The role of ductility in hot working

CoA NOTE MAT. 14

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ttCHWISCHF- HOGESWOOl C E i n ^ VUEGTUiGBOUWl^UMDE

Bi'aUOTHEEX DELR

THE COLLEGE OF AERONAUTICS

CRANFIELD

THE ROLE OF DUCTILITY IN HOT WORKING

by

THE COLLEGE OF AERONiiUTICS riEPARTI'lENT OF MATERIALS The r o l e of d u c t i l i t y i n h o t working b y -W.J. McG. T e g a r t , M . S c , P h . D . , F . I . M . S_U_^M_M_A_R_Y

Strength and ductility are the important characteristics which govern the hot working properties of a material. This paper describes test methods for measuring hot workability and then discusses deformation and fracture mechanisms in hot working. Particular emphasis is laid on the correlation of strength and ductility data in simple materials in terms of dependence on strain rate and temperature. Suitable correlations enable the identification of basic parameters controlling deformation and fracture processes. With complex materials, these correlations cannot be applied due to the occurrence of precipitation reactions and the presence of inclusions and second phases having markedly different strength and ductility characteristics.

Paper presented at Seminar on 'Ductility - Limitations, Exploitation, Utilization' organised by the American Society for Metals in Cleveland, Ohio on October l U h and 15th, 19^7.

Contents

Page No.

Methods for Studying Hot Workability 1

Tension Tests 2 Comioression Tests 3 Torsion Tests 3

Defoliation Mechanisms in Hot Working 5 Correlation of Hot Strength Data 5 Recovery as the Softening Process 6 Reciystall!zation as the Softening Process 8

Fracture Mechanisms in Hot Working 11 Correlation of Hot Ductility Data 11 Observation of Fracture Modes lU

The Interaction between Deformation and Fracture Mechanisms

in Hot Working 17 Continuous Deformation l8

Interrupted Deformation 19

Effect of Inclusions, Impurities and Structural Inhcmogcncities

on Ductility 20 Solid Solution Alloying 21

Duplex Alloys 21 Cast Structures 22 Inclusions 23 Aclaiowle dg ement s 23 References 2k Tables 30 Figures

The two c h a r a c t e r i s t i c s which determ.ine the forming p r o p e r t i e s of a material are i t s r e s i s t a n c e to p l a s t i c flow ( s t r e n g t h ) and i t s d u c t i l i t y . The f i r s t determines the s i z e of the equipment needed for the forming operation while the second determines the maximum allovrable deformation without r i s k of f r a c t u r e . Often the equipment a v a i l a b l e for hot working

i s s u f f i c i e n t l y overdesigned that i t is capable of dealing with most materials from a s t r e n g t h viewpoint and the unkno-vm quantity i s the

d u c t i l i t y . In p r a c t i c e the l i m i t of d u c t i l i t y i s often simply determined by operatives who are governed by economic incentives with respect t o throiighput of m a t e r i a l through say a breaking-do\ni m i l l . With low cost m a t e r i a l , such experience may prove s u f f i c i e n t when dealing with routine hot working procedures b u t , witli high cost m a t e r i a l s , such a s s t a i n l e s s s t e e l s and high temperature a l l o y s , suitable data must be a v a i l a b l e to decide on the- optimum working schedules from a viewpoint of s t r e n g t h , d u c t i l i t y and s t r u c t u r e .

The main features of hot working are that extremely l a r g e s t r a i n s are applied t o m a t e r i a l s at high r a t e s of s t r a i n at temperatures above about 0.7Tjn where Tjjj i s the melting p o i n t i n degrees Kelvin. Strength and d u c t i l i t y under these conditions are markedly dependent on both

tcHiiperature and r a t e of s t r a i n i n g , while d u c t i l i t y i s intimately r e l a t e d t o the deformation processes which govern p l a s t i c flow. In t h i s paper, we f i r s t discuss t e s t methods for studying hot w o r k a b i l i t y and then consider deformation and f r a c t u r e mechanisms in hot working in r e l a t i o n to t e s t data and s t r u c t u r a l observations.

Methods for Studying Hot Workability

The most r e l i a b l e method i s c l e a r l y to process m a t e r i a l under p l a n t conditions where both t h e v a r i a b l e s inherent i n t h e m a t e r i a l , i . e .

composition, s i z e , shape, ingot s t r u c t u r e , and the v a r i a b l e s inherent in the process, i . e . r a t e of s t r a i n , nature of s t r e s s •system, temperature, are simultaneously covered. However such a method 1,^ expensive and the

obvious advantages of a laboratory t e s t , e . g . ease of checking d i f f e r e n t c a s t s , ease of determining optimum conditions for new m a t e r i a l s , close control of v a r i a b l e s and pos.sibility of r e l a t i n g s t r u c t u r e and p r o p e r t i e s , have l e d to the development of a number cxf t e s t s , seme of which are

simulative in nature and others of which are designed for basic s t u d i e s An important feature of hot workability t e s t s i s t h a t they should give information on strength and d u c t i l i t y over the langes of r a t e s of s t r a i n , s t r a i n and teniperature used in p r a c t i c e . Thus, in some processes, e . g . e x t r u s i o n , t h e t o t a l s t r a i n i s applied i n one operation a t roughly constant temperature while in other processes, e . g . forging, the t o t a l s t r a i n i s applied i n a number of operations a t decreasing temperatures. A good example of these ranges in one process i s hot r o l l i n g of sheet s t e e l ( l ) . As shown in F i g . 1, the t o t a l deformation can be applied e i t h e r in one operation by a planetary m i l l or in a s e r i e s of operations e i t h e r in a continuous m i l l or in a reversing m i l l .

While t e s t data for control purposes have been gathered by a v a r i e t y of methods, there has been r e l a t i v e l y l i t t l e attemipt to r e l a t e these data t o deformation and f r a c t u r e mechanisms. Such b a s i c researdi requires data over ranges.of working conditions which are not u t i l i z e d in p r a c t i c e and more s o p h i s t i c a t e d t e s t methods have been developed. Thus in the i d e a l hot working experiment the specii-üen i s deformed uniformly a t

constant t r u e s t r a i n r a t e and temperature with continuous measurement of s t r e s s required for deformation. Rapid cooling i s often used to f a c i l i t a t e examination of the hot worked structure and the effect of continuovis

working operations i s simulated by cycles of deformation and r e s t s a t temperature.

Various reviews of experimental techniques for studying hot work-a b i l i t y work-are work-a v work-a i l work-a b l e (2-7) work-and only work-a b r i e f discussion is given h e r e of t e s t methods with p a r t i c u l a r emphasis on the r e s u l t s obtained for

strength and d u c t i l i t y . For convenience, we consider three basic methods of s t r e s s i n g - t e n s i o n , compression and t o r s i o n .

Tension T e s t s . I'/hile some workers have iised d u c t i l i t y in f e n s i l e tests"iLE"n5fmaI"sïrain r a t e s a s a control technique i n p r a c t i c a l hot working, the most useful teclmique is c l e a r l y t o examine strength and d u c t i l i t y i n t e n s i l e t e s t s a t high r a t e s of s t r a i n . F i g . 2 shows r e s u l t s obtained on an i B ^ C r - l ^ N i s t e e l in the a s - c a s t and as-forged condition in an impact t e n s i l e t e s t at a r a t e comparable to that of r o l l i n g or press forging ( 8 ) . Such r e s u l t s c l e a r l y bring out üie difference between the strength and d u c t i l i t y of the two conditions and can be used to deteimine optiravun hot world.ng ranges.

However the change i n dimensions of the t e s t piece during extension means that the s t r a i n r a t e i s continually changing imless a controlled r a t e of cross-head movement i s used. A further change in s t r a i n r a t e occurs with the onset of necking which u s u a l l y begins at a t r u e s t r a i n of l e s s than 0.7 which i s i n general much l e s s than the total, s t r a i n one wishes t o study. This necking s t r a i n i s however of the same magnitu.de as the s t r a i n occurring during each pass i n hot r o l l i n g or p r e s s forging and from t h i s viewpoint usefiol data can be obtained from t e n s i l e t e s t s . By controlling t h e r a t e of cross-head movement during uniform extension and necking, t e n s i l e t e s t s a t constant t r u e s t r a i n r a t e s have been c a r r i e d out up to t r u e s t r a i n s of roughly unity as shown i n F i g . 5 for an 0.25^Cr s t e e l at 1100°C ( 9 ) . The form of these curves w i l l be discussed l a t e r .

