Analysis of Creep in Rotating Disks Based on the Tresca Criterion and Associated Flow Rule

1956 ◽  
Vol 23 (2) ◽  
pp. 231-238
Author(s):  
A. M. Wahl
Keyword(s):  
Steady State ◽  
Creep Rate ◽  
Constant Temperature ◽  
Variable Thickness ◽  
Constant Thickness ◽  
Flow Rule ◽  
Test Results ◽  
Rotating Disks ◽  
Tresca Criterion ◽  
Associated Flow Rule

Abstract An analysis of creep deformations in rotating disks based on the Tresca criterion and the associated flow rule is presented. Assuming steady-state creep conditions and a creep rate equal to a function of stress times a function of time, the method is applied to the following cases: (a) Disk with constant thickness and constant temperature, (b) disk with variable thickness and constant temperature, and (c) disk with variable thickness and variable temperature. In many cases, the equations can be expressed in closed form. Comparison is made with test results on rotating disks at elevated temperature as reported in a previous paper. Based on certain stress-creep-rate relations, the method is also applied to the problem of calculating the transient change in stress when the stress distribution changes from an initial to a steady-state condition during the starting period. It is suggested that the simplification effected by the use of these methods may be of value for design purposes pending the development of more accurate methods based on test results.

Stress Distributions in Rotating Disks Subjected to Creep at Elevated Temperature

1957 ◽  
Vol 24 (2) ◽  
pp. 299-305
Author(s):  
A. M. Wahl
Keyword(s):  
Elevated Temperature ◽  
Creep Rate ◽  
Stress Distribution ◽  
Power Function ◽  
Constant Temperature ◽  
Creep Rupture ◽  
Flow Rule ◽  
Rotating Disks ◽  
Inside Diameter ◽  
Long Time

Abstract Assuming a creep rate proportional to a power function of the stress, curves of stress distribution as a function of the radius have been calculated for several cases of rotating disks subject to steady-state creep at elevated temperature. The disks are assumed to have central holes and to be uniformly loaded at the periphery (to simulate blade loading in turbine disks). It is also postulated that the Tresca (maximum-shear) criterion and the associated flow rule govern. The following cases are treated: (1) Disk of constant temperature and thickness with various ratios of outside to inside diameter and with various values of the exponent n in the assumed power function stress-creep rate relation. (2) Disk of constant temperature and variable thickness, the thickness at the periphery being equal to half that at the hub, for various n-values. (3) Disk with variable temperature such that the creep rate at the outside diameter is ten times that at the inside diameter for the same stress, various n-values being assumed. Limits of radial peripheral loading beyond which the derived stress-distribution curves are not valid are also determined. The results indicate that a considerable nonuniformity in stress distribution under creep conditions may exist, particularly for the lower n-values; thus creep-rupture strengths of such disks for long-time loading conditions may be lower than would be expected if based on average stress values, particularly for materials having limited ductility in long-time creep-rupture tests.

scholarly journals Creep Response of Rotating Composite Discs having Exponential Hyperbolic Linear and Constant Thickness Profiles

2020 ◽  
Vol 70 (3) ◽  
pp. 292-298
Author(s):  
Rajinder Singh ◽  
Ravindra K. Saxena ◽  
Kishore Khanna ◽  
V. K. Gupta
Keyword(s):  
Variable Thickness ◽  
Creep Behaviour ◽  
Steady State Creep ◽  
Constant Thickness ◽  
Strain Rates ◽  
Creep Response ◽  
Thickness Profile ◽  
Disc Material ◽  
Tresca Criterion ◽  
Different Thickness

The study compares the steady state creep response of rotating Al-SiC discs having constant, linear, hyperbolic and exponential thickness with different thickness profiles. All the discs are assumed to have equal volume with the same average thickness. The creep behaviour of the disc material is described by threshold stress based law while the yielding is assumed to follow Tresca criterion. The variable thickness disc is observed to have superior creep response, expressed in terms of stresses and strain rates, to a constant thickness disc. Amongst variable thickness discs, the creep response is observed to be superior for linear thickness disc, when the inner thickness of all the discs is kept the same. However, for the same outer thickness, the disc having hyperbolic thickness profile exhibits the best creep response.

Limits of Economy of Material in Plates

1955 ◽  
Vol 22 (3) ◽  
pp. 372-374
Author(s):  
H. G. Hopkins ◽  
W. Prager
Keyword(s):  
Yield Condition ◽  
Transverse Load ◽  
Constant Thickness ◽  
Flow Rule ◽  
Plate Material ◽  
Uniform Thickness ◽  
Simply Supported ◽  
Varying Thickness ◽  
Limiting Case ◽  
Associated Flow Rule

Abstract The paper is concerned with the limits of economy of material in a simply supported circular plate under a uniformly distributed transverse load. The plate material is supposed to be plastic-rigid and to obey Tresca’s yield condition and the associated flow rule. The criterion of failure adopted is that used in limit analysis. It is shown that the plate of uniform thickness has a weight efficiency of about 82 per cent. Stepped plates of segmentwise constant thickness are discussed, and the plate of continuously varying thickness is treated as the limiting case obtained by letting the number of steps go to infinity.

