Orthotropic Mechanical Properties Research Articles

Numerical simulation of the creep of a turbine blade made of a monocrystalline alloy

The article is devoted to the creep model of a monocrystalline alloy and the development of a methodology for identifying material parameters based on the results of physical experiments. A finite element analysis of the creep of a gas turbine engine blade was performed. Creep is one of the most dangerous types of deformation in the operating conditions of turbine blades. In the process of studying the problems of assessing the strength of turbine blades of aircraft engines and power plants, special attention should be paid to the study of stress redistribution during creep. The characteristics of the crystallographic structures of modern turbine blades have a very significant influence on the progress of the crack development process during engine operation. To date, turbine blades are manufactured by the method of single-crystal casting. This type of blade material structure is characterized by orthotropic mechanical properties. This study considers the steady-state creep model of an anisotropic heat-resistant single-crystal alloy with cubic symmetry. The authors carried out a numerical simulation of the material parameters using the well-known literary creep properties of single crystals. An algorithm is described that allows you to determine some creep characteristics of single crystals. The parameters of the given ratios can be obtained after conducting direct experiments, or based on micromechanical analysis, using the example of composite materials. The authors calculated the creep constants of a typical heat-resistant monocrystalline alloy as a result of the approximation of its creep curves, which were obtained experimentally. Based on the Norton-Bailey equation and using the Maple Release 2021.0 calculation complex, a graph of the dependence of the rate of creep deformation on the level of load applied to the material was plotted, and the minimum rate of deformation and creep constants were also determined. The results of the calculations were used for finite-element simulation of creep on the example of a solid-state model of a high-pressure turbine blade. Several series of calculations were carried out on the basis of the ANSYS Workbench complex, in particular, the calculation of the elastic problem when the blade is loaded by centrifugal forces, as well as the accumulation of creep deformations at different exposure times. Graphs of the change in equivalent stresses and creep deformations as a function of time are plotted.

Development of a geometric modeling strategy for the generation of representative unit cells in 2D braids

This article presents, tests and validates a method for generating representative unit cells of braided composites based on a geometrical approach. The method focuses on the geometry of the tows and uses surface minimization to obtain the minimal equivalent area of a central surface that is used for the generation of volumes and orthotropic mechanical properties of the tows. The homogenization of the yarns is solved using analytical equations and the homogenization of the cell is solved using a representative volume element technique. The robustness of the method is evaluated using a benchmark comparison with experimental and numerical results to validate the generated ge.ometry. The method is also tested and shown to be robust in modeling the geometry for several values of geometrical parameters of the tows without user intervention, including for configurations yielding a high cover factor.

An optimized hybrid finite element analyses - Artificial neural networks technique for estimating in-plane orthotropic mechanical properties of printed circuit boards

Explicitly modeling Printed Circuit Boards (PCBs) in Finite Element Analysis (FEA) is not practical due to the complex multi-component structure of PCBs. To overcome this complication, a PCB can be simplified and modeled as an orthotropic plate with equivalent mechanical properties that result in the same natural frequencies as the actual PCB. This research introduces an optimized hybrid technique combining FEA and Artificial Neural Networks (ANNs) to accurately estimate the equivalent in-plane orthotropic mechanical properties of PCBs. This study presents a systematic approach where natural frequencies obtained from FEA are used to train ANNs for predicting the equivalent representative mechanical properties. The research employs a rigorous optimization procedure involving various ANN configurations (i.e., different learning algorithms, activation functions, and number of hidden neurons) and training dataset sizes. To further ensure the reliability of the results, 10 cross-validation are carried out for each ANN configuration by employing dynamic data-splitting strategy, and all measures used for assessing the accuracy of the ANN predictions are based on averaged results for the 10 cross-validations. The accuracy of the ANN predictions is tested against both simulated and experimental data. The Mean Absolute Percentage Error (MAPE) is found to be about 4 % based on material properties against the simulated data, and about 1.2 % based on natural frequencies against the experimental data point. The results demonstrate superior predictive accuracy and efficiency compared to existing models, highlighting the potential of the proposed approach in advancing the reliability and performance of PCB mechanical property estimations.

