The free surface ductility of uniaxial compression specimens with longitudinal surface defects

Int. J. mech. Sei. Pergamon Press. 1969. Vol. 11, pp. 65-73. Printed in Great Britain

THE F R E E SURFACE DUCTILITY OF U N I A X I A L COMPRESSION SPECIMENS WITH LONGITUDINAL SURFACE DEFECTS P . F . THOMASON D e p a r t m e n t of Mechanical Engineering, University of Salford (Received 26 M a r c h 1968, and i n reviserl f o r m 14 A u g u s t 1968)

S u m m a r y - - A n investigation into the effects of longitudinal surface defects on the ductility of uniaxial compression specimens was made b y compressing cylinders of spheroidized high-carbon steel, containing artificial defects in the form of machined longitudinal grooves. The effects of specimen geometry and platen-specimen friction on the ductility of both defective and faultless cylindrical surfaces were examined. Surface grooves up to 0.005 in. deep on ¼ in. dia. cylinders were found to cause severe reductions in the ductility of the compression specimens. I n general, the apparent ductility of grooved specimens was found to increase as: the initial height-to-diameter ratio increased (to a m a x i m u m of 1.5) ; as the platen-specimen friction decreased; and as the groove depth decreased. Large concentrations of plastic flow, within surface defects, lead to early tensile plastic instability and ductile fracture at the defect root. Approximate measurements of the history of the stress components and strain increment components at the root of the artificial defects were used to estimate the point of tensile plastic instability. The equivalent strain from instability to macroscopic fracture at the groove roots was found to be of the same magnitude as t h a t at a faultless surface. A method of establishing an index of surface quality for cold heading wire is proposed. NOTATION Cfz, Crr, q8

axial, radial and circumferential principal stress components, respectively

d~e circumferential principal stress increment axial and circumferential principal strains, respectively In (W/W0), mean circumferential strain at a longitudinal groove circumferential principal strain at the root of a longitudinal groove dsz, d~ r axial and radial principal strain increments, respectively deG circumferential principal strain increment at the root of a longitudinal groove equivalent strain, S~](]) (de~ + de~ + ds~)t K ratio of principal strain increments at the root of a longitudinal groove H o, H initial and current height of cylindrical specimen, respectively Wo, W initial and current width of a longitudinal groove, respectively Do initial diameter of cylindrical specimen d o, d initial and current depth of a longitudinal groove, respectively mean coefficient of friction between compression platens and specimen ends ~z, tO 8W EG

INTRODUCTION MANY i n d u s t r i a l c o l d f o r g i n g o p e r a t i o n s a r e o f t h e u p s e t t i n g o r h e a d i n g t y p e I i n w h i c h t h e d i a m e t e r o f a b a r is i n c r e a s e d l o c a l l y a t o n e e n d b y a x i a l c o m p r e s s i o n . T h e l i m i t t o d u c t i l i t y i n a n i n d u s t r i a l h e a d i n g o p e r a t i o n is u s u a l l y s e t by the presence of longitudinal defects on the surface of the cold heading wire, which tend to open up during heading and produce localized surface fractures. ~ Most surface defects originate in the ingot and are elongated in the longitudinal 5 65

66

P . F . THo~Aso~

direction b y the subsequent rolling a n d drawing processes, a I n the fabrication of wire for cold heading operations, billet dressing processes are carried out to minimize the d e p t h of a n y surface defects, b u t it is impossible to eliminate t h e m completely b y a n y economic process. Cold heading q u a l i t y wire is usually processed to reduce the d e p t h of the surface defects to less t h a n 0.005 in. 4 The following work was carried out in an a t t e m p t to determine the effects of workpiece g e o m e t r y and die friction in heading processes on the ductility of wire containing longitudinal surface defects. The tests t h a t were carried out were the analogous operation of uniaxially compressing a cylindrical specimen containing artificial surface defects. The surface defects were in the form of m a c h i n e d longitudinal grooves, of a d e p t h similar to t h a t o f n a t u r a l defects on the surface of g o o d - q u a l i t y heading wire. EXPERIMENTAL

