Dependent Material Properties Research Articles

Recent developments in modeling and analysis of rotating functionally graded panels: A review

This article presents a comprehensive review on recent developments in the techniques for modeling and exploration of rotating functionally graded material (FGM) panels carried out between periods 2000 to 2023. Special attention is given on literature pertaining to analysis of rotating FGM panels subjected to thermo-mechanical loading. This study scrutinizes the advancements made in analysis of panels such as beam, plate, shell and blades that includes effects like porosity, thermal stress, and piezo-electric in the mathematical model. The present article also highlights the importance and ease in implementation of rule of mixture for calculation of different temperature dependent material properties used in the analysis of rotating FGM panels. An in-depth review of literature clearly indicates the importance of taking thermal effect in the estimation of elastic properties for accurate analysis of rotating FGM panels. Further, a detailed analysis of temperature profile viz., linear/non-linear, is carried out. Finally, the article concludes with the future areas that need to be explored for the analysis of rotating FGM panels.

Prediction of the sound pressure response in an enclosed cavity with sound absorbent walls using the CMA and AMA methods

The sound pressure response in an enclosed cavity with sound absorbent walls is predicted using the classical modal analysis (CMA) method and the asymptotic modal analysis (AMA) method. The sound absorbing material is represented as an equivalent fluid with frequency dependent bulk material properties. The equivalent fluid properties can be obtained from either impedance tube test data or based on micro-scale Biot material properties. In the low frequency range, the CMA method is implemented to include the frequency dependent material properties. In the medium and high frequency ranges, when modal density is high, the frequency dependence effects become cumbersome using CMA. The AMA method has been developed as an asymptotic extension of the CMA method for the mid- and high-frequency ranges and is extended here to incorporate the frequency dependence of an equivalent fluid properties of the sound absorbing materials. An enclosed rectangular box subjected to loudspeaker excitation is used to evaluate the effect of absorption materials using the CMA method for the low-frequency range and the AMA method for the mid- and high-frequency ranges. Test data have also been obtained for comparisons of the CMA method in the low frequency range. Using these procedures, the CMA and AMA methods can be applied to represent absorbent materials over a wide frequency range for enclosure architectural design.

Combined effect of temperature dependent material properties and boundary conditions on non-linear thermal stability of porous FG beams

Combined effect of temperature dependent material properties and boundary conditions on non-linear thermal stability of porous FG beams

Temperature Monitoring of Through-Thickness Temperature Gradients in Thermal Barrier Coatings Using Ultrasonic Guided Waves

Ultrasonic guided waves offer a promising method of monitoring the online temperature of plate-like structures in extreme environments, such as aero-engine nozzle guide vanes (NGVs), and can provide the resolution, response rate, and robust operation that is required in aerospace. Previous investigations have shown the potential of such a system but the effect of the complex physical environment on wave propagation is yet to be considered. This article uses a numerical approach to investigate how thermal barrier coatings (TBCs) applied to the surface of many components designed for extreme thermal conditions will affect ultrasonic guided wave propagation, and how a system can be employed to monitor through-thickness temperature changes. The top coat/bond coat boundary in NGVs has been shown to be a temperature critical point that is difficult to monitor with traditional temperature sensors, which highlights the potential of ultrasonic guided waves. Differences in application method and layer thickness are considered, and analysis of through-thickness displacement profiles and dispersion curves are used to predict signal response and determine the most suitable mode of operation. Heat transfer simulations (COMSOL) have been used to predict temperature gradients within a TBC, and dispersion curves have been produced from the temperature dependant material properties. Time dependant simulations of wave propagation are in good agreement with dispersion curve predictions of wave velocity for the two lowest order modes in three thicknesses of TBC top coat (100, 250, and 500 μm\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upmu \\hbox {m}$$\\end{document}). When wave velocity measurements from the simulations are compared to dispersion curves generated at isotropic temperatures, the corresponding temperature represents the average temperature of a gradient system well. Such a measurement system could, in principle, be used in conjunction with surface temperature measurement systems to monitor through-thickness temperature changes.

