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Program MAP_KINETICS_GRAINGROWTH_WELD2

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 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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Specification

Complete program.

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Description

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:

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

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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).

G0 - real

G0 is the initial 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).

ZENER_COEFF (k) - real

ZENER_COEFF - is a physical parameter related to grain boundary pinning efficiency.

RADIUS_PARTICLE (r) - real

RADIUS_PARTICLE - partcle radius (microns).

VOLFRAC_PARTICLE (f) - real

VOLFRAC_PARTICLE - volume fraction of the particle.

See file ags2.in

See file ags2out.m