5Fracture of Metals

5.10 In an 'ideal' metal, that is one containing no flaws or defects, fracturewill occur when atomic bonding is overcome across an atomic plane whichis perpendicular to the tensile force; but in practice metals fail at muchlower stresses than the theoretical (4.14). This is due partly to the presenceof impurities and other discontinuities in the structure (Fig. 3.16), andpartly to the polycrystalline nature of metals which in itself leads to the'pile-up' of dislocations at or near crystal boundaries. Thus fracture is acommon cause of failure in metals and whilst it will always occur when ametal is stressed beyond its tensile strength, under certain conditions it canalso occur at stresses even below the elastic limit. Thus, some metals maycreep during long periods of time, particularly at high temperatures, untilfailure occurs; whilst fracture which is the result of repeated cyclic stressis termed fatigue failure. Some metals fail by a form of brittle fracture whichis influenced by low temperature conditions.

5.11 The nature of fracture differs from one metal to another. Thetype of fracture which follows large amounts of plastic deformation isgenerally referred to as ductile fracture whilst that which occurs after littleor no plastic deformation is called brittle fracture (Fig. 5.1).

FO

RC

E

FO

RC

E

(tupcone.

EXTENSION EXTENSION

Fig. 5.1 Types of fracture (i) ductile—showing the well-known cup and cone; (ii) brittle—with a strongly 'crystalline' appearance.

It was stated in the previous chapter that during plastic deformation sliptakes place along some crystallographic planes more readily than alongothers. Similarly, metallic fracture—or cleavage—tends to follow pre-ferred crystallographic planes. Thus FCC metals are likely to suffer cleav-age along the {111} planes (3.15), whilst BCC metals cleave along the{100} planes. In CPH metals cleavage occurs along the basal planes of thehexagon (designated the {0001} planes).

Brittle Fracture

5.20 Whilst plastic deformation takes place in a ductile metal by the'rippling' of dislocations along slip planes (4.16), brittle fracture occurs asa result of complete and sudden separation of atoms as indicated in Fig.5.2. The theoretically-calculated stress necessary to achieve such separ-ation is considerable, yet in practice, the actual stress required to causebrittle fracture is often relatively small. Moreover, the results obtained fortensile strength measurements on a large number of apparently identicaltest pieces of a single brittle metal are often very variable (Fig. 5.3(i))compared with similar determinations made for a ductile metal (Fig.5.3(ii)). Such results suggest that in brittle materials some factor is presentwhich gives rise to the variability of results.

5.21 In 1920, A. A. Griffith postulated that fractures in brittle solidswere propagated from minute flaws in the material. He demonstrated thatthe strength of freshly-drawn glass fibres often approached the 'theoretical'

Fig. 5.2 Cleavage along crystallographic planes.

Fig. 5.3 The variability of results during the tensile testing of (i) a brittle material; (ii) aductile material.

value, but if these fibres were allowed to come into contact with anyother substance, including the atmosphere, even for short periods then thestrength was considerably reduced. This suggests that the strength of glassfibre was very dependent upon surface perfection and that anything likelyto initiate even minute surface irregularities would weaken it. In certainrespects these principles may also be applied to brittle metals. Engineerswill already be familiar with the concept of 'stress raisers' and stress con-centrations associated with the presence of sharp in-cut corners and thenecessity of eliminating these in engineering design whenever possible.Thus in iron castings in-cut corners are rounded by using leather 'fillets'on the wooden pattern.

5.22 Griffith's Crack Theory. Whilst the presence of a small fissure (Fig.5.4) will obviously reduce the effective cross-section of the material, thereduction in breaking stress is very much greater than can be accountedfor by this reduction in cross-sectional area. This is because an appliedstress, S, generates stress concentrations at the tip of the fissure.

Griffith concluded that the concentrated stress, Sc, is related to theapplied stress, S, the width of the crack, c, and the radius of curvature ofthe tip of the crack, r, by:

Fig. 5.4.

