Lamellar structure and plasticity micromechanisms in bulk crystalline polymers. Communication 1

It is shown by electron microscopy that the lamellar structure typical of bulk crystalline polymers is identical in its structural-morphological characteristics with the typical products of martensite transformations in metal systems. It is also established that the polymer crystallization process has the typical characteristics of transformations governed by the shear (martensite) mechanism. These conclusions are used as a basis for an examination of the principal factors controlling the formation of the real structure of bulk polymers. The thermodynamic conditions under which bulk polymers crystallize require that the lamellar-spherulitic structure be formed in accordance with a self-consistent shear mechanism. In accordance with the new model, the spherulites represent an organization of the martensite lamellae in which the structural stress fields are mutually compensated. The proposed model underlines the fact that polycrystalline polymers and metal systems in the martensitic state are structurally similar materials.E. O. Paton Electrowelding Institute, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 3, pp. 387–394, May–June, 1976.     

一个新的形状记忆合金模型

借助于Tanaka用一维形核动力学方程导出的指数形式的相变百分数,建立了一个新的形状记忆合金本构模型.提出了不同相变条件下的可恢复形状记忆应变的表达式;考虑了材料在变形过程中马氏体的重定向作用;克服了Tanaka系列模型不能描述当材料为完全马氏体状态时的力学行为的缺点.本模型较现有的形状记忆合金本构模型均简单,便于应用,实验证明了模型的正确性.     

Eulerian Rate Model for Pseudoelastic NiTi Shape Memory Alloys

A phenomenological material model for the pseudoelastic material behavior of polycrystalline NiTi is presented. It is consistently derived within the Eulerian framework using the Kirchhoff stress (weighted Cauchy stress) and the stretching tensor. Deformation–like variables such as elastic or inelastic strains are omitted. The model is based on a non–convex Helmholtz free energy function for the phases austenite and martensite, which is formulated in terms of the Kirchhoff stress, temperature, mass fraction of martensite, and a tensorial internal variable accounting for the average orientation of the martensite variants. Evolution equations for the mass fraction of martensite as well as for the average orientation of the martensite variants are derived, taking into account the restrictions imposed by thermodynamics. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical simulation of shear band formation in hyperelastic material by energy relaxation

A theorical framework for the analysis of localized failure in hyperealstic material is presented based on the energy minimization principles associated with micro-structure developments. The theory is predicated upon the assumptions that the thickness of shear band represented by its volume fraction tends to zero as well as that the energy inside shear band is a function of the norm of the deformation gradient. Shear bands are treated as laminates of first order. The existence of shear bands in the structure leads to an ill-posed problem which can be solved by means of energy relaxation. An application of the proposed formulation to Neo-Hookean material is presented. Numerical simulation is shown in order to evaluate the performance of the proposed energy relaxation. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical simulation of shear band formation in elastic material by energy relaxation

Following up the previous work, [1], a new approach to the problem of shear localization is proposed, based on energy minimization principles associated with micro-structure developments. In this approach, two different material models are included. They represent the behaviour of material at very small strain and very large strain, respectively. Herein, shear bands are treated as the micro-shearing of rank-one laminates. The thickness of a shear band represented by its volume fraction is assumed to tend to zero while the strain inside the shear band tends to infinity. The existence of shear bands in the structure leads to an ill-posed problem which can be solved by means of energy relaxation. The performance of the proposed energy relaxation is demonstrated through numerical simulation of a tension test under plane strain conditions. The presented numerical simulation shows that there is no mesh-dependence. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A second-order conservational difference scheme for the one-dimensional model of martensitic transformations with nonlinear boundary conditions

In this work, the one-dimensional equilibrium model of martensitic transformations with nonlinear boundary conditions is considered. Some a prior energy identities are obtained by a rigor mathematical analysis. A second-order conservational difference scheme is proposed and solved by the iterative method. Its efficient implement is carried out and the fixed and the random initial input are discussed. Moreover, a convergence criterion based on the total free energy and the Landau energies are proposed, which can be also used to other iterative method. The solution with nonlinear boundary conditions is obtained. The simulation of the surface martensite, the thermoelastic (shape memory) and the nonthermoelastic martensite formations and the autocatalysis are performed.     

