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Platen Friction Forces in Compression Testing
An Investigation into the Elimination of the Effects of Billet/Platen Friction Forces in Compression Testing J. Mischke, Akademia Gorniczo-Hutnicza, Krakow/Poland; F. W. Travis, Mechanical Engineering Dept., Sunderland Polytechnic/U.K. - Submitted by J. M. Alexander i'iie mrr.pression i e s t is 'I simple :‘:ems d T ~icternlnlngstress-strdin data, particuldrly at elevated temperatures or at high strain rates, where the required deformation has to be accomplished in a single, short-duration operation. However, it is well appreciated that the results obtained are affected by the presence of friction forces between the ends of the specimen and the conpression platens, and all known ways of carrying out the different forms of compression test endeavour to reduce this friction, in order to increase the accuracy of the results obtained. In the present work, the idea of using a specimen of 'hour glass' or 'cooling tower' shape is discussed, and results of tests carried out to determine the most suitable specimen geometry are presented. During the compression of such specimens, their ends remain elastic: there is thus no relative flow between the specimen ends and the compression platens, so that the level of friction acting between them is immaterial.
The effects of different specimen shapes and dimensions on major parameters such as barrelling and buckling are explored, and stress-strain curves determined usinp the presently reported method are compared with results from the traditional tensile test. Photographs of typical diametrically sectioned and etched specimens are presented, to afford an illustration of the flow of material under the present test INTRODUCTION All known ways of carrying out the compression test endeavour to avoid or minimise the disadvantage of the presence of platen/specimen friction: different specimens with different height-to-diameter ratios have been used (1) and/or lubricants have been applied to the end faces of the specimens(1-4). However, despite these steps, it is very difficult to obtain satisfactory results where there is substantial defornation of the specimen. The friction forces cause a nonuniform stress state within the specimen, the major effects of which are to cause barrelling of the cylindrical specimen walls and in severe cases to rollingup of material from the cylindrical wall surfaces onto the platen. The compressive stress-strain curves, because of the inevitable presence of friction, thus lie above the results obtained from the tensile test, which is still the only test producinq a uniaxial and uniform stress state within the specimen. The generation of friction forces at the platen/specimen interface is associated with the radially outwards flow of specinen material over the platens, and their magnitude depends upon the relative displacement of the material and on the stress-strain state ( 5 , 6 ) beneath the surface of the specimen. The friction forces also depend, to some extent, on such factors as the presence of scale (in hot tests), on the roughness of the platens, and upon the presence of traces of lubricant, water, etc. Hence the friction forces have a largely random characteristic, and work undertaken into describing the influence of friction on the flow patterns of the material have not met with sufficient success to enable accurate calculation of the effects of friction on the stress--strain curve. In the elastic stress state the friction forces can be significantly less than in the plastic state, due in part to the lesser displacement of the material over the platens: consequently, disturbance in the stress state due to the random characteristic of the friction forces can be very small. In particular, if the friction forces are imposed on the elastic part of a plastically deformed body and if that part is sufficiently far from the plastic zone, it is in order to neglect their influence on the nature of the stressstrain curve. The above observations provided the idea of a 'cooling tower' shaped specimen having different diameters along its length, such that the ends in contact with the platen remain elastic whilst the middle of the specimen is plastically deformed: some specimen shapes fulfilling these requirements are shown in Fig. 1. These specimens contain a central thin cylindrical part which has been termed the 'testing zone' and above and below it two parts of varyinq diameter called the 'separating zones'.
The purpose of the present investigations is to establish whether the testing zone satisfies the requirements of having a uniaxial and uniform compressive stress state at high levels of strain, despite possibly high roughness of the platens. The following were taken as affording evid-ence of this situation: (i) little or no barrelling of the testing zone; (ii) metallographic confirmation of uniform straining; (iii) close agreement between the present stressstrain curves and those resulting from the tensile test. SPECIMENS, EQUIPEtJ'I' , PROCEDIJXE Specimens Commercially pure aluminium and mild steel were chosen for the tests (Table l ) , some reasons for the choice of which are as follows : (i) comercially pure aluminium has nechanical properties similar to those of steel at elevated temperature: yrticularly so in respect of strain hardening; Lii) the grain structure of aluminium is clearly evident: iii) aluminium allows a fairly large plastic deformation in the tensile test; iv) the stress-strain curve for aluninium is smooth, without upper and lower yield points: v) the strain hardening of mild steel is siqnificantly different from that of aluminium and, particularly, the strain hardening is greater and near the yield point a strain instability occurs: vi) it should be possible to detect the instability Table 1
Description and Coding of Specimens
dimensions
No,
Code degrees
1
2
- I
-
-
15
15
5
5
CIS A!, C5
At
3
45
3
15
33
4
30
3
15
41
3OT3-15 A &
5
15
3
15
65
15T3-15 A!,
453T-15 A!,
6
15
20
5
59
15T20-5 A!,
7
15
26
5
61
15T26-5 A9.