METHODS

The experiments were performed on compression specimens of high-carbon tool steel of the following nominal composition: 1.0 per cent carbon, 0.4 per cent manganese, 0.2 per cent silicon, 0.04 per cent sulphur and 0.04 per cent phosphorus content. The steel was supplied in the form of ¼in. dia. ground bar in the spheroidized annealed condition; the surface of this bar was free from natural longitudinal defects. All the high-carbon O.OOl" GROOVE ':'lk!J]

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FIG. 1. Variation in longitudinal groove profile, on the equator of barrelling, for the uniaxial compression of ½in. dia. alumininm cylinders. --, Original profile; - - . - - , profile at 41 per cent compression; .... , profile at 71 per cent compression. steel specimens in the present work were cut from the same bar to give a consistent ductility in the tests. The compression specimens were ~ in. dia. cylinders of 0.375 in. and 0-225 in. lengths, respectively. The cylindrical surface of each specimen was electropolished and then a set of specimens were machined to give longitudinal surface grooves of 0.001, 0.003 and 0.005 in. depth, set 120° apart on the circumference. The cutting tool for machining the grooves was made from 22 per cent tungsten highspeed steel and was ground to give a 0.001 in. radius at the tip for each cutting operation. Each groove was cut by a single stroke planing action using carbon tetrachloride as a lubricant, the resulting grooves closely conformed to the shape of the cutting tool with

Ductility of uniaxial compression specimens with longitudinal surface defects

67

very little residual burr and no tearing of the cylindrical surface. The change in cutting tool-tip radius during the machining of a groove did not exceed 0.0001 in. The profiles of the grooves are shown in Fig. 1. The compression tests were carried out in a sub-press fitted with lapped platens. For each specimen geometry the effects of the following friction conditions were exarained: (i) no lubrication, specimen and platens cleaned with acetone at each increment; (ii) molybdenum disulphide lubricant on platens; (iii)graphite and tallow lubricant on platens. The tests on the grooved specimens were carried out in small increments of compression and at each increment measurements were made of the current height and I'C

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equatorial diameter of the barrelled specimen, and the current width W across the grooves at the equator. The specimen geometry was measured with a vernier mierometer; the groove width was measured with a measuring microscope to an accuracy of + 0.0001 in. At each increment the root of each groove was examined at a magnification of × 5 for signs of fracture. F o r the tests on cylinders of HolD o ratio 1.5, lubricated with graphite and tallow, two horizontal grid lines were marked 0.020 in. apart at the mid-height on the free cylindrical surface, to facilitate the measurement of the axial principal strain e~ at the equator. The grid dimensions were measured with the measuring microscope to an accuracy of + 0.00005 in. The experiments were repeated on the cylindrical specimens, free from longitudinal grooves, to the point of macroscopic fracture on the barrelled surface.