A hydrodynamical model for holes in silicon semiconductors: The case of non-parabolic warped bands

This paper can be considered as the natural prosecution of Mascali and Romano (2009) [5]. Here, we describe the motion of holes in silicon by also taking into account the non-parabolicity of the heavy and light bands. The model is still based on the moment method and the closure of the system of equations is obtained by using the maximum entropy principle. Comparisons are made with the results in [5], in the case of bulk silicon, in order to establish the importance of non-parabolicity.     

Modelling thermoplastic material behaviour of dual-phase steels on a microscopic length scale - numerical treatment

On a microscopic length scale dual-phase steels exhibit a polycrystalline microstructure consisting of ferrite and martensite. In this work it is assumed that the martensitic phase behaves purely thermoelastic while for the ferritic phase a thermoplastic material model was developed based on the assumption that the driving mechanism for persistent deformation is the movement of dislocations on preferred planes in preferred directions. The necessary shear stress to move dislocations at a certain temperature and deformation rate is assumed to possess contributions from the atomic lattice, alloying atoms and the dislocation structure. To consider the influence of the dislocation structure, dislocation densities are introduced as state variables for which temperature and deformation rate dependent evolution equations are formulated. Since for general loading histories the model equations cannot be integrated analytically, a time discretized form of the model equations with an appropriate solution algorithm is presented. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Imperfect interface effect for nano-composites accounting for fiber section shape under antiplane shear

This paper investigates the elastic responses of fibrous nano-composites with imperfectly bonded interface under longitudinal shear. The proposed imperfect interface model is the shear lag (or the spring layer) model; the presented nano interfacial stress model is the Gurtin–Murdoch surface/interface model; and the three-phase confocal elliptical cylinder model is the geometry model accounting for the fiber section shape. By virtue of the complex variable method, a generalized self-consistent method is employed to derive the closed from solution of the effective antiplane shear modulus of the fibrous nano-composites with imperfect interface. Five existing solutions can be regarded as the limit form the present analytic expression. The influences of the interface elastic constant, the interfacial imperfection parameter, the size of the elliptic section fiber, the fiber section aspect ratio, the fiber volume fraction and the fiber elastic property on the effective antiplane shear modulus of the nano-composites are discussed. Particularly, numerical results demonstrate that the interfacial elastic imperfection will always cause a significant reduction in the effective antiplane shear modulus; and the fiber interface stress effect on the effective modulus of the fibrous nano-composites will weaken with the interfacial imperfection increases.     

Deformation induced martensite transformation in a cold-worked forming process of austenitic stainless steel

Within the last years the goal of industrial manufacturing processes – such as tube forming – has shifted towards an optimization of technological as well as mechanical properties of the manufactured structures. For example, during the forming procedure of sheets made of austenitic stainless steel X5CrNi18-10, the content of strain-induced martensite needs to be controlled. In order to achieve optimal structural properties of the manufactured tube with respect to very high-cycle fatigue (VHCF), a martensite ratio of approximately 25% needs to be obtained [1]. On the basis of experimental investigations this contribution deals with the numerical simulation of the tube-forming process with special consideration of the martensite ratio c as a function of temperature and deformation field. For this purpose we extend an existing martensite model on polyaxial states of stress and compare experimental results and numerical simulations for the modified model. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Static and dynamic beam forms of the loss of stability of a long orthotropic cylindrical shell under external pressure

A cylindrical shell with end sections which are closed and supported by hinges, in accordance with the concepts of the rod theory, is considered to be under the action of an omnidirectional external pressure which remains normal to the lateral surface during the deformation process. It is shown that, for such shells, the previously constructed consistent equations of the momentless theory, reduced using the Timoshenko shear model to the one-dimensional equations of the rod theory, describe three forms of loss of stability: (1) static loss of stability, which occures through a bending mode from the action of the total end axial compression force since, under the clamping conditions considered, its non-conservative part cannot perform work on deflections of the axial line; (2) also a static loss of stability but one which occurs through a purely shear mode with the conversion of a cylinder with normal sections into a cylinder with parallel sloping sections and a corresponding critical load which is independent of the length of the shell; (3) dynamic loss of stability which occurs through a bending-shear form and can only be revealed by a dynamic method using an improved shear model.     

