Structural changes accompanying

7.11.3 Structural changes accompanying

fatigue

Observations of the structural details underlying fatigue hardening show that in polycrystals large variations in slip-band distributions and the amount of lattice misorientation exist from one grain to another. Because of such variations it is difficult to typify structural changes, so that in recent years this structural work has been carried out more and more on single crystals; in particular, copper has received considerable attention as being representative of a typical metal. Such studies have now established that fatigue occurs as a result of slip, the direction of which changes with the stress cycle, and that the process continues throughout the whole of the test (shown, for example, by interrupting a test and removing the slip bands by polishing; the bands reappear on subsequent testing).

Moreover, four stages in the fatigue life of a specimen are distinguishable; these may be summa- rized as follows. In the early stages of the test, the

Mechanical behaviour of materials 255 whole of the specimen hardens. After about 5% of the

life, slip becomes localized and persistent slip bands appear; they are termed persistent because they reap- pear and are not permanently removed by electropol- ishing. Thus, reverse slip does not continue throughout the whole test in the bulk of the metal (the matrix). Electron microscope observations show that metal is extruded from the slip bands and that fine crevices called intrusions are formed within the band. Dur- ing the third stage of the fatigue life the slip bands grow laterally and become wider, and at the same time cracks develop in them. These cracks spread initially along slip bands, but in the later stages of fracture the propagation of the crack is often not confined to cer- tain crystallographic directions and catastrophic rup- ture occurs. These two important crack growth stages,

i.e. stage I in the slip band and stage II roughly perpen- dicular to the principal stress, are shown in Figure 7.70 and are influenced by the formation of localized (per- sistent) slip bands (i.e. PSBs). However, PSBs are not clearly defined in low stacking fault energy, solid solu- tion alloys.

Cyclic stressing therefore produces plastic deforma- tion which is not fully reversible and the build-up of dislocation density within grains gives rise to fatigue hardening with an associated structure which is char- acteristic of the strain amplitude and the ability of the dislocations to cross-slip, i.e. temperature and SFE. The non-reversible flow at the surface leads to intru- sions, extrusions and crack formation in PSBs. These

Figure 7.70 Persistent slip band (PSB) formation in fatigue, two aspects will now be considered separately and in

and stage I and stage II crack growth . greater detail.

Fatigue hardening If a single or polycrystalline two unusual features when compared with an ordi- specimen is subjected to many cycles of alternat-

nary work-hardened material. The fatigue-hardened ing stress, it becomes harder than a similar specimen

material, having been stressed symmetrically, has the extended uni-directionally by the same stress applied

same yield stress in compression as in tension, whereas only once. This may be demonstrated by stopping

the work-hardened specimen (e.g. prestrained in ten- the fatigue test and performing a static tensile test

sion) exhibits a Bauschinger effect, i.e. weaker in com- on the specimen when, as shown in Figure 7.71, the

pression than tension. It arises from the fact that the yield stress is increased. During the process, persis-

obstacles behind the dislocation are weaker than those tent slip bands appear on the surface of the specimen

resisting further dislocation motion, and the pile-up and it is in such bands that cracks eventually form.

stress causes it to slip back under a reduced load in The behaviour of a fatigue-hardened specimen has

the reverse direction. The other important feature is

Figure 7.71 Stress–strain curves for copper after increasing amounts of fatigue testing (after Broom and Ham, 1959) .

256 Modern Physical Metallurgy and Materials Engineering that the temperature-dependence of the hardening pro-

duced by fatigue is significantly greater than that of work-hardening and, because of the similarity with the behaviour of metals hardened by quenching and by irradiation, it has been attributed to the effect of vacancies and dislocation loops created during fatigue.