A major disadvantage of t e n s i l e t e s t i n g f o r study of f i ^ c t u r e

mechanisms i s t h a t the necked region i s u n s u i t a b l e for s t r u c t u r a l studies since a t high s t r a i n r a t e s marked adiabatic heating occirrs in a small volume leading to marked temperature r i s e s . This e f f e c t may however be useful in p r a c t i c e where problems of ' h o t shortness' a r i s e due t o inhoraogeneous

Compression T e s t s . Since many hot working processes involve e s s e n t i a l l y compressive s t r e s s e s , various workers in r e c e n t years have d-3veloped compression t e s t s for obtaining strength and d u c t i l i t y data a t higli s t r a i n r a t e s . Perhaps the sifuplest t e s t for hot d u c t i l i t y i s t h a t using a flywheel press with a constant reduction i n height of a preheated cylinder in one blow. Examination of the specii.iens then enables the deteraiination of hot woiking temperatures in t e r n s of the minimum and/or max:imum tanperature at -^jhich u p s e t t i n g can be acconplishc-d without cracking. Such data can bs r e l a t e d to s t r u c t u r a l or compositional f a c t o r s as shown i n F i g . h where the amoimt of second phase is shown to have a s i g n i f i c a n t effect on the minimum upsetting temperature of a

titaniim-tin-aluminiuffi alloy with additions ( l O ) .

From the vie^•^point of strength d a t a , si:npl° axisyrametric compression t e s t s , whether of the drop hammer or press tj'pe, suffer from a similar disadvantage to t e n s i l e t e s t s in t h a t again change of dimensions of the t e s t piece dviring compression l e a d s to a v a r i a t i o n i n s t r a i n r a t e .

Wiile the complication of necking i s avoided and thus much l a r g e r s t r a i n s are possible in compression than i n t e n s i o n , the f r i c t i o n between platens and specimens leads to ' barrellii:ig' of the specimen with consequent

inliomogeneous deformation. This ' b a r r e l l i n g ' usually occurs at a true s t r a i n of about 0.7 and thus l i m i t s the usefulness of the t e s t for high

s t r a i n s . However by eliminating ijlaten/specimen f r i c t i o n and by c o n t r o l l i n g the- r a t e of compression in r e l a t i o n to the specimen dimensions as in the s o - c a l l e d 'cam plastoraeter' , compression t e s t s at a constant true s t r a i n r a t e can be c a r r i e d out up to high values of true s t r a i n s . F i g . 5 shows s t r e s s - s t r a i n curves for alunlniujn at various temperatures at a constant t r u e s t r a i n r a t e of ii-.i^/sec ( l l ) .

I t i s worth noting t h a t plane s t r a i n ccmpression has also been used in hot world.ng studies t o obtain true s t r a i n s up t o about i5 at a constsjit true s t r a i n r a t e . Ho\7ever, f r i c t i o n a l problems '-.Iso a r i s e i n t h i s type of cctipression and can l i m i t tlie lAsefulness of the technique. An advantage i s that the load requirements are smaller than i n aicisj-THmetric compression where the increase of area leads t o a continual increase in the load required for deformation.

Torsion T e s t s . A major advantage of t o r s i o n for studying hot work-a b i l i t y " r s ~ t l " work-a t " work-a " c o n s t work-a n t high s t r work-a i n r work-a t e cwork-an be r e work-a d i l y mwork-aintwork-ained up to fractvu-e by t w i s t i n g at constant higli speed since the specimen dimensions can be maintained constant. Since necking and bai-relling are not l i m i t i n g f a c t o r s , l a r g e s t r a i n s can be applied p r i o r to fracture thus simulating

more closely the conditions i n p r a c t i c a l hot worl:ing operations . D u c t i l i t y can be r e a d i l y measured by the nimiber of revolutions to f a i l u r e and r e s u l t s at various temperatures can be used t o define optimum hot working conditions as shown in F i g . 6 ( l 2 ) .

However, fracture in torsion does not take place under simple shear since dimensional changes occur at l a r g e p l a s t i c s t r a i n s and t h e i r r e s t r a i n t

k

-by imposing a fixed geometry on the specimen leads to a x i a l tens.ion or campression (15) • While the average l o n g i t u d i n a l s t r e s s e s are

r e l a t i v e l y small compared t o t h e applied shear s t r e s s , they are important in determining measured d u c t i l i t y since exterr.ally applied l o n g i t u d i n a l tension or comipression can a l t e r the values obtained for m a t e r i a l s

exhibiting r e l a t i v e l y low d u c t i l i t i e s ( l 4 , 1 5 ) . Dragan (ik) has r e c e n t l y suggested a method for correcting measured d u c t i l i t i e s of s t e e l s to

obtain a ' t r u e ' d u c t i l i t y but the assumptions involved need closer study before the method is applied more widely. In fact the success of hot

t o r s i o n t e s t s in p r e d i c t i n g optimum temper at tires for hot piercing of s t e e l s probably l i e s i n the complex s t r e s s system Imposed at f r a c t u r e .

The torque measured during hot torsion can be converted t o shear ' s t r e s s and thence to true s t r e s s so t h a t s t r e s s - s t r a i n curves can be obtained up to very high s t r a i n s at constant true s t r a i n r a t e s . In such c a l c u l a t i o n s , the surface shear s t r e s s and s h ^ r s t r a i n a r e used since

the outer l a y e r s make tJie major contribution to the measured torque. The agreement of t e n s i o n , compression and torsion data i n d i c a t e s t h a t t h i s

procedure i s an acceptable one. Clearly, however, s t r e s s , s t r a i n and s t r a i n r a t e vary with r a d i a l p o s i t i o n and care must be taken in the i n t e r p r e t a t i o n of the structtu-es of samples taken from solid specimens. The use of tubular specimens eliminates these problems but buclü-irg l i m i t s the attainment of l a r g e s t r a i n s p r i o r to f a i l u r e .

The teriperature dependence of strength and d u c t i l i t y at a constant s t r a i n r a t e i s shown by the s t r e s s - s t r a i n ctirves for aluminium and copper derived from hot t o r s i o n data (Fig. 7) ( 1 6 ) . Comparison of the

altimlnium curves with those of F i g . 5 i n d i c a t e s the much higher s t r a i n s t h a t can be obtained in t o r s i o n than in compression. F i g . 7 shoves that t h e nature of the s t r e s s - s t r a i n r e l a t i o n changes a t high s t r a i n s so that a steady s t r e s s i s required for deformation independent OLL' s t r a i n . This behaviour i s maintained over a wide range of s t r a i n r a t e s as shoim in

F i g . 8 for an 0.25'^Cr s t e e l ( l 7 ) ' At low s t r a i n r a t e s the curves show o s c i l l a t i o n s similar to those observed in t e n s i l e t e s t s at constant true s t r a i n r a t e s , cf. F i g . 3- Such o s c i l l a t i o n s are observed i n other m a t e r i a l s e . g . copper and n i c k e l , but are hardly v i s i b l e in aluminium

( F i g . 9) ( l 3 ) . The d i f f e r i n g form of the s t r e s s - s t r a i n curves for various m a t e r i a l s w i l l be discussed l a t e r .

I t is vjorth noting tiiat, i n addition to simtilating hot working processes such as extrusion or r o l l i n g with a planetary m i l l where l a r g e s t r a i n s are applied in one operation, hot t o r s i o n t e s t s can be used to simulate

deformation schediiLes involved in hot r o l l i n g or forging. Using a programmed machine, Rossard and Blain ( l ) have obtained good c o r r e l a t i o n between s t r u c t u r e s developed during hot r o l l i n g of s t e e l sheet in p r a c t i c e and l a b o r a t o r y t e s t s . A similar technique has r e c e n t l y been successfully applied to hot r o l l i n g of aluminium and i t s a l l o y s (19, 2 0 ) .

Deformation Mechanisms in Hot Working.

The s t r e n g t h , and also the d u c t i l i t y , of a m a t e r i a l during hot worldng i s governed by the balance between work hardening and dynamic softening p r o c e s s e s . If work hardening predominates, strength i s higli but d u c t i l i t y i s low while, i f softening predominates, strength is low but d u c t i l i t y i s higli. To ujiderstand d u c t i l i t y in hot working processes we must examine

the deformation mechanisms during hot working. An i n d i c a t i o n of the operative softening process should be obtained from analysis of data on r a t e of s t r a i n , s t r e s s and teirperature coupled with observations of s t r u c t u r a l changes as a r e s u l t of deformation.

