Characteristic Length Of Micro-structure Research Articles

FEM simulations applied to the failure analysis of RC structure under the influence of municipal sewage pressure

The paper discusses a failure mechanism of reinforced concrete (RC) structure with steel cover that failed under the influence of municipal sewage pressure. To explain the reasons of failure, in-situ measurements, laboratory experiments and comprehensive Finite Element Method (FEM) computations were performed. Non-destructive in-situ scanning tests were carried out to determine quantity and cover thickness of embedded reinforcement bars, simultaneously, laboratory tests regarding concrete and shotcrete thickness, density and compressive strength were performed on samples prepared from core drills taken from the RC structure. FEM computations were carried out with the constitutive continuum model for concrete and steel with material parameters designated on the basis of stress–strain curves in uniaxial compression and uniaxial tension, respectively. An isotropic coupled elasto-plastic-damage formulation based on the strain equivalence hypothesis was used. In order to describe strain localization in concrete, model was enhanced in a softening regime by a characteristic length of micro-structure by means of a non-local theory. FEM analyses were carried out for different values of sewage pressure. The main attention was paid to the evolution of steel cover deformation and strain localization of the RC ceiling slab. FEM results revealed strong dependence between a bond-slip between anchors and steel cover deformation as well as between sewage pressure value and strain localization pattern of RC structure. Mechanism of the structure failure under complex loading conditions was realistically captured and its reasons were discussed in detail.

Reflection of Elastic Waves in Dipolar Gradient Half-Space under the Control of External Magnetic Field

This paper investigated the reflection of plane waves at the interface of dipolar gradient elastic solids under the control of an external magnetic field. This study focused on the increasing influence of the microstructural effect as the incident wavelength approaches the characteristic length of the microstructure or at higher frequencies. Initially, the dispersion equation for the propagation of elastic waves was derived from the dipole strain gradient theory and Maxwell’s electromagnetic theory. Subsequently, the amplitude ratios of various reflected waves to incident P-waves and incident SV-waves were calculated based on the interface conditions. Finally, the numerical results were used to discuss the impact of the external magnetic field and microstructural characteristic length on the propagation of the reflected wave. It was observed that the microstructural effect generated new wave modes and introduced dispersion characteristics into the elastic waves. Conversely, the external magnetic field primarily influences the amplitude of the elastic wave propagation via the Lorentz force without creating new wave modes or affecting the dispersion properties of the elastic wave in the dipolar gradient elastic solid.

QSH WAVE PROPAGATION STUDY IN INFINITE FLEXOELECTRIC PIEZOELECTRIC MEDIUM

The quasi-SH (QSH) wave propagating through a flexoelectric piezoelectric infinite space is investigated in this paper. With the consideration of the microstructure effects (i.e., the flexoelectric effects, strain gradient effects, and micro-inertial effects), the frequency dispersive equations of the QSH wave propagation in infinite flexoelectric piezoelectric materials are derived. The impacts of the flexoelectric coefficient, static characteristic length, and inertial characteristic length of the microstructure upon the dispersion curves of the QSH wave are discussed numerically. We obtained that these microstructure effects have distinct impacts upon the QSH wave velocity. In particular, the micro-inertia effects have different impacts on the dispersion characteristics of the QSH wave. The results can provide very promising theoretical support for future applications of flexoelectric composites.

Grain growth competition during melt pool solidification — Comparing phase-field and cellular automaton models

A broad range of computational models have been proposed to predict microstructure development during solidification processing but they have seldom been compared to each other on a quantitative and systematic basis. In this paper, we compare phase-field (PF) and cellular automaton (CA) simulations of polycrystalline growth in a two-dimensional melt pool under conditions relevant to additive manufacturing (powder-bed fusion). We compare the resulting grain structures using local (point-by-point) measurements, as well as averaged grain orientation distributions over several simulations. We explore the effect of the CA spatial discretization level and that of the melt pool aspect ratio upon the selected grain texture. Our simulations show that detailed microscopic features related to transient growth conditions and solid–liquid interface stability (e.g. the initial planar growth stage prior to its cellular/dendritic destabilization, or the early elimination of unfavorably oriented grains due to neighbor grain sidebranching) can only be captured by PF simulations. The resulting disagreement between PF and CA predictions can only be addressed partially by a refinement of the CA grid. However, overall grain distributions averaged over the entire melt pools of several simulations seem to lead to a notably better agreement between PF and CA, with some variability with the melt pool shape and CA grid. While further research remains required, in particular to identify the appropriate selection of CA spatial discretization and its link to characteristic microstructural length scales, this research provides a useful step forward in this direction by comparing both methods quantitatively at process-relevant length and time scales.

