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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.

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

Language: | FORTRAN |

Product form: | Source code |

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

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.

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

**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}).

**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).

None.

No information supplied.

None.

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

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

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

None.

stress, martensite, transformation, driving force

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