Structural model of a microinhomogeneous cracked material

We develop a mathematical model of microscopically inhomogencous but macroscopically isotropic materials with statistically distributed components of tensors of stiffness and strength. In this model, the material is represented as the continuous set of “characteristic” (i.e., typical of a given material) disjoint microscopic domains (microvolumes). The microinhomogeneous material is identified with an “effectively homogeneous” material in such a way that, at the same points, the components of the displacement vector determined for these materials are equal. It is assumed that, for each “characteristic” microvolume the parameters of stiffness and strength of the material are constant and can be obtained as values of an arbitrary random variable distributed according to the Weibull law and averaged over a certain random interval of any length. The components of the tensor averaged as indicated above are also regarded as random variables distributed according to the normal law with the same probability of hitting any arbitrarily located “characteristic” microvolume. The model is based on the assumption that the material is isotropic both macroscopically and in any “characteristic” microvolume. The stress-strain state of the microinhomogeneous material is described by the “effective” (averaged over its volume) components of the stress tensor. The model takes into account cracks in the material if their length exceeds the size of the relevant “characteristic” volume. The model is justified for the case of an infinite microinhomogeneous cracked plane under uniaxial tension. It is shown that the parameters determining the stressed state of this plane are not independent in the vicinity of the crack tip. The relevant constraints are given by equations of the model. The choice of these parameters which ignores the indicated constraints leads to results contradicting well-known physical facts. By using the symmetry properties of the system under consideration and physical reasoning, we obtain equations for the determination of the size of “characteristic” domains and physically reasonable dependences of the maximal “effective” tensile stresses and their direction on the parameter of inhomogeneity of the material and average volume of defects. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, Lviv. Pidstryhach Institute of Applied Problems in Mechanics and Mathematics, Ukrainian Academy of Sciences, Lviv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 32, No. 4, pp. 5–16, July–August, 1996.     

Modelling of size effects on strengthening of multiphase Al based composites

A new multilevel mechanical model for multiphase metal matrix composite is proposed, accounting for size distribution effects. The matrix is considered as a micropolar elastic plastic Cosserat material and the hardening phases – as pure elastic ones. A two-steps homogenization procedure is applied to obtain the overall properties of the composite. A variational approach is used to evaluate the equivalent stress on macro level at the transition from micro to macro scale. The model is developed using information provided by microstructural investigations and EDX analysis. The elastic–plastic behaviour of rapidly solidified Al based Fe Si enriched alloys is considered. Due to fast cooling the material can be regarded as “natural” (in situ) composite, containing intermetallic and non-intermetallic compounds of different shapes, sizes, mechanical properties and volume fractions. The multistage modelling of bulk material manufacturing process is simulated using the FEM. The model is implemented as user defined subroutines into the FE code MARC. The influence of the microstructural size parameters on the hardening behaviour of the overall material is discussed.     

Effect of Styrene–Butadiene Rubber Latex on Mechanical Properties of Cementitious Materials Highlighted by Means of Nanoindentation

Abstract: In this paper, micro‐mechanical properties of styrene–butadiene rubber (SBR) latex‐modified cement pastes identified by means of the nanoindentation (NI) technique are related to macro‐mechanical properties of SBR latex‐modified mortars obtained from standard test methods, considering an SBR latex/cement ratio varying from 0% to 20%. For this purpose, the average value of the hardness and the so‐called indentation modulus of the different material phases of the cement paste, i.e. calcium–silicate–hydrate (CSH), portlandite, anhydrous cement, etc., obtained from NI are compared with the compressive and flexural strengths, on the one hand, and the dynamic elastic modulus of SBR latex‐modified mortars, on the other hand. This comparison revealed a linear correlation between the dynamic elastic modulus and the indentation modulus and between the compressive strength, flexural strength and hardness. Thus, the obtained results clearly indicate the finer‐scale origin of the macroscopic elastic and strength properties, linking the mechanical properties at the so‐called mortar scale to the cement‐paste scale.     