68

P . F . THO~ASON

I n the present w o r k the fractures always originated at the groove roots; it was, therefore, desirable to measure t h e circumferential strain ~G at the root of each groove. H o w ever, e x p e r i m e n t a l difficulties encountered in t a k i n g a c c u r a t e m e a s u r e m e n t s at the groove roots m a d e this an impracticable proposition for t h e whole series of experiments. As an a l t e r n a t i v e to m e a s u r i n g the strain ~a, m e a s u r e m e n t s of the change in groove w i d t h W were used to calculate a q u a n t i t y ~w, defined as the m e a n circumferential strain at a groove. A series of tests were carried out to d e t e r m i n e the relationship between this m e a n strain ~w and the circumferential strain eG at the groove root. E s t i m a t e s of t h e strain ~c~ were m a d e f r o m m e a s u r e m e n t s of the change in spacing of scratch marks, which were left at the root of each groove b y the c u t t i n g tool. The m e a s u r e m e n t s for ~g were of a lower order of accuracy t h a n the m e a s u r e m e n t s of W and this gives a considerable scatter in the plot of ~w against eG shown in Fig. 2. Also, owing to the difficulty in t a k i n g the first m e a s u r e m e n t of scratch m a r k s in the unstrained grooves (the p r e d o m i n a n t scratches were shrouded b y m a n y superficial m a r k s until the first i n c r e m e n t of compression was carried out), the ~a strain was subject to a zero error. This causes a systematic displacement of some of the results in Fig. 2, in a d d i t i o n to the n o r m a l scatter. H o w e v e r , w h e n allowances are m a d e for these errors in the m e a s u r e m e n t s of ~a it is clear t h a t the m e a s u r e d m e a u strain ~w is a p p r o x i m a t e l y equal to the ~G strain. I n the following w o r k the m e a n strain across the groove ~w is assumed to be equal to the strain at the root of a groove ~G. A n u m b e r of tests were p e r f o r m e d on compression specimens of annealed a l u m i n i u m (supplied to B.S. 1476 EICM) to d e t e r m i n e the change in the profile of t h e grooves w i t h continued uniaxial compression. Grooves of 0"001 in., 0'003 in. and 0.005 in. depths were m a c h i n e d on cylinders of ½ in. dia. b y ¼ in. length and the changes in groove profiles m e a s u r e d during a compression test w i t h lubricated platens. The profile m e a s u r e m e n t s were m a d e b y focusing the m e a s u r i n g microscope on to t h e groove profile at the equatorial plane of the barrelled specimens; t h e co-ordinates of a n u m b e r of points along the profile were recorded. The profiles at two stages during the compression test are shown in Fig. 1. RESULTS The equatorial m e a n circumferential strains ~w across t h e grooves are plotted in Figs. 3 and 4 against In (Ho/H) for each specimen g e o m e t r y and p l a t e n - s p e c i m e n friction condition; the results are given to the point where macroscopic fracture occurs at t h e root of each groove. Also given in Figs. 3 and 4 are the results of the compression tests to fracture on specimens free f r o m g r o o v e s ; for these tests the equatorial circumferential strain ~e is plotted. I n all the tests, increases in the initial d e p t h of the grooves caused severe reductions in t h e a p p a r e n t d u c t i l i t y of the compression specimens. R e d u c t i o n s in p l a t e n - s p e c i m e n friction increased t h e d u c t i l i t y of the grooved specimens b y large a m o u n t s . F o r a specimen g e o m e t r y of H o l D o ratio 1"5, the 0.005 in. deep groove fractured at 45 per c e n t compression w h e n compressed w i t h o u t lubrication; a specimen w i t h a faultless surface fractured at 72 per cent compression. W h e n g r a p h i t e and tallow lubrication was used on these specimens t h e 0.005 in. deep groove fractured a t 62 per cent compression and the faultless surface at 79 per cent compression. F o r a specimen o f H o l D o ratio 0"9, compressed w i t h o u t lubrication, a 0-001 in. deep groove fractured at 45 per cent compression comp a r e d w i t h 70 per cent compression for a faultless surface. F o r similar specimens, compressed w i t h g r a p h i t e and tallow lubrication, the 0.001 in. groove fractured at 72 per c e n t compression and the faultless surface at 82 per cent compression. I n general, the shortgrooved specimens (tto/1) o ratio 0.9) were found to be less ductile t h a n the long ones (HolD o ratio 1.5), for a given groove d e p t h a n d p l a t e n - s p e c i m e n friction condition. A n a p p r o x i m a t e v a l u e for the m e a n coefficient of friction/~, between the specimen a n d compression platen, was e s t i m a t e d f r o m m e a s u r e m e n t s of the compression loads, using Siebel's analysis. ~ F o r g r a p h i t e a n d tallow lubrication/~ was found to be 0.09, for molybd e n u m disulphide lubrication g was 0.12; this small difference in the values of # was consistent w i t h the fact t h a t t h e compression loads for m o l y b d e n u m disulphide lubrication were systematically higher t h a n those for g r a p h i t e a n d tallow lubrication. F o r the compression tests w i t h o u t lubrication it was assumed t h a t sticking friction occurred; for these conditions, t h e y o n Mises yield criterion gives a theoretical value of #, equal to 0.577.

