Singular crack-tip fields for pressure sensitive plastic solids

Plain strain mode-I singular plastic fields are examined for cracks embedded in pressure sensitive solids. Material response is described by a small strain deformation theory in conjunction with elliptic yield criterion and plastic potential. Non-associativity is accounted for and a pure power law is assumed to characterize strain hardening. The material does not admit a strain energy function hence it is not possible to deduce a-priori the J-integral motivated stress singularities. A standard separation of variables representation of near-tip eigenfunctions has been evaluated numerically, over a range of material parameters. It has been found that stress singularities may deviate from J-integral predictions, with increasing non-associativity, by up to nearly 20%. Sample illustrations are provided for singular field profiles and some aspects of pressure sensitive non- associated plasticity are discussed.     

Evolution of anodic stress corrosion cracking in a coated material

In the present paper, we investigate the influence of corrosion driving forces and interfacial toughness for a coated material subjected to mechanical loading. If the protective coating is cracked, the substrate material may become exposed to a corrosive media. For a stress corrosion sensitive substrate material, this may lead to detrimental crack growth. A crack is assumed to grow by anodic dissolution, inherently leading to a blunt crack tip. The evolution of the crack surface is modelled as a moving boundary problem using an adaptive finite element method. The rate of dissolution along the crack surface in the substrate is assumed to be proportional to the chemical potential, which is function of the local surface energy density and elastic strain energy density. The surface energy tends to flatten the surface, whereas the strain energy due to stress concentration promotes material dissolution. The influence of the interface energy density parameter for the solid–fluid combination, interface corrosion resistance and stiffness ratios between coating and substrate is investigated. Three characteristic crack shapes are obtained; deepening and narrowing single cracks, branched cracks and sharp interface cracks. The crack shapes obtained by our simulations are similar to real sub-coating cracks reported in the literature.     

Weak discontinuities in relativistic magnetohydrodynamics in the presence of dissipative mechanisms

In this work the study of propagation of weak discontinuities in relativistic magnetohydrodynamics in the presence of dissipative mechanisms of finite electrical and heat conductivities, is carried out. It is shown that a weak discontinuity exists only in the fluids in which the pressure is proportional to the total energy density, if the first order partial derivatives of heat flux vector are continuous across the discontinuity surface. If the latter are discontinuous then singular surfaces exist in low temperature case but not in the ultrarelativistic case. In all these cases the role of dissipation is to cause damping of the wave while shocks can occur in the case of initially compressive waves.     

On the J-integral and energy-release rates in dynamical fracture

Summary The apparent contradiction between the Eshelby formulation (consideration of a material force on the material manifold) and the more usual global-dissipation analysis (essentially, the balance of energy about the moving singular point represented by the tip of the crack) of theJ-integral and energy-release rate in dynamical fracture is resolved in both pure finite-strain elasticity and Galilean-invariant electrodynamics of electro-magneto-elastic media. The solution uses the notions of mechanical and electromagnetic pseudomomenta (canonical momenta) in finitely deformable continua with cracks.     

Strain-driven corrosion crack growth: A pilot study of intergranular stress corrosion cracking

This work proposes a model for corrosion driven crack growth. The model poses a moving boundary problem, where a chemical attack removes material from the body. The rate of the chemical attack is a function of the strain along the body surface. No crack growth criterion is needed for the analysis. A finite strain formulation is used and the material model is assumed hyperelastic. The problem is stated for a large body, containing a large crack. A low frequency cyclic loading is considered. Thus, corrosion is assumed to dissolve material with a rate approximately proportional to the strain rate. The problem is solved using finite element method based program, enhanced with a procedure handling the moving boundary. Parametric studies are performed for a series of different initial shapes of the near-tip region. Presented results show that the crack growth rate is largely dependent on the initial crack geometry. For a set of initial shapes and load levels steady-state conditions of growth are achieved, while for the others the cracks show tendency to branch.     

Strain-driven corrosion crack growth: A pilot study of intergranular stress corrosion cracking

This work proposes a model for corrosion driven crack growth. The model poses a moving boundary problem, where a chemical attack removes material from the body. The rate of the chemical attack is a function of the strain along the body surface. No crack growth criterion is needed for the analysis. A finite strain formulation is used and the material model is assumed hyperelastic. The problem is stated for a large body, containing a large crack. A low frequency cyclic loading is considered. Thus, corrosion is assumed to dissolve material with a rate approximately proportional to the strain rate. The problem is solved using finite element method based program, enhanced with a procedure handling the moving boundary. Parametric studies are performed for a series of different initial shapes of the near-tip region. Presented results show that the crack growth rate is largely dependent on the initial crack geometry. For a set of initial shapes and load levels steady-state conditions of growth are achieved, while for the others the cracks show tendency to branch.     