A multiscale micromechanical approach to model the deteriorating impact of alkali-silica reaction on concrete

The alkali-silica reaction (ASR) in concrete is one of the most harmful deterioration processes, which leads to expansion and cracking of the material. To understand the evolution of ASR in concrete and its deteriorating impact on the material, a multiscale material model, from aggregate to concrete level, is proposed. The concrete, which at macro scale is considered a homogeneous material, is micromechanically modelled by a matrix-cracks system, in which each phase is uniform and behaves elastically. The damage criterion, associated to the cracks, is formulated on the basis of linear fracture mechanics theory. The model, which is analytically solved, is based on a limited numbers of input parameters, to be determined via micro and macro experimental investigations. The model is able to predict the non-linear behaviour of concrete subject to uniaxial loading in good agreement with code formulations, which are usually input for numerical analyses of structures. For the case of ASR-affected material, the model overestimates the degradation rate of mechanical properties as a function of the expansion. On the contrary, the relationship between stiffness and strength deterioration is correctly approximated. Various model modifications are explored suggesting that the assumption of elastic behaviour of each phase should be reconsidered.     

Experimental Studies on Swelling and Non-Swelling Bentonites

Swelling and non-swelling properties of bentonite particles play an important role in their performance as well as their applications. Swelling bentonites, containing montmorillonite as the main constituent, are mainly used in drilling fluids, bonding sands in foundry molds, iron ore palletizing, and environmental sealing, while non-swelling ones are primarily used as adsorbents in bleaching earth and heavy metal removal. Experimental studies on 10 natural bentonite samples, namely S1 to S10, were conducted to identify the swelling behavior of the samples. XRD studies showed the presence of nanoporous and nanostructured montmorillonite species along with some other clay and non-clay mineral impurities. XRF studies through the measurement of CaO and Na ₂ O weight percents provided a good measure to determine swelling or non-swelling properties of bentonites. XRD and XRF analyses demonstrated that Na ₂ O in samples S5 to S8 belongs to montmorillonite, which is a clay mineral. The first main peak of montmorillonite in its XRD pattern was another guide in assigning the type of the bentonites. BET surface area measurement was employed to verify the former observations. A higher surface area was measured for swelling bentonites, while the highest surface area of 78 m ²/g was obtained for the swelling S8 bentonite. The studies showed that samples S9 and S10 are non-swelling, samples S4, S7, and S8 are swelling, samples S2, S5, and S6 are swelling/non-swelling, and sample S3 is a non-swelling/swelling bentonite.     

Synthesis and characterization of HDA/NaMMT organoclay

In this study, the rheologic and colloidal characterizations of sodium montmorillonite (NaMMT) were examined. Hexadecylamine (CH₃(CH₂)₁₅NH₂, HDA) was added to the bentonite water dispersion (2%, w/w) in different concentrations in the range 5.6 × 10⁻⁴−9.4 × 10⁻³ mmol/l. The rheological and electrokinetic behaviour of aqueous montmorillonite dispersions was investigated as a function of solid content and HDA concentration. The basal spacings of the HDA/NaMMT composites were studied by X-ray diffraction. The FTIR spectra were obtained from the modified bentonite products, which revealed the characteristic absorbances after treatment with HDA.     

胶结型含可燃冰砂土剪切特性的离散元模拟

可燃冰是一种新型清洁能源,广泛分布于深海土体和常年冻土中,对其开采需要深入认识含可燃冰土体的力学特性.该文提出了一种胶结型含可燃冰砂土离散元模型建立方法,并利用该模型完成了排水双轴剪切试验的模拟.通过与前人试验数据对比,验证了该离散元模型的准确性,结合该模型分析了剪切过程中含可燃冰砂土的宏细观变化规律.结果表明:砂土抗...     