Correlation of Hot Strength Data. As noted e a r l i e r the s i g n i f i c a n t featurë"öf~ITöw"c{n'vës~ündër"öt"working conditions i s the s t e a d y - s t a t e region where flow s t r e s s is independent of s t r a i n . Various attempts have been made to formulate a r e l a t i o n between strength ( a ) , temperature ( T ) and s t r a i n r a t e (e) for t h i s region. The most successful attonpt appears to be t h a t of S e l l a r s and Tegart ( 2 l ) who propose the r e l a t i o n

ê = A(sinlaaa)'^ exp(-'^yRT) ( l ) where A, OL, n' are temperature-independ.ent constants and Q i s an a c t i v a t i o n

energy. This r e l a t i o n s h i p is a development of the one proposed for creep by Garofalo ( 2 2 ) .

At loi7 s t r e s s e s {aa< 0 . 8 ) , eq. ( l ) reduces to a power r e l a t i o n , similar t o t h a t used for creep,

ê = A'a'''e:cp(-^/Rr) (2) and at high s t r e s s e s (Q;O'>1.2) to an exponential r e l a t i o n

ê -r-. A"expOa)exp(-^yRT) (3) The constants a and n' are r e l a t e d by P = Ctn' so t h a t o; and n' can be simply

deteiTtiined from experimental data f o r high and ICKT stresses .

F i g . 1 0 ( a ) - ( c ) i l l u s t r a t e the a p p l i c a t i o n of the r e l a t i o n t o d a t a obtained by hot t o r s i o n of an 0.25^30 s t e e l . Thus Fig. 10(a) is a log-log p l o t to t e s t the power r e l a t i o n while F i g . 10(b) i s a semilog p l o t to t e s t the exponential r e l a t i o n s h i p . The r e s u l t a n t sinh plot i s shD^m i n F i g . 10(c) and i l l u s t r a t e s the ten^ierature independence of n' . Hot working data for a number of m a t e r i a l s have been s a t i s f a c t o r i l y c o r r e l a t e d by eq. ( l ) ^ ( 2 1 , 25-26). The a c t i v a t i o n energy, Q, can t t e n be obtained from a plot of log e , a t

constant sinh Cxs, against / T . Values of Q from hot working are given i n Table 1 together with reported values for creep, s e l f - d i f f u s i o n , recovery and r e c r y s t a l - l i z a t i o n .

Rearrangement of eq. (5) to the form

Z = exp('^Vï^) = A(sinli a a ) ^ (1+) permits c o r r e l a t i a i of the data for d i f f e r e n t temperatures on a single

s t r a i g h t l i n e as shown by F i g . 1 1 . This type of p l o t provides a r e l i a b l e method for i n t e r p o l a t i n g data to obtain values of strength at any

temperature or s t r a i n r a t e within the ranges studied.

I t i s clear fran Table 1 t h a t in some cases the a c t i v a t i o n energy f o r hot deformation remains unchanged over an extremely wide range of s t r a i n r a t e s while in others there i s a marked difference between the

values for creep and hot working. In the former cases, the constant value of a c t i v a t i o n energy, close t o t h a t for ^elf-diffusion, i n d i c a t e s t h a t recovery i s operative over the whole range while in the l a t t e r cases the values suggest t h a t the softening process i s recovery under creep conditions but may be r e c r y s t a l l i z a t i o n during hot working. The p o s s i b i l i t y of

r c c r y s t a l l i z a t i o n during hot working has been discussed in several recent papers and reviews and a dichotomy of opinion e x i s t s a t the present time. Thus Stüwc (57, 38) and McQueen (6) s t r e s s the importance of dynamic

recovery as the softening process in a l l metals and dismiss r e c r y s t a l l i z a t i o n as a possible process, while Rossard (39) and S e l l a r s and Tegart ( 2 l )

maintain t h a t r c c r y s t a l l i z a t i o n occurs i n lower stacking f a u l t energy m a t e r i a l s . I n the next two s e c t i o n s , the evidence for the occurrence

of both recovery and r e c r y s t a l l i z a t i o n during hot working w i l l be b r i e f l y discussed in the l i g h t of available information.

Recovery as tiie Softening Process. In the case of aluminitim and Q!-iron"7"the"activatïön'ënërgy"forgot deformation i s similar for both

creep and hot working. The formation of well developed substructures by reco^very by cross s l i p and climb during creep of aluminitm:. and o;-iron i s well documented. In the case of hot working, if the high temperature

s t r u c t u r e i s r e t a i n e d by rapid cooling a f t e r deformation, the s t r u c t u r e s observed are similar to those a f t e r creep as shown i n Figs. 12(a) and 1 3 ( a ) . However due t o the high s t r a i n s imposed during hot working the sub-boundaries

are more c l e a r l y defined than a f t e r creep while the o r i g i n a l grain boundaries are heavily d i s t o r t e d and are often no longer apparent.

I n both hot t o r s i o n and extrusion, subgrains remain approximately equiaxed and constant i n size throughout the steady s t a t e deformation ( 2 3 , 2i)-, kO). F u r t h e r , the misorientation measured in extruded aluminium a f t e r s t r a i n s of 10 and kO are roughly constant i n the range 1-^° and are no l a r g e r than those observed a f t e r lov7 s t r a i n s in creep (25, 2k). This constancy of subgrain size and misorientation leads t o a conc:tant d i s l o c a t i o n density and hence a constant flow s t r e s s .

For the subgrains t o remain eqtiiaxed while the o r i g i n a l grains undergo marked shape changes the sub-boundaries must be able to r e l o c a t e t h e i r

p o s i t i o n . Jonas e t a l (23) stiggest t h a t t h i s i s accomplished by the continuous d i s i n t e g r a t i o n and reformation of the d i s l o c a t i o n arrays a t the

equilibrium spacing. The d i s i n t e g r a t i o n proceeds by the applied s t r e s s pushing d i s l o c a t i o n s out of sub-boundaries, the s t a b i l i t y of which has been diminished due to d i s r u p t i o n by the passage of mobile d i s l o c a t i o n s .

This process i s a s s i s t e d by a limited amount of sub-boundary migration which i s made possible by the enhanced climb of d i s l o c a t i o n s produced by

the deformation. The o v e r a l l process has been tenvied 'repolygonization' . Such a process suggests t h a t t h e size of the subgrains should be

dependent on s t r e s s . Various workers have reported that subgrain size ( t ) during high temperature deformation can be r e l a t e d t o s t r e s s by a r e l a t i o n of the form

0 = a + kt"^ (5) o ^ '

where x i s a constant of value 1 to 1.5- The b e s t value of x i s a t present u n c e r t a i n since accurate determination of subgrain size i s experimentally d i f f i c u l t . Hov/ever recent s t a t i s t i c a l analyses show t h a t f o r aluminium, high temperature creep data a r e b e s t f i t t e d by x = 1 while hot t o r s i o n and hot t e n s i l e t e s t s a t much f a s t e r s t r a i n r a t e s are b e s t f i t t e d by x = 1.5 (^O). To understand t h i s discrepancy, i t i s necessary to r e a l i s e t h a t subgrain

boundaries even a t high tem^Deratures can a c t as b a r r i e r s t o d i s l o c a t i o n movement. Tims Cotner (ko) has found that I'Then both grains and subgrains are present in an aluminium specimen before i t i s hot worked the subgrains determine the strength of the specimen during deformation. Th.e strengthening effect of substructure has been i n v e s t i g a t e d by various workers by deforming specimens at low temperature a f t e r substructure has been introduced by high temperature deformation. In t h i s case the value of the constant x in eq. (5) i s 0.5 and has been i n t e r p r e t e d in ten'ris of p i l e - u p s of dislocations against the sub-boundaries.

In the case of creep, the value of x = 1 can be understood from the inverse r e l a t i o n between s t r e s s and s l i p band spacing o r i g i n a l l y developed by Orowan sines here the s t r a i n s are a n a l l and a s t a b l e substructixrc develops from the coarse s l i p bands produced in the e a r l y stages of loading.

However in the case of repolygonization where the boundaries are being broken doajn and reformed, the b a r r i e r effect of the sub-boundaries must be important and Cotner has suggested t h a t tlie simuJ-taneous production of sub-botindaries and p i l e - u p s of d i s l o c a t i o n s against them leads to t h e observed value of X = 1.5.

