The influence of some substitutional alloys on the cleavage of ferritic steels

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Acm mefall. Vol. 35,No. 8, pp. 2027-2034,1987

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1987 Pergamon Journals Ltd

THE INFLUENCE OF SOME SUBSTITUTIONAL ALLOYS ON THE CLEAVAGE OF FERRITIC STEELS N. J. PETCH Department of Metallurgy, University of Strathclyde, Glasgow Gl IXN, Scotland (Received 4 ~e~ern~e~ 1986)

Abstract-Calculation and experiment on the effect of manganese, nickel and silicon transition temperature are compared. This considers k, (the grain size constant in the carbide thickness, alloy softening or hardening and the effective surface energy. There is agreement. At constant grain size, manganese acts principally through carbide refinement nickel through alloy softening and possibly k, lowering, silicon through alloy hardening can be softening) and k, lowering.

on the cleavage yield stress), the reasonably good and k, lowering, (although there

R&un~Nous comparons calcul et exp&ience ~n~rnant l’effet du mangantse, du nickel et du silicium sur la temperature de ~ansition du &age, en tenant compte de k, (la constante de taitle de grains dans I’expression de la limite blastique), de l’ipaisseur des carbures, de L’adoucissement ou du durcissement de l’alliage et de I’bnergie de surface effective. On trouve un accord raisonnable. Pour une taille de grains constante, le manganise agit principalement par l’affinement des carbures et par l’abaissement de k,; le nickel, par l’adoucissement de l’alliage et peut-dtre par l’abaissement de k,; le silicium, par le durcissement de l’alliage (bien qu’il puisse y avoir adoucissement) et par l’abaissement de k,. Zusammenfassuug-Berechnungen und experimentelle Ergebnisse zum EinfluD von Mangan, Nickel und Silizium auf die ~~rgangstemperatur des_Spaltbruches werden miteinander verglichen. Dieser Vergleich betrifft k, (Ko~~renzkonstante in der Beziehung fiir die FlieBsnannun~~. die Karbiddicke. die ~gierun~~ntu&i -verfestigung und die effektive ~~rfl~chenenergi~. Hinre~~~ende ~~reinstimmung besteht. Bei konstanter KorngriiBe wirkt Mangan hauptsIchlich durch Karbidverfeinerung und Absenkung von k,, Nickel durch Legierungsentfestigung und miiglicherweise durch Absenkung von k,, Silizium durch Legierungsverfestigung (obwohl Entfestigung auftreten kann) und Absenkung von k,

YIELD AT ROOM TEMPERATURE AND NORMAL STRAIN RATE (10-4s-‘)

INTRODUCTION It is well-r~ognised that substitutional alloys may influence the cleavage transition temperature through a number of factors. These include effects on grain size, on the thickness of the carbide, other precipitates or inclusions, on k,, on alloy-hardening or alloy-softening or on the effective surface energy associated with crack propagation. The aim of the present paper is to examine these influences quantitatively. At the lower end of the transition temperature range in notch impact, cleavage occurs when the tensile yield stress in the notch equals the cleavage strength. To avoid the complications of plastic deformation, this transition condition is the one examined here. Thus, the present paper considers the effect of substitutional alloys, first, on the yield stress in the notch, second, on the cleavage strength and, finally, on the combination of these two factors in the transition temperature. The substitutional alloys considered are manganese, nickel and silicon. The other important ones are the microalloys, but there grain-refinement and hardening from substitutional-interstitial interactions appears to give an adequate basis for understanding.

