Functionally Graded Structures Research Articles

Functional graded NiTi manufactured with powder bed fusion

AbstractNickel–titanium (NiTi) is a versatile material with unique inherent properties, such as shape recovery, superelasticity, and biocompatibility, that makes it suitable for various engineering applications. While NiTi can be additively manufactured using powder bed fusion for metals (PBF-LB/M), challenges arise due to the material sensitivity to process parameters and the challenge of achieving desired mechanical and functional properties. Mechanical and functional properties of NiTi are highly influenced by the alloy composition which in turn is affected by the process parameters. This study aims to investigate the feasibility of tailoring the properties of NiTi to manufacture functionally graded structures. Promising shape recovery strains of 4.16$$\%$$ % and superelastic strains of 7$$\%$$ % under compression are achieved with cycling stability outperforming the conventional manufactured NiTi. By varying the process parameters, the austenite finish temperature could be shifted between 29 ± 5 $$^\circ$$ ∘ C and 72 ± 5 $$^\circ$$ ∘ C, while achieving a maximum relative material density of 99.4$$\%$$ % . Finally, the study demonstrates the potential of powder bed fusion to manufacture complex and functional graded structures, enabling spatial control. This potential is showcased through the sequential actuation of a demonstrator structure. The findings of this research highlight the promising capabilities of powder bed fusion in producing functional graded NiTi structures, with potential applications in robotics, aerospace, and biomedical fields.

Multi-scale design of composite material structures for maximizing fundamental natural frequency

This study deals with the topology optimization (TO) of linear elastic composite structures considering fundamental natural frequency maximization. The concept of functionally graded structures (FGS) is used for anisotropic composite material structure design to improve the structural dynamic performance. The rational approximation of material properties (RAMP) method was employed as an alternative to the solid isotropic material with penalization (SIMP) method to improve the convergence stability for eigen-frequency problem. In the SIMP method, the occurrence of local eigen-modes at low frequencies in the void region causes ill-convergence, whereas the RAMP method prevents local eigen-modes from occurring. The method of moving asymptotes is used as an optimizer. Numerical verification was performed for three structural types: cantilever beam, double-clamped beam, and four-pinned beam structure. In addition, for cantilever beam design, bi-objective optimization for maximizing fundamental natural frequency as well as minimizing structural compliance was performed using the adaptive weighting method that quantitatively reflects the designer's preference by adjusting the weight for each objective function at each iteration.

Free vibration analysis of functionally graded shallow shells with variable thickness and physical neutral surface effects

The study and manufacture of functionally graded (FG) shallow shells with the variable thickness are essential for the actual application of these types of structures. Previously, many researchers have developed different approaches to analyzing the mechanical behaviors of the FG structures, in which the thickness parameter has been assumed to be constant. Moreover, studies on these types of structures with the variable thickness are still quite limited. For this reason, this paper provides an effective and simple approach via mathematical formulations for analyzing the free vibrational responses of FG shallow shells with the variable thickness. Also, the presence of porosities that can occur during the fabrication of FG materials is considered. One of the highlights here is to consider the influence of the physical neutral surface. Before conducting the analysis of these FG structures, firstly, it is important to establish governing equations based on the classical shell theory. These essential equations are used for the FG shallow shells. Then, by setting the Navier solution with the help of simply supported boundary conditions, the natural frequencies are obtained. Finally, the numerical examples will be given to illustrate the effects of porosity coefficient, material and geometry parameters as well as the physical neutral surface on the natural frequencies. In addition, two numerical examples for verification will also be performed and thereby show the accuracy of the current method and model. It is hoped that the main results of this study can be useful not only to designers and researchers but also to be extended to more complex problems.

