Fatigue crack growth rate in ferrite-martensite dual-phase steel

An empirical study is made on the fatigue crack growth rate in ferrite-martensite dual-phase (FMDP) steel. Particular attention is given to the effect of ferrite content in the range of 24.2% to 41.5% where good fatigue resistance was found at 33.8%. Variations in ferrite content did not affect the crack growth rate da/dN when plotted against the effective stress intensity factor range ΔK_eff which was assumed to follow a linear relation with the crack tip stress intensity factor range ΔK. A high ΔK_eff corresponds to uniformly distributed small size ferrite and martensite. No other appreciable correlation could be ralated to the microstructure morphology of the FMDP steel. The closure stress intensity factor K_cl, however, is affected by the ferrite content with K_cl/Kmax reaching a maximum value of 0.7. In general, crack growth followed the interphase between the martensite and ferrite.Dividing the fatigue crack growth process into Stage I and II where the former would be highly sensitive to changes in ΔK and the latter would increase with ΔK depending on the R = σ_min/σ_max ratio. The same data when correlated with the strain energy density factor range ΔS showed negligible dependence on mean stress or R ratio for Stage I crack growth. A parameter α involving the ratio of ultimate stress to yield stress, percent reduction of area and R is introduced for Stage II crack growth so that the da/dN data for different R would collapse onto a single curve with a narrow scatter band when plotted against αΔS.     

A symmetry analysis of some classes of evolutionary nonlinear (2+1)-diffusion equations with variable diffusivity

In this paper the (2+1)-nonlinear diffusion equation u _t ?div(f(u)grad u)=0 with variable diffusivity is considered. Using the Lie method, a complete symmetry classification of the equation is presented. Reductions, via two-dimensional Lie subalgebras of the equation, to first- or second-order ordinary differential equations are given. In a few interesting cases exact solutions are presented.     

Air/water two-phase flow test tunnel for airfoil studies

A test tunnel for the study of airfoil performances under air/water two-phase flow condition has been designed and constructed. This facility will serve for a better understanding of the flow phenomena and characteristics of hydraulic machinery under gas/ liquid two-phase flow operating conditions. At the test section of the tunnel, a two-dimensional isolated airfoil or a cascade of airfoils is installed in a two-phase inlet flow with a uniform velocity (up to 10 m/s) and void fraction (up to 12%) distribution. The details of the tunnel structure and the measuring systems are described and the basic characteristics of the constructed tunnel are also given. As an example of the test results, void fraction distribution around a test airfoil is shown.Dedicated to the 60th Birthday of Professor Klaus Gersten     

Postbuckling of angle-ply and anisotropic plates

Summary An analysis based on the von Kármán-type large-deflection equations of plates is presented for the postbuckling behavior of homogeneous and symmetrically laminated anisotropic rectangular plates. Boundary conditions for both simply supported and clamped edges are considered. A solution is obtained by expressing the force function and transverse deflection as double series involving the appropriate beam eigen-functions. Numerical results are presented for graphite-epoxy angle-ply laminates and homogeneous anisotropic plates. In the cases of buckling of anisotropic plates and postbuckling of isotropic and orthotropic plates, the present solution is in good agreement with existing solutions.

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Übersicht Es wird das Nachbeulverhalten von homogenen, symmetrisch geschichteten, anisotropen Rechteckplatten auf der Grundlage der von Kármán angegebenen Platten-Gleichungen für große Auslenkungen untersucht. Dabei werden sowohl einfach aufliegende, wie auch eingespannte Ränder als Randbedingungen berücksichtigt. Lösungen werden dadurch gewonnen, daß die Belastungsfunktion und die Querauslenkung als doppelte Reihen von geeigneten Balken-Eigenfunktionen angesetzt werden. Für Graphit-Epoxid-Schichtplatten und anisotrope homogene Platten werden numerische Ergebnisse mitgeteilt. Die erhaltenen Lösungen stimmen in den Fällen des Beulens von anisotropen Platten sowie des Nachbeulens von isotropen und orthotropen Platten gut mit bekannten Lösungen überein.

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The results presented in this paper were obtained in the course of research sponsored by the National Research Council of Canada.     

