Micromechanical Field Research Articles

Modeling fatigue behavior of additively manufactured alloys with an emphasis on pore defect morphology

Additively manufactured (AM) materials are prone to porosity, which limits their widespread adoption in fatigue-limited applications. Experimental campaigns are vital in understanding the effects of porosity on fatigue resistance but are costly and time consuming. This work presents a modeling framework to predict fatigue life debits in AM materials due to representative pore defects including keyhole, lack of fusion, and linearly aligned/planar pores. Materials characterization data is leveraged from specimens of alloy 718 (also known as IN718) that have been intentionally seeded with pore defect structures via a systematic modification of the process parameters. Statistically equivalent microstructure (SEM) models are generated as analogues to the experimental specimens and undergo crystal plasticity simulations. A Bayesian inference framework is used to calibrate a critical value of a damage parameter, which is used to predict the fatigue lives of SEMs seeded with pores. A strategy based on the macro-scale treatment of notches is proposed to regularize micromechanical field variables in large stress gradients in the presence of pores, or more generally, geometric discontinuities, of various sizes and morphology. The regularization volume is inversely proportional to the local pore radius of curvature and adequately smooths micromechanical fields. The framework presented here can be used to augment experimental data and rapidly evaluate the detrimental effects of porosity on fatigue resistance in AM components.

Phase‐field simulation of microscale crack propagation/deflection in SiCf/SiC composites with weak interphase

AbstractTo understand the microscale toughening mechanism, the crack propagation, and stress–strain response of unidirectional SiCf/SiC composites with h‐BN interphase under transverse and longitudinal tension are investigated by a promising micromechanical phase field (PF) method along with representative volume element. Of much interest, the calculation results are well consistent with the available experimental results. With a strong dependence on the interphase strength, the toughening mechanisms during crack propagation are well presented, for example, fiber pull‐out, crack deflection, and interphase debonding. Furthermore, the longitudinal tensile strength of SiCf/SiC composites increases with decreasing the interphase strength, where only a weak enough interphase can result in a significant crack deflection by its cracking. In particular, the ratio of the interphase strength along fibers to the matrix strength should be less than 1.254 to ensure crack deflection in the interphase and fiber pull‐out. Moreover, the transverse tensile strength of SiCf/SiC composites reaches a maximum with increasing the interphase thickness into the range of 0.25–0.5 µm.

Multiscale simulation of elastic response and residual stress for ceramic particle reinforced composites

In this study, the elastic response and residual stress of the ceramic matrix composites were simulated in multiscale view for exploring the elastic modulus of the two-phase composites reinforced with ceramic particles by diffraction method. Combined with the macroscopic stress-strain relationship of two-phase composites, the effective elastic response model under uniaxial loading was theoretically predicted by introducing the effective representative volume element (RVE). Subsequently, the effective elastic properties of the material and its constituents were calculated, along with comparison with the experimental values reported in the literature. On the basis of Eshelby's inclusion theory, a micromechanical elastic response model for the two-phase composites was established, and a series of micromechanical field equations related to the crystal planes diffraction elastic constants were derived. A comparison with the different micromechanical models for predicting the crystal planes diffraction elastic constants of the ceramic matrix and particle reinforcement was carried out, so as to qualitatively and quantitatively analyze the residual stress. It was revealed that the effective elastic parameters of the ZrB2 matrix and SiC particle reinforcement were very close to the experimental values reported in literature, and the calculated values of the elastic modulus in seven crystallographic diffraction directions were similar to the experimental values. In addition, the average residual stress of the SiC reinforcement and the ZrB2 ceramic matrix predicted by the developed model were consistent with the measured, which proved the reliability and accuracy of the theoretical model for multiscale simulation of the residual stress of two-phase composites.