Isotropic and orthotropic mechanical properties of in vivo mandible model: Assessment of computational modelling

This study assesses the various methodologies utilized in the literature for computational mandible modeling and their implications on research findings. Previous studies have explored diverse material properties for the mandible, whether modeled as a single entity, in pairs, or as multiple sub-regions. Within this framework, a finite element model of an intact mandible was created using sliced tomographic images to examine the dispersion of stress fields resulting from different sets of bone material properties sourced from specialized literature. This research introduces the methodology employed in mandible model development, strategies for achieving high precision, and the influence of mechanical properties. Through an evaluation of models proposed by different authors, significant dispersion was observed, leading to disparities ranging from 4.4% to 67.4% in stress field outcomes at the symphysis region. RMSE served as an estimator to assess the similarity between these models. The findings suggest that the Caraveo (2008) and Palka (2020) models exhibit notable convergence in predicting stress fields in the symphysis regions. By incorporating good modeling practices in the intact mandible model, a more reliable representation is ensured, laying the groundwork for future investigations involving nonlinear contact phenomena and topology optimization.

An artificial intelligence-based approach for identifying the in-plane orthotropic mechanical properties of electronic circuit boards

The finite element modeling of electronic boards is a challenging task due to the complexity of the multi-component board structure. Hence, it is acceptable to attain equivalent orthotropic in-plane mechanical properties and use them throughout the finite element analysis (FEA) simulations. This paper aims to present an artificial intelligence-based methodology, using the artificial neural networks (ANNs), to estimate the in-plane mechanical properties of the printed circuit boards (PCB). In this methodology, the ANN technique used FEA data to find the relationship between the first 10 natural frequencies and the mechanical properties, that is, modulus of elasticity, Poisson’s ratio and the shear modulus, of the test board. Subsequently, the experimentally derived natural frequency data is then imported to the ANN model to identify the equivalent orthotropic properties. The ANN-predicted properties are plugged back into FEA and provided natural frequencies and mode shapes that are in great match with experimental results.

Orthotropic mechanical properties of PLA materials fabricated by fused deposition modeling

Polylactic Acid (PLA) sample manufactured by fused deposition modeling (FDM) technique is typically assumed to be transversely isotropic without a thorough examination of its orthotropy in three-dimensional space. This study investigated the mechanical orthotropy of PLA samples with two air gap levels (0 mm and -0.05 mm) and various loading directions. Tensile strength and elastic modulus were experimentally measured and the Hill48 yield model and orthotropic elastic model were calibrated. Results revealed that the anisotropy induced by interlayer bond was more pronounced than that within layer. Introducing a -0.05 mm air gap remarkably reduced voids in printed samples, enhancing the stiffness and strength of tensile samples. It also delayed the transition of fracture modes in intra-layer samples as the filament angle increased from 0° to 90°, which shifted from filament breakage to combined fracture mode and subsequently to interface failure. Despite these improvements, the inherent anisotropy of FDM printed PLA materials remained due to the oriented molecular chains and insufficient chain diffusion. The study emphasizes the importance of orthotropic mechanical models, demonstrating their reliability through calibration with acceptable accuracy.

Simulation of cancer progression in bone by a virtual thermal flux with a case study on lumbar vertebrae with multiple myeloma

BackgroundTwo main problems examining the mechanism of cancer progression in the tissues using the computational models are lack of enough knowledge on the effective factors for such events in vivo environments and lack of specific parameters in the available computational models to simulate such complicated reactions. MethodsIn this study, it was tried to simulate the progression of cancerous lesions in the bone tissues by an independent parameter from the anatomical and physiological characteristics of the tissues, so to degrade the orthotropic mechanical properties of the bone tissues, a virtual temperature was determined to be used by a well-known framework for simulation of damages in the composite materials. First, the reliability of the FE model to simulate hyperelastic response in the intervertebral discs (IVDs) and progressive failure in the bony components were verified by simulation of some In-Vitro tests, available in the literature. Then, the progression of the osteolytic damage was simulated in a clinical case with multiple myeloma in the lumbar vertebrae. ResultsThe FE model could simulate stress-shielding and diffusion of lesion in the posterior elements of the damaged vertebra which led to spinal stenosis. The load carrying shares associated with the anterior half and the posterior half of the examined vertebral body and the posterior elements were estimated equal to 41 %, 47 % and 12 %, respectively for the intact condition, that changed to 14 %, 16 % and 70 %, when lesion occupied one third of the vertebral body. ConclusionCorrelation of the FE results with the deformation shapes, observed in the MRIs for the clinical case study, indicated appropriateness of the procedure, proposed for simulation of the progressive osteolytic damage in the vertebral segments. The future studies may follow simulation of tumor growth for various metastatic tissues using the method, established here.

