Volume Fractions Of Constituents Research Articles

Methodological features of microstructural heterogeneity estimation by the thickness of steel plates

The relationship of anisotropy coefficients estimated both by textural analysis and direct measurements has been studied using the example of low carbon low-alloy plate steel for Arctic application. The parallel between the anisotropy coefficients values and visual assessment of the structural inhomogeneity has been established, and also use cases of anisotropy coefficients to search for the “structure-property” relationships have been discussed. All the investigated coefficients with different accuracy describe the basic trends of heterogeneity changes by the thickness of the plate, but only the coefficient found by textural analysis makes it possible to evaluate the heterogeneity at any thickness point of the plate adequately, and this is always uniquely coincided with the visual assessment. The volume fraction of the coarse structural constituents with the highest anisotropy of ferritic-bainitic steel, estimated by direct measurements, can also be useful when searching for the “structure-properties” relationships.

Effect of coiling temperature on impact toughness of hot rolled ultra-high-strength multiphase steel strips

The tensile and Charpy impact properties of four strip samples from two different B-added low-C ultra-high-strength steel strips (Al-treated and Ti-treated), coiled at two different temperature ranges (360–380 °C and 450–460 °C), have been evaluated and correlated to the microstructural parameters, dislocation density, and the intensity of high-angle boundaries. The effects of coiling temperatures on the microstructural evolution and mechanical properties have been discussed. The volume fraction of the individual phase constituents (namely, granular bainite, upper bainite, lower bainite and tempered martensite) and their hardness, local deformation response and the strain-hardening ability, as determined from nanoindentation testing, influenced the bulk properties such as hardness, tensile properties (strength and ductility), Charpy impact properties (upper shelf energy, USE, and ductile-to-brittle transition temperature, DBTT) and strain-hardening abilities under both quasi-static and dynamic loading conditions. The dominance of granular bainite and upper bainite (75–90 %) reduced the strength (670–722 MPa yield strength), improved ductility (16.7–19.5 % elongation to failure) and USE (35–42 J) in the samples coiled at the higher temperatures. In contrast, a higher fraction of tempered martensite and lower bainite (78–82 %) significantly increased the strength (808–814 MPa), reduced ductility (13.0–14.5 %) and USE (19–29 J) in the lower temperature coiled samples. The DBTT showed a complex trend with the microstructural parameters. It depended on the USE level, as well as on the ‘effective grain size’ of the matrix.

An improved Artificial Neural Network using Arithmetic Optimization Algorithm for damage assessment in FGM composite plates

In this paper, two-stage approaches are proposed to study damage detection, localization and quantification in Functionally Graded Material (FGM) plate structures. Metal and Ceramic FGM plates are considered using three different composite materials: Al/Al2O3, Al/ZrO2-1, and Al/ZrO2-2. The FGM plates are modelled using IsoGeometric Analysis (IGA), which is more efficient than the classical Finite Element Method (FEM). Using a power-law distribution of the volume fractions of the plate constituents, the material properties of the plates are expected to vary continuously through their thickness. Improved damage indicator based on Frequency Response Function (FRF) is employed to predict the damaged elements in the first stage. A robust and efficient Improved Artificial Neural Network using Arithmetic Optimization Algorithm (IANN-AOA) is implemented for damage quantification problem in the second stage. The main idea is based on eliminating the healthy elements from the numerical model by the improved indicator. Next, collected data from damaged element based on damage index of an improved indicator is used as input and damage level as output. To prove the robustness of IANN-AOA, a Balancing Composite Motion Optimization (BCMO) is considered to improve ANN (IANN-BCMO) and is used for comparison. The results show that the improved indicator can predict the damaged elements with high precision. For damage quantification, IANN-AOA provides more accurate results than IANN-BCMO.