The lower yield stress CT~is controlled by the condition for propagation of plastic slip through a grain boundary and this gives a relationship to the grain size d such that by = uO+ k,d-‘!2. Here, cO is the intragranular friction on dislocations in a slip band and the constant k, reflects the difficulty of the process at the grain boundary. Mintz [I] has reviewed the effect of substitutional alloys on cry at normal strain rates, so only limited detail and some unpublished measurements will be given here. Table 1 shows yieid data for a semi-killed and an aluminium”killed steel, along with measurements where the yield point extension has been suppressed by hydrogen treatment or by gettering with titanium. The table shows the variation in a,, with composition, but, in particular, it shows the drop in k, as nitrogen is removed from the grain boundaries by killing and the further drop when interstitial removal is completed and the yield point suppressed. The grain boundary process for slip propagation then becomes easier. The k, values in the Table are based on d

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Table 1. Yield point data Steel

C

Si

Mn

N

Al

Semi-killed Al-killed H,-treated Ti-gettered

0.12 0.15 0.004

0.02 0.04 0.02

0.51 0.64 0.01

0.008 0.005 0.001

0.01 0.10 -

measurements by linear intercept. The strain rate was N lo-4s-‘. The effect of manganese on k, and o, is shown in Table 2. These measurements (Heslop and Petch [5]) are for alloys containing up to 1.9% Mn with 0.03Ul.05 C, 0.1 l-0.17 Si, 0.006-0.008 N. The specimens were from hot-rolled bar, annealed at various temperatures to vary the grain size and furnacecooled. The manganese increases co, but produces a progressive fall in k,. With 1.9% Mn, k, is nearly down to the value produced by aluminium-killing. Probably this reflects displacement of nitrogen from the grain boundaries due to the formation of manganese-nitrogen clusters within the grains. There does not appear to be much information on the effect of nickel on k,. Limited measurements by Jolley [6] on a 3.3% Ni iron (0.002 C, 0.001 N) indicate a k, of 17 N mm-312, so possibly nickel lowers k, for normal steel compositions. Table 2 also shows figures for a series of silicon steels, 0.0064.13 Si, 0.10 C, 0.003 N (Preston and Petch [7]). The specimens were from rolled bar and were furnace-cooled from the temperature used to establish the grain size. Again, there is a decrease in k, and an increase in e0 as the silicon content rises. The fall in ky is possibly due to silicon segregation to the grain boundaries, so increasing the activity there of nitrogen [8] and consequently displacing it from the boundaries [9]. YIELD AT HIGH STRAIN RATES

The yield stresses that are relevant to the production of cleavage in notch impact are those for a strain rate of about lo3 s-r. At normal rates, the temperature-dependence of the yield stress lies only in co at temperatures down to about - 150°C [lo]. At room temperature, the strain rate dependence is also only in co at rates up to > lo3 s-’ (Harding [ll]). The mechanism of this temperature and strain rate dependence, and of the alloy influence on it, is not fully established. An important feature is that at room temperature and

Table 2. Effect of Mn and Si cm on and k.. Mn (%) 0.02 0.47 0.91 1.90

(Ni&-‘) 75.0 75.0 111.0 142.0

k (Nm&3/z) 22.0 22.0 19.5 18.8

Si (%)

00 (N mm-‘)

kY (N mm-‘i2)

0.06 0.21 0.89 2.00 4.13

42.0 62.0 116.0 216.0 430.0

23.5 23.5 20.5 19.5 17.8

a0 (N mm-‘) 71.5 74.0 25.5 94.0

k, (N mm-“‘) 22.2 17.8 6.0 5.5

Reference 2 3 2 4

normal strain rates there is alloy-hardening, but, at lower temperatures and higher strain rates, there may be alloy-softening. From an engineering viewpoint, this is a happy circumstance, since the alloys then give strengthening in normal stressing, but at the high strain rate in a notch there is softening, so giving protection against cleavage. There is a lack of experimental information on the effect of alloying on the temperature-dependence of yield at high strain rates. Fortunately, there is the work of Leslie et al. [12] giving measurements at up to lo4 s-i for room temperature and up to 10-r s-i for three lower temperatures. This gives a basis for calculation. Provided one activation energy is critical to the dislocation processes, the plastic strain rate i should follow the relationship i = i,e -M@ikr

