Simulation of damage evolution in ductile metals undergoing dynamic loading conditions

A set of constitutive equations for large rate-dependent elastic-plastic-damage materials at elevated temperatures is presented to be able to analyze adiabatic high strain rate deformation processes for a wide range of stress triaxialities. The model is based on the concepts of continuum damage mechanics. Since the material macroscopic thermo-mechanical response under large strain and high strain rate deformation loading is governed by different physical mechanisms, a multi-dissipative approach is proposed. It incorporates thermo-mechanical coupling effects as well as internal dissipative mechanisms through rate-dependent constitutive relations with a set of internal variables. In addition, the effect of stress triaxiality on the onset and evolution of plastic flow, damage and failure is discussed.Furthermore, the algorithm for numerical integration of the coupled constitutive rate equations is presented. It relies on operator split methodology resulting in an inelastic predictor-elastic corrector technique. The explicit finite element program LS-DYNA augmented by an user-defined material subroutine is used to approximate boundary-value problems under dynamic loading conditions. Numerical simulations of dynamic experiments with different specimens are performed and good correlation of numerical results and published experimental data is achieved. Based on numerical studies modified specimens geometries are proposed to be able to detect complex damage and failure mechanisms in Hopkinson-Bar experiments.     

A thermodynamics-based cohesive model for interface debonding and friction

A constitutive model for interface debonding is proposed which is able to account for mixed-mode coupled debonding and plasticity, as well as further coupling between debonding and friction including post-delamination friction. The work is an extension of a previous model which focuses on the coupling between mixed-mode delamination and plasticity. By distinguishing the interface into two parts, a cracked one where friction can occur and an integral one where further damage takes place, the coupling between frictional dissipation and energy loss through damage is seamlessly achieved. A simple framework for coupled dissipative processes is utilised to derive a single yield function which accurately captures the evolution of interface strength with increasing damage, for both tensile and compressive regimes. The new material model is implemented as a user-defined interface element in the commercial package ABAQUS and is used to predict delamination under compressive loads in several test cases.     

Modelling of stress softening in elastomeric materials: foundations of simple theories

This work is concerned with formulation of constitutive relations for materials exhibiting the stress softening phenomenon (known as the Mullins effect) typical observed in elastomeric and other amorphous materials during loading–reloading cycles. It is assumed that microstructural changes in such materials during the deformation process can be represented by a single scalar-valued softening variable whose evolution is accompanied by microforces satisfying their own law of balance, besides the classical laws of mechanics underlying macroscopic deformation of a material. The constitutive equations are then derived in consistency with thermodynamics of irreversible processes with the restriction to purely mechanical theory. The general form of the derived constitutive equations is subsequently simplified through introduction of additional assumptions leading to various models of the stress softening phenomenon. As an illustration of the general theory, it is shown that the so-called pseudo-elastic model proposed in the literature may be derived without an ad hoc postulate of the variational principle.     

Nonlinear seismic waves: A model for site effects

The aim of this paper is to propose a possible mathematical model of site effects that occur when seismic waves propagate through a sediment filled basin. The model is based on the mechanical properties of the medium (that we consider as a granular material) through which the seismic waves propagate. By looking for asymptotic solutions having the features of a progressive wave, we derive an evolution equation which is a modified Korteweg–deVries–Burgers equation containing also a nonlinear dissipative term. This equation is integrated numerically and the modelled site amplification is evaluated by using the smoothed spectral ratio between the propagated profile of the wave and the initial one.     

5A06铝合金的动态本构关系实验

运用材料试验机和分离式霍普金森压杆装置(SHPB)对3种不同加工及热处理状态的5A06铝合金在常温~500 C、应变率为10-4~103 s-1 下的力学行为进行了实验研究。基于Johnson-Cook (JC) 本构模型,通过实验数据拟合得到了每种状态下材料的本构模型参量。对Johnson-Cook本构模型中的应变率强化项作了修正,修正后的Johnson-Cook本构模型与实验数据基本吻合,从而确立了3种状态下5A06铝合金的动态本构关系。     

The status of the K-BKZ model within the framework of materials with multiple natural configurations

In this paper we show how the K-BKZ model fits in within a thermodynamic framework for describing the response of materials undergoing dissipative processes. The K-BKZ model is shown to arise naturally within this framework by choosing appropriate forms for the stored energy and the rate of dissipation for describing the material. It is also shown that by relaxing some of the assumptions that lead to a K-BKZ model, it is possible to derive a host of other fluid models that are generalizations of the K-BKZ model.     

Elastic behaviour of a regular lattice for meso-scale modelling of solids

A modelling strategy is proposed to link the meso-scale mechanical response of a solid material to the macroscopic material behaviour. The model is based on a regular lattice of truncated octahedral cells, with sites at the cell centres linked by two sets of bonds. The relationship between the macroscopic elastic behaviour of the model and the elastic properties of the bonds is studied numerically. The results demonstrate that, in contrast to previously proposed lattice arrangements, any elastic properties of metallic or cementitious materials can be obtained by appropriate selection of the axial and the shear stiffness of the bonds. Discussion of the modelling approach includes the potential of the site-bond model to simulate the evolution of damage driven not only by mechanical deformation but also by processes that involve the interaction of different mechanisms.     