Prediction of the inter-fiber mechanical properties of composites: Part II Failure criterion based on micromechanics and cross-scale stress calculation

A novel inter-fiber failure criterion of composites based on micro-scale failure mechanism is proposed in this paper. The composites failure is determined by the failure of constituents near interface, where the micro-scale stress is “risk”. A cross-scale stress calculation formula is derived according to inclusion theory, and proved precise by comparing with the micro-scale simulation results. The accuracy of the failure criterion is verified through the experimental results and simulation results of micro-scale model under biaxial stress. The failure criterion considers the micro-scale stress distribution, fiber volume fraction and elastic properties of constituents, and can give precise predictions on the strength and failure angle of fiber reinforced polymer composite.

Microstructure-Impact Toughness Relationships in Quenched and Tempered Low Carbon Low Alloy Steels

The quantitative microstructure - impact toughness relationships in two batches of the same steel grade subjected to quenching and tempering (Q&T) have been established via characterization using EBSD technique and FIB visualization. The EBSD-based criterion for separation of structural constituents in microstructure of Q&T low carbon low alloy steels is proposed. Impact toughness differences between two steel batches subjected to nominally identical Q&T are caused by the changes in the volume fraction of structural constituents caused by various cooling conditions at quenching stage. High volume fraction of bainite containing more distorted bainitic ferrite and the highest amount of brittle cementite precipitates leads to the increase in strength and to the decrease in impact toughness.

A new quasi-3D theory for the study of the bending of thick FGM's plates on elastic foundation

In this work, a new theory quasi-3D shear deformation is presented to analyze the bending of thick FGM (functionally graded materials) plates resting on Pasternak elastic foundations, whose number of variables is limited to five. The mathematical model used presents a new range of displacement based on indeterminate integral variables where the stretching of thickness is taken into account according to the power laws P-FGM, E-FGM and S-FGM. The compositions and volume fractions of the constituents in the FGM are supposed to change through the thickness. The principle of virtual work, as well as the Naiver method, is used in this study to solve the governing equations of motion to study these types of plates. The equilibrium equations according to the FG plate resting on Pasternak foundations are presented. The results obtained are compared to those determined by the other authors. It was observed from the comparative studies that quasi-3D theories that take into account thickness stretching effects can predict bending behavior more accurately than other theories.

Free Vibration Analysis of FG Porous Sandwich Plates under Various Boundary Conditions

In the present work, free vibration analysis of the square sandwich plate with functionally graded (FG) porous face sheets and isotropic homogenous core is performed under various boundary conditions. For this purpose, the material properties of the sandwich plate are supposed to vary continuously through the thickness direction according to the volume fraction of constituents defined with the modified rule of the mixture including porosity volume fraction with four different types of porosity distribution over the cross-section. Furthermore, a hyperbolic shear displacement theory is used in the kinematic relation of the FG porous sandwich plate, and the equations of motion are derived utilizing Hamilton’s principle. Analytical solutions are achieved for free vibration analysis of square sandwich plates with FG porous face sheets under various boundary conditions, i.e. combinations of clamped (C), simply supported (SS), and free (F) edges are presented. Several parametrical studies are conducted to examine the effects of porosity volume fraction, type of porosity distribution model, lay-up scheme, side to thickness ratio, and boundary conditions on the free vibration of the FG sandwich plates. Finally, it is concluded that the investigated parameters have significant effects on the free vibration of the FG sandwich plates and the negative effects of porosity may be reduced by adopting suitable values for said parameters, considerably.

Development of an FEA framework for analysis of subject-specific aortic compliance based on 4D flow MRI

