NESC0667 BUCKLE

1. NAME OR DESIGNATION OF PROGRAM:  BUCKLE

3. DESCRIPTION OF PROBLEM OR FUNCTION

BUCKLE  is a  one-dimensional
computer code compiled  to calculate the change in  ovality, of an
initially oval,  closed-end finite length  tube, as a  function of
time,  temperature, neutron  flux and  uniform external  pressure.
The basic  concept employed  in BUCKLE  is that  a tube,  which is
slightly out-of-round, tends to become more out-of-round with time
when subjected  to net  uniform external  pressure.  The  timewise
change in  ovality occurs as  a consequence of  creep deformations
arising  from   tangential  compressive  and   tangential  bending
stresses  produced by  uniform  external  pressures acting  on  an
initially oval tube.

4. METHOD OF SOLUTION

BUCKLE employs two mathematical models with an  incremental approach to calculate the change in ovality of an initially oval tube, as a function of time. One mathematical model describes the interrelationships between membrane and bending stresses, strain, and ovality of a symmetrical cross section of a hollow cylinder. The second mathematical model describes the interrelationships between stress and strain rate as a function of temperature, neutron flux and time. Although the analytical mechanics model is one-dimensional, stress biaxiality and material anisotropy effects are indirectly included through the selection of  the stress coefficient in the creep equation model.
The computational procedure is based on the assumption that for a sufficiently small interval of time, the strain-producing stresses are essentially constant throughout the time interval. At the end of each time interval, the incremental creep strain that occurred during the time interval is used to calculate an incremental change  in the ovality of the tube. This increment of ovality is added to the tube ovality existing at the beginning of the time interval. This new value of ovality is then used to recalculate the shell membrane and bending stresses which are used to calculate a new increment of creep strain in the subsequent time interval. If the time intervals are sufficiently small, the solution obtained is approximate and will tend to converge to the real solution. The repetitive calculations are terminated by a specified time limit or  when the ovality and/or combined stresses equal specified values.
An option was added with Edition B to employ either a strain hardening or time hardening rule in the creep calculations.
Factors considered in the calculation include: tube dimensions, temperature-dependent material properties, external pressure, and the time-variable internal pressure, temperature and neutron flux.

5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

The assumptions used in formulating the analytical mechanics model necessarily place certain restrictions on the code's applicability to problems of buckling instability. These limitations are as follows:
(a) BUCKLE does not provide the capability to calculate  creep-buckling for a perfectly round tube. The analysis for such  a case typically uses the reduced modulus method wherein the     modulus is determined from isochronous creep curves.
(b) The time increment used in BUCKLE must be small enough so that  approximate convergence to a real solution is obtained. The  convergence is generally adequate when the time increment is  less than 2% of the collapse time. For short collapse times, a     time interval of less than 1% should be used.
(c) The stress-deflection equations used in BUCKLE are based on  linear elastic theory. For engineering purposes, the  creep-collapse time will be given with sufficient accuracy by  this simplified theory which neglects plasticity. Creep-buckling  analyses, however, should not be attempted when the stresses     exceed the yield strength of the tubing.
(d) BUCKLE does not provide the capability to calculate  creep-buckling for a tube which is subjected to an eccentric     axial load in addition to a uniform pressure load.
    Other methods must be used for the analysis in such cases.

6. TYPICAL RUNNING TIME

Running time is somewhat dependent upon the input options and to a lesser extent upon the complexity of the problem. A typical case with time-variable internal pressure, temperature, and neutron flux may require about 20 seconds.

7. UNUSUAL FEATURES OF THE PROGRAM

The form of the analytical creep
model used in  BUCKLE is one of the standard  forms generally used
to describe creep behavior.  Other  analytical creep models may be
equally  suitable for  calculating creep  strains.   The user  may
choose to specify, via input data  cards, other creep equations or
select  coefficients  so  as  to  obtain  the  best  fit  to  data
applicable to his material.

8. RELATED AND AUXILIARY PROGRAMS:

10. REFERENCES:

- P.J. Pankaskie:
  BUCKLE - An Analytical Computer Code for Calculating Creep
  Buckling of an Initially Oval Tube
  BNWL-1784 (May 1974).

11. MACHINE REQUIREMENTS:  54K  words  addressable  core  storage  are
required.

13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:   SCOPE 4.2.

14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

Problem input data are specified in FORTRAN IV NAMELIST format.

15. NAME AND ESTABLISHMENT OF AUTHOR

                 P. J. Pankaskie
                 Pacific Northwest Laboratories
                 Battelle
                 P. O. Box 999
                 Richland, Washington  99352

File name	File description	Records
BUCKLE	BUCKLE SOURCE - FORTRAN IV EBCDIC	594
BUCKLE	SAMPLE PROBLEM INPUT	34
BUCKLE	SAMPLE PROBLEM OUTPUT	2170