Distribution Of Material Properties Research Articles

Physics-guided machine learning for 3-D quantitative quasi-static elasticity imaging

We present a 3D extension of the Autoprogressive Method (AutoP) for quantitative quasi-static ultrasonic elastography (QUSE) based on sparse sampling of force-displacement measurements. Compared to current model-based inverse methods, our approach requires neither geometric nor constitutive model assumptions. We build upon our previous report for 2D QUSE and demonstrate the feasibility of recovering the 3D linear-elastic material property distribution of gelatin phantoms under compressive loads. Measurements of boundary geometry, applied surface forces, and axial displacements enter into AutoP where a Cartesian neural network constitutive model (CaNNCM) interacts with finite element analyses to learn physically consistent material properties with no prior constitutive model assumption. We introduce a new regularization term uniquely suited to AutoP that improves the ability of CaNNCMs to extract information about spatial stress distributions from measurement data. Results of our study demonstrate that acquiring multiple sets of force-displacement measurements by moving the US probe to different locations on the phantom surface not only provides AutoP with the necessary information for a CaNNCM to learn the 3D material property distribution, but may significantly improve the accuracy of the Young’s modulus estimates. Furthermore, we investigate the trade-offs of decreasing the contact area between the US transducer and phantom surface in an effort to increase sensitivity to surface force variations without additional instrumentation. Each of these modifications improves the ability of CaNNCMs trained in AutoP to learn the spatial distribution of Young’s modulus from force-displacement measurements.

Dynamical analysis of spinning functionally graded pipes conveying fluid with multiple spans

In this paper, a dynamical model of spinning multi-span pipes conveying fluid is proposed and the transverse natural and resonant frequencies and mode characteristics of such system are explored. The pipe body is considered to be composed of functionally graded materials (FGMs), in which a power law is used to govern the distribution of material properties along the pipe wall thickness. The partial differential equations (PDEs) governing two transverse motions of the pipe are derived by the extended Hamilton principle, in which the contributions of the FGM and intermediate supports are highlighted. The PDEs are discretized by the Galerkin procedure and the eigensystem theorem is applied to find the numerical solutions. The results show that various frequency characteristics can be attainable by use of different materials and mixing patterns. Attachments of intermediate supports can heighten the rigidity and improve the stability of spinning FG pipes conveying fluid, which are consequently used as “stabilizers” for the slender drill strings. Also, the mode characteristics of different spans will determine the locations of vibration amplitude of the pipes.

Assessment of the multifactorial causes of atypical femoral fractures using a novel multiscale finite element approach.

Atypical femoral fracture (AFF), which is a low energy fracture in the subtrochanteric or diaphysis region of the femur, has multifactorial causes that span macro- to microscale mechanisms including femoral geometry, cortical bone composition and structure. However, the extent of individual and combined influence of these factors on AFF is still not well understood. As a result, the aim of this study is to develop a multiscale fracture mechanics-based finite element modeling framework that is capable of quantifying the individual and combined influence of macroscale femoral geometrical properties as well as cortical bone microscale material properties and structure on AFF. In this study, three different femoral geometries with two different cortical bone microstructures, and two different material property distributions were investigated by first determining the critical AFF locations in the femur using macroscale stress analysis and then performing coupled macro-microscale fracture simulations. The simulation results showed that femoral geometry led to substantial differences in crack growth independent of cortical microstructure and tissue level material properties. The results suggest that multiple femoral geometrical properties, including neck-shaft angle and curvature, may contribute to the fracture behavior at AFF sites rather than a single macroscale geometrical feature. Osteonal area had a significant effect on microcrack propagation at AFF sites independent of microscale material property distribution and femoral geometry. In addition, cortical bone tissue level material heterogeneity improved the fracture resistance independent of femoral geometry and cortical microstructure. In summary, the computational approach developed in this study identified the individual, combined, and relative influence of multiscale factors on AFF risk. The new framework developed in this study could help identify the governing multiscale mechanisms of AFF and bring additional insight into the possible association of long-term bisphosphate treatment with AFF.

