Instytut Podstawowych Problemów Techniki

Streszczenie:

Estimation of macroscopic properties of heterogeneous materials has always posed significant problems. Procedures based on numerical homogenization, although very flexible, consume a lot of time and computing power. Thus, many attempts have been made to develop analytical models that could provide robust and computationally efficient tools for this purpose. The goal of this paper is to develop a reliable analytical approach to finding the effective elastic–plastic response of metal matrix composites (MMC) and porous metals (PM) with a predefined particle or void distribution, as well as to examine the anisotropy induced by regular inhomogeneity arrangements. The proposed framework is based on the idea of Molinari & El Mouden (1996) to improve classical mean-field models of thermoelastic media by taking into account the interactions between each pair of inhomogeneities within the material volume, known as a cluster model. Both elastic and elasto-plastic regimes are examined. A new extension of the original formulation, aimed to account for the non-linear plastic regime, is performed with the use of the modified tangent linearization of the metal matrix constitutive law. The model uses the second stress moment to track the accumulated plastic strain in the matrix. In the examples, arrangements of spherical inhomogeneities in three Bravais lattices of cubic symmetry (Regular Cubic, Body-Centered Cubic and Face-Centered Cubic) are considered for two basic material scenarios: “hard-in-soft” (MMC) and “soft-in-hard” (PM). As a means of verification, the results of micromechanical mean-field modeling are compared with those of numerical homogenization performed using the Finite Element Method (FEM). In the elastic regime, a comparison is also made with several other micromechanical models dedicated to periodic composites. Within both regimes, the results obtained by the cluster model are qualitatively and quantitatively consistent with FEM calculations, especially for volume fractions of inclusions up to 40%.

Słowa kluczowe:

Periodic composite , Micro-mechanics , Effective properties, Elasto-plasticity, Particle interactions

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Although the elastic properties of porous materials depend mainly on the volume fraction of pores, the details of pore distribution within the material representative volume are also important and may be the subject of optimisation. To study their effect, experimental analyses were performed on samples made of a polymer material with a predefined distribution of spherical voids, but with various porosities due to different pore sizes. Three types of pore distribution with cubic symmetry were considered and the results of experimental analyses were confronted with mean-field estimates and numerical calculations. The mean-field ‘cluster’ model is used in which the mutual interactions between each of the two pores in the predefined volume are considered. As a result, the geometry of pore distribution is reflected in the anisotropic effective properties. The samples were produced using a 3D printing technique and tested in the regime of small strain to assess the elastic stiffness. The digital image correlation method was used to measure material response under compression. As a reference, the solid samples were also 3D printed and tested to evaluate the polymer matrix stiffness. The anisotropy of the elastic response of porous samples related to the arrangement of voids was assessed. Young’s moduli measured for the additively manufactured samples complied satisfactorily with modelling predictions for low and moderate pore sizes, while only qualitatively for larger porosities. Thus, the low-cost additive manufacturing techniques may be considered rather as preliminary tools to prototype porous materials and test mean-field approaches, while for the quantitative and detailed model validation, more accurate additive printing techniques should be considered. Research paves the way for using these computationally efficient models in optimising the microstructure of heterogeneous materials and composites.

Słowa kluczowe:

Pore configuration, Anisotropy, Elasticity, Micro-mechanics, Additive manufacturing

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The crystal plasticity finite element method (CPFEM) is used to investigate the coupling between the cylindrical void growth or collapse and grain refinement in face-centred cubic (FCC) single crystals. A 2D plane strain model with one void is used. The effect of the initial lattice orientation, similarities, and differences between stress- and strain-driven loading scenarios are explored. To this end, boundary conditions are enforced in two different ways. The first one is based on maintaining constant in-plane stress biaxiality via a dedicated truss element, while the second one is imposing a constant displacement biaxiality factor. Uniaxial and biaxial loading cases are studied. For the uniaxial loading case a special configuration, which enforces an equivalent pattern of plastic deformation in the pristine crystal, is selected in order to investigate the mutual interactions between the evolving void and the developed lattice rotation heterogeneity. Next, biaxial loading cases are considered for three crystal orientations, one of which is not symmetric with respect to loading directions. It is analysed how stress or strain biaxility factors and initial lattice orientation influence the void evolution in terms of its size and shape. Moreover, the consequences of variations in the resulting heterogeneity of lattice rotation are studied in the context of the grain refinement phenomenon accompanying the void evolution. Scenarios that may lead to more advanced grain fragmentation are identified.

Słowa kluczowe:

Crystal plasticity , Finite element method, Void evolution, Grain refinement

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In this paper, we have investigated, using finite element calculations, the effect of initial texture on the formation of multiple necking patterns in ductile metallic rings subjected to rapid radial expansion. The mechanical behavior of the material has been modeled with the elasto-viscoplastic single crystal constitutive model developed by Marin (2006). The polycrystalline microstructure of the ring has been generated using random Voronoi seeds. Both 5000 grain and 15000 grain aggregates have been investigated, and for each polycrystalline aggregate three different spatial distributions of grains have been considered. The calculations have been performed within a wide range of strain rates varying from to , and the rings have been modeled with four different initial textures: isotropic texture, Goss texture, R Goss texture and Z fiber texture. The finite element results show that: (i) the spatial distribution of grains affects the location of the necks, (ii) the decrease of the grain size delays the formation of the necking pattern and increases the number of necks, (iii) the initial texture affects the number of necks, the location of the necks, and the necking time, (iv) the development of the necks is accompanied by a local increase of the slip activity. This work provides new insights into the effect of crystallographic microstructure on dynamic plastic localization and guidelines to tailor the initial texture in order to delay dynamic necking formation and, thus, to improve the energy absorption capacity of ductile metallic materials at high strain rates.

Słowa kluczowe:

Dynamic necking, Inertia, Crystal plasticity, Texture, Finite elements

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The aim of this study is to analyse the joint effect of reinforcement shape and packing on the effective behaviour of particulate composites. The proposed semi-analytical modelling method combines the Replacement Mori–Tanaka scheme, by means of which the concentration tensors for non-ellipsoidal inhomogeneities are found numerically, and the analytical morphologically representative pattern approach to account for particle packing. Five shapes of inhomogeneities are selected for the analysis: a sphere, a prolate ellipsoid, a sphere with cavities, an oblate spheroid with a cavity as well as an inhomogeneity created by three prolate spheroids crossing at right angles. Semi-analytical estimates are compared with the results of numerical simulations performed using the finite element method and with the outcomes of classical mean-field models based on the Eshelby solution, e.g. the Mori–Tanaka model or the self-consistent scheme.

Słowa kluczowe:

composite material, micromechanics, computational modelling, packing effect, shape effect

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Evolutionary algorithms have become an extensively used tool for identification of crystal plasticity parameters of hexagonal close packed metals and alloys. However, the fitness functions were usually built using the experimentally measured stress–strain curves. Here, the fitness function is built by means of numerical comparison of the simulated and experimental textures. Namely, the normalized texture difference index is minimized. The evolutionary algorithm with the newly developed fitness function is tested by performing crystal plasticity parameter optimization for both pure zinc and zinc-magnesium alloy. These materials are promising candidates for bioabsorbable implants due to good biocompatibility and optimal corrosion rate. Although their mechanical properties in the as-cast state do not fulfill the requirements, they can be increased by means of hydrostatic extrusion. The developed modeling approach enabled acquisition of the crystal plasticity parameters and analysis of the active deformation mechanisms in zinc and zinc-magnesium alloy subjected to hydrostatic extrusion. It was shown that although slip systems are the main deformation carrier, compressive twinning plays an important role in texture evolution. However, the texture is also partially affected by dynamic recrystallization which is not considered within the developed framework.

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Void growth and morphology evolution in fcc bi-crystals are investigated using crystal plasticity finite element method. For that purpose, representative volume element of bi-crystals with a void at the grain boundary are considered in the analysis. Grain boundary is assumed initially perpendicular/coaxial with the straight sides of the cell. Fully periodic boundary conditions are prescribed in the representative volume element and macroscopic stress triaxiality and Lode parameter are kept constant during the whole deformation process. Three different pairs of crystal orientations characterized as hard-hard, soft-soft and soft-hard have been employed for modelling the mechanical response of the bi-crystal. Simulations are performed to study the implications of triaxiality, Lode parameter and crystallographic orientation on slip mechanism, hardening and hence void evolution. The impact of void presence and its growth on the heterogeneity of lattice rotation and resulting grain fragmentation in neighbouring areas is also analysed and discussed.

