8. Mechanisms of Creep in metals: There are three basic mechanisms that cancontribute to creep in metals, namely:(i) Dislocation slip and climb.(ii) Grain boundary sliding.(iii) Diffusional flow.Dislocation slip and climb: Dislocations are line defects that slip through acrystal lattice when a minimum shear stress is applied. Dislocations initially slipalong the closest packed planes in the closest packed directions since thisrequires the least energy or applied stress. An edge dislocation consists of anunfinished atomic plane, the edge of the plane being the line of the dislocation,and it is characterised by a Burgers vector, or 'misfit strain' at 90o to thedislocation line. Screw dislocations have a Burgers vector parallel to thedislocation line and can slip on any close packed plane containing both line andBurgers vector, whereas edge dislocations only slip on the plane defined by theline and the perpendicular Burgers vector. Figure 13 shows an edge dislocationslipping through a crystal lattice (simple cubic for simplicity) and producing a unitof slip called a slip step, on the surface of the crystal.

l.Figure 13: Showing slip of an edge dislocation.When a polycrystalline metal is deformed many of the grains will have slip planessuitably aligned to the applied stress, and slip will occur when the shear stressexceeds the critical resolved shear stress. Dislocations multiply at sources,e.g. Frank-Read sources, and as the dislocation density increases, moredislocation interactions occur. Dislocations may entangle or cut through eachother, leaving slip steps on the dislocation lines called jogs, and if one of thedislocations is sessile, or immobile, the jogs can hinder slip. Dislocations arrivingat grain boundaries may not be able to slip into the next grain due to a differentorientation, and consequently will form a 'pile-up' at the boundary. Any followingdislocation will be repelled by the pile-up because of the long-range elasticforces between dislocations of a similar sign. The elastic strain energy per unitlength of a dislocation is given by: 25.0 GbE ≅ ...(5) where G is the shearmodulus of elasticity and b is the Burgers vector. (Compare this withmacroscopic strain energy: 25.05.0 εσε EU == where E is Young's modulus). Iftwo dislocations of the same sign were to be moved together, their associatedstrain would double to 2b , and the energy would quadruple to become

( ) 22 225.0 GbbGE =≅ , hence the repulsion between dislocations which must be

overcome by the applied stress. This and the above mechanisms contributes towork hardening of the metal, i.e. as the metal is deformed, plastic flow becomesincreasingly more difficult and more stress has to be applied to accomplish it. Inthe primary stage of a creep test, the stress is constant and these mechanismslead to a decreasing strain rate.During secondary or steady state creep, the increased strain energy stored in themetal due to deformation, together with the high temperature, provides a drivingforce for the process of recovery. There is therefore a balance between theprocesses of work hardening and recovery. Recovery involves the reduction indislocation density and the rearrangement of dislocations into lower energyarrays or sub-grain boundaries. In order for this to happen, dislocations have toclimb as well as slip, and this in turn requires atomic movement or self-diffusionwithin the lattice. Self-diffusion is only possible in a close packed lattice if theatoms have enough energy to jump into a neighbouring site and if there is avacancy at that site. As temperature increases atoms have more thermalenergy (proportional to RT) and the equilibrium concentration of vacancies in ametal increases exponentially. The number of vacancies vn , is given by:

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�−=RTQnn v

V exp0 ...(6), where 0n is the number of lattice sites and vQ is the

activation energy for vacancy creation and movement, (or the activation energyfor self-diffusion). For copper, where

vQ is 0.7 eV per atom, (an electron volt, 1 eV = 1.6.10-19 Joules) the ratio ov nn isabout 10-3 at 1300 K and about 10-12 at 300 K.Note: If vQ is quoted in Joules per mole, then the gas constant R is used, whereR = 8.314 J K-1 mol-1, but if vQ is quoted in joules per atom, then the formula

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�−=kTQnn v

V exp0 is used where k is the Boltzmann Constant ( k =1.38.10-23 J K-

1). This is because vQ in Joules per mole is N0 times vQ in Joules per atom,where N0

is Avogadro's Number, the number of atoms in a gram-atom or gram-mole (6.022.1023 mol-1). Since R = N0 k this gives the same ratio.The rate of steady state creep increases exponentially with increasingtemperature, since its rate is controlled by vacancies, the numbers of which alsoincrease exponentially with temperature. Figure 14 shows the mechanism ofself-diffusion by vacancy movement.