TE

NS

ILE

S

TRE

NG

TH

TE

NS

ILE

S

TR

EN

GT

H

NUMBER OF TESTS NUMBER OF TESTS

If we assume that the tip radius of such a crack is of the order of 10~10

m (roughly one atomic radius) and that such cracks are about 10~4 m inwidth, then the value SJS (which we can call the factor of stress concen-tration) is of the order of 103. This indicates that the actual stress, 5C,operating at the tip of the crack is some thousand times greater than theapplied stress, S. In this case fracture is taking place at a localised stressnearer to the theoretical value. When a crack progresses through a brittlematerial under the action of a constant applied stress, S, the concentratedstress, Sc, at the tip increases since an increase in c gives rise to an increasein the term dr. The speed of crack propagation therefore increases andfailure is certain.

5.23 So far we have considered only the effects of an applied tensilestress on a brittle material. If however the applied stress is compressivethis stress will be transmitted across existing micro-cracks without causingany stress concentrations—that is, a compressive stress will tend to 'closeup' existing fissures. For this reason many brittle metallic materials such ascast iron are relatively weak in tension but strong in compression. Failure incompression will ultimately take place when compressive forces are sohigh that they produce tensile components of sufficient magnitude alongcrystallographic planes in the region of a fissure tip.

5.24 lntercrystalline Brittle Fracture In the foregoing paragraphs wehave been dealing with brittle fracture in terms of cleavage along transcvys-talline planes. Brittle fracture also occurs by the propagation of cracksalong grain boundaries—that is, by mtercrystalline fracture. In some casesthis type of fracture is due to the presence of grain-boundary films of ahard, brittle second phase. Such films may be formed by segregation duringsolidification (3.41) so that fracture of this type is more commonly foundin cast materials. Brittle films of bismuth segregate at the crystal boundariesof copper in this way so that very small quantities of bismuth (less than0.01%) may cause excessive brittleness in copper.

Impurities present in solid solution may also segregate at grain boun-daries during the normal process of coring (8.23). A high concentration ofthe solute atoms in the grain-boundary region may give rise to brittleness.This is probably due to the pegging of dislocation movements and theconsequent initiation of micro-cracks at the grain boundaries.

5.25 Temper Brittleness This occurs in some low-alloy steels whentempered in the range 250-4000C (13.42), and is probably due to theprecipitation of films or particles of carbides at grain boundaries. Althoughtensile strength, and even ductility, are not seriously reduced a very largereduction in impact value is experienced and fracture is intercrystalline.

Ductile Fracture

5.30 As was indicated in Fig. 5.3 the stress at which a ductile metal islikely to fail is much more predictable than that stress in a brittle metal andthis fact alone makes ductile metals more suitable for fail-safe engineeringdesign. Moreover, as plastic deformation begins, the tip radius of any

micro-crack present is likely to increase and this will automatically reducethe concentrated stress, 5C, as the value of clr (in the Griffith equation)decreases. As a result of this stress relaxation propagation of the crackmay cease. The fracture which ultimately occurs in ductile materials is duepartly to strain hardening which progressively reduces the ductility whichis necessary for further stress relaxation.

5.31 It is difficult to differentiate implicitly between brittle and ductilefracture since some brittle metals undergo some ductile deformation beforefracture, whilst many ductile metals exhibit final brittle-type cleavage.However, whilst a brittle fracture is one in which the progress of the crackinvolves very little plastic deformation of the neighbouring metal, a ductilefracture is one which proceeds as a result of high localised plastic defor-mation of the metal near the tip of the crack. Thus, whilst the two extremesof these methods of failure are easily recognised, there can be no sharpdivision between brittle and ductile fracture. A fracture which is almostcompletely of the brittle variety will exhibit a mass of minute facets whichreflect light strongly and reveal the crystalline nature of the metal. Analmost completely ductile fracture, on the other hand, shows a rough, dulldirty-grey surface because much of that surface has been deformed alongthe general plane of fracture. When viewed under the scanning electronmicroscope (10.33) however the surface of a ductile fracture has a 'dimpled'appearance, caused by the presence of a multitude of minute cavitiesaccompanying the rupture process. Closer examination reveals that theformation of these minute cavities is due to the presence of very smallparticles of impurity and other phases. This confirms the observed fact thatas the purity of a metal increases so does its ductility.