Słowa kluczowe:

crystal plasticity, bi-crystals, void growth, stress triaxiality, Lode parameter, unit cell calculations

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A cluster interaction model has been proposed to account for the spatial distribution and morphology of particles when estimating the effective properties of elastic and thermoelastic composites (Molinari and El Mouden, 1996). In the present paper this approach is extended to elastic-viscoplastic composites. To this end the tangent linearization of the non-linear viscoplastic law and the concept of additive interaction equation are used. Although the extension is formulated for the non-linear case, first applications are considered for linear viscoelastic composites, a situation rich enough to evaluate the interest of the cluster interaction approach. Results of the model are compared to numerical homogenization for periodic
unit cells with two cubic configurations.

Słowa kluczowe:

homogenization, the cluster interaction model, elastic-viscoplastic composite, spatial configuration of inclusions, interaction between inclusions

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The paper reports experimental and numerical study of different deformation mechanisms activated in the AZ31B mag nesium alloy sheet subjected to cyclic in-plane tensile – compressive deformation. The influence ofslip, twinning and detwinning upon the mechanical response and texture evolution of the material is thoroughly investigated. The regime of twinning and detwinning activity is assessed based on the variation of hardening modulus in the course of the process. Velocity-based large strain crystal plasticity model accounting for twinning and detwinning is formulated. The crystal plasticity model parameters are identified using the implementation of the evolutionary algorithm. Predicted activity of deformation mechanisms is discussed with respect to the experimental data.

Słowa kluczowe:

twinning, detwinning, crystal plasticity, magnesium alloys, AZ31B, evolutionary algorithm

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The Mori–Tanaka (MT) scheme is a well-established mean-field model that combines simplicity and good predictive capabilities. The additive tangent MT scheme is a popular variant of the method that is suitable for elastic–viscoplastic composites. This work is concerned with the analysis of some intrinsic features of the additive tangent MT scheme, in particular, of spurious softening in the macroscopic response that may be encountered when the Perzyna-type viscoplasticity model is used. The resulting non-monotonic macroscopic stress–strain response is clearly non-physical, but it also has a negative impact on the efficiency and robustness of the MT model when it is used as a local constitutive model in concurrent multiscale finite-element computations. As shown in the paper, the spurious softening is more pronounced when the so-called soft isotropization is employed to compute the viscoplastic Hill tensor, but it is also observed, although for a much narrower range of material parameters, in the case of the hard isotropization and when no isotropization is applied. Moreover, the softening is promoted at low strain rates, for high elastic contrast, and for high volume fractions of inclusions. Nevertheless, if the soft isotropization is avoided, the additive tangent MT scheme proves to be a feasible and computationally robust mean-field model that can be successfully employed in finite-element computations.

Słowa kluczowe:

mean-field homogenization, Mori–Tanaka method, isotropization, composite materials, viscoplasticity

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The goal of the present work is to identify and model the elastic-viscoplastic behavior of electrodeposited copper films under tension-compression loadings. From the experimental point of view, as proposed in the literature, a film of copper is electrodeposited on both sides of an elastic compliant substrate. The overall specimen is next subjected to tensile loading-unloadings. As the substrate remains elastic, the elastic–plastic response of copper under cyclic loading is experimentally determined. A clear kinematic hardening behavior is captured. To model the mechanical response, a new elastic-viscoplastic self-consistent scheme for polycrystalline materials is proposed. The core of the model is the tangent additive interaction law proposed in Molinari (2002). The behavior of the single grain is rate dependent where kinematic hardening is accounted for in the model at the level of the slip system. The model parameters are optimized via an evolutionary algorithm by comparing the predictions to the experimental cyclic response. As a result, the overall response is predicted. In addition, the heterogeneity in plastic strain activity is estimated by the model during cyclic loading.

Słowa kluczowe:

electrodeposited copper, self-consistent scheme, elasto-viscoplasticity, kinematic hardening, experiments

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The issue of applicability of the Morphologically Representative Pattern (MRP) approach to elastic-plastic composites is addressed. The extension to the regime of non-linear material behaviour is performed by employing the concept of incremental linearization of the material response in two basic variants: tangent and secant. The obtained predictions are evaluated through comparison with the outcomes of numerical analyses. Finite Element simulations are carried out using periodic unit cells with cubic arrangements of spherical particles and representative volume elements (RVE) with 50 randomly placed inclusions. In addition to the analysis of the packing effect in two-phase composites, the size effect is also studied by assuming an interphase between the matrix and inclusions. It is concluded that the MRP approach can be used as an effective predictive alternative to computational homogenization, not only in the case of linear elasticity but also in the case of elastic-plastic composites.

Słowa kluczowe:

particulate composites, elastoplasticity, micromechanics, size effect, packing effect, morphologically representative pattern

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Anisotropic core-shell model of a nano-grained polycrystal is extended to estimate the effective elastic stiffness of several metals of hexagonal crystal lattice symmetry. In the approach the bulk nanocrystalline material is described as a two-phase medium with different properties for a grain boundary zone and a grain core. While the grain core is anisotropic, the boundary zone is isotropic and has a thickness defined by the cutoff radius of a corresponding atomistic potential for the considered metal. The predictions of the proposed mean-field model are verified with respect to simulations performed with the use of the Large-scale Atomic/Molecular Massively Parallel Simulator, the Embedded Atom Model, and the molecular statics method. The effect of the grain size on the overall elastic moduli of nanocrystalline material with random distribution of orientations is analyzed.

Słowa kluczowe:

molecular statics, elasticity, polycrystal, effective medium, hexagonal symmetry

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Texture and twinning-induced anisotropy of the yield stress and hardening of AZ31B extruded rods is investigated. The multidirectional compression tests involving strain path changes are performed in order to: i. assess which slip and twinning systems are active in the polycrystalline sample with a strong texture, ii. analyze the influence of the preliminary deformation upon twin formation, iii. observe the resulting change of the mechanical response. In order to fulfil these goals mechanical testing is supplemented by microstructure analysis. Experimental observations are used to validate the proposed crystal plasticity framework when it is combined with the viscoplastic self-consistent scheme. On the other hand, the results of numerical simulations are used to confirm an advocated interpretation of experimental findings. Finally, the experimental and numerical results are discussed with respect to the theoretical study of slip and twinning activity on the basis of the generalized Schmid criterion. It is concluded that twinning activity influences the mechanical response predominantly by the texture change and to lesser extent by modification of strain hardening due to slip-twin interactions.

Słowa kluczowe:

crystal plasticity, anisotropy, plastic deformation, twinning, hcp

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Nonlinear properties of metal matrix composites (MMCs) are studied. The research combines results of loading-unloading tensile tests, microstructural observations and numerical predictions by means of micromechanical mean-field models. AA2124/SiC metal matrix composites with SiC particles, produced by the Aerospace Metal Composites Ltd. (AMC) are investigated. The aluminum matrix is reinforced with 17% and 25% of SiC particles. The best conditions to evaluate the current elastic stiffness modulus have been assessed. Tensile tests were carried out with consecutive unloading loops to obtain actual tensile modulus and study degradation of elastic properties of the composites. The microstructure examination by scanning electron microscopy (SEM) showed a variety of phenomena occurring during composite deformation and possible sources of elastic stiffness reduction and damage evolution have been indicated. Two micromechanical approaches, the incremental Mori–Tanaka (MT) and self-consistent (SC) schemes, are applied to estimate effective properties of the composites. The standard formulations are extended to take into account elasto-plasticity and damage development in the metal phase. The method of direct linearization performed for the tangent or secant stiffness moduli is formulated. Predictions of both approaches are compared with experimental results of tensile tests in the elastic–plastic regime. The question is addressed how to perform the micromechanical modelling if the actual stress–strain curve of metal matrix is unknown.