Micromechanical modeling and calculation for diffraction elastic constants of Ni-based superalloy

A micromechanical model for Ni-based superalloys with reinforcement γ′-Ni3(AlTi) was established to investigate the elastic modulus related to crystallographic directions. In this model, grains were assumed to have spheroidal random dispersion, and the interface of matrix and inclusion phases with lattice strain and macroscopic stress being assumed were straightforwardly converted. Introducing a representative volume element, a series of micromechanical averaged field equations administrating diffraction elastic constants of the γ-(Ni–Cr–Fe) matrix phase and the γ′-Ni3(AlTi) dispersed particulate phase are presented to render qualitative and quantitative analysis in terms of scale transition formalism, respectively. Following the content of the micromechanical framework, the effective elastic properties of Ni-based superalloys were predicted. Furthermore, the numerical diffraction elastic constants of several diffraction planes were compared with those of experimental determination by neutron diffraction, whose implications of diffraction elastic constants required for experimental measurement of residual stresses were discussed.

In-Situ Grain Resolved Stress Characterization During Damage Initiation in Cu-10%W Alloy

The evolution of stress during damage initiation and accumulation in a two-phase alloy consisting of a ductile copper (Cu) matrix with a randomly dispersed brittle tungsten (W) phase was studied using multiple non-destructive experimental probes. Neutron diffraction measurements were performed to examine the macroscopic strain partitioning between the two phases during a uniaxial tension test. The same material was then examined with high-energy x-ray diffraction microscopy (HEDM) and micro-computed tomography ($$\mu \hbox {-CT}$$) measurements to monitor micromechanical field evolution. The neutron diffraction data indicated a redistribution of load between the Cu and W phases as deformation proceeds. Using HEDM to monitor individual grain micromechanical behavior, an increase followed by decrease in hydrostatic stress and a similar stress triaxiality behavior were found to occur in a subset of W grains. These same W grains were found to be in close proximity to voids observed via tomography at later stages of deformation. From these observations, we conclude that high stress triaxiality development in the W particles leads to decohesion of the interface between the Cu and W phases. The debonded regions eventually grew and coalesced with neighboring voids leading to material failure.

Micromechanical behaviour of Ni-based superalloys close to the yield point: a comparative study between neutron diffraction on different polycrystalline microstructures and crystal plasticity finite element modelling

To investigate the microstructure-dependent relationships in polycrystalline Ni-based superalloys (Haynes 282 and Inconel 718) deformed in the elastoplastic regime, the lattice strain evolution along various macroscopic directions and along various crystallographic directions is monitored via in situ neutron diffraction during uniaxial tensile loading. In addition, a crystal plasticity-based finite element model is set up to describe the micromechanical behaviour of a unit cell within a uniaxially loaded polycrystalline aggregate. Appropriate postprocessing of the (micromechanical) field quantities allows to simulate the diffraction experiment and thus to directly compare and to discuss experimental and modelling results.

In-phase thermomechanical fatigue damage evolution of long fiber-reinforced ceramic-matrix composites using fatigue hysteresis-based damage parameters

Under in-phase (IP) thermomechanical fatigue (TMF) loading, the thermal cyclic temperature changes with decreasing or increasing applied stress upon unloading or loading, and the fiber/matrix interface shear stress in the long fiber-reinforced ceramic-matrix composites (CMCs) changes with applied cycles. In this paper, the in-phase TMF damage evolution of CMCs has been investigated, considering the coupling effects of TMF loading stress level, thermal cyclic temperature and applied cycles. The interface debonding and sliding lengths are determined based the thermomechanical micromechanical stress field and the fracture mechanics approach. The relationships between the TMF hysteresis parameters, interface damage, thermal cyclic temperature and applied cycles have been developed. The damage accumulation processes subjected to in-phase TMF for different fibers volume fraction, peak stress, matrix crack spacing, interface properties and thermal cyclic temperature range have been analyzed. The distinction of the damage evolution between the in-phase TMF and isothermal fatigue (IF) loading at the same applied stress has been analyzed. The damage evolution of cross-ply CMCs subjected to the in-phase TMF and IF loading have been predicted.