5.32 Most ductile polycrystalline metals fail with the well-known cup-and-cone fracture. Fracture of this type follows the formation of a neck ina tensile test piece. Crack formation begins at the centre of the neck on aplane that is roughly normal to the applied stress axis. Small cavities formnear the centre of this cross section (Fig. 5.5(i)) and these coalesce to forma visible fissure (Fig. 5.5(iii)). As deformation proceeds the crack spreadsoutwards towards the edges of the test piece. The final fracture then occursrapidly along a surface which makes an angle of approximately 45° withthe stress axis. This leaves a circular lip on one half of the test piece anda corresponding bevel on the surface of the other half, leading to theformation of a cup on one half and a cone with a flattened apex on theother half (Fig. 5.1(i)).

Factors Leading to Crack Formation

5.40 Very pure metals are much more ductile than those of slightly lowerpurity and will often draw down to a 'chisel point' where the cross-sectionat failure is approaching zero. It is therefore reasonable to suppose thateven minute inclusions in the microstructure play an important part innucleating cracks. When slip in a metal takes place dislocations will tendto pile up at the metal/inclusion interface. Assuming that the inclusion

Fig. 5.5 The nucleation and development of a crack in a ductile material.

itself is strong and does not shear, a minute fissure will develop at theinterface (Fig. 5.6). Of course, the development of the fissure will alsodepend upon the degree of adhesion between the surface of the inclusionand that of the metal. Thus, if there is little adhesion as, for example, atthe interface between copper and cuprous oxide particles, then fissures willform easily, but if adhesion is high then the particles may indeed have astrengthening effect. Thus sintered aluminium powder (SAP), which con-tains a high proportion of aluminium oxide particles, is stronger than purealuminium because of the high adhesion at the Al/Al2O3 interface.

5.41 Other barriers to the movement of dislocations can also initiatemicro-cracks in a similar manner. Thus Fig. 5.7 suggests how a grain boun-

Fig. 5.6 A pile-up of dislocations at some obstacle leading to the formation of a crack whichwill be propagated if the stress, a, is increased.

EMBRYOCRACK

OBSTACLE(SEPARATE

PHASE) STRESS

STRESS O"

cracknucleus

Fig. 5.7 The nucleation of a grain-boundary fissure.

dary can act as a barrier to the movement of dislocations so that a pile-upoccurs and nucleates a micro-crack. Such a crack continues to grow asfurther dislocations, possibly generated from the same Frank-Readsource, move to join it. Dislocations will not cross grain boundaries sincelack of alignment and some disorder will always be present there.

Crack initiation can also be caused by movement of dislocations alongclose-packed or other planes within a crystal (Fig. 5.8(i)). These dislo-cations then pile up at the intersections of the slip planes and so form acrack (Fig. 5.8(ii)).

5.42 It was shown earlier (5.22) that, arising from Griffith's CrackTheory, at the tip of the crack:

/ Crack lengthStress concentration oc J——-—: —v Crack-tip radius

Thus the spread of a crack in a plate glass window is arrested by drillinga hole in front of the tip of the advancing crack. Similarly, catastrophicbrittle fracture in welded-steel ships (5.50) was prevented by includingdummy rivet holes to arrest the progress of cracks already initiated atstructural faults in the steel.

Fig. 5.8 The initiation of a micro-crack by a running together of dislocations (after A. H.Cottrell).

plane

plane

plane

cleavageplane

micro-crack

EDGE DISLOCATIONS

SLIP PLANE

MICRO-CRACK

Ductile-Brittle Transition in Steels

5.50 There have been many instances in the past of failure of metals byunexpected brittleness at low temperatures. That is, metals which sufferednormal ductile fracture at ambient temperatures would fail at low tempera-tures by sudden cleavage fracture and at comparatively low stresses. Thefailure of the motor sledges during the very early stages of the BritishSouth Pole Expedition of 1912-13 may well have been due to fracture ofthis type and contributed towards the final disaster which overtook thePolar party. In more recent years similar failure was experienced in thewelded 'liberty ships' manufactured during the Second World War forcarrying supplies from America to Europe and was unexpected anddangerous.