Słowa kluczowe:

metal matrix composites, tension with unloadings, damage, microstructure, non-linear effective properties

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A hyperelastic-viscoplastic model of Gum Metal is presented. The model is formulated in the large strain framework. The free energy function is postulated consisting of the hyperelastic and viscoplastic components. Original extension of the Neo-Hooke model with a power law component is proposed for hyperelasticity, which enables to describe a relatively large non-linear elastic regime observed for the alloy. Viscoplastic strain follows the Perzyna-type law with an overstress function. The model is implemented into the finite element method and used to simulate the Gum Metal response in multiple tension loading-unloading cycles. The results are compared with experimental outcomes. Good accordance of the simulation results and the available experimental data is obtained.

Słowa kluczowe:

large strain, hyperelasto-viscoplasticity, gum metal, cyclic deformation

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The goal of the present work is to propose a multi-scale approach for composite materials which accounts for kinematic hardening in the phases. For that purpose, the additive/sequential interaction rule and tangent linearization of viscoplastic response proposed for elastic–viscoplastic material can be extended in a straightforward manner. A two phase composite where each phase is elastic–viscoplastic is considered. The viscoplastic flow is governed by a J2 flow theory with an overstress. To find the overall behavior of the composite, a Mori–Tanaka model is applied. Numerical validation of the proposition is carried out by considering a representative volume element with 30 inclusions. Various configurations have been tested: hard or soft inclusion cases with or without isotropic hardening. It is shown that the quality of the model predictions is not affected by the introduction of the kinematic hardening component in the local constitutive behavior. Namely, in most cases considered in the paper the overall stress–strain response as well as the average stress–strain response per phase is accurately estimated. It has been also verified that the obtained backstress components are consistent with the ones predicted by Finite element calculations with ABAQUS Software.

Słowa kluczowe:

elastic-viscoplasticity, homogenization, finite element, metal matrix composite, Mori–Tanaka scheme, kinematic hardening

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Anisotropic core-shell model of a nano-grained polycrystal, proposed recently for nanocrystalline copper, is applied to estimate elastic effective properties for a set of crystals of cubic symmetry. Materials selected for analysis differ in the lattice geometry (face-centered cubic vs. body-centered cubic) as well as the value of a Zener factor: a ratio of two shear moduli defining elastic anisotropy of a cubic crystal. The predictions are verified by means of the atomistic simulations. The dependence of the overall bulk and shear moduli on the average grain diameter is analysed. In the mean-field approach the thickness of the shell is specified by the cutoff radius of a corresponding atomistic potential, while the grain shell is isotropic and its properties are identified by molecular simulations performed for very small grains with approximately all atoms belonging to the grain boundary zone. It is shown that the core-shell model provides predictions of satisfactory qualitative and quantitative agreement with atomistic simulations. Performed study indicates that the variation of the bulk and shear moduli with the grain size changes qualitatively when the Zener anisotropy factor is smaller or greater than one.

Słowa kluczowe:

molecular statics, elasticity, polycrystal, effective medium, cubic symmetry

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Microstructure evolution in crystalline materials subjected to different loading conditions is regularly studied using crystal plasticity finite element simulations. Accurate and reliable description of the microstructure, particularly in the case of large deformations, requires the usage of remeshing procedures and the mapping of the material state from the distorted mesh onto a new mesh. In this work, we evaluate three different solution mapping schemes, viz. closest point projection (CPP), sequential spherical linear interpolation (SLERP), and weighted spherical averages, all of which are based on the mapping of crystal plasticity variables. The results show that the mapping with CPP is generally acceptable, whilst the sequential SLERP is a more robust method with little additional computing effort.

Słowa kluczowe:

crystal plasticity, solution mapping, remeshing, severe plastic deformation SPD, equal channel angular pressing ECAP

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Several micromechanical and numerical approaches to estimating the effective properties of heterogeneous media are analyzed. First, micromechanical mean-field estimates of elastic moduli for selected metal matrix composite systems are compared with the results of finite element calculations performed for two simplified unit cells: spherical and cylindrical. Advantages and deficiencies of such numerical verification of analytical homogenization schemes are indicated. Next, predictions of both approaches are compared with available experimental data for two composite systems for tension and compression tests in the elastic-plastic regime using tangent and secant linearization procedures. In the examined range of strain and ceramic volume content, both the Mori-Tanaka averaging scheme and the generalized self-consistent scheme lead to reliable predictions when combined with the tangent linearization, while the use of secant moduli results in a too stiff response. It is also found that the mean-field predictions for a small ceramic volume content are very close to the results obtained from the finite-element analysis of a spherical unit cell.

Słowa kluczowe:

Metal-matrix composites, Effective properties, Analytical estimates, Numerical homogenization, Nonlinear analysis

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The full elasticity tensor for nano-crystalline copper is derived in molecular simulations by performing numerical tests for a set of generated samples of the polycrystalline material. The results are analysed with respect to the anisotropy degree of the overall stiffness tensor resulting from the limited number of grain orientations and their spatial distribution. The dependence of the overall bulk and shear moduli of an isotropized polycrystal on the average grain diameter is analysed. It is found that while the shear modulus decreases with grain size, the bulk modulus shows negligible dependence on the grain diameter and is close to the bulk modulus of a single crystal. A closed-form mean-field model of effective elastic properties for a bulk nano-grained polycrystal with cubic grains, i.e. made of a material with cubic symmetry, is formulated. In the model all parameters are based on the data for a single crystal and on the averaged grain size without any need for additional fitting. It is shown that the proposed model provides predictions of satisfactory qualitative and quantitative agreement with atomistic simulations.

Słowa kluczowe:

Molecular statics, Elasticity, Polycrystal, Effective medium, Nano-crystalline copper

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A three-scale crystal plasticity model is applied to simulate microstructure evolution in hcp titanium subjected to cold rolling. Crystallographic texture and misorientation angle development, as an indicator of grain refinement, are studied. The impact of twinning activity on both phenomena is accounted for by combining the original three-scale formulation with the probabilistic twin-volume consistent (PTVC) reorientation scheme. The modeling results are compared with available experimental data. It is shown that the simulated textures are in accordance with the experimental measurements. The basic components of misorientation angle distribution, especially in the range of high angle boundaries, are also well reproduced.

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Grain refinement due to severe plastic deformation is simulated using the crystal plasticity finite element method in the total Lagrangian setting. A rate-independent model with the regularized Schmid law is applied. As an example, a single pass of the equal channel angular pressing process is considered. Texture evolution, misorientation angle distributions and maps of new grains are presented. A special algorithm for tracking the creation of new grains in finite element simulations is developed. The results are analysed with respect to experimental data available in the literature. The possible mechanisms leading to the fragmentation of grains in a face centred cubic material are discussed. The influence of the quality of the microstructure representation on the simulation results is assessed

Słowa kluczowe:

crystal plasticity, severe plastic deformation, grain refinement, finite element method

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This paper deals with the numerical analysis of localized deformation for a rectangular plate in membrane tension, modelled with large strain thermoplasticity. The aim is to determine the influence of selected factors on the localization phenomena, which can result from geometrical, material, and thermal softening. Two types of boundary conditions are considered: plane stress and plane strain, as well as two yield functions, Huber–Mises–Hencky and Burzyński–Drucker–Prager, with selected values of friction angle. First, isothermal conditions are considered and next, a conductive case with thermal softening is studied. Moreover, three types of plastic behaviour are analysed: strain hardening (with different values of hardening modulus), ideal plasticity, and strain softening. Numerical tests, performed using AceGen/FEM packages, are carried out for the rectangular plate under tension with an imperfection, using three finite element discretizations. The results for plane strain in the isothermal model show that with the decrease of linear hardening modulus, we can observe stronger mesh sensitivity, while for plane stress, mesh sensitivity is visible for all cases. Furthermore, for the thermomechanical model the results also depend on the mesh density due to insufficient heat conduction regularization

Słowa kluczowe:

Thermoplasticity, Large strains, Strain localization, Parametric study

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Effects of particle packing and size on the overall elastic properties of particulate random composites are analyzed. In order to account for the two effects the mean-field Morphologically Representative Pattern (MRP) approach is employed and an additional interphase surrounding inclusions (coating) is introduced. The analytical mean-field estimates are compared with the results of computational homogenization performed using the finite element (FE) method. Periodic unit cells with cubic crystal-type arrangements and representative volume elements with random distributions of particles are used for verification purposes. The validity of the MRP estimates with respect to the FE results is assessed.