From an a n a l y s i s of extrusion data on aluminium, Jonas et a l (25)

have reported t h a t the a c t i v a t i o n energy for repolygonization i s ^4-1.8 k c a l mole, i . e . higher than t h a t for s e l f - d i f f u s i o n . However a more recent analysis of t h e i r data suggests t h a t a b e t t e r value i s 55 k c a l mole in l i n e with other workers {2k). Such a value implies t h a t the r a t e determining

s t e p i n the repolygonization i s d i s l o c a t i o n climb as in t h e case of creep. The important f e a t u r e t h a t emerges from these resu.lt s i s that i n some m a t e r i a l s under hot working conditions dynamic recovery processes can operate

extremely rapidly to reduce s t r a i n hardening and that large s t r a i n s can be accommodated by the continuous d i s i n t e g r a t i o n and reformation of sub-boundaries to maintain an equiaxed s t r u c t u r e .

I f the hot worked material i s held at the deformation temperature for seme time p r i o r to cooling, or if cooling i s very slow, then the high temperature s t r u c t u r e i s not retained and significant s t r u c t u r a l changes can occur. I n i t i a l l y there i s a sharpening of the sub-boundaries associated with gradual softening followed by the appearance of r e c r y s t a l l i z e d grains associated with a more marked softening (Fig. 1 2 ) . At higher temperatures, the s t r u c t u r a l changes during isothermal sinnealing proceed more r a p i d l y and in some cases even the most rapid quenching procedure is i n s u f f i c i e n t t o r e t a i n the hl^h temperature s t r u c t u r e . Thus a t temperatures of 500-ÖOO'C the r e s t periods in commercial hot r o l l i n g operations on aluminium a r e s u f f i c i e n t to r e s t o r e the fully annealed s t r u c t u r e before further deformation, while a t lower temperatures, say UOO°C, r e l a t i v e l y l i t t l e

change occurs (19)- Such s t r u c t u r a l changes are important when considering the d u c t i l i t y of material subjected t o cycles of deformation followed by r e s t periods a t temperature.

R e c r y s t a l l i z a t i o n as the Softening Process. In the case of l 8 / 8 stainless"stëêï7~cöppêr7"nicïcGÏ"an3~nicicëï-lTOn a l l o y s , t h e a c t i v a t i o n energies for the softening process are higher for hot working than for creep. We identify the creep process with recovery and the hot working process with r e c r y s t a l l i z a t i o n . As noted previously, t h i s view is not held by other workers in the f i e l d and we w i l l now discuss the experimental evidence for our viewpoint.

For copper and n i c k e l , the a c t i v a t i o n energies for creep determined from steady s t a t e conditions a r e similar to s e l f - d i f f u s i o n and are associated with t h e development of a poorly defined substructure indicating dynamic recovery as the softening process. F u r t h e r , observation.: on creep of s t a i n l e s s s t e e l s of I8/15 and Type 316 v a r i e t i e s chow subgrain formation again indicating dynamic recovery as t h e r a t e - c o n t r o l l i n g process ( 2 2 ) .

However, in the case of copper and n i c k e l , r e c r y s t a l l i z a t i o n associated with r a p i d changes in s t r a i n r a t e can occur during creep. Similar behaviour has been observed with gold and lead and i t has been suggested t h a t t h i s behaviour i s c h a r a c t e r i s t i c of low stacking f a u l t energy m a t e r i a l s where dynamic recovery i s expected to be slow (kl). These observations are not disputed but the main point of dispute i s whether such r e c r y s t a l l i z a t i o n can occur during hot working. I f dynamic

recovery i s r a t e c o n t r o l l i n g , then c l e a r l y the a c t i v a t i o n energy deteimined for hot worldLng should be similar to t h a t for creep and s e l f - d i f f u s i o n while i f r e c r y s t a l l i z a t i o n i s r a t e c o n t r o l l i n g then a d i f f e r e n t a c t i v a t i o n energy associated e i t h e r with boundary migration or grain boundary diffusion should be a p p l i c a b l e . I f one imagines the rapid changes in s t r a i n r a t e occurring i n creep at frequent i n t e r v a l s , then t h e creep r a t e detennined for t h e process under a given s t r e s s w i l l c l e a r l y be d i f f e r e n t from that for the steady s t a t e p r o c e s s . This i s the s i t u a t i o n that we envisage during hot working, i . e . rapid repeated r e c r y s t a l l i z a t i o n .

Observations on specimens quenched rapidly after hot torsion show that recrystallization occurs in I8/8, copper, nickel and nickel allqys (Fig. ik). Interrupted tests show that the initial deformed grains are replaced by new recrystallized grains nucleated at original grain

boundaries and that recrystallization proceeds progressively with strain after the maximum torque (16). Clearly there is a danger that structural alterations produced in the small time interval of quenching could

obliterate the true high temperature structure. Thus the new grains often appear to be equiaxed and strain free with straight annealing twins suggesting that they form after deformation. Further, if hot worked material is held at the deformation temperature for some time prior to

cooling, recrystallization rapidly ensues. At higher temperatures the recrystallization proceeds extremely rapidly and clearly in some cases the most rapid quenching procedure is insufficient to retain the high temperature structure, as in the case of dynamic recovery discussed previously.

However close examination of the structures of nickel and copper after torsional deformation shows that the grain size of the recrystallized grains increases systematically from surface to centre of the specimen. This variation is consistent with the strain rate gradient which exists during torsional deformation and contrasts with the large grains foimed at random in a recovered structure in aluminium (Fig. 12(d)) or commercially pure iron held at temperature after deformation (Fig. 13(b)). Also of interest in this respect is the observation that, in zone-refined iron tested in torsion at 500-900°C, the substructure produced in the early stages of testing is replaced by regular equiaxed grains as the strain

increases (^2). This change in restoration process from subgrain formation to recrystallization with increase in purity is consistent with the

obser'/ation that impurities retard both the start of recrystallization and the rate at which it proceeds during annealing after cold work (32).

The size of the recrystallized grains also carles systematically with stress as shov/n in Fig. 15 where the data indicate that, for copper, nickel and zone refined iron, the grain size is inversely related to stress in an analogous manner to that observed for substructure during dynamic recovery. A similar relation has been observed in hot worked nickel-iron alloys (25). Such a relationship would not be expected for randcm recrystallization over a variety of quenching times at different temperatures and strain rates but is not unexpected if one considers the model proposed for recrystallization during cretp

(^3)-Here the initial stage of the deformation process is the formation of a poorly developed substructure. These sub-boundaries pin sections of the original grain boundaries which then bulge out and migrate because of a strain energy difference across the boundary. Clearly the extent of such migration determines the resulting grain size and under conditions of con-current deformation it is reasonable to expect the migration to be restricted by the scale of the substructures which as we have seen is dependent on

10

-A f u r t h e r objection to r e c r y s t a l l i z a t i o n as a softening process i s t h a t the r a t e of r e c r y s t a l l i z a t i o n in hot worked s t r u c t u r e s would be slow since repolygonization would maintain a l l boundaries a t a s i m i l a r

m i s o r i e n t a t i o n and hence p r e f e r e n t i a l migration would be prevented. This i s c e r t a i n l y true for isothermal annealing of hot worked s t r u c t u r e s in

aluminium and s i l i c o n - i r o n but under conditions of concurrent deformation the s i t u a t i o n can be a l t e r e d . Thus in the case of nickel there is

considerable evidence to show that the time f o r r e c r y s t a l l i z a t i o n can be a c c e l e r a t e d by s t r e s s . F i g . l6 shows t h a t for creep of n i c k e l , the tims to r e c r y s t a l l i z a t i o n decreases as ( s t r e s s ) ^ and that times of < 1 sec might reeisonably be expected at the operative s t r e s s e s during hot working. A similar trend i s observed during hot t o r s i o n t e s t i n g of n i c k e l - i r o n a l l o y s over a wide range of temperatures and s t r a i n r a t e s ( 2 5 ) .