This paper presents a subject-specific in-silico framework in which we uncover the relationship between the spatially varying constituents of the aorta and the non-linear compliance of the vessel during the cardiac cycle uncovered through our MRI investigations. A microstructurally motivated constitutive model is developed, and simulations reveal that internal vessel contractility, due to pre-stretched elastin and actively generated smooth muscle cell stress, must be incorporated, along with collagen strain stiffening, in order to accurately predict the non-linear pressure-area relationship observed in-vivo. Modelling of elastin and smooth muscle cell contractility allows for the identification of the reference vessel configuration at zero-lumen pressure, in addition to accurately predicting high- and low-compliance regimes under a physiological range of pressures. This modelling approach is also shown to capture the key features of elastin digestion and SMC activation experiments. The volume fractions of the constituent components of the aortic material model were computed so that the in-silico pressure-area curves accurately predict the corresponding MRI data at each location. Simulations reveal that collagen and smooth muscle volume fractions increase distally, while elastin volume fraction decreases distally, consistent with reported histological data. Furthermore, the strain at which collagen transitions from low to high stiffness is lower in the abdominal aorta, again supporting the histological finding that collagen waviness is lower distally. The analyses presented in this paper provide new insights into the heterogeneous structure-function relationship that underlies aortic biomechanics. Furthermore, this subject-specific MRI/FEA methodology provides a foundation for personalised in-silico clinical analysis and tailored aortic device development. Statement of significanceThis study provides a significant advance in in-silico medicine by capturing the structure/function relationship of the subject-specific human aorta presented in our previous MRI analyses. A physiologically based aortic constitutive model is developed, and simulations reveal that internal vessel contractility must be incorporated, along with collagen strain stiffening, to accurately predict the in-vivo non-linear pressure-area relationship. Furthermore, this is the first subject-specific model to predict spatial variation in the volume fractions of aortic wall constituents. Previous studies perform phenomenological hyperelastic curve fits to medical imaging data and ignore the prestress contribution of elastin, collagen, and SMCs and the associated zero-pressure reference state of the vessel. This novel MRI/FEA framework can be used as an in-silico diagnostic tool for the early stage detection of aortic pathologies.

Thermomechanical Nonlinear Buckling of Pressurized Shear Deformable FGM Cylindrical Shells Including Porosities and Elastically Restrained Edges

This work proposes an effective analytical solution to study the nonlinear buckling of functionally graded material (FGM) porous cylindrical shells subjected to external pressure and elevated temperature. Volume fractions of constituents are varied through the thickness direction according to power functional rules, and effective properties are estimated according to a modified rule of mixture. The porosities are evenly or unevenly distributed within the shell. Basic equations of a simply supported shell are based on first-order shear deformation theory, including von Kármán-Donnell nonlinearity, and solved using analytical solutions and the Galerkin method. To account for practical situations, temperature-dependent properties, together with the elastic constraint of edges, are included. The suggested form of two-term deflection overcomes mathematical difficulties and is suitable for shear deformation cylindrical shells. Numerical results indicate that porosities detrimentally influence the buckling resistance of pressurized shells. Furthermore, tangential edge constraints have slight and significant effects on critical buckling loads and the pressure bearing capacity of porous shells at normal and high temperatures, respectively. Besides being an innovative approach, the presented study aims to address practical aspects in engineering applications of pressurized porous shells.

An analytical method for free vibrations of functionally graded cylindrical shells with arbitrary intermediate ring supports

An analytical method is presented to study free vibrations of functionally graded material (FGM) cylindrical shells with arbitrary intermediate ring supports. Material properties continuously vary in thickness direction in accordance with the four-parameter power-law distributions in terms of volume fractions of constituents. To establish the final governing equation, the shell is firstly divided into several shell segments according to locations of ring supports. Based on the first-order shear deformation theory (FSDT), differential equations about displacements are solved by expanding displacements as exponential functions in axial direction and Fourier series in circumferential direction. Correspondingly, five displacements and five forces at any cross section of segments are further expressed as 10 unknown coefficients for every circumferential mode number. The artificial spring technique is adopted to restrain displacements at boundaries and ring supports, and all segments are assembled to the overall shell through continuity conditions. To test the validity of the developed model, natural frequencies and mode shapes of several homogenous and FGM cylindrical shells with/without ring supports are compared with appropriate ones in the literature or calculated by finite element method (FEM), which demonstrates high accuracy and wide application of the proposed method. Furthermore, effects of ring supports and material parameters are analyzed. The results reveal that restraining radial and/or circumferential displacements at ring supports significantly affects natural frequencies, but mode shapes are mainly affected by radial displacements. In addition, natural frequencies of the FGM shell obviously vary with the power-law exponent, whereas the corresponding mode shapes almost keep unchanged.