Reliability-based robust design optimization for torque ripple reduction considering manufacturing uncertainty of interior permanent magnet synchronous motor

This study performed reliability-based robust design optimization (RBRDO) of stator and rotor shape of the IPM type electric motor to reduce the torque ripple considering uncertainties. A metamodel based on the design of experiments results, which was calculated by using 2-D electromagnetic finite element analysis, was used to calculate manufacturing uncertainties and material property distribution. As a result, the mean torque ripple of the optimum electric motor design was reduced by 56.4 % and the robustness was increased by 61.8 % compared with the initial design. The RBRDO design was compared with the designs of deterministic design optimization and reliability-based design optimization, and it was shown that, by using the RBRDO method, the optimum IPMSM can be designed to satisfying not only the minimum torque ripple but also the robustness and the reliability of output torque and torque ripple.

Fracture path interaction of two adjacent perforations subjected to different injection rate increments

During the fracturing of shale gas reservoirs, the injection rate and its variation affect the fracture propagation path and fracture connectivity between two adjacent perforations. To reveal the interaction mechanism of injection rate change on hydraulic fracture propagation of adjacent perforations, an extended finite element method (XFEM) was employed for simulating the fracture propagation and interactions between adjacent hydraulic fractures under different injection rate increments. Considering the heterogeneity of rock minerals and based on the results of shale mineral composition analysis via X-ray diffraction (XRD), a code segment was written in Python to establish a computational network model with a random distribution of different material properties. Acoustic emission (AE) data extraction and fracture location during the process of fracture propagation were realised using MATLAB programming. Simulation results revealed that the closer the injection rate increments in adjacent perforations, the greater the compressive stress between the perforations. Variations in the pressure difference and fracture width difference between the two perforations dynamically reflect their interactions; both anisotropy and stress shadow determine the fracture propagation path. This study provides a good technical basis for fracture design optimisation.

Centrosymmetric equilibrium of nested spherical inhomogeneities in first strain gradient elasticity

The first strain gradient linear elasticity theory (FSGLET) is invoked to study an inhomogeneity problem. In the setting of this centrosymmetric problem, a set of concentric hollow spheres made of different materials is considered to serve as a model for a multi-coated nanometer-sized particle which in turn can be introduced as a representative volume element (RVE) of a nanocomposite. Perfect bonding is assumed between each layer of the RVE, and this system is subjected to uniform internal and external pressures. In the context of the FSGLET, the boundary value problem (BVP) for this model is formulated rigorously in spherical coordinates and its solution is obtained by means of analytical and numerical techniques. Employing the solutions of this BVP, we examine the important cases of a two-phase RVE consisting only of filler and matrix phases and a three-phase RVE where a homogeneous or a functionally graded interphase is also taken into account. We determine the associated elastic fields inside the RVE for each of these cases to study the impact of size effects, presence or absence of an interphase and its material properties distribution on the elastic fields variations. Furthermore, based on a simple and natural definition for the effective bulk modulus of the RVE, this effective modulus is calculated in each of the aforementioned cases at different filler volume fractions and characteristic lengths, and relevant comparisons are made.

FSI analysis and simulation of flexible blades in a Wells turbine for wave energy conversion

In this paper a preliminary design and a 2D computational fluidstructure interaction (FSI) simulation of a flexible blade for a Wells turbine is presented, by means of stabilized finite elements and a strongly coupled approaches for the multi-physics analysis. The main objective is to observe the behaviour of the flexible blades, and to evaluate the eventual occurrence of aeroelastic effects and unstable feedbacks in the coupled dynamics. A series of configurations for the same blade geometry, each one characterized by a different material and mechanical properties distribution will be compared. Results will be given in terms of total pressure difference, supported by a flow survey. The analysis is performed using an in-house build software, featured of parallel scalability and structured to easy implement coupled multiphysical systems. The adopted models for the FSI simulation are the Residual Based Variational MultiScale method for the Navier-Stokes equations, the Total Lagrangian formulation for the nonlinear elasticity problem, and the Solid Extension Mesh Moving technique for the moving mesh algorithm.

Bending analysis of thick functionally graded piezoelectric rectangular plates using higher-order shear and normal deformable plate theory

In this paper, bending-stretching analysis of thick functionally graded piezoelectric rectangular plates is studied using the higher-order shear and normal deformable plate theory. On the basis of this theory, Legendre polynomials are used for approximating the components of displacement field. Also, the effects of both normal and shear deformations are encountered in the theory. The governing equations are derived using the principle of virtual work and variational approach. It is assumed that plate is made of piezoelectric materials with functionally graded distribution of material properties. Hence, exponential function is used to modify mechanical and electrical properties through the thickness of the plate. Finally, the effect of material properties, electrical boundary conditions and dimensions are investigated on the static response of plate. Also, it is shown that results of the presented model are close to the three dimensional elasticity solutions.

