Activation of deformation mechanism

Transcription

1 Activation of deformation mechanism The deformation mechanism activates when a critical amount of mechanical stress imposed to the crystal The dislocation glide through the slip systems when the required stress is imposed The critical stress required to activate the glide in a crystal can be understood in terms of CRITICAL RESOLVED SHEAR STRESS (CRSS)

2 CRITICAL RESOLVED SHEAR STRESS (CRSS) The following schematic diagram depicts slip plane in a single crystal A = cross sectional area of the crystal L = tensile load imposed on it t = tensile stress caused by the tensile load L Plane Normal Tensile axis ϕ λ χ Slip direction Slip plane

3 Continued Tensile stress on area A = L/A Area of the slip plane = A/sin χ Therefore, tensile stress on the slip plane = L/(A/sin χ) = (L/A) sinχ = t sin χ Shear stress on the slip plane resolved in the slip direction, = tensile stress on slip plane X cos = t sin χ.cos If is the angle between the tension axis and normal ON to the slip plane, = t cos. cos

4 Case 1: When tension is normal to the slip plane, = 90, = 0 Or, When tension axis is parallel to the slip plane, χ = 0, = 0 No slip, because shear stress in the slip direction is zero. Case 2: When tension is at 45 to the slip plane, = 45, When tension axis is 45 to the slip plane, χ = 45, = 0.5 t Maximum shear stress

5 Critical resolved shear stress The resulting shear stress is a constant for particular metal and the plane in a crystal = t cos. cos Crystal will commence to deform plastically when the resolved shear stress on the slip plane in the slip direction reaches a constant critical value 0, 0 = 0 sin X 0. cos 0 0 = critical resolved shear stress 0 = yield stress in tension X 0 = initial angle between slip plane and the tensile axis 0 = initial angle between slip direction and tension axis Thus, shearing is orientation dependent phenomena i.e. deformation of a polycrystalline material depends on the orientation of plane in the respective crystals (grains)

6 Deformation : General Actual planes and directions associated with slip and twinning correspond to the system with greatest resolved shear stress are differently oriented from grain to grain in a polycrystalline material. Slip or twinning initiated in one grain are confined to that grain and can be readily distinguished from those occuring in neighbouring grains. When a single crystal is deformed it is usually free to change its shape subject only to the need to comply with any external constraints - grip alignment in a simple tensile test A polycrystal responds to deformation by developing orientation that are: (i) different from grain to grain, (ii) different from region to region within an individual grain Microstructural heterogeneity

7 Microstructural hierarchy for metals deforming by slip Initial stage of deformation: evolution of dislocation substructure Second stage of deformation: evolution of dislocation boundaries Third stage of deformation: evolution of deformation bands Final stage of deformation: evolution of shear bands

8 Microstructural heterogeneity Deformation band: volume of constant orientation which is significantly different to the orientations present elsewhere in that grain arises when two zones of a grain rotate towards different orientations, as a result of local difference in stress or different combination of slip systems to yield the imposed strain rate Kink band Transition band: the region at the edge of the deformation band where the orientation T T T changes from B to A -is not a grain boundary A C A B Kink band: when deformation bands occur with approximately parallel sides and involve a double orientation change A to C and then C to A Deformation band Transition band

9 Shear bands When resolved shear stress in the fine lamellae is not sufficient for slip flow localisation in form of a shear band developes. Flat sheet like structures composed of elongated crystallites from m in width usually inclined at some angles to the rolling plane - normally 35 or 40 ND RD Courtesy: R. Madhavan

10 Deformation twinning In polycrystalline agreegates, the change in shape accompanying deformation require the operation of several slip systems Sudden localised shear process TWINNING involves a small but well defined volume of the crystal. -contrast to individual slip process, which although occurs Twinning is a major mode of deformation in fcc metals with SFE < 25 mj m -2 and in all hcp metals. Twinning may also occur in fcc metals with high values of SFE ; and in bcc metals if deformation occurs at low temperature or high strain rates.

11 Twinned region is often bounded by parallel or nearly parallel sides which corresponds with planes of low indices twin habit plane or twinning plane Extent of twinning is orientation dependent. Twinned region differs appreciably in orientation from the grain in which it is formed Courtesy: R. Madhavan Process of twinning is cooperative movement of atoms in which individual atoms move only a fraction of the interatomic spacing relative to each other, but total result is a macroscopic shear which can be is observed with naked eye.

12 The crystallographic result of such a transition is that the lattice in the twinned region is related to the untwinned crystal, usually by reflection across the twinning plane which results in the twin lattice being a mirror image of the lattice of the matrix in which it forms. A result from several different crystallographic transformation 2 K 2 K 1 1 Lattice has been twinned along a (twinning) plane K 1 in the twinning direction 1 Original atom positions New positions acquired by twinning

13 Factors influencing deformation texture 1. Rolling geometry and friction There is a neutral plane in which the relative velocity of the sample and rolls changes direction. Imposition of shear of opposite sense on the either side of the neutral plane Material near the surface undergoes shear in both directions (redundant shear) Gradients are greatest for - smaller roll diameters - small reduction per pass - thick sheet Friction 2. Deformation temperature 3. Grain size 4. Shear banding 5. Second phase particles

14 Questions 1. What are the differences between slip and twining in a crystal? 2. Why during deformation of BCC materials wavy nature of slip observed? 3. Explain stacking fault energy (SFE) and its affect on deformation of a materials. 4. How many slip system/systems is/are required to deform a single crystal? 5. Near grain boundaries the number of slip lines observed are more than grain interior. Why? 6. Determine the required tensile load along [1-10] of a FCC crystal to cause slip on (1-1-1)[01-1] if the critical resolved shear stress is 10 Mpa.