Geomechanical modelling of ground surface deformation induced by CO2 injection at In Salah, Algeria: Three wells, three responses

This study investigates the ground surface deformation above three injection wells throughout CO2 injection between mid-2004 to early-2011 in the In Salah CO2 storage project at Krechba, Algeria. A coupled three-dimensional finite element model of three wells (KB501, KB502, and KB503) was developed. The model accounts for the CO2 diffusion in the reservoir and structural features including permeable fractures and faults, as well as the poroelastic deformation of the reservoir and overburden layers which result in the ground surface deformations during CO2 injection. The character of the ground surface deformation above each injection well was different, suggesting a different CO2 plume shape in the subsurface. An ellipse-shaped heave above KB501 indicates that the CO2 plume shape followed the anisotropic permeability in the reservoir, KB502’s double-lobe surface heave pattern is associated with the activation and pressurization of a vertical fault and finally, the elongated surface uplift pattern above KB503 is linked to the presence of permeable fractured zone in vicinity of the well, as indicated by seismic surveys. The two distinctive structural features in the vicinity of KB502 and KB503 were included in the numerical model, accounting for a hydraulically conductive fault in the caprock and a fractured zone in the reservoir, respectively. The observed surface deformation was utilised to tune the orthotropic mechanical properties of the fault and the fractured zones. The simulation results are in good agreement with the measured InSAR data. In addition, assigning anisotropic permeability to the reservoir plays a significant role in successfully simulating surface uplift patterns.

Determination of the Orthotropic Mechanical Elastic Properties of Gas Diffusion Layers for PEMFCs

One of the most important components of proton exchange membrane fuel cell is the gas diffusion layer (GDL), due to its position between the catalyst layers, where the electrochemical reactions take place, and the bipolar plates supplying the reactant gases. The GDL must have an optimal mechanical stiffness to ensure the transport of the different gases and the water produced by the fuel cell operation. Measuring the mechanical properties of the different GDLs available in the market require the development of specific methodologies due to their orthotropic behavior. This article aims to assess and create a database for selecting GDLs for specific applications and assisting engineers in fuel cell modeling. This study focuses on developing robust characterization methods to assess the different properties of GDLs in different directions: within the plane, along both the machine and transverse directions, and perpendicular to the plane. These tests allow to determine parameters like in-plane tensile and shear moduli, out-of-plane compression and shear moduli, and in-plane Poisson’s ratios. By examining a wide range of commercial specimens, including different types, area weights, hydrophobic treatments, manufacturing processes, and microporous layers, this study aims to provide a comprehensive analysis of the orthotropic mechanical properties of GDLs.

High-temperature fracture behavior of carbon fiber reinforced PEEK composites fabricated via fused filament fabrication

This study investigates the influence of temperature on the mechanical and fracture properties of carbon fiber reinforced (CF) polyetheretherketone (PEEK) composites, with a specific focus on different layer heights used in the additive manufacturing process. Tensile and compact tension fracture tests were conducted at varying temperatures to evaluate the orthotropic mechanical properties and crack growth resistance curves, respectively. The key findings underscore the pronounced orthotropic mechanical behavior in additively manufactured CF-PEEK composites, showing substantial variations of up to 50% in Young's modulus and yield strength across orientations. Additionally, as test temperatures increase, crack initiation becomes easier, indicating reduced crack resistance at elevated temperatures. Notably, the effect of layer height on initiation toughness is relatively minor compared to temperature. Moreover, the study reveals that fracture energy for crack growth is less temperature-sensitive but depends on layer height, with larger defects in taller layers resulting in decreased damage resistance. These findings stress the importance of considering the distinct sensitivities of initiation and steady-state fracture energies to temperature, emphasizing the critical role of effective fracture toughness in evaluating material resistance to high-temperature fractures. These observations contribute to our understanding of the mechanical and fracture behavior of CF-PEEK composites under high operating temperatures. This understanding facilitates the optimization of their manufacturing processes and their application in various industries such as aerospace.