8
15
30
5
62
15T30-5 A!,
9
-
60
5
61
R6O-5 AP.
50
5
57
R50-5 A9.
40
5
51
R40-5 A&
30
5
46
R30-5 A9.
15
15
C15 St
5
45
I0
11
-
12 13
5
'
$
2
14 Pig. 1
Types of specinen tested (dimensions in m ) .
15
15
30
15T30-5 S t
2:
16
Annals of the CIRP Vol. 33/1/1984
151
estimated as about 0.005m. A Surfcom-Ferrantr nnchine served for recording the barrelling of the testing zone: the gain was 20Q:l whereby an offset of straightness of 3.005m was easy to detect. Before each test the diameters of thc testing zone and of the free end of each specimen were neasured by micrometer. After testing, the barrelling of the testing zone was recorded and each specimen was then dianetrica1l.y sectioned for netallographic examination. The natural logarithmic axial strain and the true axial stress were determined from the known initial diameter of the specimen and its current diameter and axial load. RESLTLTS AND DISCUSSION
Selection of Specimen Shape Selection of a suitable specimen shape involves consideration of two factors: barrelling and buckling. These two factors act at different ends of the spectrum of saecinen dimensions: an important task was to employ a slenderness ratio which was sufficient to inhibit barrelling whilst simultaneously not promoting buckling. Some examples of barrelling are shown in Fig.3a. The barrelling of T-type specimens of uniform angle s over the separating zone is shown in Fig. 3b. The increase of the initial radius R of the separating zone is presented in Fig. 3c. Barrelling of a cylindrical specimen is caused by radial friction forces acting on the end faces of the specimen, such forces producing a negative radial stress which influences the material flow. A similar resistinq Fi&. 2 Sub-press used for the compression testa: 1. euide; radial stress at the end of the testing zone can be 2. anvils; 3. specimen; 4, device for measurinc the generated by the resistance to radial expansion of the diameter of the specimen. separating zone. The testing zone became plastic before _ - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _the _ larger - _ cross section of the adjacent separating zone. Consequently,at theboundary between the elastic during the compression of mild steel if the and 2lastic zones,there is a tendency for a difference stress state is indeed uniform and uniaxial: in diarceter between neiqhbouring cross sections that (vii) mild steel allows quite large plastic deformation. could cause indirect deformation of the elastic part of the body. A large angle t , and similarly, a nonThe ?resent compression tests were carried out on uniform stress state inside the seDarating zone when a spccirnens having the shapes and dimensions shown in small value of radius F is employed, enhance this Table 1. The tensile test specimens were manufactured phenomenon. in accordance with British Standards, whilst the compression test specimens were turned with the aid of a Sensitivity to change of Poisson's ratio in the vicinity master to ensure close repeatability of shape. of the yield point was probahly bound u~ wit:? the strain
-a
I
':./
I \
Fig. 3
! I/
I
d
Barrelling of specimens: (a), ( b ) , (c) alUminium, for a mean logarithnlc strain of E = -0.50; (d) mild steel, for logarithnic strains of E = -0.50 (full line), c = -0.40 ( d o t t e d line) and E = -0.55 (chain-dotted line).