An efficient hybrid collocation scheme for vibro-acoustic analysis of the underwater functionally graded structures in the shallow ocean

In this paper, a novel hybrid collocation scheme based on the generalized finite difference method (GFDM) and the Burton–Miller singular boundary method (BMSBM) is developed to study the vibration and acoustic radiation characteristics of an underwater functionally graded (FG) structure immersed in the shallow ocean. By utilizing the individual strengths of both methods, the GFDM is adopted for the vibration analysis of the FG structures, while the BMSBM is applied for the acoustic wave radiation analysis. Numerical examples verify the accuracy and efficiency of the proposed hybrid collocation scheme for the natural frequency and acoustic radiation behavior of the underwater structures consisting of the functionally graded materials (FGMs). The influences of the material parameters, structural geometries and shallow ocean environment on the natural frequencies of the structural vibration and the underwater acoustic wave radiation field are investigated in detail. Numerical study shows that the variation trend of the natural frequencies of the structural vibration is consistent with that of the resonance peak frequencies of the underwater acoustic radiation field. The present results may provide valuable references for the design and application of underwater marine structures consisting of the FGMs.

Numerical and theoretical analysis of multiple simultaneous impact on a functionally graded porous aluminum plate

Purpose The purpose of this study is to extract the response of the simultaneous low-velocity impact of multiple impactors on a porous functionally graded (FG) aluminum plate. Design/methodology/approach To design a porous FG structure, a series of functions are applied using the porosity coefficient, and mechanical properties including Young’s modulus, shear modulus and the density of the porous structure are presented as a function of the axis placed in the direction of the plate thickness. The first-order shear deformation theory of the plate is used. To simulate the contact process between each impactor and the plate, a nonlinear Hertz contact force is considered for that impactor independently. Findings ABAQUS finite element software is used for the verification process of the theorical equations. The effects of porous function type, radius and initial velocity of impactor are investigated for the simultaneous impact of five impactors on porous FG aluminum plate with a simply supported boundary condition. Histories of contact force and displacement of the impactor placed in the center of the beam are analyzed in detail with the changes of the mentioned parameters. Originality/value Due to the advantages of porous aluminum plate such as high energy absorption and low weight, such structures may be subjected to the simultaneous impact of multiple impactors, which is studied in this research.

Optimization of functionally graded polycrystalline diamond compact based on residual stress: Numerical simulation and experimental verification

Polycrystalline diamond compact (PDC) is composed of a polycrystalline diamond layer with a tungsten carbide substrate, which is commonly used on drill bits. PDC bits are widely used in geological and petroleum drilling. There are frequently issues with failure, such as chipping of teeth during drilling, attributed to the residual stress within the PDC. Residual stresses arise from the difference in material properties between the polycrystalline diamond layer and the tungsten carbide substrate after sintering and cooling. To address the residual stresses inside the PDC, this research work optimized the design of a PDC with a functionally graded structure is reported in this paper. The effect of gradient structural parameters on the residual stresses of the PDC is analyzed using the finite element method. The results show that as the thickness of the gradient structural layer increases, the maximum residual tensile stress gradually decreases and stabilizes. Since the total thickness of the gradient structural layer is fixed, increasing the layer number (decreasing the thickness of the single layer) cannot reduce the maximum tensile stress, but it can minimize the sudden change of axial stress across the interface, thus resulting in less interface cracking. The optimum gradient structure design parameters are obtained and the optimal graded PDC is prepared via fused deposition modeling and sintering technology, resulting in a 62% reduction in maximum shear stress, a 70% decrease in maximum axial stress, and a 40% drop in maximum radial stress compared to conventional PDC. The accuracy of the finite element calculations is demonstrated by the Raman spectroscopy results. This work will provide a reliable guide for the design of functional graded structure PDCs and lay the foundation for their preparation and application.

Exact solutions for the symmetric elastoplastic response of functionally graded pressure vessels

With the development of functionally graded (FG) composite material technology, mechanical analyses of FG pressure vessels have attracted attention. Due to the non-uniform stress distributions inside such vessels, irreversible plastic deformation first occurs in some zones of the structure under the action of external loads. It is necessary to perform an elastoplastic analysis of FG structures to determine their load-bearing capacities. In this paper, exact solutions are obtained for the purely elastic, partially plastic, and fully plastic deformation of FG cylindrical and spherical shell pressure vessels under mechanical loads. The material properties (elastic modulus and yield strength) are assumed to vary nonlinearly in the radial direction of the vessel and the Poisson's ratio is assumed to be constant due to Poisson's ratio slight variations in the engineering materials. The novelty of the current work lies in the presentation of complete exact elastoplastic solutions for FG thick cylindrical and spherical shell pressure vessels, taking into account all deformation zones. Tresca's yield criterion is used to formulate four different deformation zones for an ideal plastic material. All of these states of deformation are studied in detail. It is shown that the elastoplastic response of the FG pressure vessels is notably affected by the radial variation of the material properties. With an increase in the FG parameter β, the first yielding position of the FG pressure vessels changes from the inner surface to the outer surface. The conclusions of this work should help with developing designs of FG pressure vessels to prevent yielding under excessive circumferential stresses.

