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Jeevan Jaidi

Research Scholar,

Mechanical Engineering Department,

Indian Institute of Science,

Bangalore-560012,

INDIA.

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

Added to MAP: December 2002.

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

Language: | FORTRAN-90 |

Product form: | Source code |

Complete program.

When grain growth occur in the presence of growing precipitates, the
limiting grain size (g_{lim} = k*r/f) is no longer a constant,
since the ratio (r/f) increases with time. When the peak
temperature of the thermal cycle is below the equilibrium solvus of the
precipitates, the precipitates will coarsen at almost constant volume
fraction (f = f_{o}).

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

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 800^{o}C -
500^{o}C) 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 growing precipitates, the limiting grain size is expressed by the following:

where I_{2} is the kinetic strength of the thermal cycle with respect to
the precipitate coarsening and is given by the following expression:

and

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

**DT (dt) - real**- DT is the time interval (seconds).
**G0LIM - real**- G0LIM is the limiting grain size (microns).
**ISTART - integer**- ISTART is the N
^{th}starting data point for heating or cooling period. **IEND - integer**- IEND is the N
^{th}ending data point for heating or cooling period. **LL - integer**- LL is the number of data points.
**M0 (M**_{o}^{*})- real- M0 is a physical parameter related to the grain boundary
mobility (microns
^{2}/s). **TN (n) - real**- TN is the time exponent (assumed n = 0.5).
**QG (Q**_{app}) - real- QG is the activation energy with respect to the grain growth (J/mol).
**QP (Q**_{s}) - real- QP is the activation energy with respect to growing precipitates (J/mol).
**R - real**- R is the universal gas constant (J/mol-k).
**T - real array**- T is the temperature (absolute).
**PSTRENGTH (I**_{2}) - real- PSTRENGTH is the kinetic strength of the thermal cycle w.r.t particle coarsening.
**ZENER_COEFF (k) - real**- ZENER_COEFF - is a physical parameter related to grain boundary pinning efficiency.
**RADIUS_PRECIP (r**_{o})- real- RADIUS_PRECIP - initial radius of the precipitate (microns).
**VOLFRAC_PRECIP (f**_{o})- real- VOLFRAC_PRECIP - initial volume fraction of the precipitate.

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

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

No information supplied.

None.

Complete program.

See file ags3.in

See file ags3out.m

None

Average grain size, peak temperature, thermal cycle, growing precipitates.

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