Small scale ductility tests

1533

Journal ofNucleacMaterials 103& 104(1981)1533-1538 North-Holland Publishing Company

SMALL SCALE DUCTILITY TESTS M. Dooley, G.E. Lucas, J.W. Sheckherd Department of Chemical and Nuclear Engineering University of California, Santa Barbara A study was undertaken to investigate the potential applicability of a bulge test for extracting ductility information from small, thin sheet specimens. A bulge testing apparatus was fabricated and used to test to failure 13 different materials under balanced biaxial tension. Uniaxial tensile data were also obtained for these materials. The bulge test was found to be useful in characterizing plastic instability and in evaluating a ductile failure parameter. 1.

INTRODUCTION

Near term devices which are (or will be) available to provide high energy neutron the fusion irradiation environments for materials development program have, by their nature, somewhat limited test volumes. A need therefore exists to develop small volume specimens and the test techniques necessary to extract both microstructural and mechanical property information from them. One such test is a ductility test. ductility has numerous Quantitatively, definitions which has, at times, led to some ductility. discussions of ambiguity in However, qualitatively, ductility is taken as the ability of a material to plastically deform without failing. Changes in ductility with neutron irradiation are of particular interest to the fusion materials program for several reasons. Ductility has some engineering significance for structural design. Moreover, to certain ductility is sensitive microstructural features, especially small second phase particles and extended defects; thus ductility changes can be used to monitor microstructural and microchemical evolution. Finally, ductility parameters may serve as important input to fracture correlation models and failure criteria [l]. In addition to the standard tensile test a number of techniques have been developed to measure ductility. Many of these have been developed in conjunction with the sheet metal forming industry to address the question of stress state effects. Such tests include the hydraulic bulge test [Z], sheet stretching over hemisphericalpunches [3], the Swift (41, Fukui 131, and Marciniak [6] cup tests, sheet bend tests [7] and punch tests 181. More recently a disc bend test has been developed to assess the relative ductility of irradiated TEM discs 191. In addition, a considerable literature has evolved to address the question of interpreting the data generated in these tests in terms of a metal's ability to deform and its susceptibility to fail under multiaxial stresses. Of the tests developed, sheet stretching over a hemispherical punch -- referred to here as a

bulge test -- has received the most attention, experimentally. and analytically both undertaken to Consequently, this study was assess 1) the adequacy of existing theories and analyses for extracting from the bulge test information pertinent to the fusion materials development program and 2) the potential for scaling the bulge test down to TEM disc-type specimens.

From a review of existing theories and analyses of the bulge test, it is evident that the bulge test may be generally useful in characterizing two types of phenomena which affect ductility; namely, plastic instability and failure. Typically, plastic deformation prior to failure consists initially of uniform deformation after which plastic instability results in some nonuniform thinning, or necking, of the sample. The nature of this necking may be diffuse or localized [3]. Specifically, then, the bulge test may be useful in characterizing 1) the onset and nature of the plastic instability and the magnitude of the local plastic 2) deformation prior to failure under a specific biaxial stress state. More importantly, however, the possibility exists to use the bulge data in conjunction with instability or failure criteria to predict these phenomena for a general state of stress. The criterion for plastic instability is still under debate although the picture is improving. Consid&re originally proposed 1101 1atZ instability criterion which was generalized by Keeler and Backofen [3] to predict both localized and diffuse necking for uniaxial and biaxial stress states. Although their theory predicted that localized necking would not occur for balanced biaxial tension, such necking was observed experimentally [6]; and considerable theoretical and experimental work to understand this has ensued [6,11,12]. Most recently, Ghosh [13] and Ghosh and Hecker [14] have proposed that the onset of diffuse and localized necking occurs in the bulge test as the result of the particular strain and strain rate distributions which arise from imposed geometric and frictional constraints and not as a consequence of some existing or imposed inhomogeneity in the sample. The