Numerical Modeling of Mechanical Behavior of Functionally Graded Polylactic Acid-Acrylonitrile Benzidine Styrene Produced via Fused Deposition Modeling: Experimental Observations.

Functionally graded materials (FGM) have attracted considerable attention in the field of composite materials and rekindled interest in research on composite materials due to their unique mechanical response achieved through material design and optimization. Compared to conventional composites, FGMs offer several advantages and exceptional properties, including improved deformation resistance, improved toughness, lightness properties, and excellent recoverability. This study focused on the production of functionally graded (FG) polymer materials by the additive manufacturing (AM) method. FG structures were produced by the fused deposition modeling (FDM) method using acrylonitrile benzidine styrene (ABS) and polylactic acid (PLA) materials, and tensile tests were performed according to ASTM D638. The effects of different layer thicknesses, volume ratios, and total thicknesses on mechanical behavior were investigated. The tensile standard of materials produced by additive manufacturing introduces geometric differences. Another motivation in this study is to reveal the differences between the results according to the ASTM standard. In addition, tensile tests were carried out by producing single-layer samples at certain volume ratios to create a numerical model with the finite element method to verify the experimental data. As a result of this study, it is presented that the FG structure produced with FDM improves mechanical behavior.

Assessment of porosity influence on thermo-mechanical stability characteristics of skew functionally graded plates using higher order shear deformation theory

The current article presents the modeling and investigation of thermo-mechanical buckling behavior for the porous functionally graded (FG) plates of rectangular and skew geometry. In this article, the modified rule of mixture and power law distribution is incorporated in the Third order Shear Deformation Theory (TSDT) to establish the governing equations using principle of minimum potential energy (PMPE). Finite element meshing is introduced using four node rectangular elements to discretize the FG plate for stability analysis. The constituents of the FG plate are continuous and vary over the thickness in accordance with modified power-law. Porosity is associated as locally distributed density and estimated using modified power law. To ascertain the effective boundary restraints skewness to the FG plate is imposed via transformation matrix. The computation of the critical non-dimensional buckling load for the structures subjected to uni-axial compressive and different thermal loads is executed via Gauss numerical integration. The assessment of the present formulation is performed against the buckling parameter available in the reference literature. Stability characteristics is evaluated under three different temperature distributions. The impact of material compositions, different thermal load, porosity distributions and various other parameters on the stability characteristics of porous FG structures are thoroughly investigated.

Grading Threads. Exploiting Viscous Thread Instability for the additive fabrication of Functionally Graded Structures via sensor-adaptive robotic control

We present a novel computational fabrication method for the production of Functionally Graded Structures (FGS) via robotic control of Viscous Thread Instability (VTI). Of interest in several fields and at different scales of application, the fabrication of FGS is often relying on offline fabrication workflows and on stable material conditions. By introducing partial control in the process of spatial deposition of an extruded clay thread in a state of instability, our method extends the design and fabrication possibilities of VTI to the production of FGS. Traditionally exploited for the industrial production of not-graded two-dimensional nonwoven textiles or for surface treatments in design-related 3d printing applications, we frame VTI as the main design and fabrication driver for the computational fabrication of functionally graded clay volumetric structures. Without relying on predictive physical simulation models, our method relies on feedback information provided by sensing equipment in combination with an industrial 6 axis robotic manipulator integrated with a numerically controlled clay extruder. The sensed information is used to retroactively update the inputs of a computational model programmed to guide the robotic additive fabrication of user-defined functional volumetric gradients. We illustrate the main design- and fabrication-related parameters and a set of material experiments designed to validate the accuracy of our model. We present a set of fabricated outputs to illustrate the flexibility of the model to accommodate a variety of design intentions and, finally, we discuss its potential for further research involving cross-scalar and trans-disciplinary applications.

