Micro-mechanical analyses of the effect of stress triaxiality and the Lode parameter on ductile damage and failure

The paper deals with the effect of different stress states on plastic deformations, damage and fracture of ductile materials. To be able to model these effects a continuum damage model has been introduced taking into account the dependence of stress-state on the constitutive equations. The model is based on the introduction of damaged and fictitious undamaged configurations. All parameters appearing in the constitutive equations are stress-state-dependent which can be characterized by the stress intensity, the stress triaxiality and the Lode parameter. Only experiments are not adequate enough to determine all constitutive parameters. Thus, additional series of three-dimensional micro-mechanical simulations of representative volume elements have been performed to get more insight in the complex damage mechanisms. These simulations cover a wide range of stress triaxialities and Lode parameters in tension, shear and compression domains. After all, the results from the micro-mechanical simulations are used to suggest the damage equations and to identify corresponding parameters. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Three-dimensional cell model analysis of ductile damage under dynamic loading condition

The paper deals with the damage and fracture behavior of ductile metals under dynamic loading conditions. The in [1–3] presented phenomenological continuum damage and fracture model, which takes into account the rate- and temperature-dependence of the material, provides reasonable results of experiments with high strain rates while the identification of the corresponding material parameters results difficult from the available experimental data. This lack of information can be resolved by micro-mechanical numerical simulations of void containing unit-cells. In this context results of dynamic micro-mechanical simulations are presented which can be used to study the damage effects on the micro-scale and to validate the rate-dependent continuum damage model. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Constitutive equations of non-isothermal polymer melt

Constitutive equations of non-isothermal polymer melt are presented by the analysis of entropic free energy contribution of the macromolecular chains, which are treated as elastic dumbbell models. With describing non-isothermal dumbbell spring, as the function of temperature, the non-linear elastic coefficient expression causes the appearance of temperature gradient in stress constitutive equations. Following the constitutive equation of Hookean dumbbell model, non-isothermal stress constitutive equations of FENE and FENE-P models are derived. In deriving process of constitutive equations, the second moment approximation is used to closure FENE model. Using the non-isothermal constitutive equations, numerical simulations of polymer flow through shear cavity and planar contraction cavity are presented. And the distributions of correlative stress functions and the effects of different temperatures on stress functions are discussed. The present results are shown to explore the non-isothermal constitutive equations of elastic dumbbell models, and to search more accurately describing way of non-isothermal polymer melt.     

Influence of structural hypotheses on the elastic-viscoplastic response of shock wave-loaded plates

If circular metal plates are subjected repeatedly to impulsive loadings, damage and failure of the structures can occur. In order to predict the damage evolution in finite element simulations, a structural theory combined with viscoplastic constitutive equations acounting for damage is used. However, different structural hypotheses, used in the theoretical model, can lead to variations in the numerical result. Therefore, first- and third-order shear deformations theories are applied in a finite element code. Moreover, local and non-local damage approaches are used. The aim is to determine the numerical model, which leads to the most accurate results compared to experiments. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Two-layer flows of generalized immiscible second grade fluids in a rectangular channel

Unsteady one-dimensional flows of two incompressible and immiscible generalized second grade fluids in a rectangular channel are studied. A constant pressure gradient acts in the flow direction, while the channel walls have oscillating translational motions in their planes. The generalization considered in this paper consists into a mathematical model based on constitutive equations of second grade fluid with Caputo time-fractional derivative in which the history of the shear stress influences the velocity gradient. The velocity and shear stress fields in the Laplace transform domain are obtained. Numerical solutions for the real velocity and shear stress have been found by employing the Stehfest numerical algorithm for the inverse Laplace transform. The influence of the fractional parameters on the velocity and shear stress has been studied by numerical simulations and graphical illustrations. It is found that the memory effects are significant only for small values of the time t.     

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)     

A tensorial framework for strain induced damage of plastically deformed metals

A tensorial framework for strain induced ductile damage of plastically deformed metals is developed in terms of both plastic flow theory and continuum damage mechanics. A symmetric second order damage rate tensor is used in order to study various processes with large finite deformations in combination with damage analysis. The definition of this tensor is physically meaningful since its volumetric and deviatoric parts describe the damage increments caused by an increase in the void volume and by a change in the shape of the void, respectively. Such a view on damage kinetics leads to the introduction of two measures for damage assessment which allow predicting not only a risk of macroscopic failure but also the onset of void coalescence. Material functions appearing in the constitutive equations for damage are determined both by own experiments and by known results from literature. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Experiments and numerical simulations on damage behavior of biaxially loaded specimen

