Tempering of martensite

8.3.5 Tempering of martensite

The presence of martensite in a quenched steel, while greatly increasing its hardness and TS, causes the material to be brittle. Such behaviour is hardly surpris- ing, since the formation of martensite is accompanied by severe matrix distortions. The hardness and strength of martensite increase sharply with increase in C con- tent. Contributions to the strength arise from the carbon in solution, carbides precipitated during the quench, dislocations introduced during the transformation and the grain size.

Although the martensite structure is thermodynam- ically unstable, the steel will remain in this condition more or less indefinitely at room temperature because for a change to take place bulk diffusion of car- bon, with an activation energy Q of approximately

83 kJ/mol atom is necessary. However, because there is an exponential variation of the reaction rate with temperature, the steel will be able slowly to approach the equilibrium structure at a slightly elevated temper-

a carefully controlled tempering treatment, the quench- ing stresses can be relieved and some of the carbon can precipitate from the supersaturated solid solution to form a finely dispersed carbide phase. In this way, the toughness of the steel can be vastly improved with very little detriment to its hardness and tensile properties.

The structural changes which occur on tempering may be considered to take place in three stages. In the primary stage, fine particles of a cph carbide phase (ε-carbide) of composition about Fe 2,4

C, pre- cipitates, with the corresponding formation of low- carbon martensite. This low-carbon martensite grows at the expense of the high-carbon martensite until at the end of this stage the structure consists of retained austenite, ε-carbide and martensite of reduced tetrago- nality. During the second stage any retained austenite in the steel begins to transform isothermally to bainite, while the third stage is marked by the formation of cementite platelets. The precipitation of cementite is accompanied by a dissolution of the ε-carbide phase so that the martensite loses its remaining tetragonality and becomes bcc ferrite. The degree to which these three stages overlap will depend on the temperature of the anneal and the carbon content. In consequence, the final structure produced will be governed by the initial choice of steel and the properties, and hence thermal treatment, required. Alloying elements, with the exception of Cr, affect the tempering of marten- site. Plain carbon steels soften above 100 °

C owing to the early formation of ε-carbide, whereas in Si-bearing steels the softening is delayed to above 250 °

C, since

Strengthening and toughening 283 Si stabilizes ε-carbide and delays its transformation

elements should therefore be chosen to produce the to cementite. Alloying additions (see Table 8.2) thus

maximum retardation of tempering for minimum enable the improvement in ductility to be achieved at

depression of M s ; Table 8.2 shows that (1) C should higher tempering temperatures.

be as low as possible, (2) Si and Co are particularly When a steel specimen is quenched prior to temper-

effective, and (3) Mo is the preferred element of the ing, quenching cracks often occur. These are caused

Mo, W, V group since it is easier to take into solution by the stresses which arise from both the transfor-

than V and is cheaper than W. mation and the differential expansion produced when

Some elements, particularly Mo and V, produce different parts of the specimen cool at different rates.

quite high tempering temperatures. In quantities above To minimize such cracking, the desired properties of

about 1% for Mo and 1 % for V, a precipitation reac- toughness and strength are often produced in the steel

tion is also introduced which has its maximum hard- 2 by alternative heat-treatment schedules; examples of

C. This phenomenon of increased these schedules are summarized in Figure 8.28, from

ening effect at 550 °

hardness by precipitation at higher temperatures is which it will become evident that advantage is taken of

known as secondary hardening and may be classified the shape of the TTT curve to economize on the time

as a fourth stage of tempering. 2–2 1 Mo addition pro- the specimen is in the furnace, and also to minimize

duces adequate temper resistance and changes the pre- 2 quenching stresses. During conventional annealing, for

cipitate to Mo 2 C which is more resistant to overageing example, the steel is heated above the upper critical

