A variational model for the functional fatigue in polycrystalline shape memory alloys

Shape memory alloys show a very complex material behavior associated with a diffusionless solid/solid phase transformation between austenite and martensite. Due to the resulting (thermo-)mechanical properties – namely the effect of pseudoelasticity and pseudoplasticity – they are very promising materials for the current and future technical developments. However, the martensitic phase transformation comes along with a simultaneous plastic deformation and thus, the effect of functional fatigue. We present a variational material model that simulates this effect based on the principle of the minimum of the dissipation potential. We use a combined Voigt/Reuss bound and a coupled dissipation potential to predict the microstructural developments in the polycrystalline material. We present the governing evolution equations for the internal variables and yield functions. In addition, we show some numerical results to prove our model's ability to predict the shape memory alloys' complex inner processes. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Regularized Sharp Interface Model for Martensitic Phase Transformations at Large Strains

The macroscopic mechanical behavior of many functional materials crucially depends on the formation and evolution of their microstructure. When considering martensitic shape memory alloys, this microstructure typically consists of laminates with coherent twin boundaries. We suggest a variational-based phase field model for the dissipative evolution of microstructure with coherence-dependent interface energy and construct a suitable gradient-extended incremental variational framework for the proposed dissipative material. We use our model to predict laminate microstructure in martensitic CuAlNi. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A micromechanical model for the transformation induced plasticity in polycrystalline steels

Due to the effect of transformation induced plasticity (TRIP) , TRIP-steels are very promising materials, e.g. for the automobile industry. The material behavior is characterized by very complex inner processes, namely phase transformation coupled with plastic deformation and kinematic hardening. We establish a micromechanical model which uses the volume fractions of the single phases, the plastic strain and the hardening parameter in every grain of the polycrystalline material as internal variables. Furthermore, we apply the Principle of the Minimum of the Dissipation Potential to derive the associated evolution equations. The use of a coupled dissipation functional and a combined Voigt/Reuss bound directly results in coupled evolution equations for the internal variables and in one combined yield function. Additionally, we show numerical results which prove our model's ability to give a first prediction of the TRIP-steels' complex material behavior. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical Modeling of Functional Fatigue in NiTi Wires

Motivated by the high potential of shape memory alloys (SMA) in several industrial applications, we investigate the material response under cyclic loading. In particular, the focus is set on the modelling of functional fatigue, which results in the deterioration of the specific features of SMA. In fact, functional fatigue restricts SMA in terms of its applicability for real structures and workpieces. This necessitates the development of material models which take this phenomenon into account. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical Simulation of the Application of NiTi Alloys in Medical Technologies

Shape memory alloys are nowadays already established as a material which is able to solve exceptional tasks in practical applications. Particularly, its utilization in the field of medical technologies increases steadily. For example micro tools (staple, catheters) and implants (coronary stents) are made out of Nickel-Titanium well known as a basic shape memory alloy. Apart from the advantages like the avoidance of auxiliary components and joints in the system and to utilize the high volume specific work of shape memory alloys, NiTi alloys exhibit a good biocompatibility. This property is necessary with regard to either permanent or temporary implants. To optimize the use of NiTi alloys in the scope of medical technologies, the support of the development of applicable tools by numerical simulations is highly recommended. However the complex material behaviour containing a profoundly thermomechanical coupling poses indeed a big challenge to the material modeling and its implementation into a finite element code. Particularly, the material model proposed by Helm [1] proves to be a firm model containing the most common properties of shape memory alloys, as the pseudoelasticity, the shape memory effect and the two-way effect. In the present contribution the FE modelling of a medical staple used in foot surgery is presented by considering the model of Helm which was investigated by the authors to improve its performance in the finite element method [2]. The foot staple, produced by a group of members of the SFB 459 which is funded by the DFG, avails the shape memory effect to excite the desired clamping effect [3]. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Pseudoelasticity of Shape Memory Alloys - a 1D Material Model and Finite Element Implementation

This contribution is concerned with the formulation of a 1D-constitutive model accounting for the pseudoelastic behavior of shape memory alloys. The stress-strain-relationship is idealized by a hysteresis both in the compression as in the tension loading range. It is characterized by an upper loading path, which is to be ascribed to the transformation of the lattice to a martensitic structure. Unloading the material, a lower path is described, because of the reverse transformation into austenitic lattice. The constitutive model is based on a switching criterion which serves as a potential function for the evolution of the internal state variables. The model distinguishes between local and global variables to describe the hysteresis effects for the compression and tension range. A strain driven algorithm which captures the complete nonlinear material behavior is presented. The boundary value problem is solved for a truss element applying the finite element method. A consistent linearization of the nonlinear equations is derived. Simple examples will demonstrate the applicability of the proposed model. For future developments the usage of shape memory alloys within civil engineering structures is aimed. The advantage of the material is the very good damping behavior and the potential to overcome great strains. Both properties are distinguished to be of engineering interest. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling of Shape Memory Alloys and Experimental Verification