Functionally graded doubly-curved shell with temperature dependent material properties and surface-mounted MEE layers

In the present work, the geometrically nonlinear behavior of a simply supported functionally graded doubly curved shell with a surface-mounted magneto-electro-elastic layer is investigated based on Donnell’s theory. Kirchoff’s assumption and von Kármán’s strain-displacement relationship are used to obtain the governing differential equations. The through-the-thickness shell temperature is computed using Fourier’s heat conduction equation. Elastic material properties are assumed to be temperature-dependent and follow the power-law distribution function of the constituent ceramic-metal volume fractions. The magneto-electro-elastic layer is polarized along the thickness direction, which is subjected to electric and magnetic potentials. Gauss’s laws for electrostatics and magnetostatics are satisfied for magneto-electric materials. Nonlinear partial differential equations of motion are reduced to ordinary differential equations by introducing a stress function and using a single-term time-dependent assumed displacement function. Nonlinear free vibration response is obtained by direct numerical integration. After comparing the derived model with published literature results, numerical studies on the effects of applied electric and magnetic coupled fields of surface-mounted magneto-electro-elastic layers on shell vibration are reported. The nonlinear frequency ratios with respect to specified displacement for both spherical and cylindrical shells with thin Piezoelectric BaTiO 3 and Piezomagnetic CoF e 2 O 4 panels across material compositions, the radius of curvature, and thermal conduction are studied.

Wear Evolution on PVD Coated Cutting Tool Flank and Rake Explained Considering Stress, Strain and Strain-Rate Dependent Material Properties

Impact loads developed on a tool cutting edge when milling into a workpiece material are prevailing metrics for explaining coating fatigue failure and the subsequent tool-wear evolution. For predicting related stress and strain fields in the compound coating-substrate, stress, strain, and strain-rate, dependent material properties are required. The attainment of such data is briefly described in the paper. Considering these data, the occurring strains in the cutting edge at various entry impact durations, i.e., strain rates, were calculated and compared with fatigue-critical strains. In this way, the wear phenomena causing the coating failure on the flank and rake during milling were clarified. The attained results were also correlated to corresponding ones in turning, where the dynamic loads of the cutting edge are comparably negligible. The conducted investigations showed that the fatigue-critical strains strongly diminish, when the relevant strain rates increase; thus, leading to a remarkable tool-life reduction. This happens, because the increase of the strain-rate restricts the time for the dislocations movements; thus, regions with stress concentrations occur, deteriorating the material ductility, increasing its brittleness, and diminishing the fatigue critical strains. In cutting operations, where the coating fatigue is the main wear factor, the tool-life can be predicted considering these phenomena. In the paper, relevant experimental analytical procedures are introduced.

A multiphase modeling for investigating temperature history, flow field and solidification microstructure evolution of FeCoNiCrTi coating by laser cladding

In this work, a multiphase numerical model was established to investigate the non-isothermal flow and microstructure evolution during laser cladding. The model considered the beam-powder interaction, temperature dependent material properties, the effect of buoyancy and surface tension on convection. The accuracy of the model was verified comparing the simulated coating geometric morphology with the experimental results. Simulation indicated that the temperature and flow of the molten pool were interactive and mutually causal. On the one hand, the temperature field affected the tension gradient and the liquid flow direction. On the other hand, the velocity field significantly affected the heat transfer in the molten pool. Specifically, the maximum fluid velocity was 9.58 mm/s and the Peclet number (PeT) value was less than 5 at the initial stage, indicating that conduction dominated in heat transfer. Furthermore, the PeT value was greater than 200 when the maximum velocity reached 344 mm/s. The heat transfer in the molten pool was mainly thermal convection. In addition, the distribution diagram of solidification parameters (G and R) was calculated to quantitatively establish the internal correlation between solidification parameters and microstructure combing with experimental observation, and revealed the columnar-to-equiaxed transition (CET). Eventually, the microhardness results showed that HEA coating could improve the Ti6Al4V surface microhardness. Simultaneously, the CET behavior significantly affected the microhardness of the coating.

