A Study of the Plane Strain Compression Test*

A Study of the Plane Strain Compression Test* M. Pietrzyk, University of Mining and Metallurgy, Krakow/Poland; J. G. Lenard (I), G. M. Dalton, University of Waterloo, Waterloo/Canada Received on January 29,1993

The applicabiliry of the plane strain compression test to simulate the flat rolling process is examined. analytically and through experiments. The resistance to deformation and the rise of temperature of a 6061-T6 aluminum alloy is determined in plane strain compression. A thermal-mechanical finite element model. developed to analyze both the rolling and compression processes is then introduced. Its ability to calculate the distributions of the variables is substantiated by comparing the tim-temperature profiles measured during plane strain cornpression tests with those predicted by the model. Following next arc comparisons of the distributions of stress, strain rate and temperature in the two processes. leading to the conclusion thaG in general, good similarity among the parameters is observed and that the plane shain compression test gives a reasonable simulation of the flat rolling process. provided the shape factors are comparable

KEYWORDS:Rolling, Compression, Temperature INTRODUCTION The mathematical model of a bulk metalforming process involves the equations of motion, thermal balance, criterion of plastic flow, geometrical relations between the deformations, velocities, strains and rates of strain and the notion of plastic incompressibility. Some of these relations are based on natural laws; some of them are the results of time-honoured and well substantiated observations. They are, of course, subject to constraints - the initial and boundary conditions. The boundary conditions involve the initial values of the temperatures and their distributions at the boundaries of the dom.ain and the normal and shear stresses there. Traditionally, these are handled by the prescription of a heat transfer coefficient and a coefficient of friction in addition to potentially existing front and back tensions or pressures, such as the interstand tensions on the finishing train of a hot strip mill. Further, one may define the initial conditions as the material's resistance to deformation and its metallurgical structure.

predicted stress, strain and strain rate distribution in the flat rolling process to those of the plane strain compression test then allows one to conclude if and under what conditions the two metalforming phenomena are indeed similar. THE MATHEMATICAL MODEL

The model is composed of two parts. The first is the mechanical component, computing the stress, strain and strain rate variations during the compression process. This is then coupled to a model of the heat transfer during the experiment: the thermalcomponent.The first part has beendescribed indetail in [lo]; the thermal portion is briefly reviewed below. The temperature field in the deformation zone is calculated by the finite element solution of the general diffusion equation

dT

Tension, torsion and compression tests are routinely carried out when the material's flow strength needs to be determined. The relative advantages and disadvantages of the three testing techniques are well understood [l].Briefly, they refer to the ease of conducting a tension test and the difficulty of coping with the low levels of possible straining before the triauiality of the stresses develops: the interfacial friction and the attendant barreling of compression samples and the need for some interpretation of the results of a torsion test, demanded by the variation of the stresses and strains along the radius of the sample. In an ideal situation the flow curves obtained by these tests should be identical; in fact, in those relatively few cases where comparison has been attempted, they are not [2]. These differences in the flow strength of metals, some of which were detailed in [ 11 may well be due to the different stress and strain distributions within the deforming sample. A consensus appears to be beginning among material scientists, leading to the realization that the test, used to establish a material's constitutive behaviour should resemble the forming process which is being modelled. Specifically, the distribution of stresses and strains in the two processes should be similar. The experiments used to determine the material's flow strength are often employed to simulate its behaviour in any one of the bulk deformation processes. Among the most prevalent uses is for flat rolling where simulation techniques lead to significant savings of time and money.

Or(kvT)+Q-pc dt where k is the conductivity, T represents the temperature, Q stands for the rate of heat generation due to plastic work, P is the density, c, designates the specific heat and t is time. Discretization of the problem and application of a variational principle leads to a set of simultaneous, linear equations [ll]:

The first suggestion of the use of the plane strain compression tests appears to be by Nadai [4]. As Watts and Ford [S] mention, Ford used plane strain compression to determine flow curves of annealed materials [6]. There are somegeometrical restrictionson the experiment; the width ofthecompression platen should be between 2 and 4 times the strip thickness.