Designing micromechanical field of culture matrix for manipulation of cellular mechanobiology

Designing micromechanical field of culture matrix for manipulation of cellular mechanobiology

WANG TILES LOCAL TILINGS CREATED BY MERGING EDGE-COMPATIBLE FINITE ELEMENT MESHES

In this contribution, we present the concept of Wang Tiles as a surrogate of the periodic unit cell method (PUC) for modelling of materials with heterogeneous microstructures and for synthesis of micro-mechanical fields. The concept is based on a set of specifically designed cells that compresses the stochastic microstructure into a small set of statistical volume elements – tiles. Tiles are placed side by side according to matching edges like in a game of domino. Opposite to the repeating pattern of PUC the Wang Tiles method with the stochastic tiling algorithm preserves the randomness for reconstructed microstructures. The same process is applied to obtain the micro-mechanical response of domains where the evaluation as one piece would be time consuming. Therefore the micro-mechanical quantities are evaluated only on tiles (with surrounding layers of tiles of each addressed tile included into the evaluation) and then synthesized to the micro-mechanical field of whole domain.

Viscoelectroelastic closed form models for frequency and time dependent effective properties of reinforced viscoelectroelastic composites

In this paper, closed form models of time and frequency dependent effective properties of reinforced viscoelectroelastic composites are elaborated. Based on the correspondence principle of linear viscoelectroelasticity and the Mori-Tanaka micromechanical mean field approach, the effective properties are derived in the Laplace-Carson domain and then inverted numerically to the time domain. New analytical models for decoupled and coupled effective properties of transversely isotropic viscoelectroelastic materials are elaborated using compact matrix formulations. Explicit relationships are presented for different effective viscoelectroelastic moduli of piezoelectric materials with various inclusions shapes. Various viscoelastic time dependent models for the phases can be used. Only few Eshelby tensor coefficients are required to be analytically or numerically computed. Results based on the elaborated effective viscoelectroelastic models are presented for various types of piezoelectric inclusions and compared to the available predictions. These models are suitable for designers to predict composite viscoelectroelastic moduli of heterogeneous materials with optimized active and passive characteristics.

Viscomagnetoelectroelastic effective properties’ modeling for multi-phase and multi-coated magnetoelectroelastic composites

In this article, the effective properties of new active–passive multifunctional viscomagnetoelectroelastic composite materials are modeled and numerically predicted. The correspondence principle, extended to linear viscomagnetoelectroelasticity, and the Carson transform are coupled to the Mori–Tanaka micromechanical mean field approach. Based on the viscomagnetoelectroelastic convolution integral equations and the interfacial operators, the concentration tensors are derived for multi-phase and multi-coated viscomagnetoelectroelastic composites. The effective properties are derived in the frequency domain and then inverted numerically to the time domain using the inverse transform. The effective properties are thus obtained in both frequency and time domains. The obtained hybrid multifunctional coefficients can be used for their active and passive properties. The resulting visco-magneto-electro-elastic effects can be enhanced by a proper choice of the shape and volume fraction of reinforcements as well as by coating thickness.

Design of a microelectromechanical systems resonant electric field sensor with sensitivity robustness

Studies indicate that driving circuit and drift error in resonance frequency influence the sensitivity of micromechanical resonant electric field sensors. This study proposes an electric field sensor with a comb structure for driving and sensing. A dynamic model is built for the microsensor, which analyzes the behavior and sensitivity of the system on different closed-loop self-excited circuits using the averaging method. Theory and simulation results show that with the use of a proportional–integral controller, the sensitivity remains constant regardless of the variations in the resonance frequency of the shielding layer and Q-factor. The sensitivity is higher with a suitable proportional–integral controller than without a proportional–integral controller. If the parameters of the proportional–integral controller fail to satisfy the constraint relationship, output voltage becomes unstable, and the sensitivity is distorted.

