Advances in Damage Mechanics: Metals and Metal Matrix Composites

Abstract

viiiThe material appearing in this text is limited to plastic deformation and damage in ductile materials (e.g. metals and metal matrix composites). The authors elect to exclude many of the recent advances made in creep, brittle fracture, and temperature effects. The authors feel that these topics require a separate volume for this presentation. Furthermore, the applications presented in the book are the simplest possible ones and are mainly based on the uniaxial tension test. The presentation of more challenging examples is left to the researchers in this field. This book does not claim to revolutionize the way in which research is done in this area, but it does advance a few new ideas and it does have several noteworthy features:

On the elastic moduli and compliances of transversely isotropic and orthotropic materials

“…The formulas are applied to calculate the elastic constants for a transversely isotropic monocrystalline zinc and an orthotropic human femural bone. Apart from the analytical point of view, the derived results may be of interest for the analysis of anisotropic elastic and inelastic material response (with an elastic component of strain or stress) in the mechanics of fiber reinforced composite materials [Hyer 1998;Vasiliev and Morozov 2001], creep mechanics [Drozdov 1998;Betten 2002], damage-elastoplasticity ], mechanics of brittle materials weakened by anisotropic crack distributions [Krajcinovic 1996;Voyiadjis and Kattan 1999], and biological materials (membranes or tissues) with embedded filament networks [Evans and Skalak 1980;Fung 1990;Humphrey 2002;Lubarda and Hoger 2002;Asaro and Lubarda 2006]. …”

Craters in concrete slabs due to detonation – drawbacks of material models with a Mohr-Coulomb yield surface

“…The term A 0 /(A 0 − A R ) is consequently a second order tensor and in principle the inverse of the damage tensor D. A formal relationship taking also the direction of the traction and the normal vector of the crack surface into account is given by Voyiadjis et al [5]:…”

“…Details are given in the original reference [5]: Using the Voigt's notation for the stress tensor σ = (σ x , σ y , σ z , τ xy , τ xz , τ zx ) the fourth order tensor M is transformed to a second order tensor as: …”

Foundational aspects of a multi-scale modeling framework for composite materials

“…The hypothesis of equivalent elastic energy is used to evaluate M ijkl and establish a relation between the damaged and undamaged stiffnesses [50,51]. The hypothesis, detailed in [52,53], specifically assumes that the elastic complimentary energy W C in a damaged material with the actual stress is equal to that in a hypothetical undamaged material with the fictitious effective stress, i.e.,…”