I Fig. 4
_ _ _ _ _ _ _ _ _ _ _ _ - _ _ _ - - - - - Equipment and Procedure All compression and tensile tests were carried out on a hydraulic universal testing machine, where the accuracy of load measurement was 0.1N and 1N for aluminium and steel respectively. To ensure axial loading, the subpress shown in Fig. 2 was manufactured. The compression faces of the anvils were roughened with course abrasive paper to secure the greatest possible degree of friction between the specimen ends and the platens. The displacement of the anvils (indicating the current height of the specimen) was neasured by means of a dial A special strain gauge gauge to an accuracy of O.@lmm. device was used for recordinq the current diameter of the testing zone: before testing, tne device wds calibrated using slip gauges and its accuracy was
Schematic diaeram illustratine the influence of Poisson's ratio and the nature of the work-hardening characteristics of the material on the compressed shape of type T specimens: full line continuous strain hardening (such as for mild steel); thin lines (figure c) - barrelling of the specimen. (a) the variation of Poisson's ratio with reduction in heieht of the testing zone; (b) the stressstrain curves; (c) the shape 09 the Fompreqsed - specgnens.
-
_ _ _ - _ _ - _ - _ -
hardening characterics of the material: particularly, instability of deformation could affect it strongly. Pn example of possible differences in behavior of two kinds of material is illustrated in Fig. 4 , where a scheme for deformation of a material with and without plastic instability in its yield point is illustrated. For simplification, it was assumed that both of the materials have the same yield point and that Poisson's ratio changed within 0.2'4 of plastic defornation. The loadimposed on both specimens is assumed sufficient
Fie.5
-
9O02 i '
Curvature of t h e t e s t i n e zone v e r s u s (a) angle r ; (h) radius R ; ( c ) displacement o i t h e c e n t r e of t h e mid-leneth c r o s s s e c t i o n from t h e a x i s o f the Specimen d i v i d e d by t h e t e s t i n g zone diameter
s t r a i n E = -0.50 and t h e continuous and dotted l i n e s r e f e r r e s p e c t i v e l y to 5-type and T-type aluminium Specimens.
-
- - - - - - - _ - _ _ _ _ _ _ _ _ _ _ _ _ _ for the achievement of the axial compressive yield stress in the border cross sections of the testing zone. curves correspond to Points ABCI) on the stress-strain points A ' B ' C ' D ' on the silhouettes of the deformed specimens (Fig. 4c),to their diameters, and to the reduction of the height of the testing zone. C0nsid.ering this scheme, it would ap?ear that a naterial with plastic instabilityin its yield point causes greater barrelling: this view was confirmed by the greater barrelling for the mild steel specimen (Fig. 3d) than for the aluminium specimen (Fig. 3c). Barrelling of most of the R-type s-,ecimenswas not of a regular nature (Fig. 3 ~ ) . The camber became very irregular and for aluminium was close to or even less than that arising from the roughness 0 5 the specimen side surfaces. The carber penarally extended some way beyond the current lenath of the testing zone and sometimes beyond the original length of the testin? zone. The maximum value of the camber did not exceed 0.02m (aluminium at a logarithmic strain of E = -0.72) and 0.07m (mild steel at a logarithmic strain of i = -0.55)
(a) I .
(b) I ,
(middle l e f t )
(b) 11. (middle r i g h t ) (c) I. (c) ~
To enable a conparison fcr different types of specimen the mean curvature of the camber was calculated as follows (Fiq. 5a): 1 = _8c _ P
(top l e f t )
(a) 11. ( t o p Tight)
Ir.
(on l e f t ) (below) ~
L'
Decreasing the angle a decreased the average curvature of T-type specimens (Fig. 5a). The curvature of most R-type specimens remained small but indicated a clear tendency tcwards increase for larger values of radius R (Fig. 5b). Buckling (Fig. 5c) varied with the slenderness (Table 1): Buckling for the mild steel R30-5 specimens was less than that of aluminium (rig. 5 c ) and did not exceed 0.5mm deflection of the centre of the cross section from the specimen axis. Type R30-5 specimens secured both the least bucklinq and barrelling. Etch diametrical cross sections of this type of spechen (FicJ. 6) showed almost exactly parallel patterns in the crystal structure surrounding the testing zone. There were no indications of bands of concentrated shear stress which are a characteristic feature of compressed cylindrical specimens (Fig. 6). These results indicated that the R30-5 type specimens are the most suitable for the purposes of the present research. Stress-strain Curves For the reasons discussed above, type R30-5 specimens were used to establish compressive stress-strain curves for aluminium (Fig.7a) and mild steel (Figs.7b,c). The measured points lay within a narrow band parallel to the tensile curve: for aluminium (Fig.7a) they straddled the tensile curve, whilst for mild steel (Fig.7b) they lay very close, but above, the tensile curve. Some of the compressive stress-strain curves for the cylindrical specimens lay above the tensile curve, and at increasing distance from it with increasing deformation. Close to the yield point, sone of the measured
Fig. 6
Etched d i a m e t r i c a l sections: (a) R30-5AP. (E = -0.43 and E = - 0 . 5 0 ) ; (b) R30-5St ( E = - 0 . 4 5 and E = - 0 . 5 5 ) ; (C) C15AL ( 6 = -0.56) and C 1 5 S t ( E = -0.40).