Strong evidence for a difference in softening process between alvminium and commercially pure irons on one hand and copper, nickel and zone refined i r o n on the other comes from the form of the torque-revolution curves. Aluminium and commercially pure irons exhibit no i n i t i a l peak in torque as expected from a gradual development of s u b s t r u c t u r e . In c o n t r a s t , n i c k e l , copper and zone-refined iron e x h i b i t an i n i t i a l peak followed by a drop to the steady s t a t e region a s expected from the more abrupt change in structtire associated with r e c r y s t a l l i z a t i o n . I f t h e m a t e r i a l s are defoimed at low r a t e s of s t r a i n the differences become more marked i n that the curve for aluminium i s f a i r l y smooth while the curves f o r copper and n i c k e l e x h i b i t marked regular o s c i l l a t i o n s "vdiich can be correlated with s i g n i f i c a n t changes in grain s i z e (Fig. 9)- Such behaviour is r e a d i l y understood i f the o s c i l l a t i o n s are considered as sinalogous to t h e changes i n s t r a i n r a t e associated with repeated r e c r y s t a l l i z a t i o n during c r e e p . S i m i l a r l y the torque-revolution curves for Fe-25^Cr and Fe-it-^Si which show only substructure foimation are smooth a t low s t r a i n r a t e s while s t a i n l e s s s t e e l shows o s c i l l a t i o n s (l7)« I t i s i n t e r e s t i n g t o note that carbon s t e e l s in the 7-range also e x h i b i t marked o s c i l l a t i o n s a t low r a t e s of s t r a i n and that for these m a t e r i a l s the a c t i v a t i o n energies for creep and hot working are higher than f o r s e l f - d i f f u s i o n . Unfortunately the phase transformation on cooling masks the t r u e 7 s t r u c t u r e but there are indications t h a t the softening process i s r e c r y s t a l l i z a t i o n .

The important f e a t u r e that emerges from t h i s discussion i s that i n some m a t e r i a l s under hot working conditions r e c r y s t a l l i z a t i o n can operate extremely r a p i d l y to reduce s t r a i n hardening and that large s t r a i n s can be accommodated by repeated r e c r y s t a l l i z a t i o n t o maintain an equiaxed

s t r u c t u r e .

While the d i s t i n c t i o n between repeated r e c r y s t a l l i z a t i o n and repolygonization may appear to be academic since both lead to similar ends, i t i s important since the i n t e r a c t i o n of the softening process and the f r a c t u r e mechanism determines the d u c t i l i t y during hot working.

Fracture Mechanisms in Hot Working.

In the case of creep, the rupture mechanisms have been closely r e l a t e d t o the deformation mechanisms and these are now well understood. In the case of hot working, l i t t l e has been done tcT linlc f r a c t u r e behaviour closely to deformation mechanisms mainly due to the f a c t t h a t , u n t i l r e c e n t l y ,

r e l a t i v e l y few systematic studies had been reported. D u c t i l i t y in hot working must be intimately linked to the deformation mechanisms since any process which removes s t r a i n hardening w i l l allow g r e a t e r deformation. Thus d u c t i l i t y , as meastured by various t e s t s , increases with increased temperature and with increased s t r a i n r a t e . From our previous discussion both of these f a c t o r s would be expected to increase the r a t e of dynamic softening and hence reduce s t r a i n hardening. As with s t r e n g t h , a more d e t a i l e d p i c t u r e of f r a c t u r e mechanisms should be obtained from analysis of data on d u c t i l i t y as a function oi s t r e s s , r a t e of s t r a i n and temperatujre coupled with observations of fractirre modes.

C o r r e l a t i o n of Hot D u c t i l i t y Data. The major d i f f i c u l t y with c o r r e l a t i o n of hot d u c t i l i t y data i s that d u c t i l i t y measured in one type of s t r e s s system may not be r e l a t e d to d u c t i l i t y measured in another type of s t r e s s system or oven the same s t r e s s system with d i f f e r e n t specimen s i z e s .

Attempts have been made to r e l a t e d u c t i l i t y t o temperature and s t r a i n r a t e , but u n t i l r e c e n t l y , d u c t i l i t y data have not been a v a i l a b l e over a s u f f i c i e n t l y wide range of s t r a i n r a t e s and temperatures.

Thus an attempt to llnlc d u c t i l i t y to atomic mobility was made by Robbins et a l (kk) who proposed a r e l a t i o n of the form

P = SD2f(x) (6) t o describe the high temperature d u c t i l i t y of iron in hot t o r s i o n at a constant

s t r a i n r a t e . Here P i s d u c t i l i t y (revolutions to f a i l u r e ) , S is a constant roughly equal t o the number of active s l i p systems, D i s s e l f - d i f f u s i v i t y and f ( x ) a function of f a c t o r s such a s p u r i t y , amount of grain boundary s l i d i n g , e t c . The exponent of -g- was j u s t i f i e d i n terms of the atomic processes involved in s e l f - d i f f u s i o n during deformation. Robbins e t a l presented l i m i t e d data to support t h e i r proposed r e l a t i o n but l a t e r work by Reynolds and Tegart (U5) on irons of similar p u r i t y indicated that the i n i t i a l agreement was f o r t u i t o u s . Another attempt to r e l a t e d u c t i l i t y to r a t e of s t r a i n has been made by White and Rossard {k6) who showed that for a constant temperature there was a power r e l a t i o n s h i p between ntmber of revolutions t o f a i l u r e and s t r a i n r a t e for an iron-25^ nickel alloy tested in hot t o r s i o n . I n view of the success of the sinh r e l a t i o n s h i p in c o r r e l a t i n g strength data for both creep and hot working, i t i s not unreasonable t o examine the possible extension of a similar approach t o r u p t u r e . Thus for short rupture times i n c r e e p , the time to rupture (t^,) i s inversely r e l a t e d t o the steady s t a t e creep r a t e (22, kj) which in turn can be r e l a t e d t o the applied s t r e s s through the sinh r e l a t i o n s h i p . Thus i t i s p o s s i b l e to w r i t e :

-- 12

t^ = A"'(sinh aa)'^ cxp(^/RT) (7) At low s t r e s s l e v e l s , t h i s can be approximated

by:-t^ = A^''a"'''exp(Q/RT) (8) while at higli s t r e s s l e v e l s , t h i s reduces t o :

-t^ = A\-^^exp(Q/RT) (9) The v a l i d i t y of such an approach has been t e s t e d using data on a

s e r i e s of n i c k e l - i r o n a l l o y s obtained by using hot torsion over a wide range of s t r a i n r a t e s and temperatures. Resvlts for a nickel-20/o iron a l l o y are shown in F i g . I 7 . Thus Fig. 17(a) i s a log-log plot t o t e s t

the power r e l a t i o n -vAiile F i g . 17(b) is a semilog p l o t t o t e s t the exponential r e l a t i o n s h i p . The r e s u l t a n t sinh plot i s shown in F i g . 17(c) and i l l u s t r a t e s the temperature independence of n' ., The value of n' obtained f ran s t r e n g t h data i s compared i n Table 2 with that obtained fron rupture d a t a .

Since the Lines are p a r a l l e l on the sinh plot i t i s possible to obtain a value of Q from a p l o t of log t^,, a t constant sinh cca, against 1 / T .

Values calculated in t h i s manner are compared in Table 2 with those

c a l c u l a t e d from strength d a t a . There is a remarkable degree of agreement i n the values computed from the two c o r r e l a t i o n s .

Muller (26) has a l s o applied the proposed rupture c o r r e l a t i o n to h i s data on f r a c t u r e of a s e r i e s of nickel-chromium s t a i n l e s s s t e e l s . The r e s u l t s for the wholly a u s t e n i t i c alloy together with those on two phase a l l o y s consisting mainly of a u s t e n i t e f a l l in a s e r i e s of s t r a i g h t l i n e s on a sinh plot but the data f o r the wholly f e r r i t i c alloy give a poorer c o r r e l a t i o n , presumably'- due to a d i f f e r e n t f r a c t u r e mode as discussed l a t e r . I n the case of the a u s t e n i t i c a l l o y , the n ' and Q values calculated from rupture data ai-e in good agreement with those calculated from strength d a t a .

As i n the case of strength data, the use of a temperature compensated parame t e r

Z = t^exp(-Q/RT) = A'"(sinh da)'^ (lO) permits c o r r e l a t i o n of data for different temperatures on a single straigjit

l i n e as shown i n F i g . I 8 . For pure n i c k e l , creep rupture data can be c o r r e l a t e d with hot t o r s i o n rupture data in a s i m i l a r fashion to s t r e n g t h . This confirms the close r e l a t i o n s h i p between high temperature creep and hot working suggested by the strength c o r r e l a t i o n (21). From a p r a c t i c a l viewpoint such a rupture c o r r e l a t i o n could be useful in p r e d i c t i n g ruptture behaviour for d i f f e r e n t s t r e s s e s , and hence, from the e a r l i e r c o r r e l a t i o n ,

As in the case of creep, eq. (7) - (9) d.o not provide specific knowledge concerning the factors which govern the nucleation and

growth of cavities during hot working. They do indicate however that nucleation and growth of cavities is closely related to deformation processes during hot working.