Under normal conditions the stress required to cause cleavage is higherthan that necessary to cause slip, but if, by some circumstances, slip issuppressed, brittle fracture will occur when the internal tensile stressincreases to the value necessary to cause failure. This situation can ariseunder the action of bi-axial or tri-axial stresses within the material. Suchstresses may be residual from some previous treatment, and the presenceof points of stress concentration may aggravate the situation. The libertyships mentioned above were fabricated by welding plates together to forma continuous body. Cracks usually started at sharp corners or arc-weldspots and propagated right round the hull, so that, finally, the ship brokein half. Had the hull been riveted, the crack would have been arrested atthe first rivet hole it encountered. Some riveted joints are now in factincorporated in such structures to act as crack arresters.

5.51 The relationship between mechanical properties and the methodof stress application has already been mentioned (2.52) with particularreference to the impact test. Plastic flow depends upon the movement ofdislocations and this occurs in some finite time. If the load is applied veryrapidly it is possible for stress to increase so quickly that it cannot berelieved by slip. A momentary increase of stress to a value above the yieldstress will produce fracture.

5.52 As temperature decreases, the movement of dislocations becomesmore difficult and this increases the possibility of internal stress exceedingthe yield stress at some instant. Brittle fracture is therefore more commonat low temperatures. This is supported by the fact that the liberty shipswere in service in the cold North Atlantic.

5.53 Those metals with a FCC structure maintain ductility at low tem-peratures, whilst some metals with structures other than FCC tend toexhibit brittleness. BCC ferrite is particularly susceptible to brittle fracture,which follows a transcrystalline path along the (100) planes (see 4.12). Thisoccurs at low temperatures as indicated in Fig. 5.9 and the temperature atwhich brittleness suddenly increases is known as the transition temperature.

Other things being equal, as the carbon content of a steel increases sodoes the transition temperature, making steel more liable to brittle fracturenear ambient temperatures. Phosphorus has an even stronger effect in

Fig. 5.9 The relationship between brittle fracture and temperature for ferritic and austeniticsteels.

raising the transition temperature in steel and this is one reason why phos-phorus is one of the least desirable impurities in ordinary carbon steels.Some elements, notably manganese and nickel, have the reverse effect inthat they depress the transition temperature. Thus, for applications involv-ing atmospheric temperatures the transition temperature can be reducedto safe limits by increasing the manganese-carbon ratio of the steel, whilstat the same time controlling the grain size by small additions of aluminium.A suitable steel contains 0.14% carbon and 1.3% manganese. Where lowertemperatures are involved it is necessary to use low-nickel steels.

Fatigue

5.60 Engineers have long been aware that either 'live' loads or alternatingstresses of relatively small magnitude can cause fracture in a metallic struc-ture which could carry a much greater static or 'dead' load. Under theaction of repeated or fluctuating stresses a metal may become fatigued.Some of the earliest quantitative research into metal fatigue was carriedout in 1861 by Sir William Fairbairn. He found that raising and loweringa 3-tonne mass onto a wrought iron girder some 3 x 106 times would causethe girder to break, yet a static load of 12 tonnes was necessary to causefailure of a similar girder. From further investigations he concluded thatthere was some load below 3 tonnes which could be raised and lowered aninfinite number of times without causing failure. Some ten years laterWohler did further work in this direction and developed the fatigue-testingmachine which bears his name.

Many engineering metals are subjected to fluctuating stresses duringservice. Thus the connecting rods in a piston engine are successively pushed

IMP

AC

T VA

LUE

(j)

AUSTENITIC (F.C.C.) STEEL

FERRITIC(B(ZC.)STEEL

DUCTILEFRACTURE

8 O % BRITTLEWITH DUCTILEFRACTURE ATRIM

BRITTLEFRACTURE

TEMPERATURE ( 0 C)

and pulled; contact springs in electrical switch gear are bent to and fro;rotating axles suffer a reversal of stress direction through every 180° ofrotation; and aircraft wings are continually bent back and forth as theypass through turbulent air. Often a structure will vibrate in sympathy withsome external vibration emanating from equipment such as an air com-pressor. This too may initiate fatigue failure so that fracture by fatigue isprobably the most common cause of engineering failure in metals.