(1)

where i, is the potential strain rate if each activated attempt were successful and Q(u) is the stressdependent activation energy. Then lni =lni,-Q(e)/kT Thus, plots of log i at various constant activation energies (i.e. constant stresses) against l/T should give a family of straight lines. Then, at any particular strain rate, values of stress and the corresponding l/T can be obtained. In this, the stresses that need to be constant are the o,, stresses, but, provided there is no change in k,d- ‘I2, this is given by constant try values. The measurements by Leslie et al. [12] were on a pure iron gettered with 0.15% Ti to remove interstitials and on alloys of this with, amongst others, 1.5 and 3.0 wt% of manganese, nickel or silicon. The final heat treatment given to the iron was an anneal at 860°C and, to the alloys, anneals in the range 66@76O”C. Figure 1 shows the family of lines for log i against l/T for 1.5% Mn. The use of equation (1) appears justified within this temperature range. Measurements below - 120°C were not used with the aim of avoiding any changes in the deformation process. In this way, the temperature dependence of eY at 103s-’ was obtained for the iron and the alloys. From uY, the basic intragranular friction stress on the dislocations, co, was calculated by subtracting k,d-‘12. In spite of the gettering, the nickel and, to a less extent, the silicon alloys showed a lower yield point extension, presumably due to segregation of alloy atoms to the grain boundaries. From Morrison and Leslie [4], the k, values (N mm-3’2) used were 16 for the 3% Ni, 10 for the 1.5% Ni and 3% Si and 6

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l-

N ‘E I: I

400

-

300

-

tD* 200 -

r

LIII’I’II“’ 200

300 OK

400

Fig. 3. Temperature dependence of co at a strain rate of lo3 s-‘. Measurements for iron, 1.5 and 3.0 wt% nickel. 1000/T

OK-’

Fig. 1, Extra~lations of log C against 1000,Q’at constant activation energies (constant yield stresses). Measurements between 200 and 475 N mmSz at intervals of 25 N mm-? for 1.5% manganese iron.

for the rest. Figures 2-4 show the temperaturedependence of q, so obtained for the iron and alloys at a strain rate of lo3 s--l.

E\

Mn

I’lll~l”l”l

\

50

.Yt..

2ooc

t~ll1lll”J 200

In Fig. 2, 1.5% Mn gives a little alloy-softening, but this will largely disappear in normal nitrogencontaining steels because of the hardening arising from clustering of manganese and nitrogen atoms in solution. The 3% Mn gives greater alloy-softening at low temperatures, but there is a change to alloyhardening at higher temperatures. Figure 3 shows that 1.5% nickel gives alloy softening that goes from 20 to 50 N mmm2 over the temperature range 200-300 K. With 3% Ni, there is a softening of 7&80Nmm-2. For silicon, Fig. 4 indicates a great deal of alloy-

300

\

-

400

Fig. 2. Temperature dependence of ctOat a strain rate of 103s-‘. Measurements for iron, 1.5 and 3.0wt% manganese.

Fig. 4. Temperature dependence of a, at a strain rate of 10’ SS’. Measurements for iron, 1.5 and 3.0 wt% silicon.

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hardening, but with the 1.5% Si there is a change to alloy-softening below N 0°C. THE CLEAVAGE

STRENGTH

Cleavage of a ferritic steel in notch impact is normally initiated in a grain boundary carbide film, other precipitate or inclusion by the stress from a blocked slip band. The critical event is the propagation of this crack into the ferrite. The propagation stress required for the breakout into ferrite of an assembly consisting of an acrossgrain dislocation pile-up and an across-carbide crack, when there is dislocation equilibrium between the two, is independent of grain size [ 131.However, there is good experimental evidence that the cleavage strength at constant carbide thickness does vary with grain sizes [ 14, 151. In explanation of this, it has been suggested that an equilibrium approach may be inappropriate [16]. Initially, there is no crack; when one forms, its growth across the carbide is unstable, and dynamic, non-equilibrium collapse of the pile-up into the crack may occur. Then, the crack hitting the ferrite is wedged open by approximately all the dislocations in the pile-up. On this basis, the cleavage strength is given by k d’12 _A--.

