State Of Homogeneous Deformation Research Articles

A VFM-based identification method for the dynamic anisotropic plasticity of sheet metals

The anisotropic plasticity of sheet metals at high strain rates is a critical factor that can influence the fabrication and service safety of engineering parts under dynamic loading conditions. The characterization of dynamic anisotropic plasticity using conventional testing methods usually suffers from the limitations resulted from the homogeneous deformation state and one-dimensional wave propagation preconditions. In this work, a highly efficient approach is proposed for the simultaneous identification of the anisotropic yielding and hardening constitutive parameters at high strain rates based on the heterogeneous impact test and the virtual fields method. First, the identification framework that combines the selected anisotropic plasticity constitutive models and the principle of virtual work concerning the dynamic kinematics term is introduced. In order to validate the proposed identification algorithm, simulated virtual impact tests were performed to provide reference parameters and unpolluted inertial acceleration/strain/strain rate field data. These data were then processed to extract the target dynamic anisotropic parameters. The results show that using the double-notched impact configuration and the proposed identification algorithm the selected anisotropic yielding and hardening parameters can be reasonably identified from a single impact test, significantly simplifying the testing procedures compared to conventional dynamic testing methods. Also, the effects of different processing parameters and influential factors on the identification accuracy have been investigated. From the sensitivity studies, the preferred ranges of the processing parameters have been determined and the robustness of the proposed method within these verified.

Fiber-Matrix Interaction and Fiber Orientation in Simple Shearing of Fibrous Soft Tissues

Fiber-reinforcement is a common feature of many soft biological tissues. The response of fibrous biotissues to applied shear is thus of considerable current interest. We consider here the fundamental deformation of simple shear within the framework of transversely isotropic incompressible hyperelastic materials for fiber-reinforced specimens with a single family of parallel fibers oriented at a general angle to the direction of shear. It is well known that the normal stress effect characteristic of nonlinear elasticity plays a crucial role in maintaining an homogeneous deformation state in the bulk of the specimen. Here we investigate the effects of fiber-matrix interaction on the shear and lateral normal stresses. The inclusion of fiber-matrix interaction stiffens the shear stress response. As regards the normal stress, it is shown that the confining normal traction that needs to be applied to the top and bottom faces of a block in order to maintain simple shear can be compressive or tensile depending on the degree of anisotropy, fiber-matrix interaction and on the angle of orientation of the fibers. In the absence of such an applied traction, an unconfined sample tends to bulge outwards or contract inwards perpendicular to the direction of shear so that one has the possibility of both a positive or negative Poynting effect. It is shown that the fiber-matrix interaction enhances both the positive and negative Poynting effects. The results are illustrated using experimental data obtained by other authors for porcine brain white matter. In particular, it is shown that, for sufficiently small angles of orientation, a transition amount of shear exists at which the normal stress changes character from tensile to compressive with increasing amount of shear. An increase in the degree of fiber-matrix interaction enlarges the range of orientation angles for which this transition can occur and decreases the transition amount of shear. These transition amounts of shear are well within the physiological strain regime. The results obtained here are relevant to the development of accurate shear test protocols for the determination of constitutive properties of fibrous biological soft tissues.

Inertia-Based Identification of Elastic Anisotropic Properties for Materials Undergoing Dynamic Loadings Using the Virtual Fields Method and Heterogeneous Impact Tests

The characterization of material anisotropic properties at high strain rates remains a challenging work due to the limitations of the conventional dynamic testing methods. In this study, a novel inverse identification strategy is proposed based on the dynamic virtual fields method (VFM) to enable a simultaneous identification of the anisotropic constitutive parameters from a single high speed impact test of a non-uniform specimen. This is implemented by taking advantage of the heterogeneous full-field strain and inertial acceleration data, in which the restrictions of one-dimensional stress wave propagation and homogeneous deformation states for the conventional methods are released. Specifically, the dynamic VFM-based identification algorithm is developed first. Then, several virtual impact tests with different specimen configurations are designed to provide distinct stress/strain distributions. Next, the simulated full-field strain and acceleration data are utilized to extract the input target orthotropic stiffness components. The results show that the identification accuracy of the anisotropic parameters is highly dependent on the heterogeneity of the stress/strain distributions. Also, the identification results are unstable for different time steps but can be significantly improved using a minimization algorithm on multiple time steps. Finally, the influences of noise, impact speed and loading mode are analyzed in the sensitivity study.

