A Yield Criterion of Porous Materials With Anisotropy Caused by Geometry or Distribution of Pores

1991 ◽  
Vol 113 (4) ◽  
pp. 425-429 ◽  
Author(s):  
T. Hisatsune ◽  
T. Tabata ◽  
S. Masaki
Keyword(s):  
Velocity Field ◽  
Porous Materials ◽  
Upper Bound ◽  
Volume Fraction ◽  
Yield Criterion ◽  
Longitudinal Direction ◽  
Axisymmetric Deformation ◽  
The Other ◽  
The Matrix ◽  
Spherical Cells

Axisymmetric deformation of anisotropic porous materials caused by geometry of pores or by distribution of pores is analyzed. Two models of the materials are proposed: one consists of spherical cells each of which has a concentric ellipsoidal pore; and the other consists of ellipsoidal cells each of which has a concentric spherical pore. The velocity field in the matrix is assumed and the upper bound approach is attempted. Yield criteria are expressed as ellipses on the σm σ3 plane which are longer in longitudinal direction with increasing anisotropy and smaller with increasing volume fraction of the pore. Furthermore, the axes rotate about the origin at an angle α from the σm-axis, while the axis for isotropic porous materials is on the σm-axis.

The effects of interfacial debonding on the elastoplastic response of unidirectional silicon carbide—titanium composites

2010 ◽  
Vol 224 (2) ◽  
pp. 259-269 ◽  
Author(s):  
M J Mahmoodi ◽  
M M Aghdam ◽  
M Shakeri
Keyword(s):  
Volume Fraction ◽  
Yield Criterion ◽  
Fibre Volume Fraction ◽  
Three Dimensional ◽  
Fibre Volume ◽  
Interfacial Debonding ◽  
Successive Approximation Method ◽  
Interface Damage ◽  
The Matrix ◽  
Von Mises

A three-dimensional micromechanics-based analytical model is presented to investigate the effects of initiation and propagation of interface damage on the elastoplastic behaviour of unidirectional SiC—Ti metal matrix composites (MMCs) subjected to off-axis loading. Temperature-dependent properties are considered for the matrix. Manufacturing process thermal residual stress (RS) is also included in the model. The selected representative volume element consists of r× c unit cells in which a quarter of the fibre is surrounded by matrix sub-cells. The constant compliance interface model is used to model interfacial debonding and the successive approximation method together with von Mises yield criterion is used to obtain elastoplastic behaviour. Dominance mode of damage including fibre fracture, interfacial debonding, and matrix yielding and ultimate tensile strength of the SiC—Ti MMC are predicted for various loading directions. The effects of thermal RS and fibre volume fraction on the stress—strain response of the SiC—Ti MMC are studied. Results revealed that for more realistic predictions, both interface damage and thermal RS effects should be considered in the analysis. The contribution of interfacial debonding and thermal RS in the overall behaviour of the material is also investigated. Comparison between results of the presented model shows very good agreement with the finite-element micromechanical analysis and experiment for various off-axis angles.

scholarly journals The Effects of Solutionizing and Aging temperature on the Microstructure of Allvac 718plus

2019 ◽  
Author(s):  
Geeta Kumari ◽  
Carl Boehlert ◽  
S. Sankaran ◽  
M. Sundararaman
Keyword(s):  
Grain Boundaries ◽  
Microstructural Evolution ◽  
Aging Temperature ◽  
Volume Fraction ◽  
Aging Treatment ◽  
High Volume ◽  
The Other ◽  
Gamma Prime ◽  
The Matrix ◽  
Δ Phase