The paper deals with the effect of stress state on damage and failure behavior of isotropic ductile metals. In the continuum damage model the damage behavior of ductile metals is adequately described by a generalized damage condition and an anisotropic damage rule. The damage criterion is based on series of uniaxial experiments with differently notched specimens and corresponding numerical simulations as well as on various numerical calculations on the micro-scale. Different branches of the damage criterion depending on stress triaxiality and Lode parameter are considered. To be able to validate the proposed stress-state-dependent functions new experiments with two-dimensionally loaded specimens have been developed. Corresponding numerical simulations show that these shear-tension and shear-compression tests cover a wide range of stress triaxialities and Lode parameters. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A network evolution model for the anisotropic Mullins effect

In this contribution, a micro-mechanical constitutive model for filled rubberlike materials is proposed. Rubber network is decomposed into two parts, elastic rubber network and polymer-filler network. As a consequence of filler contribution, the last one is subjected to damage. A non-Gaussian strain energy function for a single chain with a constant valence angle has been postulated. Damage in different directions is governed by the corresponding maximal micro-stretch and is considered as a result of network evolution. Directional network rearrangement as a consequence of network evolution has been employed in order to describe induced anisotropy and permanent set. The model shows good agreement with experimental data on uniaxial tension tests in two orthogonal directions. (© 2008 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On dynamic finite element analysis of viscoplastic thin-walled structures with non-local damage

In this article we propose a non-local damage model for dynamic finite element computation of viscoplastic thin-shell structures. To take void nucleation and growth into account, the free energy function is enhanced phenomenologically in terms of a non-local damage variable and its gradient on the mid-surface of shell structures. The dynamic thin-shell elastic theory including large rotations proposed by Simo and Tarnow (1994) is used to capture finite deformation. Local constitutive laws considering viscoplastic behaviour, isotropic hardening and isotropic ductile damage leading to softening in Velde et al. (2009) are employed. The performance of the proposed approach is demonstrated through the preliminary numerical simulations of shock-wave loaded structures, which are validated by comparision with the experimental results. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysis of damage and fracture mechanisms on the micro-scale

The paper deals with generalized damage and failure criteria taking into account different mechanisms on the micro-scale. Some micro-mechanical numerical results are discussed and compared with the macroscopic analysis based on the continuum damage model. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Experiments and numerical simulations of new biaxially loaded specimens to characterize the behavior of thin metal sheets

The paper deals with the development of new biaxially loaded specimens to study the damage behavior of ductile metals under different loading conditions. Based on numerical simulations newly designed biaxial specimens are developed and numerically studied while an experimental program has been realized in continuation. The experimental results have been evaluated by digital image correlation (DIC) and compared with the results of finite element simulations. By concideration of different biaxial loading conditions it is possible to cover a wide range of stress triaxialities and Lode parameters in tension, shear and compression domains and consequently the newly proposed specimens facilitate a controlled study of damage and fracture at different stress states. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

脆性材料损伤应变软化的数学模型

本文提出一种脆性材料损伤应变软化的数学模型，本构方程是基于热力学原理建立的。虽然是各向同性损伤模型，用标量表示损伤状态，但通过等效损伤应变的定义，能区分拉伸、压缩和剪切载荷对材料损伤的不同响应。由于本构模型中的多数参数均可由材料材料手册简单确定，便于工程应用。     

Response of Kidney Tissue to Dynamical Loading

In shock-wave lithotripsy – a medical procedure to fragment kidney stones – the patient is subjected to hypersonic waves focused at the kidney stone. Although this procedure is widely applied, the physics behind this medical treatment, in particular the question of how the injuries of the surrounding kidney tissue arise, is still under investigation. Here we contribute to the solution of this problem with large scale numerical simulations of a human kidney under shock-wave loading. For this purpose we developed a complex constitutive model of the bio-mechanical kidney system. Assuming a multiplicative decomposition of the deformation gradient and adopting an internal variable formulation for the inelastic deformation the model is able to handle large deformations, time-effects, rate-sensitivity and material damage. By finite element simulations we study the shock-wave propagation into the kidney tissue and analyze the resulting stress states. Unknown material parameters are adapted and special attention is paid on the bubble expansion within the soft tissue. The numerical simulations predict localized damage in the human kidney within the focal region of the shock waves. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Ⅰ阶梯度损伤理论