At the start of cyclic deformation the initial slip bands (Figure 7.72a) consist largely of primary dis- locations in the form of dipole and multipole arrays; the number of loops is relatively small because the frequency of cross-slip is low. As the specimen work- hardens slip takes place between the initial slip bands, and the new slip bands contain successively more secondary dislocations because of the internal stress arising from nearby slip bands (Figure 7.72b). When the specimen is completely filled with slip bands, the

Figure 7.73 Schematic diagram showing (a) vein structure specimen has work-hardened and the softest regions

of matrix and (b) ladder structure of PSBs . are now those where slip occurred originally since

these bands contain the lowest density of secondary annihilation exists in the PSBs. Multiplication occurs dislocations. Further slip and the development of PSBs

by bowing-out of the walls and annihilation takes place takes place within these original slip bands, as shown

schematically in Figure 7.72c by interaction with edge dislocations of opposite sign As illustrated schematically in Figure 7.73, TEM of

(³75b apart) on glide planes in the walls and of screw copper crystals shows that the main difference between

dislocations (³200b apart) on glide planes in the low- the matrix and the PSBs is that in the matrix the dense

dislocation channels, the exact distance depending on arrays of edge dislocation (di- and multipoles) are in

the ease of cross-slip.

the form of large veins occupying about 50% of the volume, whereas they form a ‘ladder’-type structure

7.11.4 Crack formation and fatigue failure

within walls occupying about 10% of the volume in PSBs. The PSBs are the active regions in the fatigue

Extrusions, intrusions and fatigue cracks can be formed process while the matrix is associated with the inactive

at temperatures as low as 4 K where thermally acti- parts of the specimen between the PSBs. Steady-

vated movement of vacancies does not take place. state deformation then takes place by the to-and-fro

Such observations indicate that the formation of intru- glide of the same dislocations in the matrix, whereas

sions and cracks cannot depend on either chemical or an equilibrium between dislocation multiplication and

thermal action and the mechanism must be a purely geometrical process which depends on cyclic stressing.

Two general mechanisms have been suggested. The first, the Cottrell ‘ratchet’ mechanism, involves the use of two different slip systems with different direc- tions and planes of slip, as is shown schematically

in Figure 7.74. The most favoured source (e.g. S 1 in Figure 7.74a) produces a slip step on the surface at P during a tensile half-cycle. At a slightly greater stress

in the same half-cycle, the second source S 2 produces

Figure 7.72 Formation of persistent slip bands (PSBs) Figure 7.74 Formation of intrusions and extrusions (after during fatigue .

Cottrell; courtesy of John Wiley and Sons) .

Mechanical behaviour of materials 257

a second step at Q (Figure 7.74b). During the com- is probably also due to the unstable nature of the alloy

pression half-cycle, the source S 1 produces a surface

and to the influence of vacancies.

step of opposite sign at P 0 (Figure 7.74c), but, owing

In pure metals and alloys, transgranular cracks ini-

tiate at intrusions in PSBs or at sites of surface rough- plane as the first and thus an intrusion is formed. The

to the displacing action of S 2 , this is not in the same

ness associated with emerging planar slip bands in

low SFE alloys. Often the microcrack forms at the QQ 0 (Figure 7.74d) in a similar manner. Such a mech-

subsequent operation of S 2 produces an extrusion at

PSB-matrix interface where the stress concentration is anism requires the operation of two slip systems and,

high. In commercial alloys containing inclusions or in general, predicts the occurrence of intrusions and

second-phase particles, the fatigue behaviour depends extrusions with comparable frequency, but not in the

on the particle size. Small particles ³0.1 µ m can have same slip band.

beneficial effects by homogenizing the slip pattern The second mechanism, proposed by Mott, involves

and delaying fatigue-crack nucleation. Larger parti- cross-slip resulting in a column of metal extruded from

cles reduce the fatigue life by both facilitating crack the surface and a cavity is left behind in the interior

nucleation by slip band/particle interaction and increas- of the crystal. One way in which this could happen

ing crack growth rates by interface decohesion and is by the cyclic movement of a screw dislocation

voiding within the plastic zone at the crack tip. The along a closed circuit of crystallographic planes, as

formation of voids at particles on grain boundaries shown in Figure 7.75. During the first half-cycle the

can lead to intergranular separation and crack growth. screw dislocation glides along two faces ABCD and