7 3 which is present in most alloy steels. High nace. In isothermal annealing the steel is allowed to

than Cr C

temperature and allowed to cool slowly in the fur-

V additions lead to undissolved V 4 C 3 at the quench- transform in the furnace, but when it has completely

ing temperature, but 0.5 V in conjunction with 2Mo transformed, the specimen is removed from the fur-

does not form a separate carbide during tempering but nace and allowed to air-cool, thereby saving furnace

dissolves in the Mo 2 C. Cr also dissolves in Mo 2 C time. In martempering, the knee of the TTT curve is

but lowers the lattice parameters of the carbide and avoided by rapid cooling, but the quench is interrupted

hence lowers the temper resistance by decreasing the above M s and the steel allowed to cool relatively

matrix/carbide mismatch. However, 1Cr may be toler- slowly through the martensite range. With this treat-

ated without serious reduction in temper resistance and ment the thermal stresses set up by very rapid cooling

reduces the tendency to quench crack. Si decreases the are reduced. Such a procedure is possible because at

lattice parameter of matrix ferrite and hence increases the holding temperature there is ample time for the

temper resistance. A typical secondary hardening steel temperature to become equal throughout the sample

usually contains 0.4C, 2Mo, 0.5V, 0.5Si and 1.5Cr, before the transformation begins, and as a result the 2 with 1.8 GN/m TS and 15% elongation.

transformation occurs much more uniformly. After the transformation is complete, tempering is carried out

8.3.6 Thermo-mechanical treatments

in the usual way. In austempering, quenching is again arrested above M s and a bainite product, having sim-

To produce steels with an improved strength/ductility ilar properties to tempered martensite, is allowed to

ratio the heat-treatment may be modified to include form.

a deformation operation in the process. The combined Alloying elements also lower the M s temperatures

use of mechanical working and heat-treatment is gener- and, consequently, greater stresses and distortion are

ally called thermo-mechanical treatment (THT). Three introduced during quenching. This can be minimized

types of treatment have proved successful with marten- by austempering and martempering as discussed

sitic and bainitic steels. These may be classified as above, but such treatments are expensive. Alloying

follows:

1. Deformation in the stable austenite range above A 3

Table 8.2 Influence of alloying additions on tempering

before transformation, i.e. (HTHT).

2. Deformation below A 1 before transformation; this Element

(LTHT) low-temperature thermo-mechanical treat- tempering per 1%

Retardation in

Ratio of retardation

ment is called ausforming. addition

of tempering to

depression of M s

3. Deformation during isothermal transformation to pearlite, i.e. below A 3 , known as isoforming.

C 40 negative

Co

8 > 8 The main advantage of HTHT is in grain refine- Cr

0 0 ment, and steels such as silicon-steels that recrystallize Mn

8 0.24 slowly are particularly suitable. It can, however, be Mo

17 0.8 applied to low-alloy high-carbon tool steels which are Ni

8 0.5 not suitable for ausforming, with significant increases Si

in strength and toughness. The fatigue limit is also

V 30 1.0

10 0.9 improved in many steels provided the deformation is limited to 25–30%. In ausforming, the deformation is

284 Modern Physical Metallurgy and Materials Engineering

Figure 8.28 Diagrams showing the heat-treatment procedure during (a) isothermal annealing, (b) martempering and (c) austempering .

usually carried out in the range 450–550 °

C and hence

the steel must have a large bay in the TTT diagram to enable the deformation to be carried out. A suitable steel is Fe–0.35C–0.5Mn–1.5Ni –1.25Cr–0.25Mo for which the strength increases by about 4.6–7.7 MN/m 2 for each per cent of deformation. The properties are improved as the deformation temperature is lowered, provided it is not below M s , and with high deformation treatments ⊲>70%⊳ strengths up to about E/70 with good ductility have been achieved. A very fine carbide dispersion is produced in the austenite during deforma- tion together with a high density of dislocations. The removal of carbon from solution in the austenite means that during transformation the martensite formed is less

Figure 8.29 Model for estimating the theoretical fracture supersaturated in C and thus has lower tetragonality

and is more ductile. The carbides also pin the dis- locations in the austenite, helping to retain some of

where u is the displacement from the equilibrium them together with those formed during the transfor-

mation. The martensite formed is therefore heavily dis- located with relatively stable dislocations (compared to t

planes it is necessary to supply the surface energy those which would be formed by deforming marten-

and hence

site at room temperature), and has superior strength and toughness. Such steels are, of course, somewhat

difficult to machine.

du D Isoforming has potential in improving the toughness 0

D t sin

of low-alloy steels. During isoforming to pearlite the so that the theoretical tensile strength is given by normal ferrite/pearlite structure is modified, by the polygonization of sub-grains in the ferrite and the

(8.22) spheroidizing of cementite particles. Isoforming to bainite is also possible.

t D ⊲E /b⊳

Glass fibres and both metallic and non-metallic whiskers have strengths approaching this ideal value of about E/10, but bulk metals even when tested under

