[MAP Logo]

Materials Algorithms Project
Program Library


  1. Provenance of code.
  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.

Top | Next


This code calculates the grain size (diameter) variation at a given position within the heat-affected zone (HAZ) in the presence dissolving precipitates (carbides/nitrides) during a weld cycle.

Top | Next | Prev


Language: FORTRAN-90
Product form: Source code

Complete program.

Top | Next | Prev


In general, depending up on the the peak temperature and heating/cooling rates the precipitates will either coarsen or dissolve or coarsen and dissolve. In continous welds, the heating period is less significant as compared to the cooling period. This is due to short heating period (2 - 3 seconds). Thus, at a given position within the HAZ whether the precipitates coarsen or dissolve depend primarily on the peak temperature of the thermal cycle.

If the peak temperature of the thermal cycle is higher than the equilibrium solvus of the precipitates then the precipitiates will dissolve during the cooling period. During the process of precipitate dissolution, the grain boundary pinning force will retard. As a result, the grain growth rate will become faster.

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 dissolving precipitates, the limiting grain size is given by the following expression:

Equation x of reference y.

where I3 is the kinetic strength of the thermal cycle w.r.t dissolving precipitates and is given by the following expression:

Equation x of reference y.


Equation x of reference y.

Top | Next | Prev


  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.

Top | Next | Prev


Input parameters

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

G0LIM - real
G0LIM is the limiting 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).

PSTRENGTH (I3) - real
PSTRENGTH is the kinetic strength of the thermal cycle w.r.t precipitates dissolution.

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

RADIUS_PRECIP (ro) - real
RADIUS_PRECIP - initial radius of the precipitate (microns).

VOLFRAC_PRECIP (fo) - real
VOLFRAC_PRECIP - initial volume fraction of the precipitates.

ALFA - real
ALFA is the dimensionless super saturation.

DIFFUSE (Dm) - real
DIFFUSE is the soulte element diffusivity (microns2/s).

Output parameters

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

Top | Next | Prev

Error Indicators

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

Top | Next | Prev


No information supplied.

Top | Next | Prev

Further Comments


Top | Next | Prev


1. Program text

Complete program.

2. Program data

See file ags4.in

3. Program results

See file ags4out.m

Top | Next | Prev

Auxiliary Routines


Top | Next | Prev


Average grain size, peak temperature, thermal cycle, precipitate dissolution.

Top | Next | Prev


Download source code

Top | Prev

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

Top | Program Index | MAP Homepage Valid HTML 3.2!