Double enhanced energy storage density via polarization gradient design in ferroelectric poly(vinylidene fluoride)-based nanocomposites

Encapsulating ferroelectric ceramic nanofillers into polymer matrix with various architectures has been demonstrated as an effective strategy for ultrahigh energy storage density. Nevertheless, large discrepancy in permittivities between ceramic fillers and polymer requires sophisticated interfacial modification to alleviate local charge concentration. The idea to design graded permittivity from the filler center to surrounding matrix in composites is promising, yet remains a big challenge. Here coaxial electrospinning technique has been employed to control the polarization gradient distribution in TiO2 nanofibers (TOnf) and poly(vinylidene fluoride)/poly(vinylidene fluoride-co-trifluoroethylene) [PVDF/P(VDF-TrFE)] core-shell structured hybrid nanocomposites system where TOnf is fixed at volume fraction 2%, and the polarization gradient of the polymer is adjusted via altering the volume ratios of PVDF and P(VDF-TrFE) in the coaxial electrospun polymer blends in two layers, respectively. Compared with nanocomposites made from mixed solution electrospun randomly and oriented TOnf-PVDF/P(VDF-TrFE) at the same constituent volume fraction, the dielectric losses of coaxial-spun films decrease more than twice, from 0.087 for random nanocomposite film to 0.028, and more intriguingly, the discharged energy storage density (Ue) doubled increasing from 6.5 J cm−3 for random nanocomposite film to 12.7 J cm−3 for coaxial electrospun film with medium polarization gradient. Finite element analyses reveal the polarization and local electric field distribution in the nanocomposites with various polarization gradient design, and the results unambiguously demonstrate that Ue can be significantly boosted via controlled polarization gradient design.

Investigating the heat input effect of the GTAW process upon the microstructure and HAZ extension of HSLA-100 steel weld joints using thermal cycles

In the current research, the welding of HSLA-100 steel was accomplished with three different heat inputs using the GTAW process. The microstructure of various joint zones was investigated utilizing an optical microscope and scanning electron microscope. For the purpose of assessing the impact of thermal cycles upon the extension and alterations in the heat-affected zone, the thermocouples were placed at distinct distances from the fusion line. The results indicated that the weld metal microstructure comprised of acicular ferrite and a number of polygonal and quasi-polygonal Ferrite with M/A constituent. An epitaxial growth was observed in the fusion line in all heat inputs. It was determined that the heat-affected zone microstructure consisted of two regions, namely a coarse-grained heat-affected zone with a granular and lath bainite microstructure and a fine-grained heat-affected zone with the prevailing microstructure of granular Bainite. The results indicated that increasing the heat input leads to a decrease in the amount of acicular ferrite and M/A constituent volume fraction in the weld metal and an increase in lath bainite in coarse-grained zone. It was found that by increasing the heat input from 0.78kJ/mm to 1.42 kJ/mm, the grain size increases from 29.2μm to 76.5 μm and from 15.7μm to 32.5μm in coarse-grained and fine-grained zone, respectively. The thermal cycles evaluation pertinent to the implanting of a thermocouple disclosed that the heat-affected zone width is extended from 3.6 mm to 4.5mm by increasing the heat input from 0.78kJ/mm to 1.42 kJ/mm.

