technical note an empirical relation between yield ...

Engineering Fracture Mechanics Printed in Great Britain.

Vol. 42, No. 6, pp. 1047-1049,

1992 c

0013-7944/92 $5.00 + 0.00 1992 Pergamon Press Ltd.

TECHNICAL NOTE AN EMPIRICAL GENERAL YIELD

RELATION BETWEEN YIELD STRESS AND LOAD FOR A CHARPY U-NOTCH SPECIMEN

P. R. SREENIVASAN,

S. K. RAY, K. G. SAMUEL

and

S. L. MANNAN

Materials Development Division, Indira Gandhi Centre for Atomic Research, Kalpakkam 603 102, India Abstract-An empirical expression for obtaining the dynamic yield stress, crydrfrom the general yield load, Pay, of a Charpy U-notch specimen has been experimentally derived assuming: (i) crydis the same for both Charpy U- and V-notch specimens; and (ii) the functional relations between PGy and or,, for both the geometries are the same except for a dimensionless proportionality constant.

ANALYTICAL expressions have been theoretically derived for computing the dynamic yield stress, uyd, from the general yield

load, Pov, for impact tested Charpy V-notch (CVN) specimens [l-3]. Similar expressions, however, are not available for Charpy-U-notch @UN) specime&In this note, we experimentally derive such a relation using instrumented impact data from CVN and CUN specimens (Type A and Type C specimens, respectively, as per ASTM E 23 standard [4] designation) of identical materials. The crucial assumption in the derivation is that rruAis identical in both U- and V-notch specimens. The test material was a commercial grade AISI 316 stainless steki (SS) [chemical composition (wt.%):-(X4.06, Ni-11.95, Cr-16.92, MO-2.21, Mn-1.60, Si--O.54, P-0.036, m.021 subjected to various ageing conditions. Impact tests were carried out at room temperature in a Tinius Olsen model 74 impact machine with Dynap Model 500 instrumentation. Most of the tests were done using standard (full-thick) CVN specimens (length, L = 40 mm; thickness, B = width; W = 10 mm; and notch depth, a = 2 mm) and full-thick CUN specimens [L = 40 mm; B = 10 mm; and a (within two standard deviations) = 5.24 + 0.12 mm]; a few half-thick (B = 5 mm) specimens were also tested. The Charpy impact energies, Cv and Co for V- and U-notch specimens, respectively, and values of PGy obtained from the oscilloscope load-time traces are reported in Tables 1 and 2, respectively. The analysis of these data and the results are described below. In Tables 1 and 2 the results for full-thick and half-thick specimens are reported separately.

THEORETICAL

BACKGROUND

Using plane-strain slip-line field analysis for perfectly plastic materials, the general expression relating the yield stress or and the general yield load PGy for a V-notch three-point-bend-specimen can be expressed as [2]

-~)2~,1,

gy = Pov~I]~(~

(1)

where k, = a dimensionless constant. The same relation is used for dynamic conditions during an impact test, and cry,,is used to indicate the corresponding dynamic yield stress. From considerations of dimensional analysis, a similar expression,

Table 1. Instrumented impact test results for Charpy V-notch specimens of AISI 316 stainless steel Ageing condition (a) Full-thick specimens 823 K/0.5 h 823 K/2 h 923 K/2 h 973 K/2 h

(b)

& (c)

286 272 258 295 256 243

11.34 11.49 12.2 11.66 11.33 11.42

Average Two standard deviations Half-thick specimens 973 K/0.5 h 973 K/O.5 h

93 93

4.59 5.02

Mean

(d) 528.9 535.90 569.0 543.8 528.5 532.6

556.4 528.5 532.6

539.7 30.8

537.5 25.6

424.5 463.5 444.0

TComputed using eq. (1) with k, = 1.34. 1047

Mean cyd (MPa) (e)

532.4

-

1048

Technical Note Table 2. Instrumented

impact test results for Charpy U-notch specimens of AISK 316 stainless steel

Ageing condition (a)

(b)

cd)

CrJ

Full-thick specimens 823 K,ltl.S h

211 211 205 134 203 115 211 217 195 138 10.5

823 K/2 h 923 K/2 h 973 K/2h 823 K/5 h 873 K/2 h 1023 K/2 h Average Two standard deviations Half-thick specimens 973 K/OS h 973 K/OS h Mean

(J)

k, with cr,‘, taken from column (e) of Table 1 (MPa)

5.71 5.71 5.1 5.1 5.62 5.47 5.67 5.67 5.15 5.65 5.11

79 79

(e)

1.8983

1.8727

1.6224 I.8853 I.8179

1.6127 1.8431 I .7939

-

1.8595 I .6889

1.8530 I.6759

1.8060 0.25

----1~--

k, with (Tyd= 539.7 (MPa)

1.96

1.500

2.05

1.677

1.7825 0.18

1.589

with a different constant k, replacing kv in eq. (l), should apply for a U-notch specimen also. Thus the expression for oyd for the CUN specimens can be written as VYd= fJoy L/[B( W - a)Jk,].