Ductility of uniaxial compression specimens with longitudinal surface defects

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E s t i m a t e s of t h e e q u a t o r i a l stress c o m p o n e n t s az a n d a o a t t h e r o o t of t h e grooves w~re m a d e for t h e t e s t s o n t h e s p e c i m e n of H o / D o = 1"5, l u b r i c a t e d w i t h g r a p h i t e a n d tallow. T h e stress c o m p o n e n t s were c a l c u l a t e d , b y m e t h o d s w h i c h were d e s c r i b e d p r e v i o u s l y , 5 f r o m t h e r e l a t i o n s h i p b e t w e e n t h e s~ a n d s(~ s t r a i n s , see Fig. 5. T h e c a l c u l a t e d values of t h e stress c o m p o n e n t s a~ a n d ae a n d t h e e q u i v a l e n t s t r a i n g a t t h e r o o t of t h e grooves are g i v e n in Fig. 6 as f u n c t i o n s of sG; t h e ar stress c o m p o n e n t is zero a t t h e free surface of t h e g r o o v e root. I t h a s b e e n s u g g e s t e d ~ t h a t microscopic f r a c t u r e is i n i t i a t e d a t a free p l a s t i c surface w h e n a s t a t e of tensile plastic i n s t a b i l i t y is r e a c h e d ; t h e p r e s e n t results were u s e d to t e s t t h i s h y p o t h e s i s . T h e c o n d i t i o n for i n s t a b i l i t y a t t h e r o o t of a groove is difficult to d e r i v e b e c a u s e t h e stress s y s t e m is complex. H o w e v e r , t h e stress s y s t e m is b a s i c a l l y s i m i l a r to t h a t a t t h e e q u a t o r of a b a r r e l l e d c o m p r e s s i o n s p e c i m e n s a n d in t h e following w o r k t h e c r i t e r i o n for i n s t a b i l i t y o n t h e free surface o f a b a r r e l l e d s p e c i m e n s is used as a n a p p r o x i m a t i o n for t h e i n s t a b i l i t y c r i t e r i o n a t a g r o o v e root. T h e c r i t e r i o n for i n s t a b i l i t y is therefore dao_ d~G

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I n t h e p r e s e n t w o r k t h e f r a c t u r e s s t a r t e d i n t h e r o o t of e a c h g r o o v e a t t h e m i d - h e i g h t of t h e s p e c i m e n . T h e first s m a l l c r a c k s were o r i e n t a t e d a t 45 ° t o t h e l o n g i t u d i n a l axis of t h e grooves a n d w i t h c o n t i n u e d d e f o r m a t i o n t h e s e c r a c k s j o i n e d u p to f o r m a large zig-zag c r a c k a l o n g t h e r o o t of t h e grooves, see Fig. 7. A s e c t i o n t a k e n t h r o u g h a s p e c i m e n , w h e r e f r a c t u r e s were j u s t visible, s h o w e d t h a t t h e f r a c t u r e s s t a r t a t t h e free surface of t h e g r o o v e r o o t a n d do n o t o r i g i n a t e b e l o w t h e surface. A n e x p e r i m e n t w a s c a r r i e d o u t t o d e t e r m i n e t h e effect of r o o t r a d i u s o n t h e f r a c t u r e c h a r a c t e r i s t i c s of g r o o v e d specimens. A h i g h - c a r b o n steel s p e c i m e n o f H o / D o = 1-5 was m a c h i n e d w i t h t h r e e g r o o v e s of 0.003 in. d e p t h ; t h e r o o t r a d i i of t h e s e grooves were, a p p r o x i m a t e l y : 0.0005, 0.001 a n d 0.0015 in. respectively. T h e specin~en was c o m p r e s s e d

Ductility of uniaxial compression specimens with longitudinal surface defects

71

with graphite and tallow lubrication until the first signs of macroscopic fracture occurred at one of the grooves : the additional amount of compression to cause fracture at the other two grooves was found to be less t h a n 0.5 per cent. This result suggests t h a t the depth of the groove is the primary parameter controlling the ductility of the specimen; the profile of the groove root does not appear to be of primary importance. Natural surface defects occur in m a n y forms, depending on their origin in the fabrication processes and very seldom

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take the form of a sharp c r a c k ) The root radius of a natural defect m a y be of an appreciable size, in comparison to the depth of the defect, 8 and in practically all cases will be far greater than the root radius of a brittle crack. I t is, therefore, probable t h a t the open grooves, in the present work, will be equivalent in fracture behaviour to a natural defect of the same depth. Work was carried out to determine the effect of specimen diameter on the plastic flow of grooves of a particular size. I t was found that, under similar conditions of specimen geometry and platen friction, the plastic flow at grooves of 0-001, 0-003 and 0.005 in. depth on ¼ in. dia. specimens closely corresponded to the flow at 0"002, 0.006 and 0'010 in. deep grooves on specimens of ~ in. dia. Hence, ff the surface defect size were to be converted to a ratio of defect depth to specimen radius, the present results for ¼ in. dia. bar could be applied generally to other bar diameters.