A thermodynamic approach to the boundary layer flow system

A thermodynamic approach to the boundary layer flow system is used to investigate the control rule underlying the flow field. Application of Pontryagin's Maximum Principle from control theory shows minimum rate of entropy production to be the control rule for the flow field, in common with other dissipative processes. This result is used to investigate possible organised motion in the turbulent boundary layer and the generation of longitudinal vortices which is known to be an intrinsic characteristic of turbulence.     

Deformation and damage due to drying-induced salt crystallization in porous limestone

This paper presents a computational model coupling heat, water and salt ion transport, salt crystallization, deformation and damage in porous materials. We focus on crystallization-induced damage. The theory of poromechanics is employed to relate stress, induced by crystallization processes or hygro-thermal origin, to the material's mechanical response. A non-local formulation is developed to describe the crystallization kinetics. The model performance is illustrated by simulating the damage caused by sodium chloride crystallization in a porous limestone. The results are compared with experimental observations based on neutron and X-ray imaging. The simulation results suggest that the crystallization kinetics in porous materials have to be accurately understood in order to be able to control salt damage. The results show that the effective stress caused by salt crystallization depends not only on the crystallization pressure but also on the amount of salt crystals, which is determined by the spreading of crystals in the porous material and the crystallization kinetics.     

A principle of virtual work for combined electrostatic and mechanical loading of materials

The equations governing mechanics and electrostatics are formulated for a system in which the material deformations and electrostatic polarizations are arbitrary. A mechanical/electrostatic energy balance is formulated for this situation in terms of the electric enthalpy, in which the electric potential and the electric field are the independent variables, and charge and electric displacement, respectively, are the conjugate thermodynamic forces. This energy statement is presented in the form of a principle of virtual work (PVW), in which external virtual work is equated to internal virtual work. The resulting expression involves an internal material virtual work in which (1) material polarization is work-conjugate to increments of electric field, and (2) a combination of Cauchy stress, Maxwell stress and a product of polarization and electric field is work-conjugate to increments of strain. This PVW is valid for all material types, including those that are conservative and those that are dissipative. Such a virtual work expression is the basis for a rigorous formulation of a finite element method for problems involving the deformation and electrostatic charging of materials, including electroactive polymers and switchable ferroelectrics. The internal virtual work expression is used to develop the structure of conservative constitutive laws governing, for example, electroactive elastomers and piezoelectric materials, thereby determining the form of the Maxwell or electrostatic stress. It is shown that the Maxwell or electrostatic stress has a form fully constrained by the constitutive law and cannot be chosen independently of it. The structure of constitutive laws for dissipative materials, such as viscoelastic electroactive polymers and switchable ferroelectrics, is similarly determined, and it is shown that the Maxwell or electrostatic stress for these materials is identical to that for a material having the same conservative response when the dissipative processes in the material are shut off. The form of the internal virtual work is used further to develop the structure of dissipative constitutive laws controlled by rearrangement of material internal variables.     

Energy release rates in rubber during dynamic crack propagation

The theoretical understanding of the fracture mechanics of rubber is not as well developed as for other engineering materials, such as metals. The present study is intended to further the understanding of the dissipative processes that take place in rubber in the vicinity of a propagating crack tip. This dissipation contributes significantly to the total fracture toughness of the rubber and is therefore of great interest from a fracture mechanics point of view. To study this, a computational framework for analysing high-speed crack growth in a biaxially stretched rubber under plane stress is therefore formulated. The main purpose is to investigate the energy release rates required for crack propagation under different modes of biaxial stretching. The results show, that inertia comes into play when the crack speed exceeds about 50 m/s. The total work of fracture by far exceeds the surface energy consumed at the very crack tip, and the difference must be attributed to dissipative damage processes in the vicinity of the crack tip. The size of this damage/dissipation zone is expected to be a few millimetres.     

Rate effects on toughness in elastic nonlinear viscous solids

A micromechanics-based constitutive relation for void growth in a nonlinear viscous solid is proposed to study rate effects on fracture toughness. This relation is incorporated into a microporous strip of cell elements embedded in a computational model for crack growth. The microporous strip is surrounded by an elastic nonlinear viscous solid referred to as the background material. Under steady-state crack growth, two dissipative processes contribute to the macroscopic fracture toughness—the work of separation in the strip of cell elements and energy dissipation by inelastic deformation in the background material. As the crack velocity increases, voids grow in the strain-rate strengthened microporous strip, thereby elevating the work of separation. In contrast, the energy dissipation in the background material decreases as the crack velocity increases. In the regime where the work of separation dominates energy dissipation, toughness increases with crack velocity. In the regime where energy dissipation is dominant, toughness decreases with crack velocity. Computational simulations show that the two regimes can exist in certain range of crack velocities for a given material. The existence of these regimes is greatly influenced by the rate dependence of the void growth mechanism (and the initial void size) as well as that of the bulk material. This competition between the two dissipative processes produces a U-shaped toughness-crack velocity curve. Our computational simulations predict trends that agree with fracture toughness vs. crack velocity data reported in several experimental studies for glassy polymers and rubber-modified epoxies.     