8.4 Fracture and toughness

favourable conditions (e.g. at 4 K) can rarely withstand stresses above E/100. Griffith, in 1920, was the first to

suggest that this discrepancy was due to the presence Most materials break at a stress well below the theo-

8.4.1 Griffith micro-crack criterion

of small cracks which propagate through the crystal

and cause fracture. Griffith’s theory deals with elastic to pull apart two adjoining layers of atoms. This stress

t , required

cracks, where at the tip of the crack atomic bonds varies with the distance between the atom planes and,

exist in every stage of elongation and fracture. As the as shown in Figure 8.29, may be approximated to a

crack grows, each of the bonds in its path take up the sine curve of wavelength such that

strain, and the work done in stretching and breaking these bonds becomes the surface energy of the fractured faces. If separation of the specimen between

t sin

two atomic layers occurs in this way, the theoretical

Strengthening and toughening 285 strength only needs to be exceeded at one point at a

time, and the applied stress will be much lower than the theoretical fracture stress. The work done in breaking the bonds has to be supplied by the applied force, or by the elastic energy of the system. Assuming for a crack of length 2c that an approximately circular region of

2 by the presence of the crack, the condition when the elastic strain of energy balances the increase

of surface energy is given by

D ⊲ dc 2c ⊳ 2E dc and leads to the well-known Griffith formula

crack of length 2c. The Griffith criterion therefore depends on the assumption that the crack will spread if the decrease in elastic strain energy resulting from an increase in 2c is greater than the increase in surface energy due to the increase in the surface area of the crack.

Griffith’s theory has been verified by experiments on glasses and polymers at low temperatures, where a simple process of fracture by the propagation of elastic cracks occurs. In such ‘weak’ brittle fractures there is little or no plastic deformation and is mainly

Figure 8.30 Variation of stress from the tip of a crack and

the surface energy ⊲³1–10 J m 2 ⊳ and the fracture

the extent of the plastic zone, radius r y .

f ³ 10 5 E . In crystalline solids, however, the cracks are not of the elastic type and a plastic zone

so that equation (8.23) becomes the Orowan–Irwin exists around the crack tip as shown in Figure 8.30.

relationship

In such specimens, fracture cannot occur unless the (8.24)

t . For an atomically sharp crack (where the

4 2 2 radius of the root of the crack r is of the order of b) of 3 Here, G might be ¾10 Jm f ³ 10 –10 E . p

⊲c/r⊳ which, if the crack is

8.4.2 Fracture toughness

to propagate, must be equal to the theoretical fracture In engineering structures, particularly heat-treated stress of the material at the end of the crack. It follows

steels, cracks are likely to arise from weld defects,

inclusions, surface damage, etc. and it is necessary to leads to the Griffith formula of equation (8.23).

t in equation (8.22)

design structures with the knowledge that cracks are Figure 8.30 shows the way the magnified stress

already present and capable of propagation at stresses drops off with distance from the tip of the crack.

below the macroscopic yield stress as measured in a Clearly, at some distance r y the stress reaches the

tensile test. Since different materials show different yield stress and plastic flow occurs. There is thus a

crack propagation characteristics (e.g. hard steel and zone of plastic flow around the tip of radius r y . The

glass) it is necessary for the design engineers to find larger the plastic zone, as in ductile metals, the more

the limiting design stress in terms of some property energy is absorbed in fracture. In ceramics this zone

or parameter of the material. For this reason, a is usually small.

fracture toughness parameter is now being employed In ‘strong’ fractures is greatly increased by the

to measure the tendency of cracks of given dimensions contribution of the plastic work around the crack

to propagate under particular stress conditions. p tip which increases the work required for crack

propagation. The term must now be replaced by ⊲ C ⊲EG⊳ , which indicates that fast fracture will occur p ⊳ where p is the plastic work term; generally ⊲ C p ⊳ is replaced by G, the strain energy release rate,

reaches some critical size, or alternatively when a

286 Modern Physical Metallurgy and Materials Engineering material containing a crack is subjected to some critical

y is also required. The chart shows that

steel satisfies both these requirements and indicates length for fast fracture is a constant, ⊲EG⊳ for the

why it is still the best material for highly stressed material, where E is Young’s modulus and G is the p

structures where weight is not important.