Thermal Nonlinear Buckling of Shear Deformable Functionally Graded Cylindrical Shells with Porosities

In this paper, for the first time, two-term deflection is suggested for nonlinear analysis of shear deformable cylindrical shells and, to the authors’ knowledge, a first investigation on thermal nonlinear buckling behavior of functionally graded material (FGM) cylindrical shells including porosities is presented. Material properties are assumed to be temperature dependent, volume fractions of constituents are graded in the thickness direction according to a power law, and effective properties of porous FGM are estimated according to a modified rule of mixture. Porosities are evenly or unevenly distributed within the shell. Mathematical formulations are based on a first-order shear deformation theory taking into account geometrical nonlinearity and elasticity of in-plane restraints of edges. Two-term deflection and a multiterm stress function are assumed to satisfy simply supported boundary conditions. The Galerkin method and an iteration procedure are employed to evaluate critical buckling temperatures and trace temperature-deflection paths in the postbuckling region. The two-term solution of deflection is a significant suggestion for nonlinear buckling analysis of shear deformable cylindrical shells in general and thermal postbuckling analysis of porous FGM cylindrical shells in particular. This two-term solution includes inherent uniform deflection at the prebuckling state and overcomes mathematically tremendous difficulty in using three-term deflection for shear deformable cylindrical shells. Besides this innovative approach, the obtained results are of great interest for many engineering applications. Unlike the case of mechanical loads, porosities have beneficial influences on the stability of thermally loaded FGM cylindrical shells.

Buckling analysis of functionally graded plates using HSDT in conjunction with the stress function method

In this article, the mechanical buckling analysis of simply-supported functionally graded plates is carried out using a higher shear deformation theory (HSDT) in conjunction with the stress function method. The proposed formulation is variationally consistent, does not use a shear correction factor and gives rise to a variation of transverse shear stress such that the transverse shear stresses vary parabolically through the thickness satisfying the surface conditions without stress of shear. The properties of the plate are supposed to vary across the thickness according to a simple power law variation in terms of volume fraction of the constituents of the material. Numerical results are obtained to study the influences of the power law index and the geometric ratio on the critical buckling load.

Analysis on the buckling of imperfect functionally graded sandwich plates using new modified power-law formulations

A new simple solution for critical buckling of FG sandwich plates under axial and biaxial loads is presented using new modified power-law formulations. Both even and uneven distributions of porosity are taken into account in this study. Material properties of the sandwich plate faces are assumed to be graded in the thickness direction according to a modified power-law distribution in terms of the volume fractions of the constituents. Equilibrium and stability equations of FG sandwich plate with various boundary conditions are derived using the higher-order shear deformation plate theory. The results reveal that the distribution shape of the porosity, the gradient index, loading type and functionally graded layers thickness have significant influence on the buckling response of functionally graded sandwich plates.

Investigation on the dynamic response of porous FGM beams resting on variable foundation using a new higher order shear deformation theory

In this work, the dynamic response of functionally graded beams on variable elastic foundations is studied using a novel higher-order shear deformation theory (HSDT). Unlike the conventional HSDT, the present one has a new displacement field which introduces undetermined integral variables. The FG beams were assumed to be supported on Winkler-Pasternak type foundations in which the Winkler modulus is supposed to be variable in the length of the beam. The variable rigidity of the elastic foundation is assumed to be linear, parabolic and sinusoidal along the length of the beam. The material properties of the FG porous beam vary according to a power law distribution in terms of the volume fraction of the constituents. The equations of motion are determined using the virtual working principle. For the analytical solution, Navier method is used to solve the governing equations for simply supported porous FG beams. Numerical results of the present theory for the free vibration of FG beams resting on elastic foundations are presented and compared to existing solutions in the literature. A parametric study will be detailed to investigate the effects of several parameters such as gradient index, thickness ratio, porosity factor and foundation parameters on the frequency response of porous FG beams.