In what follows, the suitability of the plane strain compression test to simulate the flat rolling process is examined. This is done by comparing the calculated distributions of strains, temperatures and die pressures in the two forming techniques. A rigid-plastic finite element method is used, which, as suggested by Lee and Kobayashi [7], is particularly useful for the simulation of metalformingprocesses involving large strains. Use of the technique has beenshown to be successful in describing the compression process [S,9].Here a thermal analysis is coupled with mechanical simulation. After a brief introduction of the method, the validity of the model is substantiated by comparing its predictions of temperature rise to measurements taken during plane strain compression of 6061-T6 aluminum strips. A comparison of the model's

Annals of the ClRP Vol. 42/1/1993

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(2)

where

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and

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It appears then that the compression test conducted on flat or iuially symmetrical samples - should be the preferred technique to follow when the simulation of bulk forming processes is contemplated. Zeroing in on the process of flat rolling, hot, cold or warm, the plane strain compression tests may well be the best to evaluate the strength characteristics of the metal to be rolled. Analysis of the distributions the stresses and strains in a rolled metal and in a specimen subjected to plane strain compression [3] indicates some similarities, showing that the above hypothesis may be correct.

3

3

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In the above h represents the heat transfer coefficient at the contact surface, N is the shape function, T ois the ambient or the die temperature and ystands for the rate of heat generation caused by frictional forces between the compression platens and the sample. The Lagrangian formulation is used in the solutionofthe problem. Automatic meshgenerationand remeshing[l2] allow large grid distortions during the deformation process. Remeshing is applied to avoid computational difficulties. A typical, undeformed mesh, showing all boundary conditions, is given in Figure 1.

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Figure 1: An undeformed mesh, showing the thermal and mechanical boundary conditions for plane strain compression

331

where f x . f are surface the tractions and n7designates the friction factor. The die velocity is u Gand the velocity components in the x and y directions areu, ,is,, respectively. The heat flux through the boundary isaand the shear stress on the surface is '1. ~

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Table 1 The chemical composition of the test material, by weight %

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In the calculations the material's strain hardening curve, determined in independent compression tests, was found to be

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where the flow strength is designated by u and is given in MPa.

Figure 2: The distorted mesh The deformed mesh of anoriginally 9.4 mm thick aluminum strip. compressed to a thickness of 3.63 mm. is shown in Figure 2. The large distortions of the elements near the corners of the die and the concentration of strains there are clearly visible.

RESULTS AS'D DISCUSSION Time-temperature profiles The calculated time-temperature profiles are compared to the measured ones in Figures 6 to 10.

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thickness 9.4 mm

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Figure 3: The strain distribution during plane strain compression

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a a I prediction, centre ooooa measurement, centre

The distribution of the effective strains during the compression process is given in Figure 3 and the temperature field after the deformation is indicated in Figure 4.

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thickness 9.4 mm 'reduction 5.77 mm

lhickness 9.4 mm reduclian 6.63 rnm die velocity 1.18 mm/s wialh of die 6.4 mm

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width of the die 12.7 mm Figure 4: The temperature distribution during plane strain compression EXPERIMENTAL EQUIPMENT, PROCEDURE AND MATERIAL Equipment: A schematic diagram of the plane strain press used in the experiments is shown in Figure 5 . The press has facilities for easy and fast exchange of the compression dies which are made of 01 tool steel (KEEWATIN), hardened to Rc 55 and ground to have a surface finish of 1.8 t i , peak to valley. The loads are measured by a strain gauge-based loadcell; the displaccments are monitored by a DCDT. The temperatures are measured by type T (copper-constantan) thermocouples of 1.6 mm outside diameter, stainless steel sheaths and exposed beads. One thermocouple is embedded in each sample, located centrally in the deformation zone. HYDRAULIC CYLINDER