Słowa kluczowe:

Composite materials, Elasticity, Micro-mechanics, Packing and size effects

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A consistent algorithmic treatment of the incremental Mori–Tanaka (MT) model for elasto-plastic composites is proposed. The aim is to develop a computationally efficient and robust micromechanical constitutive model suitable for large-scale finite-element computations. The resulting overall computational scheme is a doubly-nested iteration-subiteration scheme. The Newton method is used to solve the nonlinear equations at each level involved. Exact linearization is thus performed at each level so that a quadratic convergence rate can be achieved. To this end, the automatic differentiation (AD) technique is used, and the corresponding AD-based formulation is provided. Excellent overall performance of the present MT scheme in threedimensional finite-element computations is illustrated.

Słowa kluczowe:

Mori–Tanaka method, Composite materials, Elasto-plasticity, Finite element method, Automatic differentiation

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This paper presents experimental and numerical results of a polyurethane shape memory polymer (SMP) subjected to cyclic tensile loading. The goal was to investigate the polymer yielding phenomena based on the effects of thermomechanical coupling. Mechanical characteristics were obtained with a testing machine, whereas the SMP temperature accompanying its deformation process was simultaneously measured in a contactless manner with an infrared camera. The SMP glass transition temperature was approximately 45oC; therefore, when tested at room temperature, the polymer is rigid and behaves as solid material. The stress and related temperature changes at various strain rates showed how the SMP yield limit evolved in subsequent loading-unloading cycles under various strain rates. A two-phase model of the SMP was applied to describe its mechanical response in cyclic tension. The 3D Finite Element model of a tested specimen was used in simulations. Good agreement between the model predictions and experimental results was observed for the first tension cycle.

Słowa kluczowe:

Shape memory polymer, Tension cyclic loading, Thermomechanical coupling, Yield limit, Thermoelastic effect, Constitutive model

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The incremental Mori–Tanaka model of elasto-plastic composites is discussed, and the corresponding finite-step formulation is shown to lead to discontinuities in the overall response at the instant of elastic-to-plastic transition in the matrix. Specifically, two situations may be encountered: the incremental equations may have two solutions or no solution. In the former situation, switching between the two solutions is associated with a jump in the overall stress. Response discontinuities are studied in detail for a special case of proportional deviatoric loading. The discontinuities constitute an undesirable feature of the incremental Mori–Tanaka scheme that apparently has not been discussed in the literature so far. Remedies to the related problems are briefly discussed.

Słowa kluczowe:

mean-field homogenization, Mori–Tanaka method, incremental scheme, composite materials, elasto-plasticity

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The paper deals with the thermomechanical extension of a large strain hyperelasto-plasticity model and focuses on algorithmic aspects and localization simulations. The formulation includes the degradation of the yield strength due to the increase of an averaged plastic strain measure and temperature, thus, three sources for loss of stability are included in the description. A gradient-enhancement of the model is incorporated through an additional differential equation, but localization is also influenced by heat conduction. The finite element analysis is performed for an elongated plate in plane strain conditions, using different finite elements and values of material parameters related to regularization (internal length scales are related to gradient averaging as well as heat conduction). In particular, the influence of the F-bar enrichment on the simulation results is studied. All computational tests are performed using selfprogrammed user subroutines prepared within a symbolic-numerical tool AceGen which is equipped with automatic differentiation options, allowing for automatic linearization of the governing equations.

Słowa kluczowe:

thermoplasticity, softening, gradient averaging, strain localization, automatic linearization, AceGen package

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This paper presents experimental and modeling results of the effects of thermomechanical couplings occurring in a polyurethane shape memory polymer (SMP) subjected to tension at various strain rates within large strains. The SMP mechanical curves, recorded using a testing machine, and the related temperature changes, measured in a contactless manner using an IR camera, were used to investigate the polymer deformation process at various loading stages. The effects of thermomechanical couplings allowed the determination of the material yield point in the initial loading stage, the investigation of nucleation and development of the strain localization at larger strains and the estimation of the effects of thermoelastic behavior during the unloading process. The obtained stress–strain and thermal characteristics, the results of the dynamic mechanical analysis and estimated values of the shape fixity and shape recovery parameters confirmed that the shape memory polymer (T g = 45°C) is characterized by good mechanical and shape memory properties, as well as high sensitivity to the strain rate. The mechanical response of the SMP subjected to tension was simulated using the finite element method and applying the large strain, two-phase model. Strain localization observed in the experiment was well reproduced in simulations and the temperature spots were correlated with the accumulated viscoplastic deformation of the SMP glassy phase.

Słowa kluczowe:

shape memory polymer, thermomechanical coupling, infrared camera, tension test, strain rate, strain localization, constitutive model

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A new three-scale model of polycrystal accounting for grain refinement is proposed. The model is embedded into the crystal plasticity framework. With the experimental reference to the development of the dislocation induced cell substructure, a single crystallite in the representative grain aggregate is initially subdivided into subdomains with the crystallographic orientations slightly misoriented with respect to the nominal orientation of a parent grain. The predicted misorientation evolution of subgrains with respect to the reference orientation of a crystallite is an indicator of grain refinement. The correlation between the increase of a misorientation angle and a slip activity pattern is analyzed. The model predictions are compared with available experimental data.

Słowa kluczowe:

Crystal plasticity, Severe plastic deformation, Grain refinement

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Significant research effort is concentrated worldwide on development of graphene-based metal-matrix composites with enhanced thermomechanical properties. In this work, we apply two classical micromechanical mean-field theories to estimate the effective thermoelastic properties that can be achieved in practice for a copper–graphene composite. In the modelling, graphene is treated as an anisotropic material, and the effect of its out-of-plane properties, which are less recognized than the in-plane properties, is studied in detail. To address the severe difficulties in processing of graphene-based metal-matrix composites, the copper–graphene composite is here assumed to additionally contain, due to imperfect processing, particles of graphite and voids. It is shown quantitatively that the related imperfections may significantly reduce the expected enhancement of the effective properties. The present predictions are also compared to the experimental data available in the literature.

Słowa kluczowe:

Metal-matrix composites (MMCs), Mechanical properties, Thermal properties, Micro-mechanics, Graphene

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This work deals with the prediction of the macroscopic behavior of two-phase composites, based on the Mori–Tanaka scheme combined with an additive/sequential interaction rule and tangent linearization of viscoplastic response. Cyclic tension compression loadings are considered to further validate the approach. The composite is made of spherical inclusions dispersed in a matrix. Both materials have an elastic–viscoplastic behavior. In a second part, finite element calculations are performed using ABAQUS/STANDARD software in order to validate the proposed homogenization technique. A representative volume element is analyzed with 30 randomly distributed inclusions. Comparisons between the additive tangent Mori–Tanaka scheme and finite element calculations are made for different volume fractions of inclusions, different contrasts in elastic and viscous properties and different strain rates and strain amplitudes. These comparisons demonstrate the efficiency of the proposed homogenization scheme. The effect of isotropization of the viscoplastic tangent stiffness is also investigated. It is concluded that quality of predictions does not benefit from such simplification, contrary to the known result for elastic–plastic case.

Słowa kluczowe:

Elasto-viscoplasticity, Homogenization, Finite element, Composite, Mori–Tanaka scheme

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In this paper extensive research on the polyurethane shape memory polymer (PU-SMP) is reported, including its structure analysis, our experimental investigation of its thermomechanical properties and its modelling. The influence of the effects of thermomechanical couplings on the SMP behaviour during tension at room temperature is studied using a fast and sensitive infrared camera. It is shown that the thermomechanical behaviour of the SMP significantly depends on the strain rate: at a higher strain rate higher stress and temperature values are obtained. This indicates that an increase of the strain rate leads to activation of different deformation mechanisms at the micro-scale, along with reorientation and alignment of the molecular chains. Furthermore, influence of temperature on the SMP's mechanical behaviour is studied. It is observed during the loading in a thermal chamber that at the temperature 20°C below the glass transition temperature (Tg) the PU-SMP strengthens about six times compared to the material above Tg but does not exhibit the shape recovery. A finite-strain constitutive model is formulated, where the SMP is described as a two-phase material composed of a hyperelastic rubbery phase and elastic-viscoplastic glassy phase. The volume content of phases is governed by the current temperature. Finally, model predictions are compared with the experimental results.