Delamination Buckling of Composite Conical Shells Under External Pressure

Airframe construction in conical form is the most desired shape of flight hardware due to their low drag profileand are located at the fore-end region of flight vehicles encountering high drag loads. Owing to their tailoringcapability, materials with orthotropic mechanical properties are preferred choice. Delamination defects formed inthem while manufacturing or when subjected to loads would unfavorably influence the mechanical performanceof the orthotropic airframe. In the current work, FE simulation of delamination which is embedded in orthotropiccone shaped shells under external pressure load is performed as per the method cited in published literature. A layer wise element based on shell theory has been used and the effect of delamination size and its through the thickness position on the mechanical performance of the cone shaped shell is investigated. Circumferential and rectangular shapes of defects have been simulated. The investigation is performed for metal and composite materials with 3 types of stacking sequences generally used in practical designs. Verification of the procedure is carried out by equating with the procedure cited in published studies on shells of thin orthotropic cylinders. The eigen value of the first mode is taken as the critical buckling factor under external pressure. The buckling factor of the delaminated cone is normalized with the buckling factor of the ideal cone. The normalized buckling factor is showed graphically with the normalised defect size. Global, as well as local buckling and also symmetric as well as asymmetric buckling shapes, are observed in the results of the simulation. Shift from global mode to local mode of buckling is also observed in certain cases. Drastic reduction in buckling capability with the local mode is observed when the defect location is close to the surface and more prominent for an outer surface case.

Bio-inspired design, mechanical and mass-transport characterizations of orthotropic TPMS-based scaffold

To obtain porous scaffolds with bionic anisotropic structures similar to human bone, the orthotropic triply periodic minimal surface (TPMS)-based structures were proposed in this study. The orthotropic Schoen’s I-WP (AP) and orthotropic Gyroid (AG) were designed based on isotropic I-WP (IP) and isotropic Gyroid (IG). The four scaffolds with 70% porosity were fabricated by electron beam melting, and then were scanned by microcomputer tomography to evaluate their manufacturability. The anisotropic degrees of elastic properties of the scaffolds were calculated using the homogenization approach. Compression test along the three orthogonal directions was conducted on the scaffolds to analyze their mechanical properties. Computational fluid dynamics was performed to the scaffolds along the three orthotropic directions to characterize their mass transport properties. Results show that AP and AG possess irregular pores and perform well in manufacturability compared with IP and IG. Similar to human bone, AP and AG exhibit orthotropic mechanical properties and mass transport performances. Furthermore, the elastic modulus ratio of AG along the three orthogonal directions is close to the value of cancellous bone. The designed scaffolds are advantageous for their bionic mechanical and mass transport properties of human bone and can be the proper candidates in bone graft surgery.

Study on Free Vibration Analysis of a Rotating Fibre-Graphene-Reinforced Hybrid Polymer Composites Pre-Twist Shel

The present work aims to develop a computational procedure for investigating the vibration behaviour of pre-twisted laminated composite shell containing graphene inclusions in their matrix. According to nanoscopic empirical equations, graphene's mechanical properties are determined by its size dependence. It has been demonstrated that the orthotropic mechanical properties of composite laminates made from carbon fibres and hybrid matrix can be evaluated. Based on pre-twist and geometric configurations, finite element methods have been used to model hybrid materials shells that include carbon fibre, graphene, and graphene-fibre reinforcement. As part of the validation process, the proposed method is compared with other methods when possible. Finally, the vibrational behaviour of the composite shell is extracted by imposing a twisted angle on a cantilever boundary condition. An analysis of vibrations for each configuration is presented in this paper, as well as the effects of graphene inclusions on natural frequencies. As graphene volume fractions in the matrix increase, the natural frequencies of every mode also increase. When the hub radius and rotational speed are increased, the frequency parameter increases with an increase in graphene volume in the hybrid polymer composite pre-twisted shell.