Shear flow over a rotating plate

A shear flow interacts with a rotating boundary. The three dimensional Navier-Stokes equations reduce to a set of ninth order, nonlinear, ordinary differential equations which are partially decoupled. Universal similarity velocity profiles are found by numerical integration. If the shear is high enough, reverse flow occurs and the mean drag may be negative. The solution is a rare exact similarity solution of the Navier-Stokes equations.     

Stokes Flow through an Array of Staggered Strips

The Stokes flow through a periodic array of thin staggered strips is studied. The method of eigenfunction expansion and collocation is used to obtain detailed flow and pressure fields. The permeabilities in the three principle directions are found to be different and their characters depend heavily on the geometry. Approximate formulas are also obtained.     

On a stress function method of a thermoelastic problem expressed in cylindrical coordinates in a multiply-connected region exhibiting temperature-dependent material properties

Summary This paper is concerned with the formulation of a plane thermoelastic problem in a multiplyconnected region exhibiting temperature-dependent material properties in terms of a stress function by deriving the integral conditions necessary for the assurance of the single-valuedness of the rotation and displacements, i.e., new Michell's conditions and the finite difference representation of the resulting fundamental equations.The method of solution for the thermoelastic problem in the multiply-connected region is applied to a transient plane-strain thermal stress problem in a hollow circular cylinder having temperature-dependent material properties subjected to an asymmetrical heating by a high-temperature fluid on the inner surface of the cylinder.

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Zur Methode der Spannungsfunktion bei thermoelastischen Problemen mit mehrfach zusammenhängendem Gebiet und temperaturabhängigen Materialeigenschaften

Übersicht In dieser Untersuchung wird ein thermoelastisches Problem mit mehrfach zusammenhängendem Gebiet und temperaturabhängigen Materialeigenschaften mit Hilfe einer Spannungsfunktion behandelt. Die Bedingungen für Eindeutigkeit von Rotation und Verschiebung werden hergeleitet. Die Grundgleichungen des Problems werden mit der Methode der finiten Differenzen gelöst.Als Anwendungsbeispiel wird ein hohler Kreiszylinder mit temperaturabhängigen Werkstoffeigenschaften betrachtet. Der Zylinder wird dabei durch eine Flüssigkeit mit hoher Temperatur in seinem Innern einer symmetrischen Erwärmung unterworfen.

     

Nonlinear analysis of the forced response of a beam with three mode interaction

An analysis is presented for the primary resonance of a clamped-hinged beam, which occurs when the frequency of excitation is near one of the natural frequencies,_n . Three mode interaction (₂ 3₁ and _{3 1} + 2₂) is considered and its influence on the response is studied. The case of two mode interaction (₂ 3₁) is also considered to compare it with the case of three mode interaction. The straight beam experiencing mid-plane stretching is governed by a nonlinear partial differential equation. By using Galerkin's method the governing equation is reduced to a system of nonautonomous ordinary differential equations. The method of multiple scales is applied to solve the system. Steady-state responses and their stability are examined. Results of numerical investigations show that there exists no significant difference between both modal interactions' influences on the responses.     

A Lattice Boltzmann model with high Reynolds number in the presence of external forces to describe microfluidics

We present here a lattice Boltzmann model with high Reynolds number in the presence of external force fields to describe electrokinetic phenomena in microfluidics, by considering pressure as the only external force for liquid flow. Our results from a 9-bit square lattice Boltzmann model are in excellent agreement with experimental data in pressure-driven microchannel flow that could not be fully described by electrokinetic theory. The difference between the predicted and experimental Reynolds numbers from pressure gradients are well within 5%. Our results suggest that the lattice Boltzmann model described here is an effective computational tool to predict the more complex microfluidic systems that might be problematic using conventional methods.     

Analytical approximation to large-amplitude oscillation of a non-linear conservative system

This paper deals with non-linear oscillation of a conservative system having inertia and static non-linearities. By combining the linearization of the governing equation with the method of harmonic balance, we establish analytical approximate solutions for the non-linear oscillations of the system. Unlike the classical harmonic balance method, linearization is performed prior to proceeding with harmonic balancing, thus resulting in a set of linear algebraic equations instead of one of non-linear algebraic equations. Hence, we are able to establish analytical approximate formulas for the exact frequency and periodic solution. These analytical approximate formulas show excellent agreement with the exact solutions, and are valid for small as well as large amplitudes of oscillation.