The Steady-State Response of a Rotating Damped Disk of Variable Thickness

1980 ◽  
Vol 47 (4) ◽  
pp. 896-900 ◽  
Author(s):  
T. Irie ◽  
G. Yamada ◽  
S. Aomura
Keyword(s):  
Steady State ◽  
Variable Thickness ◽  
Flexural Vibration ◽  
Rotating Disk ◽  
Outer Edge ◽  
Steady State Response ◽  
Rotating Disks ◽  
Annular Disk ◽  
State Response ◽  
The Matrix

The stress distribution and steady-state response of a rotating damped annular disk of variable thickness are determined by means of the matrix method. The equation of equilibrium and the equations for the flexural vibration of the rotating disk are written as a respective coupled set of first-order differential equations by use of the matrices of the disk. The elements of the matrices are calculated by numerical integration of the equations, and the stress components and the driving-point impedance and force transmissibility of the disk are obtained by using these elements. The method is applied to free-clamped rotating disks with linearly, exponentially, and hyperbolically varying thickness driven by a harmonic force at the free outer edge, and the effects of the angular velocity and the variable thickness are studied.

Steady-state creep of orthotropic rotating disks of variable thickness

1986 ◽  
Vol 91 (2) ◽  
pp. 121-141 ◽  
Author(s):  
N.S. Bhatnagar ◽  
Mrs P.S. Kulkarni ◽  
V.K. Arya
Keyword(s):  
Steady State ◽  
Variable Thickness ◽  
Steady State Creep ◽  
Rotating Disks

Control of the adiabatic flow reactor by feeding the catalyst solution

1979 ◽  
Vol 44 (8) ◽  
pp. 2352-2365
Author(s):  
Josef Horák ◽  
Zina Sojková ◽  
František Jiráček
Keyword(s):  
Steady State ◽  
Constant Temperature ◽  
Reaction Temperature ◽  
Control Algorithm ◽  
Flow Reactor ◽  
Operating Temperature ◽  
Temperature Deviation ◽  
Adiabatic Flow ◽  
Dosing Frequency ◽  
Laboratory Reactor

Control algorithm of the operating temperature is described in the reactor, which is operated at constant temperature and composition of the inlet mixture. The temperature is controlled by dosing a constant volume of the catalyst solution. The dosing frequency is determined according to the reaction temperature (deviation of the temperature from the desired value and the sign of the derivative of temperature). The control algorithm has been verified experimentally for the laboratory reactor in unstable steady state.

Exact solution for free vibration analysis of linearly varying thickness FGM plate using Galerkin-Vlasov’s method

2020 ◽  
pp. 146442072098049
Author(s):  
V Kumar ◽  
SJ Singh ◽  
VH Saran ◽  
SP Harsha
Keyword(s):  
Free Vibration ◽  
Variable Thickness ◽  
Vibration Analysis ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Constant Thickness ◽  
Engineering Structures ◽  
Property Variation ◽  
Varying Thickness

The present paper investigates the free vibration analysis for functionally graded material plates of linearly varying thickness. A non-polynomial higher order shear deformation theory is used, which is based on inverse hyperbolic shape function for the tapered FGM plate. Three different types of material gradation laws, specifically: a power (P-FGM), exponential (E-FGM), and sigmoid law (S-FGM) are used to calculate the property variation in the thickness direction of FGM plate. The variational principle has been applied to derive the governing differential equation for the plates. Non-dimensional frequencies have been evaluated by considering the semi-analytical approach viz. Galerkin-Vlasov’s method. The accuracy of the preceding formulation has been validated through numerical examples consisting of constant thickness and tapered (variable thickness) plates. The findings obtained by this method are found to be in close agreement with the published results. Parametric studies are then explored for different geometric parameters like taper ratio and boundary conditions. It is deduced that the frequency parameter is maximum for S-FGM tapered plate as compared to E- and P-FGM tapered plate. Consequently, it is concluded that the S-FGM tapered plate is suitable for those engineering structures that are subjected to huge excitations to avoid resonance conditions. In addition, it is found that the taper ratio is significantly affected by the type of constraints on the edges of the tapered FGM plate. Some novel results for FGM plate with variable thickness are also computed that can be used as benchmark results for future reference.

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