Fracture toughness requirements are now written the symbol K and is called the stress intensity factor

is given

into the general specification of high-technology alloys with units MN m 3/2 . Fast fracture will then occur

when K D K c , where K c [D p ⊲EG c ⊳ ] is the critical

and hence it is necessary to determine the effect

of heat-treatment and alloying additions on fracture stress intensity factor, or more commonly the fracture

toughness parameters. Processes such as ausforming toughness parameter.

and controlled rolling improve the fracture toughness The fracture toughness of a material can alter

of certain steels. Carbon has a considerable effect and markedly depending on whether the elastic-plastic

there are advantages in reducing the C-level below field ahead of the crack approximates to plane strain

0.1% where possible. High-strength low-alloy (HSLA) or plane stress conditions, much larger values being

steels have C ⱽ 0.1% and the Nb, V and Ti addi- obtained under plane stress conditions as operate in

tions form fine carbides which together with the small thin sheets. The important and critical factor is the

grain sizes enable good strength levels and acceptable size of the plastic zone in relation to the thickness of

fracture toughness values to be achieved. Maraging the section containing the crack. When this is small,

steels with high alloy and low carbon ⊲<0.04%⊳ give as in thick plates and forgings, plane strain conditions

very high strength combined with high toughness (see prevail and the hydrostatic tension ahead of the crack

Chapter 9).

results in a semi-brittle ‘flat’ fracture. When the value The brittleness of ceramics is directly linked to their is large as in thin sheets of ductile metals plane stress

high notch-sensitivity. The fracture toughness of most conditions operate and the tension at the crack front is

ceramics is low: expressed in quantitative terms, it is commonly less than 8 MN m smaller, giving rise to a more ductile mode of failure. 3/2 . Flaws, often very

At intermediate values a mixed fracture, with a flat minute, are almost invariably present in ceramics and centre bordered by shear lips, is obtained. Thus with-

act as stress-concentrating notches. It is extremely dif- out changing the structure or properties of the materials

ficult to prevent these flaws from forming during man- in any way it is possible to produce a large differ-

ufacture and service. In terms of engineering practice, ence in fracture toughness by changing the section

brittle ceramic components are intolerant of misalign- thickness. For thick sections, when a state of complete

ment and poor fits within assemblies. The presence of constraint is more nearly approached, the values of K c flaws is also responsible for the variability or ‘spread’

and G c approach minimum limiting values. These val- of results from mechanical tests and introduces uncer-

ues are denoted by K Ic and G Ic and are considered to

tainty into the design process. (The ‘spread’ is much

be material constants; the subscript I denotes the first less for metallic materials.) Design procedures have mode of crack extension, i.e. the opening mode (see

moved well beyond the principle that ceramics are only Figure 8.31).

safe when compressive stresses are dominant. Prob- The general procedure in measuring the fracture

abilistic assessments of mechanical test results from toughness parameter is to introduce a crack of suit-

ceramics now tackle the difficult task of allowing for able size into a specimen of suitable dimension and

randomness in the size, shape and distribution of flaws geometry. The specimen is then loaded at a slow rate

(see Section 10.6).

and the crack extension measured up to the critical Despite these underlying problems, progress has

been made in producing tough ‘ductile ceramics’. plastic zone size is small (by a factor 10) in relation

condition. The measurement of K Ic will be valid if the

to the cross-section of the specimen. The zone size r y may be obtained by equating the stress field of the crack at r D r y

y of the material and

is given by r y DK 2 Ic 2 / y

An Ashby property chart of fracture toughness versus strength, given in Figure 8.32, shows that the size of the zone (broken lines) varies from atomic dimensions for brittle ceramics to tens of centimetres for ductile metals.

In designing safe structures for a given load, the structure is required to yield before it breaks. For a minimum detectable crack size of 2c this condition is

p . The safest material is the

given by ⊲K Ic y ⊳½

Figure 8.31 Variation in the fracture toughness parameter

one with the greatest value of K Ic y . Clearly, a high

with section thickness .

Strengthening and toughening 287

Figure 8.32 Ashby property chart of fracture toughness versus strength (Ashby, 1989, pp. 1273–93; with permission of Elsevier Science Ltd) .