Constitutive modeling for hot deformation behavior of ZA27 alloy

The hot deformation behavior of ZA27 alloy was investigated in the temperature range of 473–523 K with the strain rates in the range of 0.01–5 s⁻¹ and the height reduction of 60 % on Gleeble-1500 thermo mechanical simulator. Based on the experimental results, constitutive equations incorporating the effects of temperature, strain rate, and strain have been developed to model the hot deformation behavior of ZA27 alloy. Material constants, α, n, ln A, and activation energy Q in the constitutive equations were calculated as a function of strain. The results showed that the stress–strain curves of ZA27 alloy predicted by the constitutive equations are in good agreement with experimental results, which validates the efficiency of the constitutive equations in describing the hot deformation behavior of the material.     

Effects of strain and strain rate on electronic behavior of metal surfaces under bending and tension tests

Surface electronic behavior of MEMS and NEMS can be characterized using the Kelvin probe technique by measurements of work function (WF). However, the physical mechanism responsible for such electronic behavior of a surface subjected to mechanical loading has not been completely understood. In this study, changes in WF of copper and aluminum with respect to strain and strain rate under bending and tension tests were measured using a scanning Kelvin probe. The results showed that plastic strain and strain rate can decrease WF although elastic strain may lead to complex changes in WF, which can be explained well using the electrostatic energy model on dislocation density.     

Influence of viscosity on the motion of quasi-particles associated with surface acoustic waves

Selecting this case as a tractable example, this work constructs an original quasi-particle mechanics associated with the dissipative continuum wave solution of so-called Bleustein–Gulyaev (BG) surface acoustic waves (SAWs). These propagate along an elastic semi-infinite space of appropriate crystalline symmetry allowing for the existence of a pure shear-horizontal (SH) displacement but with small viscosity treated as a perturbation. This association is built through the consideration of the canonical conservation (or non-conservation) of energy and wave momentum integrated over a material volume representative of the wave process in the presence of viscous dissipation. At the considered order of approximation, the resulting point mechanics is that of a quasi-particle moving at constant velocity (equal to that of the non-viscous case), but the motion is no longer inertial – due to viscosity – exhibiting a varying “mass” in time, in fact decreasing during the progress of the wave through the viscous material. This “mass” is characteristic of the amplitude of the wave signal, of the behavior of the wave in depth in the substrate, of the present electromechanical coupling, and of the boundary conditions assumed at the top surface, here enriched by the viscous effect. The mechanics obtained reminds us of the Leibnizian “vis-viva”, when the energy variation is considered.     

Molecular dynamics study of surface effect on martensitic cubic-to-tetragonal transformation in Ni–Al alloy

Molecular dynamics (MD) study of martensitic transformation (MT) in nickel and aluminum alloy is performed. The behavior focused on is transformation between crystalline structures from B2 cubic cell to body-centered tetragonal cell, which is simply realized by uniaxial tensile loading. The potential function used is Finnis–Sinclair type having only single energy minimum where B2 structure exists. The availability of this specific many-body potential for stress-induced MT phenomena under uniaxial loading is fully discussed. In MD simulations, martensite phase is induced by tensile stress or strain in the atomic system, as predicted by a potential energy map. It is understood that the characteristic of the potential energy function with regard to deformation is crucial for MT studies and investigating energy-strain or stress–strain map is worthwhile. The MT behavior in the atomic system occurs during a plateau region of stress–strain (S–S) curve of the whole specimen, that is typical for experimental superelastic or shape-memory alloys under uniaxial loading. It is found that, during each MT event, large jump of atomic strain is observed. Owing to single energy minimum, the atomic system shows almost perfect recovery in S–S curve, where the graph comes completely back to initial state after unloaded. Besides, the present paper focuses on surface effect for MT behavior. Since the surface effect is dominant in MT phenomena especially in microscopic specimens, a novel computational scheme for stabilizing condition in which uniaxial loading is always applied together with arbitrary periodic boundary condition(s) is devised. By comparing one-, two-, and three-dimensional models under uniaxial loading, it is recognized that the nucleation behavior depends strongly on the existence of free surface region (including corner edge). When there is no surface, a chaotic nucleation of martensite is observed. On the other hand, the free surface induces first martensite because of less constraint in tensile deformation of unit cells. It is confirmed that the tendency toward MT nucleation corresponds to yield stress or strain of the specimen. In order to define and detect martensite structure as for each atom, an atomic strain measure (ASM) with our own formation is introduced. It is shown that the ASM is very effective to distinguish martensite bct unit structure from others.     