2fi

nt

Fig. 5. The cleavage strength at yield for various carbide thicknesses @m) and grain sizes. Data for k, at 17.5 Nmn-3’2 (full lines) and for k, at 22.0 Nmm-‘12

(2)

Here, p is the rigidity modulus, v is Poisson’s ratio, t is the carbide thickness and yp is the effective surface energy for crack passage from carbide to ferrite [16]. In this, it will be seen that the cleavage strength depends on grain size, carbide thickness, k, and yp, so any effect of alloys on these factors will affect cleavage. Figure 5 gives calculated values of a, against grain size for a range of carbide thicknesses. This uses yp = 10 Jm-2 and two k, values, 17.5 and 22.0Nmm-3’2. At any carbide thickness, there is a cut-off along OA, given by

(broken lines).

event. The position of OB in Fig. 5 is based on experimental values in the literature. In considering calculated values of a,, it should be recognised that some simplification is used in the derivation of equation (2), the value of yp is not exactly known and usually there is some uncertainty about the precise value of the carbide thickness involved. Thus, high accuracy in predicted ec values cannot be expected. THE IMPACT TRANSITION TEMPERATURE, T,

8py,d-“2 Cc = (1 + l/,,‘?)(l

- v)k;

Cleavage perature

The explanation of this is that at coarser grain sizes, although the crack may initiate in the carbide, eventually, growth from the carbide into the ferrite is no longer the critical propagation step. The crack has to be extended to a length exceeding the carbide thickness before it becomes unstable. The OA stresses have been calculated using yp = 10 Jmm2, but a somewhat lower value, giving lower stresses, could well be more appropriate, since the critical growth step occurs within the ferrite, and so does not involve the orientation change present when the event is at the carbide/ferrite boundary. There is another cut-off along OB. This gives a, when the cleavage successfully breaks out across the grain, but penetration of the ferrite/ferrite grain boundary becomes the critical

can

occur

in notch

impact

at a tem-

for which

6, N 2.2 oy where this e,, is the high strain rate value. This condition gives the lower end of the transition range. The various factors influencing T, can now be considered. The particular aim is to compare quantitative predictions with experimental observations. Grain size

The grain size affects both the yield and cleavage stresses and so affects T,. This has already been discussed [16] in terms of equation (2). If there is some carbide refinement along with grain refinement, then the normally observed lowering of T, by 1&15X per mm-1’2 increase in d-“2 is under-

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standable. However, as can be realised from Fig. 5, if the carbide is very fine, the grain size dependence of T, wiil increase. Also, with coarser carbides at finer grains, there is the possibility that r, actually increases, instead of decreasing, with grain refinement. This is when the rate of increase in 6, with d “Z becomes too low relative to the rate of increase in o>. Grain size depends very much on the mechanical work and heat-treatments given, but alloys can affect the result. Lowering the y/y transformation tem~rature favours fine grains; also, alloys may reduce the grain boundary mobility. Both Mn and Ni promote grain refinement. As an illustration, in the series of laboratory manganese alloys in Table 2, after similar forging and rolling, followed by 2 h at 900-C and furnace cooling, de’:’ for the 0.02 Mn was 5.6 mm-“, but it was 9.8 mm-‘:’ for the 1.9% Mn. Silicon raises the y/a transformation temperature, but in the quantity normally present in constructional steels (up to -0.3%) there is not much effect on grain size. There is a little coarsening on normalising. However, there may be some inhibition of recrystallisation, giving minor grain refinement in asrolled bar [17]. k, Ex~rimental observations [2,3] on the effect of k, on the transition temperature (13.5 J, f size Charpy) are iilustrated in Fig. 6. This is for two -0.7% Mn mild steels, furnace cooled, one semi-killed, the other fully aluminium-killed. The k, values were 22.2 and 17.8 N mm-“* respectively; there was negligible 6” difference. Consider now the calculated effect of the k,change on T, Lowering k, lowers the yield stress by Akd -1,1 and so lowers T,. If this were all, the lowering would fade out at coarse grains. However, the reduction in