Fracture toughness values above 20 MN m 3/2 have These remarks refer to tensile stresses since compres- been achieved. Typical measures include elimination

sive stresses will, of course, tend to close the crack. of flaws (microcracks, pores), incorporation of crack-

In some polycrystalline ceramics, such as magnesia, retarding phases (in zirconia) and reduction of average

the von Mises criterion for maintenance of cohesions grain size (below 1 mm).

is not satisfied. Slip is limited and cracks are not effec- At ambient temperature, fracture surfaces of ceram-

tively blunted. However, raising the temperature often ics are conchoidal (glassy), intergranular or cleavage

enables the necessary minimum of five independent in character, depending on the material. The strain

deformation modes to operate, leading to ductility. Any at fracture is very small, being about 0.001. At ele-

treatments which eliminate surface flaws will natu- vated temperatures, under creep conditions, fracture

rally enhance this ductility. (Against this background, strain is greater. Conventional ceramics have little

one can readily appreciate why fabrication methods or no capacity for slip and crack tips therefore tend

for polycrystalline ceramic components, in contrast to to remain sharp. As the crack propagates, the load-

those for metals, are not based upon bulk deforma- supporting cross-section gets smaller and the general

tion.) At these higher temperatures the environment level of stress increases so that failure can be sudden.

becomes increasingly more likely to react with surfaces

288 Modern Physical Metallurgy and Materials Engineering of the ceramic: it may even penetrate an open texture

to brittle cleavage behaviour is quite spectacular and and cause crack-blunting. The mechanisms of flow

has led to several engineering catastrophes. In general, in polycrystalline ceramics at elevated temperatures

brittle cleavage can occur in metals with bcc and cph are similar to those encountered in metallic systems

under the appropriate conditions while in fcc materials (e.g. glide and climb of dislocations, vacancy diffu-

it does not. The most important factor linking these sion, grain boundary sliding). The similarity between

three different structures is the Peierls stress and the deformation processes in polycrystalline ceramics and

way the yield stress varies with temperature. In steel, metals is evident if one compares the layout of the

for example, the yield stress increases rapidly with corresponding deformation-mechanism maps. A minor

lowering of temperature below room temperature such phase is usually present at grain boundary surfaces in

that plastic deformation at the crack tip is minimized ceramics, functioning as a ceramic bond, and if it soft-

and the fracture mechanism changes from plastic tear- ens with rise in temperature, then the grains may be

ing to cleavage. Even in these materials some plastic able to slide past each other. These regions tend to

deformation does occur.

liquefy before the actual grains so that it is advisable Several models have been suggested for the pro- not to exceed the solidus temperature. Grain boundary

cess whereby glide dislocations are converted into surfaces are particularly susceptible to the nucleation

micro-cracks. The simplest mechanism, postulated by of cracks. As in the final accelerating stage of metal-

Stroh, is that involving a pile-up of dislocations against lic creep, these cracks form in planes normal to the

a barrier, such as a grain boundary. The applied direction of applied stress.

stress pushes the dislocations together and a crack forms beneath their coalesced half-planes, as shown

8.4.3 Cleavage and the ductile –brittle

in Figure 8.33a. A second mechanism of crack for-

transition

mation, suggested by Cottrell, is that arising from the junction of two intersecting slip planes. A dislocation

The fracture toughness versus strength chart, shown gliding in the ⊲1 0 1⊳ plane coalesces with one gliding in Figure 8.32, indicates the wide spread of values

in the ⊲1 0 1⊳ plane to form a new dislocation which for the different classes of material. Metals dissi-

lies in the ⊲0 0 1⊳ plane according to the reaction, pate much energy in the plastic zone, which accounts for the difference between the fracture energy G Ic a/ 2[1 1 1] C a/2[1 1 1] ! a[0 0 1] and the true surface energy . The larger the zone,

The new dislocation, which has a Burgers vector K Ic ⊲³100 MN m 3/2 ⊳ . Ceramics and glasses fracture

the more energy is absorbed; G Ic is high and so is

a [0 0 1], is a pure edge dislocation and, as shown without much plastic flow to blunt the cracks by sim-

in Figure 8.33b, may be considered as a wedge, one ply breaking atomic bonds, leading to cleavage; for

lattice constant thick, inserted between the faces of the these materials K Ic is less than 10 MN m 3/2 .