Słowa kluczowe:

shape memory polyurethane, thermomechanical couplings, infrared camera, temperature change, dynamic mechanical analysis, strain rate, constitutive model

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Texture evolution in commercially pure titanium deformed by equal-channel angular pressing (ECAP) and extrusion with forward–backward rotating die (KoBo) is studied both experimentally and numerically. New results are provided that demonstrate the effects of distinct and complex deformation paths on the texture in the ultra-fine grained (UFG) material obtained after severe plastic deformation (SPD). The numerical simulations are based on the self-consistent viscoplastic method of grain-to-polycrystal scale transition. A recently proposed modification of the probabilistic scheme for twinning is used that provides consistent values of the twin volume fraction in grains. The basic components of the experimentally observed texture are reasonably well reproduced in the modelling. The numerical simulations provide an insight into the internal mechanisms of plastic deformation, revealing substantial activity of mechanical twinning in addition to the basal and prismatic slip in titanium processed by ECAP.

Słowa kluczowe:

Texture evolution, UFG materials, SPD processes, Crystal plasticity, Twinning

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The optimization procedure is worked out for finding an optimal content of phases in metal–ceramic composites in case of conflicting objectives regarding thermo-mechanical properties of the material for a specific target application. Relationships between the material composition and effective properties of the composite are calculated by employing several methods of continuum micromechanics. A constrained minimization problem is solved for a single objective function based on the weighted squared distances from the best available thermo-mechanical properties for the material system selected. A compound block diagram is proposed for quick assessment of the consequences of deviating from the optimal composition. The developed procedure is applied to practical examples of Al2O3–Cu composites for brake disks and Al2O3–NiAl composites for valves of potential use in automotive industry.

Słowa kluczowe:

Metal–matrix composites (MMCs), Thermomechanical, Plastic deformation, Micro-mechanics, Multi-criteria optimization

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Streszczenie:

Multifunctional new material—polyurethane shape memory polymer (PU-SMP)—was subjected to tension carried out at room temperature at various strain rates. The influence of effects of thermomechanical couplings on the SMP mechanical properties was studied, based on the sample temperature changes, measured by a fast and sensitive infrared camera. It was found that the polymer deformation process strongly depends on the strain rate applied. The initial reversible strain is accompanied by a small drop in temperature, called thermoelastic effect. Its maximal value is related to the SMP yield point and increases upon increase of the strain rate. At higher strains, the stress and temperature significantly increase, caused by reorientation of the polymer molecular chains, followed by the stress drop and its subsequent increase accompanying the sample rupture. The higher strain rate, the higher stress, and temperature changes were obtained, since the deformation process was more dynamic and has occurred in almost adiabatic conditions. The constitutive model of SMP valid in finite strain regime was developed. In the proposed approach, SMP is described as a two-phase material composed of hyperelastic rubbery phase and elastic-viscoplastic glassy phase, while the volume content of phases is specified by the current temperature.

Słowa kluczowe:

constitutive model, dynamic mechanical analysis, shape memory polyurethane, strain rate, temperature change, thermomechanical couplings

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In applications to sensors, actuators, guide wires, special grips for handicapped people, a shape memory alloy (SMA) or shape memory polymer (SMP) are used as working elements that perform cyclic motions. In order to evaluate the reliability of the shape memory materials (SMM), cycling and fatigue deformation properties are investigated. Since the SMM are very sensitive to temperature, not only mechanical properties but also their related temperature changes accompanying the deformation process should be taken into account. The presented paper embraces experimental investigation of effects of thermomechanical couplings occurring in shape memory alloy and shape memory polymer subjected to various kinds of cycling loading. The deformation was carried out on MTS 858 Testing machine. The strain was measured by a mechanical extensometer, so the stress-strain characteristics were elaborated with high accuracy. Furthermore, a fast and sensitive FLIR Co Phoenix infrared (IR) measurement system was used in order to record infrared radiation from the sample surface. It enables obtaining temperature distribution of the sample as a function of the deformation parameters. For each strain cycle, an increase in temperature during the loading and the temperature decrease during the unloading processes was observed. It was found that the temperature increment recorded during the cyclic deformation depends on the strain rate, the kind of the material and the test conditions. The higher the strain rate the higher the stress and temperature changes were obtained, since the deformation process was more dynamic and has occurred in almost adiabatic conditions. It was shown that various deformation mechanisms are active during various loading stages.

Słowa kluczowe:

shape memory alloy, shape memory polymer, cyclic deformation, thermomechanical coupling, infrared camera

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Streszczenie:

This paper deals with the development of a family of gradient-enhanced elasticity-damage-plasticity models for the simulation of failure in metallic and composite materials. The model incorporates finite deformations and is developed with the assumption of isotropy and isothermal conditions. The gradient enhancement applied to the damage part of the model aims at removing pathological sensitivity to the finite element discretization which can occur due to material softening.
The attention is focused on the algorithmic aspects and on the implementation of the model using AceGen tool. The numerical verification tests of the described model are performed using the Mathematica-based package AceFEM. Particularly, uniaxial tension test for a bar with a variable cross-section and tension of a perforated plate are examined.

Słowa kluczowe:

arge strains, damage, plasticity, gradient-enhancement, AceGen package

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Streszczenie:

The paper is aimed at modelling of evolution of crystallographic texture in KOBO extrusion which is an unconventional process of extrusion assisted by cyclic torsion. The analysis comprises two steps. In the first step, the kinematics of the KOBO extrusion process is determined using the finite element method. A simplifying assumption is adopted that the material flow is not significantly affected by plastic hardening, and thus a rigid-viscoplastic material model with no hardening is used. In the second step, evolution of crystallographic texture is modelled along the trajectories obtained in the first step. A micromechanical model of texture evolution is used that combines the crystal plasticity model with a self-consistent grain-to-polycrystal scale transition scheme, and the VPSC code is used for that purpose. Since each trajectory corresponds to a different deformation path, the resulting pole figures depend on the position along the radius of the extruded rod.

Słowa kluczowe:

plasticity, microstructure, crystallographic texture, KOBO extrusion

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Streszczenie:

Different approaches to account for twinning in crystal plasticity models are discussed. In particular, three main issues related to this mechanism of plastic deformation are addressed: modelling of texture evolution in the presence of twinning, impact of slip-twin interactions on hardening laws formulation and influence of layered substructure on the macroscopic response of materials. Some of the discussed modelling tools are illustrated with an example of titanium aluminide

Słowa kluczowe:

crystal plasticity, twinning, texture evolution, hardening

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In the paper the theoretical analysis of bounds and self-consistent estimates of overall properties of linear random polycrystals composed of arbitrarily anisotropic grains is presented. In the study two invariant decompositions of Hooke’s tensors are used. The applied method enables derivation of novel expressions for estimates of the bulk and shear moduli, which depend on invariants of local stiffness tensor. With use of these expressions the materials are considered for which at the local level constraints are imposed on deformation or some stresses are unsustained

Słowa kluczowe:

Creep, Anisotropic material, Polycrystalline material, Invariant decompositions

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The paper addresses the problem of suitable approximation of the interaction between phases in heterogeneous materials that exhibit both viscous and elastic properties. A novel approach is proposed in which linearized subproblems for an inhomogeneity-matrix system with viscous or elastic interaction rules are solved sequentially within one incremental step. It is demonstrated that in the case of a self-consistent averaging scheme, an additional accommodation subproblem, besides purely viscous and elastic subproblems, is to be solved in order to estimate the material response satisfactorily. By examples of an isotropic two-phase material it is shown that the proposed approach provides acceptable predictions in comparison with the existing models.