Inertia-based identification of elastic anisotropic properties for materials undergoing dynamic loadings using the virtual fields method and heterogeneous impact tests

The characterization of material anisotropic properties at high strain rates remains a challenging work due to the limitations of the conventional dynamic testing methods. In this study, a novel inverse identification strategy is proposed based on the dynamic virtual fields method (VFM) to enable a simultaneous identification of the anisotropic constitutive parameters from a single high speed impact test of a non-uniform specimen. This is implemented by taking advantage of the heterogeneous full-field strain and inertial acceleration data, in which the restrictions of one-dimensional stress wave propagation and homogeneous deformation states for the conventional methods are released. Specifically, the dynamic VFM-based identification algorithm is developed first. Then, several virtual impact tests with different specimen configurations are designed to provide distinct stress/strain distributions. Next, the simulated full-field strain and acceleration data are utilized to extract the input target orthotropic stiffness components. The results show that the identification accuracy of the anisotropic parameters is highly dependent on the heterogeneity of the stress/strain distributions. Also, the identification results are unstable for different time steps but can be significantly improved using a minimization algorithm on multiple time steps. Finally, the influences of noise, impact speed and loading mode are analyzed in the sensitivity study.

Mean‐field homogenization based constitutive modeling of austenitic TRIP‐steels at the single crystal scale

AbstractIn order to accurately describe the effective mechanical behavior of single‐crystalline, austenitic TRIP‐steels, a two‐phase mean‐field homogenization scheme is presented in a finite deformation framework, which also includes transformation‐induced eigendeformations. The constitutive behavior of the two phases, namely austenite and martensite, is described by a rate‐independent single‐crystal plasticity model that captures elastic anisotropy as well as anisotropic slip and hardening behavior. The response of the two‐phase model under homogeneous deformation states is investigated and a particle strengthening effect is predicted in the absence of transformation‐induced eigendeformations and a suitable choice of material constants, while upon the inclusion of eigendeformations a gradual stress softening is observed.

Influence of microstructure morphology on multi-scale modeling of low-alloyed TRIP-steels

PurposeThe purpose of this study is to quantify the impact of the variation of microstructural features on macroscopic and microscopic fields. The application of multi-scale methods in the context of constitutive modeling of microheterogeneous materials requires the choice of a representative volume element (RVE) of the considered microstructure, which may be based on some idealized assumptions and/or on experimental observations. In any case, a realistic microstructure within the RVE is either computationally too expensive or not fully accessible by experimental measurement techniques, which introduces some uncertainty regarding the microstructural features.Design/methodology/approachIn this paper, a systematical variation of microstructural parameters controlling the morphology of an RVE with an idealized microstructure is conducted and the impact on macroscopic quantities of interest as well as microstructural fields and their statistics is investigated. The study is carried out under macroscopically homogeneous deformation states using the direct micro-macro scale transition approach.FindingsThe variation of microstructural parameters, such as inclusion volume fraction, aspect ratio and orientation of the inclusion with respect to the overall loading, influences the macroscopic behavior, especially the micromechanical fields significantly.Originality/valueThe systematic assessment of the impact of microstructural parameters on both macroscopic quantities and statistics of the micromechanical fields allows for a quantitative comparison of different microstructure morphologies and a reliable identification of microstructural parameters that promote failure initialization in microheterogeneous materials.

Fiber orientation effects in simple shearing of fibrous soft tissues

Fiber-reinforcement is a common feature of many soft biological tissues. Continuum mechanics modeling of the mechanical response of such tissues using transversely isotropic hyperelasticity is now well developed. The fundamental deformation of simple shear within this framework is examined here. It is well known that the normal stress effect characteristic of nonlinear elasticity plays a crucial role in maintaining a homogeneous deformation state in the bulk of the specimen. Here we consider the effect of anisotropy and fiber-orientation on the shear and normal stresses. It is shown that the confining traction that needs to be applied to the top and bottom faces of a block in order to maintain simple shear can be compressive or tensile depending on the degree of anisotropy and on the angle of orientation of the fibers. In the absence of such an applied traction, an unconfined sample tends to bulge outwards or contract inwards perpendicular to the direction of shear so that one has the possibility of both a positive or negative Poynting effect. The results are illustrated using experimental data obtained by other authors for porcine brain white matter. The general results obtained here are relevant to the development of accurate shear test protocols for the determination of constitutive properties of fibrous biological soft tissues.