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ALLOYS ON CLEAVAGE

203 I

k, also reduces the number of dislocations in a blocked slip band and so, in the argument of equation 2, reduces the wedging of the carbide crack, thus raising the cleavage strength. This effect is larger for coarse grains (Fig. 5). For these two steels, (a) the reduction in k, on killing decreases the yield stress by 18.5 N mm ’ at d-l’? _- 4mm-. 1:2 and by 37N mm-? at d-l,* = 8 mm-’ ‘. This is independent of strain rate. Restoration of the yield stress for cleavage will require temperature lowerings of -9 and - 18°C respectively. (b) Additionally~ 5, increases with the k, decrease [equation (211.Carbide thicknesses were not measured for these steels, but subsequent measurements on similar steels, similarly treated, indicate a coarsest-10% carbide of -2pm. From equation (2), at this carbide thickness and d-l” = 4 mm- I:‘, the decrease in k, increases a, by 70 N mme2. Cleavage will then require an increase in the high strain rate yield stress of -30 N mm-’ [equation (3)], and this will require a further decrease in temperature of -15’C. At &‘Z=8mm-‘;2 , the decrease in k, increases a, by -40 N mm-*, and cleavage will then require a temperature decrease of 9-C. (c) Thus, the predicted total lowering of T, as a result of the k, decrease on killing is 24°C at d-“’ = 4 mm-“’ and 27°C at d-l * = 8mm-“I. This is in fairly good agreement with the grain-size independent decrease of 22°C in Fig. 6. With finer carbides, the effect of killing on T,, through the effect on rr,, will be greater (Fig. 5). Manganese

Figure 7 shows transition temperatures (13.5 J, $ size Charpy) for the series of furnace-cooled, 0.04 C manganese steels listed in Table 2. Over the Mn range of O.OZ-1.90%, k, falls from 22.0 to 18.8Nmm-“:‘. Again, the changes in Q, and r+ have to be considered to understand T,.

I

I 5

d

-l/2

;;1/2

9

Fig. 6. T, vs d-‘!2 for (a) semi-killed, f/J) killed low-carbon steel.

Fig. 7. T, vs d--“’ for irons containing up to 1.9% man-

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(a) It is well recognised that increase in a, by carbide refinement is important with manganese [18, 191.A full study of the carbide thickness was not carried out at the time of the Fig. 7 measurements. Subsequent examination at d ~ liz = 5 mm-‘” showed that the 10% thickest carbide decreased from 1.8 to 1,i ym over the manganese range. Equation (2) indicates that this change in carbide thickness, along with the change in k,, will increase the cleavage strength at d-‘!2 = 5 mm- r’z by 200 Nmme2. To reach this higher cleavage strength, the high rate yield stress will have to be raised by -90 N mn? [equation (311, which will require a temperature lowering of -45°C. (b) Manganese also changes rrY.As already pointed out, there is probably little alloy softening or hardening by manganese in high-rate yield stress. However, the drop in k, lowers aY at d-‘j2 = 5 mm-“’ by 15 N mm-’ over the manganese range. To counteract this for the production of cleavage, an additional temperature lowering of -8°C will be required. (c) Thus, the predicted fall in T, over the composition range adds up to 53°C at de”’ = 5 mm”-‘/2. The observed drop in Fig. 7 is somewhat lower at 40°C‘

