Macroscopic Material Behavior Research Articles

COMPARISON STUDY OF SPHERICAL AND MULTI-SPHERICAL PARTICLES UNDER CYCLIC UNIAXIAL COMPRESSION

Numerical simulation of cyclic compression of granular material by performing oedometric test has been performed. Discrete Element Method (DEM) has been employed for simulation. A comparison study has aimed to examine the differences in macroscopic behaviour of material discretized by spherical (S) and non-spherical shape models of a particle. During the study, microscopic data of sand from Klaipėda were used for modelling the shape of particles. The nonspherical particles were described by multi-spherical (MS) models retaining distributions for size and aspect ratios. Two DE models of tested specimens were developed and the deformation behaviour under cyclic uniaxial compression was simulated numerically by applying the commercial EDEM code. The variation of the oedometric elasticity modulus was investigated and influence of particle shape on void ratio changes was demonstrated. It was clearly shown that application of S particles is much more sensitive to rearrangement of particles during densification DEM. Simulations illustrated that the elasticity modulus of material corresponding to MS particles is approximately 1.9 times larger comparing with material corresponding to S particles. Therefore, one must improve the magnitude of elasticity modulus by introducing a respective correction factor.

Erratum to: Investigating the micromechanical evolutions within inherently anisotropic granular materials using discrete element method

This paper investigates the mechanical behavior of inherently-anisotropic granular materials from macroscopic and microscopic points of view. The study is achieved by simulating biaxial compression tests performed on granular assemblies by using numerical discrete element method. In the same category of numerical studies found in the literature, the simulations were performed by considering elliptical/oval particles. In the present study, however, the shape of particles is considered as convex polygons, which mostly resembles real sand grains. Particle assemblies with four different bedding angles were tested. Similar to what observed in experiment, inherent anisotropy has a significant effect on macroscopic mechanical behavior of granular materials. The shear strength and dilative behavior of assemblies were found to decrease as the bedding angle increases. Evolution of the microstructure of all samples and the influence of bedding angle on the fabric and force anisotropy during loading process were investigated. It is seen that the microscopic evolutions in the fabric can justify well the macroscopic behavior of granular assemblies. It is found that the long axis of particles tend to be inclined perpendicular to the loading axis, which results in generating more stable column-like microstructures in order to transfer the applied load. Moreover, the number of contacts as well as the magnitude of forces among particles varies in different directions during the loading process and the initial anisotropy condition totally evolves due to the induced anisotropy within samples.

Material characterization of Inconel 718 from free bulging test at high temperature

Macroscopic superplastic behavior of metallic or non metallic materials is usually represented by the strain-rate sensitivity, and it can be determined by tensile tests in uniaxial stress state and bulging tests in multi axial stress state, which is the actual hot forming process. And macroscopic behavior of Non-SPF grade materials could be described in a similar way as that of superplastic materials, including strain hardening, cavity and so on. In this study, the material characterization of non-SPF grade Inconel 718 has been carried out to determine the material parameters for flow stress throughout free bulging test under constant temperature. The measured height of bulged plate during the test was used for estimation of strain-rate sensitivity, strain-hardening index and cavity volume fraction with the help of numerical analysis. The bulged height obtained from the simulation showed good agreement with the experimental findings. The effects of strain-hardening and cavity volume fraction factor for flow stress were also compared.

Elastic behaviour of a regular lattice for meso-scale modelling of solids

A modelling strategy is proposed to link the meso-scale mechanical response of a solid material to the macroscopic material behaviour. The model is based on a regular lattice of truncated octahedral cells, with sites at the cell centres linked by two sets of bonds. The relationship between the macroscopic elastic behaviour of the model and the elastic properties of the bonds is studied numerically. The results demonstrate that, in contrast to previously proposed lattice arrangements, any elastic properties of metallic or cementitious materials can be obtained by appropriate selection of the axial and the shear stiffness of the bonds. Discussion of the modelling approach includes the potential of the site-bond model to simulate the evolution of damage driven not only by mechanical deformation but also by processes that involve the interaction of different mechanisms.

Singular Behavior of Laminated Skew Composite Materials with Cross-Ply Stacking

This study deals with effects depending on skew angles in skewed-laminated composite materials in macroscopic point of view. Based on higher-order approximation of displacements, subparametric layer-wise finite elements are used to analyze skewed-laminated composite systems. The elements have higher-order shape functions derived from the Lobatto shape functions. The modes of the elements are classified into three groups such as vertex, side, and internal modes. The vertex modes have physical meaning, while side and internal modes with respect to the increase of order of the Lobatto shape functions do not have physical meaning but improve accuracy of analysis. Therefore, fixing mesh arrangement of present analysis, the quality of the analysis can be enhanced without re-meshing work. The approach based on p-version of finite element method is implemented with three-dimensional elasticity theory, while shape functions are developed by combination of one- and two-dimensional shape functions, not using three-dimensional shape functions. Using the accurate and practical proposed technique, macroscopic behavior of skewed-laminated composite materials is investigated.