从热力学基本定律出发,将应变张量、标量损伤变量、损伤梯度作为Helmholtz自由能函数的状态变量,利用本构泛函展开法在自然状态附近作自由能函数的Taylor展开,未引入附加假设,推导出Ⅰ阶梯度损伤本构方程的一般形式．该形式在损伤为0时可退化为线弹性应力-应变本构方程,在损伤梯度为0时可退化为基于应变等效假设给出的线弹性局部损伤本构方程．一维解析解表明,随着应力增大,损伤场逐步由空间非周期解变为关于空间的类周期解,类周期解的峰值区域形成局部化带．局部化带内的损伤变量将不同于局部化带外的损伤变量,由此可以反映出介质的局部化特征．损伤局部化并不是与损伤同时发生,而是在损伤发生后逐渐显现出来,模型的局部化机制开始启动;损伤局部化的宽度同内部特征长度成正比．     

Linear and nonlinear vibrations of fractional viscoelastic Timoshenko nanobeams considering surface energy effects

In this paper, the linear and nonlinear vibrations of fractional viscoelastic Timoshenko nanobeams are studied based on the Gurtin–Murdoch surface stress theory. Firstly, the constitutive equations of fractional viscoelasticity theory are considered, and based on the Gurtin–Murdoch model, stress components on the surface of the nanobeam are incorporated into the axial stress tensor. Afterward, using Hamilton's principle, equations governing the two-dimensional vibrations of fractional viscoelastic nanobeams are derived. Finally, two solution procedures are utilized to describe the time responses of nanobeams. In the first method, which is fully numerical, the generalized differential quadrature and finite difference methods are used to discretize the linear part of the governing equations in spatial and time domains. In the second method, which is semi-analytical, the Galerkin approach is first used to discretize nonlinear partial differential governing equations in the spatial domain, and the obtained set of fractional-order ordinary differential equations are then solved by the predictor–corrector method. The accuracy of the results for the linear and nonlinear vibrations of fractional viscoelastic nanobeams with different boundary conditions is shown. Also, by comparing obtained results for different values of some parameters such as viscoelasticity coefficient, order of fractional derivative and parameters of surface stress model, their effects on the frequency and damping of vibrations of the fractional viscoelastic nanobeams are investigated.     

Constitutive modeling of void-growth-based tensile ductile failures with stress triaxiality effects

In most metals and alloys, the evolution of voids has been generally recognized as the basic failure mechanism. Furthermore, stress triaxiality has been found to influence void growth dramatically. Besides strain intensity, it is understood to be the most important factor that controls the initiation of ductile fracture. We include sensitivity of stress triaxiality in a variational porous plasticity model, which was originally derived from hydrostatic expansion. Under loading conditions rather than hydrostatic deformation, we allow the critical pressure for voids to be exceeded so that the growth due to plasticity becomes dependent on the stress triaxiality. The limitations of the spherical void growth assumption are investigated. Our improved constitutive model is validated through good agreements with experimental data. Its capacity for reproducing realistic failure patterns is also indicated by a numerical simulation of a compact tensile (CT) test.     

Interfacial model for crash resistant adhesives of ductile-modified epoxy resins

Debonding in adhesive joints is modelled and analyzed with the concept of interfacial mechanics. Material equations are presented for the inelastic behaviour of ductile-modified epoxy resins. A two surface function for the onset of yielding is advantageously expressed in terms of the stress vector on the interface. The theory may be extended to material softening due to damage and to rate dependency. This simple constitutive model is not stable in the sense of Drucker's postulate. Therefore, the non-associated flow rule is modified with a quadratic stress-dependent plastic potential. The material parameters are identified by means of the finite-element simulation of the experimental setup for a bluntly glued double steel tube sample. The numerical performance of this modified model is tested at an adhesively bonded joint in the form of a T-intersection. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A material model of nonlinear fractional viscoelasticity

Multiscale methods are frequently used in the design process of textile reinforced composites. In addition to the models for the local material structure it is necessary to formulate appropriate material models for the constituents. While experiments have shown that the reinforcing fibers can be assumed as linear elastic, the material behavior of the polymer matrix shows certain nonlinearities. These effects are mainly due to strain rate dependent material behavior. Fractional order models have been found to be appropriate to model this behavior. Based on experimental observations of Polypropylene a one-dimensional nonlinear fractional viscoelastic material model has been formulated. Its parameters can be determined from uniaxial, monotonic tensile tests at different strain rates, relaxation experiments and deformation controlled processes with intermediate holding times at different load levels. The presence of a process dependent function for the viscosity leads to constitutive equations which form nonlinear fractional differential equations. Since no analytical solution can be derived for these equations, a numerical handling has been developed. After all, the stress-strain curves obtained from a numerical analysis are compared to experimental results. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)