Papers by Keyword: Micromechanics

Abstract: The critical resolved shear strength of pure metals is given by the Peierls-Nabarro equation; impurities or alloying elements will significantly increase . Additional strength is introduced by strain hardening (SH), the grain size effect (GSE), precipitates and particle dispersion. The combination of these mechanisms is generally described in an additive manner, which can be justified by the Taylor expansion of a multivariate function. This approach is highly empirical and involves extensive parameter fitting. The Kocks-Mecking model (KM) and discrete dislocation dynamics show that SH is mainly due to forest effects (latent hardening). Consequently, the main explanation for alloy strength must be sought in the resistance against dislocation percolation through a field of obstacles with different strengths, with the slip length limited by the grain diameter. This hypothesis is explored by reviving early graphical simulations to the percolation problem by introducing a grain boundary and variable obstacle strength in an efficient computer program. Such simulations and theoretical considerations demonstrate the limitations of the additive description of combined hardening. An alternative approximation is proposed, based on the statistical analysis of dislocation percolation, dislocation junctions and dislocation-grain boundary interaction.

Abstract: Hail impact is a critical loading situation for unidirectional fiber reinforced composites in automotive and aerospace applications. Therefore, it was already analyzed frequently in literature, focusing on thin-walled structural components and panels. Discontinuous fiber reinforced materials, such as sheet molding compounds (SMCs), and their behavior under local, high velocity impact of hail, was not considered in detail so far. The current study is aimed to investigate the fracture behavior of 2 mm and 4 mm thick SMCs sheets under a high velocity ice ball impact (80 m/s) from a numerical and experimental point of view. The strain-rate dependent material modeling of ice balls is based on an elasto-plastic material model and utilizes smooth particle hydrodynamic (SPH) modeling. Each unidirectional fiber bundle of the SMC plate was modeled individually and the space between these discrete patches was filled by elements representing the matrix material. A micromechanical analysis using representative volume elements (RVEs) was conducted to determine the homogenised strain rate dependent response of the SMC fiber bundle. In addition, a 3D Maximum Stress and Hashin damage model was calibrated to simulate the fracture of the SMC sheets. The accuracy of the applied models was evaluated by comparing the numerical model to results gathered from experimental hail impact trials. Hereby, a high-speed camera system was used to record the experiment and to gain insight into the fracture behavior of the composite structures. In general, it was observed that a 2 mm thick SMC plate was not able to withstand the impact of an ice ball whereas the 4 mm thick sheet was not visually affected. Computer tomography measurements of the impacted region revealed significant damage within the 4 mm thick SMC plate.

Abstract: This paper shows a mathematical model of shear stress transfer at the interface between fiber and matrix composite. The stress transfer is a key parameter determining the quality of fiber-matrix interface, which directly correlates with the composite performance as load-bearing structures. The model is derived from the energy balance approach in prior and post fiber cracking. The debonding process is included in the model by implementing traction-separation law. The results show the developed model can predict the shear stress along with the interface. There are significant differences in shear stress by considering the debonding process compared with conventional models. The debonding process must be regarded to assure an accurate evaluation of the interface quality.

Abstract: The effect of fiber cross-section on effective elastic and piezoelectric coefficients of piezoelectric fiber reinforced composites (PFRC) is investigated through two micromechanical analyzes viz. modified strength of materials (MSM) approach and energy approach. Results are verified with that of strength of materials (SM) approach available in the literature. A constant electric field is considered in the direction transverse to the fiber direction and is assumed to be same both in the fiber and matrix phases. It is observed that MSM and strength of materials (SM) approach predictions for the effective piezoelectric coefficient of the PFRC assessing the actuating capability in the fiber direction are in excellent agreement and also when the fiber volume fraction exceeds a critical value, this effective piezoelectric coefficient becomes significantly larger than the corresponding coefficient of the piezoelectric material of the fiber as investigated by both SM and MSM approaches. However, results of energy approach differ from both MSM and SM results and effective piezoelectric constant never exceeds to that of fiber as obtained by energy approach. It has been found for the piezoelectric fibers, cross-section of fiber has insignificant effect on the effective properties as predicted by MSM and energy approaches. Nomenclature