5.61 The yield strength of a material is a measure of the static stress itcan withstand without permanent deformation, and is applicable only tocomponents which operate under static loading. Metals subjected to fluc-tuating or repeated forces fail at lower stresses than do similar metalsunder the action of 'dead' or steady loads. A typical relationship betweenthe number of cycles of stress (N) and the stress range (S) for a steel isshown in the S-N curve (Fig. 5.10 (H)). This indicates that if the stress inthe steel is reduced then it will endure a greater number of stress cycles.The curve eventually becomes almost horizontal indicating that, for thecorresponding stress, the member will endure an infinite number of cycles.The stress born under these conditions is called the fatigue limit, 5D. Formany steels the fatigue limit is approximately one half of the tensilestrength as measured in a 'static' test.

5.62 Most non-ferrous metals and alloys and also some steels operatingunder conditions of corrosion, give S-N curves of the type shown in Fig.5.10(iii). Here there is no fatigue limit as such and a member will failultimately if subjected to the appropriate number of stress reversals evenat extremely small stresses. With such materials which show no fatigue

Str

ess

(S)

Str

ess

(S)

Fig. 5.10 (i) Represents a test piece suffering alternating stress of range S about a meanvalue of zero; (ii) a typical S-N curve for steel; (iii) an S-N curve typical of many non-ferrousalloys and some steels, particularly those operating under conditions promoting corrosion.

No. of Stress Cycles (N)Na of Stress Cycles (N)

fatigue limit(%) endurancelimit i\)

cantilevertest-piece No. of Stress Cycles (N)

limit an endurance limit, SN, is used instead. This is the maximum stresswhich can be sustained for a stated number, N, of cycles of stress.Components made from materials of this type must therefore be designedwith some specific life (in terms of stress cycles) in mind and then 'junked'—as our American friends put it—after an appropriate working life, thatis, before the number of cycles (N) for the corresponding stress (S) hasbeen reached.

It should be noted that many authorities now use the terms 'fatigue limit'and 'endurance limit' to mean the same, but the above distinction stillseems valid in differentiating between the two classes of S-N curveobtained for different materials.

5.63 Fatigue-testing machines vary in design but many are based onthe original Wohler concept (Fig. 5.11). Here the test piece is in the formof a cantilever which rotates in a chuck, the load, W, being applied at the'free' end. For every rotation of 180° the stress will change from W in onedirection to W in the opposite direction. Thus the stress-range will be 2Wwith a mean value of zero. To determine the fatigue limit (or endurancelimit) a number of test pieces are tested in this way, each at a differentvalue of W, until failure occurs, or alternatively, until an infinite numberof stress reversals have been endured—since it is somewhat impracticableto apply an infinite number of reversals, a large number (say 20 x 106) isused instead.

ST

RE

Ss

(S)

Fig. 5.11 The principles of a simple fatigue-testing machine in which the stress range, S= 2W.

NUMBER OF REVERSALS OF STRESS ( N )

FATIGUE LIMIT

S/N CURVE

EQUIVALENTCANTILEVEREFFECT

FINAL TEAR

(CRYSTALLINE)

FATIGUE CRACK(BURNISHED)

REVOLUTIONCOUNTER

BALL RACE

TEST PIECECHUCK

LOADING SYSTEM

5.64 The Mechanism of Fatigue Failure Fatigue failure begins quiteearly in the service life of the member by the formation of a small crack,generally at some point on the external surface. This crack then developsslowly into the material in a direction roughly perpendicular to the maintensile axis. Ultimately the cross-sectional area of the member will havebeen so reduced that it can no longer withstand the applied load andordinary tensile fracture will result. A fatigue crack 'front' advances a verysmall amount during each stress cycle and each increment of advance isshown on the fracture surface as a minute ripple line. These ripple linesradiate out from the origin of fracture as a series of approximately concen-tric arcs. The individual ripples are far too small to be visible on thefractured surface except by using very high-powered metallographicmethods, but under practical conditions a few ripples much larger than therest, probably corresponding to peak stress conditions, are produced andthese are visible on the fractured surface showing the general path whichthe crack has followed (Fig. 5.12).

Fig. 5.12 The progress of fatigue failure.A fatigue fracture is often easy to identify because the crack-growth region is burnished bythe mating surfaces rubbing together as stresses alternate. The ultimate fracture is strongly'crystalline' in appearance.