A phase field model incorporating strain gradient viscoplasticity: Application to rafting in Ni-base superalloys

The first formulation of a phase field model accounting for size-dependent viscoplasticity is developed to study materials in which microstructure evolution and viscoplastic behavior are strongly coupled. Plasticity is introduced using a continuum strain gradient formalism which captures the size effect of the viscoplastic behavior. First, the influence of this size effect on the mechanical behavior of the material is discussed in static microstructures. Then, the dynamic coupling between microstructure evolution and viscoplastic activity is addressed and illustrated by the rafting of the microstructure observed in Ni-base superalloys under creep conditions. It is found that the plastic size effect has only a moderate impact on the shape of the rafts but is crucial to reproduce the macroscopic mechanical behavior of that particular material.

Discrete element modeling of inherently anisotropic granular assemblies with polygonal particles

In the present article, we study the effect of inherent anisotropy, i.e., initial bedding angle of particles and associated voids on macroscopic mechanical behavior of granular materials, by numerical simulation of several biaxial compression tests using the discrete element method (DEM). Particle shape is considered to be irregular convex-polygonal. The effect of inherent anisotropy is investigated by following the evolution of mobilized shear strength and volume change during loading. As experimental tests have already shown, numerical simulations also indicate that initial anisotropic condition has a great influence on the strength and deformational behavior of granular assemblies. Comparison of simulations with tests using oval particles, shows that angularity influences both the mobilized shear strength and the volume change regime, which originates from the interlocking resistance between particles.

Substrate effects from force chain dynamics in dense granular flows

Granular materials are composed of solid, discrete particles and exhibit mechanical properties that range from fluid to solid behavior. Some of the complexity exhibited by granular systems arises due to the long‐range order that develops due to particle‐particle contact. Inter‐particle forces in granular materials often form a distributive network of filamentary force‐accommodating chains (i.e., force chains), such that a fraction of the total number of particles accommodates the majority of the forces in the system. The force chain network inherent to a system composed of granular materials controls the macroscopic behavior of the granular material. Force transmission by these filamentary chains is focused (or localized) to the grain scale at boundaries such as the granular flow substrate. This investigation addresses the effects of force localization on the substrate by dynamic force chain processes and the implications for bed entrainment in dense, unconfined, two‐dimensional, gravity‐driven granular flows. Our experimental system employs photoelastic techniques and provides an avenue for quantitative force analysis via image processing and provides a data set that can be used validate discrete element modeling approaches. We show that force chains cause extreme bed‐force localization in dynamic granular systems, and that these localized forces can propagate extensively into the substrate, even ahead of the flow front.

Contact Force Distribution and Induced Anisotropy in Granular Materials under Biaxial Test

A 2-dimensional granular assembly, subjected to isotropic consolidation and biaxial compression, is simulated by applying discrete element method and the particle flow code of PFC2D. The contact force network and distribution are examined and compared to an analogous photoelastic experiment carried out by other studies. The current study shows that the assembly undergoes dilatation and strain-softening after peak strength, and the coordination number (average contact number of particles) increases a little in the initial stage of strain hardening followed by a sharp dropping before the onset of softening. This is correlated with the contact force chain establishment and the evolution of structural anisotropy. The distribution of the normal force and the ratio of tangential to normal force for both the isotropically compressed and sheared stages indicates that the strong normal contacts are crucial for the force chain transmitting stress through assembly. The angular distribution of the contact forces supported this point and could help visualizing the induced anisotropy. These issues are vital for gaining a deeper understanding of the macroscopic behavior of granular material from microscopic analysis.

Contact Force Distribution and Induced Anisotropy in Granular Materials under Biaxial Test

A 2-dimensional granular assembly, subjected to isotropic consolidation and biaxial compression, is simulated by applying discrete element method and the particle flow code of PFC2D. The contact force network and distribution are examined and compared to an analogous photoelastic experiment carried out by other studies. The current study shows that the assembly undergoes dilatation and strain-softening after peak strength, and the coordination number (average contact number of particles) increases a little in the initial stage of strain hardening followed by a sharp dropping before the onset of softening. This is correlated with the contact force chain establishment and the evolution of structural anisotropy. The distribution of the normal force and the ratio of tangential to normal force for both the isotropically compressed and sheared stages indicates that the strong normal contacts are crucial for the force chain transmitting stress through assembly. The angular distribution of the contact forces supported this point and could help visualizing the induced anisotropy. These issues are vital for gaining a deeper understanding of the macroscopic behavior of granular material from microscopic analysis.

