Dear Kedharnath Arumugakani,

Shearing is a characteristic of martensitic transformations. Martensite forms as platelets within grains. Each platelet is accompanied by a shape change which means that there is a strain associated with the transformation. The shape change appears to be a simple shear parallel to a habit plane (the common, coherent plane between the phases) and a uniaxial expansion (dilatation) normal to the habit plane. Figures attached below may be useful to understand the concept of "shear" in martensitic transformations.

The martensitic transformation happens when a steel is cooled rapidly from the austenitic domain. The equilibrium transformation usually involves the transformation of austenite (Face centered cubic) to ferrite (centered cubic)+ cementite, thus carbon has to diffuse out from austenite. During fast cooling diffusion is not possible and this transformation cannot happen. Cementite cannot form and carbon is trapped. Thus, the room temperature ferrite has to accomodate to carry the carbon that stays in solid solution. The cubic cristallography is then deformed to a quadratic one where the ratio of the lattice a/c depends on the carbon content of the steel. This accomodation is possible only by shear of the cubic parent phase crystallographic planes. Shear happens at the crystallographic level. This induces high internal residual stresses. The highest the carbon content, the highest are the residual stresses.

This is in simple words the scenario of the shear martensitic transformation. Hope it helps.

Diffusionless implies atoms moves cooperatively or in a military way  (V.S. civilian transformation, r.f. Christian's book) from one structure to the other. The transformation strain is accommodated by the sub-structure, i.e. twin or slip.