A fatigue fracture thus develops in three stages—nucleation, crackgrowth and final catastrophic failure. Since the crack propagates slowlyfrom the source, the fractured surfaces rub together due to the pulsatingnature of the stress and so the surfaces become burnished whilst stillexhibiting the conchoidal markings representing the large ripples. Finalfracture, when the residual cross section of the member is no longer ableto carry the load, is typically crystalline in appearance. Fatigue failures inmetals are therefore generally very easy to identify.

Fatigue cracks are not the result of brittle fracture but of plastic slip.During cyclic stressing, at stresses above the fatigue limit, plastic defor-mation is produced continuously and alternately positive and negative. Itis this continuous to-and-fro plastic deformation in localised regions whichultimately propagates and spreads a fatigue crack. The continual plasticoscillation of metal layers along slip planes in and out of the surface causes

burnishedcrystalline

FRACTURECRACK GROWTHNUCLEATION

some of the metal to produce ridges as work hardening sets in to resist'back slip'. These ridges are forced up at the surface and are termedextrusions (Fig. 5.13). Narrow fissures or intrusions are formed in a similarmanner. Several of these intrusions may then interconnect to initiate thestart of a fatigue crack.

Fig. 5.13 (i) Stages in the formation of an extrusion by movements of blocks of atomsalong slip planes; (ii) the nature of extrusions and intrusions.

5.65 Some Causes of Fatigue Failure Since the fatigue character-istics of metals can be measured accurately, it seems reasonable to supposethat fatigue failure due to a lack of appropriate allowances in design shouldnot occur. This is of course true, yet fatigue failure does continue to happeneven in the most sophisticated items of engineering equipment. The cata-strophic fatigue failure in Comet airliners some years ago is a case in point.In many such instances a member may be designed to carry a static load(well above 5Dor SN), yet it may be suffering undetected vibrations whichgive rise to reversal of stress at a value above SD (or SN). Such vibrationsare often sympathetic.

Other design faults include the presence of such stress raisers as a sharp-cornered key way in a shaft or an unduly sharp radius in an in-cut corner.Poor workmanship in the shape of surface roughness, scratches or carelesstoolmarks can also cause stress concentrations. Minute quench cracks inheat-treated steels are also a source of fatigue failure as are the presenceof small cavities, inclusions or other discontinuities just below the surfaceof the material. A surface weakened by decarburisation or other types ofdeterioration which have led to the softening and weakening of the surfacelayers also favours the initiation of micro-cracks via the formation ofintrusions.

Corrosive conditions in the environment can also provide stress-raisersin the form of etch-pits and other surface intrusions such as grain boundaryattack. Ordinary surface oxidation may have a similar effect and conse-quently nucleate a fatigue crack.

5.66 Methods of Improving Fatigue Strength In order to maintainfatigue strength it follows from the above that surface finish should always

slipplane EXTRUSION

INTRUSION

slipplanes

be good. Engineer craftsmen of the past were not wasting their time whenproducing a high surface polish on many of their items of equipment.

Since the fatigue strength of a metal is approximately proportional to itstensile strength, any method used to increase the tensile strength of thematerial will correspondingly improve the fatigue strength. As fatigue fail-ure nearly always commences at the surface, methods of surface hardeningwill be most effective in limiting the initiation of fatigue cracks. Thus,work-hardening of the surface by shot-peening is beneficial, whilst thecarburising and nitriding (19.10) of steels will improve fatigue strength. Acase-hardened axle provides a good all-round combination of core tough-ness, surface wear-resistance and fatigue resistance.

Creep

5.70 So far in this description of plastic deformation and ultimate failureof metals little mention has been made of the part played by time. Never-theless, metals in service are often required to withstand steady stressesover long periods of time and it has been shown that under these conditionsgradual deformation of the metal may occur at all temperatures andstresses. Metals can therefore fail in this way at a stress well below thetensile strength at that particular temperature. This phenomenon of con-tinuous gradual extension under a steady force is known as creep.

The effects of creep in most engineering metals are not serious at ambi-ent temperatures though some metals of low melting point (Tm) such aslead exhibit noticeable creep under these conditions. Lead sheeting whichmay have been protecting a church roof for centuries is sometimes foundto be slightly thicker near the eaves than at the ridge. The lead has 'crept'under its own weight over the centuries.