theory, supported by experiments, be may applied to predict the onset of local plastic instability if the strain history of the specimen can be predicted, and if the constitutive equation of the material (specifically the strain hardenability and strain rate sensitivity) is known. This may be complicated, however, by the stress state dependence of strain hardening [12]. As in the case of plastic instability, a number of criteria have been proposed to describe ductile failure in thin sheets and thus to predict the total strain to failure under various stress states. Included in these failure criteria are such continuum mechanics relations as the “maximum shear stress” [ 151, “maximum volume strain” [7], and “maximum tensile work” [ 161 rules, as well as criteria based on the micromechanisms of ductile fracture, such as the shear linking or coalescence of voids [17,18]. In general, these theories all predict a decrease in the total strain to failure with increasing hydrostatic tension. However, there seems to be conflicting evidence about the applicability and usefulness of these theories, especially with respect to bulge testing of thin sheet samples. To further evaluate existing instability and failure criteria and to evaluate the itself, a scalability of the bulge test research program was initiated in three parts. The first part of the program was directed at finite-element finite-difference, using the code STEALTH [19] to track the strain history the bulge sample. This would be quite of in coupling with the useful, for instance, of Ghosh and plastic instability criterion This aspect of the program is Hecker (141. The second ongoing and is not reported here. part of the program addressed the usefulness of several ductile failure criteria in predicting failure for planar stress states by means of balanced uniaxial and comparisons between The third part of the biaxial failure data. program addressed the scalability of the bulge The results of test to small sample sizes. these latter parts of the program are described below. 3.

EXPERIMENTALPROCEDURE

Thirteen metals were selected for testing. aluminum, yellow brass, mild These were copper, various steel in and stainless steel ranging from highly conditions metallurgical All metals were cold-worked to recrystallized. obtained as sheet stock 0.51mm or 0.64mm in thickness. tests were performed For baseline data, tensile on flat tensile specimens with a gage section 2.54cm long x 0.635cm. wide machined from the

sheet stock. A square grid of O.ZOmm wide lines spaced l.Omm apart was applied to the section of each sample by J gage photoetch/bluing technique. Three samples OL each material type were tested in an Instrou 1122 testing machine at a cross head speed of O.O2lmm/s. Macroscopic length gage displacements were determined with a clip gage extensometer. Local grid deformations, including deformations at the failure site, were determined along both principal axes by measuring the grids directly with a travelling microscope and by measuring micrographs of the grids. Through-thickness strains were measured with a micrometer and by measuring micrographs of the sample after it had been sectioned and mounted on its side in a metallographic mount. The data were analyzed to determine K and n (in the parabolic hardening relation u = KE", where u is the flow stress at a true plastic strain R (the planar anisotroey coefficient), the c), uniform tensile strain E and thet three principal Strains at faiYur)e Ekf and E?i E5f (where 1 = test axis, 2 = iiidth, 3 = In all cases, d final thickness direction). localized neck formed which was smaller in extent than the grid. Hrncet ~if was taken as the negative sum of sif and E ?f’ Rulge tests were performed on samples large relative to TEM discs to facilitate testing and to develop a working underst.anding of the test for scaling down the parameters important The bulge test apparatus, which sample size. is shown in Fig. 1, was used in the following way. The two plates were used to clamp square sizes beneath a right various samples of cylindrical hole in the upper plate and over a The radius tapered hole in the bottom plate. of the taper shoulder was 0.635 cm, the same as The assembly was mounted the cylindrical hole. in an MTS 810 testing machine, which was used to force a small ram, tipped with a 1 .27cm through the top hole and diameter steel ball, By backing the sample with a into the sample. the sample could be forced to neoprene sheet, fail at the tip of the ram where the stress tension. balanced biaxial state was one of Failure was signaled by a sudden load drop. The most important scaling parameters were found to be the ratio of the sample width to the hole diameter and the ratio of the sample with samples For thickness. width to and a below 30 ratios width-to-thickness lgidth-to-hole-diameter ratio less than 3 (i.e., less than 4.0 cm) there was a sample width insufficient material around the edges to keep the sample clamped in place during bulging. facilitate a samples, spaced 0.25 specimen by used for failure the

'CO

bulged analysis of strain square grid of 0.05 mm wide lines mm apart was applied to each the same photoetch/bluing technique Following samples. tensile the sample was removed and grid

M. Dooley

et al. / Small scale ductility

1535

tests

The deformations analyzed as described above. mounted in a sectioned, then sample was metallographic mount and photographed, and the specimen thickness as a function of distance from the failure site was measured from the Unlike the tensile tests, photomicrographs. only two materials for which a there were localized neck formed prior to failure. In these cases the extent of tbhe neck was again was taken as than grid, and smaller A typical bulge% specimen and its -S+W in are shown corresponding photomicrographs Fig. 2. 4.