Figure 14: Vacancy movement or self-diffusion.

Dislocations slip is hindered by obstacles suchas (i) grain boundaries, (ii) impurity particles, (iii) the stress field around soluteatoms in solution or(iv) the strain fields of other dislocations.Pile-ups may form at obstacles as shown in Figure 15.

Figure 15: Pile-up ofdislocations at an obstacle.

Vacancies diffusing onto thebottom of dislocations willcause jogs in the dislocation, but eventually when the whole line of atoms alongthe bottom of the dislocation extra plane have diffused away, the dislocation willhave climbed normal to its slip plane by one atomic spacing. When thedislocation has climbed to an unobstructed slip plane, it will then be free to slippast the obstacle. Dislocations of opposite sign attract each other and by aprocess of climb and slip can move together and annihilate each other.Dislocations of the same sign, by similar processes, will align vertically aboveeach other into a dislocation wall. This occurs because the stress field aroundan edge dislocation is compressive above the slip plane and tensile below, soaligning vertically tends to balance out these stress fields and reduces the totalenergy of interaction. A dislocation wall is in effect a low angle tilt boundary,and evidence from X-Ray diffraction, optical and electron microscopy shows thatthe grains in a metal become sub-divided into sub-grains (calledpolygonisation) during steady state creep. These processes are illustrated inFigures 16 to 19.

Figure 16: Dislocationclimb and slip past anobstacle.

Figure 17: Dislocations of oppositesign climb and slip to annihilation. Figure 18: Dislocation wall produced

during recovery by slip and climb.

Figure 19: Sub-grain structure in 12%chromium steel produced during steady statecreep, revealed by transmission electronmicroscopy (TEM).

The above mechanisms represent only part ofthe picture. The situation in solid solutions ismore complex due to the strain fields aroundsolute atoms. Climb is, however, still the basiccontrolling mechanism in steady-state creepof solid solution alloys.

Grain Boundary sliding: The onset oftertiary creep is a sign that structural damage has occurred in an alloy. Roundedand wedge shaped voids are seen mainly at the grain boundaries (Figure 20),and when these coalesce creep rupture occurs. The mechanism of voidformation involves grain boundary sliding which occurs under the action of shearstresses acting on the boundaries. (Figures 21, 22 and 23).

Figure 20: Voids in creep rupturedNimonic 80A.(1023 K and 154 MNm-2)X150

Evidence for grain boundary slidingis the displacement of scratch lines duringcreep testing. (Figure 21)

Figure 21: Showing scratch lines displacedacross a grain boundary in aluminium.

Figure 22: A model for the formation of cracks due to grain boundary sliding.

Figure 23: The formation of wedge cracksduring grain boundary sliding.

The more rounded voids are possiblyproduced where there is a step on the grainboundary which initially gives a square voidas the grains slide, but this is rounded off by

diffusion which reduces thesurface area and energy of the void. The grainboundary sliding may account for 10% to 65% of the total creep strain, thecontribution increasing with increasing temperature and stress and reducinggrain size. Above about 0.6 TM the grain boundary region is thought to have alower shear strength than the grains themselves, probably due to the looseratomic packing at grain boundaries. Boundaries lying at about 45o to the appliedtensile stress experience the largest shear stress and will slide the most.Vacancy or atomic diffusion along the boundary is also easier, and may play arole in sliding since it has been observed that processes such as ordering andprecipitation which makes slip within the grains more difficult, also decrease thegrain boundary strain contribution by the same factor.Diffusional Flow: The third distinct mechanism for creep is significant at lowstress and high temperature. Under the driving force of the applied stress shownin Figure 24, atoms diffuse from the sides of the grains to the tops and bottoms.The grain becomes longer as the applied stress does work, and the process willbe faster at high temperatures as there are more vacancies. (Atomic diffusion inone direction is the same as vacancy diffusion in the opposite direction). Fordiffusion paths through the grains theatoms have a slower jump frequency, butmore paths, and is called Nabarro-Herringcreep. Along the grain boundaries thejump frequency is higher, but fewer pathsexist, and if this mechanism is called Coblecreep. Needless to say, the rate controllingmechanism is again vacancy diffusion, orself-diffusion.Figure 24: Diffusional flow.