Prestrained shape memory alloys change their length when heated above their transformation temperature. This effect can be used to generate high forces in a small workspace, which has particular advantages in actuator design. The optimization and control of the shape memory actuator requires a comprehensive simulation of the material behavior. However, many of the existing models are limited to specific load cases or offer rough approximations only. A material model for shape memory alloys from Seelecke [1] is examined in this paper. This model describes the behavior of a shape memory wire, which is heated by electric current. It is implemented in a simulation program to investigate the actuator output and to improve the performance. Finally, the parameters of the simulation are adapted to experimental results.     

Fatigue crack growth under variable-amplitude loading: Part I – Model formulation in state-space setting

This two-part paper presents formulation and validation of a non-linear dynamical model of fatigue crack growth in ductile alloys under variable-amplitude loading including single-cycle overloads, irregular sequences, and random loads. The model is formulated in the state-space setting based on the crack closure concept and captures the effects of stress overload and reverse plastic flow. The state variables of the model are crack length and crack opening stress. This paper, which is the first part, presents formulation of the state-space model that can be restructured as an autoregressive moving average (ARMA) model for real-time applications such as health monitoring and life extending control. The second part is the companion paper that is dedicated to model validation with fatigue test data under different types of variable-amplitude and spectrum loading.     

Derivation of Orowan's Law from the Peierls–Nabarro Model

In this paper we consider the time dependent Peierls-Nabarro model in dimension one. This model is a semi-linear integro-differential equation associated to the half Laplacian. This model describes the evolution of phase transitions associated to dislocations. At large scale with well separated dislocations, we show that the dislocations move at a velocity proportional to the effective stress. This implies Orowan's law which claims that the plastic strain velocity is proportional to the product of the density of dislocations by the effective stress.     

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)     

Fatigue crack growth under variable-amplitude loading: Part II – Code development and model validation

A state-space model of fatigue crack growth has been formulated based on the crack closure concept in the first part of the two-part paper. The unique feature of this state-space model is that the constitutive equation for crack-opening stress is governed by a low-order non-linear difference equation without the need for storage of a long load history. Therefore, savings in the computation time and memory requirements are significant. This paper, which is the second part, provides information for code development and validates the state-space model with fatigue test data for different types of variable-amplitude and spectrum loading in 7075-T6 and 2024-T3 aluminum alloys, respectively. Predictions of the state-space model are compared with those of the FASTRAN and AFGROW codes.     

Mathematical modelling of plastic deformation instabilities with two delays

In this paper we present a new model describing the temporal evolution for multi-instabilities of plastic deformation of stressed monocrystal. This model generalizes that with a single delay presented in [12] and [13]. The plastic instability is due to the increase in dislocation density and the mutual interaction between dislocations, and can be explained by a phase shift, characterized by a time delay between the nucleation and the propagation of dislocations. Here, we consider the general case when several deformation-mechanisms are active, leading to several delays. Using a linear analysis, we deduce a differential equation with two delays. We present some results on existence and stability of the solution according to the characteristics of material and the two delays. Numerical examples for stability and instability of material close to a mean stress using the MATLAB software are also investigated.     

Modeling and Simulation of Polyoxymethylene

This essay is aimed at a brief representation of a constitutive model for a plastic called polyoxymethylene. This kind of plastic shows phenomena like tension-compression asymmetry, non-linear rate-dependence as well as a pronounced relaxation behaviour. The tension-compression asymmetry is modelled by the elastic part of the equilibrium stress state whereas the hysteretic part is described by an Armstrong&Frederick-type evolution equation. A particular viscosity function is used for describing the evolution of the viscous strains occuring in the overstress part. The model is able to represent most of the aforementioned phenomena in tension, compression and torsion experiments. In the second part of the article, the implementation of the constitutive model into the .nite element program ANSYS is described followed by a test calculation treating a nut of a bolt. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the thermo-mechanically coupled simulation of poly-crystalline Shape Memory Alloys

We present a thermo-mechanically coupled model for poly-crystalline shape memory alloys which accounts both for the localized phase transformations and the resulting heat production. The model is based on the physical principles of energy conservation and entropy maximization. Choosing an appropriate ansatz for the entropy production the evolution equation for the phases can be derived as well the heat conduction equation. The results show good agreement to experimental findings. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Elastoplastic deformation during projectile–wall collision

