scholarly journals Constructing material interfaces from data sets with volume-fraction information

2002 ◽  
Author(s):  
K.S. Bonnell ◽  
D.R. Schikore ◽  
K.I. Joy ◽  
M. Duchaineau ◽  
B. Hamann
Keyword(s):  
Volume Fraction ◽  
Data Sets ◽  
Material Interfaces

Influence of surface relaxations on X-ray intensities of microcrystals

1995 ◽  
Vol 210 (6) ◽  
Author(s):  
R. B. Neder
Keyword(s):  
Volume Fraction ◽  
Structure Refinement ◽  
Perfect Crystal ◽  
Data Sets ◽  
Near Surface ◽  
X Ray ◽  
Simulation Techniques ◽  
Small Crystals ◽  
Structure Simulation ◽  
Standard Structure

AbstractThe influence of surface relaxations on the intensity of microcrystals was investigated. Since the volume fraction of near surface atoms becomes appreciable for submicrometer crystals, it is important to estimate whether observed intensities of submicrometer crystals can be interpreted with standard structure refinement methods or whether surface relaxations produce a significant deviation from the intensities of the perfect crystal.Structure simulation techniques were applied in order to calculate the intensity of microcrystals of various sizes. Different models of surface relaxations were applied. Structure refinements on the data sets calculated for these models showed that submicrometer crystals down to 0.5 μm in diameter are not affected by surface relaxations. Smaller crystals below 0.1 μm in diameter are significantly affected by surface relaxations. Great care will have to be taken when refining observed intensities of these small crystals.

A Constitutive Model for Soft Mud Considering the Initial State of Effective Stress

2017 ◽  
Author(s):  
Chunyang Xu ◽  
Yongping Chen ◽  
Lili Yu
Keyword(s):  
Fractal Dimension ◽  
Constitutive Equation ◽  
Effective Stress ◽  
Volume Fraction ◽  
Soft Clay ◽  
Data Sets ◽  
Initial State ◽  
Floc Size ◽  
Sediment Volume ◽  
Self Similar

Consolidation is one of the most important processes that are needed to be accounted for in the model of cohesive sediment transport. Previous studies have shown that the consolidation paths for soil elements are not unique at low effective stress (here low effective stress means the effective stress is smaller than a threshold effective stress, which is short as TES and denoted as σb) In this study, a new theoretical constitutive equation for the effective stress of soft mud is derived to describe the non-unique consolidation paths at low effective stress. Firstly, based on the concept of fractal dimension, the mud flocs are treated as self-similar fractal entities and the relationship between mud floc size and sediment volume fraction is established. Due to the fact that the fractal dimension decreases as the floc size increases, the variation of fractal dimension is accounted for. Based on the self-similar model, the theoretical constitutive equation for the effective stress of soft mud is derived. The constitutive equation is validated using two data sets obtained from consolidation tests in a settling column for soft clay. At low effective stress, the model results curves follow the data trends and the non-uniqueness of consolidation paths are captured. The model results are also compared with existing numerical results and better agreement is presented especially when η is less than 0.5.

Evaluation of High Strain Rate Characteristics of Metallic Sandwich Specimens

2019 ◽  
Vol 141 (3) ◽  
Author(s):  
Danish Iqbal ◽  
Vikrant Tiwari
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Volume Fraction ◽  
Split Hopkinson Pressure Bar ◽  
Three Dimensional ◽  
Wave Theory ◽  
Hopkinson Pressure Bar ◽  
Material Interfaces ◽  
Element Analysis ◽  
Pressure Bar

An attempt is made to investigate the dynamic compressive response of multilayered specimens in bilayered and trilayered configurations, using a split Hopkinson pressure bar (SHPB) and finite element analysis. Two constituent metals comprising the multilayered configurations were Al 6063-T6 and IS 1570. Multiple stack sequences of trilayered and bilayered configurations were evaluated at three different sets of strain rates, namely, 500, 800, and 1000 s−1. The experiments revealed that even with the same constituent volume fraction, a change in the stacking sequence alters the overall dynamic constitutive response. This change becomes more evident, especially in the plastic zone. The finite element analysis was performed using abaqus/explicit. A three-dimensional (3D) model of the SHPB apparatus used in the experiments was generated and meshed using the hexahedral brick elements. Dissimilar material interfaces were assigned different dynamic coefficients of friction. The fundamental elastic one-dimensional (1D) wave theory was then utilized to evaluate the stress–strain response from the nodal strain histories of the bars. Predictions from the finite element simulations along with the experimental results are also presented in this study. For most cases, finite element predictions match well with the experiments.

scholarly journals ACCURACY OF ESTIMATES OF VOLUME FRACTION

2011 ◽  
Vol 19 (3) ◽  
pp. 199 ◽  
Author(s):  
Joanne Chia ◽  
Adrian Baddeley
Keyword(s):  
Volume Fraction ◽  
Bootstrap Method ◽  
Statistical Modelling ◽  
Alternative Methods ◽  
Data Sets ◽  
Type I ◽  
Large Sample ◽  
Point Counts ◽  
Statistical Assumptions ◽  
The Bootstrap Method