⊲ 0 0 1⊳ planes. It is considered that the crack can then At low temperatures some metals, notably steels,

grow by means of other dislocations in the ⊲1 0 1⊳ and also become brittle and fracture by cleavage. Since

⊲ 1 01⊳ planes running into it. Although the mechanism they are ductile at room temperature this transition

readily accounts for the observed ⊲1 0 0⊳ cleavage

Figure 8.33 Formation of a crack (a) by the piling up of dislocations against a grain boundary after strain and (b) by the dislocations on ⊲1 0 1 ⊳ and ⊲10 1 ⊳ planes running together (after Cottrell, 1958, p. 192) .

Strengthening and toughening 289 plane of bcc metals, examples have not been directly

here to be half the grain diameter). Once a microcrack observed.

is formed, however, the whole applied tensile stress While these dislocation coalescence mechanisms may operate in single-phase materials, in two-phase

y ð constant), where the constant is included to alloys it is usually easier to nucleate cracks by piling up

account for the ratio of normal stress to shear stress. dislocations at particles (e.g. grain boundary cementite or cementite lamellae in pearlite). The pile-up stress

(equation (8.25)) then fracture should be able to occur then leads to cracking of either the particle or the

y and particle/matrix interface. A brittle–ductile transition can then be explained on the basis of the criterion

(8.27) that the material is ductile at any temperature, if the

where C is a constant. The importance of the avalanche yield stress at that temperature is smaller than the

of dislocations produced at the yield drop can be seen if stress necessary for the growth of these micro-cracks,

i ) but if it is larger the material is brittle. If cleavage

yi

y D i Ck y d 1/2 , when cracks are formed by such a dislocation mechanism,

equation (8.27) becomes

the Griffith formula may be rewritten to take account

i d of the number of dislocations, n, forming the crack. 1/2 Ck y ⊳k y (8.28) Thus, rearranging Griffith’s formula we have

where ˇ is a constant which depends on the stress

2 /E system; ˇ ³ 1 for tensile deformation and ˇ ³ 1 3 for a

notched test.

This is a general equation for the propagation of a the maximum displacement between the faces of the

crack at the lower yield point and shows what factors crack. This displacement will depend on the number

are likely to influence the fracture process. Alternative of dislocations forming the cleavage wedge and may

models for growth-controlled cleavage fracture have

be interpreted as a pile-up of n edge dislocations, each been developed to incorporate the possibility of carbide of Burgers vector a, so that equation (8.23) becomes

particles nucleating cracks. Such models emphasize the importance of yield parameters and grain size as

well as carbide thickness. Coarse carbides give rise to and gives a general criterion for fracture. Physically,

low fracture stresses, thin carbides with high fracture this means that a number of glide dislocations, n, run

stresses and ductile behaviour. together and in doing so cause the applied stress acting

8.4.4 Factors affecting brittleness of steels

on them to do some work, which for fracture to occur must be at least sufficient to supply the energy to create

Many of the effects of alloying, heat treatment, and the new cracked faces, i.e. ⊲ C p ⊳ .

condition of testing on brittle fracture can be rational- Qualitatively, we would expect those factors which

ized on the basis of the above ‘transition’ equation. influence the yield stress also to have an effect on the

ductile–brittle fracture transition. The lattice ‘friction’ Ductile–brittle transition Under conditions where

i , dislocation locking term k y , and grain size 2d the value of the left-hand side of equation (8.28) is less should also all be important because any increase in

than the value of the right-hand side, ductile behaviour

i and k y , or decrease in the grain size, will raise the should be observed; when the left-hand side exceeds yield stress with a corresponding tendency to promote

the right-hand side the behaviour should be brittle. brittle failure.

Since the right-hand side of equation (8.28) varies only These conclusions have been put on a quantitative

slowly with temperature, it is the way in which changes basis by Cottrell, who considered the stress needed

occur in values of the terms on the left of the equation to grow a crack at or near the tensile yield stress,

which are important in determining the ductile–brittle y , in specimens of grain diameter, 2d. Let us con-

transition. Thus, in a given material brittleness should

be favoured by low temperatures and high strain-rate, actual shear stress operating, the effective shear stress

y is the

i and k y ,

i ⊳ , where, it

and by large grain sizes. On the right-hand side, the

i is the ‘friction’ stress resist- typical effect of a sharp notch is to raise the transition ing the motion of unlocked dislocations arising from

temperature of structural steel from around 100 K for the Peierls–Nabarro lattice stress, intersecting disloca-

a normal tensile test into the range of 200–300 K, tions or groups of impurities. The displacement na is

because the value of ˇ is lowered. then given by

Effects of composition and grain size At a con-

i and k y remain fixed, the transition point will occur at a critical grain size above which the metal is brittle and below

of the slip band containing the dislocations (assumed

which it is ductile.