Creep becomes very serious with many metals at temperatures above0.4rm where Tm, as noted previously (4.42) is measured on the Kelvin (or'absolute') scale. Thus Tm for lead is equivalent to 327 + 273 or 600 K.Hence 0.4 Tm (for lead) is 240 K or -33°C. This explains why lead sheetingon a church roof will be likely to creep appreciably at ambient temperaturesbetween, say, — 100C and 300C. Similarly the effects of creep must be veryseriously considered in the design of gas and steam turbines, steam andchemical plant and furnace equipment. Creep is thus associated in practicalterms with both time and temperature and is basically due to slip by themovement of dislocations.

5.71 Fig. 5.14 shows the type of creep curve obtained when a metal issuitably stressed. This curve indicates that, following the initial elasticstrain, the plastic strain associated with creep occurs in three stages:

(i) Primary, or transient creep, EP, beginning at a fairly rapid ratewhich then decreases with time because work-hardening sets in.

(ii) Secondary, or steady-rate creep, PS, in which the rate of strain isuniform and at its lowest value.

(iii) Tertiary creep, SX, in which the rate of strain increases rapidly

TIME

Fig. 5.14 A typical creep curve, showing three stages of creep during a long-time, hightemperature creep test.

until fracture occurs at X. This stage coincides with necking of the testpiece.The form of relationship which exists between stress, temperature and

the resultant creep rate is shown in Fig. 5.15. At a low stress and/or a lowtemperature (curve A) some primary creep occurs but this falls to a neglig-ible value as strain-hardening prevents further slip from taking place. Withincreased stress and/or temperature (curves B and C) the rate of secondarycreep also increases leading to tertiary creep and ultimate failure.

STR

AIN

STR

AIN

primary" creep

secondarycreep

tertiarycreep

initial elastic strain

low temperatureand/or low stress

high temperatureand/or high stress

TIME

Fig. 5.15 Variations of creep rate with stress and temperature.In curve A the creep rate soon becomes negligible as work-hardening sets in. In curve Cthe creep rate is higher than in curve B because of the use of either higher stress or highertemperature.

5.72 In creep testing, the specimen, in form similar to a tensile testpiece, is enclosed in a thermostatically controlled electric tube furnacewhich can be maintained with accuracy over long periods at any giventemperature up to 10000C or more. A simple lever system is often used toload the test piece, and some form of delicate extensometer or strain-gaugesystem employed to measure the resultant extension at suitable time inter-vals. The extensometer is sometimes of the optical type, using mirrors,scales and telescopes.

Creep values were originally assessed in terms of the limiting creep stress.This was defined as that stress at any given temperature, below whichno measurable creep takes place. Obviously this value depends upon thesensitivity of the measuring equipment and in any case it is now knownthat some creep occurs at all combinations of stress and temperature.Moreover, since formal creep tests involve long periods of time sometimesrunning into many months, other related tensile values are now usedinstead of the old concept of 'limiting creep stress'.

Most tests involve measuring the stress which will give rise to somepredetermined rate of creep during the secondary stage of uniform defor-mation. The creep rate will therefore be equivalent to the slope of thecurve during the secondary stage of creep. The Hatfield 'time-yield value'is derived from such a short-term creep test. It determines the stress at agiven temperature which will produce a strain of 0.5% of the gauge lengthin the first twenty-four hours and a further strain of not more than onepart per million of the gauge length in the next forty-eight hours. Creeptests of this type do not attempt to derive a 'creep limit' but are practicalvalues upon which engineering design can be based.

5.73 The Mechanism of Creep Creep is a deformation process inwhich three main features appear to be involved:

(i) the normal movement of dislocations along slip planes;(ii) a process known as 'dislocation climb' which is responsible for

rapid creep at temperatures above 0.5 Tm\(iii) slipping at grain boundaries.