72

P . F . THO~ASON DISCUSSION

The results in Figs. 3 and 4 show t h a t the stress concentration effect at longitudinal surface defects results in large concentrations of plastic circumferential strain within the groove. This causes tensile plastic instability a n d ductile fracture, a t t h e root of the grooves, at an earlier stage of compression t h a n for a faultless cylindrical surface; hence the surface defect causes a reduction in the a p p a r e n t d u c t i l i t y of the specimen. I n general, the greater t h e d e p t h of a defect the greater is the r e d u c t i o n in a p p a r e n t ductility. The results also show t h a t reductions in friction between the specimen and compression platens reduce the stress c o n c e n t r a t i o n effect and thus increase the a p p a r e n t d u c t i l i t y of th(~ specimens for a g i v e n d e p t h of surface groove. Short specimens ( H o l d o = 0.9) containing surface grooves are m u c h less ductile t h a n long specimens (HolD o --- 1.5) w h e n compressed b y u n l u b r i c a t e d platens. H o w e v e r , for compression tests w i t h lubricated platens there is little difference in a p p a r e n t d u c t i l i t y for the two specimen geometries. These results, for the influence of p l a t e n - s p e c i m e n friction and specimen g e o m e t r y on t h e stress concentration effect at longitudinal grooves, are in q u a l i t a t i v e a g r e e m e n t with previous work, a which showed t h a t reductions in p l a t e n - s p e c i m e n friction and increases in the Ho/D o ratio of compression specimens reduced the m a g n i t u d e of the free surface stress components. F o r specimens compressed w i t h o u t lubrication it is clear t h a t e v e n v e r y small gro()ves, less t h a n 0.001 in. deep on ~ in. dia. bar, would cause m u c h earlier fracture t h a n occurs with faultless surfaces, see Figs. 3 and 4. This result suggests t h a t a n y surface defect, no m a t t e r how small, will cause an a p p a r e n t r e d u c t i o n in ductility, if the u p s e t t i n g operation is carried far enough. It owever, in the case of a particular heading process there will be a certain critical d e p t h of surface defect which will be related to the a m o u n t of u p s e t t i n g and to the m a t e r i a l properties of the wire; a n y defect smaller t h a n this critical value will not reach a state of ductile fracture during the heading operation. E s t i m a t e s of p l a t e n - s p e c i m e n friction show that, for a particular groove depth, a r e d u c t i o n in t h e m e a n coefficient of friction/~ from 0.577 to 0.12 gives only a relatively small increase in a p p a r e n t d u c t i l i t y (of the order 10-20 per cent compression), b u t a reduction in/~ f r o m 0.12 to 0.09 gives a relatively large increase (of the order 10 per cent compression), see Figs. 3 and 4. This result is in q u a l i t a t i v e a g r e e m e n t w i t h previous work, 5 which showed t h a t significant reductions in the m a g n i t u d e of the free surface stress components will not occur unless t h e coefficient of friction at the platens is reduced to the order of 0-1 or less. These results illustrate the i m p o r t a n c e of m a i n t a i n i n g good lubrication in u p s e t t i n g and heading processes, to achieve m a x i m t u n ductility. The m e a s u r e m e n t s of the groove profiles at various stages of compression, see Fig. l, show that, w i t h continued compression, the w i d t h of the groove W increases greatly but the d e p t h d increases only slightly. This is a result of the unusual m o d e of plastic flow at the free surface of a barrelled compression specimen. I t has been shown previously a that, at the equator, the initial tensile radial strain i n c r e m e n t quickly approaches zero with continued deformation and t h e n becomes compressive ; this limits the g r o w t h of a groove in the radial direction. The present results for t h e compression of a grooved specimen of Ho/D o ratio 1.5, lubricated w i t h g r a p h i t e and tallow, give values of e q u i v a l e n t strain from instability to fracture, at the groove roots, in the range of 0.106 to 0.118, see Fig. 6. This compares with e q u i v a l e n t strains from instability to fracture of 0.165 to 0.27 for faultless compression specimens cut from the same bar of high-carbon steel. ~ These results support the suggestion ~ t h a t ductile fracture d a m a g e is initiated b y tensile plastic instability, irrespective of w h e t h e r external local necking occurs. The m e a n circumferential strain ew to fracture at each groove, for a particular specim e n g e o m e t r y and friction condition, is a p p r o x i m a t e l y equal to the t o t a l circumferential strain e0 to fracture for a similar specimen free from defects, see Figs. 3 and 4. I t should therefore be possible to c o n s t r u c t graphs of ew against In (Ho/H), for a range of groove depths, in a n y t y p e of u p s e t t i n g or heading operation. A m e t a l of high ductility, e.g. p u r e aluminium, could be used for this w o r k because the plastic flow in a heading operation is highly constrained by t h e tooling, so t h a t the strains across the grooves ew would p r o b a b l y be similar to those for steel specimens. 5 W i t h graphs of this n a t u r e it would be possible to establish the m a x i m u m allowable defect d e p t h in the heading