points for cylindrical specimens deviated frcm the tensile curves (Fig. 7,9). The latter was probably caused bcth by insufficient accuracy in detecting height differences at such low levels of strain, and by local deformation of the specimen end faces - despite careful grinding before testing - in bedding down onto the platens. In a small number of tests, ug?er and lower yield points were observed (mild steel, Fig.7c), which indicated unrestrained deformation of the testing zone. CONCLUSIONS (i)
The above described research established that 'hour glass' shaped specimens, particularly type R30-5, secure uniform and uniaxial stress within the testing zone, irrespective of the presence of high platen/specimen interface friction.
153
(ii) The degree of buckling and barrelling of the s2ecimens depends on their shape and on their mechanical pro9erties: hence in the selection of the best shape consideration should be given to both cf these factors. The present investigations indicate that the 'hour glass' type separating zones, with their gentle blending into the testing zone, lead to a more uniform stress state than arises with the conical shaped (T-type) separating zones. (iii) Comparison of the compression test results with the tensile test results established better agreement fcr aluniniun. This suggests that the presently described test may be used with accuracy for the compression of steel at elevated temperatures. (iv) The accuracy necessary for the detection of the yield point appears to be easier to achieve with 'hour glass' s?ecimens than with the T-type ones. It was found possible to detect both the upper and the lower yield points. (v) The range of deformation in using the ?resent 'hour glass' specimens is limited by the necessity of avoiding plastic deformation of their end faces. The mean pressure on the end of the specimen should not exceed the yield point, or at least not exceed it to a substantial degree. Hence, a high degree of strain hardening should contribute to the range of deformation that may be employed. Apart from allowing the determination of the stressstrain data from continuous observation of the increase in diameter with load of the reduced-diameter midlength "testing zone", this test alsc permits the postprocess determination of such data by measurement of the deformed "transition zone", as the varying crosssectional area of ti-.is zone along its length results in a varying deoree of strain: knowing the final load, a simple corcparison of the pre- and post- process profiles of the specimen thus enables a relatively quick and simp1.e assessment of the stress-strain relationship. This feature is to be reported in reference 7 . REFE4ENCES
1. 2.
3.
4.
5.
6.
7.
Fig. 7
S t r e s k s t r a i n curves f o r : ( a ) aluminium specimens; (b) mild steel specimens; and ( c ) mild steel specimens where t h e m a t e r i a l d i s p l a y s a pronounced y i e l d p o i n t . Round p o i n t s , square p o i n t s and t r i a n e u l a r p o i n t s r e f e r r e s p e c t i v e l y t o specimens of type R30-5, type C 5 and
- - -
t y p e c15.-
154
-
-
-
-
- -
I
-
-
-
- - - -
-
FEN!IER A. J., Mechanical Testing of Materials, Newnes, London, (1955). KUDO H., Some Analytical and Experimental Studies of Axi-symmetric Cold Forging and Extrusion - 11, Int.J.Mech.Sci., 3 (1961) 91-11:. CLATEF R. A. C., J O H N S O N W., and AKU, S. Y., Fast Upsetting of Short Circular Cylinders of Plain Medium Carbon (0.55aC) Steel at lioom Temperature, Proc. 9th Int.Mach.Too1 Des.Res. Conf., Manchester, Sept. 1963, Pergamon, Oxford, (1969) 115-133. KROKHA V. A., The Stresses Arising on Sizing Spechen with Cylindrical End Recesses packed with Solid Lubricant, Problemy prochnosti, 12 (1978) 83-91. (S.S.S.R.) DOBRUCKI Wy., and ODPZYVOgEK E., Analyse des Elethodes de Determination par Refoulage du Coefficient de Frottement - Entre L'Outilage et le Metal en Etat d'Ecoulement Plastique Bases sur le Procede de Refoulage, J.Plech.Work. Tech., 4 (1980) 155-176. DOBRUCKI WY., 3DROYWOLEX E . , Correlation entre le Frcttement sur la Surface de Contact Outil/ Metal Deforne Plastiquement et le Mode d'Ecoulement des Couches Internes du Metal, J.Mech.YIork.Tech., 4 (1980) 351-368. MISCHKE J., and TPAVIS P. V., Determination of the Compressive Stress-strain Relationship from the Shape-Change of a Specinen of 'Hour Glass' Form, J.Yech.Work.Tech., (in Press).
