# Materials Algorithms Project Program Library

## Subroutine MAP_STEEL_TRANS_PLASTICITY

### Provenance of Source Code

Saurabh Kundu and H. K. D. H. Bhadeshia
Materials Science and Metallurgy, University of Cambridge, U. K.

E-mail: sk459@cam.ac.uk

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### Purpose

Calculation of transformation strain when austenite transforms into martensite/bainite.

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### Specification

 Language: FORTRAN

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### Description

Calculation of transformation strain of the 24 variants of martensite or bainite that form in austenite grains in arbitrary orientations. This program has the inputs consisting of the habit planes, shape deformations of the 24 variants of martensite or bainite per austenite grain, and the crystallographic orientation of the austenite grain. All these input parameters are generated using MAP_STEEL_TEXTURE3. The output is the transformation strain and orientation of each of the martensite or bainite plates.

1. It assumes three unit vectors in the principal directions of the applied stress.
2. It calculates the interaction energies for each variant in every grain and rank all the variants according to the interaction energies.
3. Assuming n number (n vary from 1 to 24) of variants forming in each grain it allows the unit vectors to get deformed by the shape deformation matrix of each variant.
4. The final vector is calculated.
5. The ratio between the final and initial length of the vectors gives the strain.
6. User can change the number of grains and amount of martensite / bainite.

### Inputs when running the program

WRITE THE NUMBER OF GRAINS:
500
FRACTION OF MARTENSITE/BAINITE:
0.63
INITIAL TEXTURE:
0=RANDOM
1=COPPER
2=BRASS
3=GOSS
4=CUBE
5={110}<111>
6=MIXTURE
0
FIRST ELEMENT OF THE STRESS TENSOR:
200.0

### Name

#### trans_plast_tensor.for

This is a source code of this program. For the execution, it needs to be compiled.
compile example :
g77 trans_plast_tensor.for -o name.out

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### References

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### Parameters

HABIT# - double precision array of dimension 24X3, # represents numbers.
Matrix that stores 24 habit planes.

DIRECTION# - Double precision array of dimension 24X3
Matrix that stores 24 displacement directions for 24 variants of martensite.

GM_J_AL# - Double precision array of dimension 72X3.
It contains 24 matrix representing orientation relationship between martensite and austenite, following Bowles and MacKenzie notation can be written as (gamma J alpha).

AL_J_GM# - Double precision array of dimension 72X3.
It contains 24 matrix representing orientation relationship between martensite and austenite, following Bowles and MacKenzie notation can be written as (alpha J gamma).

DEF_MAT# - Double precision array of dimension 3X3.
DEF_MAT# This matrix stores stress tensor of the applied stress in the crystal axis.

STRESS_TENSOR - Double precision array of dimension 3X3.
Matrix represents the stress tensor in trhe sample axis.

TRANS_MATRIX - Double precision array of dimension 3X3.
Rotational matrix represnting the orientation relationship between any austenite grain relative to the sample axes.

SH, VOL, TOT - DOUBLE PRECISION
The shear, volume and total strain associated with any marteniste/bainite variant.

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### Error Indicators

None.

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### Accuracy

No information.

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None.

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### Example

#### 1. Program Compile

``` g77 [sourcecode name] -o [executable file name]
```

```

```

```
Auto generated.

```

#### 4. Program results

```

```

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### Auxiliary Routines

No auxiliary routines

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### Keywords

Transformation strain, martensite, steels, crystallography

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