Numerical analysis of shear bands in solids by means of computational homogenization

A novel fully three–dimensional framework for the numerical analysis of shear bands in solids undergoing large deformations is presented. The effect of micro shear bands on the macroscopic material response is computed by means of a homogenization strategy. More precisely, a strain–driven approach which complies well with displacement–driven finite element formulations is adopted. The proposed implementation is based on periodic boundary conditions for the micro–scale. Details about the implementation of the resulting constraints into a three–dimensional framework are discussed. The shear bands occurring at the micro–scale are modeled by a cohesive zone law, i.e., the tangential component of the traction vector governs the relative shear sliding displacement. This law is embedded into a Strong Discontinuity Approach (SDA). To account for realistic sliding modes, multiple shear bands are allowed to form and propagate in each finite element. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Visco‐elasto‐plastic model for martensitic phase transformation in shape‐memory alloys

Evolution of fine structure in martensite undergoing an isothermal process is modelled on a microscopic level by using a positive homogeneous dissipation potential which can reflect a specific energy needed for a phase transformation between different variants of martensite. The model thus naturally incorporates an activation phenomenon. Existence of a weak solution is proved together with convergence of finite‐element approximations. Numerical experiments showing the expected rate‐independent hysteresis response are also presented. Copyright © 2002 John Wiley & Sons, Ltd.     

Simulation of short crack propagation under hydrogen influence using a hybrid boundary element technique for anisotropic elastic solids

A two-dimensional model for stage I short crack propagation on multiple slip planes under the influence of hydrogen is presented. It considers elastic-plastic material behaviour by allowing sliding on the active slip planes in the corresponding slip directions. A crack propagation law based on the crack tip sliding displacement is used to simulate crack growth. The activation of slip bands and the sliding on these active slip bands will be influenced by the local hydrogen concentration. The model is solved numerically using the boundary element method. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Magneto-Sensitive Elastomers: An Experimental Point of View

Magneto-sensitive elastomers (MSEs) are smart materials changing their shape and mechanical properties in the presence of a magnetic field. Focussing on model systems, silicone based MSEs are prepared by a multi-step mixing process and characterised using a rotational rheometer (plate-plate). Data obtained by relaxation tests is used to set-up a material model coupling the theories of viscoelasticity and magnetoelasticity. The behaviour of MSEs in quasi-static and dynamic mechanical shear experiments can be successfully predicted by the analytical model using parameters received by fitting the transient experiments. The model is validated for small shear deformations (γ = 0.02) and low magnetic fields (𝔹 = 0.2 T). (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Extended Finite Element Method for hygro-mechanical analysis of crack propagation in porous materials

In computational structural analyses, strong discontinuities, such as propagating cracks in concrete structures, joints in rocks or shear bands in soft soils, the highly accelerated moisture transport in the opening discontinuities has to be taken into account. The paper is concerned with an Extended Finite Element model for the numerical representation of crack propagation in partially saturated porous materials. Based on an extended variational formulation for the simulation of moisture transport in cracks, enhanced approximations of the displacement field and the moisture flux across the discontinuity are adopted. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Identification of the Material Parameters of a Micropolar Model for Granular Materials

Granular frictional materials show a complex stress‐strain behaviour depending on the stress state and the load history. Furthermore, biaxial experiments exhibit the occurrence of shear band phenomena as the result of the localization of plastic strains. It is well known that the onset of shear bands is associated with microrotations of the granular microstructure, which has a significant influence on the macroscopic behaviour. Consequently, the macroscopic material must result in a micropolar model, which incorporates rotational degrees of freedom. After the formulation of the constitutive equations and the numerical implementation, it is necessary to determine all required material parameters. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)