.-

DIES

LOADCELLS

Figure 6: Temperature rise during plane strain compression at a velocity of 1.18 mm/sec. Theheat transfercoefficient usedinthemodelwastaken tobe20000W/m2K. In each plot the temperature in"C is shown on the ordinate and the time in seconds is given along the abscissa. In all figures the solid squares indicate the calculated temperatures and the open squares designate the measurements. The die velocity in the first experiment - see Fig. 6 - was fairly slow, at 1.18 mm/second. The die width was 6.4 mm and the originally 9.4 mm thick and 38 mm wide sample was compressed to a final thickness of 2.77 mm. The average strain rate during the process is computed to be 0.28 sec-1. The temperature rise as a result of plasticwork is measured to be 24'C. The initial rate of temperature rise is approximately 2t°C/sec. The velocity of compression in the second test was increased to5.2 mm/second and the die width was increased to twice its value in the first test, to 12.7 mm. The average strain rate in the experiment is calculated to be 1.27sec-1. almost five times the rate in the previous example. As shown in Fig. 7, both the temperature rise and the rate of rise are significantly higher than before; the strip's temperature increased by W C at a rate of nearly 160"C/sec. 110 100 90 80 6 70

. ? = Figure 5: Schematic diagram of the plane strain press Procedure: Before the compression test, the dies and the samples were carefully cleaned with an alcohol based solvent. The flat specimen was placed in the press and it was aligned to be perpendicular to the dies. The thermocouple was placed in the exact centre of the deformation zone. The top die was then lowered slowly until it just about contacted the top surface of the sample. The computer based data acquisition system was readied and triggered when the compression began. Compressive force, the displacement and the temperature were recorded simultaneously using the microprocessor's A/D converter. After the test a postprocessor computed the true stresses and the true strains. Material: 6061-T6aluminum alloys of 9.4 mm thickness, 38 mm width and 200 mm length were used in the study. The chemical composition of the metal is given in Table 1, above. The Brine11 hardness was measured to be 92.

332

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thickness 9.4 m m reduction 6.77 rnm

time, s Figure 7: Temperature rise during plane strain compression at a velocity of 5.2 mm/sec. In the next three experiments mineral seal oil was used to minimize friction at the compression platen-strip interfaces. In the slower tests conclusions are similar to those above; that is, the model is capable of predicting both the temperature gain and its rate of rise quite well. In the test, shown in Figure

10, the velocity of compression is 3.9 mm/sec. The different time response of the embedded thermocouple is apparent in the results, probably caused by the insulating effects of the lubricant. The predicted final temperature is still near the measured value, differing by approximately 5%.

distortion of the heat flow in the interrupted solid or the stress concentration that must be present around the embedded bead. These effects are being studied at present. Comparison of the flat rolling and the plane strain compmsion processes Having shown that the mathematical model is capable of good predictions of the temperature distribution, it is assumed that its predictions of the distributions of the stress fields as well as the strain and strain rate distributions are equally accurate. A numerical experiment is then conducted to compare the distributions of the dependent variables in a compression test to those occurring during flat rolling.

a20' thickness 9.4 mm reduction 6.63 m m die velocily 1.55 mm/s wiath of die 6.4 mm

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Figure 8: Temperature rise during plane strain compression at a velocity of 1.65 mm/sec; mineral seal oil is the lubricant o.6 0.4

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Figure 9: Temperature rise during plane strain compression at a velocity of 1.34 mm/sec; mineral seal oil is the lubricant 110 100