Intermittent microplasticity in the presence of a complex microstructure

We demonstrate the gradual shift from scale-free intermittent microplasticity to a scale-dependent behavior via the introduction of a variety of microstructural features within the Al-Cu binary alloy system. As long as the obstacles to dislocation motion remain shearable, the statistics of intermittent microplasticity has fat-tailed contributions. The introduction of incoherent precipitates leads to a complete transition from scale-free power-law scaling to an exponential and scale-dependent distribution. These results demonstrate how non-Gaussian interactions survive across different microstructures and further suggest that characteristic microstructural length scales and obstacle pinning-strengths are of secondary importance for the intermittency statistics, as long as dislocations can shear their local environment.

Reflection and transmission of waves at the common interface of piezoelectric half-spaces with microstructure

The present article deals with the reflection and transmission of waves at an interface of piezoelectric (ALN & PZT-5T) half-spaces with microstructures. Unlike the classical piezoelectric material, in the considered media, five coupled waves (2 bulk and 3 surface) [namely the Quasi-longitudinal wave (QP), Quasi-transverse wave (QSV), Electric-acoustic wave (EA), P-type surface wave (SP) and S-type surface wave (SS)] are generated in response to an oblique incident Quasi plane wave. The main objective of this study is to investigate the influence of the characteristic length of microstructure, the inertial characteristic length and flexoelectric coefficients on the reflection and transmission coefficients. For this purpose, the linear algebraic equation, continuity conditions at the common interface are contracted. The linear system of equations comprising the reflection and transmission coefficients is derived, which is solved by using the Cramer's rule. The consequence of this electromechanical phenomenon may be advantageous in certain engineering applications that involve smart nano-composites.

Effect of convection on directional solidification in transparent succinonitrile–2.2wt.%(d)camphor alloy

Interaction of melt flow with solidification microstructures is of fundamental interest and technical relevance due to its effect on the selection of characteristic microstructural features and length scales. Here, we report on in-situ optical observation of both melt flow at the solidification front and microstructural evolution in polycrystalline cellular and dendritic microstructures during upwards directional solidification of a transparent succinonitrile-2.2wt.%(d)camphor alloy in a bulk rectangular sample. Melt flows at different flow intensity levels were applied and the microstructures were characterized in terms of morphology, spacing and growth direction.Under unforced or natural convection, transitions from planar to cellular and further to dendritic solid/liquid interface morphology were obtained (having cellular/dendritic spacing with similar trends as reported in literature data). Under forced convection, after a plateau, decreasing dendrite spacing with increasing shear flow intensity was observed. Also, an increasing inclination of cellular and dendritic growth in the downstream direction was established. Furthermore, for the first time a flow-mediated transition from dendritic to seaweed-type microstructures and vice-versa was observed. Finally, an oscillation of dendrite tip positions with fixed frequency was found for a certain parameter range. The results indicate the large variety of flow effects at different length scales and corresponding physical mechanism, which are discussed.

Limits of enhanced of macro- and meso-scale continuum models for studying size effect in concrete under tension

The paper investigates a mechanical quasi-static size effect in concrete during splitting tension at the macro- and meso-level. In experiments, five different diameters of cylindrical concrete specimens were tested. Two-dimensional plane strain finite element (FE) simulations were carried out to reproduce the experimental size effect. The size effect in experiments by Carmona et al. was also simulated. Two enhanced continuum concrete models (elasto-plastic and damage) were used which were enriched in softening by a characteristic length of micro-structure with the help of a non-local theory. In macro-level simulations, the effect of crucial geometric and material parameters on the size effect was carefully studied such as the width of loading/supporting strips, concrete fracture energy in tension, concrete compressive strength and stiffness of loading/supporting strips. The focus was on the distribution of primary and secondary strain localization zones. In addition, some 2D size effect calculations were performed within enriched elasto-plasticity at the meso-scale by considering the real heterogeneous meso-structure of concrete from the front side of experimental specimens. The calculated size effect on the splitting tensile strength at the macro- and meso-scale proved to be weaker than in our experiments. Shortcomings of enhanced continuum models for size effect simulations were outlined.

