A Fracture Theory for Brittle Anisotropic Materials

1974 ◽  
Vol 96 (2) ◽  
pp. 91-96 ◽  
Author(s):  
T. G. Priddy
Keyword(s):  
Orthotropic Materials ◽  
Necessary Condition ◽  
Material Strength ◽  
Interaction Coefficients ◽  
Cubic Equation ◽  
Simple Cubic ◽  
Failure Theory ◽  
Tension And Compression ◽  
Fracture Theory ◽  
Macroscopic Failure

This paper outlines the development of a general macroscopic failure theory. The result is a relatively simple cubic equation where interaction coefficients for tension-tension and compression-compression strengths may be defined separately. Approximations for biaxial and triaxial normal stress interactions are included to reduce the number of experimental data to nine for brittle three-dimensionally orthotropic materials and to two for brittle isotropic materials. A necessary condition that the theory closely describe brittle isotropic material strength is satisfied for a comprehensive set of cast iron biaxial strength data. The surface is graphically illustrated for various materials.

Fracture of High Polymers

1967 ◽  
Vol 40 (4) ◽  
pp. 1036-1048 ◽  
Author(s):  
W. Retting
Keyword(s):  
Physics Of Failure ◽  
Elongation At Break ◽  
Failure Theory ◽  
Experimental Parameters ◽  
Failure Properties ◽  
Tearing Energy ◽  
Viscoelastic Substances ◽  
Breaking Energy ◽  
Macroscopic Failure ◽  
High Polymers

Abstract General considerations of the physics of failure of high polymeric substances were reviewed using the example of one dimensional testing. It is shown that classical failure theory can be applied only with difficulty to viscoelastic substances. Relations between macroscopic failure properties and the parameters of test are reviewed. Several recent investigations have shown a direct relation between relaxation time spectra of high polymers and breaking energy, tensile strength, and elongation at break through their dependence on time and temperature. Finally, the relation between microscopic failure properties and experimental parameters are discussed. The processes occurring at the tip of the failure are determined by relaxation mechanisms just as are the processes which lead to sites of failure in the macroscopic specimen. These are illustrated by recent work in which the specific tearing energy is determined as a function of time and temperature of tearing. From all of the work referred to here, it follows that the very complicated relations at fracture of high polymers are essentially determined by their mechanism of molecular motion in a way analogous to other mechanical properties and are therefore determined by their molecular structure.

scholarly journals A Distortion Energy Failure Theory for Orthotropic Materials

1972 ◽  
Vol 94 (4) ◽  
pp. 1073-1076 ◽  
Author(s):  
G. W. Forman
Keyword(s):  
Experimental Studies ◽  
Three Dimensional ◽  
Algebraic Method ◽  
Orthotropic Materials ◽  
Rational Basis ◽  
State Of Stress ◽  
Failure Theory ◽  
Distortion Energy ◽  
Energy Theory ◽  
Energy Failure

Of the numerous methods developed to predict failure of isotropic materials exposed to a three-dimensional state of stress, experimental studies tend to confirm the validity of the distortional energy theory. To date no rational basis of predicting inelastic action in an orthotropic material exposed to principle stresses coincident with the material axes has been proposed. This study assumes that distortion energy may be used to predict failure of orthotropic materials, and a usable algebraic method of predicting failure is developed.

Explosive resonant interaction of baroclinic Rossby waves and stability of multilayer quasi-geostrophic flow

1995 ◽  
Vol 291 ◽  
pp. 83-107 ◽  
Author(s):  
Jacques Vanneste
Keyword(s):  
Nonlinear Stability ◽  
Stability Condition ◽  
Rossby Waves ◽  
Normal Modes ◽  
Resonant Interaction ◽  
Necessary Condition ◽  
Amplitude Equations ◽  
Interaction Coefficients ◽  
Stability Diagrams ◽  
Parallel Shear Flow

The amplitude equations governing the nonlinear interaction among normal modes are derived for a multilayer quasi-geostrophic channel. The set of normal modes can represent any wavy disturbance to a parallel shear flow, which may be stable or unstable. Orthogonality in the sense of pseudomomentum or pseudoenergy is used to obtain the amplitude equations in a direct fashion, and pseudoenergy and pseudomomentum conservation laws permit the properties of the interaction coefficients to be deduced. Particular attention is paid to triads exhibiting explosive resonant interaction, as they lead to nonlinear instability of the basic flow. The relationship between this mechanism and the most recently discovered nonlinear stability conditions is discussed.Situations in which the basic velocity is constant in each layer are treated in detail. A particular formulation of the stability condition is given that emphasizes the close connection between linear and nonlinear stability. It is established that this stability condition is also a necessary condition: when it is not satisfied, and when the flow is linearly stable, explosive resonant interaction of baroclinic Rossby waves acts as a destabilizing mechanism. Two- and three-layer models are specifically considered; their stability features are presented in the form of stability diagrams, and interaction coefficients are calculated in particular cases.

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