90 80

+

10

- 8

thickness 9.4 rnm reductian 6.63 mm die velocity 3.9 mm/s width of die 12.7 mm

Figure 11: The distributions of effective strains during plane strain compression and rolling Cold rolling of an aluminum strip of 10 mm thickness, 100 mmwidth, reduced to a final thickness of 6 mm. in one pass, is considered. The work rolls are taken to have a diameter of 200 mm and are rotating at 4.1 p m . The parameters of the compression test must then be chosen carefully for the two processes to be comparable. The velocity of compression is therefore taken to be 10 mm/s. The width of the compression dies is determined such that the shape factors in the two experiments should be identical. In the flat rolling example - 10 mm thickness, 200 mm diameter rolls, 40% reduction - the shape factor is calculated to be 0.28 when integrating to determine the average strip thickness [16].For the plane strain test to be comparable, a die width of 28 m m is then required which is near the dimension suggested by the original publication of Watts and Ford [ 5 ] .To check the effect of the die width, two dies are used in the calculations that follow, 28 mm and 10 mm wide. The strain fields in the two processes are investigated first. The distribution of the effective strains across the thickness of the deformed samples are shown in Figure 11.The distributions are similar for the two experiments, provided the wider die is used in the compression process. A minor difference is observed: the maximum strains during rolling appear to be near the surface while during compression, the centre portion is worked more than the edge. Using the narrower die results in a highly nonuniform distribution, with the centre of the strip strained much more than the surface. It is apparent that the similarity of the shape coefficients isof some significance for the simulation to be reasonable.

time, s

Figure 10: Temperature rise during plane strain compression at a velocity of 3.9 mm/sec; mineral seal oil is the lubricant

In all five experiments the predictive ability of the model is shown to be reasonable. Both the temperature rise and the rate of rise are computed to be very close to the measured values. The thermal-mechanical model employed in the present study has been used before in analyzing the temperature fields during rolling of strips and plates [13,14]. In those instances the model was very accurate in its predictions of the final temperatures but not quite so accurate in calculating the rates of temperature rise. In most cases the computed rate of rise was somewhat above the measured one. In an unpublished study [IS] the computed rate of temperature rise lagged significantly behind the measurements during hot upsetting of axially symmetrical samples. Since in both cases the same type of thermocouples were used, their time response may be safely ignored; the difference of the predictive capabilities is therefore found in the different strain distributions occurring in the two metalformingprocesses. In flat rolling the regions closer to the roll/strip contact are strained, most while in upsetting it is the central regions that experience the highest amount of plastic work. In the present work the strain distribution across the compressed sample appears to be quite uniform and this fact is probably responsible for the model's ability to predict the rate of temperature rise quite closely. The model ignores the existence of finite thermocouple beads, the possibility of the

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Figure 12: Comparison of the pressure distributions during plane strain compression and rolling The pressures on the forming tools as a function of time are examined next. These aregiveninFigure 12where thestrain-hardeningcurve ofthe aluminum alloy is also shown. The loads on the forming tools the work roll and the compression platen are observed to be quite close and again it may be

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333

concluded that using the plane strain compression test to simulate flat rolling is acceptable. As well, the effectsof friction in the compression process appear to be somewhat higher than in rolling, no doubt because of the large die width. The temperature increase due to plastic deformation in the two forming tests is demonstrated in Figures 13a for compression with the wider die and 13b for rolling, in the forms of isotherms. Time-temperature profiles are shown in Figure 14. The maximum temperature in compression is predicted to be about 10°C lower than in rolling. This is no doubt due to the higher rate of conduction in the compression experiment where the contact conditions remain unchanged during the deformation. To examine this hypothesis further, calculationswere done using higher velocities leading to shorter contact times. In the rolling problem 41 rpm was assumed and in the compression test 100 mm/s was considered. The difference in the results is immediately noticeable in Figures 15, and b; the temperature rise in the two processes is now comparable.

REFERENCES

1.

2. 3.

4. 5.

6. 7.

8.

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5

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uoI

3

1

10

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,

,

ROLL-

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SI I! g . 18 8IP B I 20

9.

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30

40

50

10.

Figure 13: A comparison of the temperature distributions during plane strain compression and rolling 11.

12. CONCLUSIONS

13.

