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Optimal Scaling in Ductile Fracture


Fokoua Djodom, Landry (2014) Optimal Scaling in Ductile Fracture. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/B1TW-2D81.


This work is concerned with the derivation of optimal scaling laws, in the sense of matching lower and upper bounds on the energy, for a solid undergoing ductile fracture. The specific problem considered concerns a material sample in the form of an infinite slab of finite thickness subjected to prescribed opening displacements on its two surfaces. The solid is assumed to obey deformation-theory of plasticity and, in order to further simplify the analysis, we assume isotropic rigid-plastic deformations with zero plastic spin. When hardening exponents are given values consistent with observation, the energy is found to exhibit sublinear growth. We regularize the energy through the addition of nonlocal energy terms of the strain-gradient plasticity type. This nonlocal regularization has the effect of introducing an intrinsic length scale into the energy. We also put forth a physical argument that identifies the intrinsic length and suggests a linear growth of the nonlocal energy. Under these assumptions, ductile fracture emerges as the net result of two competing effects: whereas the sublinear growth of the local energy promotes localization of deformation to failure planes, the nonlocal regularization stabilizes this process, thus resulting in an orderly progression towards failure and a well-defined specific fracture energy. The optimal scaling laws derived here show that ductile fracture results from localization of deformations to void sheets, and that it requires a well-defined energy per unit fracture area. In particular, fractal modes of fracture are ruled out under the assumptions of the analysis. The optimal scaling laws additionally show that ductile fracture is cohesive in nature, i.e., it obeys a well-defined relation between tractions and opening displacements. Finally, the scaling laws supply a link between micromechanical properties and macroscopic fracture properties. In particular, they reveal the relative roles that surface energy and microplasticity play as contributors to the specific fracture energy of the material. Next, we present an experimental assessment of the optimal scaling laws. We show that when the specific fracture energy is renormalized in a manner suggested by the optimal scaling laws, the data falls within the bounds predicted by the analysis and, moreover, they ostensibly collapse---with allowances made for experimental scatter---on a master curve dependent on the hardening exponent, but otherwise material independent.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Optimal scaling, strain-gradient plasticity, ductile fracture, void sheet, multiscale modeling.
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Aeronautics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Ortiz, Michael
Thesis Committee:
  • Ravichandran, Guruswami (chair)
  • Bhattacharya, Kaushik
  • Weinberg, Kerstin
  • Ortiz, Michael
Defense Date:26 September 2013
Funding AgencyGrant Number
ASC/PSAAP Center for the Predictive Modeling and Simulation of High Energy Density Dynamic Response of Materials (Caltech)DE-FC52-08NA28613
U.S. National Science Foundation through the Partnership for International Research and Education (PIRE) 0967140
Record Number:CaltechTHESIS:10162013-221817628
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7993
Deposited By: Landry Fokoua Djodom
Deposited On:20 Nov 2013 17:50
Last Modified:04 Oct 2019 00:03

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