The Smoothed Particle Hydrodynamics method for elastic solid deformation is modified to include von Mises plasticity with linear isotropic hardening and is then used to investigate high speed collisions of elastic and elastoplastic bodies. The Lagrangian mesh-free nature of SPH makes is very well suited to these extreme deformation problems eliminating issues relating to poor element quality at high strains that limits finite element usage for these types of problems. It demonstrates excellent numerical stability at very high strains (of more than 200%). SPH can naturally track history dependent material properties such as the cumulative plastic strain and the degree of work hardening produced by its strain history. The high speed collisions modelled here demonstrate that the method can cope easily with collisions of multiple bodies and can also naturally resolve self-collisions of bodies undergoing high levels of plastic strain. The nature and the extent of the elastic and plastic deformation of a rectangular body impacting on an elastic wall and of an elastic projectile impacting on a thin elastic wall are investigated. The final plastically deformed shapes of the projectile and wall are compared for a range of material properties and the evolution of the maximum plastic strain throughout each collision and the coefficient of restitution are used to make quantitative comparisons. Both the elastoplastic projectile–elastic wall and the elastic projectile–elastoplastic wall type collisions have two distinct plastic flow regimes that create complex relationships between the yield stress and the responses of the solid bodies.     

Creep-fatigue analysis of the steel AISI type 316 component failure

The purpose of this work is to extend a typical creep-damage model in order to describe material behavior under variable thermal and mechanical loading in wide stress range. The model basis is creep constitutive law in form of hyperbolic sine stress response function proposed by Nadai. The constitutive law is extended to assume the damage process under creep and fatigue by the introduction of scalar damage parameters and appropriate evolution equations according to Kachanov-Rabotnov concept. The material constants for model are identified by fitting the experimental creep and low-cycle fatigue data for the steel AISI type 316 at the range of temperatures 500°C – 750°C. The development of such model is motivated by the well described failure case study of high-temperature components at unit 1 of Eddystone power plant, which have operated during 130520 hours under creep-fatigue interaction conditions. The main steam piping (MSP) from this power plant is selected for thermo-mechanical creep-fatigue analysis applying the proposed material model. The estimated values of damage parameters comply with the real location of the component failure and a scatter of experimental data on creep-fatigue interaction diagram. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Small‐strain heterogeneous elastoplasticity revisited

The elastoplastic quasi‐static evolution of a multiphase material—a material with a pointwise varying yield surface and elasticity tensor, together with interfaces between the phases—is revisited in the context of conservative globally minimizing movements. Existence is shown, and classical evolutions are recovered under natural constraints on the plastic dissipation potential. Special attention is paid to the interfaces where the correct dissipation has to be enforced on the interfaces. Further, the evolution is shown to be a limit of that obtained for a model with linear isotropic hardening as the hardening becomes vanishingly small. The duality between plastic strains and admissible stresses is also revisited for Lipschitz boundaries, and its role in deriving a classical evolution is circumscribed. © 2012 Wiley Periodicals, Inc.     

A finite elasto-plasticity model for thick adhesive layers based on generalized stress-strain measure

The collective term adhesives includes a wide field of materials with a diversity of different material properties. Regarding high-strength adhesives, the assumption of small strains often holds according to their brittle behavior. The experience with plasticity models based on the additive decomposition into elastic and inelastic strains indicates an appropriate approach to characterize such materials. In some cases, due to a more ductile material response, the assumption of infinitesimal strains is not valid anymore. In particular this is the case for high-strength adhesives with additives like rubber. But ductile behavior is also observed for specific stress states in one adhesive, e.g. when the behavior for tensile is quite brittle while large shear-strains could appear. The objective of this work is to overcome the theoretical restriction of small strains and to archive the practical experiences. For the failure criterion two stress invariants are used, which involves the hydrostatic pressure as well as the deviator stress state. The flowrule is introduced for the evolution of the inelastic variables. Herein the flow rule has to be of non-associated type to ensure the thermodynamical consistency of the model. The plasticity model also includes hardening as well as softening. The presented finite strain model makes use of the fact that the eigenvalues for Green-Lagrange strains and generalized strains are the same. Thus the limit of applicability is extended to finite strains. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of pseudo-plasticity in shape-memory-alloys

The name shape memory originates from the material's capability to recover its original shape after an apparent plastic deformation. The secret of this property lies in the specific microstructure. During mechanical loading, alloys of this particular kind change their crystallographic structure from randomly orientated martensite to ordered martensite. With austenite as high-temperature inter-state induced by heat supply, a recovery from the ordered to the unordered martensite is possible. This is accompanied by a macroscopic "healing" process. We apply our material model for shape-memory alloys to this special property and present numerical results. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)