The effects of different specimen shapes and dimensions on major parameters such as barrelling and buckling are explored, and stress-strain curves determined usinp the presently reported method are compared with results from the traditional tensile test. Photographs of typical diametrically sectioned and etched specimens are presented, to afford an illustration of the flow of material under the present test INTRODUCTION All known ways of carrying out the compression test endeavour to avoid or minimise the disadvantage of the presence of platen/specimen friction: different specimens with different height-to-diameter ratios have been used (1) and/or lubricants have been applied to the end faces of the specimens(1-4). However, despite these steps, it is very difficult to obtain satisfactory results where there is substantial defornation of the specimen. The friction forces cause a nonuniform stress state within the specimen, the major effects of which are to cause barrelling of the cylindrical specimen walls and in severe cases to rollingup of material from the cylindrical wall surfaces onto the platen. The compressive stress-strain curves, because of the inevitable presence of friction, thus lie above the results obtained from the tensile test, which is still the only test producinq a uniaxial and uniform stress state within the specimen. The generation of friction forces at the platen/specimen interface is associated with the radially outwards flow of specinen material over the platens, and their magnitude depends upon the relative displacement of the material and on the stress-strain state ( 5 , 6 ) beneath the surface of the specimen. The friction forces also depend, to some extent, on such factors as the presence of scale (in hot tests), on the roughness of the platens, and upon the presence of traces of lubricant, water, etc. Hence the friction forces have a largely random characteristic, and work undertaken into describing the influence of friction on the flow patterns of the material have not met with sufficient success to enable accurate calculation of the effects of friction on the stress--strain curve. In the elastic stress state the friction forces can be significantly less than in the plastic state, due in part to the lesser displacement of the material over the platens: consequently, disturbance in the stress state due to the random characteristic of the friction forces can be very small. In particular, if the friction forces are imposed on the elastic part of a plastically deformed body and if that part is sufficiently far from the plastic zone, it is in order to neglect their influence on the nature of the stressstrain curve. The above observations provided the idea of a 'cooling tower' shaped specimen having different diameters along its length, such that the ends in contact with the platen remain elastic whilst the middle of the specimen is plastically deformed: some specimen shapes fulfilling these requirements are shown in Fig. 1. These specimens contain a central thin cylindrical part which has been termed the 'testing zone' and above and below it two parts of varyinq diameter called the 'separating zones'.
The purpose of the present investigations is to establish whether the testing zone satisfies the requirements of having a uniaxial and uniform compressive stress state at high levels of strain, despite possibly high roughness of the platens. The following were taken as affording evid-ence of this situation: (i) little or no barrelling of the testing zone; (ii) metallographic confirmation of uniform straining; (iii) close agreement between the present stressstrain curves and those resulting from the tensile test. SPECIMENS, EQUIPEtJ'I' , PROCEDIJXE Specimens Commercially pure aluminium and mild steel were chosen for the tests (Table l ) , some reasons for the choice of which are as follows : (i) comercially pure aluminium has nechanical properties similar to those of steel at elevated temperature: yrticularly so in respect of strain hardening; Lii) the grain structure of aluminium is clearly evident: iii) aluminium allows a fairly large plastic deformation in the tensile test; iv) the stress-strain curve for aluninium is smooth, without upper and lower yield points: v) the strain hardening of mild steel is siqnificantly different from that of aluminium and, particularly, the strain hardening is greater and near the yield point a strain instability occurs: vi) it should be possible to detect the instability Table 1
Description and Coding of Specimens
dimensions
No,
Code degrees
1
2
- I
-
-
15
15
5
5
CIS A!, C5
At
3
45
3
15
33
4
30
3
15
41
3OT3-15 A &
5
15
3
15
65
15T3-15 A!,
453T-15 A!,
6
15
20
5
59
15T20-5 A!,
7
15
26
5
61
15T26-5 A9.