Słowa kluczowe:

Micromechanics, Viscoelasticity, Viscoplasticity, Homogenization, Self-consistent scheme

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Micromechanical model of polycrystalline materials with lamellar substructure is presented. The lamellar microstructure of grains is accounted for using the well-established framework developed for layered composites. Within the approach different scale transition rules between the level of lamellar grain and the polycrystalline sample can be employed. The model capabilities are tested using the example of TiAl intermetallic. Elastic properties and the initial yield surface for the lamellar grain (PST crystal) and for the untextured polycrystal are estimated. Elastic and plastic anisotropy degree is analyzed

Słowa kluczowe:

micromechanics, homogenization, lamellar substructure, anisotropic material, anisotropy degree

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Twinning has been incorporated into a crystal plasticity model with the regularized Schmid law. In order to account for the appearance of twin-related orientations, a new probabilistic twin reorientation scheme that maintains the number of reoriented grains consistent with the accumulated deformation by twinning within the polycrystalline element, has been developed. A hardening rule describing slip–twin interactions has been also proposed. Model predictions concerning material response and texture evolution have been analyzed for fcc materials of low stacking fault energy.

Słowa kluczowe:

Crystal plasticity, Twinning, Hardening, Texture, Anisotropic material, Polycrystal model

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Streszczenie:

Analytical solutions for bounds of overall properties are derived for single-phase polycrystalline materials of random texture, composed of grains with arbitrary anisotropy and described by the linear constitutive law. Self-consistent estimates are found for these materials and they are studied in more details when anisotropic grains are volumetrically isotropic. Reduction of the above solutions for incompressible materials or materials with constraint modes of deformation is also derived. Existence and uniqueness of the obtained solutions are discussed. In order to obtain the solutions, simultaneously the spectral and harmonic decomposition of fourth order Hooke’s tensor are used. Utility of the obtained results is demonstrated on the examples of metals and alloys of high specific strength and stiffness

Słowa kluczowe:

anisotropic materials, self-consistent estimates, polycrystals

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The rigid-plastic crystal plasticity model accounting for the effect of micro-shear banding mechanism on the reduction of the global strain hardening rate is presented. The instantaneous contribution of micro-shear bands in the rate of plastic deformation is described by means of the constitutive function that depends on the type of strain path specified by the current direction of strain rate tensor. The capabilities of the model are explored by studying the strain-stress behavior of polycrystalline material together with the crystallographic texture evolution in the polycrystalline element

Słowa kluczowe:

Crystallographic texture, Anisotropic material, Crystal plasticity, Polycrystalline material, Micro-shear banding

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Streszczenie:

The spectral decomposition of elasticity tensor for all symmetry groups of a linearly elastic material is reviewed. In the paper it has been derived in non-standard way by imposing the symmetry conditions upon the orthogonal projectors instead of the stiffness tensor itself. The numbers of independent Kelvin moduli and stiffness distributors are provided. The corresponding representation of the elasticity tensor is specified

Słowa kluczowe:

linear elasticity, anisotropy, symmetry group, spectral decomposition

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Dynamic localization failure of a thin sheet made of AISI 316H steel is considered on the macroscopic and mesoscopic level for proportional and nonproportional stress paths. On the macroscopic level, we propose: (1) the replacement of time as independent variable by a function of plastic dissipation and (2) dependence of the initial equivalent yield stress on stress rate. On the mesoscopic level - the regularized Schmid model for description of the single grain behavior is used and the polycrystalline yield surface generated by the texture development enables to improve the Forming Limit Diagrams for the sheet element.

Słowa kluczowe:

dynamic localization failure, Forming Limit Diagrams, regularized Schmid law, sheet textures

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The rigid-plastic crystal plasticity model with single yield surface of 2n-degree is applied to simulate the polycrystalline behaviour and the crystallographic texture development under non-proportional deformation paths. The role of two controlling parameters: the amplitude and frequency for the processes of tension or compression assisted by cyclic torsion of thin-walled tubes made of copper is analysed. The effect of micro-shear bands on the reduction of global hardening rate is described by means of the contribution function of shear banding in the rate of plastic deformation. The conclusions drawn from the study can find also application in the extension of the analysis for high strength and hard deformable materials.

Słowa kluczowe:

micromechanics, modelling of materials, rigid-plastic solids, crystal plasticity, texture, cyclic torsion, non-proportional deformation path, micro-shear bands

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Technological metal forming processes of extrusion, forging and rolling with imposed cyclic torsion or shear deformation have been recently studied in view of their advantages with respect to monotonic loading processes, cf. Bochniak and Korbel [2–4]. The present work is aimed to analyze such process in the case of simple tension or compression of a cylindrical tube with imposed cyclic torsional deformation. The material element response is assumed to be rigid-perfectly plastic or elastic-perfectly plastic. For these models, the analytical solutions can be provided for the steady cyclic responses and the effect of two process parameters, namely the ratio of shear and axial strain rates η and the amplitude of shear strain γm, can be clearly demonstrated. Three different regimes of cyclic response can be visualized in the plane η, γm. The cyclic response of a cylinder under combined axial compression and cyclic torsion is predicted by considering a simplified model of a set of concentric tubes and neglecting their radial stress interaction. The axial force and torsional moment are then specified by averaging the responses of consecutive tubes. The cyclic response diagrams for the cylinder are then generated in terms of axial force and torsional moment related to axial deformation and angle of twist

Słowa kluczowe:

cyclic torsion, plastic deformation of cylinders, elastic-perfectly plastic model, rigid-perfectly plastic model, analytical solutions of cyclic response of a cylinder

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The rigid-plastic model for the single grain is developed in which the velocity gradient is split into two parts connected with crystallographic slip and micro-shear bands respectively. For crystallographic slip the regularized Schmid law proposed by Gambin is used. For the micro-shear bands the model developed by Pęcherski, which accounts for the contribution of this mechanism in the rate of plastic deformation by means of a function fms is applied. Different constitutive equations for the plastic spin due to two considered mechanisms of plastic deformation are used. The present model is applied to simulate crystallographic texture evolution in the polycrystalline element.

Słowa kluczowe:

crystallographic texture, modelling of texture, micro-shear bands, regularized Schnid law, plastic spin

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Streszczenie:

Model of evolution of plastic anisotropy due to crystallographic texture development, in metals subjected to large deformation processes, is presented. The model of single grain with the regularized Schmid law proposed by Gambin is used. Evolution of crystallographic texture during drawing, rolling and pure shear is calculated. Phenomenological texture-dependent yield surface for polycrystalline sheets is proposed. Evolution of this yield surface is compared with evolution of phenomenological higher order yield surfaces proposed by Hill and Barlat with Lian for drawing, rolling and pure shear processes. The change of the Hill yield surface and the Barlat–Lian yield surface is obtained by replacing material parameters present in these conditions by texture-dependent functions.

Słowa kluczowe:

Crystallographic texture, Anisotropic material, Crystal plasticity, Polycrystalline material

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In the paper description of anisotropy of textured metals using macro and micro models is compared. In the present macro-approach the texture anisotropy is described by introducing a second order microstructure tensor whose principal directions specify the orthotropy axes. A scalar orientation parameter $\eta$ is introduced in order to specify the relative orientation of the generalized traction vector with respect to anisotropy axes. The yield stress is assumed to depend on the parameter $\eta$ with specific forms introduced in order to provide quantitative description of yield stress variation with loading orientation. The phenomenological approach is next confronted with the microstructural approach based on the analysis of crystallographic slip and induced lattice reorientation in a representative grain aggregate. The resulting yield surface for polycrystalline aggregate is then compared with the macroscopic description based on the orientational variation of the yield stress. The proposed macro description seems much simpler from micro-approach and could prove convenient in the analysis of technological processes for textured materials.

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This paper deals with the numerical investigation of ellipticity of the boundary value problem for isothermal finite strain elasto-plasticity. Ellipticity can be lost when softening occurs. A discontinuity surface then appears in the considered material body and this is associated with the ill-posedness of the boundary value problem. In the paper the condition for ellipticity loss is derived using the deformation gradient and the first Piola-Kirchhoff stress tensor. Next, the obtained condition is implemented and numerically tested within symbolic-numerical tools AceGen and AceFEM using the benchmark of an elongated rectangular plate with imperfection in plane stress and plane strain conditions.