Finite element modelling of rubber-like materials — a comparison between simulation and experiment

In this work finite element simulations are used based on the micro structure of polymers in order to transfer the information of the micro level to the macro level. The microscopic structure of polymers is characterized by a three-dimensional network consisting of randomly oriented chain-like macromolecules linked together at certain points. Different techniques are used to simulate the rubber-like material behaviour of such networks. These techniques range from molecular dynamics to the finite element method.The proposed approach is based on a so-called unit cell. This unit cell consists of one tetrahedral element and six truss elements. To each edge of the tetrahedron one truss element is attached which models the force-stretch behaviour of a bundle of polymer chains. The proposed method provides the possibility to observe how changes at the microscopic level influence the macroscopic material behaviour. Such observations were carried out in [1]. The main focus of this work is the validation of the proposed approach. Therefore the model is compared to different experimental data and other statistically-based network models describing rubber-like material behaviour.     

Diffusion with micro-sorption in bentonite: evaluation by molecular dynamics and homogenization analysis

We here give a numerical analysis method of a diffusion problem including sorption chemistry for bentonite clay. Bentonite predominantly consists of the microscopic smectitic clay minerals (mainly montmorillonite and beidellite). Physico-chemical properties of smectite clays such as diffusivity of chemical species and adsorptivity on surface of clay mineral are characterized by crystalline structure of hydrated smectite minerals. To obtain the microscopic properties of the hydrated smectite, the molecular behavior is analyzed by a molecular dynamic (MD) simulation. We understand at least two types of adsorption are formed on the smectite surface; outer sphere complex and inner sphere complex. The inner sphere complex occurs on the edge sites of clay minerals. The amount of mono-layer of cations on the edge surface is considered as the adsorptivity of smectite in the microscopic level. A multiscale homogenization analysis (HA) is applied to extend the microscopic characteristics of the hydrated smectite to the macroscopic behavior. The diffusion and adsorption of a radioactive specie, cesium (Cs), is introduced by this analysis. The calculated results appear to be acceptable.     

Statistical criteria of yield for various mechanisms of shear formation

Statistical criteria of the start of macroyield for various mechanisms of shear formation, including the correlation coefficient of tangential microstresses, which makes it possible to take into consideration the mutual influence of the single crystalline grains, are formulated for a model of a polycrystalline material, a microinhomogeneous medium possessing local anisotropy of mechanical properties and consisting of grains with a cubic type of crystalline lattice. Known criteria of strength are compared and it is shown that they are particular cases of the proposed statistical criteria for certain values of this correlation coefficient.Translated from Problemy Prochnosti, No. 3, pp. 46–52, March, 1990.     

Plasticity and space distribution of the phases in an iron/silver two-phase material

In order to check the influence of the space phase distribution on the overall plastic behaviour of microinhomogeneous materials, a study of an iron/silver aggregate has been undertaken. The first results show a strong influence of phase concentration on the yielding and plastic flow stages. A qualitative explanation in terms of phase connectivity is proposed for yielding and a systematic discrepancy between a two-phase self-consistent model prediction and the experimental results is established for the plastic flow stage.     

Versagensverhalten eines Kohlenstoff‐Faserverbundwerkstoffs unter Druckbeanspruchung

In this work the properties of Carbon/Carbon‐material are investigated under quasi‐static compression and model‐like characterized. The investigated material was produced by pyrolysis of a Carbon/Carbon – composite of bidirectionally reinforced fabric layers. For the compression tests, a device to prevent additional bending stress was made. The stress‐strain behaviour of this material has been reproduced in various publications. This will be discussed on the fracture behaviour and compared the experimental results from the compression tests with the characteristics of tensile and shear tests. The different compression and tensile properties of stiffness, poisson and strength were assessed. Differences between the tensile and compression behaviour resulting from on‐axis tests by micro buckling and crack closure and off‐axis experiments by superimposed pressure normal stresses that lead to increased shear friction.     

