Applied Mechanics and Materials Vol. 784

Abstract: The present paper addresses the continuum model describing deformation and accumulation of microdamages in electroelastic materials based on the generalized Eshelby principle. The microdamageability is considered as a process of appearance of flat elliptic or circular microcracks randomly dispersed over volume, the concentration of which increases with a load. The Eshelby method is based on the principle of equivalence of the deformation energy of fractured piezoelectric materials and the energy of medium, which is modeling these materials as a continuous medium. The key point of this approach is to determine the densities of the released elastic and electric energy.

Abstract: A new micromechanical modelling approach for brittle damage in initially orthotropic materials is presented. The proposed strain-based energy formulation allows to derive a fully anisotropic multilinear model for microcracked materials with arbitrary oriented defects. The thermodynamics framework provides a standard procedure for the damage evolution law. The new model explicitly accounts for the interaction between primary and induced anisotropies. Moreover, the very challenging issue of opening-closure effects (unilateral behavior) is addressed in this framework.

Abstract: Failure of weld joints under single and cyclic pulsating loading conditions is under consideration. A weld joint is modeled by three-layer composite. Stepwise propagation of the internal I mode crack under cyclic loading is investigated. Delamination of bimaterial composed of two structured materials is considered when a crack is located at the interface between two media. Loads under pulsating loading conditions are studied for elastic-plastic material. For analysis of this process, diagrams of quasi-brittle fracture of solids under cyclic loading conditions are proposed to be used. One of curves of the proposed diagram bears resemblance to the Kitagawa-Takahashi diagram. Estimates of average dimensionless velocity of stepwise crack propagation per loading cycle have been obtained in an explicit form for plain specimens of finite width. The relations derived for the average crack growth rate can be considered as structural expressions for plotting Paris’ curves.

Abstract: To predict a complete process of failure evolution, discontinuous bifurcation analysis has been performed to link elastoplasticity and damage models with decohesion models. To simulate multi-phase interactions involving failure evolution, the Material Point Method (MPM) has been developed to discretize localized large deformations and the transition from continuous to discontinuous failure modes. In a recent study for the Sandia National Laboratories (SNL) challenge, the decohesion modeling is improved by making the failure mode adjustable and by replacing the critical normal and tangential decohesion strengths with the tensile and shear peak strengths, in order to predict the cracking path in a complex configuration with the least computational cost,. It is found that there is a transition between different failure modes along the cracking path, which depends on the stress distribution around the path due to the nonlocal nature of failure evolution. Representative examples will be used to demonstrate the recent advances in simulating failure evolution with the MPM.

Abstract: A micro-cell size dependent damage law is proposed by the multi-scale damage representation to remedy the mesh sensitivities involving in the numerical simulations. The homogenization based multi-scale damage representation is firstly introduced in obtaining the macro-damage evolution from micro-cell analysis. Then, the micro-cells with different sizes are generated and the corresponding simulations are given. Based on the simulation results, we define the micro-cell size dependent damage law. Finally, the accuracy and efficiency of the proposed damage law are verified by the notched beam simulation results.

Abstract: The process of damage in quasi-fragile materials is characterized by loss of isotropy for certain load levels, the strain localization, the cooperative effect between damaged regions and the avalanche of ruptures are particular features in the damage process of this kind of material. This behavior is not easy to represent with a continuous approach. In the present work a version of the Lattice Discrete Element Method (LDEM) is employed. This methodology allows the simulation of fracture and fragmentation in natural way. Different indexes will be shown to perform the measurement of the damage evolution in the context of LDEM. The performance of these indexes to evaluate the damage evolution is discussed in this paper.

Abstract: Much effort has been put in the development of proper continuum damage mechanics models, in which damage is either represented as a scalar, vectorial or tensorial quantity. In this work the anisotropic damage theory of Lemaitre et al. (2000), which describes damage as a second order tensor, is utilized. Two numerical time integration algorithms, namely a fully implicit and a partially explicit scheme, are compared by means of finite element computations of a plate with a circular hole. The convergence behavior of the two algorithms is studied and compared regarding the number of time steps.

Abstract: This paper presents the study of failure surface obtained in the truss-like Discrete Element Method (DEM). The element constitutive law considers the fracture energy of the material and its spatial variation is used to take into account the heterogeneity of the simulated materials. It is studied the influence of spatial distribution of fracture energy and the spatial lattice perturbation on the DEM failure surface. A DEM failure criterion is compared with concrete and rock failure.

Abstract: In this paper, we focus on the stress-strain behavior prediction of the bimodal bulk Al5083 series which are comprised of ultra-fine grains (UFG) separated by coarse grain (CG) regions. The CGs in the UFG matrix effectively prevents microcracks from propagation, leading to enhance ductility and toughness while the strength remains high. In this work, initially, XFEM is implemented for bimodal materials considering various fracture criteria for brittle and ductile phases in maximum traction and cohesive law. Then the stress-strain behavior dependency of the model on the CG distribution in a constant volume fraction is investigated by extraction of RVEs from optical microscopy (OM) images of the real material. The solution convergence of such a problem with irregular geometry, plasticity and crack initiation-propagation demanded extreme efforts that accomplished by refining and arranging meshes as well as adding damage stabilizations. As a result of the above procedures, the sensitivity of the modeling procedure to various RVEs is obtained, the crack initiation-propagation pattern in microscale is predicted and consequently, the global stress-strain behavior result is calculated. It is shown that the predicted results are in good agreement with the available experimental results.

Abstract: The paper presents a simulation model for the creep process of rotating disks under radial tensional pressure subjected to of body force. The finite strain theory is applied. The material is described by the Norton-Bailey law generalized for true stresses and logarithmic strains. The mathematical model is formulated in form of set of four partial differential equations with respect to radial coordinate and time. Necessary initial and boundary conditions are also given. To make the model complete, the numerical procedure for solving this set is proposed. What is worth noticing the classical FEM is not applicable, because not only geometry, but also loading (body forces) change in time during the creep process. It would demand redefinition of finite elements at each time step. In uniaxial problem similar model was presented in [4], but now it is developed for complex stress state. Possible different formulations of initial and boundary conditions may be found in [5]. The procedure may be useful in problems of optimal design of full disks in [6].