In the case of nickel, the values of activation energy obtained from strength and rupture data are lower than that for lattice diffusion but are similar to those for grain boundary migration (Table l ) . The latter values are very dependent on purity and Detert and Dressier {k8) have recently reported a value of 30 k cal mole for grain boundary

migration in zone-refined nickel. However, while the value of 5^ k cal mole is lower than that for lattice diffusion, it is in the range of values reported for grain boundary diffusion {k9). Thus the activation

energy for grain boundary diffusion is independent of the misfit angle

from 20° to 70° with a value of 26 ± I.5 k cal mole while beyond these limits the activation energy increases smoothly to the activation energy for lattice s elf -d if fus ion.

These results on nickel during hot working can be compared with those of Hull and RlDmier (50) on creep rupture of copper where the value of the activation energy for rupture (25 - k cal mole) was also appreciably lower than that for self-diffusion but close to that expected for grain boundary diffusion (~ 20 k cal mole). A value of 29 k cal mole was also obtained by Boettnc-r and Robertson (5I) for growth of voids in copper. On this basis, grain boundary diffusion of vacancies has been identified as the process controlling intergrantilar void grovjth in creep rupture.

Further support for this viewpoint comes from the work of Ratcliffe and Greenwood (52) who showed that cavity development could be eliminated by the application of a hydrostatic pressure equal to the creep stress.

Other contributions to the growth process, e.g. by plastic deformation processes, were ruled out by the further observation that xn severely

cavitated specimens no void growth occurred when ^ hydrostatic pressure equal to the creep stress was applied although the material continued to creep at a rate unaffected by the pressure.

The Importance of a hydrostatic component of stress in minimising cracld.ng is familiar to those engaged in hot working of metals. However relatively few systematic st:udies are available. Thus Dieter et al (15) have shcnm that during hot torsion of Inconel 60O at 650-870°C the application

of a longitudinal compressive stress equal to '^Ofo of the yield stress increased the strain to fracture by a factor of 8-10. In contrast the application of a corresponding tensile stress only reduced the fracture strain by roughly one-third.

While such effects can be understood in terms of a rupture mechanism based on grain boundary diffusion of vacancies as in cavitation creep, there is considerable evidence to show that triple point cracking occurs

extensively during hot world.ng, as discussed in the next section. Further, the success of the proposed correlation for both single phase and tvro phase

Ik

-a l l o y s where interph-ase cr-acking i s known to occur (26) suggests t h -a t other processes may control crack growth. I t i s thus s i g n i f i c a n t t h a t recent work of Waddington and Williams (53) shows t h a t , f o r an aliaminium-2C5i zinc alloy which f r a c t u r e s i n t e n s i l e creep by t r i p l e - p o i n t cracking, the a p p l i c a t i o n of a h y d r o s t a t i c pressure equal to the creep s t r e s s increases both f r a c t u r e l i f e and t o t a l elongation at f r a c t u r e . Since t r i p l e point cracks nucleate as a consequence of s t r e s s concentrations produced by shearing along g r a i n boundaries, nucleation should be unaffected by the a p p l i c a t i o n of h y d r o s t a t i c pressure equal t o the creep s t r e s s . Thus the r e s u l t s of Waddington and Williams c l e a r l y i n d i c a t e that d u c t i l i t y is

a l t e r e d because the crack growth r a t e i s reduced under h y d r o s t a t i c p r e s s u r e . A rupture mechanism based on propagation of t r i p l e point cracks controlled by g r a i n boundary migration thus offers an a l t e r n a t i v e explanation for the e f f e c t s of h y d r o s t a t i c s t r e s s e s in hot working.

Observation of Fracture Modes. I n the case of creep-rupture, numerous observaEï5ns"in3rcatë"£fiê"öccürrênce of apparently two types of f r a c t u r e . The f i r s t are wedge, or w-type, cracks which are associated with t r i p l e p o i n t s . Rupture occurs by the joining of f i s s u r e s generated by these cracks. The second are round or e l l i p t i c a l , or r - t y p e , voids which are associated with g r a i n boundaries transverse to the applied t e n s i l e s t r e s s . Rupture occurs by the coalescence of a nunber of such voids. In the case of creep of Nimonic 90^ McLean (5^) has r e l a t e d the occurrence of these f r a c t u r e modes to s t r e s s and has shown t h a t w-type cracks are not observed below a t e n s i l e s t r e s s of 5 tons/in^ at temperatures between 750 and 950°C.

However, the problem of nucleation of cracks has r e c e n t l y been

discussed in some d e t a i l by Smith and Barriby (55)^ SiUd they point out sane corrections and amendments to the previously accepted models for t r i p l e point cracking due to g r a i n boundary sliding as based on the work of Stroh (56). The nucleation s t r e s s , T , in the modified form of Stroh' s analysis i s

T = (10)

where 7 i s surface energy of g r a i n boundary, B

G i s shear modulus, V i s Poisson's r a t i o ,

L i s s l i d i n g distance (assumed equal t o g r a i n diameter),

and p r e d i c t s nucleation to be appreciably easier than the o r i g i n a l form of the equation used, for example, by McTrean (5^)- For V = O.3, t h i s becomes

•1.77gGn2

Smith and Barnby (50) have considered a d e t a i l e d model of nucleation i n terms of the i n t e r a c t i o n between two orthogonal d i s l o c a t i o n p i l e - u p s and develop a f r a c t u r e nucleation c r i t e r i o n of

100b„ ^^^> E

where b^, i s a magnitude of Burgers v e c t o r of edge components of the d i s l o c a t i o n s . This i s a lower s t r e s s than that deduced from the Stroh r e l a t i o n with a reasonable assumption of the number of d i s l o c a t i o n s involved in t h i s p i l e - u p mechanism, namely

(13) They conclude t h a t the procedure of c o r r e l a t i n g experimental r e s u l t s on

the appearance of t r i p l e point cracks with t h e o r i g i n a l Stroh r e l a t i o n is invalid since nucleation would be expected t o occur a t much lower s t r e s s e s . I t i s suggested t h a t the- observed s t r e s s e s correspond to those required t o make cracks grow to an observable length since very small cracks can form at s t r e s s e s much lower than those predicted by Stroll' s o r i g i n a l formula .

The case of w-type cracking corresponds to a s i t u a t i o n where high s t r e s s e s generated by d i s l o c a t i o n p.ile-ups are supported by an i n f i n i t e amount of m a t e r i a l . In c o n t r a s t , r - t y p e voids correspond t o a s i t u a t i o n where the s t r e s s e s are supported by f i n i t e q u a n t i t i e s of m a t e r i a l , e.g. grain boundary ledges or p r e c i p i t a t e p a r t i c l e s . Smith and Barnby (57) have considered crack nucleation i n such cases and show t h a t , if l o c a l s t r e s s e s generated by g r a i n boundary s l i d i n g are not relaxed p r i o r to t h e onset of cracking, then p a r t i c l e s of width 2c at an i n t e r p a r t i c l e spacing of 2d in a botindary can nucleate cracks when:

1 ^ - , 1

rt / c 2 kyo, ( i - v ) d

d.

(c « d) (14)

For a given s i t u a t i o n , t h i s e::cpresEion p r e d i c t s t h a t nucleation w i l l occur as a much smaller s t r e s s than t h a t from S t r o h ' s a n a l y s i s using 2d as the s l i d i n g distance in place of L. However in such cases i t may not be p o s s i b l e for subsequent grain boundary s l i d i n g to enlarge the nucleated void up to the c r i t i c a l s i z e required for vacancy growth.

These recent treatments show c l e a r l y that the s t r e s s e s required for crack nucleation are much smaller than previously believed. Further they suggest t h a t the difference between w and r - t y p e voids i s more apparent

than r e a l since cracks can form r e a d i l y at both t r i p l e points and along g r a i n boundaries due to s t r e s s e s generated by grain boundary s l i d i n g . Their r a t e of growth w i l l then determine t h e i r subsequent size and shape.

16

-studying the propagation of t r i p l e point cracks i n an aluminium-20^ zinc alloy found t h a t , although crack growth was s e n s i t i v e to s t r e s s , a l l the f r a c t u r e times could be c o r r e l a t e d with s t r e s s according to eq. ( 9 ) . Moreover, at low s t r e s s e s in addition t o t r i p l e point cracks at grain

boundary j u n c t i o n s , c a v i t i e s or secondary cracks fonned at s e r r a t i o n s i n the grain boundaries. During gro^vTth the l a r g e r t r i p l e point cracks linlcc-d up with these secondary cracks. Crack growth was slov/ and in most cases was proportional to the amount of grain boundary sliding

entering the crack. As a consequence the growth r a t e of wedge cracks was dependent on the angle between the growing crack and the s t r e s s a x i s , increasing by an order of magnitude as the angle changed from 90° to 50-6o°.

