Local fields in two-phase fibrous piezo-composites with 622 constituents

2016 ◽  
Vol 40 (9) ◽  
pp. 3221-3229 ◽  
Author(s):  
Ransés Alfonso-Rodríguez ◽  
Julián Bravo-Castillero ◽  
Leslie D. Pérez-Fernández
Keyword(s):  
Local Fields ◽  
Two Phase

On transformation strains and uniform fields in multiphase elastic media

1992 ◽  
Vol 437 (1900) ◽  
pp. 291-310 ◽  
Keyword(s):  
Concentration Factor ◽  
Elastic Stiffness ◽  
Local Fields ◽  
Influence Functions ◽  
Elastic Solids ◽  
Two Phase ◽  
General Properties ◽  
Multiphase Systems ◽  
Concentration Factors ◽  
Mechanical Influence

The effect of local eigenstrain and eigenstress fields, or transformation fields, on the local strains and stresses is explored in multiphase elastic solids of arbitrary geometry and material symmetry. The residual local fields caused by such transformation fields are sought in terms of certain transformation influence functions and transformation concentration factor tensors. General properties of these functions and concentration factors, and their relation to the analogous mechanical influence functions and concentration factors, are established, in part, with the help of uniform strain fields in multiphase media. Specific estimates of the transformation concentration factor tensors are evaluated by the self-consistent and Mori-Tanaka methods. It is found here that although the two methods use different constraint tensors in solutions of the respective dilute problems, their estimates of the mechanical, thermal, and transformation concentration factor tensors, and of the overall stiffness of multiphase media have a similar structure. Proofs that guarantee that these methods comply with the general properties of the transformation influence functions, and provide diagonally symmetric estimates of the overall elastic stiffness, are given for two-phase and multiphase systems consisting of, or reinforced by, inclusions of similar shape and alignment. One of the possible applications of the results, in analysis of overall instantaneous properties and local fields in inelastic composite materials, is described in the following paper.

scholarly journals Field statistics in nonlinear composites. I. Theory

2006 ◽  
Vol 463 (2077) ◽  
pp. 183-202 ◽  
Author(s):  
Martín I Idiart ◽  
Pedro Ponte Castañeda
Keyword(s):  
Effective Potential ◽  
Second Order ◽  
Local Fields ◽  
Two Phase ◽  
Effective Potentials ◽  
Second Moments ◽  
Local Potentials ◽  
Homogenization Methods ◽  
Derivatives Of ◽  
Nonlinear Composites

This work presents a means for extracting the statistics of the local fields in nonlinear composites from the effective potential of suitably perturbed composites. The idea is to introduce a parameter in the local potentials, generally a tensor, such that differentiation of the corresponding effective potential with respect to the parameter yields the volume average of the desired quantity. In particular, this provides a generalization to the nonlinear case of well-known formulas in the context of linear composites, which express phase averages and second moments of the local fields in terms of derivatives of the effective potential. Such expressions are useful since they allow the generation of estimates for the field statistics in nonlinear composites, directly from homogenization estimates for appropriately defined effective potentials. Here, use is made of these expressions in the context of the ‘variational’, ‘tangent second-order’ and ‘second-order’ homogenization methods, to obtain rigorous estimates for the first and second moments of the fields in nonlinear composites. While the variational estimates for these quantities are found to be identical to those proposed in previous works, the tangent second-order and second-order estimates are found be different. In particular, the new estimates for the first moments given in this work are found to be entirely consistent with the corresponding estimates for the macroscopic behaviour. Sample results for two-phase, power-law composites are provided in part II of this work.

scholarly journals Field statistics in nonlinear composites. II. Applications

2006 ◽  
Vol 463 (2077) ◽  
pp. 203-222 ◽  
Author(s):  
Martín I Idiart ◽  
Pedro Ponte Castañeda
Keyword(s):  
Transversely Isotropic ◽  
Second Order ◽  
Local Fields ◽  
Two Phase ◽  
Second Moments ◽  
Constituent Phase ◽  
Homogenization Methods ◽  
Exact Relations ◽  
Nonlinear Homogenization ◽  
Nonlinear Composites

Part I of this work provided a methodology for extracting the statistics of the local fields in nonlinear composites, from the effective potential of suitably perturbed composites. In particular, exact relations were given for the first and even moments of the fields in each constituent phase. In this part, use is made of these exact relations in the context of the ‘variational’, ‘tangent second-order’ and ‘second-order’ nonlinear homogenization methods to generate estimates for the phase averages and second moments of the fields for two-phase, power-law composites with isotropic and transversely isotropic microstructures. The accuracy of these estimates is assessed by confronting them against corresponding exact results for sequentially laminated composites. Among the nonlinear homogenization estimates considered in this work, the second-order estimates are found to be, in general, the most accurate, especially for large heterogeneity contrast and nonlinearity. Thus, these estimates are able to capture, for example, the strong anisotropy in the strain fluctuations that can develop inside nonlinear porous and rigidly reinforced composites.