The effect of different forms of strain energy functions in hyperelasticity‐based crystal plasticity models on texture evolution and mechanical response of face‐centered cubic crystals

Micro‐mechanical and macro‐mechanical behavior of face‐centered cubic (FCC) crystals is investigated by using different forms of strain energy functions in hyperelastic material models in crystal plasticity finite element framework. A quadratic strain energy function with anisotropic elastic constants, a polyconvex strain energy function with invariants associated with the cubic symmetry, and a strain energy function from an inter‐atomic potential are considered in hyperelastic material models to describe the elastic deformation of FCC crystals. In our numerical experiments, the trajectories of {111} poles in the pole figure and the accumulated plastic slips of FCC coppers under uniaxial tension and simple shear depend on the choice of strain energy functions when the slip resistance of the slip systems is high. The ability of strain energy functions in this study to represent elastic lattice distortions in crystals varies with the amount of elastic deformation and the shape of deformed lattice. However, numerical results show that the change of macroscopic mechanical behavior of FCC coppers is not significant for the choice of strain energy functions, compared with the change of crystallographic texture evolution. Copyright © 2014 John Wiley & Sons, Ltd.     

Application of energy density theory on finite cracked bodies

Abstract

A new concept of the energy release rate of a finite cracked body is proposed. Considering the global view of the strain energy density field, the new fracture parameter presented here is different from the conventional energy release rate that only depends on the stress field around the crack tip but neglects the influences induced by the boundary conditions on the far field. Based on the hypothesis of the energy density theory, fracture initiation and termination, respectively can be predicted by the local and global relative minima of the strain energy density function. The new energy release rate is then defined as the integration of the strain energy density along the fracture trajectory from the initiation point to the destination point. The results show that the difference between the new and the conventional energy release rate becomes more pronounced if the material has a large core region (or the material is more ductile) and if the height‐width ratio of a finite cracked plate is comparatively small.     

Strain energy density – a molecular appraisal

Abstract

The interaction potential between two clusters simulating the crack tip on the lattice level is derived in this work. Employing molecules as the building blocks and the Lennard‐Jones potential as the Green's function, the close‐form solution shows that the 1/r‐type of singularity is an intrinsic behavior of the energy field when mutual attraction dominates the lattice interactions. This behavior is now proven, explicitly, to be independent of the constitutive equation of the material.     

On the necessity of surface growth terms for the consistency of jump relations at a singular surface

Summary.  When a singular surface is present in the region under consideration, the local forms of the equations of balance must be accompanied by jump relations in order to connect the different values of the discontinuous entities at the two sides of the singular surface. The classical general form of these jump relations is provided by the Kotchine relation. In the present contribution, we exemplary deal with balance of mass, momentum and kinetic energy, as well as with balance of total energy, denoted as the first law of thermodynamics, and with balance of internal energy. We first derive an extension of the Kotchine relation with respect to surface growth terms. By a surface growth term we mean an entity which equivalently describes the balance of some quantity associated with the material that is instantaneously located at or in the vicinity of the singular surface. In a more detailed modelling, a singular surface is often described by a thin shell-type region or layer of transition. Surface growth terms may represent a non-vanishing rate of change of the respective quantity, or they may characterise some sources of this quantity. As a main result of the present paper, we show that surface growth terms are needed in order to ensure consistency between the jump relations for balance of mass, momentum and kinetic energy, and between the jump relations for balance of total energy and balance of internal energy. Even when surface growth terms for mass, balance of momentum and total energy are absent, one generally must take into account surface growth terms for balance of kinetic energy and balance of internal energy. The presented results refer to both, a singular surface, as well as to a thin region of transition. The jump relations in the latter case are referred to an equivalent singular surface, replacing the region of transition. The uni-axial flow of a fluid in a diffusor is used to demonstrate that the present results may be used even in cases in which the region of transition is not thin. Received July 17, 2002 Published online: May 20, 2003 The present paper is a contribution to the K+ Linz Center of Competence in Mechatronics (LCM), Strategic Project 4.4. Support of this work by the Austrian K+ Fund and the Government of Upper Austria is gratefully acknowledged.     

Thermodynamic format and heat generation of isotropic hardening plasticity

Summary Heat generation due to plastic deformation of metals and steel is studied. Whereas in many investigations it is assumed that the fraction η of the plastic work transformed into heat is constant throughout the deformation process, the fraction η is here derived from thermodynamic considerations in a large-strain setting. It is shown that for elasto-plasticity the fraction η follows as a result of the choice of free energy, potential function and yield function. Taking the stress-strain response and the dissipative properties of the material as basis for calibration, it is shown that the thermodynamic framework of a thermoplastic material is non-unique for the general situation of non-associated plasticity. In the investigation conducted here, the mechanical response and the portion of the plastic work converted into heat (or into stored energy) during plastic deformations is predicted by means of isotropic hardening von Mises plasticity. It is shown that for a situation in which the internal variable is taken as the effective plastic, close fitting to experimental data requires a non-associated format of the evolution law for the internal variable.     