(Invited) Bubble Trouble: Simulation of Molten Oxide Electrolysis in Reduced Gravity

Molten Oxide Electrolysis (MOE) is a leading contender for processing extra-terrestrial minerals because it produces oxygen and liquid metal without the use of consumables. During electrolysis a gravitational field stratifies gas, electrolyte, and metal from each other by density. Processing on the moon, with ~1/6g, or Mars, with ~1/3g, will reduce the buoyancy force slowing bubble velocity and lowering convection intensity. Low thermal conductivity, (~1Wm-1K-1) and high viscosity, (~1Pa⋅s) of molten regolith contribute to thermal and chemical transport being dominated by convection, even as convection velocity decreases. We explore MOE system dynamics in Earth’s (1g), Mars’ (1/3g), and the Moon’s (1/6g) gravity through simulations that include composition and temperature dependent material properties and two phase flow. We implement the level set method to track the interface between the bubble laden flow near the anode and the bubble free flow far from the anode. By grouping bubble dynamics into the material properties of the fluid near the anode we relax the requirements for a fine mesh to track individual bubble-fluid interfaces, and are able to use a mesh that is finer than that required for a bubbly flow mixture model. Thus, all physics can be captured on one mesh. This is particularly relevant because bubble sizes for proposed systems are 1/10 to 1/100 of the system scale. While other simulations have been presented and experiments performed in micro and zero gravity for gas evolving electrolysis systems, none have investigated the downward facing electrode, heat transfer, or species diffusion. The focus of this work is to address this gap in the literature through simulation. Here, multiphysics simulation is supported by inspection of dimensionless groups and observations from other electrolysis systems. This work demonstrates that combining heat and mass transfer with temperature and composition dependent material properties is critical to designing MOE and other electrolysis systems for earth and beyond.

Thixomolding of Magnesium - Efficient Process Industrialization by Combining a Digital Twin and Systematic Casting Trials

Besides the realization of the technical specification of a casting, aspects such as resource minimization, cost awareness and robustness of the defined quality requirements are taking major priority, especially in the current global economic situation. Lightweight design, in that respect, is a central topic far beyond the automotive industry and characterizes in particular the ongoing research and development of innovative magnesium cast components. As a resource-efficient alternative to traditional die casting, magnesium-thixomolding offers the benefit of low energy consumption and eschews the necessity of protective gases. The identification of significant influencing factors between process settings, shear and time dependent material properties of semi-solid magnesium, the machine capabilities and the resulting casting quality are the basis for effective product and process design of magnesium thixomolding. Obtaining this knowledge is only possible through methodical process analysis and systematic design of experiments. YIZUMI Germany, together with MAGMA, demonstrates the methodical evaluation of a reliable process window for an AZ91D magnesium “box” component, using a demo mold on a UN1250MGII thixomolding machine. The work shows how a systematic combination of virtual and real casting experiments is used to identify a concrete process layout and generate important knowledge on process variations, robustness as well as control limits. In particular, the comparison of virtual and real casting experiments using statistical methods generates a comprehensive understanding of the impact and limits of different process variables, such as fraction solid, mold temperature and injection speeds. Furthermore it is possible to predict the influence of the gating and component design on the process. The methodological use of qualified casting simulation enables the development of an optimized component design and the determination of a suitable process window with minimized economic or productive risks long before the first component is manufactured – a step towards more resource efficiency and sustainability!

A review on experimentally observed mechanical and microstructural characteristics of interfaces in multi-material laser powder bed fusion

Additive manufacturing (AM) is a revolutionary technology. One of the key AM categories, metal powder-based fusion processes, has many advantages compared to conventional methods for fabricating structural materials, such as permitting increased geometric complexity. While single material metal powder AM has advanced significantly in the past decade, multi-material AM is gradually attracting more attention owing to the recent breakthrough in multi-material feedstock delivery and the growing interest of fabricating functionally graded components. Multi-material AM offers an alternative route for applications that require location dependent material properties and high geometrical complexity. The AM community has invented several ways to achieve compositional gradients and discrete boundaries in two and three dimensions using mechanical spreading, nozzle-based, electrophotographic, and hybrid techniques. This article reviews the current state of laser powder bed fusion based multi-material AM of metals with focuses on the characteristics of the material interface as well as the properties and performance of the AM built functionally graded materials. We show the common challenges and issues related to material transitions, such as defects, segregation, phase separation, and the efficacy of some potential solutions including material and process optimizations. Additionally, this study evaluates the applicability and limitations of the existing testing standards and methods for measuring mechanical performance of functionally graded materials. Finally, we discuss mechanical testing development opportunities, which can help multi-material AM move towards higher technological maturity. In general, we find that the link between gradient microstructure and mechanical properties is not well understood or studied and suggest several mechanical tests that may better inform this knowledge gap.

