scholarly journals Effects of Plastic Anisotropy and Void Shape on Full Three-Dimensional Void Growth

2018 ◽  
Vol 85 (5) ◽  
Author(s):  
Brian Nyvang Legarth ◽  
Viggo Tvergaard
Keyword(s):  
Void Growth ◽  
Volume Fraction ◽  
Plastic Anisotropy ◽  
Three Dimensional ◽  
Stress Triaxiality ◽  
Principal Stresses ◽  
Unit Cells ◽  
3D Effects ◽  
Void Shape ◽  
Transverse Stresses

Void growth in an anisotropic ductile solid is studied by numerical analyses for three-dimensional (3D) unit cells initially containing a void. The effect of plastic anisotropy on void growth is the main focus, but the studies include the effects of different void shapes, including oblate, prolate, or general ellipsoidal voids. Also, other 3D effects such as those of different spacings of voids in different material directions and the effects of different macroscopic principal stresses in three directions are accounted for. It is found that the presence of plastic anisotropy amplifies the differences between predictions obtained for different initial void shapes. Also, differences between principal transverse stresses show a strong interaction with the plastic anisotropy, such that the response is very different for different anisotropies. The studies are carried out for one particular choice of void volume fraction and stress triaxiality.

Prediction of internal geometry and tensile behavior of 3D woven solid structures by mathematical coding

2021 ◽  
pp. 152808372110013
Author(s):  
Vivek R Jayan ◽  
Lekhani Tripathi ◽  
Promoda Kumar Behera ◽  
Michal Petru ◽  
BK Behera
Keyword(s):  
Volume Fraction ◽  
Three Dimensional ◽  
Areal Density ◽  
Woven Fabrics ◽  
Tensile Behavior ◽  
Geometrical Parameters ◽  
Fiber Volume ◽  
Acceptable Error ◽  
Internal Geometry ◽  
Unit Cells

The internal geometry of composite material is one of the most important factors that influence its performance and service life. A new approach is proposed for the prediction of internal geometry and tensile behavior of the 3 D (three dimensional) woven fabrics by creating the unit cell using mathematical coding. In many technical applications, textile materials are subjected to rates of loading or straining that may be much greater in magnitude than the regular household applications of these materials. The main aim of this study is to provide a generalized method for all the structures. By mathematical coding, unit cells of 3 D woven orthogonal, warp interlock and angle interlock structures have been created. The study then focuses on developing code to analyze the geometrical parameters of the fabric like fabric thickness, areal density, and fiber volume fraction. Then, the tensile behavior of the coded 3 D structures is studied in Ansys platform and the results are compared with experimental values for authentication of geometrical parameters as well as for tensile behavior. The results show that the mathematical coding approach is a more efficient modeling technique with an acceptable error percentage.

Three-dimensional braided composites with zero, negative and isotropic thermal expansion behavior

2020 ◽  
Vol 54 (13) ◽  
pp. 1761-1781
Author(s):  
SA Pottigar ◽  
B Santhosh ◽  
RG Nair ◽  
P Punith ◽  
PJ Guruprasad ◽  
...  
Keyword(s):  
Thermal Expansion ◽  
Volume Fraction ◽  
Coefficient Of Thermal Expansion ◽  
Three Dimensional ◽  
Braided Composites ◽  
Fiber Volume ◽  
Braided Composite ◽  
Expansion Behavior ◽  
Unit Cells ◽  
Composite Configuration

Three-dimensional braided composites with zero, negative and isotropic coefficient of thermal expansion are presented based on an analytical homogenization technique. The configuration of the braided composites is worked out considering the exact jamming condition leading to higher fiber volume fraction. A total of four configurations of three-dimensional-braided composite representative unit cells were analyzed. Among these, two arrangements are 4-axes and the other two are 5-axes. Special emphasis is given on the detailed description of the representative unit cells. Analysis reveals that a three-dimensional-braided composite configuration with thermoelastic isotropic properties having same coefficient of thermal expansion along x-, y-, and z-axes is achievable. As a special case, the homogenization model is used to predict, for the first time, a configuration of braided architecture and material leading to zero coefficient of thermal expansion along x-, y- and z-directions.

A New Perspective on the Mathematical Modeling of Highly Nonlinear Anisotropic Plastic Flows in a Heterogeneous Solid

2005 ◽  
Vol 105 ◽  
pp. 271-276 ◽  
Author(s):  
Wei Tong
Keyword(s):  
Biaxial Tension ◽  
Flow Behavior ◽  
Plastic Anisotropy ◽  
Mathematical Formulation ◽  
Three Dimensional ◽  
Mathematical Representation ◽  
Principal Stresses ◽  
Anisotropic Plasticity ◽  
Highly Nonlinear ◽  
Anisotropic Plastic

A new mathematical formulation is presented for describing the three-dimensional anisotropic plastic flow behavior of a heterogeneous polycrystalline solid. By using three principal stresses, three loading orientation angles, and a generally non-quadratic, real-valued stress exponent, a mathematical theory of anisotropic plasticity is formulated as two coupled orthogonal series expansions in both the 3D principal stress space (the p–plane) and the 3D loading orientation space. A geometrical interpretation of the new mathematical representation of anisotropic plasticity is offered. Specific examples are given to illustrate the application of the proposed theory for modeling the plastic anisotropy of orthotropic polycrystalline sheets under uniaxial and biaxial tension.