Thermal and chemical effects in shear and compaction bands

Strain localization zones in the form of shear bands or compaction bands in geomaterials are observed across scales from sub-millimetric (grain size) to kilometric scale (geological structures). Triggering and evolution of such narrow zones of localized deformation depend on many factors. The mechanical behavior of geomaterials is central for the formation of such zones. However, thermal, pore-pressure and chemical effects play a crucial role in shear and compaction banding. Temperature increase and activation of chemical reactions such as mineral dehydration, carbonate decomposition, as well as dissolution/precipitation control the triggering and the evolution of localized deformation zones. Moreover, the inherent heterogeneous microstructure of geomaterials plays a significant role during strain localization. The purpose of this paper is to provide a review of recent research regarding the effects of temperature, pore-pressure, chemical reactions and microstructure on strain localization in geomaterials. Examples have been taken in relation with seismic slip and with compaction banding. Strain localization is treated as an instability from a homogeneous deformation state. Different types of instabilities may (co-) exist depending on different multi-physical couplings and micro-mechanisms. Finally, a comparison of rate dependent Cauchy continuum and rate independent generalized continua (Cosserat continuum) is made. This comparison leads to an analog expression for the instability condition and the thickness of the localized zone.

Microstructure and deformation mechanisms in nanocrystalline Ni–Fe. Part II. In situ testing during X-ray diffraction

Deformation mechanisms in nanocrystalline electrodeposited Ni (26nm) and Ni–Fe (12nm) are studied by strain rate sensitivity experiments and in situ mechanical testing during X-ray diffraction. We find a relatively low strength for Ni–Fe, which may be ascribed to a weakening of dislocation pinning points. Furthermore, the strain rate sensitivity of Ni–Fe is relatively low. The in situ studies allow the macroscopic mechanical response of Ni to be divided into three different deformation regimes: elastic, microplastic and macroplastic. For Ni–Fe, recovery mechanisms seem particularly important, resulting in an extended microplastic regime and necking before a state of homogeneous deformation can be reached.

EXPERIMENTAL CHARACTERIZATION AND MODELLING OF LARGE-STRAIN VISCOELASTIC BEHAVIOR OF A THERMOPLASTIC POLYURETHANE ELASTOMER

ABSTRACTThermoplastic polyurethane elastomers (TPUs) are a kind of elastomer that can be processed as thermoplastics. These elastomers exhibit a highly nonlinear behavior characterized by hyper-elastic deformability. Furthermore, the mechanical behavior of these elastomers is time-dependent, that is, they exhibit a viscoelastic behavior. We describe the material response of a TPU under moderate strains (ɛ < 1) by using an overlay visco-hyperelastic model assuming separation of time dependence from nonlinear stress–strain behavior. To achieve this goal, cyclic loading–unloading experimental tests are carried out for two homogeneous deformation states, uniaxial tension and pure shear, and the strain–stress data are then analyzed to fit a hyperelastic model. Conversely, a viscoelastic model is obtained from relaxation tests. Finally, the visco-hyperelastic model is implemented in a finite element calculation tool (ABAQUS), and the numerical results show a reasonable correlation with experimental data. As a result, a overlay visco-hyperelastic model depending on maximum strain is proposed.

Comparison of bifurcation and imperfection analyses of localized necking in rate-independent polycrystalline sheets

Plastic flow localization into a narrow band is investigated for a rate-independent polycrystalline sheet. Strain localization is considered to initiate at a point of bifurcation from the homogeneous deformation state or to result from the growth of a preexisting imperfection. Bifurcation analysis based on the rate-independent crystal plasticity model is found to give limit strains at a realistic strain level in the biaxial-stretching range. Limit strains predicted by the imperfection analysis are lower than those for bifurcation analysis and tend to approach those strain levels with decreasing amount of initial imperfection. Then, the bifurcation analysis is applied to the simulation of the forming limit for strongly textured sheets. The bifurcation analysis reveals the same trend of a texture dependence of limit strains as that for the imperfection analysis employing a rate-dependent model reported in the literature.