Reconstruction of the heat flux input of coated gun barrel with the interfacial thermal resistance

A 2-D inversion model to reconstruct the transient inner wall heat flux of the coated barrel is proposed in this paper. Indirect measurement of the inner wall temperature of the barrel under harsh conditions is realized. Measurement points locate at specified distances from the inner surface. Temperature calculated from a direct problem plus the measurement errors is taken as measured temperature. Variations of the temperature dependent thermo-physical properties of materials are taken into consideration. The total heat input of the firing and thermal resistance between chromium coating and gun steel are determined by depths of gun steel phase transition and chromium recrystallization after firing. The direct problem, sensitivity problem and adjoint problem are solved with the finite difference method (FDM). After verifying the reliability of the inversion model with a special numerical example, it is promoted to reconstruction of general heat flux varying with time and space. Results indicate that decreasing the measurement error and increasing the number of measurement points can effectively improve the performance of the model. As well, measurement points closer to the inner wall offer superior accuracy. The inversion model herein can serve as a promising indirect measurement method of the inner wall temperature.

A chemo-viscoelastic model and a numerical scheme to study stress-diffusion interactions in Lithium ion battery electrode particles

A mathematical model and an associated numerical framework is developed for an isotropic viscoelastic electrode particle. The ensuing differential equations are solved using FEM with the help of an open source C++ library (deal.ii). The developed model is then used to understand the effects of time dependent material property (stress relaxation function) on the stress distribution of a viscoelastic electrode particle under potentiostatic boundary conditions. In contrast to a purely elastic particle, it is observed that the radial stresses become compressive and tangential stresses tensile towards the outer end of the particle. On varying the values of the characteristic time constant (τ), it is observed that stress relaxes faster for lower values of τ when compared to larger ones. Furthermore, the interactions between stress evolution, stress relaxation function, and diffusion is studied by varying τ and the electrode particle size. The study reveals that viscoelastic effects are apparent for a range of τ depending on the particle size. Thus, the interactions between the rate of diffusion, which varies with particle sizes, and τ affect the stress relaxation function, resulting in a complex mechanical response.

Experimental and numerical investigation of the thermal properties and related microstructural influences of an interpenetrating metal ceramic composite at elevated temperatures

An interpenetrating metal-ceramic composite (IMCC), consisting of an open-porous alumina preform (26vol%), infiltrated with an AlSi10Mg alloy is investigated for its thermal properties and the microstructural impact on the thermal cycling behavior. Specific heat capacity, thermal conductivity and the coefficient of thermal expansion are investigated experimentally. Next to dilatometry experiments, an in-situ SEM setup with digital image correlation of the natural microstructure of the composite is used as a recognizable pattern on the sample surface to evaluate strain and microstructural changes during heating and cooling. The interpenetrating phase composite is also modelled based on reconstructed and generated microstructures. Extensive numerical studies are conducted with varying boundary conditions, interface properties, initial cooling temperatures, temperature dependent material properties and inclusion of pores. Microstructural investigations show phenomena of plasticity, creep, crack formation and interface detachment which is supported by numerical findings. Microstructural changes during heating and cooling in form of crack formation occur in the metallic phase and metallic precipitation. The influence of the microstructural processes on the thermal expansion behavior are discussed in comparison to existing hypotheses from literature.

