scholarly journals A Comprehensive Theory of Yielding and Failure for Isotropic Materials

2007 ◽  
Vol 129 (2) ◽  
pp. 173-181 ◽  
Author(s):  
Richard M. Christensen
Keyword(s):  
Stress State ◽  
Brittle Failure ◽  
Three Dimensional ◽  
Present Theory ◽  
Full Density ◽  
Isotropic Materials ◽  
Comprehensive Theory ◽  
General Material ◽  
Ductile Behavior ◽  
Limiting Case

A theory of yielding and failure for homogeneous and isotropic materials is given. The theory is calibrated by two independent, measurable properties and from those it predicts possible failure for any given state of stress. It also differentiates between ductile yielding and brittle failure. The explicit ductile-brittle criterion depends not only upon the material specification through the two properties, but also and equally importantly depends upon the type of imposed stress state. The Mises criterion is a special (limiting) case of the present theory. A close examination of this case shows that the Mises material idealization does not necessarily imply ductile behavior under all conditions, only under most conditions. When the first invariant of the yield/failure stress state is sufficiently large relative to the distortional part, brittle failure will be expected to occur. For general material types, it is shown that it is possible to have a state of spreading plastic flow, but as the elastic-plastic boundary advances, the conditions for yielding on it can change over to conditions for brittle failure because of the evolving stress state. The general theory is of a three-dimensional form and it applies to full density materials for which the yield/failure strength in uniaxial tension is less than or at most equal to the magnitude of that in uniaxial compression.

The Theoretical Measure of the Ductility of Failure for All Isotropic Materials in All States of Stress1

2016 ◽  
Vol 83 (6) ◽  
Author(s):  
Richard M. Christensen
Keyword(s):  
Stress State ◽  
Brittle Failure ◽  
Failure Stress ◽  
Isotropic Materials ◽  
Failure Theory

The ductile/brittle failure theory for homogeneous and isotropic materials is extended to give a rational and mathematically rigorous measure for the ductility of failure. This new failure number methodology is completely developed and proved to be valid and general. It applies to all isotropic materials as subjected to any and all states of stress. Not only does the failure theory predict the safety or failure for any given stress state, it then projects the quantitative ductility level for the failure stress state. Many important examples are given with detailed interpretations of the results and with guides for general usage.

A Finite Element for the Analysis of Shell Intersections

1996 ◽  
Vol 118 (4) ◽  
pp. 399-406 ◽  
Author(s):  
W. J. Koves ◽  
S. Nair
Keyword(s):  
Finite Element ◽  
Stress State ◽  
Three Dimensional ◽  
Shell Element ◽  
Theory Of Elasticity ◽  
Shell Elements ◽  
Asme Code ◽  
Form Theory ◽  
Computation Scheme ◽  
Shell Intersections

A specialized shell-intersection finite element, which is compatible with adjoining shell elements, has been developed and has the capability of physically representing the complex three-dimensional geometry and stress state at shell intersections (Koves, 1993). The element geometry is a contoured shape that matches a wide variety of practical nozzle configurations used in ASME Code pressure vessel construction, and allows computational rigor. A closed-form theory of elasticity solution was used to compute the stress state and strain energy in the element. The concept of an energy-equivalent nodal displacement and force vector set was then developed to allow complete compatibility with adjoining shell elements and retain the analytical rigor within the element. This methodology provides a powerful and robust computation scheme that maintains the computational efficiency of shell element solutions. The shell-intersection element was then applied to the cylinder-sphere and cylinder-cylinder intersection problems.

scholarly journals THREE-DIMENSIONAL STABILITY ANALYSIS OF OPEN CHANNEL FLOW OVER AN ERODIBLE BED

1971 ◽  
Vol 2 (2) ◽  
pp. 93-108 ◽  
Author(s):  
FRANK ENGELUND ◽  
JØRGEN FREDSØE
Keyword(s):  
Open Channel ◽  
Three Dimensional ◽  
Open Channel Flow ◽  
Present Theory ◽  
Bed Load ◽  
Lower Range ◽  
First Order ◽  
Stability And Instability ◽  
Regions Of Stability ◽  
Bed Waves

The formation of ripples and dunes (lower range bed waves) is assumed to be related to the transport of sediment as bed load. From the present theory it is concluded that the formation of the upper range bed configurations (standing waves, antidunes) may be explained on the assumption that the predominant part of the sediment transport is in suspension. The paper presents a mathematical model of the formation of double-periodic antidunes, first-order potential flow theory being applied. It differs from previous models in taking account of the non-uniform distribution of the suspended load. The theory predicts regions of stability and instability. Results are compared with measurements made by different observers.

scholarly journals Triglobal infinite-wing shock-buffet study

2021 ◽  
Vol 925 ◽  
Author(s):  
Wei He ◽  
Sebastian Timme
Keyword(s):  
Stability Analysis ◽  
Three Dimensional ◽  
Base Flow ◽  
Sweep Angle ◽  
Aspect Ratios ◽  
Spatially Periodic ◽  
Time Marching ◽  
High Reynolds ◽  
Limiting Case ◽  
Base Flows

This article uses triglobal stability analysis to address the question of shock-buffet unsteadiness, and associated modal dominance, on infinite wings at high Reynolds number, expanding upon recent biglobal work, aspiring to elucidate the flow phenomenon's origin and characteristics. Infinite wings are modelled by extruding an aerofoil to finite aspect ratios and imposing a periodic boundary condition without assumptions on spanwise homogeneity. Two distinct steady base flows, spanwise uniform and non-uniform, are analysed herein on straight and swept wings. Stability analysis of straight-wing uniform flow identifies both the oscillatory aerofoil mode, linked to the chordwise shock motion synchronised with a pulsation of its downstream shear layer, and several monotone (non-oscillatory), spatially periodic shock-distortion modes. Those monotone modes become outboard travelling on the swept wing with their respective frequencies and phase speeds correlated with the sweep angle. In the limiting case of very small wavenumbers approaching zero, the effect of sweep creates branches of outboard and inboard travelling modes. Overall, triglobal results for such quasi-three-dimensional base flows agree with previous biglobal studies. On the contrary, cellular patterns form in proper three-dimensional base flow on straight wings, and we present the first triglobal study of such an equilibrium solution to the governing equations. Spanwise-irregular modes are found to be sensitive to the chosen aspect ratio. Nonlinear time-marching simulations reveal the flow evolution and distinct events to confirm the insights gained through dominant modes from routine triglobal stability analysis.

Evaluation of Ductile/Brittle Failure Theory and Derivation of the Ductile/Brittle Transition Temperature

2015 ◽  
Vol 83 (2) ◽  
Author(s):  
Richard M. Christensen
Keyword(s):  
Transition Temperature ◽  
Brittle Failure ◽  
Evaluation Process ◽  
Isotropic Materials ◽  
Brittle Transition ◽  
Failure Theory ◽  
Ductile Brittle Transition Temperature ◽  
Brittle Transition Temperature ◽  
Materials Failure

A recently developed ductile/brittle theory of materials failure is evaluated. The failure theory applies to all homogeneous and isotropic materials. The determination of the ductile/brittle transition is an integral and essential part of the failure theory. The evaluation process emphasizes and examines all aspects of the ductile versus the brittle nature of failure, including the ductile limit and the brittle limit of materials' types. The failure theory is proved to be extraordinarily versatile and comprehensive. It even allows derivation of the associated ductile/brittle transition temperature. This too applies to all homogeneous and isotropic materials and not just some subclass of materials' types. This evaluation program completes the development of the failure theory.

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