Derivation of 3D masonry properties using numerical homogenization technique

Lots of research work has been conducted on homogenization technique, which derives global homogenized properties of masonry from the behaviour of the constitutive materials (brick and mortar). Such a technique mainly focused on two‐dimensional media in the previous studies with the out‐of‐plane properties of masonry material neglected. In this paper, homogenization technique and damage mechanics theory are used to model a three‐dimensional masonry basic cell to numerically derive the equivalent elastic properties, strength envelope, and failure characteristics of masonry material. The basic cell is modelled with distinctive consideration of non‐linear material properties of mortar and brick. Various displacement boundaries are applied on the basic cell surfaces in the numerical simulation. The detailed material properties of mortar and brick are modelled in a finite element program in the numerical analysis. The stress–strain relations of masonry material under various conditions are obtained from the simulation. The homogenized elastic properties and failure characteristics of masonry material are derived from the simulation results. The homogenized 3D model is then utilized to analyse the response of a masonry panel to airblast loads. The same panel is also analysed with distinctive material modelling. The efficiency and accuracy of the homogenized model are demonstrated. The homogenized material properties and failure model can be used to model large‐scale masonry structure response. Copyright © 2006 John Wiley & Sons, Ltd.     

A Gibbs‐energy‐barrier‐based computational micro‐sphere model for the simulation of martensitic phase‐transformations

We introduce a material model for the simulation of polycrystalline materials undergoing solid‐to‐solid phase‐transformations. As a basis, we present a scalar‐valued phase‐transformation model where a Helmholtz free energy function depending on volumetric and deviatoric strain measures is assigned to each phase. The analysis of the related overall Gibbs energy density allows for the calculation of energy barriers. With these quantities at hand, we use a statistical‐physics‐based approach to determine the resulting evolution of volume fractions. Though the model facilitates to take into account an arbitrary number of solid phases of the underlying material, we restrict this work to the simulation of phase‐transformations between an austenitic parent phase and a martensitic tension and compression phase. The scalar model is embedded into a computational micro‐sphere formulation in view of the simulation of three‐dimensional boundary value problems. The final modelling approach necessary for macroscopic simulations is accomplished by a finite element formulation, where the local material behaviour at each integration point is governed by the response of the micro‐sphere model.Copyright © 2014 John Wiley & Sons, Ltd.     

Multi‐scale modeling of surface effects in nano‐materials with temperature‐related Cauchy‐Born hypothesis via the modified boundary Cauchy‐Born model

In nano‐structures, the influence of surface effects on the properties of material is highly important because the ratio of surface to volume at the nano‐scale level is much higher than that of the macro‐scale level. In this paper, a novel temperature‐dependent multi‐scale model is presented based on the modified boundary Cauchy‐Born (MBCB) technique to model the surface, edge, and corner effects in nano‐scale materials. The Lagrangian finite element formulation is incorporated into the heat transfer analysis to develop the thermo‐mechanical finite element model. The temperature‐related Cauchy‐Born hypothesis is implemented by using the Helmholtz free energy to evaluate the temperature effect in the atomistic level. The thermo‐mechanical multi‐scale model is applied to determine the temperature related characteristics at the nano‐scale level. The first and second derivatives of free energy density are computed using the first Piola‐Kirchhoff stress and tangential stiffness tensor at the macro‐scale level. The concept of MBCB is introduced to capture the surface, edge, and corner effects. The salient point of MBCB model is the definition of radial quadrature used at the surface, edge, and corner elements as an indicator of material behavior. The characteristics of quadrature are derived by interpolating the data from the atomic level laid in a circular support around the quadrature in a least‐square approach. Finally, numerical examples are modeled using the proposed computational algorithm, and the results are compared with the fully atomistic model to illustrate the performance of MBCB multi‐scale model in the thermo‐mechanical analysis of metallic nano‐scale devices. Copyright © 2013 John Wiley & Sons, Ltd.     