290 Modern Physical Metallurgy and Materials Engineering

Figure 8.34 Influence of hydrogen on fracture behaviour showing (a) time-dependence and (b) temperature-dependence .

i contribution, due to the forma- term, d 1/2

The inclusion in equation (8.28) of the grain-size

tion of intersecting dislocations, vacancy aggregates many previous metallurgical misunderstandings to be

i term, enables

and other lattice defects.

cleared up. It shows that there is no simple connection The importance of twins in fracture is not clear as between hardness and brittleness, since hardening pro-

there are several mechanisms other than twinning for duced by refining the grain size reduces the brittleness,

the formation of a crack which can initiate fracture,

and there is good evidence that micro-cracks form in the brittleness.

i increases

steel in the absence of twins, and that cracks start Heat treatment is generally used to control the grain

at inclusions. Nevertheless, twinning and cleavage are size of the sample and refine the structure. ‘Killed’

generally found under similar conditions of tempera- steel has very good notch toughness, because alu-

ture and strain-rate in bcc transition metals, probably minium additions refine the grain size. Manganese

because both phenomena occur at high stress levels. reduces the grain size and by combining with car-

The nucleation of a twin requires a higher stress than bon also reduces the k y value so that this addition

the propagation of the twin interface. is especially beneficial in improving low-temperature

Irradiation-hardening also embrittles the metal. ductility. It is fairly evident that an improved notch

According to the theory of this type of hardening toughness steel, compared with that used for welded

outlined in Chapter 7, radiation damage can produce ships in World War II, is given by increasing the man-

an increase in both k y (migration to dislocations ganese content and decreasing the carbon content, i.e. a

i (formation of dislocation loops and other aggregated defects).

high manganese-to-carbon ratio. Other additions, par- However, for steel, radiation-hardening is principally ticularly nickel and chromium, have a similar effect on

i contribution, presumably because the dislocations in mild steel are already too

low-temperature ductility.

The Group 6A metals (Cr, Mo and W) are more heavily locked with carbon atoms for any change susceptible to brittle fracture than the Group 5A met-

in the structure of the dislocation to make any als (V, Nb and Ta). A comparison of these metals in

appreciable difference to k y . Nevertheless, a neutron terms of cleavage fracture is difficult, however, since

dose of 1.9 ð 10 23 nm 2 will render a typical fine- Cr, Mo and W are susceptible to grain boundary frac-

grained, unnotched mild steel, which is normally ture because segregation of impurities to such regions

C, quite brittle. Moreover, experiments reduces the effective surface energy . However, even

on notched fine-grained steel samples (see Figure 7.1c) if this effect is eliminated by lowering the impurity

show that this dose increases the ductile–brittle level, it appears that Ta, Nb and V are more ductile

transition temperature by 65 ° C. than Fe, Mo, Cr and W, presumably because they have

Microstructure The change in orientation at indi-

a lower k y ratio, and a higher value. vidual grain boundaries impedes the propagation of Work-hardening and irradiation-hardening Small

the cleavage crack by (1) creating cleavage steps, amounts of plastic deformation at room temperature,

(2) causing localized deformation, and (3) tearing near which overcomes the yield point and unlocks some of

the grain boundary. It is the extra work done ⊲ p ⊳ in the dislocations, improves the ductility at low temper-

such processes which increases the apparent surface atures. The room-temperature ductility of chromium is

energy to ⊲ s C p ⊳ . It follows, therefore, that the similarly affected by small amounts of plastic deforma-

smaller the distance a crack is able to propagate with- tion at 400 °

C. In general, however, plastic deformation out being deviated by a change of orientation of the which leads to work-hardening embrittles the metal

cleavage plane, the greater is the resistance to brittle

Strengthening and toughening 291 fracture. In this respect, the coarser high-temperature

products of steel, such as pearlite and upper bainite, have inferior fracture characteristics compared with the finer lower bainite and martensite products. The fact that coarse carbides promote cleavage while fine carbides lead to ductile behaviour has already been discussed.