Abstract A study on the microstructural evolution of a Ni-based superalloy, Allvac 718Plus, in the forged condition, was performed by varying the solutionizing temperature. Different solutionizing temperatures were chosen to obtain different fractions of the gamma prime (Ni3(Al,Ti,Nb), γ’) and delta (Ni3Nb, δ) phase precipitates. The solutionizing temperatures ranged between 945°C to 1100°C. After solutionizing, the samples were subjected to a standard two-step aging treatment (788°C for 8h followed by 704°C for 8h). The 954°C solutionizing treatment resulted in incomplete dissolution of the γ’ phase and a relatively high volume fraction of the δ phase, which formed preferentially at grain boundaries. The γ’ phase was completely dissolved during each of the other three solutionizing treatments (1000°C, 1050°C, and 1100°C), while the fraction of the δ phase decreased with increasing solutionizing temperature. The 1100°C solutionizing treatment led to significant growth of the matrix grains (Ni (FCC), γ).

scholarly journals An Upper Bound Solution for the Compression of an Orthotropic Cylinder

Materials ◽  
2021 ◽  
Vol 14 (18) ◽  
pp. 5253
Author(s):  
Lihui Lang ◽  
Sergei Alexandrov ◽  
Yun-Che Wang
Keyword(s):  
Velocity Field ◽  
Upper Bound ◽  
Yield Criterion ◽  
Limit Load ◽  
Compression Force ◽  
Orthotropic Cylinder ◽  
Upper Bound Theorem ◽  
Admissible Velocity ◽  
Bound Theorem ◽  
Quick Estimate

The upper bound theorem is used in conjunction with Hill’s quadratic yield criterion for determining the force required to upset a solid cylinder. The kinematically admissible velocity field accounts for the singular behavior of the real velocity field in the vicinity of the friction surface if the maximum friction law is adopted. The regime of sticking is also taken into consideration. The effect of this regime on the upper bound limit load is revealed. In particular, the kinematically admissible velocity field that includes the regime of sticking may result in a lower upper bound than that with no sticking. The boundary value problem is classified by a great number of geometric and material parameters. Therefore, a systematic parametric analysis of the effect of these parameters on the compression force is practically impossible. An advantage of the solution found is that it provides a quick estimate of this force for any given set of parameters.

A Theory of Plasticity for Porous Materials and Particle-Reinforced Composites

1992 ◽  
Vol 59 (2) ◽  
pp. 261-268 ◽  
Author(s):  
Y. P. Qiu ◽  
G. J. Weng
Keyword(s):  
Porous Materials ◽  
Upper Bound ◽  
Energy Criterion ◽  
Plastic State ◽  
Hydrostatic Tension ◽  
Stress Strain Relation ◽  
Hardening Modulus ◽  
The Matrix ◽  
Spherical Voids ◽  
Particle Reinforced Composite

An energy criterion is introduced to define the effective stress of the ductile matrix, and with which Tandon and Weng’s (1988) theory of particle-reinforced plasticity is capable of predicting the desired plastic volume expansion under a pure hydrostatic tension. This modification also makes the theory suitable for application to porous materials at high triaxiality. Despite its simplicity, it offers a reasonable range of accuracy in the fully plastic state and is also versatile enough to account for the influence of pore shape. The theory is especially accurate when the work-hardening modulus of the ductile matrix is high, consistent with the concept of a linear comparison material adopted. If the matrix is also elastically incompressible, the theory with spherical voids is found to coincide with Ponte Castaneda’s (1991) lower bound for the strain potential (or upper bound in the sense of flow stress) of the Hashin-Shtrikman (1963) type, and with any other randomly oriented spheroidal voids, it provides an overall stress-strain relation which lies below this upper-bound curve. This energy approach is finally generalized to a particle-reinforced composite where the inclusions can be elastically stiffer or softer than the matrix, and it is also demonstrated that the prediction by the new theory is always softer than Tandon and Weng’s original one.

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.

