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Program MAP_KINETICS_GRAINGROWTH_WELD4

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,
Bangalore-560012,
INDIA.

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

Added to MAP: December 2002.

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Purpose

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.

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Specification

Complete program.

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Description

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:

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^oC - 500^oC) 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:

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

and

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References

1. Oystein Grong, Metallurgical Modelling of Welding, 2^nd 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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Parameters

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 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 (microns²/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).

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 (r_o) - real

RADIUS_PRECIP - initial radius of the precipitate (microns).

VOLFRAC_PRECIP (f_o) - real

VOLFRAC_PRECIP - initial volume fraction of the precipitates.

ALFA - real

ALFA is the dimensionless super saturation.

DIFFUSE (D_m) - real

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

See file ags4.in

See file ags4out.m