In the primary stages of creep, dislocations move quickly at first butsoon become piled-up at various barriers. Nevertheless, thermal activationenables them to surmount some barriers, though at a decreasing rate sothat the creep rate is reduced. At temperatures in excess of 0.5 Tm, thermalactivation is sufficient to promote a process known as 'dislocation climb'(Fig. 5.16). This would bring into use new slip planes and so reduce therate of work hardening. Hence creep is a process in which work hardeningis balanced by thermal softening which allows slip to continue. At lowtemperatures recovery does not take place due to lack of thermal activation(Curve A—Fig. 5.15) and so unrelieved work-hardening leads to a re-duction in the creep rate almost to zero.

In addition to plastic deformation by dislocation movement, deformationby a form of slip at the grain boundaries also occurs during the secondarystage of creep. These movements possibly lead to the formation of 'vacantsites', that is lattice positions from which atoms are missing, and this inturn makes possible 'dislocation climb' (Fig. 5.16). The relationship

Fig. 5.16 Two examples illustrating 'dislocation climb'.In each case this is made possible by the presence nearby of a 'vacant site' (or 'vacancy'),ie a lattice position not occupied by an atom. In both (a) and (b) the dislocation has 'climbed'on to a new slip plane.

between grain boundaries and creep is indicated by the fact that at hightemperatures fine-grained metals creep more than coarse-grained metalsof the same compositions, presumably because the fine-grained metalscontain a higher proportion of grain-boundary region per unit volume ofmetal. At low temperatures, where the grain-boundary material is more'viscous', fine-grained metals are more creep-resistant and generallytougher.

In the tertiary stage of creep micro-cracks are initiated at grain boun-daries due largely to the movement of dislocations, but in some cases tothe migration of vacant sites there. Necking and consequent rapid failurefollow.

5.74 Creep Resistance This can be increased by impeding the move-ment of dislocations in a metal and also by inhibiting the formation of newones. Thus the presence of solute atoms (8.21) which do not diffuse rapidlywill 'pin down' dislocations effectively; whilst the presence of small dis-persed particles of a hard, strong constituent will have a 'particle-hardening' effect (8.62) by acting as barriers to the movement of adislocation front. The high-temperature 'Nimonic' series of alloys (18.32)rely on this type of strengthening mechanism.

Exercises1. Distinguish, with the aid of sketches, between ductile and brittle fracture. (5.20

and 5.30)2. Show how Griffith's Crack Theory explains the considerable effects which the

presence of microstructural faults have as stress raisers in a metal in tension.Why is cast iron weak in tension but strong in compression? (5.22)

3. What are the principal causes of intercrystalline brittle fracture? (5.24)

vacantsite

(a)

(b)

4. What are the main factors leading to crack formation in metals under the influ-ence of mechanical stress? (5.40)

5. Discuss the relationship between impact value and service temperature for a0.2% carbon steel. How may the properties of such a steel be improved forservice at sub-zero temperatures? (5.50)

6. Write a short account of the importance of a consideration of fatigue in engineer-ing design. (5.60)

7. Define the term fatigue limit and show how the character of this value varies asbetween ferrous and non-ferrous materials. Describe a method used to deter-mine the fatigue limit of a given steel. (5.61 and 5.63)

8. Why is the concept of limiting creep stress no longer used as a criterion of creepphenomena? What other values are used to quantify creep and how are theyderived? (5.72)

9. Creep is a high-temperature phenomenon. Show by what stages and mechanismsit proceeds. (5.71 and 5.73)

Bibliography

American Society for Metals, Case Histories in Failure Analysis.Biggs, W. D., The Brittle Fracture of Steel, Macdonald and Evans, 1960.Chell, G. G., Developments in Fracture Mechanics, Applied Science, 1979.Colangelo, V. J. and Heiser, F. A., Analysis of Metallurgical Failures, John Wiley,

1974.Duggan, T. V. and Byrne, J., Fatigue as a Design Criterion, Macmillan, 1977.Fuchs, H. O. and Stephens, R. I., Metal Fatigue in Engineering, John Wiley, 1980.Kennedy, A. J., Processes of Fatigue and Creep in Metals, Oliver and Boyd.Osborne, C. J., Fracture, Butterworths, 1979.Smallman, R. E., Modern Physical Metallurgy, Butterworths, 1985.Sully, A. H., Creep, Butterworths.BS 3518: 1984 Methods of Fatigue Testing.BS 3500: 1987 Methods for Creep and Rupture Testing of Metals.