On the Numerical Prediction of Process-Dependent Properties of Current High-Performance Materials with Material Model *MAT_254 in LS-DYNA

Over the last years, the forecast quality in production and especially (cold) forming simulations has reached a high level at least for standard materials. It has become state-of-the-art to take the results of these process simulations into account e.g. for crashworthiness analyses. For most of the currently used high-performance materials, however, the manufacturing processes do not only result in plastic deformation and thinning of the parts. There usually is a thermal component to these processes, which significantly influences the microstructure of the material and results in a spatial distribution of material properties within the final part. In order to predict the later behavior of the part with the same quality as for standard materials and standard processes, the virtual process chain has to be closed and material models have to be used that are able to simulate the microstructure evolution during the process. The press-hardening of the manganese-boron steel grade 22MnB5 is, for example, a standard in automotive industry. For this material FEM software for process simulation tools like LS-DYNA were extended in the past to take the microstructure evolution into account. The implemented material models are tailored for this certain alloy and process. To ensure the usability of the simulation tool the material models were generalized. In LS-DYNA, material model *MAT_GENERALIZED_PHASECHANGE (*MAT_254) has been devised to serve this purpose. Core of the model is a phase evolution table that takes into account up to 24 individual phases and consequently defines up to 552 possible phase transformations, not all of which have to be defined. The appropriate transformation law for each of the phase changes can be chosen from a list of generic phase change mechanisms. Due to its relatively flexible input structure and generality of the implementation, the model has been successfully used for different processes such as press-hardening, welding, additive manufacturing, and heat treatment, and for different materials, such as ultra-high strength steels, aluminum 6xxx alloys and titanium. This contribution will introduce the material formulation in detail and show the recent extensions based on the microstructure evolution of titanium.

Free Vibration Analysis of Simply Supported P-FGM Nanoplate Using a Nonlocal Four Variables Shear Deformation Plate Theory

Abstract This paper shows an analysis of the free vibration of functionally graded simply supported nanoplate. The nonlocal four variables shear deformation plate theory is used to predict the free vibration frequencies of functionally graded nanoplate simply supported using non-local elasticity theory with the introduction of small-scale effects. The effect of the material properties, thickness-length ratio, aspect ratio, the exponent of the power law, the vibration mode is presented, the current solutions are compared to those obtained by other researchers. Equilibrium equations are obtained using the virtual displacements principle. P-FGM Power law is used to have a distribution of material properties that vary across the thickness. The results are in good agreement with those of the literature.

Innovative methods for random field establishment and statistical parameter inversion exemplified with 6082-T6 aluminum alloy

This paper aims to eliminate the disharmony between simulation and experiment, and takes the mechanical properties of 6082-T6 Al alloy as an example. In order to obtain the equivalent distribution of material properties after considering the randomicity of materials, a new inversion method combining with stochastic finite element method (SFEM) is proposed. Besides, the discrete random field in SFEM is established by an innovative method to overcome some discretization difficulties in conventional methods. In summary, the generic methods proposed in this study can give a new solution for the correlation of meso-structure and macro-performance in computational materials science.

Three-phase-lag thermoelastic heat conduction model with higher-order time-fractional derivatives

In the last few years, the theory of fractional calculus has been successfully used in thermoelasticity theories and many models of thermoelasticity with fractional order are established by several authors. In the present article, a new model of three-phase-lag thermoelastic heat conduction of higher-order time-fractional derivatives has been derived based on fractional calculus. Using the approach of the Taylor series expansion of time-fractional order developed by Jumarie (Comput Math Appl 59:1142, 2010), an alternative construction model is established extending Ezzat and others (Arch Appl Mech 82:557, 2012) and Roychoudhuri (J Therm Stress 30:231, 2007) models. This new model includes high-order time-fractional derivative approximations of three-phase-lags in the heat flux vector, the temperature gradient and in the thermal displacement gradient. We applied the resulting formulation to an infinite non-homogeneous orthotropic thermoelastic functionally graded medium having a spherical cavity with a power-law distribution of material properties along the radial direction. The effects of high-order time-fractional derivative parameters and non-homogeneity index on various distributions are discussed in detail and represented graphically and tabular forms. Finally, to illustrate the validity and accuracy of the proposed model, a comparison was made with various previous models, which are considered as special cases of our model.