In silico quantification of 3D thermal gradients and voids during fused filament fabrication deposition to enhance mechanical and dimensional stability

Fused filament fabrication (FFF) is one of the most widely used additive manufacturing techniques for polymeric materials. However, the mechanical and dimensional quality of the final printed parts are still deviating from the maximal performance, due to the presence of voids, and incomplete inter- and intralayer bond formation implying suboptimal molecular chain entanglement. The current work puts forward a three-dimensional Ansys Polyflow® computational study in which temperature gradients and void formation are analysed for the deposition of up to eight strands, accounting compared to the state of the art for (i) bond formation at the strand interfaces by material deformation; (ii) non-Newtonian viscosity variations; (iii) measured temperature dependent material properties, including conductivity, specific heat capacity and viscosity; and (iv) convection. Selecting acrylonitrile butadiene styrene (ABS) as polymeric material, it is demonstrated that a dynamic heat transfer is obtained with contributions from the heated bed to layers printed above, and from just printed warmer layers to colder layers printed before in both the vertical and transversal direction. These extra heat transfers renew the interlayer contact between two strands, as the temperature at the weld line can be pushed several times above the glass transition temperature. A tuning of this renewable welding is possible based on a variation of the bed and nozzle temperature; the latter more relevant upon increasing the number of layers printed. It is further highlighted that the void shape and size is different close and away from the bed (2.5-8% void percentage variation). Moreover, a novel computational method is put forward to quantify the surface roughness based on edge analysis (80-120 μm variation).

Optimization of Brake Disc Profile Based on the Thermal Performance for Electric Vehicles

The brake disc market has reached the value of USD 20.9 billion in 2021 at a CAGR of 4.9% and it is expected to grow to USD 26.5 billion by 2026. However, the difficulties associated with the brake discs are significant rise in the temperature which results in, early wear, thermal cracks and brake fade leading to uneven braking and premature replacement. In this context many researchers have been studying the parameters like brake disc material and type of ventilation. The objective of the work was to study of the effect of ventilation types on thermal responses and optimize the brake disc profile for better thermal performances. Center of gravity and dynamic load transfer were calculated for two wheeler electric vehicle experimentally which was followed by computing the force required for braking process and heat flux on the brake disc analytically. Ventilation of type cross drilled holes (CD) was adopted in brake disc modelling, and was carried out in SOLIDWORKS 2022 and finite element model for the brake disc was created in ANSYS 17.2 with mesh size of 2 mm for lamellar graphite iron (LGI) with temperature dependent material properties. The transient thermal analysis for three braking cycles were carried out with the considerations such as: initial velocity of the vehicle of 96 km/h, ambient temperature of 22°C, conduction and convection modes of heat transfer and 5 s of deceleration and acceleration time. Transient thermal analysis was carried out by applying the heat flux on the frictional surface of the brake disc. For the solid disc without ventilation, it was found that the maximum temperature at the end of first braking cycle (0 to 5 s) was 157.72°C, at end of second braking cycle (10 to 15 s) was 256.95°C and at the end of third braking cycle (20 to 25s) was 349.73°C. As the wear rate for lamellar graphite iron grows exponentially beyond 300°C, ventilations were provided on the brake disc to reduce the temperature on the disc. For the optimized brake disc with ventilation type VT-12, it was found that maximum temperature at the end of first braking cycle (0 to 5 s) was 139.43°C, at end of second braking cycle (10 to 15 s) was 222.68°C and at the end of third braking cycle (20 to 25s) was 299°C. The overall character of these shows a quick rise in temperature at the start of the process, followed by the achievement of the maximum value and, eventually there is a drop in temperature. In this research the future work can be carried out by implementing the noise, vibration and harness studies which would benefit the industry with better braking system.

Torsional postbuckling characteristics of functionally graded graphene enhanced laminated truncated conical shell with temperature dependent material properties

Buckling and postbuckling characteristics of laminated graphene-enhanced composite (GEC) truncated conical shells exposed to torsion under temperature conditions using finite element method (FEM) simulation are presented in this study. In the thickness direction, the GEC layers of the conical shell are ordered in a piece-wise arrangement of functionally graded (FG) distribution, with each layer containing a variable volume fraction for graphene reinforcement. To calculate the properties of temperature-dependent material of GEC layers, the extended Halpin-Tsai micromechanical framework is used. The FEM model is verified via comparing the current results obtained with the theoretical estimates for homogeneous, laminated cylindrical, and conical shells, the FEM model is validated. The computational results show that a piece-wise FG graphene volume fraction distribution can improve the torque of critical buckling and torsional postbuckling strength. Also, the geometric parameters have a critical impact on the stability of the conical shell. However, a temperature rise can reduce the crucial torsional buckling torque as well as the GEC laminated truncated conical shell's postbuckling strength.

