Materials Algorithms Project
Program Library

Program MAP_KINETICS_GRAINGROWTH_WELD3

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.

Top | Next

Purpose

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.

Top | Next | Prev

Specification

Complete program.

Top | Next | Prev

Description

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^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 growing precipitates, the limiting grain size is expressed by the following:

where I₂ is the kinetic strength of the thermal cycle with respect to the precipitate coarsening and is given by the following expression:

and

Top | Next | Prev

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.

Top | Next | Prev

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).

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 (I₂) - 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.

See file ags3.in

See file ags3out.m