TRIP and phase evolution for the pearlitic transformation of the steel 100Cr6 under. step‐wise loads

The investigation of complex material behaviour of steel like transformation‐induced plasticity (TRIP) and stress‐dependent phase transformation (SDPT) is a large field of current research. The simulation of the material behaviour of work‐pieces in complex situations requires a knowledge as deep as possible about such phenomena. In addition, there are effects in the case of non‐constant stress which cannot be explained by the widely used Leblond model for TRIP. Therefore, we consider a TRIP model taking into account back stress due to TRIP itself. Based on experimental data for the isothermal pearlitic transformation of the steel 100Cr6 (SAE52100) under step‐wise loads we calculate material parameters for the extended TRIP model. Regardless of the preliminary character of the performed tests, all experiments show a back‐stress effect with a decrease of the TRIP strain after unloading.     

Prediction of apparent properties with uncertain material parameters using high‐order fictitious domain methods and PGD model reduction

This contribution presents a numerical strategy to evaluate the effective properties of image‐based microstructures in the case of random material properties. The method relies on three points: (1) a high‐order fictitious domain method; (2) an accurate spectral stochastic model; and (3) an efficient model‐reduction method based on the proper generalized decomposition in order to decrease the computational cost introduced by the stochastic model. A feedback procedure is proposed for an automatic estimation of the random effective properties with a given confidence. Numerical verifications highlight the convergence properties of the method for both deterministic and stochastic models. The method is finally applied to a real 3D bone microstructure where the empirical probability density function of the effective behaviour could be obtained. Copyright © 2016 John Wiley & Sons, Ltd.     

Fatigue Behaviour of SiC Particulate‐Reinforced A359 Aluminium Matrix Composites

Abstract: In this work, we describe the fatigue behaviour of silicon carbide (SiC_P)‐reinforced A359 aluminium alloy matrix composite considering its microstructure and thermo‐mechanical properties. A variety of heat treatments have been performed for the 20 vol. % SiC_p composite, which resulted in different strength and elongation behaviour of the material. The fatigue behaviour was monitored, and the corresponding S–N curves were experimentally derived for all heat treatments. The fatigue strength was found to depend strongly on the heat treatment. In addition, the fatigue behaviour was monitored non‐destructively via the use of lock‐in thermography. The heat wave, generated by the thermo‐mechanical coupling and the intrinsic dissipated energy during mechanical loading of the sample, is detected by a thermal camera.     

Modification of fatigue strain‐life equation for sheet metals considering anisotropy due to crystallographic texture

The fatigue behaviour of cold rolled and annealed sheet metals are influenced by the anisotropy of mechanical properties due to crystallographic texture. However, the existing fatigue strain‐life models are primarily meant for isotropic material behaviour. In the present work, the Coffin‐Manson equation for strain‐life is modified to include the effect of anisotropy using phenomenological plasticity models. It is observed that the variation of strain hardening exponent is critical to model the strain‐life behaviour. Variation of strain hardening exponent with orientation is modelled using existing anisotropic yield criteria. The prediction of fatigue life using the proposed model correlates well with the experimental results of Al6061‐T6 along different orientations. The proposed model can be used to predict the fatigue properties along any orientation from the fatigue data along one orientation and monotonic mechanical properties along longitudinal, transverse and diagonal directions.     

Thermal Effects During Tensile Deformation of Ti‐6Al‐4V at Different Strain Rates

An in‐depth analysis of the effect of heat generated by plastic work on the observed tensile behaviour of Ti­6Al­4V at different strain rates is presented. Special emphasis is put on the transition from isothermal to adiabatic conditions and how this transition is affected by several process parameters such as material properties, environmental conditions and sample geometry. Experiments are performed in isothermal conditions at moderate temperatures, from ?10 to 70 °C, as well as at strain rates from quasi‐static speeds to more than 1000 s^?1 using a split Hopkinson tensile bar setup. This experimental data is used in conjunction with numerical simulations to determine the evolution of temperature during the experiments and the temperature and strain rate sensitivity of the material, as well as the Taylor–Quinney coefficient. Finally, a full model of the material behaviour is presented and used to define clear limits for adiabatic and isothermal conditions.