Anisotropic Transport in Microcrystalline P-I-N Devices

1999 ◽  
Vol 557 ◽  
Author(s):  
M. Vieira ◽  
A. Fantoni ◽  
M. Fernandes ◽  
A. Maçarico ◽  
I. Martins ◽  
...  
Keyword(s):  
Near Infrared ◽  
Open Circuit Voltage ◽  
Spectral Response ◽  
Forward Bias ◽  
Infrared Region ◽  
Open Circuit ◽  
Local Fields ◽  
Two Phase ◽  
Enhanced Sensitivity ◽  
Percolation Path

AbstractEntirely μc-Si:H p-i-n structures presenting an enhanced sensitivity to the near infrared region and a positive spectral response under forward bias higher than the open circuit voltage are analysed under different external voltage bias and illumination conditions.A two phase model to explain the transport properties is proposed using as input parameters the measured experimental data. The results suggest that the transport is preferentially concentrated inside the crystalline grains. The conduction within the amorphous regions is poor. The percolation path is different for electrons and holes and is determined by the local fields at the boundaries. These local fields are independent of the externally applied condition, and they can be related to the persistence of the small photocurrent observed when a bias voltage higher than the open circuit voltage is applied.

Effect of Shock Loading on the Microstructure of Uniloy 326

1974 ◽  
Vol 32 ◽  
pp. 504-505
Author(s):  
K. P. Staudhammer ◽  
L. E. Murr
Keyword(s):  
Grain Size ◽  
Shock Loading ◽  
Current Investigation ◽  
Two Phase ◽  
05 C ◽  
Shock Deformation ◽  
Heat Treated

The effect of shock loading on a variety of steels has been reviewed recently by Leslie. It is generally observed that significant changes in microstructure and microhardness are produced by explosive shock deformation. While the effect of shock loading on austenitic, ferritic, martensitic, and pearlitic structures has been investigated, there have been no systematic studies of the shock-loading of microduplex structures.In the current investigation, the shock-loading response of millrolled and heat-treated Uniloy 326 (thickness 60 mil) having a residual grain size of 1 to 2μ before shock loading was studied. Uniloy 326 is a two phase (microduplex) alloy consisting of 30% austenite (γ) in a ferrite (α) matrix; with the composition.3% Ti, 1% Mn, .6% Si,.05% C, 6% Ni, 26% Cr, balance Fe.

Exsolution and inversion in pigeonite from the Whin Sill, Northern England

1978 ◽  
Vol 36 (1) ◽  
pp. 474-475
Author(s):  
P.P.K. Smith
Keyword(s):  
High Temperature ◽  
Low Temperature ◽  
Homogeneous Nucleation ◽  
Silicate Mineral ◽  
Antiphase Boundaries ◽  
Two Phase ◽  
Primitive Form ◽  
The Core ◽  
Nucleation Mechanisms ◽  
And Inversion

Grains of pigeonite, a calcium-poor silicate mineral of the pyroxene group, from the Whin Sill dolerite have been ion-thinned and examined by TEM. The pigeonite is strongly zoned chemically from the composition Wo8En64FS28 in the core to Wo13En34FS53 at the rim. Two phase transformations have occurred during the cooling of this pigeonite:- exsolution of augite, a more calcic pyroxene, and inversion of the pigeonite from the high- temperature C face-centred form to the low-temperature primitive form, with the formation of antiphase boundaries (APB's). Different sequences of these exsolution and inversion reactions, together with different nucleation mechanisms of the augite, have created three distinct microstructures depending on the position in the grain.In the core of the grains small platelets of augite about 0.02μm thick have farmed parallel to the (001) plane (Fig. 1). These are thought to have exsolved by homogeneous nucleation. Subsequently the inversion of the pigeonite has led to the creation of APB's.