Predictions of material properties in cold-rolled austenitic stainless steel tubular sections

Material properties in cold-rolled stainless steel members are significantly different from those in annealed sheets (e.g. considerable enhancement in 0.2% proof stress), which provides a potential to reduce the initial cost of stainless steel structures in the design stage. This study is aimed at proposing reasonable predictive formulas for the enhanced material properties in cold-rolled stainless steel tubular sections. A total of 130 tensile coupons were extracted from three types of material statuses (i.e. the coil, the circular hollow section and the square/rectangular hollow section) occurred in four cold-rolling production routes. Tensile coupon tests were then conducted to illustrate the change of material properties from coils to square/rectangular hollow sections (SHS/RHSs) as well as the detailed distributions of material properties in cross-sections. Based on test data, predictive formulas were developed for all material parameters in cold-rolled stainless steel hollow sections according to the “through thickness averaged plastic strain” method originally proposed by Gardner's group in Imperial College London. The predictions of the proposed formulas were evaluated using the test results in this study and in existing literature. Comparisons indicate that proposed models provide not only accurate predictions for the key material properties (e.g. the 0.2% proof stress, the 1% proof stress and the ultimate tensile strength), but also reasonable predictions for full-range stress-strain curves in cold-rolled stainless steel hollow sections. The predictions of the proposed models can be used in finite element analysis and advanced design methods for cold-rolled stainless steel hollow sections.

A numerical investigation on ultrasonic bulk wave propagation features in functionally graded plates

The goal of this research is to numerically look for a proper feature for functionally graded materials mechanical property distribution function evaluation based on through transmitted ultrasonic bulk wave amplitude variation. A numerical approximation called homogenous layers approximation is introduced and employed for wave propagation formulation in functionally graded plate, followed by finite element utilization for verification. As the amplitude of the propagated ultrasonic wave is affected by acoustic impedance and wave divergence angle variation in the functionally graded material plate thickness, while neglecting the attenuation phenomenon, numerical investigation has been performed in order to quantify the contribution of each mechanism on the wave amplitude behavior. One-dimensional investigations, using homogenous layers approximation and finite element method, show that the final value of the wave amplitude is the same for all functionally graded material property distribution function power index, while two-dimensional results, obtained from finite element method, provide a suitable amplitude variation manner based on the wave divergence angle variation in functionally graded material thickness direction. The final results shows that it is possible to calibrate the received wave amplitude distribution on the receiving side of the plate, in a through transmission test, for the material property distribution function power index evaluation. Moreover, the concept of functionally graded material ultrasonic shoe is introduced, suitable for beam focusing applications instead of expensive phased array systems.

Isogeometric size optimization of bi-directional functionally graded beams under static loads

This paper is firstly presented to deal with the material optimization for the compliance minimization of bidirectional functionally graded (BFG) structures under a static load. In this approach, the distribution of the BFG material properties is described by two-dimensional Non-Uniform Rational B-spline (NURBS) functions. Meanwhile, one dimensional NURBS basis functions are used to represent the exact structural geometry and approximate the unknown solution in finite element analysis (FEA). In which, design variables are the ceramic volume fraction values at control points through the x and z directions constructed by isogeometric analysis (IGA) method. Differential evolution (DE) algorithm is chosen as a tool for solving the optimization problem. By using two-dimensional NURBS functions, the obtained optimum material distributions are illustrated. In order to investigate the effectiveness and reliability of the proposed approach, the BFG Timoshenko beam is considered. The numerical solutions gained by the proposed method are verified by comparing with those of published ones. Several numerical examples are performed to search the optimal material distribution of the BFG beam with different parameters consisting of ceramic volume fraction constraint, boundary condition and the length-to-thickness ratio (L/H). Additionally, optimum results are achieved to be beneficial for the fabrication of BFG beams.

Free vibrations and static analysis of functionally graded sandwich plates with three-dimensional finite elements

A three-dimensional modelling of free vibrations and static response of functionally graded material (FGM) sandwich plates is presented. Natural frequencies and associated mode shapes as well as displacements and stresses are determined by using the finite element method within the ABAQUS™ code. The three-dimensional (3-D) brick graded finite element is programmed and incorporated into the code via the user-defined material subroutine UMAT. The results of modal and static analyses are demonstrated for square metal-ceramic functionally graded simply supported plates with a power-law through-the-thickness variation of the volume fraction of the ceramic constituent. The through-the-thickness distribution of effective material properties at a point are defined based on the Mori-Tanaka scheme. First, exact values of displacements, stresses and natural frequencies available for FGM sandwich plates in the literature are used to verify the performance and estimate the accuracy of the developed 3-D graded finite element. Then, parametric studies are carried out for the frequency analysis by varying the volume fraction profile and value of the ceramic volume fraction.

