Applied Mechanics and Materials Vol. 784

Abstract: The concept of complex damage variables is introduced in this work. These damage variables have both real and imaginary parts. They are introduced not to use them in practical applications but to try to derive a direct relationship between the damage due to cross-sectional area reduction and the damage due to elastic stiffness degradation. In addition this concept can provide an insight in addressing the concept of healing that the authors have extensively published as well as the concept of undamageable materials. Toward this goal some success is achieved in the sense that some complicated relationships between the two damage processes are formulated. These relationships and the complex variable approach are novel ideas in Continuum Damage Mechanics. Throughout the formulation the hypothesis of strain equivalence is used in order to simplify the mathematical equations. This work can be extended and generalized by substituting the hypothesis of energy equivalence but this will complicate the equations unnecessarily.

Abstract: In this paper, yield surface distortion was studied by considering the combination of nonlinear kinematic hardening model of Chaboche and a new anisotropic continuum damage evolution model. The constitutive relations for anisotropic damage of elastoplasic materials were developed based on irreversible thermodynamics. The internal state manifold which consists of internal variables to specify the thermodynamic state of solids was described by a 2nd rank symmetric damage tensor, the kinematic hardening tensor and tensor of movement of damage potential surface. In order to describe the damage state, the fictitious continuum domain was considered and the consistent relations between real and fictitious domains were developed. It was indicated that the combination of the Chaboche’s model and model of anisotropic continuum damage leads to the well description of the subsequent yield surface.

Abstract: The creep damage is discussed within Rice thermodynamic theory with internal state variable (ISV). A viscoelastic-viscoplastic model with damage is derived by giving the complementary energy density function and kinetic equations of ISVs. The viscoelastic equation covers classical component model, and three creep phases with hardening and damage effect can be described by this model. The model parameter cabibration is conducted through uniaxial creep test of analogue material by loading and unloading method. Then intrinsic thermodynamic properties in three creep stages are indicated. The thermodynamic state of material system tends to equilibrate without damage and depart from equilibrate with damage.

Abstract: The toughness transition behavior of ferritic steel results from the fact that two competing fracture mechanisms can be activated independently or progressively. Temperature, strain rate and the material ́s hardening properties are the major influences affecting the result of this competition between cleavage and ductile fracture mechanisms. An elastic visco-plastic plasticity model with stress-state dependent yielding and isotropic hardening forms the basis of a model to predict the Charpy impact toughness properties of steels with bcc crystal structure for transition behavior. A scalar damage variable is coupled into the yield potential in order to capture the effects of damage induced softening. The corresponding damage evolution law considers damage initiation criteria for both mentioned fracture mechanisms. Material parameter identifications and successful model application in terms of Charpy impact toughness tests are demonstrated.

Abstract: The paper discusses an anisotropic continuum damage model. It takes into account the effect of stress state on damage and failure conditions as well as on evolution equations of damage strains. To validate the proposed framework experiments with biaxially loaded specimens and corresponding numerical simulations are performed covering a wide range of stress states. In addition, scanning electron microscope images of the fracture surfaces show different fracture modes corresponding to stress states revealed by numerical analyses.

Abstract: The problem undertaken in the present work concerns the kinetics of evolution of radiation induced damage under mechanical loads. Furthermore, coupling between the radiation induced nanodamage and the mechanically induced micro-damage is taken into account. The evolution of radiation induced damage is combined with the evolution of classical mechanically induced damage within the common framework of Continuum Damage Mechanics (CDM). Closed form analytical solutions for the problem of periodic irradiation combined with cyclic axial loads, corresponding to Rice & Tracey law was obtained.

Abstract: The fatigue problem of concrete has long been studied through many different methods. However, the fatigue process and failure patterns of concrete structures have never been well simulated due to the lack of comprehensive understanding of the material properties under fatigue loads. In order to carry out an accurate simulation of the fatigue behavior of concrete structures, this paper proposes a new damage theory based fatigue constitutive model for concrete. The present model adopts two damage variables to describe the degradation of macro mechanical properties of concrete under tension and compression, respectively. And the tensile and compressive damage evolutions are related to the corresponding effective stress spaces. Specifically, by implementing the present model into the nonlinear finite element package, the bending fatigue process of a concrete beam is simulated. Meanwhile a set of numerical tests are presented, through which the validity and effectiveness of the proposed model for the simulation of concrete structures are illustrated.

Abstract: The coupling between mechanical and chemical behaviors is investigated. The Generalized Eigenstrain Method is used and enables to take easily into account several couplings, such as damage and corrosion. Modeling is then performed and compared for different configurations. Chemical reactions and diffusion effects are thus described in order to improve accuracy of such a micromechanical time-dependent model. Application is then performed on a steel reinforced concrete material. Moreover, a particular and original coupling has been introduced, which is justified by thermodynamics arguments.

Abstract: In the present paper, the Preisach model of hysteresis is extended to structural analysis of trusses damaged under cyclic loading in plastic range. Parameters for the Preisach model of cyclic plasticity are obtained from uniaxial loading experiment. Damage, as a consequence of micro cracks appearance due to alternating loading in plastic domain, is modeled using brittle elements according to Preisach procedure. Results of this research are compared with the already existing in the literature. In the paper examples of trusses under various cyclic loadings are presented.