Lenard, J.G. and A.N. Karagiozis, 1987,Accuracy of High-Temperature, Constant Rate of Strain Flow Curves, inFactors ThurAffcr rhePrecision ofMececlianica1 Tests, eds. Papirno, R. and Weiss, H.C. STP 1025,ASTM, Bal Harbour, 206-216. Semiatin. S.L. and Jonas, J.J.. 1984, Formability and Workability of Metakplasric instability andflow localizarion.ASM. Metals Park, Ohio. Pietrryk, M.and Lenard. J.G., 1989. On the Significance of the Evaluation of Temperature Fields during Metal Forming Processes, Meralurgia i Odlewnichvo, 15369-382. Nadai. A., 1931, Plasticity, McGraw Hill, New York and London. Watts, A.B. and Ford, H., 1952, An Experimental Investigation of the Yielding of Strip Between Smooth Dies, Proc.f.Mech.E., 1B:448-453. F0rd.H.. 1948, Researches into the Deformation of Metals by Cold Rolling", Proc. f.Mec/i.E., 159:115-143. Lee, C.H. and Kobayashi. S., 1973, New Solution to Rigid-Plastic Deformation Deformation Problems Using a Matrix Method, ASME, J.End.lnd, 95~865-873. Chen, C.C. and Kobayashi, S.. 1978, Rigid-Plastic Finite Element Analysis of Ring Compression, in Application of Numerical Merho& to Forming Prcxesses, ASME. ADM, 28163-174. Matsumoto, H., Oh, S-I. and Kobayashi, S.. 1977,A Note on the Matrix Method for Rigid-Plastic Analysis of Ring Compression, Proc. 18th MTDR Con$, London, 3-9. Glowacki, M. and Pietrzyk, M.. 1989, Experimental Substantiation of Rigid-PlasticFinite Element Modelling of Three-Dimensional Forming Processes,J.Mech. Working Techn., 19295-304. Pietrzyk, M. and Lenard, J.G., 1988, Experimental Substantiation of Modelling Heat Transfer in Hot Flat Rolling, Proc. 25th Nut. Heat Trnnrfer Conf: (Ed. Jac0bs.H.R.). Houston, 347-53. Pietrzyk. M., 1991, Zastosowanie metody elementow skonczonych do symulacji procesu spemnia, ffurnik, 58:60-63 (in Polish). Pietrzyk, M., Lenard,J.G. and Sousa, A.C.M., 1989, Study of Temperature Distribution in Strips During Cold Rolling, Int. J. Heat and Techn. 7:12-25. Pietrzyk, M. and Lenard, J.G., 1989. A Study of Heat Transfer During Flat Rolling, Proc. NUMfFORM'89, (Eds. Thompson, E., Wood, R.D., Zienkiewin, O.C. and Samuelsson, A.), Fort Collins, 343-348.

The predictive capabilities of a thermal-mechanical model were tested by comparing its predictions to measurements of the temperature rise taken during plane-strain compression of flat aluminum samples. Both the temperature rise and the rate of temperature rise were predicted with very good accuracy.

14.

As well, the suitability of the plane strain compression test, as one that may be used to simulate the events occurring during flat rolling, was considered. It was concluded that as long as the shape factor in the two tests is comparable, the simulation would likely give valid results.

15. Karagiozis, A.N., 1986, MASc Thesis, Department of Mechanical Engineering, University of New Brunswick. 16. Pietrzyk, M. and Lenard, J.G., 1991, Thermal-Mechanical Modelling of the Flat Rolling Process, Springer-Verla& Heidelberg.

temperature, "C

,20

ACKNOWLEDGEMENTS

,101 100

The financial assistance of the Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged.

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70 60 50 40

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temperature,

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100

90 80 70

60 50 40

30 20 10 6

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rolling, surfoce centre

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0 ~ 0 0 0 compression,

surface

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Figure 15: A comparison of the distributions of temperature in plane strain compression and rolling at moderately high speeds

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