Taplin and Wingrove (59) in a study of i n t e r g r a n u l a r f a i l u r e of iron by e l e c t r o n microscopy using r e p l i c a techniques found that over a wide range of conditions t r i p l e point and grain boundary cracks were developed

simultaneously. The subsequent growth of these depended on both temperature and s t r a i n r a t e with mechanical tearing predominating a t low temperatures and h i { ^ s t r a i n r a t e s and with dlffusional processes predominating at high temperatures and low s t r a i n r a t e s .

Returning to the case of f r a c t u r e of nickel under hot working conditions we can make an estimate of the s t r e s s e s for w-type cracldng using the value of 700 ergs/cm^ for the grain boundary energy of nickel at 900°C as suggested by Inman and T i p l e r ( 6 0 ) . Thus from eq. ( l 2 ) T = 2.8 x 10^ dyne/cm^ ~ 4000 p s i while from eq. ( l l ) with L = l o " ^ cm and G = 4 x lO-"-^ dynes/cm^ (a value appropriate to 900-1000°C), T = 2.2 x 10^ dynes/cm^ ~ 3100 p s i , a somewhat surprising r e s u l t i n view of Smith and Barnby's conclusions. No q u a n t i t a t i v e information on the v a r i a t i o n of grain boundary energy with composition i s a v a i l a b l e but if i t i s assumed that 7^ for the 20^ alloy is roughly half of that f o r pure nickel (a not unreasonable assumption in view of reported reductions of grain boundary energy due to i m p u r i t i e s ) , then from cq. (12) T ~ 2000 p s i while from eq. ( l l ) , T ~ 5100 p s i . ( i n the case of the alloys,

the grain s i z e i s f i n e r and a value of 5 x lO"-^ cm i s more a p p r o p r i a t e ) .

Although Smith and Barnby's c r i t e r i o n gives a smaller s t r e s s in t h i s case, the difference i s not as marked as they suggest. However such s t r e s s e s are

r e a d i l y reached i n t e s t s at high temperatures even at low s t r a i n r a t e s and we expect both t r i p l e point and grain boundary cracks i n hot worked m a t e r i a l s .

While various workers have reported some d e t a i l s of fracture modes during studios of hot working, r e l a t i v e l y few systematic studies have been reported. However the fracture behaviour of several pure irons has been extensively

studied by Reynolds and Tegart (ij-5) and Keane et al (^2) over the range 700-1250°C a t s t r a i n r a t e s of 0.8 and 8 sec"-^ using hot t o r s i o n . In the Oi region where repolygonization i s believed t o be the softening process, although small voids associated with o r i g i n a l grain boundaries appear in the specimens, f i n s l f r a c t u r e occurs by propagation of cracks into the specimen from surface

i r r e g u l a r i t i e s . In the 7 region wheie r e c r y s t a l l i z a t i o n i s believed to be

the softening process, extensive i n t e r g r a n u l a r cracking occurred at temperatures low in the 7 range and f a i l u r e occurred by linlcing up of these cracks. At higher temperatures in the 7 range, i n t e r g r a n u l a r cracking was reduced and

of these voids bj-- ductile fracture to give large internal cavities. In the temperature remge of the (X - 7 transformation, where two phase structures were observed, failure was associated with internal voids developed by

interjphase cracking.

Recently a systematic stijdy of fracture modes in an iron-25^ nickel alloy, where recrystallization is believed to be the softening process, was carried out over a range of strain rates and temperatures by White and Rossard (46). In specimens that failed at low ductilities, they shov-7ed

the presence of craclcs at both triple points and at grain boundaiy irregularities in tlie initial grain boundaries (Fig. 19)- These then llnlcc-d up to give intergranuJLar fracture (Fig. 20(a)). Although the triple point cracks were often larger than the grain boundary cracks, the differences appear to be associated with the relative amounts of grain boundary sliding in the two cases rather than with a difference in

mechanism in agreement with earlier discussion. In specimens that failed at high ductilities, the initial cracks were isolated from the original grain boundaries which disappeared due to recrystallization (Fig. 20(b)). New cracks foimed in the boundaries of the new grains. These observations are strikingly s.lmilar to those of Williams (57) discussed earlier. During further work on an iron-25fj chromium alloy, where repolygonization is

believed to be the softening process, VJhitc (6l) observed that fracture resulted froa the formation of very large holes in the interior of the specimen with a distinct absence of narked intergranular cracking.

These obsei'vations suggest that while cracks can be- readily nucleated during high temperature deformation, their subsequent propagation and the final mode of failure is dependent on the interaction between defoimation and fracture mechanisms.

The Interaction between Deformation and Fracture Mechanisms in Hot Working The fracture mechanisms operating during ho:^ working arc similar to those operating durüig creep yet very much larger strains can be imposed prior to fracture in hot working than in creep where failure occurs after a few per cent elongation. While the presence of compressive stresses will retard the growth of cracks, there must clearly be an interaction between deformation and fracture mechanisms which further slows dov7n the growth of cracks during hot working permitting large strains prior to failure.

Such an interaction has been briefly discussed by Davies and Wilshire (62) when considering creep results on \'arious grades of nickel and a nickel alloy. They suggest that whenever recovery processes in the region of the grain

boundaries cannot take place, low ductilities and a high crack incidence will result. Waerx either complete recrystallization in the necking region or grain boundary migration can occur, ductile fractures are obtained, with little or no intercrystalline cracking. Similarly Harris (63) suggests that recrystallization in grain boundary regions leads to enhanced tensile ductility of magnesium during high temperature deformation.

IS

-Rhines and Wray {6k) observed a minimum in t e n s i l e elongation a t an intermediate temperature region i n a number of face-centred cubic metals and alloys and suggested t h a t t h i s r e s u l t e d from marked grain botmdary s l i d i n g on the o r i g i n a l grain boundaries below the temperature range for rapid r e c r y s t a l -l i z a t i o n which cou-ld wipe out the o r i g i n a -l boundaries and thus reduce grain boundary s l i d i n g . A similar minimura around 760°C was observed during hot

t o r s i o n s t u d i e s on Inconel 600 by Dieter et al (15) while r e c r y s t a l l i z a t i o n in t h i s m a t e r i a l was not observed t i l l 50-6o°C h i g h e r .

Detailed s t u d i e s of i n t e r a c t i o n under hot woiking conditions have been made r e c e n t l y by White and Rossard (46) using hot t o r s i o n of an iron-25/i nickel a l l o y in which r e c r y s t a l l i z a t i o n i s the softening process, and by White (61) using hot t o r s i o n of an iron-25^ chromium a l l o y in which repolygonization i s the softening p r o c e s s . While some of the observations are s p e c i f i c a l l y r e l a t e d to the s t r e s s system operating during hot t o r s i o n (see 'Methods for Studying Hot Workability' ) , the ideas are applicable to hot working g e n e r a l l y . We consider

two cases of importance in p r a c t i c e namely continuous and i n t e r r u p t e d deforrüation. Continuous Deformation. The suggested model is tliat the i n i t i a l s t r e s s developed'för"an a p p i ï ê d " s t r a i n r a t e i s s u f f i c i e n t t o form craclis at the o r i g i n a l grain boundaries both at t r i p l e points and a t i r r e g u l a r i t i e s developed in the boundary. These cracks can then grov7 ^onder the combined action of vacancy diffusion along grain boundaries and applied t e n s i l e s t r e s s e s . ( i n hot t o r s i o n these are generated by r e s t r a i n t of the specimen but in mary working processes secondary t e n s i l e s t r e s s e s are o p e r a t i v e ) . Conditions of low d u c t i l i t y c o r r e s -pond to the propagation and coalescence of these cracks to give intergrantilar rupture along e s s e n t i a l l y the o r i g i n a l grain boundaries.