8
15
30
5
62
15T30-5 A!,
9
-
60
5
61
R6O-5 AP.
50
5
57
R50-5 A9.
40
5
51
R40-5 A&
30
5
46
R30-5 A9.
15
15
C15 St
5
45
I0
11
-
12 13
5
'
$
2
14 Pig. 1
Types of specinen tested (dimensions in m ) .
15
15
30
15T30-5 S t
2:
16
Annals of the CIRP Vol. 33/1/1984
151
estimated as about 0.005m. A Surfcom-Ferrantr nnchine served for recording the barrelling of the testing zone: the gain was 20Q:l whereby an offset of straightness of 3.005m was easy to detect. Before each test the diameters of thc testing zone and of the free end of each specimen were neasured by micrometer. After testing, the barrelling of the testing zone was recorded and each specimen was then dianetrica1l.y sectioned for netallographic examination. The natural logarithmic axial strain and the true axial stress were determined from the known initial diameter of the specimen and its current diameter and axial load. RESLTLTS AND DISCUSSION
Selection of Specimen Shape Selection of a suitable specimen shape involves consideration of two factors: barrelling and buckling. These two factors act at different ends of the spectrum of saecinen dimensions: an important task was to employ a slenderness ratio which was sufficient to inhibit barrelling whilst simultaneously not promoting buckling. Some examples of barrelling are shown in Fig.3a. The barrelling of T-type specimens of uniform angle s over the separating zone is shown in Fig. 3b. The increase of the initial radius R of the separating zone is presented in Fig. 3c. Barrelling of a cylindrical specimen is caused by radial friction forces acting on the end faces of the specimen, such forces producing a negative radial stress which influences the material flow. A similar resistinq Fi&. 2 Sub-press used for the compression testa: 1. euide; radial stress at the end of the testing zone can be 2. anvils; 3. specimen; 4, device for measurinc the generated by the resistance to radial expansion of the diameter of the specimen. separating zone. The testing zone became plastic before _ - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _the _ larger - _ cross section of the adjacent separating zone. Consequently,at theboundary between the elastic during the compression of mild steel if the and 2lastic zones,there is a tendency for a difference stress state is indeed uniform and uniaxial: in diarceter between neiqhbouring cross sections that (vii) mild steel allows quite large plastic deformation. could cause indirect deformation of the elastic part of the body. A large angle t , and similarly, a nonThe ?resent compression tests were carried out on uniform stress state inside the seDarating zone when a spccirnens having the shapes and dimensions shown in small value of radius F is employed, enhance this Table 1. The tensile test specimens were manufactured phenomenon. in accordance with British Standards, whilst the compression test specimens were turned with the aid of a Sensitivity to change of Poisson's ratio in the vicinity master to ensure close repeatability of shape. of the yield point was probahly bound u~ wit:? the strain
-a
I
':./
I \
Fig. 3
! I/
I
d
Barrelling of specimens: (a), ( b ) , (c) alUminium, for a mean logarithnlc strain of E = -0.50; (d) mild steel, for logarithnic strains of E = -0.50 (full line), c = -0.40 ( d o t t e d line) and E = -0.55 (chain-dotted line).
I Fig. 4
_ _ _ _ _ _ _ _ _ _ _ _ - _ _ _ - - - - - Equipment and Procedure All compression and tensile tests were carried out on a hydraulic universal testing machine, where the accuracy of load measurement was 0.1N and 1N for aluminium and steel respectively. To ensure axial loading, the subpress shown in Fig. 2 was manufactured. The compression faces of the anvils were roughened with course abrasive paper to secure the greatest possible degree of friction between the specimen ends and the platens. The displacement of the anvils (indicating the current height of the specimen) was neasured by means of a dial A special strain gauge gauge to an accuracy of O.@lmm. device was used for recordinq the current diameter of the testing zone: before testing, tne device wds calibrated using slip gauges and its accuracy was
Schematic diaeram illustratine the influence of Poisson's ratio and the nature of the work-hardening characteristics of the material on the compressed shape of type T specimens: full line continuous strain hardening (such as for mild steel); thin lines (figure c) - barrelling of the specimen. (a) the variation of Poisson's ratio with reduction in heieht of the testing zone; (b) the stressstrain curves; (c) the shape 09 the Fompreqsed - specgnens.
