 to 39%, increased the strain rate for dynamic recrystallization (DRX) from 0.001 to 0.1 s-1 and improved the hot workability. Alpha-beta brasses with and without zirconium exhibit a domain in the temperature range from 550 to 750-degrees-C and at strain rates lower than 1 s-1 with a maximum efficiency of power dissipation of nearly 50 % occurring in the temperature range of 700 to 750-degrees-C and a strain rate of 0.001 s-1. In the domain, the alpha phase undergoes DRX and controls the hot deformation of the alloy whereas the beta phase deforms superplastically. The addition of zirconium to alpha-beta brass has not affected the processing maps as it gets partitioned to the beta phase and does not alter the constitutive behavior of the alpha phase

Flow Instabilities and fracture in Ti-6Al-4V deformed in compression at 298 K to 673 K

Uniaxial compression tests were conducted on Ti-6Al-4V specimens in the strain-rate range df 0.001 to 1 s(-1) and temperature range of 298 to 673 K. The stress-strain curves exhibited a peak flow stress followed by flow softening. Up to 523 K, the specimens cracked catastrophically after the flow softening started. Adiabatic shear banding was observed in this regime. The fracture surface exhibited both mode I and II fracture features. The state of stress existing in a compression test specimen when bulging occurs is responsible for this fracture. The instabilities observed in the present tests are classified as ''geometric'' in nature and are state-of-stress dependant, unlike the ''intrinsic'' instabilities, which are dependant on the dynamic constitutive behavior of the material.

Sensing of delaminations in composite laminates using embedded magnetostrictive particle layers

This is an exploratory study to illustrate the feasibility of detecting delamination type of damage in polymeric laminates with one layer of magnetostrictive particles. One such beam encircled with excitation and sensing coils is used for this study. The change in stress gradient of the magnetostrictive layer in the vicinity of delamination shows up as a change in induced voltage in the sensing coil, and therefore provides a means to sense the presence of delamination. Recognizing the constitutive behavior of the Terfenol-D material is highly nonlinear, analytical expressions for the constitutive relations are developed by using curve fitting techniques to the experimental data. Analytical expressions that relate the applied excitation field with the stress and magnetic flux densities induced in the magnetostrictive layer are developed. Numerical methods are used to find the relative change in the induced voltage in the sensing coil due to the presence of delamination. A typical example of unidirectional laminate, with embedded delaminations, is used for the simulation purposes. This exploratory study illustrates that the open-circuit voltage induced in the sensing coil changes significantly (as large of 68 millivolts) with the occurrence of delamination. This feature can be exploited for device off-line inspection techniques and/or linking monitoring procedures for practical applications.

Energy principle of ferroelectric ceramics and single domain mechanical model

Many physical experiments have shown that the domain switching in a ferroelectric material is a complicated evolution process of the domain wall with the variation of stress and electric field. According to this mechanism, the volume fraction of the domain switching is introduced in the constitutive law of ferroelectric ceramic and used to study the nonlinear constitutive behavior of ferroelectric body in this paper. The principle of stationary total energy is put forward in which the basic unknown quantities are the displacement u (i) , electric displacement D (i) and volume fraction rho (I) of the domain switching for the variant I. Mechanical field equation and a new domain switching criterion are obtained from the principle of stationary total energy. The domain switching criterion proposed in this paper is an expansion and development of the energy criterion. On the basis of the domain switching criterion, a set of linear algebraic equations for the volume fraction rho (I) of domain switching is obtained, in which the coefficients of the linear algebraic equations only contain the unknown strain and electric fields. Then a single domain mechanical model is proposed in this paper. The poled ferroelectric specimen is considered as a transversely isotropic single domain. By using the partial experimental results, the hardening relation between the driving force of domain switching and the volume fraction of domain switching can be calibrated. Then the electromechanical response can be calculated on the basis of the calibrated hardening relation. The results involve the electric butterfly shaped curves of axial strain versus axial electric field, the hysteresis loops of electric displacement versus electric filed and the evolution process of the domain switching in the ferroelectric specimens under uniaxial coupled stress and electric field loading. The present theoretic prediction agrees reasonably with the experimental results given by Lynch.

Crack growth by grain boundary cavitation in the transient and extensive creep regimes

Crack growth due to cavity growth and coalescence along grain boundaries is analyzed under transient and extensive creep conditions in a compact tension specimen. Account is taken of the finite geometry changes accompanying crack tip blunting. The material is characterized as an elastic-power law creeping solid with an additional contribution to the creep rate arising from a given density of cavitating grain boundary facets. All voids are assumed present from the outset and distributed on a given density of cavitating grain boundary facets. The evolution of the stress fields with crack growth under three load histories is described in some detail for a relatively ductile material. The full-field plane strain finite element calculations show the competing effects of stress relaxation due to constrained creep, diffusion and crack tip blunting. and of stress increase due to the instantaneous elastic response to crack growth. At very high crack growth rates the Hui-Riedel fields dominate the crack tip region. However. the high growth rates are not sustained for any length of time in the compact tension geometry analyzed. The region of dominance of the Hui-Riedel field shrinks rapidly so that the near-tip fields are controlled by the HRR-type field shortly after the onset of crack growth. Crack growth rates under various conditions of loading and spanning the range of times from small scale creep to extensive creep are obtained. We show that there is a strong similarity between crack growth history and the behaviour of the C(t) and C(t) parameters. so that crack growth rates correlate rather well with C(t) and C(t). A relatively brittle material is also considered that has a very different near-tip stress field and crack growth history.

Nanoindentation of biological and biomimetic materials

Nanoindentation techniques have recently been adapted for the study of biological materials. This feature will consider the experimental adaptations required for such studies. Following a brief review of the structure and constitutive behavior of biological materials, we examine the experimental aspects in detail, including working with hydrated samples, time-dependent mechanical behavior and extremely compliant materials. The analysis of experimental data, consistent with the constitutive response of the material, will then be treated. Examples of nanoindentation data collected using commercially-available instruments are shown, including nanoindentation creep curves of biological materials and relaxation responses of biomimetic hydrogels. Finally, we conclude by examining the current state and future needs of the biological nanoindentation community. © 2011, Society for Experimental Mechanics.