Preparation of Electron Transparent Metal-Matrix Composites

1968 ◽  
Vol 26 ◽  
pp. 334-335 ◽  
Author(s):  
M. R. Pinnel ◽  
A. Lawley
Keyword(s):  
Stainless Steel ◽  
Load Transfer ◽  
Volume Fraction ◽  
Steel Wire ◽  
Initial Step ◽  
Interfacial Region ◽  
Matrix Composites ◽  
Specific Test ◽  
The Matrix ◽  
The One

Numerous phenomenological descriptions of the mechanical behavior of composite materials have been developed. There is now an urgent need to study and interpret deformation behavior, load transfer, and strain distribution, in terms of micromechanisms at the atomic level. One approach is to characterize dislocation substructure resulting from specific test conditions by the various techniques of transmission electron microscopy. The present paper describes a technique for the preparation of electron transparent composites of aluminum-stainless steel, such that examination of the matrix-fiber (wire), or interfacial region is possible. Dislocation substructures are currently under examination following tensile, compressive, and creep loading. The technique complements and extends the one other study in this area by Hancock.The composite examined was hot-pressed (argon atmosphere) 99.99% aluminum reinforced with 15% volume fraction stainless steel wire (0.006″ dia.).Foils were prepared so that the stainless steel wires run longitudinally in the plane of the specimen i.e. the electron beam is perpendicular to the axes of the wires. The initial step involves cutting slices ∼0.040″ in thickness on a diamond slitting wheel.

Pembobotan Berdasarkan Tingkat Kesamaan Semantik pada Metode Fuzzy Semi-Supervised Co-Clustering untuk Pengelompokkan Dokumen Teks

2014 ◽  
Vol 6 (2) ◽  
pp. 46-51
Author(s):  
Galang Amanda Dwi P. ◽  
Gregorius Edwadr ◽  
Agus Zainal Arifin
Keyword(s):  
Supervised Learning ◽  
Semantic Similarity ◽  
The Other ◽  
Classification Result ◽  
Document Similarity ◽  
The Matrix ◽  
Index Terms ◽  
Membership Value ◽  
Degree Of Similarity

Nowadays, a large number of information can not be reached by the reader because of the misclassification of text-based documents. The misclassified data can also make the readers obtain the wrong information. The method which is proposed by this paper is aiming to classify the documents into the correct group.  Each document will have a membership value in several different classes. The method will be used to find the degree of similarity between the two documents is the semantic similarity. In fact, there is no document that doesn’t have a relationship with the other but their relationship might be close to 0. This method calculates the similarity between two documents by taking into account the level of similarity of words and their synonyms. After all inter-document similarity values obtained, a matrix will be created. The matrix is then used as a semi-supervised factor. The output of this method is the value of the membership of each document, which must be one of the greatest membership value for each document which indicates where the documents are grouped. Classification result computed by the method shows a good value which is 90 %. Index Terms - Fuzzy co-clustering, Heuristic, Semantica Similiarity, Semi-supervised learning.

scholarly journals Prediction of Effective Thermal Conductivities of Four-Directional Carbon/Carbon Composites by Unit Cells with Different Sizes

2021 ◽  
Vol 11 (3) ◽  
pp. 1171
Author(s):  
Chang Xu ◽  
Zhihong Sun ◽  
Guowei Shao
Keyword(s):  
Carbon Fiber ◽  
Longitudinal Direction ◽  
Unit Cell ◽  
Carbon Composites ◽  
Temperature Boundary ◽  
The Matrix ◽  
Unit Cells ◽  
Experimental Values ◽  
Different Diameters ◽  
Thermal Conductivities

Two-unit cells developed to predict the effective thermal conductivities of four-directional carbon/carbon composites with the finite element method are proposed in this paper. The smaller-size unit cell is formulated from the larger-size unit cell by two 180° rotational transformations. The temperature boundary conditions corresponding to the two-unit cells are derived, and the validity is verified by the temperature and heat flux distributions at specific positions of the larger-size unit cell and the smaller-size unit cell. The thermal conductivities of the carbon fiber bundles and carbon fiber rods are measured firstly. Then, combined with the properties of the matrix, the effective thermal conductivities of the four-directional carbon/carbon composites are numerically predicted. The results in transverse direction predicted by the larger-size unit cell and the smaller-size unit cell are both higher than experimental values, which are 5.8 to 6.2% and 7.3 to 8.2%, respectively. In longitudinal direction, the calculated thermal conductivities of the larger-size unit cell and the smaller-size unit cell are 6.8% and 6.2% higher than the experimental results, respectively. In addition, carbon fiber rods with different diameters are set to clarify the influence on the effective thermal conductivities of the four-directional carbon/carbon composites.