RESULTS

Results of the uniaxial tension tests are given in Table 1. Several points are notable. Not all the metals exhibited strictly parabolic hardening; some instead exhibited a transition in K and n after some accumulated strain (e.g., SAl, SA2, SSA3 and SSA4). For these metals the values given for K and n are those after the transition.

Fig. 2. Representative photograph of a corresponding photomicrographs of both the

Fig. 1.

Photograph apparatus.

of the bulge test

In all of the materials the onset of plastic instability appeared to occur by the formation of a diffuse neck. In most cases the uniform axial strain was approximately equal to the

gridded bulge sample tested grid and the sample thickness

to failure and the at the failure site.

1536

M. Dooley et al./Small scalecl'uctilit?; tests

TABLE 1 TENSILE AND BIAXIAL TEST DATA Uniaxial Sample

K (MPa)

CUAR

352 196 565 550 641 765 513 508 2534 1552 1410 1636 1436

ALAR BAR BAl BA2 SAR SAl SA2 SSAR SSAl SSAZ SSA3 ,%A4

Data

Biaxial

n

R

28 24 18 19 25 02 16 20 11 05 06 34 17

.52 .16 .18 .51 .92 3.00 .45 .71 .94 .55 12 :60 .78

Et u ,310 140 :207 .191 .225 ,005 .217 .252 .012 .012 .015 .404 ,270

t Elf

t -s2f

1.01 .93 .84 .82 76 164 1.22 1.38 .50 .47 .53 .93 .71

.22 18 :16 .19 19 :02 .32 .37 .21 11 :05 .31 .32

strain hardening exponent, i.e. $J ?Z n, in agreement with the criterion of Keeler and Backofen 131. For the materials SAR, SSAR, SSAl, and SSAZ, there was poor agreement with such a relationship. This may be largely due to the low ductility and hence greater uncertainty in both 4 and n. The results of the biaxial tests are also given in Table 1. Here si is defined as the principal grid strain accumulated prior to failure in grids adjacent to the failure site; hence, sb contains both uniform and diffuse neck stra!ns but not the local necking strain. In agreement with earlier findings [3], the biaxial strains E: are all larger than the corresponding values of &t. That is , with the suppression of local net E.ing and the extension of diffuse necking strains in biaxial tests, the macroscopic deformation of bulge samples over uniaxial was considerably enhanced this was particularly true for the samples; values of materials exhibiting very small &i (i.e., SAR, SSAR, SSAl and SSAZ). If allbbut two of the materials, CUAR and ALAR, indicating the samples failed without Em z?lf' For CUAR and ALAR sb < &kf, local necking. indicating local necking took placemprior to These observations were consistent failure. with the through-thickness profiles of the For example, the sample shown bulged samples. in Fig. 2 failed with no local necking; after diffuse necking, failure occurred abruptly by shear.

uniaxial

t -a3f

sb m 42 37 37 38 35 14 67 67 16 13 18 49 27

79 175 .69 .62 .57 .63 .90 1.01 .29 .36 .43 .62 .40

Data

b Elf

b -s3f

.52 .56 .35 .38 .37 17 166 .64 .13 11 :21 .45 .24

1.04 1.11

:;t, .73 .34 1.31 1.28 .25 .22 .41 .90 .48

data.

The criterion of Ghosh [18] was the only one which adequately fit the data. This failure criterion is based on the linkage of growing microvoids shear stress is when a critical achieved in the material between the voids. It is given by (1 + a) o; = K

(1)

cr

where u = CJ /o1, and a2 = principal 01 stresses, and I? 1s a material parameter which accounts for 'lClnclusions and second phase particle size and shape distributions and In theory, if one can microvoid growth rates. in one type of test (i.e. at one determine I$ stress state r it can be used to predict failure (and failure strains) under other conditions, given a stress state, a constitutive equation, and a flow rule. For the particular failure (biaxial) predicted from the

case at hand, the bulge sb should be strain t%rsion failure uniaxial

2-P' l+a;-P'a

U

where p' = 2R l+R

(2) These data were used to test the applicability of the failure criteria listed earlier, with the exception of the criterion of McClintock shape and for which inclusion size, i171, spacing and microvoid growth rate information All the other criteria could be are required. tested with the available data by using them to predict a biaxial strain to failure from the

