Materials Algorithms Project
Program Library

Subroutine MAP_STEEL_MECH

1. Provenance of code.
2. Purpose of code.
3. Specification.
4. Description of subroutine's operation.
5. References.
6. Parameter descriptions.
7. Error indicators.
8. Accuracy estimate.
9. Any additional information.
10. Example of code
11. Auxiliary subroutines required.
12. Keywords.
13. Download source code.
14. Links.

Provenance of Source Code

H.K.D.H. Bhadeshia,
Phase Transformations Group,
Department of Materials Science and Metallurgy,
University of Cambridge,
Cambridge, U.K.

Added to MAP: August 1999.

Top | Next

Purpose

Estimates the contribution of an externally applied stress to the driving force for martensitic transformation.

Top | Next | Prev

Specification

SUBROUTINE MAP_STEEL_MECH(SHE,DIL,THETA,SIGMA,GCHEM,GMECH,GRATIO)

DOUBLE PRECISION DIL,GCHEM,GMECH,GRATIO,SHE,SIGMA,THETA

Top | Next | Prev

Description

The martensite reaction can be regarded as a strain transformation with shear and dilatational displacements parallel and perpendicular to the habit plane respectively. When an external force is applied, a change in the driving force for the martensitic transformation occurs (with a consequent change in the martensite start temperature). This contribution to the driving force from the external force is calculated by MAP_STEEL_MECH from the mechanical work done on or by the transforming region as the resolved shear and normal components of the applied stress are carried through the corresponding transformation strains. The work done per unit volume of austenite which has reacted to martensite, U, is calculated as

where t and s are the stresses resolved perpendicularly and normally to the habit plane, and g_o and e_o are respectively the dilatation and shear strains [1]. This energy can be added algebraically to the chemical free energy change of the martensitic reaction to calculate the change in the martensite start temperature.

Top | Next | Prev

References

1. J.R. Patel and M. Cohen, 1953, Acta Metallurgica, 1, 531-538.

Top | Next | Prev

Parameters

Input parameters

SHE - real

SHE is the shear strain along the habit plane.

DIL - real

DIL is the dilation strain normal to the habit plane.

THETA - real

THETA is the angle between the stress axis and the normal to the potential habit plane (degrees).

SIGMA - real

SIGMA is the applied uniaxial stress (Pascals).

GCHEM - real

GCHEM is the chemical driving force for growth of martensite. The units of GCHEM are Joules per unit volume of transformed austenite to martensite (Jm^-3).

Output parameters

GMECH - real

GMECH is the mechanical driving force for growth of martensite. The units of GMECH are Joules per unit volume of transformed austenite to martensite (Jm^-3)

GRATIO - real

GRATIO is the ratio of the mechanical to the chemical driving forces for martensitic growth (GMECH / GCHEM).

Top | Next | Prev

Error Indicators

None.

Top | Next | Prev

Accuracy

No information supplied.

Top | Next | Prev

Further Comments

None.

Top | Next | Prev

Example

1. Program text

      DOUBLE PRECISION SHE,DIL,THETA,SIGMA,GCHEM,GMECH,GRATIO
C
      WRITE(*,*) 'Enter shear strain:'
      READ (*,*) SHE
      WRITE(*,*) 'Enter dilational strain:'
      READ (*,*) DIL
      WRITE(*,*) 'Enter angle beween stress axis and normal to',
     &           ' habit plane (degrees):'
      READ (*,*) THETA
      WRITE(*,*) 'Enter applied unixial stress (Pascals):'
      READ (*,*) SIGMA
      WRITE(*,*) 'Enter chemical driving force for growth (J/m^3):'
      READ (*,*) GCHEM 
      CALL MAP_STEEL_MECH(SHE,DIL,THETA,SIGMA,GCHEM,GMECH,GRATIO)
      WRITE(*,1) GMECH
      WRITE(*,2) GRATIO
      STOP
    1 FORMAT(/'Mechanical driving force for growth',11X,'= ', D13.4,
     &        ' J/m^3')
    2 FORMAT('Ratio of mechanical to chemical driving force = ', 
     &        D13.4,' J/m^3'/)
       END

2. Program data

 Enter shear strain:
 0.2
 Enter dilational strain:
 0.05
 Enter angle beween stress axis and normal to habit plane (degrees):
 20
 Enter applied unixial stress (Pascals):
 7E7
 Enter chemical driving force for growth (J/m^3):
 118E6

3. Program results

Mechanical driving force for growth           =    0.7590D+07 J/m^3
Ratio of mechanical to chemical driving force =    0.6432D-01 J/m^3

Top | Next | Prev

Auxiliary Routines

None.

Top | Next | Prev

Keywords

stress, martensite, transformation, driving force

Top | Next | Prev

Download

Download source code

Top | Prev