Electro-Elasto-Statics of porosity-gradient smart functionally graded plates with piezoelectric fibre-reinforced composite

Smart structures offer functional advantages over conventional composites through capabilities of material tailoring and controlled response under external actuation/sensing. The porosity induced in functionally graded (FG) materials due to manufacturing processes can be detrimental to the strength and durability characteristic of aerospace/automobile components. On the other hand, porosities act favourably for biomedical implants with blood circulation functionality in connecting tissues and stress shielding effect with compatibility between the natural and implant components. To accurately model smart porous FG structures under electrical and mechanical loads, a polynomial-based higher order shear and normal deformation theory (HOSNT) is utilized for the first time in this work. The governing equations are derived using the variational energy principle, and analytical solutions are obtained using Navier's solution method. The transverse shear stresses are obtained using a one-step stress recovery process. The influence of various porosity distribution models is studied on the bending response of smart porous FG plates. The effect of actuation voltage, porosity coefficient, material gradation index are critically assessed, and benchmark solutions for the class of problems are proposed. It is observed that stress response through thickness doesn't change monotonically with the change in porosity coefficient; instead, regions of higher and lower stresses are obtained with respect to the non-porous plate. Voltage-actuated FG plates are shown to have a steeper fall in stresses away from the piezo-layer compared to the conventional composites.

A new higher-order mixed four-node quadrilateral finite element for static bending analysis of functionally graded plates

In this paper, a new C0 four-node quadrilateral plate element (MiQ4) is proposed for the static bending analysis of functionally graded (FG) plates based on a C0 higher-order shear deformation theory. By introducing a quadratic shape function for higher-order terms and a constant shear result, which is eliminated at the element level, the transverse shear stresses are free on two surfaces of the plates. The present finite element model has high accurateness and a fast rate of convergence, especially for both thin and very thin plates. In addition, the proposed element is insensitive to distorted mesh, hence, it is compatible with the investigation of complex geometrical plates. Although the proposed element does not need any shear correction coefficients and selected or reduced integrations, the shear-locking phenomenon does not appear even for very thin plates. Therefore, the computation cost and time are reduced and the spurious deformation or hourglass modes are avoided. A large number of examples have been exhibited that help to validate the convergence rate, correctness, and reliability of the proposed element. Then the present element is applied for analysis of FG structures to demonstrate the potential applications of the present plate element. Significantly, the paper provides a good element that can be used in many areas of engineering for the design, testing, analysis, and optimization of complex structures to reduce the computation cost and time as well as increase the reliability of the numerical results.

Thermally induced fracture analysis of CNT reinforced FG structures with multiple discontinuities using XIGA

In this paper, the authors have employed XIGA to perform the fracture analysis of carbon nanotubes (CNT) reinforced functionally graded (FG) structures with discontinuities subjected to a coupled loading condition (thermo-mechanical load). For the first time, XIGA is used to analyse cracked CNT reinforced FG structures. The exponential rule is supposed to regulate the material property gradation in FG (which is made up of metal (Ti–6Al–4V) and ceramic (ZrO2)) structures. Several micromechanics models are utilized for evaluating the equivalent mechanical and thermal properties of CNTs (SWCNT and MWCNT) reinforced FG structure. To capture the discontinuity along the singular fields near the crack tip and the crack face, appropriate enrichment functions are used. Investigations are performed to estimate the effects of inclusions and holes on the SIFs of FG structures reinforced with CNT. Also, the effect of mechanical properties (Young’s modulus) of inclusion and percentage content of CNTs (SWCNT & MWCNT) on SIFs is explored. Furthermore, the authors have investigated the effect of different loading conditions on the SIFs.