Phase modulated magnetoelectric delta-E effect sensor for sub-nano tesla magnetic fields

We present a resonant micromechanical magnetic field sensor, which utilizes the magnetically induced change in elastic modulus, i.e., the delta-E effect. The sensor is based on magnetoelectric thin film composites, resulting in high sensitivity at room temperature and at low frequencies. The cantilever is electrically excited and read out by a 2 μm AlN piezoelectric layer. Depending on its magnetization, the 2 μm thin film of amorphous (Fe90Co10)78Si12B10 changes its elasticity, which results in a shift of the cantilever's resonance frequency. The sensor is operated in the first or second transversal bending mode at 7.6 kHz or 47.4 kHz. With a limit of detection of 140 pTHz−0.5 at 20 Hz under a magnetic bias field and 1 nTHz−0.5 without external bias field, this sensor exceeds all comparable designs by one order of magnitude.

Efficient fixed point and Newton–Krylov solvers for FFT-based homogenization of elasticity at large deformations

In recent years the FFT-based homogenization method of Moulinec and Suquet has been established as a fast, accurate and robust tool for obtaining effective properties in linear elasticity and conductivity problems. In this work we discuss FFT-based homogenization for elastic problems at large deformations, with a focus on the following improvements. Firstly, we exhibit the fixed point method introduced by Moulinec and Suquet for small deformations as a gradient descent method. Secondly, we propose a Newton–Krylov method for large deformations. We give an example for which this methods needs approximately 20 times less iterations than Newton’s method using linear fixed point solvers and roughly $$100$$ times less iterations than the nonlinear fixed point method. However, the Newton–Krylov method requires 4 times more storage than the nonlinear fixed point scheme. Exploiting the special structure we introduce a memory-efficient version with 40 % memory saving. Thirdly, we give an analytical solution for the micromechanical solution field of a two-phase isotropic St.Venant–Kirchhoff laminate. We use this solution for comparison and validation, but it is of independent interest. As an example for a microstructure relevant in engineering we discuss finally the application of the FFT-based method to glass fiber reinforced polymer structures.

Frequency and time viscoelectroelastic effective properties modeling of heterogeneous and multi-coated piezoelectric composite materials

In this paper, the time and frequency dependent effective behaviors of multi-phase and multi-coated viscoelectroelastic composites are investigated. The correspondence principle, extended to linear viscoelectroelasticity, and the Mori–Tanaka micromechanical mean field approach are used. Based on integral equations and on the obtained viscoelectroelastic interfacial operators closed form expressions of the concentration tensors for viscoelectroelastic composites are derived. The effective properties are obtained in the Carson domain and then inverted numerically to the time domain. They are presented in frequency and time domains for various types, shapes and volume fractions of inclusions as well as for various thicknesses of the coating and showed relaxation effects on all resultant electroelastic coefficients. The frequency dependent storage and loss factors of the obtained effective electroelastic coefficients as well as their cycle limits are elucidated. By this methodological approach, new hybrid composite materials can be obtained and their active–passive properties can be optimized with respect to phase, coating layer and inclusion characteristics.

Frequency-based magnetic field sensing using Lorentz force axial strain modulation in a double-ended tuning fork

This paper presents a frequency-based silicon micromechanical resonant magnetic field sensor with a high quality factor by using a double-ended tuning fork (DETF). The sensing mechanism is based on the detection of resonant frequency shift of the DETF resonator due to the exertion of a Lorentz force generated under the presence of a magnetic field. By designing the strain-sensitive resonator as a DETF, we are able to achieve a quality factor (Q) of over 100,000 for the anti-phase mode. An analytical and finite element (FE) model describing the sensitivity of the magnetic field sensor is presented. Good agreement between the FE model and measurements is obtained, which are close to the analytical model estimates. Through more careful choice of the device physical dimensions, we show that the current sensitivity of 215.74ppm/T can be improved tenfold. Given this level of field sensitivity, we envisage that magnetic noise floor levels in the μT range are achievable using the device concepts described in this paper.

