Publisher Summary This chapter describes the mixed mode cracking in layered materials. There is ample experimental evidence that cracks in brittle, isotropic, homogeneous materials propagate such that pure mode I conditions are maintained at the crack tip. An unloaded crack subsequently subject to a combination of modes I and II will initiate growth by kinking in such a direction that the advancing tip is in mode I. The chapter also elaborates some of the basic results on the characterization of crack tip fields and on the specification of interface toughness. The competition between crack advance within the interface and kinking out of the interface depends on the relative toughness of the interface to that of the adjoining material. The interface stress intensity factors play precisely the same role as their counterparts in elastic fracture mechanics for homogeneous, isotropic solids. When an interface between a bimaterial system is actually a very thin layer of a third phase, the details of the cracking morphology in the thin interface layer can also play a role in determining the mixed mode toughness. The elasticity solutions for cracks in multilayers are also elaborated.

Mixed mode cracking in layered materials

Methods of quasi-static deformation and fracture analysis are developed for a class of nonlinear viscoelastic media and sample applications are given. Selection of the class of media is guided by actual rheological behavior of monolithic and composite materials as well as the need for simplicity to be able to understand the effect of primary material and continuum parameters on crack growth behavior. First, pertinent aspects of J integral and energy release rate theory for nonlinear elastic media are discussed. Nonlinear viscoelastic constitutive equations are then given, and correspondence principles which establish a simple relationship between mechanical states of elastic and viscoelastic media are developed. These principles provide the basis for the subsequent extension of J integral theory to crack growth in viscoelastic materials. Emphasis is on predicting mechanical work available at the crack tip for initiation and continuation of growth; some examples show how viscoelastic properties and the J integral affect growth behavior. Included is the problem of a crack in a thin layer having different viscoelastic properties than the surrounding continuum. The Appendix gives an apparently new constitutive theory for elastic and viscoelastic materials with changing microstructure (e.g. distributed damage) and indicates the conditions under which the fracture theory in the body of the paper is applicable.

Correspondence principles and a generalized J integral for large deformation and fracture analysis of viscoelastic media

The paper describes a method for modelling progressive mixed-mode delamination in fibre composites. The procedure, which is incorporated within the non-linear finite element method, is based on the use of interface elements in conjunction with softening relationships between the stresses and the relative displacements. Fracture mechanics is indirectly introduced by relating the areas under the stress/displacement curves to the critical fracture energies.

Progressive Delamination Using Interface Elements

Characterization and analysis of delamination fracture in composites: An overview of developments from 1990 to 2001

A viscoelastic continuum damage model and its application to uniaxial behavior of asphalt concrete

The nonlinear, viscoelastic behavior of a unidirectional, glass fiber-epoxy composite material is characterized by using isothermal, uniaxial creep and recovery tests together with a constitutive equation based on thermodynamic theory. The nonlinear constitutive equation for uniaxial loading is described first, and then fourth-order tensor transformations relating principal linear viscoelastic creep compli ances, uniaxial creep compliance, and fiber angle are summarized. Following a discussion of experimental aspects, creep and recovery data obtained from several different specimens (each having a differ ent fiber orientation relative to the loading axis) are reduced using a graphical shifting procedure and tensor transformations to evaluate all material properties, including the principal creep compliances. As a check on the constitutive theory, the data are shown to be in ternally consistent. Some simplicity in the analytical representation of the data is found; viz. the nonlinear, uniaxial creep compli...

Viscoelastic Characterization of a Nonlinear Fiber-Reinforced Plastic

Prediction of Energy Release Rate for Mixed-Mode Delamination Using Classical Plate Theory

The problem of an orthotropic cantilevered plate subjected to a uniformly distributed end load is solved by the Rayleigh-Ritz energy method. The result is applied to laminated composite, double cantilevered specimens to estimate the effect of crack tip constraint on the transverse curvature, deflection and energy release rate. The solution is also utilized to determined finite width correction factors for fracture energy characterization tests in which neither plane stress nor plane strain conditions apply.

R.A. Schapery

Papers

Viscoelastic Characterization of a Nonlinear Fiber-Reinforced Plastic

Prediction of Energy Release Rate for Mixed-Mode Delamination Using Classical Plate Theory

Effect of Finite Width on Deflection and Energy Release Rate of an Orthotropic Double Cantilever Specimen

A micromechanical model for non-linear viscoelastic behavior of particle-reinforced rubber with distributed damage

A technique for predicting mode I energy release rates using a first-order shear deformable plate theory