-
_ _ _ - _ _ - _ - _ -
hardening characterics of the material: particularly, instability of deformation could affect it strongly. Pn example of possible differences in behavior of two kinds of material is illustrated in Fig. 4 , where a scheme for deformation of a material with and without plastic instability in its yield point is illustrated. For simplification, it was assumed that both of the materials have the same yield point and that Poisson's ratio changed within 0.2'4 of plastic defornation. The loadimposed on both specimens is assumed sufficient
Fie.5
-
9O02 i '
Curvature of t h e t e s t i n e zone v e r s u s (a) angle r ; (h) radius R ; ( c ) displacement o i t h e c e n t r e of t h e mid-leneth c r o s s s e c t i o n from t h e a x i s o f the Specimen d i v i d e d by t h e t e s t i n g zone diameter
s t r a i n E = -0.50 and t h e continuous and dotted l i n e s r e f e r r e s p e c t i v e l y to 5-type and T-type aluminium Specimens.
-
- - - - - - - _ - _ _ _ _ _ _ _ _ _ _ _ _ _ for the achievement of the axial compressive yield stress in the border cross sections of the testing zone. curves correspond to Points ABCI) on the stress-strain points A ' B ' C ' D ' on the silhouettes of the deformed specimens (Fig. 4c),to their diameters, and to the reduction of the height of the testing zone. C0nsid.ering this scheme, it would ap?ear that a naterial with plastic instabilityin its yield point causes greater barrelling: this view was confirmed by the greater barrelling for the mild steel specimen (Fig. 3d) than for the aluminium specimen (Fig. 3c). Barrelling of most of the R-type s-,ecimenswas not of a regular nature (Fig. 3 ~ ) . The camber became very irregular and for aluminium was close to or even less than that arising from the roughness 0 5 the specimen side surfaces. The carber penarally extended some way beyond the current lenath of the testing zone and sometimes beyond the original length of the testin? zone. The maximum value of the camber did not exceed 0.02m (aluminium at a logarithmic strain of E = -0.72) and 0.07m (mild steel at a logarithmic strain of i = -0.55)
(a) I .
(b) I ,
(middle l e f t )
(b) 11. (middle r i g h t ) (c) I. (c) ~
To enable a conparison fcr different types of specimen the mean curvature of the camber was calculated as follows (Fiq. 5a): 1 = _8c _ P
(top l e f t )
(a) 11. ( t o p Tight)
Ir.
(on l e f t ) (below) ~
L'
Decreasing the angle a decreased the average curvature of T-type specimens (Fig. 5a). The curvature of most R-type specimens remained small but indicated a clear tendency tcwards increase for larger values of radius R (Fig. 5b). Buckling (Fig. 5c) varied with the slenderness (Table 1): Buckling for the mild steel R30-5 specimens was less than that of aluminium (rig. 5 c ) and did not exceed 0.5mm deflection of the centre of the cross section from the specimen axis. Type R30-5 specimens secured both the least bucklinq and barrelling. Etch diametrical cross sections of this type of spechen (FicJ. 6) showed almost exactly parallel patterns in the crystal structure surrounding the testing zone. There were no indications of bands of concentrated shear stress which are a characteristic feature of compressed cylindrical specimens (Fig. 6). These results indicated that the R30-5 type specimens are the most suitable for the purposes of the present research. Stress-strain Curves For the reasons discussed above, type R30-5 specimens were used to establish compressive stress-strain curves for aluminium (Fig.7a) and mild steel (Figs.7b,c). The measured points lay within a narrow band parallel to the tensile curve: for aluminium (Fig.7a) they straddled the tensile curve, whilst for mild steel (Fig.7b) they lay very close, but above, the tensile curve. Some of the compressive stress-strain curves for the cylindrical specimens lay above the tensile curve, and at increasing distance from it with increasing deformation. Close to the yield point, sone of the measured
Fig. 6
Etched d i a m e t r i c a l sections: (a) R30-5AP. (E = -0.43 and E = - 0 . 5 0 ) ; (b) R30-5St ( E = - 0 . 4 5 and E = - 0 . 5 5 ) ; (C) C15AL ( 6 = -0.56) and C 1 5 S t ( E = -0.40).