Dispersion and attenuation of shear wave in couple stress stratum due to point source

This study discusses the propagation of a horizontally polarised shear wave in a layered composite structure consisting of couple stress stratum over a functionally graded orthotropic viscoelastic substrate due to point source existing at an imperfect interface of the stratum and substrate. Because of the CS effect in the stratum, the existence of the second kind of dispersive (shear) wave is established along with conventional first kind of a shear wave. The closed-form dispersion equations and damping equations of the first and second kind of a dispersive wave are derived by adopting non-traditional boundary conditions and Green’s function technique. The effect of characteristic length of microstructure, imperfect bonding parameter and functional gradient parameters on velocity profiles and attenuation profiles of the first and second kind of dispersive wave has been computed numerically and delineated graphically. For validation, established results are matched with the classical one.

Shear fracture of longitudinally reinforced concrete beams under bending using Digital Image Correlation and FE simulations with concrete micro-structure based on X-ray micro-computed tomography images

The paper presents experimental and numerical investigations of the shear fracture in rectangular concrete beams longitudinally reinforced with steel or basalt bar under quasi-static three point bending. Shear fracture process zone formation and development on the surface of beams was investigated by Digital Image Correlation (DIC) whereas thorough analyses of 3D material micro-structure, air voids, width and curvature of shear cracking were carried out by X-ray micro-computed tomography (micro-CT). Moreover, the 2D shear fracture patterns in beams were numerically simulated with the finite element method (FEM) using isotropic coupled elasto-plastic-damage constitutive model for concrete enhanced by a characteristic length of micro-structure. Concrete meso-structure was modelled as a random heterogeneous four-phase material composed of aggregate particles, cement matrix, ITZ zones and air voids on the basis of X-ray micro-CT images. Experimental and numerical results revealed a satisfactory agreement regarding to the mechanism of failure, load-bearing capacity as well as cracking pattern.

Finite element analysis on failure of reinforced concrete corner in sewage tank under opening bending moment

The paper discusses a failure mechanism of reinforced concrete (RC) sewage tank in a wall corner that failed during a filling test through excessive horizontal displacements of walls under opening bending moment. To explain the reasons for failure, comprehensive finite element (FE) calculations of the RC sewage tank were carried out under plane strain conditions. Concrete was modeled with a coupled elasto-plastic-damage constitutive model. The model was enriched in a softening regime by a characteristic length of micro-structure to provide the mesh objective results. FE analyses were performed for different arrangements of flexural reinforcement in the corner. The focus was on the evolution of strain localization and corner strength. Reasons for the tank failure were discussed. The FE results showed a high sensitivity of both the load bearing capacity of the tank wall corner and strain localization to flexural reinforcement arrangement. In addition, two laboratory experiments on RC corners subjected to opening bending moments were numerically analyzed under plane stress conditions.

Numerical analyses of novel prefabricated structural wall panels in residential buildings based on laboratory tests in scale 1:1

The paper presents experimental and numerical investigations on novel prefabricated composite building wall panels for residential building constructions. The wall panels were composed of reinforced concrete ribbed elements with the core from the EPS foam as the thermal insulation. The wall panels in the full-scale 1:1 were subjected to vertical loads. In the first step, the experiments were analysed with simple usual static methods. Next they were analysed numerically using the finite element method based on two different constitutive continuum models for concrete. First, an elasto-plastic model with the Drucker-Prager criterion defined in compression and with the Rankine criterion defined in tension was used. Second, a coupled elasto-plastic damage formulation based on the strain equivalence hypothesis was used. In order to properly describe strain localization in concrete, both models were enhanced in a softening regime by a characteristic length of micro-structure by means of a non-local theory. A satisfactory agreement between the experiments and FE analyses was achieved. In addition, the FE results with the non-local approach were compared with the crack band model.