Application of uncertainty quantification techniques to ductile damage predictions in the third Sandia Fracture Challenge

This report documents predictions in response to the third Sandia Fracture Challenge (Kramer et al. in Int J fract, 2019) that employs 3D component built with additive manufacturing processes. These predictions employ a modeling and simulation framework that supports uncertainty quantification by rigorous statistical methods and fast-running surrogate models. This work introduces a novel ductile damage formulation supported by recent experimental observations. This report details a calibration process that updates prior material property distributions to posterior distribution by aligning distributions of computational experiments to measurements. Finally, we discuss in detail the assumptions (with rationales) and techniques employed to set-up the challenge analyses and to process these results. Blind predictions of the challenge geometry align with global measurements in the elastic and plastic regimes. There is less agreement after the onset of ductile failure, and this lack of agreement is discussed at the end of the report. Local measurements show additional variability not captured by the statistical processes. Results in this study support the use of existing continuum-scale material models for additively manufactured components.

Effect of Volume Element Geometry on Convergence to a Representative Volume

To accurately simulate fracture, it is necessary to account for small-scale randomness in the properties of a material. Apparent properties of statistical volume element (SVE) can be characterized below the scale of a representative volume element (RVE). Apparent properties cannot be defined uniquely for an SVE, in the manner that unique effective properties can be defined for an RVE. Both constitutive behavior and material strength properties in SVE must be statistically characterized. The geometrical partitioning method can be critically important in affecting the probability distributions of mesoscale material property parameters. Here, a Voronoi tessellation-based partitioning scheme is applied to generate SVE. Resulting material property distributions are compared with those from SVE generated by square partitioning. The proportional limit stress of the SVE is used to approximate SVE strength. Superposition of elastic results is used to obtain failure strength distributions from boundary conditions at variable angles of loading.

On the use of heterogeneous thermomechanical and thermophysical material properties in finite element analyses of cast components

Cast components generally show a heterogeneous distribution of material properties, caused by variations in the microstructure that forms during solidification. Variations caused by the casting process are not commonly considered in structural analyses, which might result in manufacturing of sub-optimised components with unexpected in-use behaviour. In this paper, we present a methodology which can be used to consider both thermomechanical and thermophysical variations using finite element analyses in cast components. The methodology is based on process simulations including microstructure modelling and correlations between microstructural features and material properties. Local material data are generated from the process simulation results, which are integrated into subsequent structural analyses. In order to demonstrate the methodology, it is applied to a cast iron cylinder head. The heterogeneous distribution of material properties in this component is investigated using experimental methods, demonstrating local variations in both mechanical and physical behaviour. In addition, the strength-differential effect on tensile and compressive behaviour of cast iron is considered in the modelling. The integrated simulation methodology presented in this work is relevant to both design engineers, production engineers as well as material scientists, in order to study and better understand how local variations in microstructure might influence the performance and behaviour of cast components under in-use conditions.

Approach to qualification using E-PBF in-situ process monitoring in Ti-6Al-4V

Traditional design and qualification methodologies for parts manufactured by traditional methods are being applied to Additive Manufacturing (AM) without understanding the nuances of the machines. While mapping process variables and tracking build data is helpful, some variables such as build geometry, support structure, and part melt order have not been researched in depth. Changing these variables can result in significant variations in material properties and defect structure such that the process appears to be unreliable compared to traditional manufacturing. Therefore, this research focuses on the need to understand the effects of overlooked variables such as melt order and nested geometry on the distribution of defects and bulk material properties in Ti-6Al-4 V alloy builds manufactured using the Arcam AB ® electron beam powder bed fusion process11Description of equipment vendor, Arcam AB, does not mean endorsement by the authors. . This study collected and analyzed process log data and near infrared (NIR) images for every layer to correlate trends in porosity formation and mechanical performance. The location of pores, while naturally stochastic, is heavily influenced by the cross-sectional area as detected by NIR images and correlates with the failure sites from uniaxial testing.