Variational principles in dissipative electro‐magneto‐mechanics: A framework for the macro‐modeling of functional materials

This paper presents a general framework for the macroscopic, continuum‐based formulation and numerical implementation of dissipative functional materials with electro‐magneto‐mechanical couplings based on incremental variational principles. We focus on quasi‐static problems, where mechanical inertia effects and time‐dependent electro‐magnetic couplings are a priori neglected and a time‐dependence enters the formulation only through a possible rate‐dependent dissipative material response. The underlying variational structure of non‐reversible coupled processes is related to a canonical constitutive modeling approach, often addressed to so‐called standard dissipative materials. It is shown to have enormous consequences with respect to all aspects of the continuum‐based modeling in macroscopic electro‐magneto‐mechanics. At first, the local constitutive modeling of the coupled dissipative response, i.e. stress, electric and magnetic fields versus strain, electric displacement and magnetic induction, is shown to be variational based, governed by incremental minimization and saddle‐point principles. Next, the implications on the formulation of boundary‐value problems are addressed, which appear in energy‐based formulations as minimization principles and in enthalpy‐based formulations in the form of saddle‐point principles. Furthermore, the material stability of dissipative electro‐magneto‐mechanics on the macroscopic level is defined based on the convexity/concavity of incremental potentials. We provide a comprehensive outline of alternative variational structures and discuss details of their computational implementation, such as formulation of constitutive update algorithms and finite element solvers. From the viewpoint of constitutive modeling, including the understanding of the stability in coupled electro‐magneto‐mechanics, an energy‐based formulation is shown to be the canonical setting. From the viewpoint of the computational convenience, an enthalpy‐based formulation is the most convenient setting. A numerical investigation of a multiferroic composite demonstrates perspectives of the proposed framework with regard to the future design of new functional materials. Copyright © 2011 John Wiley & Sons, Ltd.     

A Global/Local approach to lengthwise cracked beams: dynamic analysis

A simple model is developed for the calculation of dynamic stress intensity factors for lengthwise cracked beams subjected to impact or transient loading. The model is based on a Global/Local approach that separates the Global structural dynamics from the Local crack tip zone dominated by singular stresses. The Global model is that of connected waveguides while the Local model is based on a novel application of the J-integral that converts dynamic structural resultants directly into strain energy release rate. The accuracy of this approach is assessed by comparing it to a fully two-dimensional finite element analysis in which the modified crack closure integral is used to calculate the dynamic strain energy release rate. Both mode I and mode II examples are given, and situations with multiple wave reflections are emphasized.     

On evolution equations for elastic deformation and the notion of hyperelasticity

For elastic-plastic and elastic-viscoplastic materials it is possible to introduce an evolution equation for an elastic deformation measure. Also, it is possible to develop constitutive equations for which the stress and strain energy are functions of elastic deformation only, the stress is determined by a derivative of the strain energy function and the associated material response is rate-independent and non-dissipative in the absence of the rate of inelasticity. Yet, these equations do not necessarily exhibit hyperelastic response in the elastic range. The objective of this paper is to emphasize the importance of satisfying an additional condition that requires the work done between two configurations to be insensitive to the history and rate of total deformation. This work condition places restrictions on the evolution equation which ensure that the integrated elastic deformation measure is a function of total deformation only. Also, it is argued that there is no need to complicate the evolution equation for elastic deformation to accommodate alternative strain measures since the nonlinearities of these strain measures can be absorbed into the form of the strain energy function.     

Bonding analysis of carbon/epoxy composites with viscoelastic acrylic adhesive

This paper focuses on the analysis of viscoelastic bonding strength of carbon/epoxy laminates with different surface treatments. Bonding is a well known technique, and is widely used in many industrial applications. Rigid bonding aims at transferring structural and vibration loads from one laminate to the other. The use of dissipative bonding material also helps reducing structural vibrations in many key applications. In this work, the bonding strength of carbon/epoxy substrates with viscoelastic acrylic adhesive was measured by means of a wedge test. The surface finish, which plays an important role in bonding, was characterized using a surface profiler and the Ondulo^MD system. Surface roughness and concentration of surface porosities were measured to define the quality of the laminate surface. It is shown that the final crack length decreases with increasing wedge penetration rate and increasing density of surface porosities. The surface pre-treatment with primer also reduces crack length, and thus increases fracture energy. The fracture energy ranges between 300 J/m² and 3000 J/m². The proportion of this energy which is due to dissipation in the adhesive, increases with the wedge penetration rate and reaches up to 60% of the total fracture energy.