On the Normal Stresses in Simple Shearing of Fiber-Reinforced Nonlinearly Elastic Materials

We are concerned with a particular aspect of the simple shear problem within the framework of nonlinear elasticity for a class of incompressible transversely-isotropic fiber-reinforced materials. It is well known that, for isotropic hyperelastic materials, the normal stress effect characteristic of nonlinear elasticity is crucial in order to maintain a homogeneous deformation state in the bulk of the specimen. For the fiber-reinforced materials of concern here, we show that the confining traction that needs to be applied to the top and bottom faces of a block in order to maintain simple shear can be compressive or tensile depending on the degree of anisotropy and on the angle of orientation of the fibers. Inclusion of the second invariant in the isotropic part of the strain-energy used is shown to be of crucial importance in assessing the nature of the confining traction. In the absence of such an applied traction, an unconfined sample tends to bulge outwards or contract inwards perpendicular to the direction of shear. The character of the normal component of traction on the inclined faces is also investigated. The results are relevant to the development of accurate shear test protocols for the determination of constitutive properties of fiber-reinforced rubber-like materials and fibrous biological soft tissues.

Simple shearing of soft biological tissues

Shearing is induced in soft tissues in numerous physiological settings. The limited experimental data available suggest that a severestrain-stiffeningeffect occurs in the shear stress when soft biological tissues are subjected to simple shear in certain directions. This occurs at relatively small amounts of shear (when compared with the simple shear of rubbers). This effect is modelled within the framework of nonlinear elasticity by consideration of a class of incompressibleanisotropicmaterials. Owing to the large stresses generated for relatively small amounts of shear, particular care must be exercised in order to maintain a homogeneous deformation state in the bulk of the specimen. The results obtained are relevant to the development of accurate shear test protocols for the determination of constitutive properties of soft tissues. It is also demonstrated that there is a fundamental ambiguity in determining thenormalstresses in simple shear when soft tissues are modelled as incompressible hyperelastic materials owing to the arbitrary nature of the hydrostatic pressure term. Two physically well-motivated approaches to determining the pressure are presented here, and the resulting hydrostatic stresses are compared and contrasted. The possible generation of cavitational damage owing to critical hydrostatic stress levels is briefly discussed.

A computational micro‐sphere model applied to the simulation of phase‐transformations

AbstractWe present an efficient model for the simulation of polycrystalline materials undergoing solid to solid phase transformations. As a basis, we use a one‐dimensional, thermodynamically consistent phase‐transformation model. This model is embedded into a micro‐sphere formulation in order to simulate three‐dimensional boundary value problems. To solve the underlying evolution equations, we use a newly developed explicit integration scheme which could be proved to be unconditionally A‐stable. Besides the investigation of homogeneous deformation states, representative finite element examples are discussed. It is shown that the model nicely reflects the overall behaviour.

Experimental characterisation and constitutive modelling of RTM-6 resin under impact loading

The response to mechanical loading of the thermosetting resin system RTM-6 has been investigated experimentally as a function of strain rate and a constitutive model has been applied to describe the observed and quantified material behaviour. In order to determine strain rate effects and to draw conclusions about the hydrostatic stress dependency of the material, specimens were tested in compression and tension at strain rates from 10−3 to 104s−1. A Standard screw-driven tensile machine was used for quasi-static testing, with an ‘in house’ hydraulic rig and Hopkinson bars for medium and high strain rates, respectively. At all rates appropriate photography and optical metrology have been used for direct strain measurement, observation of failure and validation of experimental procedures. In order to enable the experimental characterisation of this brittle material at very high rates in tension, a novel pulse shaping technique has been applied. With the help of this device, strain rates of up to 3800s−1 have been achieved while maintaining homogeneous deformation state until specimen fracture in the gauge section of the tensile specimens. The yield stress and initial modulus increased with increasing strain rate for both compression and tension, while the strain to failure decreased with strain rate in tension. An existing constitutive model, the Goldberg model has been extended in order to take into account the nonlinear strain rate dependence of the elastic modulus. The model has been validated against 3-point impact bending tests of prismatic RTM-6 beams.