When estimating a volume fraction VV from point count fractions PP using Delesse's principle VV = PP, very little information on the accuracy of the estimator can be obtained from the basic theory of stereology. Existing methods for quantifying the variability of PP are mainly large-sample approximations such as Cochran's formula for the variance of a ratio. Cruz-Orive proposed an alternative method, but this requires statistical assumptions to be made on the point counts P, that do not hold in general. We introduce two alternative methods for quantifying the variability of PP, namely the bootstrap method and explicit statistical modelling of the bivariate distribution. The bootstrap method requires few statistical assumptions about the point counts but requires large sample size. The explicit statistical modelling method does make assumptions, but they can be checked directly from the data. To explore this approach, we propose a statistical model, the Type I Bivariate Binomial (BVB) distribution to model the pairs of count data (P, P). We show how to fit the BVB model to the data and how to assess the goodness-of-fit of this model. A formula for the variance of PP under the BVB model is also derived. The three approaches are compared in their application to nine example data sets taken from macroscopic sections of cerebral hemispheres of selected domesticated animals. The BVB model appears to be a good fit to these data sets. Implications for stereological estimation are discussed.

Mineral substitution: Separating the effects of fluids, minerals, and microstructure on P- and S-wave velocities

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. D197-D210 ◽  
Author(s):  
Nishank Saxena ◽  
Gary Mavko ◽  
Ronny Hofmann ◽  
Sean Dolan ◽  
L. Taras Bryndzia
Keyword(s):  
Volume Fraction ◽  
Data Sets ◽  
Effective Moduli ◽  
S Wave ◽  
Quadratic Formula ◽  
Wave Velocities ◽  
Linear Formula ◽  
A New Technique ◽  
Rock Microstructure ◽  
New Formula

We have developed a new technique of mineral substitution that accurately predicts the change in rock stiffness upon changes in the elastic properties of the rock mineral frame, assuming no changes in the microstructure or mineral volume fraction. The method is rigorous, the results are realizable, and the predictions are always within bounds. We have applied mineral substitution to separate the effects of composition (mineralogy and pore fill) on the rock stiffness from the effects of microstructure, i.e., porosity and pore shape. Application of mineral substitution on laboratory measured data sets of effective moduli (sandstones, limestones, and dolomites) revealed that if the original minerals making up the frame of sandstones (predominantly quartz) were replaced (or substituted) with calcite mineral properties, the newly predicted P- ([Formula: see text]) and S-wave velocity ([Formula: see text]) trends for the modified sandstones were very similar to the previously observed quadratic [Formula: see text]-[Formula: see text] empirical trends for limestones. Similarly, the [Formula: see text]-[Formula: see text] trends for modified limestones, with original minerals replaced by quartz mineral properties, were very similar to the observed linear [Formula: see text]-[Formula: see text] empirical trends for sandstones. The remaining minor differences between the modified and previously observed [Formula: see text]-[Formula: see text] trends might be attributed to the differences in rock microstructure. These findings are striking and suggest that [Formula: see text]-[Formula: see text] trends of natural rocks are dominated by mineralogy and the effects of microstructure are minor. We also found new [Formula: see text]-[Formula: see text] trends for rocks composed of various minerals, including zeolite, feldspar, pyrite, alpha-cristobalite, and halite.

scholarly journals An enhanced void-crack-based Rousselier damage model for ductile fracture with the XFEM

2018 ◽  
Vol 28 (6) ◽  
pp. 943-969 ◽  
Author(s):  
MIM Ahmad ◽  
JL Curiel-Sosa ◽  
S Arun ◽  
JA Rongong
Keyword(s):  
Ductile Fracture ◽  
Volume Fraction ◽  
Damage Model ◽  
Ductile Material ◽  
Integration Scheme ◽  
Extended Finite Element ◽  
Material Interfaces ◽  
Mapping Algorithm ◽  
Return Mapping ◽  
Return Mapping Algorithm

This work presents a modelling strategy for ductile fracture materials by implementing the Rousselier damage model with the extended finite element method (XFEM). The implicit integration scheme and consistent tangent modulus based on a radial return mapping algorithm for this constitutive model are developed by the user-defined material subroutine UMAT in ABAQUS/Standard. To enhance the modelling of the crack development in the materials, the XFEM is used that allows modelling of arbitrary discontinuities, where the mesh does not have to be aligned with the boundaries of material interfaces. This modelling strategy, so-called Rousselier-UMAT-XFEM (RuX) model, is proposed to connect both concepts, which gives an advantage in predicting the material behaviour of ductile material in terms of voids and crack relation. This is the first contribution where XFEM is used in ductile fracture analysis for micromechanical damage problems. The results indicate that the RuX model is a promising technique for predicting the void volume fraction damage and crack extension in ductile material, which shows a good agreement in terms of stress–strain and force–displacement relationships.