Analyse par le modèle multiphasique du comportement macroscopique de matériaux renforcés par fibres

A multiphase model is developed for the analysis of the macroscopic behaviour of composite materials constituted of an elastic matrix reinforced with continuously oriented fibres exhibiting a softening behaviour. The model is then performed to develop analytical and semi-analytical solutions for solid structures subjected to uniaxial loadings (oedometric test and traction test) and flexural loading, showing the capacity of the model to quantify the macroscopic softening behaviour of such a composite material.

Improving the Reliability of EBSD-Based Texture Analysis by a New Large Area Mapping Technique

The relevance of EBSD-based investigations for statements on the macroscopic or mesoscopic behavior of materials is critically relying on the statistical representativeness of the data. Particularly, the statistical reliability of the EBSD-based results (e.g. texture, phase fraction or grain size) remains an open question since the areas observed by the EBSD technique are quite small compared to XRD techniques. It has already been shown that covering larger areas and probing more grains with the help of large step sizes is beneficial in terms of representativeness [1]. On the other hand, small step sizes are beneficial in terms of grain reconstruction and data clean-up. However, step sizes significantly smaller than the average grain size of the material lead to either covered areas or number of probed grains being too small to be representative or to very large datasets and correspondingly long measurement times. In this contribution, the benefits of a new mapping technique [1] that joins the advantages of large and small step size measurements will be demonstrated. The representativeness of the EBSD datasets obtained by classical and this new mapping techniques were compared by calculating the pole figure symmetries of a TRIP steel. The results show that the proposed mapping technique significantly improves the reliability and representativeness of EBSD-based texture measurements.

A Regularized Sharp Interface Model for Martensitic Phase Transformations at Large Strains

AbstractThe macroscopic mechanical behavior of many functional materials crucially depends on the formation and evolution of their microstructure. When considering martensitic shape memory alloys, this microstructure typically consists of laminates with coherent twin boundaries. We suggest a variational‐based phase field model for the dissipative evolution of microstructure with coherence‐dependent interface energy and construct a suitable gradient‐extended incremental variational framework for the proposed dissipative material. We use our model to predict laminate microstructure in martensitic CuAlNi. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A RVE‐based micro mechanical model for short fiber reinforced plastic materials including matrix damage and fiber fracture

AbstractThe representative volume element (RVE) method is applied to a fiber reinforced polymer material undergoing matrix damage and fiber fracture. Results of RVE computations are compared to uniaxial tensile tests performed with the composite material. It is shown that the macroscopic behavior of the composite material can accurately be predicted by RVE computations. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Compression and shear-wave velocities in discrete particle simulations of quartz granular packings: Improved Hertz-Mindlin contact model

The Hertz-Mindlin (HM) contact model has been a cornerstone for the development of several effective medium theories (EMTs) aimed at describing the mesoscopic and macroscopic mechanical behavior of granular materials like unconsolidated sands. In addition, this model is at the core of most of the discrete particle method designs used to numerically solve for the responses of these heterogeneous materials to external perturbations, like acoustic and stress-strain experiments. However, this model has shown shortcomings in the description of the shear response characterization of granular materials, partly due to the non-affine motions experienced by the grains. We have developed a correction of the model based on a detailed calibration of our acoustic numerical results with previous empirical data. Using a microscopic approach to the grain-grain contact surfaces, the nature of the corrections found appear to be related to the shear resistant asperities and the smaller scale of the grain-grain contact areas compared to the total area assumed by the HM model. An improved HM model characterized by a tangential stiffness weakening is based on these surface corrections. Using this observation an enhanced EMT theory emerges based not only on the tangential stiffness modification but also on the velocity-pressure dependence obtained during the calibration of our numerical model.

High-energy synchrotron diffraction study of a transformation induced plasticity steel during tensile deformation

Energy-dispersive x-ray diffraction offers the possibility for measurement and evaluation of diffraction spectra containing information of various diffraction lines of all contributing crystalline phases of a material. Combined strain imaging and diffraction analysis was conducted during the tensile test of a low alloyed transformation-induced plasticity (TRIP) steel in order to investigate the transformation induced plasticity, strain hardening, and load partitioning effects. Optical strain imaging allowed for determination of localized true strains from three-dimensional deformations measured in situ. High-energy synchrotron radiation has permitted diffraction analysis in transmission mode to gather information from the material interior. Phase-specific stress evolution during loading could be observed applying the sin2ψ technique during certain load steps. The strains of the individual lattice planes were determined in different locations under varying angles between loading and perpendicular direction. Using energy-dispersive methods it was also possible to determine the transformation behaviour during elastic and plastic regime taking into account a large number of diffraction lines. The results show that the approach practised here enables one to pull together macroscopic and phase-specific microscopic material behaviour in order to improve existing models for prediction of complex load situations.