Design of a functionally graded porous uncemented acetabular component: Influence of polar gradation.

The functionally graded porous metal-backed (FGPMB) acetabular component has the potential to minimize strain-shielding induced bone resorption, caused by stiffness mismatch of implant and host bone. This study is aimed at a novel design of FGPMB acetabular component, which is based on numerical investigations of the mechanical behavior of acetabular components with regard to common failure scenarios, considering various daily activities and implant-bone interface conditions. Both radial and polar functional gradations were implemented, and the effects of the polar gradation exponent on the failure criteria were evaluated. The relationships between porosity and orthotropic mechanical properties of a tetrahedron-based unit cell were obtained using a numerical homogenization method. Strain-shielding in cancellous bone was relatively lesser for the FGPMB than solid metal-backing. Few nodes around the rim were susceptible to implant-bone interfacial debonding, irrespective of the polar gradation exponent. Although the most favorable bone remodeling predictions were obtained for a polar gradation exponent of 0.1, a sudden change in the porosity was observed near the rim of FGPMB. Bone remodeling patterns were similar for polar gradation exponent of 5.0 and solid metal-backing. Moreover, the volumetric wear was maximum and minimum for polar gradation exponents of 0.1 and 5, respectively. Furthermore, the micromotions of different polar gradation exponents were within a range (20-40 μm) that might facilitate bone ingrowth. Considering common failure mechanisms, the FGPMB having polar gradation exponents in the range of 0.1-0.5 appeared to be a viable alternative to the solid acetabular component, within which a gradation exponent of 0.25 seemed the most appropriate design parameter.

Investigating the Poisson Ratio of 3D Printed Concrete

Poisson’s ratio, defining the lateral to longitudinal strain of a material under uniaxial load, is an extensively used material property in engineering analysis and design. For conventionally cast concrete, an isotropic static Poisson ratio typically ranges between 0.15 to 0.25. However, no ratio has been established for 3D printed concrete, and is currently widely assumed to be 0.2 and isotropic in computational modelling applications. This layer-wise additive manufacturing technology is notorious for yielding orthotropic mechanical properties due to the presence of weak interlayer regions at the structural level and elongated oblate voids at the material level. This study therefore aims to characterise the static Poisson ratio of printed concrete. Specimens were prepared from a printed element and uniaxially tested both parallel and perpendicular to the printing direction. Digital image correlation technology was employed to facilitate the capturing of specimen strains, followed by micro-computed tomography scans to determine void topography. The results indicate larger Poisson ratios apply for 3D printed concrete compared to its cast counterpart; up to 17 and 33% increases were obtained when printed specimens were tested perpendicular and parallel to the printing direction, respectively. This orthotropic behaviour is ascribed to the oblate voids present in the printed specimens.

Comparing structural models of linear elastic responses to bending in inosculated joints

Key messageMechanical models of inosculations benefit from moderate geometric detail and characterisation of the structurally optimised area of interwoven tension-resistant fibres between the branches.Living architecture is formed by shaping and merging trees, often in combination with non-living technical elements. These structures often employ the mechanical and physiological adaptations of living trees to support structural loads. Designed and vernacular buildings utilise inosculations to redistribute forces, redirect growth, and provide redundancy. Mechanical models of inosculations in living architecture must be built according to the adaptations available to the tree. Here, mass allocation and fibre orientation are examined. Under typical gravity loads, a zone at the top of the inosculation is subject to tension. This is of particular interest because a trade-off in fibre orientation between mechanical and physiological optimisation is necessary. In tree forks, this results in specifically adapted interwoven fibres. In this study, Finite Element Analysis (FEA) is used to develop different mechanical models to fit bending experiments of four Salix alba inosculations, comparing the models’ accuracy in replicating rotations in the joint. Nine models were developed. Three levels of detail of mass allocation are considered for global isotropic (3 models) and orthotropic (3 models) mechanical properties as well as a model including the interwoven tension zone, a model of local branch and trunk orthotropy, and a model combining these two localised features. Results show significant accuracy gains come from moderate geometric accuracy and consideration of the tension-zone optimisation. The construction of the tension zone in FEA is simple and applicable to natural and artificially induced inosculations.