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Experimental results of effects of thermomechanical couplings occurring in polyurethane shape memory polymer (PU-SMP) during tension at different strain rates are presented. Stress-strain curves were recorded by MTS 858 testing machine. The temperature changes were estimated by using a fast and sensitive infrared camera (Phoenix FLIR IR System). The stress and temperature vs. strain characteristics obtained during the tension enable to investigate the SMP deformation process and distinguish 3 different stages: the first, accompanied by a drop in temperature called thermoelastic effect, related to a limit of the material reversible deformation, the second plastic stage, associated with change of the material structure and significant increase in temperature, and the third - related to the mechanisms of damage - a breaking of the polymer chains, leading to the specimen rupture.

Słowa kluczowe:

shape memory polymer, thermomechanical coupling, tension, infrared camera

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Streszczenie:

Experimental results of effects of thermomechanical couplings occurring in polyurethane shape memory polymer (PU-SMP) subjected to cyclic loading at various strain rates are presented. Stress-strain characteristics were recorded by the testing machine, whereas the specimen temperature changes were measured by a fast and sensitive infrared camera. The influence of strain rate on the polymer thermomechanical behaviour was studied. It was found that the SMP is very sensitive to the strain rate. The higher the strain rate, the higher the values of the stress and temperature changes were obtained. In the initial stage of deformation a drop in temperature called thermoelastic effect, determining a limit of the material reversible deformation, was investigated.

Słowa kluczowe:

thermomechanical couplings, polyurethane shape memory polymer, cyclic loading, various strain rates, sensitive infrared camera, thermoelastic effect, thermoelastic effect, reversible deformation

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A computationally efficient procedure for modelling of microstructural changes on complex and spatially nonuniform deformation paths of severe plastic deformation (SPD) is presented. The analysis follows a two-step procedure. In the first step, motivated by saturation of material hardening at large accumulated strains, the steady-state kinematics of the process is generated for a non-hardening viscoplastic model by using the standard finite element method for a specified SPD scheme. In the second step, microstructural changes are investigated along the deformation-gradient trajectories determined in the first step for different initial locations of a material element. The aim of this study is to predict texture evolution and grain refinement in a non-conventional process of cold extrusion assisted by cyclic rotation of the die, called KOBO process, which leads to an ultra-fine grain structure. The texture evolution is calculated for fcc and hcp metals by applying crystal visco-plasticity combined with the self-consistent scale transition scheme. In parallel, by applying the simplified phenomenological model of microstructure evolution along the trajectories, grain refinement is modelled. The results are compared with available experimental data.

Słowa kluczowe:

SPD processes, Texture evolution, UFG materials, Crystal plasticity, Grain refinement

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Streszczenie:

The paper presents experimental evaluation and modelling of effects of thermomechanical couplings in shape memory alloy (SMA) and shape memory polymer (SMP). TiNi SMA and polyurethane PU-SMP are subjected to tension on MTS Testing machine. Fast infrared camera (IR) Phoenix FLIR System enable obtaining temperature distribution and average temperature changes of the specimens during the deformation process. Mechanical and infrared characteristics recorded during the SMA loading show that after initial, macroscopically homogeneous deformation a localized transformation develops, accompanied by significant temperature changes. Inclined bands of higher temperature accompanying exothermic forward transformation are recorded during the loading, whereas bands of lower temperature related to endothermic reverse transformation are observed during the unloading process. The infrared imaging and average temperature of the SMA sample compared to their mechanical characteristics allow to investigate the current stage of the stress-induced transformation process. A decrease of the specimen temperature reveals the saturation stage of the transformation. Both mechanical and thermal effects significantly depend on the strain rate; the higher the strain rate, the higher the temperature and stress are obtained. Similar experimental methodology is applied to investigate effects of thermomechanical couplings in shape memory polyurethane subjected to tension at various strain rates. Constitutive model valid in finite strain regime is proposed, where the SMP is described as a two-phase material composed of hyperelastic rubbery phase and elastic-viscoplastic glassy phase, while the volume content of phases is specified by the current temperature. Experimental results and modelling show that the SMP deformation process strongly depends on the strain rate, much stronger than for metals and alloys. At higher strain rate higher stress and temperature changes are obtained, since the deformation process is more dynamic and occurs in almost adiabatic conditions. It is shown that during the SMP loading process various deformation mechanisms are active at various strain rates.

Słowa kluczowe:

shape memory alloy, transformation bands, infrared camera, constitutive model, shape memory polymers, elastic modulus, yield stress, glass transition temperature, shape fixity, shape recovery

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Streszczenie:

Experimental results of effects of thermomechanical couplings occurring in polyurethane shape memory polymer (PU-SMP) subjected to cyclic loading at, are presented. Stress-strain characteristics were recorded by the testing machine, whereas the specimen temperature changes were measured by a fast and sensitive infrared camera. The influence of strain rate on the polymer thermomechanical behaviour is studied. It was found that PU-SMP is very sensitive to the strain rate. The higher the strain rate, the higher the values of stress and temperature changes were obtained. In the initial stage of deformation a drop in temperature called thermoelastic effect was recorded determining a limit of the material reversible deformation.

Słowa kluczowe:

thermomechanical couplings, polyurethane shape memory polymer, cyclic loading, different strain rates, infrared camera, thermoelastic effect

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Streszczenie:

Micromechanical modelling of metal-ceramic composites has been carried out to obtain a material of required thermo-mechanical properties. Quantitative transition from phase properties and morphology to macroscopic properties of a composite has been modelled by mean-field approaches, including the self-consistent scheme. An optimization method has been developed for the objective function that expresses a distance between the required values of macro-variables and those determined for a given set of microstructural parameters. The presented example concerns application of Al2O3-Cu composite to brake disks.

Słowa kluczowe:

multi-objective optimization, composite selection, metal matrix composites

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Streszczenie:

This paper deals with the development of a family gradient-enhanced elasticity-damage-plasticity models for the simulation of failure in metallic and composite materials. The model incorporates finite deformations and is developed with the assumption of isotropy and isothermal conditions. The gradient enhancement applied to the damage part of the model aims at removing pathological sensitivity to the finite element discretization which can occur due to material softening. The attention is focused on the algorithmic aspects and on the implementation of the model using AceGen tool for automatic code generation, thus circumventing the cumbersome derivation of the consistent tangent for the Newton’s method. Numerical verification tests of the described model are performed with the Mathematica-based package AceFEM. Particularly, uniaxial tension test for a bar with a variable cross-section and tension of a perforated plate are examined.

Słowa kluczowe:

large strain, damage, plasticity, gradient-enhancement, AceGen package

Afiliacje autorów:

Słowa kluczowe:

mean-field modelling, numerical homogenization, elasto-plasticity

Afiliacje autorów:

Słowa kluczowe:

Mean-field homogenization, Mori-Tanaka method, Composite materials, Finite element method

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Streszczenie:

Optimization of sheet metal forming processes requires a very good knowledge of material forming ability. During the forming of industrial parts, very complex strain paths are usually observed and can affect the formability of the sheet. Therefore, it is necessary to better understand and more accurately investigate deformation behaviour of sheet alloys. It should be noted that material testing of flat specimens under compression within a large deformation range procures many difficulties, and the buckling phenomenon seems to be the most im-portant. This paper shows the results of tension-compression tests carried out on specimens made of ultralight magnesium alloys AZ31B with nominal thickness equal to 1 mm using the anti-buckling fixture to avoid buckling problem.

Słowa kluczowe:

Bauschinger effect, cyclic loading, buckling, fixture, thin sheet

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Słowa kluczowe:

Micromechanics, Sequential linearization, Self-Consistent Scheme, Polycrystals, Finite Element

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Streszczenie:

This work deals with the prediction of the macroscopic behavior of two-phase composites, based on the Mori-Tanaka scheme combined with an additive/sequential interaction rule and tangent linearization of viscoplastic response. Cyclic tension compression loadings are considered to further evaluate the approach. The composite is made of spherical inclusions dispersed in a matrix. Both materials have an elastic-visco-plastic behavior. In the second part, finite element calculations are performed using ABAQUS/STANDARD software in order to validate the proposed homogenization technique. A representative volume element is analyzed with 30 randomly distributed inclusions.

