Rate-dependent Damage Research Articles

Study of Tertiary Creep of Rock Salt

It appears from macro- and microexperiments that the essential response feature beyond the secondary stage of rock salt creep is characterized by the evolution of localized damage that results in the formation and propagation of macrocracks. To predict the creep response of rock salt, a modeling framework with a corresponding integration scheme is developed based on thermodynamic restrictions. The jump forms of conservation laws are used to identify the transition from continuous to discontinuous failure modes. To obtain a continuum tangent stiffness tensor for bifurcation analyses, a simple creep model is formulated from the modeling framework by combining a viscoplastic part with an implicitly rate-dependent damage part. Sample problems are considered to illustrate the proposed procedure.

A viscoelastic continuum damage model and its application to uniaxial behavior of asphalt concrete

Abstract An existing viscoelastic constitutive model which accounts for the effects of rate-dependent damage growth is described and applied successfully to characterize the uniaxial stress, constant strain rate behavior of asphalt concrete. The special case of an elastic continuum damage model with multiaxial loading, which is based upon thermodynamics of irreversible processes with internal state variables, is first reviewed and then it is shown how this model has been extended to a corresponding viscoelastic damage model through the use of an elastic-viscoelastic correspondence principle. The general mathematical model is next specialized to uniaxial loading. A rate-type evolution law, similar in form to a crack growth law for a viscoelastic medium, is adopted for describing the damage growth within the body. Results from laboratory tests of uniaxial specimens under axial tension at different strain rates are then shown to be consistent with the theory. The discussion of data analysis describes the specific procedure used here to obtain the material parameters in the constitutive model for uniaxial loading and how the method may be generalized for multiaxial loading.

Rate Dependent Damage Model for Concrete in Dynamics

This paper presents a rate dependent damage model and its implementation in transient dynamics. The rate dependent model is derived from a rate independent damage model simply by changing the expression of the damage evolution equation. The principle of the model follows the format of Perzyna viscoplasticity whereby the definition of the plastic multiplier is modified compared to a standard rate independent plasticity model. The rate dependent model can reproduce very well the major effects of the rate of loading on the response of concrete; that is, an increase of the material strength and a decrease of the softening tangent modulus with increasing strain rate. The wave propagation problem is assessed. We show that the resulting equations of motion are unconditionally hyperbolic. Well-posedness and mesh objectivity are verified numerically on a simple one-dimensional (1D) problem. As an example of implementation in a finite element calculation, the computation of the response of a reinforced concrete beam subjected to an impact is presented.

Continuum damage modeling of impact fracture in ceramic materials

The expanded use of ceramic materials in a variety of engineering applications demands improved capabilities for the simulation of anisotropic microcracking and fracture processes. Damage mechanics provides a continuum-based description of such processes which can be readily implemented in the Lagrangian finite element codes most often employed in structural analysis and design. The use of anisotropic damage models in three-dimensional impact simulations demands that large rotation effects be accounted for, in a computationally efficient way. In addition, ceramic materials call for consideration of rate-dependent damage evolution equations. A second-order tensor-based elastic-brittle damage model for ceramic materials may be formulated, which is both suitable for large rotation analysis and thermodynamically consistent in its treatment of rate-dependent damage evolution.

Dose rate effects on damage formation in ion-implanted gallium arsenide

The residual damage in GaAs was measured by ion channeling following implantation of either 100 keV 30Si + at temperatures of 300 or 77 K, or 360 keV 120Sn + at 300 K. For room-temperature Si implants and fluences between 1 and 10 × 10 14Si/cm 2, the amount of damage created was strongly dependent upon the ion current density, which was varied between 0.05 and 12 μ |A/cm 2. Two different stages of damage growth were identified by an abrupt increase in the damage growth rate as a function of fluence, and the threshold fluence for the onset of the second stage was found to be dependent on the dose rate. The dose rate effect on damage was substantially weaker for 120Sn + implants and was negligible for Si implants at 77 K. The damage was found to be most sensitive to the average current density, demonstrating that the defects which are the precursors to the residual dose rate dependent damage have active lifetimes of at least 3 × 10 −4 s. The dose rate effect and its variation with ion mass and temperature are discussed in the context of homogeneous nucleation and growth of damage during ion irradiation.

Silicon implantation into GaAs: Observations of dose rate dependent electrical activation and damage

The electrical activation of ion-implanted silicon in GaAs has been studied as a function of dose rate (i.e., ion-current density). For a fluence of 1014 cm−2, the Hall sheet carrier activation is shown to depend strongly on the dose rate at which the implant was carried out. Carrier concentrations of 7×1018 cm−3 were produced at a 50×10−9 A/cm2 ion-current density. The variation in electrical activation is believed to be the result of a dose rate dependence of the ion-induced damage of GaAs which can be clearly seen in Rutherford backscattering (RBS) channeling measurements of 1015 cm−2 implants.

Strain- and stress-based continuum damage models—II. Computational aspects

In Part I of this work we developed continuum isotropic and anisotropic elastoplastic-damage models, formulated either in strain space on the basis of the effective stress concept, or in stress space and employing the dual notion of effective strain. In Part II we consider in detail the variational formulation and subsequent numerical implementation of these models. The former relies crucially on the notions of maximum plastic and maximum damage dissipation. The latter makes systematic use of the operator splitting methodology to derive unconditionally stable algorithms for the numerical integration of the elastoplastic-damage equations of evolution. Appropriate extensions to treat the proposed rate-dependent (viscous) damage are also presented. For stress-based damage models, our numerical treatment relies on a new three-step operator split. The algorithms developed lead to simple and efficient stress update procedures suitable for large-scale finite element calculations. Application is made to a class of inviscid and rate-dependent cap models with an isotropic strain-based damage mechanism. Remarkably good agreement with existing experimental data that includes complicated stress paths is obtained. Numerical examples are also presented that demonstrate the good performance of the proposed algorithms.

Strain- and stress-based continuum damage models—II. Computational aspects

In Part I of this work we developed continuum isotropic and anisotropic elastoplastic-damage models, formulated either in strain space on the basis of the effective stress concept, or in stress space and employing the dual notion of effective strain. In Part II we consider in detail the variational formulation and subsequent numerical implementation of these models. The former relies crucially on the notions of maximum plastic and maximum damage dissipation. The latter makes systematic use of the operator splitting methodology to derive unconditionally stable algorithms for the numerical integration of the elastoplastic-damage equations of evolution. Appropriate extensions to treat the proposed rate-dependent (viscous) damage are also presented. For stress-based damage models, our numerical treatment relies on a new three-step operator split. The algorithms developed lead to simple and efficient stress update procedures suitable for large-scale finite element calculations. Application is made to a class of inviscid and rate-dependent cap models with an isotropic strain-based damage mechanism. Remarkably good agreement with existing experimental data that includes complicated stress paths is obtained. Numerical examples are also presented that demonstrate the good performance of the proposed algorithms.

Rate Dependent Void Growth In DuctileMetals Submitted To Large Deformation

In this paper, we present a rate-dependent damage model based on a generalization of the Perzina viscoplastic law applied to the Gurson-Tvergaard damage model. In a numerical example, this model is shown to be useful as a regularization method for problems with bifurcation difficulties due to softening. Other applications are also briefly overviewed.