Unsteady Numerical and Experimental Study of Cavitation in Axial Pump

2014 ◽  
Vol 4 (1) ◽  
pp. 55-68
Author(s):  
Mohamed Adel ◽  
Nabil H. Mostafa
Keyword(s):  
Numerical Simulation ◽  
Void Growth ◽  
High Speed ◽  
Volume Fraction ◽  
Numerical Study ◽  
Three Dimensional ◽  
Axial Flow ◽  
Two Phase ◽  
Impeller Blade ◽  
Axial Pump

This paper presents an experimental and three-dimensional numerical study of unsteady, turbulent, void growth and cavitation simulation inside the passage of the axial flow pump. In this study a 3D Navier-Stokes code was used (CFDRC, 2008) to model the two-phase flow field around a four blades axial pump. The governing equations are discretized on a structured grid using an upwind difference scheme. The numerical simulation used the standard K-e turbulence model to account for the turbulence effect. The numerical simulation of void growth and cavitation in an axial pump was studied under unsteady calculating. Pressure distribution and vapor volume fraction were completed versus time at different condition. The computational code has been validated by comparing the predicated numerical results with the experiment. The predicted of cavitation growth and distribution on the impeller blade also agreed with that visualized of high speed camera.

Measurement of Three Dimensional Geometry of Creep Void and Grain Boundary With Combining 3D-EBSD Method and SEM Images

2011 ◽  
Author(s):  
Kenta Yamagiwa ◽  
Satoshi Kataoka ◽  
Satoshi Izumi ◽  
Shinsuke Sakai
Keyword(s):  
Grain Boundary ◽  
Void Growth ◽  
Volume Fraction ◽  
Void Nucleation ◽  
Three Dimensional ◽  
Creep Damage ◽  
Oblate Spheroid ◽  
Rotor Steel ◽  
Sem Images ◽  
Ebsd Method

A-parameter, void area ratio and other methods about creep void are used to estimate creep damage resulting from creep voids. However, these methods are based on not three-dimensional but two-dimensional geometry, though creep voids are three-dimensional cavities. By combining the 3D-EBSD method with SEM images, we have observed the three-dimensional shape of creep voids and their geometrical relationship with grain boundaries at first. The method is applied to 1Cr-1Mo-0.25V turbine rotor steel subjected to a creep rupture test (580°C, 180MPa). Also, interrupted creep specimens are prepared to observe the progress of void growth. Forty sections with 0.5 μm interval and 100μm × 100μm area are measured by mechanical polishing in order to reconstruct the three-dimensional shapes. In the results, four types of creep void are observed. One is sphere type whose radius is approximately 1μm. It is observed in the specimen whose creep life fraction is 25%. In the specimens with 50% and 75% creep damage, prolate and oblate spheroid whose radius is approximately 2.5μm are observed. Finally, connected voids are located within ruptured specimen. As the creep damage is progressed, not only void growth but also void nucleation is observed. Especially, on prior austenite grain boundary which is three-dimensionally perpendicular to the stress direction, creep voids are nucleated and grow in a concentrated manner. However, such nucleated small voids do not affect the void volume fraction.

Topological Design of Three-Dimensional Microstructure Based on Homogenization Effective Method

2006 ◽  
Vol 532-533 ◽  
pp. 705-708
Author(s):  
Ke Peng Qiu ◽  
Wei Hong Zhang ◽  
Shi Ping Sun ◽  
Ji Hong Zhu
Keyword(s):  
Volume Fraction ◽  
Three Dimensional ◽  
Optimization Method ◽  
Homogenization Method ◽  
The Finite Element Method ◽  
Topological Design ◽  
Unit Cells ◽  
Material Volume ◽  
Specific Material ◽  
Optimal Material

Nowadays, the topology optimization method is extensively adopted for the design of material microstructures to achieve desired behaviors. The present work is concerned with the optimal design of the stiffness and thermal conductivity of 3D microstructure unit cells with the specific material volume fraction in conjunction with the homogenization method and the finite element method. Numerical examples are given to demonstrate that optimal material layouts are successfully achieved and the initial layout has a great effect on the optimal microstructure.