ALLOYS ON CLEAVAGE

the 3.0% Ni, the softening is 80 N mm-= and this should lower T, by -40°C. (b) Further, as already noted, 3.3% Ni ~ssibly reduces k,, to 17Nmmm3’*. This reduces the yield stress at dvi12 = 5 mm-“’ by 25 N mm-’ and so reduces T, by N 12°C. At this grain size and a carbide thickness of - 1.5 pm, such k, lowering should also raise the cleavage strength by -80 N mm-*. For cleavage, the high rate yield stress will then have to increase by -35 N rnrnw2 [equation (3)], which will need a further tem~~ture lowering of -20°C. (c) Thus, the totaf predicted Iowering of T, fur the high nickel steel is -70°C. It is concluded that the effect of nickel on T, is predominantly due to alloy-softening and possibly k, reduction, On this basis, there is good agreement between predicted and observed T, values. A further point from Jolby’s work was the observation that elimination of the carbide from the 3.28% Ni steel, by reduction of the carbon to 0.002%, lowered T, by 65°C. The grain size was little changed, d - ‘I2= 5.0 mm-“‘. Unless any other particles assume control, the carbide removal will increase (F~up to the value on OA (Fig. 5) corresponding to d-“j2 = 5 mm-r’*. Measurement of the original carbide thickness was not given by Jolley, but the optical micrograph suggest it may be - 1.5 pm (bearing in mind the liability to overestimate carbide thickness in optical measurements [ZO]). Then, provided there is no change in ky and that it is - 17 N mm->;*, the removal of the carbide should increase cr, by -400 N mm-*. Consequently, cteavage will require an increase in the high rate yield stress of - 180 N mme2, and this will need a temperature decrease of -90°C. This is rather greater than the observed fall in T, on carbide removal As already considered, the calculated stress for OA may be somewhat high. If yP = 9 Jrn-= were used in the calculation of OA, as discussed in the manganese section, the predicted increase in a, on carbide removal would be - 300 N mme2. Cleavage would then require an increase in the high rate yield stress of - 135 N mm-*, so T, would fail by - 70°C.

Jolley fl9J observed a greater effect of manganese. furnace-cooIed, 0.04% C, 1.8% Mn steel, d-‘!2 = 5.4 mrnii2 had a T, 30°C lower than in Fig. 7, In this case, optical mi~rographs indicate that the carbide was considerably finer, but no thickness measurements were given. It appears that the carbide could well be below the critical thickness (-0.5 pm at this grain size) for effect on of. In that case, (T,is given by OA (Fig. 5). This indicates an increase of 290 N mm-’ above the calculated a, for the 1.1 pm carbide of Fig. 7. An additional drop in T, of 65°C would then be required, which is considerably greater than the observed 30°C. It may be that the carbide in Jolley’s steel was in fact thicker than the critical value. However, as already commented, OA may well be at too high a stress. The 30°C lower T, observed by Jolley could be explained if a, were determined by OA with r, at 9 Jme2. It is concluded that the effect of manganese on T, arises predominantly from carbide refinement and /rY lowering. There is reasonable agreement between Silicon observed and calculated T, changes. Alloy-hardening (Fig. 4) is clearly a major factor in the influence of silicon on T,. Further, as the figure shows, the tem~rature-de~nden~ of the yield is reduced, so a greater temperature change is required Measurements on the influence of nicke1 on T, are to allow For any hardening. available from Jolley [6, 191.With two steets, 0.04 and Some comparison of predicted and obsess T, 0.03 C, 0.03 and 3.28 Ni, d-‘i* of 5.0 and 5.4 mm-“*, changes by silicon can be made for the gettered alloys the higher nickel lowered T, (13.5 J, i size Charpy) by used by Leslie et al. 114 in the strain rate mea75°C. surements. This comparison is not entirely complete Jolley found there was no re~nement of the grain because of a lack of data on the size of the particies boundary carbide in these furnace-cooled specimens, [probably Ti (C, N)] that nucleate cleavage. so this does not contribute to the T, lowering. T, for the pure iron was - 34°C and, for the 3% Si (a) As shown in Fig. 3, nickel produces significant iron, + IOOYL There should be some increase in T, alloy-softening at the high strain rate in a notch. With for this Si iron because of its higher k,, but there A

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60 0

0.9 40

l

0

*

2033

and Mintz [22] observed no significant effect of low silicon on carbide growth. It is concluded that the effect of silicon on T, is predominantly the result of alloy-hardening (or softening) and k, reduction. There is reasonable agreement between calculation and observation.