I n the case of materials where r e c r y s t a l l i z a t i o n i s the softening process, conditions of high d u c t i l i t y corixsspond to the migration or r e c r y s t a l l i z a t i o n of the o r i g i n a l grain boundaries, thus i s o l a t i n g the i n i t i a l cracks and

preventing further immediate growth. Further growth occurs by ' c a p t u r i n g ' a moving grain boundary for a s u f f i c i e n t time for vacancy diffusion and the

applied t e n s i l e s t r e s s to lengthen the crack a l i t t l e befoj-e the boundary again breaks away. New cracks may form in the boundaries of the r e c r y s t a l l i z e d grains and these would then proceed t o grow in a similar manner to the i n i t i a l cracks. The controlling process in crack propagation i s thus grain boundary migration.

In the case of m a t e r i a l s where repolygonization i s the softening p r o c e s s , although the o r i g i n a l boundaries tend t o lose t h e i r i d e n t i t i e s , the migrating sub-boundaries would not be expected to sweep üirough the material in the same way as grain boundaries. F u r t h e r , the measured average low angles of

mis-o r i e n t a t i mis-o n mis-of the sub-bmis-oundaries waild nmis-ot favmis-our vacancy diffusimis-on almis-ong boundaries over vacancy diffusion through the l a t t i c e and hence growth by t h i s process would be expected to be slow. However, in l o c a l i s e d zones adjacent t o the o r i g i n a l grain boundaries, higji misorientations can be achieved and further cracking ca.n occur at these new t r i p l e points and boundary s e r r a t i o n s . These can linlc up under the aiDplied s''"ress giving a s e r r a t e d , cracked boundary region as observed by Williams (58) during creep. The controlling process in crack propagation i s thus repolygonization which a c t s to maintain a l l sub-boundaries at the same small average m i s o r i e n t a t i o n .

During cold working, when the applied s t r e s s i s high, these materials are not s i g n i f i c a n t l y more d u c t i l e than those viilch re c r y s t a l l i z e , but during hot working the s i t u a t i o n i s markedly a l t e r e d and m a t e r i a l s exhibiting

by some hot t o r s i o n r e s u l t s on various m a t e r i a l s of similar I n i t i a l grain size at the same value of V'^'m = 0 . 7 ( l 3 ) - I t was found that copper, nickel and O-iron (0.2^C) f a i l e d a t shear s t r a i n s of 34, 23 and 54 r e s p e c t i v e l y while an i r o n - 3 V 4 ^ s i l i c o n a l l o y , an iron-25^ chrom.ium alloy and altuninium f a i l e d a t shear s t r a i n s of l 8 2 , 57 and 87 r e s p e c t i v e l y . The work of White (61) on an iron-25^ chromium a l l o y l e a d s hira to conclude t h a t , in the absence of

i n c l u s i o n s , the d u c t i l i t y of t h i s material i s ' q u a s i - i n f i n i t e ' .

The nature of the softening process is thus seen to be the major f a c t o r in determining the d u c t i l i t y of pure metals and a l l o y s during continuous deformation.

I n t e r r u p t e d Deformation. In many hot woiking p r o c e s s e s , the workpiece i s noE"Ëübjëctë3~tö"a continuously applied d e f o l i a t i o n but instead undergoes a s e r i e s of deformations separated by various times of holding at temperatures . During these holding p e r i o d s , s t r u c t u r a l changes can occur and we would expect

these to be r e f l e c t e d in changes in d u . c t i l i t y . R e l a t i v e l y l i t t l e a t t e n t i o n has been paid to t h i s aspect of hot v7orking . Thus White and Rossard (46) have reported r e s u l t s for an iron-25^ nickel a l l o y under programmed hot t o r s i o n while Cotner (40) has studied a s e r i e s of alimilnl van-magnesium a l l o y s using a similar technique.

In the case of the i r o n - n i c k e l a l l o y . White and Rossard c a r r i e d out a s e r i e s of t e s t s a t 1100°C a t a s t r a i n r a t e of 2 sec •^, using shear s t r a i n increments of 3-85 separated by holding times of 5 seconds, 1 rain, or 10 min. For continuous deformation the specimen f a i l e d a f t e r a shear s t r a i n of 44, while i n i n t e r r u p t e d t e s t s with the above holding times, the specimens f a i l e d a f t e r shear s t r a i n s of 38, 34 and 54 r e s p e c t i v e l y . I n a l l these t e s t s , the shear s t r a i n increment of 5«85 had already been shown to form grain boundary cracks and a further t e s t was made i n which the deformation was applied in shear s t r a i n increments of 0.77 separated by holding times of 1 min. In t h i s case the specimen f a i l e d a f t e r a siicar s t r a i n of

119-While these t o t a l s t r a i n s are c l e a r l y g r e a t e r than any imposed in p r a c t i c e , the r e s u l t s i n d i c a t e the marked effect t h a t defor^iiation schedttles can have on d u c t i l i t y . Thus d u c t i l i t y is improved e i t h e r by applying a l a r g e s t r a i n coupled with a l a r g e time intai-^/al or a small s t r a i n coupled with a small time i n t e r v a l . I n the former case the conditions are such that the o r i g i n a l grain structure i s replaced by a completely new structure and growth of t h e i n i t i a l large cracks i s i n h i b i t e d . In the l a t t e r case the i n i t i a l cracks a r e very s n a i l and although only p a r t i a l r e c r y s t a l l i z a t i o n occurs the growth of the cracks i s s t i l l I n h i b i t e d . However a s i t u a t i o n can a r i s e where the i n i t i a l era cks are l a r g e and the amount of r e c r y s t a l l i z a t i o n i s i n s t ï f f i c i e n t t o remove the i n i t i a l structure . Further deformation cycles of a similar type can then lead to more rapid f a i l u r e than in the continuous case.

In the case of super-pure aluminium and aluminium-magnesium a l l o y s , Cotner (4o), c a r r i e d out a s e r i e s of t e s t s over the temperature range from

150°C t o 600°C at a s t r a i n r a t e of 0.86 sec"^. The main features of the r e s u l t s a r e shown by the data in Table 3 on the 2^ magnesium a l l o y .

Thus below 350-400°C, prograr.mied deformation leads to g r e a t e r d u c t i l i t y , the g r e a t e s t d u c t i l i t y being obtained with the longest r e s t period. However, above 380°-400°C, programmed deformation l e a d s t o lower d u c t i l i t y , the lowest d u c t i l i t y being obtained with the longest r e s t period. This behaviour can

20

-be understood in terms of the competition -between recovery and recrystal-lization in this material. As pointed out earlier for pure aluminium isothermal annealing studies of hot worked material show that there is initially static recovery characterised by a sharpening of the subgrains with gradual softening followed by recrystallization associated with a more marked softening. For the altiminiura-2^ magnesium alloy, Cotner found that after a shear strain of 1.27, the times to rou^^ly 50^ recrystallization decreased rapidly with increased tanperature as 390 sees at 400°C, 42 sees at 450°C and 1 sees at 500°C.

Tlius, at the lower temperatures, appreciable static recovery during the rest periods allows migration of the sub-boundaries in the region of the original grain boundaries so that any initial cracks are isolated and their propagation is slowed down. This process would be enhanced by increased time allowing greater migration. About the critical range, the time between rest periods is such that marked migration and rearrangement occurs allowing some coalescence to give an increased subgrain size and greater angles of misorientation. With only a slight increase in temperature this structure changes to one consist.lng of subgrains having such high misorientation that cracks can develop in a similar fashion to those developed in the original grain boundaries. With further increase in temperature, recrystallization occurs to give a ccanpletely new grain structure which on further deformation develops further cracks. These will eventually linlc up to give failure but as the results show, ductility under interrupted deformation is lelatlvely

insensitive to temperature above 400°C. The increased rest period presumably leads to grain coarsening and hence a greater propensity to cracking.

Thus again the natuie of the softening process is seen to be the major factor in determining ductility of pure metals and alloys during interrupted defoimation. Further systematic studies are clearly necessary to improve our understanding of the fracture behaviour of materials in practical hot working processes.

Effect of Inclusions^ Impurities and Structural IrLomogeneities on Ductility The discussion of the previous section has been confined to pure metals and some homogeneous single phase alloys. Wnile such materials can give basic information on deformation and fracture mechanisms, they constitute a small fraction of the tonnage of hot worked products and the majoriiy of materials contain inclusions, impurities and structural inliomogeneities. VThile tlie effects of some of these can be understood in terms of the basic

ideas presented earlier, in large sections of complex alloys, particularly in the cast state, inliomogeneity of structure leads to localised situations which are not representative of the bulk material. Such situations which give rise to many of the problems associated with hot working operations e.g. hot shortness associated with local melting of a segregated phase or

preferential cracking due to interdendritic segregation or massive carbide phases, usually cannot be predicted from laboratory tests.