Słowa kluczowe:

Multiscale Modeling, Elasto-viscoplasticity, Mori Tanaka Scheme, Composite

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Streszczenie:

The application of the sequential method for estimating the mechanical response of elastic-viscoplastic polycrystals of high viscous anisotropy is discussed. The results are compared with other averaging schemes. Since the anisotropy of viscous response is high the estimated overall response is dramatically different for different averaging schemes. Additionally the effect of different linearization procedure for the viscous part is studied, denoted as secant, affine and tangent. The results are compared to the recent FFT analysis available in the literature. For the studied example the tangent variant provides the overall response that agrees best with the FFT predictions.

Słowa kluczowe:

Micromechanics, Sequential linearization, Self-Consistent Scheme, Polycrystals

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Streszczenie:

Texture evolution and grain refinement in materials subjected to severe plastic deformation (SPD), in particular the ECAP and KoBo extrusion processes are examined in this work. The well known ECAP process consists in extruding a billet through an angular channel. In the KOBO process material is extruded with assistance of cyclic rotation of a die. Both processes lead to considerable grain refinement and often to strong texture evolution [2,5]. The VPSC code itself provides different variants of self-consistent (SC) micro-macro transition scheme. It was combined with the proposed crystal plasticity framework and has been used to simulate texture evolution. However, this model is two-scale and does not predict the grain refinement. In order to examine the latter phenomenon three-scale model of microstructure evolution was developed. The model is able to combine two micro-macro transition schemes to simulate the evolution of orientations inside a grain and decide if the formation of subgrains has occurred.

Słowa kluczowe:

texture evolution, grain refinement, SPD processes, crystal plasticity, micromechanics

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Streszczenie:

The paper concerns investigation of polyurethane shape memory polymer (SMP) properties. Shape fixity and shape recovery, important parameters for the SMP applications, were quantitatively estimated in thermomechanical cyclic loading; three subsequent thermomechanical loading cycles were performed. It was observed that the shape fixity is proper and does not depend on the cycle number. The obtained mean values of shape fixity parameters are 97-98 %. Although the shape recovery is poor (=83 %) in the first cycle of the thermomechanical loading, it is excellent in the subsequent cycles (=99-100 %). The evaluated parameters confirm good shape memory properties of the SMP.

Słowa kluczowe:

Shape memory polyurethane, shape fixity, shape recovery, thermomechanical loading, cyclic loading

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Streszczenie:

Different approaches to model packing and size effects are studied to model overall properties of particulate composites of different morphological features of phase distribution. The micromechanical schemes originating in the composite sphere model and its extension by morphologically-based pattern approach are taken as a basis. Analytical predictions are compared with results of computational homogenization performed on the generated representative volume elements of prescribed statistical characteristics.

Słowa kluczowe:

micromechanics, morphologically representative pattern, computational homogenization, size and scale effect

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Streszczenie:

Micromechanical modelling of magnesium alloys is presented. The applied model combines the crystal plasticity framework accounting for twinning with the self-consistent grain-to-polycrystal scale transition scheme. The mechanical response of the material in the experiments involving the strain path changes is studied, together with the prediction of the accompanying texture evolution. It is demonstrated that the evolution of microstructure has an important impact on the overall material behaviour. The model predictions will be verified in experiments performed on the rolled sheets made of AZ31B alloy

Słowa kluczowe:

micromechanics, crystal plasticity, twinning, texture evolution

Afiliacje autorów:

Streszczenie:

Polimery z pamięcią kształtu, podobnie jak niektóre stopy metali, wykazują efekt pamięci kształtu. Wykorzystuje się w nich różnicę właściwości termomechanicznych poniżej i powyżej temperatury zeszklenia Tg, w której polimer radykalnie zmienia swe własności, m.in. wartość modułu sprężystości. Materiały te posiadają możliwość szybkiej zmiany właściwości fizycznych w zależności od temperatury. Stają się miękkie po podgrzaniu powyżej Tg i pozwalają się łatwo formować, a podczas schłodzenia poniżej tej temperatury odzyskują poprzednią sztywność. Nadal pamiętają swój oryginalny kształt i wracają do niego podczas ponownego podgrzania powyżej Tg. Umożliwia to ich różnorodne praktyczne zastosowania, m.in. w przemyśle medycznym i farmaceutycznym, tekstylnym, spożywczym, lotniczym i kosmicznym.

Słowa kluczowe:

Polimery z pamięcią kształtu, temperatura zeszklenia, wartość modułu sprężystości, kamera termowizyjna

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Experimental evaluation and modeling of a new polyurethane shape memory polymer (SMP) subjected to cyclic tension and stress-relaxation tests are presented. The influence of effects of thermomechanical couplings on the SMP thermomechanical behaviour for various strain rates was studied, basing on the sample temperature changes measured by a fast and sensitive infrared camera. The constitutive model valid in finite strain regime was developed following [5]. In the proposed approach SMP is described as a two-phase material composed of hyperelastic rubbery phase and elastic-viscoplastic glassy phase while the volume content of phases is specified by the current temperature.

Słowa kluczowe:

Experimental evaluation, constitutive modeling, polyurethane shape memory polymer, cyclic tension, stress-relaxation tests, effects of thermomechanical couplings, thermomechanical behaviour, various strain rates, temperature changes, sensitive infrared camera, hyperelastic rubbery phase, elastic-viscoplastic glassy phase

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Microstructure evolution in hcp polycrystals subjected to severe plastic deformation, in particular in the KOBO extrusion and the equal channel angular pressing (ECAP) processes, are examined in this work, using the crystal plasticity framework. Modelling approach combines the large strain crystal plasticity model accounting for twinning and the tangent variant of the self-consistent (SC) scale transition scheme.

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hcp polycrystals, twinning, SPD processes, crystal plasticity, self-consistent model, microstructure evolution

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A constitutive model of SMP, formulated at large strain format, is developed. SMP is described as a two-phase material composed of a soft rubbery phase and a hard glassy phase. The volume fraction of each phase is postulated as a logistic function of temperature. Identification of model parameters has been performed using the experimental tensile loading-unloading tests with different strain rates conducted at thermal chamber at different temperatures.

Słowa kluczowe:

shape-memory polymers, two-phase model, large strain framework

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Shape memory polymers (SMP) are new unique and attractive materials which demonstrate shape memory properties. It means that the materials, as a result of an external stimulus such as temperature, can recover their original (permanent) shape from deformed (temporary) shape. The mechanical characteristics of SMP, e.g. the elastic modulus and the yield stress, change significantly below and above their glass transition temperature Tg. It can be explained by differences of molecular motion of the polymer chains below and above Tg [1, 2]. Two phenomena due to this can be observed in the SMP. The first one is a shape fixity which means that it is possible to fix a temporary shape by cooling the deformed SMP below Tg. The second phenomenon, called a shape recovery, denotes the property that the original shape, changed due to deformation, is recovered during subsequent heating above the SMP Tg temperature. Preliminary estimation of these two parameters, crucial to assess SMP potential applications, is the subject of this paper [1].

Słowa kluczowe:

Shape memory polymers, elastic modulus, yield stress, glass transition temperature, shape fixity, shape recovery

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This paper presents experimental evaluation of a new polyurethane shape memory polymer (PU-SMP) produced by SMP Technologies Inc. It discusses mechanical characteristics and temperature changes of the SMP specimens subjected to tension test performed at room temperature with various strain rates. Basing on the mechanical data and the relevant temperature changes, we have studied the thermomechanical properties of the PU-SMP and influence of the strain rate on the strain localization behavior. Finally, we have identified the material parameters for the one-dimensional rheological model of the SMP.

Słowa kluczowe:

shape memory polyurethane, tension test, dynamic mechanical analysis, infrared camera, temperature change, thermomechanical properties, rheological model

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Initial experimental evaluation of a new polyurethane shape memory polyner (PU-SMP) subjected to uniaxial tension carrięd out at different stlain rates is presented. The stress and strain data were recorded and temperature changes from the SMP specimen surface was deternrined using fast and sensitive infrared camera. Basing on themechanical characteristics and their relevant temperature changes, the SMP thernromechanical properties have been stLrdied. lnfluence of the strain rate on the SMP temperature, its structure and behaviour are discussed. Identification of the PU-SMP parameters for onc-dimensional rheological model proposed by Tobushi et. ttl. will be performed.

Słowa kluczowe:

Shape memory polymers, elastic modulus, yield stress, glass transition temperature

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