The preferential deformation of ‘soft’ precipitate-free BB 0 C 0 C of the band, and during the second half-cycle

zones (PFZs) associated with grain boundaries in

age-hardened alloys also provides a mechanism of the Cottrell mechanism this process can be operated

returns along the faces B 0 C 0 A 0 D and A 0 D 0 DA . Unlike

intergranular fatigue-crack initiation and growth. To with a single slip direction, provided cross-slip can

improve the fatigue behaviour it is therefore necessary occur.

to avoid PFZs and obtain a homogeneous deforma- tion structure and uniform precipitate distribution by

Neither mechanism can fully explain all the heat-treatment; localized deformation in PFZs can be experimental observations. The interacting slip mech-

restricted by a reduction in grain size. anism predicts the occurrence of intrusions and extru-

From the general appearance of a typical fatigue sions with comparable frequency but not, as is often

fracture, shown in Figure 7.76, one can distinguish two found, in the same slip band. With the cross-slip mech-

distinct regions. The first is a relatively smooth area, anism, there is no experimental evidence to show that

through which the fatigue crack has spread slowly. cavities exist beneath the material being extruded. It

This area usually has concentric marks about the point may well be that different mechanisms operate under

of origin of the crack which correspond to the positions different conditions.

at which the crack was stationary for some period. In a polycrystalline aggregate the operation of

The remainder of the fracture surface shows a typi- several slip modes is necessary and intersecting slip

cally rough transcrystalline fracture where the failure unavoidable. Accordingly, the widely differing fatigue

has been catastrophic. Electron micrographs of the rel- behaviour of metals may be accounted for by the

atively smooth area show that this surface is covered relative ease with which cross-slip occurs. Thus,

with more or less regular contours perpendicular to the those factors which affect the onset of stage III in

direction of the propagation front. These fatigue stri- the work-hardening curve will also be important in

ations represent the successive positions of the propa- fatigue, and conditions suppressing cross-slip would,

gation front and are spaced further apart the higher the in general, increase the resistance to fatigue failure,

i.e. low stacking-fault energy and low temperatures. Aluminium would be expected to have poor fatigue properties on this basis but the unfavourable fatigue characteristics of the high-strength aluminium alloys

Figure 7.75 Formation of an extrusion and associated cavity by the Mott mechanism .

Figure 7.76 A schematic fatigue fracture .

258 Modern Physical Metallurgy and Materials Engineering

Figure 7.77 Schematic illustration of the formation of fatigue striations .

velocity of propagation. They are rather uninfluenced followed by transcrystalline propagation. When by grain boundaries and in metals where cross-slip is

fatigued at elevated temperatures ⱚ 0.5T m , pure metals easy (e.g. mild steel or aluminium) may be wavy in

and solid solutions show the formation of discrete appearance. Generally, the lower the ductility of the

cavities on grain boundaries, which grow, link up material, the less well defined are the striations.

and finally produce failure. It is probable that Stage II growth is rate-controlling in the fatigue fail-

vacancies produced by intracrystalline slip give rise ure of most engineering components, and is governed

to a supersaturation which causes the vacancies to by the stress intensity at the tip of the advancing crack.

condense on those grain boundaries that are under a The striations seen on the fracture surface may form by

high shear stress where the cavities can be nucleated

a process of plastic blunting at the tip of the crack, as by a sliding or ratchet mechanism. It is considered shown in Figure 7.77. In (a) the crack under the ten-

unlikely that grain boundary sliding contributes to sile loading part of the cycle generates shear stresses

cavity growth, increasing the grain size decreases the at the tip. With increasing tensile load the crack opens

cavity growth because of the change in boundary area. up and new surface is created (b), separation occurs

Magnox (Mg) and alloys used in nuclear reactors up to in the slip band and ‘ears’ are formed at the end of

0.75T m readily form cavities, but the high-temperature the crack. The plastic deformation causes the crack to

nickel-base alloys do not show intergranular cavity