Comparison of Test Specimens for Characterizing the Dynamic Properties of Rubber

Dynamic material properties inferred via experiment can be strongly influenced by the choice of test specimen geometry unless care is taken to ensure that mechanical fields (stress, strain, etc.) within the specimen adequately reflect the ideal homogeneous deformation state. In this work, finite element models of simple shear, cylindrical compression, simple tension, and bi-conical shear test specimens were analyzed in order to quantify the relative conformity of each specimen to its corresponding ideal. Three metrics of conformity were evaluated, based respectively on the distributions of stress, strain, and strain energy density. The results show that a simple shear specimen provides superior conformity. Other factors involved in the selection of test specimen geometry are also discussed. Such factors include relative linearity and symmetry of measured stress–strain data, grip slip, and heat build up.

Simulations of necking during plane strain tensile tests

A hydrodynamic code is used to simulate plane strain tension experiments: extension of sheets and expansion of cylinders. The material is characterized by an elastic-plastic constitutive law. The stress state in the structure is first approximately uniform, but numerical fluctuations proper to the hydrodynamic code grow and give birth to a non homogeneous deformation state. The last step shows the concentration of plastic deformation in necks, prior to rupture. Simulations show very clearly that the wavelength of instabilities and the instant of their appearance depends on some physical values: traction speed, aspect ratio, parameters of the constitutive law. Simulations of plane strain expansion of rings are compared to experimental results of expansion of cylinders. Several fragments are created and their size is similar, which validates partly the simulations.

A viscoelastic model for fiber-reinforced composites at finite strains: Continuum basis, computational aspects and applications

This paper presents a viscoelastic model for the fully three-dimensional stress and deformation response of fiber-reinforced composites that experience finite strains. The composites are thought to be (soft) matrix materials which are reinforced by two families of fibers so that the mechanical properties of the composites depend on two fiber directions. The relaxation and/or creep response of each compound of the composite is modeled separately and the global response is obtained by an assembly of all contributions. We develop novel closed-form expressions for the fourth-order elasticity tensor (tangent moduli) in full generality. Constitutive models for orthotropic, transversely isotropic and isotropic hyperelastic materials at finite strains with or without dissipation are included as special cases. In order to clearly show the good performance of the constitutive model, we present 3D and 2D numerical simulations of a pressurized laminated circular tube which shows an interesting `stretch inversion phenomenon' in the low pressure domain. Numerical results are in good qualitative agreement with experimental data and approximate the observed strongly anisotropic physical response with satisfying accuracy. A third numerical example is designed to illustrate the anisotropic stretching process of a fiber-reinforced rubber bar and the subsequent relaxation behavior at finite strains. The material parameters are chosen so that thermodynamic equilibrium is associated with the known homogeneous deformation state.

Influence of Sintering Temperature on Pore Morphology, Microstructure, and Fatigue Behaviour of MoNiCu Alloyed Sintered Steel

The influence of sintering temperature on the pore morphology, microstructure, and fatigue behaviour of a MoNiCu alloy is presented. Besides pore area, shape factors for bulkiness, elongation, and roughness of the pores were determined. Energy dispersive spectroscopy X-ray analyses were used to examine the distribution of alloying elements in the bulk of the material. Cyclic stress-strain, cyclic stress-temperature, and cyclic stress-electrical resistance responses were studied simultaneously to obtain a more comprehensive description of the fatigue behaviour. With increasing sintering temperature the pores are larger and more regular and, owing to a more homogeneous distribution of alloying elements, the solid solution hardening is more pronounced. Nevertheless, there is only a slight increase in the endurance limit. The higher sintering temperature leads to lower plastic strain amplitudes, temperature, and electrical resistance changes. This corresponds to less pronounced slip features at a lower density. The energy equivalent exponent and the temperature/electrical resistance ratio reveal the less homogeneous deformation state and the higher crack sensitivity of this material. PM/0787

Effect of Constitutive Parameters on Formation of a Spherical Void in a Compressible Nonlinear Elastic Material

Void formation in materials under isotropic tension is considered within the theory of finite elasticity. This phenomenon is described as the bifurcation of the solution containing a spherical cavity from the state of homogeneous deformation of a solid hyperelastic sphere. The equation giving the bifurcation point is derived, and the critical stretch and stress are numerically calculated for a special class of compressible nonlinear elastic materials for which the strain energy function was proposed by Hill. The effects of constitutive parameters on the post-bifurcation behavior as well as on the critical stretch and stress are discussed.