Combined effect of carbon nanotubes distribution and orientation on functionally graded nanocomposite beams using finite element analysis

Structural tailoring can provide a promising performance for Functionally Graded (FG) components in engineering. Moreover, utilizing advanced Carbon Nanotube (CNT) as embedded reinforcement in nanocomposite structures, excellent mechanical properties can be tailored and designed to meet requirements. This research addressed the issue of a particular effect for CNT orientation and gradation distribution on static and free vibration analysis of Functionally Graded CNT-Reinforced Composite (FG-CNTRC) beams. First, an efficient finite beam element capable of controlling both parameters was derived based on the Timoshenko beam theory. Single-Walled CNT (SWCNT) was used as primary reinforcement and graded through-thickness. Then, an extensive parametric study was done for model convergence, static, and dynamic analysis. The proposed model offers unique shape function depends on material properties and cross-section geometry, high-accuracy, and expanded to cover both orientations and grading exponents. This expansion allows passive-control of the beam stiffness and strength without any increment in structural weight. Wherein constituent materials quantities and volume fractions were not changed. Finally, obtained findings concerned about orientation angle and power-law exponent, which showed that they significantly affect the structural response, and therefore offer a practical approach of structure tailoring for applied loads, required response, and specific weight limitations.

Optimization of FGM Composition for Better Environment Material

In functionally graded heat-resisting material, the volume fraction of constituents varies functionally and continuously, and these are examined for high temperature engineering applications. By the spatial distribution of the volume fraction the thermal behaviour of FGMs is strongly influenced. Thus, the determination of volume fraction distribution becomes a critical part in the FGM design for a given loading condition and specification. In present work, averaging estimation approach viz, modified rule of mixture is considered. The present work is concerned with the Optimization of FGM Composition for better environment material. The investigation is carried out for uniform heating condition through the plate thickness. Classical laminate theory is used to determine residual stress. The code is developed on MATLAB for constrained minimization and the MATLAB function ‘fmincon’ is employed. The comparative study of three different thermal loading is presented. The effectiveness of residual stress minimization is explored for various boundary conditions.

Optimization of functionally graded material under thermal stresses

In functionally graded heat-resisting material, the volume fraction of constituents investigated for high-temperature engineering applications and varies functionally and continuously. Strongly influenced the thermal behaviour of FGMs is the volume fraction by the spatial distribution. In the FGM design, the determination of distribution of volume fraction becomes a critical part for a specification and given loading condition. In present work, averaging estimation approach, modified rule of mixture is considered. The present work is concerned with the optimization of functionally graded material under thermal stresses. The analysis is carried out during the plate thickness for uniform heating situation. Curvature is used determine by the classical laminate theory. For constrained minimization, the code is developed on MATLAB and the ‘fmincon’ MATLAB function is engaged. The thermal loading comparative study is presented.. For various boundary conditions, the usefulness of curvature minimization is explored.

Physical and Numerical Simulations of Closed Die Hot Forging and Heat Treatment of Forged Parts.

The paper describes physical and numerical simulations of a manufacturing process composed of hot forging and controlled cooling, which replace the conventional heat treatment technology. The objective was to investigate possibilities and limitations of the heat treatment with the use of the heat of forging. Three steels used to manufacture automotive parts were investigated. Experiments were composed of two sets of tests. The first were isothermal (TTT) and constant cooling rate (CCT) dilatometric tests, which supplied data for the identification of the numerical phase transformation model. The second was a physical simulation of the sequence forging-cooling on Gleeble 3800, which supplied data for the validation of the models. In the numerical part, a finite element (FE) thermal-mechanical code was combined with metallurgical models describing recrystallization and grain growth during forging and phase transformations during cooling. The FE model predicted distributions of the temperature and the austenite grain size in the forging, which were input data for further simulations of phase transformations during cooling. A modified JMAK equation was used to calculate the kinetics of transformation and volume fraction of microstructural constituents after cooling. Since the dilatometric tests were performed for various austenitization temperatures before cooling, it was possible to include austenite grain size as a variable in the model. An inverse algorithm developed by the authors was applied in the identification procedure. The model with optimal material parameters was used for simulations of hot forging and controlled cooling in one of the forging shops in Poland. Distributions of microstructural constituents in the forging after cooling were calculated. As a consequence, various cooling sequences during heat treatment could be analyzed and compared.