Abstract: The paper deals with the experimental and theoretical results of elastic constants of polymer modified high strength concrete with high fibre volume fraction. To evaluate elastic properties of this composite system, compressive and flexural strengths were obtained experimentally. Elastic properties such as modulus of elasticity and Poisson’s ratio are first obtained based on experimental results. Simplified equations based on micromechanics, and solid mechanics theories are utilized for the evaluation of elastic properties of polymer modified randomly oriented short steel fibre reinforced high strength concrete. The micromechanics equations for the modulus of elasticity and the Poisson’s ratio are based on the fibre volume fraction and the elastic moduli of the fibre and polymer modified concrete matrix. The existing empirical equations are also used to obtain elastic constants. These equations are applied in the full range of fiber volume fraction (1% to 10%). The comparison of experimental results with theoretical values shows the good agreement with each other. The novelty of the present paper is that the modulus of elasticity of this composite system is obtained experimentally using four point bending test and the Poisson’s ratio is obtained as a function of flexural and compressive strengths with excellent accuracy for the first time.

Abstract: Misfit precipitates greatly contribute to precipitation hardening in wrought aluminum alloys, where attractive and repulsive interactions are expected by stress-strain field of fine misfit precipitates. There are two types of dislocation cutting manner of {001} GP-zone and θ’ phase in Al-Cu alloys; one is dislocation burgers vector intersects (001) variant by 0 deg. (Type A), the other is dislocation Burgers vector intersects (001) variant by 60 deg. (Type B). In order to simulate the interaction of dislocation and fine misfit precipitates, internal stress fields by dislocation and precipitate are computed by Micromechanics based Green’s function method. The elastic field inside and outside a precipitate is deduced from Eshelby’s inclusion theory, where misfit strain of a (001) precipitate is assumed by unidirectional eigenstrain across the disk shaped inclusion. Dislocation motion under three different kinds of dislocation Burgers vector is tested by computing interaction force acted on the discretized dislocation line elements. The interaction force caused by (001) misfit precipitate is varied with types of dislocation cutting manner, magnitude of the interaction force associated with dislocation glide is increased by Type B variant (60 deg.), whereas that is minutely zero for Type A variant (parallel).

Abstract: The paper presents a mathematical model of a finite element for modeling imperfect interface conditions for two contacting surfaces. The element is used in the numerical implementation of the Asymptotic Averaging Method (AAM) for the determination of effective elastic properties of composite materials under investigation. Numerical experiments are carried out to calculate the elastic properties taking into account the adhesion layer using a displacements field jump condition at the phase boundary. Results are compared with adhesion modeling using an additional bulk phase.

Abstract: A microscale formulation for low-cycle fatigue degradation in heterogeneous materials is presented. The interface traction-separation law is modelled by a cohesive zone model for low-cycle fatigue analysis, which is developed in a consistent thermodynamic framework of elastic-plastic-damage mechanics with internal variables. A specific fatigue activation condition allows to model the material degradation related to the elastic-plastic cyclic loading conditions, with tractions levels lower than the static failure condition. A moving endurance surface, in the classic framework of kinematic hardening, enables a pure elastic behaviour without any fatigue degradation for low levels of cyclic traction. The developed model is then applied to micro-structured materials whose micro-mechanics is analysed using a boundary integral formulation. Preliminary results demonstrate the potential of the developed cohesive model. The future application of the proposed technique is discussed in the framework of multiscale modelling of engineering components and design of micro-electro-mechanical devices (MEMS).

Abstract: In this contribution we present an application of the lowest order Virtual Element Method (VEM) to the problem of material computational homogenization. Material homogenization allows retrieving material properties through suitable volume averaging procedures, starting from a detailed representation of the micro-constituents of the considered material. The representation of such microstructure constitutes a remarkable effort in terms of data/mesh preparation, especially when there is not evident microstructural regularity. For such a reason, computational micromechanics may represent a challenging benchmark for showing the potential of VEM. In this contribution, polycrystalline materials are considered as an application. The proposed technique constitutes a first step towards modelling of damage processes in micro-structured materials

Abstract: In this article, the effect of particle shape is examined from the comparison of results of numerically simulated constant volume compression tests carried out on planes assemblies of disks and ellipses with equal porosity and similar gradation and test conditions. The results show that particle shape is a decisive fabric component that contributes directly and indirectly to the strength of assemblies of particles to resist shearing deformation. The results confirm previously established facts that elongated particle shapes favour particle interlocking and create, more easily than ideal spheres, stable clusters of particles through which external loads can be transferred hence resisting higher shearing stresses.