Modelling of Ductile Fracture in the Presence of Two Populations of Voids - Applications to Aluminium Alloys

2006 ◽  
Vol 519-521 ◽  
pp. 829-834 ◽  
Author(s):  
Damien Fabrègue ◽  
D. Lassance ◽  
Thomas Pardoen
Keyword(s):  
Aluminium Alloys ◽  
Volume Fraction ◽  
Micromechanical Model ◽  
Stress Triaxiality ◽  
Type Model ◽  
Void Coalescence ◽  
Element Mesh ◽  
Gurson Model ◽  
Surrounding Matrix ◽  
Void Shape

A micromechanical model has been developed in order to capture the influence of a second population of voids on the coalescence of large primary voids. FE unit cell simulations have been performed by introducing the primary voids explicitly in a finite element mesh and by using a Gurson type model for the surrounding matrix in order to reproduce the influence of the second population. These simulations have guided the development of a closed-form void coalescence model. The new coalescence condition accounts for the softening introduced by the second population by integrating the Gurson model based on an approximate solution for the stress and strain field near the surface of the primary voids. The evolution of the primary voids is modelled using an advanced Gurson model involving an evolution law for the void shape. The model is applied to the prediction of the fracture strain of 6xxx aluminium alloys measured on smooth and notched round bars. The model successfully captures, without any parameter adjustment, the variation of the ductility as a function of the stress triaxiality for various shapes of the primary particles and various volume fraction of second population.

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.

Crystal Structure Analysis of Cu-Zr Alloys by Convergent Beam Diffraction

1981 ◽  
Vol 39 ◽  
pp. 354-355
Author(s):  
A. F. Marshall ◽  
J. W. Steeds ◽  
D. Bouchet ◽  
S. L. Shinde ◽  
R. G. Walmsley
Keyword(s):  
Crystal Structure ◽  
Point Group ◽  
Intermetallic Phase ◽  
Three Dimensional ◽  
Crystal Structure Analysis ◽  
Ion Milling ◽  
Composition And Structure ◽  
Unit Cells ◽  
Sputter Deposited ◽  
Convergent Beam

Convergent beam electron diffraction is a powerful technique for determining the crystal structure of a material in TEM. In this paper we have applied it to the study of the intermetallic phases in the Cu-rich end of the Cu-Zr system. These phases are highly ordered. Their composition and structure has been previously studied by microprobe and x-ray diffraction with sometimes conflicting results.The crystalline phases were obtained by annealing amorphous sputter-deposited Cu-Zr. Specimens were thinned for TEM by ion milling and observed in a Philips EM 400. Due to the large unit cells involved, a small convergence angle of diffraction was used; however, the three-dimensional lattice and symmetry information of convergent beam microdiffraction patterns is still present. The results are as follows:1) 21 at% Zr in Cu: annealed at 500°C for 5 hours. An intermetallic phase, Cu3.6Zr (21.7% Zr), space group P6/m has been proposed near this composition (2). The major phase of our annealed material was hexagonal with a point group determined as 6/m.

Comparison of Conventional and Pontic Fixed Partial Dentures Over Implants Using the Finite Element Method: Three-Dimensional Analysis of Cortical and Medullary Bone Stress

2020 ◽  
Vol 46 (3) ◽  
pp. 175-181
Author(s):  
Marcelo Bighetti Toniollo ◽  
Mikaelly dos Santos Sá ◽  
Fernanda Pereira Silva ◽  
Giselle Rodrigues Reis ◽  
Ana Paula Macedo ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Three Dimensional ◽  
The Finite Element Method ◽  
Medullary Bone ◽  
Principal Stresses ◽  
Bone Stress ◽  
Bone Damage ◽  
Rehabilitation System ◽  
Minimum Requirements

Rehabilitation with implant prostheses in posterior areas requires the maximum number of possible implants due to the greater masticatory load of the region. However, the necessary minimum requirements are not always present in full. This project analyzed the minimum principal stresses (TMiP, representative of the compressive stress) to the friable structures, specifically the vestibular face of the cortical bone and the vestibular and internal/lingual face of the medullary bone. The experimental groups were as follows: the regular splinted group (GR), with a conventional infrastructure on 3 regular-length Morse taper implants (4 × 11 mm); and the regular pontic group (GP), with a pontic infrastructure on 2 regular-length Morse taper implants (4 × 11 mm). The results showed that the TMiP of the cortical and medullary bones were greater for the GP in regions surrounding the implants (especially in the cervical and apical areas of the same region) but they did not reach bone damage levels, at least under the loads applied in this study. It was concluded that greater stress observed in the GP demonstrates greater fragility with this modality of rehabilitation; this should draw the professional's attention to possible biomechanical implications. Whenever possible, professionals should give preference to use of a greater number of implants in the rehabilitation system, with a focus on preserving the supporting tissue with the generation of less intense stresses.

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