Consideration of Phase Transformations in the Study of Shear Bands in a Dynamically Loaded Steel Block

We study plane strain thermomechanical deformations of a square block made of steel, and model a material defect in it by a rigid non-heat-conducting ellipsoidal inclusion located at the center of the block. The boundaries of the block are presumed to be thermally insulated, and its top and bottom surfaces compressed vertically at a prescribed rate. The loading pulse is assumed to be made up of three parts; an initial segment in which the speed increases from zero to the steady value, the steady part, and the third part in which the speed decreases gradually to zero and is maintained at zero subsequently. In the undeformed state, the specimen is assumed to be fully annealed, isotropic, and its microstructure to be a mixture of coarse ferrite and cementite. A material point is presumed to start transforming into austenite once its temperature exceeds the transformation temperature; the rate of transformation is controlled by a simple kinetic equation. Proper account is taken of the latent heat required for the transformation, the associated volume change, and the variation in the thermophysicalproperties. The complete thermomechanical problem is analyzed during the loading and unloading phase till all of the body points have essentially come to rest, and the energy equation is solved subsequently. It is found that the austenite is quenched rapidly enough by the surrounding material for it to be converted into martensite rather than pearlite or a mixture of pearlite and martensite.