On the effects of orthotropic materials in flutter protection of wind turbine flexible blades

Decarbonization requirements have extended the use of wind turbines by orders of magnitude. Due to their high stiffness-to-weight ratio, composite materials have been widely used for manufacturing the turbine blades in the recent years. As a consequence of the orthotropic mechanical properties of these materials, the structural behavior of the blade is conditioned by the orientation of the fibers. This article gives a general idea of the benefits of optimizing the composite material ply angle. Along the paper, two different structures are analyzed, a quasi-isotropic material and a structure with oblique fibers. The analysis is conducted using a reduced order model solver which couples a beam element structural solver with the blade element momentum and Theodorsen pitching airfoil theories. The solvers are validated, and then, the flutter conditions are obtained and used to limit the whole operation curve for both blades. The oblique layup structure is evidenced to increase the critical wind velocity by 10% for a defined control law and electrical system. Therefore, the importance of a correct structural analysis is demonstrated to be crucial in the design and manufacturing of the following generation of wind turbine blades.

Anisotropic cyclic plasticity modeling for additively manufactured nickel‐based superalloys

AbstractThe additively manufactured materials show anisotropic mechanical properties. In the present paper, a constitutive model for a nickel‐based superalloy made by selective laser melting was established to characterize cyclic mechanical behaviors under multiaxial loading conditions. Detailed material tests revealed that the effects from the building orientation decrease with multiaxial cyclic loads. A cyclic constitutive model based on the Hill criterion was introduced for the superalloy and considered the orthotropic mechanical properties depending on loading cycles. The computation confirms the model can reasonably simulate the cyclic elastic‐plastic behavior under non‐proportional complex loading conditions and provides an applicable method for engineering applications.

Multiple elastic or rigid line inclusions in a multilayered orthotropic solid

This paper studies the problem of multiple line inclusions in a non-homogeneous medium. The formulation and solutions for rigid line inclusions and homogeneous medium are special cases when the stiffness values of the inclusions are infinite and the non-homogeneity of the material vanishes. The model built in this study is capable of dealing with any material non-homogeneity (material properties vary continuously or in step-wise form), orthotropic mechanical properties, isotropic mechanical properties, and any number of parallel or collinear inclusions. More importantly, the inclusions are not limited to rigid (they can be elastic). Dependence of the inclusion tip fields on the strain intensity factor is given in closed form. Numerical results are given for the situations of mechanical load as well as thermal load applied in the medium.

Numerical Prediction of Failure in Unidirectional Fiber Reinforced Composite

Fiber-reinforced polymer composites exhibit orthotropic mechanical properties and particularly low strength in the out-of-plane direction. The use of classical failure criteria that consider transverse isotropy to evaluate these composite materials implies an overestimation of their out-of-plane strength, which could lead to a nonconservative and even catastrophic design. The Molker failure criteria developed for orthotropic materials consider the LaRC05 failure modes as a basis, with two additional failure modes for the out-of-plane direction of noncrimp fiber (NCF)-reinforced composites. Given the similarity in configuration and orthotropic behavior of unidirectional fiber fabric reinforced composites to NCF-reinforced composites, Molker failure criteria are implemented and applied in this research to determine the initiation of out-of-plane failure in unidirectional fiberglass fabric composites. The criteria are programmed in the form of a module coupled to a constitutive model available in a finite element method (FEM) package. Then, the mechanical properties and failure parameters of the unidirectional fiber-reinforced composite are determined. Model validation is accomplished by comparing numerical and experimental results of out-of-plane failure in a corrugated panel. In addition, several failure criteria used in unidirectional fiber-reinforced composite that consider transverse isotropy are evaluated. The results of critical load at the onset of transverse out-of-plane failure obtained by using the Molkerorthotropic criterion prove to be superior in accuracy compared to those obtained with the criteria commonly applied to this type of materials.