On the stored and dissipated energies in heterogeneous rate-independent materials

The present paper is a part of a work that aims at building a dissipative model of microcrack friction in quasi-brittle energetic materials. The latter is viewed as an assembly of elementary cells containing the most salient features of the microstructure heterogeneity. It is intended here to build an analytical model describing the mechanical and energetic response of such an elementary cell under confined tension. This is achieved by applying a previously published theory that allows for the determination of the amount of dissipated and stored energies in heterogeneous dissipative structures containing microcracks and other dissipative components.     

Assessment of creep damage in austenitic steel X-8-CrNiMoNb-16-16 at elevated temperature

A phenomenological model of creep deformation is developed by introduction of a function that represents intrinsic creep resistance to damage. The Lévy-Mises relation in plasticity is modified in deriving the time dependent creep strain and/or strain rate expression. Results correlated well with the experimental creep data of the X-8-CrNiMoNb-16-16 austenitic steel.     

一种基于材料延性耗散模型的疲劳损伤研究方法

本文从疲劳损伤导致材料延性下降这一事实出发,采用疲劳损伤延展性耗散模型,对低周疲劳定义了一种新的损伤变量,并进行了实验测量研究。结果表明,新损伤变量具有明确的物理意义,测定方法简单,能直接与材料机械性能相联系。     

Damage initiation and growth in metals. Comparison between modelling and tomography experiments

Damage in heterogeneous model materials was measured using high-resolution X-ray absorption tomography. The material consisted of an aluminium matrix containing 1% and 4% of spherical ceramic particles acting as nucleation sites for an interface decohesion mechanism of damage. The damage initiation stage was quantified using the global population of particles in the 4% material. A strain path change experiment was then applied to the 1% material. The sample was first deformed in tension in order to create elongated cavities and then compressed at 45^° to rotate and close these cavities. The results of a model based on the Rice and Tracey approach accounting for the presence of particles inside the cavities and calculating their rotation with assuming a linear hardening plastic behaviour of the matrix were compared with the observations. The model was modified to account for the damage initiation phase. It was shown to give a good global prediction of the void volume fraction provided that the physical, mechanical and morphological information are corresponding in the experimental and the model cases. The cavity rotation experiment was also shown to compare well with the calculation although only one cavity was sufficiently opened after compression to allow the comparison.     

On evolving deformation microstructures in non-convex partially damaged solids

The paper outlines a relaxation method based on a particular isotropic microstructure evolution and applies it to the model problem of rate independent, partially damaged solids. The method uses an incremental variational formulation for standard dissipative materials. In an incremental setting at finite time steps, the formulation defines a quasi-hyperelastic stress potential. The existence of this potential allows a typical incremental boundary value problem of damage mechanics to be expressed in terms of a principle of minimum incremental work. Mathematical existence theorems of minimizers then induce a definition of the material stability in terms of the sequential weak lower semicontinuity of the incremental functional. As a consequence, the incremental material stability of standard dissipative solids may be defined in terms of weak convexity notions of the stress potential. Furthermore, the variational setting opens up the possibility to analyze the development of deformation microstructures in the post-critical range of unstable inelastic materials based on energy relaxation methods. In partially damaged solids, accumulated damage may yield non-convex stress potentials which indicate instability and formation of fine-scale microstructures. These microstructures can be resolved by use of relaxation techniques associated with the construction of convex hulls. We propose a particular relaxation method for partially damaged solids and investigate it in one- and multi-dimensional settings. To this end, we introduce a new isotropic microstructure which provides a simple approximation of the multi-dimensional rank-one convex hull. The development of those isotropic microstructures is investigated for homogeneous and inhomogeneous numerical simulations.     

On the stability of a circular system subjected to nonlinear dissipative forces

A circular system is a mechanical system subjected to potential forces and positional nonconservative forces (circular forces). The latter linearly depend on the coordinates and are characterized by a skew-symmetric matrix. The influence of linear dissipative forces on the stability of a circular system is ambiguous: on the one hand, they can stabilize a stable circular system (making it asymptotically stable); on the other hand, they can destabilize it [1–4]. The action of linear dissipative forces on a circular system results in the so-called destabilization paradox: the stability threshold decreases by a finite value.A detailed survey of this phenomenon can be found in [5]. The destabilization effect is also preserved under the action of nonlinear dissipative forces. The influence of these forces on the stability of the Ziegler pendulum with a tracking force was studied in [6]. It was shown that the critical value of the tracking force decreases by a finite value. A similar effect was discovered in the analysis of a continual system in [7].In the present paper, we study how nonlinear dissipative forces affect the stability of the equilibrium of a circular mechanical system with two degrees of freedom. The stability problem is solved without any references to specific mechanical systems. The results are used to analyze the stability of a gimbal gyro with allowance for dry friction in the rotor bearings.