Energy-based modeling of localization and necking in plasticity

Date

2014-07-04

Author

Yalçınkaya, Tuncay

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

116
views

0
downloads

In this paper two different non-local plasticity models are presented and compared to describe the necking and fracture through a non-convex energy, where fracture is regarded as the extreme localization of the plastic strain. The difference between the models arises from the evolution of plastic deformation. The first (rate-dependent) approach, proposed in Yalcinkaya et al. (2011) follows the principle of virtual work to get balance equations and the dissipation inequality, in order to obtain the plastic evolution equation. The free-energy is given by the sum of a non-convex plastic term, and two quadratic terms with respect to the elastic deformation and the plastic deformation gradient. In the second (rate-independent) model, developed in Del Piero et al. (2013a), the plastic evolution is determined by incremental minimization of an energy functional which is equal to the free-energy of the previous model. The numerical example considers a convex-concave plastic energy to address the response of a tensile steel bar, where plastic strains localize intrinsically up to fracture. The numerical results exhibit good agreement between the two models. The solutions provided by the rate-dependent model approach those of the rate independent model, as the imposed deformation rate reduces.

Subject Keywords

Non-convexity, Strain-gradient plasticity, Necking, Localization

URI

https://hdl.handle.net/11511/39374

DOI

https://doi.org/10.1016/j.mspro.2014.06.261

Collections

Department of Aerospace Engineering, Conference / Seminar

Suggestions

OpenMETU
Core

Computational Methods for Inclined Cracks in Orthotropic Functionally Graded Materials Under Thermal Stresses Dağ, Serkan; TOPAL, SERRA (2013-10-03) This article sets forth two different computational methods developed to evaluate fracture parameters for inclined cracks lying in orthotropic functionally graded materials, that are under the effect of thermal stresses. The first method is based on the J(k)-integral, whereas the second entails the use of the J(1)-integral and the asymptotic displacement fields. The procedures introduced are implemented by means of the finite element method and integrated into a general purpose finite element analysis softw...
Thermal stress problem for an FGM strip containing periodic cracks Köse, Ayşe; Kadıoğlu, Fevzi Suat; Department of Mechanical Engineering (2013) In this study the plane linear elastic problem of a functionally graded layer which contains periodic cracks is considered. The main objective of this study is to determine the thermal stress intensity factors for edge cracks. In order to find an analytic solution, Young’s modulus and thermal conductivity are assumed to be varying exponentially across the thickness, whereas Poisson ratio and thermal diffusivity are taken as constant. First, one dimensional transient and steady state conduction problems are ...
Hybrid finite element for analysis of functionally graded beams Sarıtaş, Afşin; Soydas, Ozan (2017-01-01) A hybrid finite element model is presented, where stiffness and mass distributions over a beam with functionally graded material (FGM) are accurately modeled for both elastic and inelastic material responses. Von Mises and Drucker-Prager plasticity models are implemented for metallic and ceramic parts of FGM, respectively. Three-dimensional stress-strain relations are solved by a general closest point projection algorithm, and then condensed to the dimensions of the beam element. Numerical examples and veri...
Plastic slip patterns through rate-independent and rate-dependent plasticity Lancioni, Giovanni; Yalçınkaya, Tuncay (2014-05-09) Plastic deformation induces various types of dislocation microstructures at different length scales, which eventually results in a heterogeneous deformation field in metallic materials. Development of such structures manifests themselves as macroscopic hardening/softening response and plastic anisotropy during strain path changes, which is often observed during forming processes. In this paper we present two different non-local plasticity models based on non-convex potentials to simulate the intrinsic rate-...
MULTI-SCALE CHARACTERIZATION OF DEFORMATION IN ALUMINUM Güler, Baran; Efe, Mert (2018-06-22) Materials with deformation behavior sensitive to their microstructure may need deformation analysis at multiple scales to establish the relationship between the microstructure and response to deformation processing. In this work, we use in-plane biaxial test (cruciform) to measure the macro- and microstructure-scale mechanical behavior of a 6061-T6 aluminum alloy at various strain paths. We report flow curves, forming and fracture limits as examples to the macromechanical behavior. As an alternative to the ...

Citation Formats

T. Yalçınkaya, “Energy-based modeling of localization and necking in plasticity,” 2014, vol. 3, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/39374.