scholarly journals Effects of SiC Fibers and Laminated Structure on Mechanical Properties of Ti–Al Laminated Composites

Materials ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 1323
Author(s):  
Chenyang Hou ◽  
Shouyin Zhang ◽  
Zhijian Ma ◽  
Baiping Lu ◽  
Zhenjun Wang
Keyword(s):  
Volume Fraction ◽  
Raw Materials ◽  
Laminated Composites ◽  
Intermetallic Layer ◽  
Longitudinal Direction ◽  
Fracture Mechanisms ◽  
Compact Structure ◽  
Laminated Structure ◽  
Sic Fibers ◽  
Sic Fiber

Ti/Ti–Al and SiCf-reinforced Ti/Ti–Al laminated composites were fabricated through vacuum hot-pressure using pure Ti foils, pure Al foils and SiC fibers as raw materials. The effects of SiC fiber and a laminated structure on the properties of Ti–Al laminated composites were studied. A novel method of fiber weaving was implemented to arrange the SiC fibers, which can guarantee the equal spacing of the fibers without introducing other elements. Results showed that with a higher exerted pressure, a more compact structure with fewer Kirkendall holes can be obtained in SiCf-reinforced Ti/Ti–Al laminated composites. The tensile strength along the longitudinal direction of fibers was about 400 ± 10 MPa, which was 60% higher compared with the fabricated Ti/Ti–Al laminated composites with the same volume fraction (60%) of the Ti layer. An in situ tensile test was adopted to observe the deformation behavior and fracture mechanisms of the SiCf-reinforced Ti/Ti–Al laminated composites. Results showed that microcracks first occurred in the Ti–Al intermetallic layer.

scholarly journals Continuous Cooling Transformation Behaviour and Bainite Transformation Kinetics of 23CrNi3Mo Carburised Steel

Metals ◽  
2020 ◽  
Vol 11 (1) ◽  
pp. 48
Author(s):  
Wenjun Song ◽  
Min Lei ◽  
Mingpan Wan ◽  
Chaowen Huang
Keyword(s):  
Phase Transformation ◽  
Volume Fraction ◽  
Austenite Formation ◽  
Steel Matrix ◽  
Transformation Kinetics ◽  
Bainite Transformation ◽  
Continuous Cooling ◽  
The Matrix ◽  
Dimensional Growth ◽  
Kinetics Of

In this study, the phase transformation behaviour of the carburised layer and the matrix of 23CrNi3Mo steel was comparatively investigated by constructing continuous cooling transformation (CCT) diagram, determining the volume fraction of retained austenite (RA) and plotting dilatometric curves. The results indicated that Austenite formation start temperature (Ac1) and Austenite formation finish temperature (Ac3) of the carburised layer decreased compared to the matrix, and the critical cooling rate (0.05 °C/s) of martensite transformation is significantly lower than that (0.8 °C/s) of the matrix. The main products of phase transformation in both the carburised layer and the matrix were martensite and bainite microstructures. Moreover, an increase in carbon content resulted in the formation of lamellar martensite in the carburised layer, whereas the martensite in the matrix was still lath. Furthermore, the volume fraction of RA in the carburised layer was higher than that in the matrix. Moreover, the bainite transformation kinetics of the 23CrNi3Mo steel matrix during the continuous cooling process indicated that the mian mechanism of bainite transformation of the 23CrNi3Mo steel matrix is two-dimensional growth and one-dimensional growth.

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