Cracks in heterogeneous materials with rotating constituents – Small and Intermediate scale Cosserat continua

Cosserat continuum modelling of crack propagation in particulate materials with microrotations and in layered materials with sliding requires the analysis of the Cosserat characteristic lengths in their relation with the characteristic length of the material microstructure. The Cosserat lengths that are of the order of the microstructural characteristic length should be set to zero to derive the main asymptotic terms. When all Cosserat characteristic lengths are of the microscopic length the obtained continuum is termed the Small scale Cosserat continuum. Cracks of Modes I, II, III have conventional stress singularity, as well as the moment stress singularity. Moment stresses can cause bending failure of the bonds connecting the grains in the particulate material or layers in the layered material. Cases are identified when the bending stress induced by moment stress singularity exceeds tensile stresses induced by the conventional stress singularity by an order of magnitude. Then the main mechanism of crack propagation is bending failure produced by the moment stress, which explains, in a unified fashion the often-observed in-plane propagation of cracks of the classical modes. Another interesting case is when some Cosserat characteristic lengths are large. This gives what we term the Intermediate scale Cosserat continuum. An example is given by layered material with sliding layers that keep full contact during sliding. In this case the crack normal to the layering also propagates by bending failure produced by the moment stress singularity.

Wave propagation through a flexoelectric piezoelectric slab sandwiched by two piezoelectric half-spaces

Reflection and transmission of plane waves through a flexoelectric piezoelectric slab sandwiched by two piezoelectric half-spaces are studied in this paper. The secular equations in the flexoelectric piezoelectric material are first derived from the general governing equation. Different from the classical piezoelectric medium, there are five kinds of coupled elastic waves in the piezoelectric material with the microstructure effects taken into consideration. The state vectors are obtained by the summation of contributions from all possible partial waves. The state transfer equation of flexoelectric piezoelectric slab is derived from the motion equation by the reduction of order, and the transfer matrix of flexoelectric piezoelectric slab is obtained by solving the state transfer equation. By using the continuous conditions at the interface and the approach of partition matrix, we get the resultant algebraic equations in term of the transfer matrix from which the reflection and transmission coefficients can be calculated. The amplitude ratios and further the energy flux ratios of various waves are evaluated numerically. The numerical results are shown graphically and are validated by the energy conservation law. Based on these numerical results, the influences of two characteristic lengths of microstructure and the flexoelectric coefficients on the wave propagation are discussed.

A coupled constitutive model for fracture in plain concrete based on continuum theory with non-local softening and eXtended Finite Element Method

The paper presents a constitutive model for concrete which combines a continuous and discontinuous fracture description. In a continuum regime, two different constitutive laws were used. First, a plasticity model with a Rankine failure criterion and an associated flow rule was used. Second, a constitutive law based on isotropic damage mechanics was formulated. In order to capture the width of a localized zone and to obtain mesh-independent results, both models were equipped with a characteristic length of micro-structure by applying a non-local theory of an integral format. In order to describe a macro-crack as a displacement jump along/across a localized zone, the eXtended Finite Element Method (XFEM) was used. A transition algorithm between a non-local continuum model and XFEM was formulated. The implementation details of a coupled approach were given. The performance of two coupled models were numerically analysed based on several 2D benchmarks with a dominating mode-I (e.g. uniaxial tension and bending) and under mixed-mode conditions. The numerical results were compared with our experimental ones. The advantages of a continuous–discontinuous coupling in describing crack patterns were outlined.

Reflection and transmission through a microstructured slab sandwiched by two half-spaces

Abstract The reflection and transmission of a plane wave through a microstructured slab sandwiched by two half-spaces are studied in this paper. First, the wave propagation in a micro-structured solid of the dipolar gradient elasticity is formulated. Then, the reflection and transmission properties of a plane wave through a micro-structured slab sandwiched by two half-spaces are considered. The nontraditional interfacial conditions by requiring the auxiliary monopolar tractions, the auxiliary dipolar tractions, the displacements and the normal derivative of displacements continuous across the two interfaces are used to determine the amplitude ratio. The energy fluxes carried by various waves and the reflection and transmission coefficients in terms of energy flux ratio with respect to incident wave are calculated numerically. Based on these numerical results, the microstructure effects on the reflection and transmission waves for the incident P wave and incident SH wave with different wavelength are discussed. In particular, the influences of three characteristic lengths, namely, the incident wavelength, the thickness of slab and the characteristic length of microstructure, on the reflection and transmission waves are analyzed. It is found that the microstructure effect results in the appearance of evanescent wave mode. The reflection and transmission coefficients are evidently dependent upon the microstructure parameters and become more pronounced when the incident wavelength is close to the characteristic length of microstructure.