FIG. 7. The root of a longitudinal groove showing ductile fracture ( x 35).

the development

of

Ductility of uniaxial compression specimens with longitudinal surface defects

73

wire for a particular process, once the circumferential strain e0 to fracture on a faultless surface had been determined for the particular wire material. CONCLUSIONS The circumferential stress concentration at longitudinal surface defects, in a uniaxial compression specimen, causes the defects to open up in the circumferential direction. The concentration of plastic flow within a defect appears to give early tensile plastic instability, which results in ductile fracture at the root at a much earlier stage in a compression test t han would occur for a specimen with a faultless surface. The equivalent strain from instability to macroscopic fracture at the root of a defect was estimated to be of the same order as t h a t on a faultless surface; this gives support to the suggestion 6 t h a t the ductile fracture process is initiated at the onset of tensile plastic instability. The results indicate that, within the limits of stable upsetting (i.e. H o l D o < 1.8), the greater the free height-to-diameter ratio in a heading operation, the lower is the stress concentration effect at surface defects and hence the greater the apparent ductility. Friction between the specimen and compression platens also has an important influence on the stress concentration effect and the fracture at longitudinal surface defects; reductions in platen-specimen friction caused a large increase in the apparent ductility of the grooved compression specimens. The apparent ductility of a specimen decreases, primarily, with increase in defect depth; variations in the root radius of the defect appear to have only a secondary influence on ductility. This suggests t h a t machined grooves and natural defects, of the same depth, might have an equivalent effect on the apparent ductility of a specimen. The circumferential strain to fracture on a faultless surface was found to be approximately equal to the mean circumferential strain to fracture at a groove. I t should therefore be possible to establish an index of surface quality for any particular heading operation. This would give the m axi m um amount of upsetting which could be performed for a given maximum depth of surface defect on a particular t ype of wire. Acknowledgements--The author gratefully acknowledges encouragement during this work

from Professor A. W. J. Chisholm and Mr. B. Fogg of the Department of Mechanical Engineering, University of Salford. The author also acknowledges valued advice by G.K.N. Group Research Laboratories, Wolverhampton.

1. 2. 3. 4. 5. 6. 7.

REFERENCES S. BILLIGMANN,Draht 1, 49 (1950). J. B x ~ I G M ~ , Stauchen und Pressen, Bild 46. Carl Hanser Verlag, Miinchen (1953). Iron and Steel Inst. Spec. Rep. No. 63, Part II, 25 (1958). T. G. BR~LDBURy,Proc. Met. Soc. Conf. Pittsburgh, 12, 29 (1961). P. F. THOMASON,Int. J. mech. Sci. 10, 501 (1968). P. F. THOMASON,to be published. E. SIEBEL,Stahl und Eisen 43, 1295 (1923).