Size Dependent Strength of Fiber Eutectics and Transformation Particles Composite Ceramic

Fiber eutectics and transformation particles composite ceramic possessed good strengths and creep resistance. It is mainly composed of fiber eutectics with random orientation and transformation particles. First, on basis of the strong constraining effect of the microstructure in fiber eutectics, the micromechanical stress field in fiber eutectics is determined by shear stress that develop between the fiber- inclusion and matrix is obtained. Then, the stress concentration duo to the dislocation pileup on the fiber- matrix interphase is analysised, and the maximum stress in matrix is obtained. Letting maximum stress in matrix equaled to theoretical strength of matrix, the micro strength formation of fiber eutectics is gotten. Finally, considering random orientation and length of fiber eutectics, the macro mechanical strength model of fiber eutectics and transformation particles composite ceramic is built. Result indicates that the fracture strength of composite ceramic has obvious size dependence: the fracture strength of composite ceramic will increase as the diameter of the fiber inclusion in fiber eutectics decrease.

Micromechanical Strength of Particle in Composite Ceramic with Partial Debonding Interphase

The four-phase model is used to predict the strength of particles in composite ceramic with partial debonding interphase. Firstly the external strain of three-phase cell is determined. Based on the disturbance strain tensor of three-phase cell, the micromechanical stress field of the particle is obtained. Then based on the generalized thermodynamic force of the particle in damage process, the damage equivalent stress of the particle in the three-phase cell can be calculated. As the damage equivalent stress is equal to the ultimate stress of the particle, the micromechanical strength of particles in composite ceramic with partial debonding interphase is obtained. Finally, For Al2O3-ZrO2 composite ceramic with partial debonding interphase, the variations of the micromechanical strength of particles for different orientation angle and different particle diameter are analyzed. The result shows that the micromechanical strength of particles is determined by the 50° orientation three phase cell, and has obvious size dependence. The micromechanical strength of particle will decrease when the particle diameter increase.

Micromechanical effective elastic moduli of continuous fiber-reinforced composites with near-field fiber interactions

A higher-order micromechanical framework is presented to predict the overall elastic deformation behavior of continuous fiber-reinforced composites with high-volume fractions and random-fiber distributions. By taking advantage of the probabilistic pair-wise near-field interaction solution, the interacting eigenstrain is analytically derived. Subsequently, by making use of the Eshelby equivalence principle, the perturbed strain within a continuous circular fiber is accounted for. Further, based on the general micromechanical field equations, effective elastic moduli of continuous fiber-reinforced composites are constructed. An advantage of the present framework is that the higher-order effective elastic moduli of composites can be analytically predicted with relative simplicity, requiring only material properties of the matrix and fibers, the fiber–volume fraction and the microstructural parameter γ. Moreover, no Monte Carlo simulation is needed for the proposed methodology. A series of comparisons between the analytical predictions and the available experimental data for isotropic and anisotropic fiber reinforced composites illustrate the predictive capability of the proposed framework.

Micromechanics and effective elastic moduli of particle-reinforced composites with near-field particle interactions

A micromechanical framework is proposed to predict effective elastic moduli of particle-reinforced composites. First, the interacting eigenstrain is derived by making use of the exterior-point Eshelby tensor and the equivalence principle associated with the pairwise particle interactions. Then, the near-field particle interactions are accounted for in the effective elastic moduli of spherical-particle-reinforced composites. On the foundation of the proposed interacting solution, the consistent versus simplified micromechanical field equations are systematically presented and discussed. Specifically, the focus is upon the effective elastic moduli of two-phase composites containing randomly distributed isotropic spherical particles. To demonstrate the predictive capability of the proposed micromechanical framework, comparisons between the theoretical predictions and the available experimental data on effective elastic moduli are rendered. In contrast to higher-order formulations in the literature, the proposed micromechanical formulation can accommodate the anisotropy of reinforcing particles and can be readily extended to multi-phase composites.