Chemical partitioning of elements in Ni-base MC-carbide reinforced eutetic superalloys

1983 ◽  
Vol 41 ◽  
pp. 250-251
Author(s):  
E. F. Koch ◽  
E. L. Hall ◽  
S. W. Yang
Keyword(s):  
Alloy Composition ◽  
Volume Fraction ◽  
Lattice Mismatch ◽  
Turbine Blades ◽  
Eutectic Alloys ◽  
Alloy Matrix ◽  
X Ray ◽  
Gas Turbine Blades ◽  
Analytical Electron ◽  
Analytical Electron Microscope

The plane-front solidified eutectic alloys consisting of aligned tantalum monocarbide fibers in a nickel alloy matrix are currently under consideration for future aircraft and gas turbine blades. The MC fibers provide exceptional strength at high temperatures. In these alloys, the Ni matrix is strengthened by the precipitation of the coherent γ' phase (ordered L12 structure, nominally Ni3Al). The mechanical strength of these materials can be sensitively affected by overall alloy composition, and these strength variations can be due to several factors, including changes in solid solution strength of the γ matrix, changes in they γ' size or morphology, changes in the γ-γ' lattice mismatch or interfacial energy, or changes in the MC morphology, volume fraction, thermal stability, and stoichiometry. In order to differentiate between these various mechanisms, it is necessary to determine the partitioning of elemental additions between the γ,γ', and MC phases. This paper describes the results of such a study using energy dispersive X-ray spectroscopy in the analytical electron microscope.

Morphology, Distribution and Identification of Micro-Constituents Along Grain Boundaries in Nickel-Base Alloys

1973 ◽  
Vol 31 ◽  
pp. 176-177
Author(s):  
D. E. Fornwalt ◽  
A. R. Geary ◽  
B. H. Kear
Keyword(s):  
Electron Microscope ◽  
Grain Boundaries ◽  
Volume Fraction ◽  
Rupture Life ◽  
Stress Rupture ◽  
High Volume ◽  
Precipitate Morphology ◽  
Stress Rupture Life ◽  
Nickel Base ◽  
Scanning Electron

A systematic study has been made of the effects of various heat treatments on the microstructures of several experimental high volume fraction γ’ precipitation hardened nickel-base alloys, after doping with ∼2 w/o Hf so as to improve the stress rupture life and ductility. The most significant microstructural chan§e brought about by prolonged aging at temperatures in the range 1600°-1900°F was the decoration of grain boundaries with precipitate particles.Precipitation along the grain boundaries was first detected by optical microscopy, but it was necessary to use the scanning electron microscope to reveal the details of the precipitate morphology. Figure 1(a) shows the grain boundary precipitates in relief, after partial dissolution of the surrounding γ + γ’ matrix.

Instrumentation For Quantitative Microscopy

1977 ◽  
Vol 35 ◽  
pp. 206-209
Author(s):  
B. Ralph ◽  
A.R. Jones
Keyword(s):  
Volume Fraction ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Automatic Data ◽  
Phase Volume Fraction ◽  
Statistical Confidence ◽  
Resultant Data ◽  
Automatic Data Collection ◽  
Third Dimension ◽  
Evolution Of Microstructure

In all fields of microscopy there is an increasing interest in the quantification of microstructure. This interest may stem from a desire to establish quality control parameters or may have a more fundamental requirement involving the derivation of parameters which partially or completely define the three dimensional nature of the microstructure. This latter categorey of study may arise from an interest in the evolution of microstructure or from a desire to generate detailed property/microstructure relationships. In the more fundamental studies some convolution of two-dimensional data into the third dimension (stereological analysis) will be necessary.In some cases the two-dimensional data may be acquired relatively easily without recourse to automatic data collection and further, it may prove possible to perform the data reduction and analysis relatively easily. In such cases the only recourse to machines may well be in establishing the statistical confidence of the resultant data. Such relatively straightforward studies tend to result from acquiring data on the whole assemblage of features making up the microstructure. In this field data mode, when parameters such as phase volume fraction, mean size etc. are sought, the main case for resorting to automation is in order to perform repetitive analyses since each analysis is relatively easily performed.

Formation of Persistent Slip Band in Fatigued Copper Single Crystals

1982 ◽  
Vol 40 ◽  
pp. 470-471
Author(s):  
N. Y. Jin
Keyword(s):  
Volume Fraction ◽  
Fatigue Cracks ◽  
Wall Structure ◽  
Matrix Structure ◽  
Dislocation Dipole ◽  
Slip Bands ◽  
Persistent Slip Bands ◽  
The Matrix ◽  
Hard Shell ◽  
Copper Single Crystals

Localised plastic deformation in Persistent Slip Bands(PSBs) is a characteristic feature of fatigue in many materials. The dislocation structure in the PSBs contains regularly spaced dislocation dipole walls occupying a volume fraction of around 10%. The remainder of the specimen, the inactive "matrix", contains dislocation veins at a volume fraction of 50% or more. Walls and veins are both separated by regions in which the dislocation density is lower by some orders of magnitude. Since the PSBs offer favorable sites for the initiation of fatigue cracks, the formation of the PSB wall structure is of great interest. Winter has proposed that PSBs form as the result of a transformation of the matrix structure to a regular wall structure, and that the instability occurs among the broad dipoles near the center of a vein rather than in the hard shell surounding the vein as argued by Kulmann-Wilsdorf.

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