Evaluation of Cu-Ti dissimilar interface characteristics for wire arc additive manufacturing process

PurposeThe purpose of this research is to show the characteristics of a Cu–Ti dissimilar interface produced by a wire arc-based additive manufacturing process. The purpose of this research was to determine the viability of the Cu–Ti interface for the fabrication of functionally graded structures (FGS) using the wire arc additive manufacturing (WAAM) process.Design/methodology/approachThis paper used the WAAM process with variable current vis-à-vis heat input to demonstrate multiple Ti-6Al-4V (Ti64) and C11000 dissimilar fabrications. The hardness and microstructure of the dissimilar interfaces were investigated thoroughly. The formation of Cu–Ti intermetallic at the Ti64/Cu fusion interface is been revealed by scanning electron microscopy and energy dispersive X-ray analysis, while X-ray diffraction was used to identify various Cu–Ti intermetallic phases. The effect of microstructure on interfacial sensitivity and hardness are also investigated.FindingsThe formation of CuTi intermetallic and the β-phase transformation in Ti-6Al-4V are found to be heat input dependent. The Cu diffusion length increases as the heat input for Ti64 deposition increases, resulting in a greater Cu–Ti intermetallic thickness. The Cu–Ti interface properties improve when the heat input is less than approximately 250 J/mm or the deposition current is less than 90 A. The microhardness ranges from 55 to 650 HV from the Cu-side to the interface and from 650 to 350 HV from the interface to the Ti-side. Higher current increases interface hardness, which increases brittleness and makes the interface more prone to interfacial cracking.Originality/valueNonlinear components are needed for a variety of extreme engineering applications, which can be met by FGS with varying microstructure, composition and properties. FGS produced using the WAAM process is a novel concept that requires further investigation. Despite numerous studies on Ti-clad Cu, information on Cu–Ti interface characteristics is lacking. Furthermore, the suitability of the WAAM process for the development of Cu–Ti FGS is unknown. As a result, the goal of this research article is to fill these gaps by providing preliminary information on the feasibility of developing Cu–Ti FGS via the WAAM process.

A Hybrid Level Set Method for the Topology Optimization of Functionally Graded Structures

This paper presents a hybrid level set method (HLSM) to design novelty functionally graded structures (FGSs) with complex macroscopic graded patterns. The hybrid level set function (HLSF) is constructed to parametrically model the macro unit cells by introducing the affine concept of convex optimization theory. The global weight coefficients on macro unit cell nodes and the local weight coefficients within the macro unit cell are defined as master and slave design variables, respectively. The local design variables are interpolated by the global design variables to guarantee the C0 continuity of neighboring unit cells. A HLSM-based topology optimization model for the FGSs is established to maximize structural stiffness. The optimization model is solved by the optimality criteria (OC) algorithm. Two typical FGSs design problems are investigated, including thin-walled stiffened structures (TWSSs) and functionally graded cellular structures (FGCSs). In addition, additively manufactured FGCSs with different core layers are tested for bending performance. Numerical examples show that the HLSM is effective for designing FGSs like TWSSs and FGCSs. The bending tests prove that FGSs designed using HLSM are have a high performance.

Analytical solution of stress in functionally graded cylindrical/spherical pressure vessel

For the exact solution of the stress in the functionally graded (FG) cylindrical/spherical pressure vessel, this paper presents a unified form of the basic equations of the FG hollow cylinder/spherical shell by introducing parameter, and then, the axial/spherical symmetry mechanical problems of FG hollow shells are studied under three different boundary conditions, respectively. Assume that the Young's modulus of the material changes with thickness distribution of cylinder/shell in the form of power functions and the value of Poisson’s ratio is constant, the analytical solutions of the displacement and stress of the FG hollow cylindrical/spherical pressure vessel are derived under different boundary conditions. By comparing the analytical solutions of the FG hollow cylinder/spherical shell obtained in this paper with the existing classical theoretical solutions and numerical solutions, the correctness of the analytical solution given in this paper is verified. In the numerical discussion, the distributions of displacement, radial stress and circumferential stress of the FG hollow cylinder/spherical shell under different gradient parameters and different size conditions are given, respectively. Finally, based on the difference numerical method, the stress distribution of FG hollow cylinder/spherical shell with the Young's modulus and Poisson's ratio along thickness distribution in the form of power functions is analyzed numerically. The results show that gradient parameter and geometric size have a great influence on the mechanical response of FG structure under different boundary conditions.

