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  2. Purpose of code.
  3. Specification.
  4. Description of program's operation.
  5. References.
  6. Parameter descriptions.
  7. Error indicators.
  8. Accuracy estimate.
  9. Any additional information.
  10. Example of code
  11. Auxiliary routines required.
  12. Keywords.
  13. Download source code.
  14. Links.

Provenance of Source Code

Jeevan Jaidi
Research Scholar,
Mechanical Engineering Department,
Indian Institute of Science,

E-mail: jaidi@mecheng.iisc.ernet.in

Added to MAP: December 2002.

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This code calculates the grain size (diameter) variation at a given position within the heat-affected zone (HAZ) in the presence of stable particles. Stable particles mean that the particles neither coarsen nor dissolve (oxides and sulphides) during a weld thermal cycle.

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Language: FORTRAN-90
Product form: Source code

Complete program.

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In alloy steels, the presence of second phase particles (precipitates or inclusions) will retard the grain growth rate and hence limit the average grain size during a weld cycle. Every position within the heat-affected zone (HAZ) will experience a variable temperature with time. At a given position within the HAZ, the average grain size depends on the peak temperature as well as the heating/cooling rates, which, in turn, depends on how far is the position from the solid-liquid interface.

The rate of change of average grain size in the presence of precipitating elements or impurities is expressed by the following semi-empirical equation:

Equation x of reference y.

The time exponent, n, is a strong function of temperature. For most metals and alloys, n varies typically in the range of (0.1 - 0.4). According to Akselsen et al., if the time constant (time to cool from 800oC - 500oC) is less than 15 seconds, the time exponent would be expected to be high and close to the upper theoretical limit (n = 0.5) at all the temperatures.

In the presence of stable particles, the limiting grain size is independent of the thermal cycle and is given by the following expression:

Equation x of reference y.

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  1. Oystein Grong, Metallurgical Modelling of Welding, 2nd edition, published by the Insitute of Materials, London.
  2. I. Andersen and O. Grong, 1995, Acta Metall. Mater., 43, 2673-2688.
  3. O. M. Akselsen, O. Grong, N. Ryum and N. Christensen, 1986, Acta Metall., 34, 1807-1815.

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Input parameters

DT (dt) - real
DT is the time interval (seconds).

G0 - real
G0 is the initial grain size (microns).

ISTART - integer
ISTART is the Nth starting data point for heating or cooling period.

IEND - integer
IEND is the Nth ending data point for heating or cooling period.

LL - integer
LL is the number of data points.

M0 (Mo*)- real
M0 is a physical parameter related to the grain boundary mobility (microns2/s).

TN (n) - real
TN is the time exponent (assumed n = 0.5).

QG (Qapp) - real
QG is the activation energy with respect to the grain growth (J/mol).

R - real
R is the universal gas constant (J/mol-k).

T - real array
T is the temperature (absolute).

ZENER_COEFF (k) - real
ZENER_COEFF - is a physical parameter related to grain boundary pinning efficiency.

RADIUS_PARTICLE - partcle radius (microns).

VOLFRAC_PARTICLE - volume fraction of the particle.

Output parameters

G - real
G is the average grain size (microns).

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Error Indicators

The ISTART and IEND for heating/cooling periods must be given correctly, else result in incorrect temperature during interpolation.

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No information supplied.

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Further Comments


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1. Program text

Complete program.

2. Program data

See file ags2.in

3. Program results

See file ags2out.m

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Auxiliary Routines


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Average grain size, peak temperature, thermal cycle, stable particles.

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Download source code

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MAP originated from a joint project of the National Physical Laboratory and the University of Cambridge.

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