Radiative energy transfer model for high frequency vibration of functionally graded beams in thermal environment

A simple and efficient energy flow model is developed by radiative energy transfer method (RETM) to predict the high frequency vibration response of functionally graded(FG) beams in thermal environment. The Timoshenko beam theory is applied to derive the motion governing equations. Thermal effects are incorporated into the dynamic model through the temperature dependent material properties and the thermal stresses. The wavenumber and group velocity associated with thermal stress are included in the energy governing equation. By introducing the artificial springs to simulate different boundary conditions, the energy conversion relationship of the two waves at boundaries are deduced. The response of FG beam loaded by a high-frequency harmonic force is described by energy density and energy flow intensity. They are composed of energy rays from the real source at the load point and energy rays reflected from the imaginary sources at the boundaries. Numerical simulations are performed in various forms of thermal environments to verify the proposed model. The RETM results are compared with those obtained by the wave propagation approach under different parameters, and good consistencies are observed. Numerical results show that the vibrational energy density of FG beams are affected by thermal effects and can be reduced by optimising the gradient factors.

Modeling the interfacial failure and resulting mechanical properties of z-pinned additively manufactured composites

The mechanical properties of Fused Filament Fabrication (FFF) parts are limited in the build direction, albeit advantages such as design flexibility and in-house customization. In this paper, a novel z-pinning approach that enhances mechanical properties in the build direction by depositing material across multiple layers within the part was investigated through numerical simulations and validated experimentally. A finite element model for z-pinned composite structures was developed by assigning fiber-orientation dependent material properties obtained using a micromechanics approach to beads and pins. The bead-to-bead and pin-to-pin adhesions within the z-pinned structures were modeled using a cohesive traction separation law. The properties of cohesive elements for carbon fiber-reinforced polylactic acid (CF-PLA) z-pinned composites were calibrated using tensile experiments. The elastic modulus and tensile strength of CF-PLA z-pinned composites in the build direction were predicted with the developed numerical model. The numerical investigation on various geometrical parameters revealed that the largest pin volume increases the stiffness and tensile strength by 40% and thus, has the greatest influence on the mechanical properties of the z-pinned composites. The effect of z-pin geometrical parameters on the mechanical properties was summarized to aid in the design of z-pinned additively manufactured composite structures.

Estimation of aerothermal heating for a thermal protection system with temperature dependent material properties

In this paper the aerothermal heating of a reusable launch vehicle with the material parameters depending on temperature is retrieved. An additional information, necessary for solving the corresponding inverse problem, is taken from the temperature values in the selected point of thermal protection system. Minimization of the constructed functional, defining the error of approximate solution, is executed with the aid of Levenberg–Marquardt method. Whereas the direct problem, needed to be solved in order to determine the value of functional mentioned above, is solved by using the implicit scheme of the finite difference method. In this approach a system composed from three layers is considered, which represents an integrated thermal protection system with material parameters depending on temperature.

Higher-order models for the passive damping analysis of variable-angle-tow composite plates

In this paper, the damped free-vibration and frequency response analysis of variable-angle-tow composite plates embedding viscoelastic layers with frequency-dependent properties are performed. The governing equations are derived from the Principle of Virtual Displacements and higher-order Layer-Wise models are used for the unknown variables description in the thickness direction, furthermore a nine-node finite plate element is employed to solve them. The plate formulation presented in this paper is more efficient with respect to three-dimensional approaches, typically used for this kind of structures, and it is more accurate than existing reduced order methods thanks to the use of the mixed interpolation of tensorial components technique, employed to solve the problem of the shear and membrane locking phenomena. Different multilayered structures have been considered, laminated with unidirectional cross-ply layers or with curvilinear fibers path ones. The use of viscoelastic soft sheets permits to have a passive damping of the structural vibration. The frequency dependent properties of the viscoelastic materials are described through the use of a Kelvin-Voigt model. Numerical solutions are presented for the analysis of variable-angle-tow composites with different boundary-conditions and various lamination schemes.