”

”

ALLOYS ON CLEAVAGE

l

20

'*a *

Y

0.2

: I-00 0 'I) -2o\.

\ \I

-40

"A\

t

-60 t

d

I

-5/2&/2

Fig. 8. T, vs &‘I2 for irons containing 0.2 and 0.9 wt% silicon.

should also be a decrease because of a somewhat finer grain size. The nett effect will be fairly small. From Fig. 4, because of the alloy-hardening, the temperature of the 3% S&iron will need to be - 120°C higher for it to have the same o,, as the pure iron at - 34°C. Thus, a difference of - 120°C in the T, values is predicted, which is close to the observed 134°C. The 1.5% Si iron in Fig. 4 is of interest. At + 3O”C, there is alloy hardening of - 10 N mm-‘. Thus a temperature rise of - 10°C would be needed to bring go down to equal that of pure iron. This would raise T, for the Si iron by N 10°C above that for the pure iron at the same grain size. In contrast, at -3O”C, there is alloy softening that will lower T, by - 10°C. Transition temperature data for a 1.5% Si steel are not available, but Fig. 8 shows limited measurements of T, vs de”’ for the 0.2 and 0.9% Si steels of Table 2 [7]. Broadly, this is in line with the prediction from Fig. 4. T, is raised for the 0.9% Si at the higher temperature, but lowered at the lower temperature. It is generally said that silicon additions up to -0.5% have a beneficial effect on T, (through k, lowering), but higher concentrations are deleterious. The above shows this is not a general truth. If the grain size can be kept sufficiently fine, so that T, is low from that viewpoint, limited higher additions of Si can give further T, benefit, and this is combined with strengthening by raised aYat normal strain rates. Another possible effect of silicon on T, may be through carbide re~nement, but there does not appear to be definite evidence on this. Pope et al. [21]

There may be some effect of alloys on the effective surface energy associated with a crack at the critical stage of passing through the carbide/ferrite boundary. Reduced dislocation locking may cause an increase, so y,, may rise with a fall in k,. This would reinforce the beneficial effect on T, of reduced k,. However, within the accuracy of the present treatment, there is no certain indication of a need for special consideration of yp. Cross-slip is another factor that can be significant in the avoidance of cleavage [23]. This is essentially related to the yp theme, since cross-slip may determine whether or not a stress concentration can be relieved by plastic deformation or by cleavage. There have been suggestions that the low T, of nickel steels is because macroscopic cross-slip, indicated by wavy, rather than planar slip bands, persists to lower temperatures. Reversing this argument, it amounts to suggesting that the higher T, in the absence of nickel is because planar slip develops. However, T, values for such steels are around room temperature and Harding [l l] has shown that, even at strain rates exceeding lo3 s-l at this temperature, there is no increase in k,, as would arise if planar slip developed. It is concluded that T, for ordinary nickel-free steels does not involve planar slip. However, it is true that if the other factors involved promise very low T,, avoidance of planar slip may avoid spoiling this promise.

CONCLUSIONS

1. The effect of alloys on T, at constant grain size has been considered in terms of k, , carbide thickness, alloy hardening or softening and yp. The treatment has been quantitative. Although there are uncertainties in the ~l~ulations, pa~i~ularly about some of the data available, there is reasonably good agreement with observed I;: changes. 2. The intluence of aluminium-killing is through k,. 3. Manganese acts predominantly through carbide refinement and k, lowering. 4. Nickel acts predominantly through alloy softening and possibly k, lowering. 5. Silicon acts predominantly through alloy hardening and k, lowering, but there can be alloysoftening. Acknowledgements-Thanks are due to the Leverhulme Trust for help in finishing this work through an Emeritus Fellowship.

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