[(l+R) ci

U

p, + 2R1

= [2 + 2R + Rpu]

A comparison of the predicted values of cfwith the observed values is shown in Fig. 3 along line representing a perfect fit. with the 45

M. Dooley et al. /Small scale ductility tests

As can be seen the agreement is quite good, indicating the validity of the Ghosh criterion for this application. 5.

CONCLUSIONS

A considerable amount of information has been developed in the literature to describe the deformation and failure of thin metal sheets. Much of this appears applicable to bulge testing small thin metal sheet samples and thus to providing information for the selection of metals to be used in thin-walled structures like the first wall of a fusion reactor. There are currently analytical and semi-empirical methods of predicting the onset of plastic instability in such samples for a variety of planar stress states, although these have yet to be tested for irradiated material. Moreover, the ductile failure criterion of Ghosh appears to be quite successful in correlating uniaxial with biaxial data.

0.25cm diameter punch. Such a sample would be of the order of TEM discs in size. Moreover, the test data could be used in conjunctionwith flow properties obtained either from other tests or from some extension of the test itself to determine a failure parameter like K . Such a parameter would actually have m$Ee utility than some direct measure of ductility since it 1) has a direct microstructural relationship, 2) can be used to predict ductilities under various stress states and 3) could be used in place of ductility as an input parameter for some correlation model for fracture.

The authors would like to thank the Department of Energy Office of Fusion Energy for support of this work. REFERENCES

111 Odette, C.R., Ritchie, R.O., McConnell,

The bulge test, or some modification of the bulge test, is a potentially attractive test for extracting ductility information. Although the samples and the punch used in this study were relatively large (4.0cm square samples and a 1.27cm diameter punch), it should be relatively straight-forwardto scale this down to smaller sample and punch sizes. For example, using the scaling rules determined in this study, bulge testing should be feasible with a 0.75cm x 0.75cm x .025cm thick sample and a

1OOr

t 80 t -2

L

t

PREDICTED

&,f (%)

Fig. 3. Comparison of measured and predicted biaxial strains to failure.

1537

Pr, Server, W., this conference. 121 Ranta-Eskola, A.J., Int. .I.Mech. Sci., 21 (1979) 457. I31 Keeler, S.P. and Backofen, W.A., Trans. ASM, 56 (1963) 25. Newby, J.R., ASTM-STP-647 (1978) 4. ;:]I Moore, G.G. and Wallace, J.F., J. Inst. of Metals, 93 (1964-65) 33. 161 Marciniak, Z. and Kuczynski, K., Int. J. Mech. Sci., 9 (1967) 609. I71 Weiss V., Proc. Third Int. Conf. Mech. Behavior of Mater., Kyoto, Japan, (1971) 458. [81 Ludwigson, D.C., J. Test Eval., 7, 6 (1979) 301. 191 Manahan, M.P., Argon, A.J., Harling, O., this conference. [lOI ConsidCre, A., Ann. Ponts Chaussies, 9, 6 (1885) 574. Azrin, M., and Backofen, W.A., Met. Trans., 1 (1970) 2857. Ghosh, A.K., and Backofen, W.A., Met. Trans., 4 (1973) 1113. Ghosh, A.K., Met. Trans. 5 (1974) 1607. Ghosh, A.K., and Hecker, S.S., Met. Trans., 6A (1975) 1065. J., Mechanical Behavior of t151 Marin, Engineering Materials (Prentice Hall, London, 1963). [I61Cockroft, M.G., Ductile Fracture in Cold Working Operations, in Ductility (ASH, Metals Park, Ohio, 1968). [1?1 McClintock, F.A., J. Appl. Mech., 35 (1968) 363. 1181 Ghosh, A.K., Met. Trans., 7A (1976) 523. [191 Hofman, R., EPRI-NP-260, Electric Power Research Institute, (1976).