Bending analysis of functionally graded porous nanocomposite beams based on a non-local strain gradient theory

In the present work we study the static response of functionally graded (FG) porous nanocomposite beams, with a uniform or non-uniform layer-wise distribution of the internal pores and graphene platelets (GPLs) reinforcing phase in the matrix, according to three different patterns. The finite-element approach is developed here together with a non-local strain gradient theory and a novel trigonometric two-variable shear deformation beam theory, to study the combined effects of the non-local stress and strain gradient on the FG structure. The governing equations of the problem are solved introducing a three-node beam element. A comprehensive parametric study is carried out on the bending behavior of nanocomposite beams, with a particular focus on their sensitivity to the weight fraction and distribution pattern of GPLs reinforcement, as well as to the non-local scale parameters, geometrical properties, and boundary conditions. Based on the results, it seems that the porosity distribution and GPLs pattern have a meaningful effect on the structural behavior of nanocomposite beams, where the optimal response is reached for a non-uniform and symmetric porosity distribution and GPLs dispersion pattern within the material.

Geometrically exact beam element with rational shear stress distribution for nonlinear analysis of FG curved beams

Based on the geometrically exact beam theory, a first-order shear deformable curved beam element is developed for geometrically nonlinear analysis of functionally graded (FG) curved beams. In order to accurately predict the distribution of transverse shear stress, the stress equilibrium condition is introduced into the element formulation by using the mixed finite element method with displacements and internal forces as independent fields. The element nodal force vector and consistent tangent stiffness matrix for nonlinear iterative solution are obtained by going through a consistent linearization procedure. Numerical examples are presented to validate the present formulation. As indicated by the numerical results, the proposed element demonstrates a high level of solution accuracy and good applicability. Furthermore, using the proposed element, an investigation is conducted into the nonlinear stability of FG structures with different material distribution parameters, and the accuracy loss caused by unreasonable distribution of shear stress is discussed.

Free Vibrational Behaviour of Multi-Directional Porous Functionally Graded Structures

The free vibrational frequencies of a multi-directional functionally graded (FG) structure are investigated for the first time in this paper considering the influences of variable grading (power-law, sigmoid, exponential) and porosity distribution (even and uneven type). Also, the structural properties (Young’s modulus, density and Poisson's ratio) varied along with two different directions simultaneously, i.e., the longitudinal and transversional ones, respectively. The present multi-directional grading model of the FG structure is reconstructed mathematically for the numerical analysis by considering adequate state-space deformation kinematics with the help of higher-order displacement functions and shear stress continuity. The general motion equation of a multi-graded structure is expressed using Hamilton’s principle and the finite element method including the necessary porosity effect. Initially, model consistency is verified and the eigenvalues obtained in the analysis are compared with the ones found in the literature. The comparison also includes the directional grading effect on their frequencies. Further, the influence of different parameters, i.e., power exponents (nz and nx), aspect ratio, thickness ratio, geometry, end support conditions, curvature ratio, porosity index, porosity distribution and material grading patterns, on the vibration characteristics of the multi-directional FG structure is computed. The analysis of the numerical results confirms that material grading; porosity distribution pattern and other design parameters have a significant influence on the frequency response characteristics of a single/multi-directional porous FG structure.

Modeling and simulation of functionally graded flexoelectric micro-cylinders based on the mixed finite element method

The direct flexoelectricity in solid dielectrics, as an electromechanical mechanism coupling polarization and strain gradient, exhibits strong size dependence and structures associated (geometry or microstructure). In this work, a novel asymmetric micro-cylinder composed of functionally graded (FG) materials is designed to evaluate computationally the role of flexoelectricity in the electromechanical response. However, analytical solutions involving strain gradient elasticity and flexoelectricity make the universal coupling phenomenon in multiple fields difficult for such asymmetric graded structure. Based on the mixed finite element method (FEM), we introduce Lagrange multipliers to enforce the kinematic relationship between the displacement field and its gradient, so as to help understand the flexoelectric performance of the proposed FG micro-cylinder. Code verification as well as validation of the mixed FEM for the present FG structure is obtained by comparing numerical results with analytical solutions for a traditional composite micro-cylinder. The simulated results show that the designed FG configuration highlights the critical role of material composition and material distribution on the effective electromechanical response. At the same time, a reasonable gradient function can greatly improve the mechanical and electrical properties of materials. Our results suggest that computer simulations can help to understand and quantify the physical properties of flexoelectric devices.