Computational modeling of flow‐induced anisotropy of polar ice for the EDML deep drilling site, Antarctica: The effect of rotation recrystallization and grain boundary migration

SUMMARYIn this contribution we model flow‐induced anisotropy of polar ice in order to gain a better understanding for the underlying microstructure and its influence on the deformation process. In particular, a continuum‐mechanical, anisotropic flow model that is based on an anisotropic flow enhancement factor (CAFFE model) is applied. The polycrystalline ice is regarded as a mixture whose grains are characterized by their orientation. The approach is based on two distinct scales: the underlying microstructure influences the macroscopic material behavior and is taken into account phenomenologically. To achieve this, the orientation mass density is introduced as a mesoscopic field, i.e. it depends on a mesoscopic variable (the orientation) in addition to position and time. The classical flow law of Glen is extended by a scalar, but anisotropic enhancement factor. Four different effects (local rigid body rotation, grain rotation, rotation recrystallization, grain boundary migration) influencing the evolution of the grain orientations are taken into account. All modeling parameters are either measurable in or derivable from field observations or laboratory experiments. A finite volume method is chosen for the discretization procedure. Numerical results simulating the ice flow at the site of the EPICA ice core in Dronning Maud Land (referred to as EDML), Antarctica, are presented. They go beyond earlier results by Seddikit et al. (J. Glaciol. 2008; 54(187):631–642) in which only local rigid body rotation and grain rotation were accounted for. By comparing simulated and observed fabrics, we come up with reference values for the parameters in the constitutive equations for rotation recrystallization and grain boundary migration. Down to 2045 m depth, good agreement can be achieved; however, further down the observed fabric cannot be reproduced well due to numerical issues. Additionally, we study the influence of the two superposed deformation regimes of vertical compression and simple shear separately and demonstrate that the numerical problems are due to the predominant shear regime near the bottom, whereas vertical compression only produces stable results everywhere. Copyright © 2011 John Wiley & Sons, Ltd.

The Effect of Interface Damage on Macroscopic Constitutive Behavior of Composite Materials

Base on the finite element method, the effect of interface damage on macroscopic constitutive behavior of composite materials subjected to uniaxial tension was studied. A bilinear cohesive law, which relates the traction and displacement jumps, was adopted to model the debonding of particle/matrix interface. Stress-strain curves for a material with different interface properties, particle size and volume fraction were discussed in detail. The results show that the damage due to debonding of particle/matrix interfaces can significantly affect the macroscopic response of composite materials, and that the interaction of particles is innegligible in multi-particle structure.

Simulation of Fracturing Process for Heterogeneous Material under Uniaxial Compression

A novel numerical model for simulating fracturing process of the heterogeneous materials such as rock or rocklike material has been developed and implemented in the FLAC, which is the numerical code for the engineering mechanics analysis. A constitutive model that captures an essential component of brittle material failure, that is, cohesion weakening and frictional strengthening (CWFS) is improved by taking accounting the elastic modulus of element may degrade when the element failure. Furthermore, a new energy index, Local Energy Release Rate (LERR), is put forward to simulate energy release during failure process by tracking the peak and trough values of elastic strain energy intensity before and after brittle failure. The numerical model has applied to simulate the initiation, propagation and coalescence of cracks in the failure processes of brittle material. Using this numerical model, we studied the failure processes of simulated rock specimens with different heterogeneity. The results suggest that the model is a powerful approach to the study of macroscopic fracturing behaviour of heterogeneous material.

Multiscale XFEM‐modelling and simulation of the inelastic material behaviour of textile‐reinforced polymers

AbstractThis paper addresses the multiscale simulation of fibre‐reinforced polymers. The considered composite materials exhibit a hierarchical material structure with three distinct length scales—micro, meso and macro. This feature of the morphology allows for the application of homogenization techniques based on a representative volume element (RVE) that is entirely typical for the local, periodic material structure. The effective macroscopic material behaviour of the composite can be predicted from the properties of the individual constituents and the geometric arrangement of the reinforcing fibres based on the simulation of the material behaviour in the RVE.The heterogeneous material structure in an RVE is modelled by the eXtended finite element method (XFEM). To this, two special element types, called X‐element and 2X‐element, are derived. They can represent one or two material interfaces within the element domain. For an efficient modelling process, an automated model generation procedure that determines the required element types, locates the material interfaces and performs the subdivision of the X‐elements into tetrahedral integration domains has been developed. Problems related to a consistent interface approximation and a continuous displacement field are discussed.In the generated RVE models, a viscoplastic material model accounts for the inelastic material behaviour of the polymeric matrix, whereas the glass‐fibres are assumed to have a linear elastic stress–strain behaviour. Using periodic displacement boundary conditions, effective stress–strain curves are computed for glass‐fibre‐reinforced polypropylene with unidirectional and woven arrangements of the reinforcing fibres. Copyright © 2010 John Wiley & Sons, Ltd.