points for cylindrical specimens deviated frcm the tensile curves (Fig. 7,9). The latter was probably caused bcth by insufficient accuracy in detecting height differences at such low levels of strain, and by local deformation of the specimen end faces - despite careful grinding before testing - in bedding down onto the platens. In a small number of tests, ug?er and lower yield points were observed (mild steel, Fig.7c), which indicated unrestrained deformation of the testing zone. CONCLUSIONS (i)
The above described research established that 'hour glass' shaped specimens, particularly type R30-5, secure uniform and uniaxial stress within the testing zone, irrespective of the presence of high platen/specimen interface friction.
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(ii) The degree of buckling and barrelling of the s2ecimens depends on their shape and on their mechanical pro9erties: hence in the selection of the best shape consideration should be given to both cf these factors. The present investigations indicate that the 'hour glass' type separating zones, with their gentle blending into the testing zone, lead to a more uniform stress state than arises with the conical shaped (T-type) separating zones. (iii) Comparison of the compression test results with the tensile test results established better agreement fcr aluniniun. This suggests that the presently described test may be used with accuracy for the compression of steel at elevated temperatures. (iv) The accuracy necessary for the detection of the yield point appears to be easier to achieve with 'hour glass' s?ecimens than with the T-type ones. It was found possible to detect both the upper and the lower yield points. (v) The range of deformation in using the ?resent 'hour glass' specimens is limited by the necessity of avoiding plastic deformation of their end faces. The mean pressure on the end of the specimen should not exceed the yield point, or at least not exceed it to a substantial degree. Hence, a high degree of strain hardening should contribute to the range of deformation that may be employed. Apart from allowing the determination of the stressstrain data from continuous observation of the increase in diameter with load of the reduced-diameter midlength "testing zone", this test alsc permits the postprocess determination of such data by measurement of the deformed "transition zone", as the varying crosssectional area of ti-.is zone along its length results in a varying deoree of strain: knowing the final load, a simple corcparison of the pre- and post- process profiles of the specimen thus enables a relatively quick and simp1.e assessment of the stress-strain relationship. This feature is to be reported in reference 7 . REFE4ENCES
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Fig. 7
S t r e s k s t r a i n curves f o r : ( a ) aluminium specimens; (b) mild steel specimens; and ( c ) mild steel specimens where t h e m a t e r i a l d i s p l a y s a pronounced y i e l d p o i n t . Round p o i n t s , square p o i n t s and t r i a n e u l a r p o i n t s r e f e r r e s p e c t i v e l y t o specimens of type R30-5, type C 5 and
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FEN!IER A. J., Mechanical Testing of Materials, Newnes, London, (1955). KUDO H., Some Analytical and Experimental Studies of Axi-symmetric Cold Forging and Extrusion - 11, Int.J.Mech.Sci., 3 (1961) 91-11:. CLATEF R. A. C., J O H N S O N W., and AKU, S. Y., Fast Upsetting of Short Circular Cylinders of Plain Medium Carbon (0.55aC) Steel at lioom Temperature, Proc. 9th Int.Mach.Too1 Des.Res. Conf., Manchester, Sept. 1963, Pergamon, Oxford, (1969) 115-133. KROKHA V. A., The Stresses Arising on Sizing Spechen with Cylindrical End Recesses packed with Solid Lubricant, Problemy prochnosti, 12 (1978) 83-91. (S.S.S.R.) DOBRUCKI Wy., and ODPZYVOgEK E., Analyse des Elethodes de Determination par Refoulage du Coefficient de Frottement - Entre L'Outilage et le Metal en Etat d'Ecoulement Plastique Bases sur le Procede de Refoulage, J.Plech.Work. Tech., 4 (1980) 155-176. DOBRUCKI WY., 3DROYWOLEX E . , Correlation entre le Frcttement sur la Surface de Contact Outil/ Metal Deforne Plastiquement et le Mode d'Ecoulement des Couches Internes du Metal, J.Mech.YIork.Tech., 4 (1980) 351-368. MISCHKE J., and TPAVIS P. V., Determination of the Compressive Stress-strain Relationship from the Shape-Change of a Specinen of 'Hour Glass' Form, J.Yech.Work.Tech., (in Press).