Computational simulations of concrete behaviour under dynamic conditions using elasto-visco-plastic model with non-local softening

The paper presents results of FE simulations of the strain-rate sensitive concrete behaviour under dynamic loading at the macroscopic level. To take the loading velocity effect into account, viscosity, stress modifications and inertial effects were included into a rate-independent elasto-plastic formulation. In addition, a decrease of the material stiffness was considered for a very high loading velocity to simulate fragmentation. In order to ensure the mesh-independence and to properly reproduce strain localization in the entire range of loading velocities, a constitutive formulation was enhanced by a characteristic length of micro-structure using a non-local theory. Numerical results were compared with corresponding laboratory tests and available analytical formulae.

Microstructural characteristics and mechanical properties of peritectic Cu–Sn alloy solidified within ultrasonic field

Abstract The dynamic solidification of peritectic Cu–70%Sn alloy was accomplished within a 20 kHz ultrasonic field under the power range up to 440 W. The ultrasound promotes the nucleation of primary e(Cu3Sn) phase and prevents the bulk undercooling of liquid alloy. As sound power increases, the ultrasonic field brings about a striking size refinement effect to the primary e intermetallic compound by more than one order of magnitude. Meanwhile, it facilitates or even completes the usual peritectic transformation (L + e → η) which occurs only to a very limited extent during static solidification. This is mainly because the refinement of primary e phase induced by ultrasound greatly reduces the characteristic length of peritectic microstructure, which increases solid state Fourier number by more than one order of magnitude. The dramatic increase in the volume fraction of peritectic phase and the prominent grain refinement effect due to ultrasound lead to the remarkable improvement of mechanical properties for Cu–70%Sn alloy, whose compressive strength and microhardness are increased by factors of 4.8 and 1.45, respectively.

Reflection and transmission of elastic waves at the interface between two gradient-elastic solids with surface energy

The reflection and transmission of an incident plane wave at an interface between two gradient elastic solids with surface energy are studied. First, some functions of strain energy density with the surface effects taken into consideration are postulated and the surface effects of gradient elastic solid are incorporated into the constitutive relations. Then, the nontraditional interface conditions by requiring the auxiliary monopolar tractions and the auxiliary dipolar tractions continuous across the interface are used to determine the reflection and transmission coefficients. Some numerical results of the reflection and transmission coefficient in terms of energy flux ratio are given for different microstructure parameters and surface parameters. The microstructure effects and the surface energy effects on the reflection and transmission waves are discussed based on the numerical results. It is found that the microstructure effects result in the appearance of two surface waves and the surface energy effects have apparent different influence on the body waves in gradient elastic solids and the surface waves at the interface. However, this phenomenon becomes pronounced only when the incident wavelength is close to the characteristic length of microstructure. (C) 2015 Elsevier Masson SAS. All rights reserved.

Reflection and transmission of plane waves at the interface between two different dipolar gradient elastic half-spaces

The reflection and transmission of plane waves at the interface between two different dipolar gradient elastic solids are studied. First, the auxiliary monopolar tractions and the auxiliary dipolar tractions are introduced and the explicit expressions of them are derived for the dipolar gradient elastic solid. Then, the nontraditional interface conditions requiring the auxiliary monopolar tractions and the auxiliary dipolar tractions continuous across the interface are used to determine the amplitude ratio of the reflection and transmission waves with respect to the incident wave. Our aim is to investigate the microstructure effects on the reflection and transmission waves at the interface of two microstructured solids, and to show the possible deviation from the classical elastic solids without microstructure effects. It is found that the microstructure effects make the propagating waves dispersive and create the evanescent waves that become the surface waves at interface. Some numerical examples are given for the amplitude ratio and the phase shift of reflection and transmission waves. The numerical results are validated by consideration of energy conservation. It is found from the numerical results that the reflection and transmission waves are significantly dependent upon the microstructure parameters and the microstructure effects become more pronounced as the incident wavelength is close to the characteristic length of microstructure.