Shock consolidation of Ni-Ti alloy powder

1986 ◽  
Vol 44 ◽  
pp. 430-431
Author(s):  
Naresh N. Thadhani ◽  
Thad Vreeland ◽  
Thomas J. Ahrens
Keyword(s):  
Alloy Powder ◽  
Amorphous Material ◽  
Ti Alloy ◽  
Two Phase ◽  
Near Surface ◽  
Optical Micrograph ◽  
Shock Compaction ◽  
Powder Particles ◽  
Ti Powder ◽  
Rapidly Solidified

A spherically-shaped, microcrystalline Ni-Ti alloy powder having fairly nonhomogeneous particle size distribution and chemical composition was consolidated with shock input energy of 316 kJ/kg. In the process of consolidation, shock energy is preferentially input at particle surfaces, resulting in melting of near-surface material and interparticle welding. The Ni-Ti powder particles were 2-60 μm in diameter (Fig. 1). About 30-40% of the powder particles were Ni-65wt% and balance were Ni-45wt%Ti (estimated by EMPA).Upon shock compaction, the two phase Ni-Ti powder particles were bonded together by the interparticle melt which rapidly solidified, usually to amorphous material. Fig. 2 is an optical micrograph (in plane of shock) of the consolidated Ni-Ti alloy powder, showing the particles with different etching contrast.

A Comparison of Tem and Apfim to the Interpretation of Modulated Microstructures

1985 ◽  
Vol 43 ◽  
pp. 70-71
Author(s):  
M.G. Burke ◽  
M.K. Miller
Keyword(s):  
Low Temperature ◽  
Microstructural Characterization ◽  
Superlattice Reflection ◽  
High Volume ◽  
Atom Probe ◽  
Dark Field ◽  
Miscibility Gap ◽  
Second Phase ◽  
Two Phase ◽  
Probe Field

Interpretation of fine-scale microstructures containing high volume fractions of second phase is complex. In particular, microstructures developed through decomposition within low temperature miscibility gaps may be extremely fine. This paper compares the morphological interpretations of such complex microstructures by the high-resolution techniques of TEM and atom probe field-ion microscopy (APFIM).The Fe-25 at% Be alloy selected for this study was aged within the low temperature miscibility gap to form a <100> aligned two-phase microstructure. This triaxially modulated microstructure is composed of an Fe-rich ferrite phase and a B2-ordered Be-enriched phase. The microstructural characterization through conventional bright-field TEM is inadequate because of the many contributions to image contrast. The ordering reaction which accompanies spinodal decomposition in this alloy permits simplification of the image by the use of the centered dark field technique to image just one phase. A CDF image formed with a B2 superlattice reflection is shown in fig. 1. In this CDF micrograph, the the B2-ordered Be-enriched phase appears as bright regions in the darkly-imaging ferrite. By examining the specimen in a [001] orientation, the <100> nature of the modulations is evident.

A TEM study of the influence of microstructure on the superplastic behavior of a U-5.8 wt.% Nb alloy

1986 ◽  
Vol 44 ◽  
pp. 568-569
Author(s):  
G. Mackiewicz Ludtka
Keyword(s):  
Grain Size ◽  
Heating Rate ◽  
Phase Field ◽  
Single Phase ◽  
Superplastic Behavior ◽  
Two Phase ◽  
Single Phase Field

Historically, metals exhibit superplasticity only while forming in a two-phase field because a two-phase microstructure helps ensure a fine, stable grain size. In the U-5.8 Nb alloy, superplastici ty exists for up to 2 h in the single phase field (γ1) at 670°C. This is above the equilibrium monotectoid temperature of 647°C. Utilizing dilatometry, the superplastic (SP) U-5.8 Nb alloy requires superheating to 658°C to initiate the α+γ2 → γ1 transformation at a heating rate of 1.5°C/s. Hence, the U-5.8 Nb alloy exhibits an anomolous superplastic behavior.

Transition alpha structure in beta-isomorphous Nb-Hf alloys

1987 ◽  
Vol 45 ◽  
pp. 232-233
Author(s):  
R.W. Carpenter ◽  
Changhai Li ◽  
David J. Smith
Keyword(s):  
Solid Solution ◽  
Solution Phase ◽  
Miscibility Gap ◽  
Large Strains ◽  
Solid Solution Phase ◽  
Two Phase ◽  
Diffuse Intensity ◽  
Metastable Form ◽  
The Matrix ◽  
Equilibrium Morphology

Binary Nb-Hf alloys exhibit a wide bcc solid solution phase field at temperatures above the Hfα→ß transition (2023K) and a two phase bcc+hcp field at lower temperatures. The β solvus exhibits a small slope above about 1500K, suggesting the possible existence of a miscibility gap. An earlier investigation showed that two morphological forms of precipitate occur during the bcc→hcp transformation. The equilibrium morphology is rod-type with axes along <113> bcc. The crystallographic habit of the rod precipitate follows the Burgers relations: {110}||{0001}, <112> || <1010>. The earlier metastable form, transition α, occurs as thin discs with {100} habit. The {100} discs induce large strains in the matrix. Selected area diffraction examination of regions ∼2 microns in diameter containing many disc precipitates showed that, a diffuse intensity distribution whose symmetry resembled the distribution of equilibrium α Bragg spots was associated with the disc precipitate.

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