(21

For standard CVN specimens, in eq. (I), Green and Hundy [I] give kv = 1.21, and Server [Z] gives kv = 1.34. Since Server’s value is based on a reanalysis of various slip-line field results, and is widely used in instrumented impact test analyses, the same has been used here for computing eYdfrom the V-notch specimen data. Our methodology for determining k, simply consists in determining uyd from the PGy data for V-notch specimens using eq. (l), taking k, = 1.34, and then substituting this computed uyd in eq. (2) along with experimentally determined PG., for U-notch specimens, to compute the value of k,. The same procedure was repeated using the load values obtained for half-thick specimens, assuming that k, = 1.34 for half-thick CVN specimens also. The validity {or otherwise) of this methodology is discussed later.

RESULTS AND DISCUSSION First let us consider the results for full-thick specimens. In Table I, for each heat-treatment, the computed values of oYd are reported in column (d), and the corresponding mean values are given in column (e). For the range of heat-treatments employed here, the observed range of uYdis low and within the expected experimental scatter bands from these tests (see the average and standard deviation values in Table 1); therefore an average oYd= 539.7 MPa can be assumed for all the heat-trea~ent conditions. In Tabie 2, k, values computed using the procedure described above with a separate eYdvalue for each heat-treatment are indicated in column (d) and those computed using the average eYd= 539.7 MPa for all heat-treatment conditions am given in column (e). The latter results include some heat-treatments not reported in Table I. The difference between mean values of k, from columns (d) and (e) of Table 2 is very small, and a mean value (with two standard deviations indicated in brackets) of 1.79 + (0.25) can be taken for k, of full-thick CUN specimens. For the same steel and with ageing treatments simifar to those used in the present work, Samuel [5] used half-thick CVN specimens, and eq. (I) with an identical kv value to determine uyd; the reported values of ayd are rather insensitive to the ageing treatments employed and show a mean value of about 425 MPa. Our limited results for half-thick CVN specimens yield a mean cry,,of 444 MPa, in good agreement with Samuel’s results. The mean k, determined for half-thick CUN specimens was 1.59 (Table 2), about 12% lower than the k, determined for full-thick specimens. The vaIues of cr_,reported for the full-thick and half-thick specimens in Table I and also the results of Samuel quoted earlier show that, for the CVN specimens, the oYdcomputed is not a material property as it depends on specimen size and shape. Now, the yield strength values determined by tensile testing of smooth specimens can be taken to be a material property and hence can be used as a reference for comparison. Since yield stress is sensitive to both strain rate and temperature, to facilitate comparison with the present results we have quoted below the results of only ambient temperature tests. For an AISI 316H SS, Albertini et uf. [6] have reported tensile yield stress values of 267 and 471 MPa at IO-’ s-’ and 750 s-i; i.e. a 1.76-fold increase in yield stress over this strain rate range. As the higher strain rate is similar to 1000 s-‘, the typical strain rate in CVN testing, the “ideal” value of eyd from a Charpy test can also be expected to be 1.76 times the quasistatic tensile yield stress, oY. Now, for the materials of our own and Samuel’s tests, ur (from tension) is about 280 MPa, insensitive to the ageing treatments employed in the present investigations [S]. Thus from the results in Table 1, the a,&, ratio for half-thick CVN specimens computes to 1.57, and 1.93 for full-~ck CVN specimens. The latter result is in excellent agreement with the ratio of 1.95 for full-thick CVN specimens of a 316 SS of somewhat lower yield strength (try = 232 MPa) reported by Sheckherd et al. [7].

Technical Note

1049

From the above it can be seen that, to obtain the “ideal” uYd/oYratio of 1.76, kv should equal 1.47 for full-thick and 1.18 for half-thick CVN specimens. If these thickness dependent kv values are used, it can be readily verified that k, would compute to about 1.96 for full-thick and 1.40 for half-thick CVN specimens. Chopra and Chung [8], by comparing yield stress results from slow-rate tensile and three-point-bend tests on some cast SSs, obtained a value of 2.60 for k, in eq. (1). In any case, as Lucas et al. [9] and Norris [lo] have pointed out, eq. (1) does not fully account for material deformation (e.g. flow localisation as observed in low work-hardening materials) and specimen size dependencies (i.e. constraints to deformation). The constancy of the CT~,,/U~ ratio for full-thick specimens over a range of rsY(230-280 MPa) suggests that, in a limited sense, cyd for a given thickness, computed from eq. (1) or (2) can be considered to be a material property. This is to say that, strictly, k, for U-notch specimens computed here should have additional size dependence. This size dependence reflects the differences in the notch acuity and constraints to deformation in the CVN and CUN specimens and may be significantly affected by work-hardening and deformation characteristics of the material. Nevertheless, it would seem that this method should apply provided V- and U-notch specimens with identical thickness values are used.

REFERENCES A. P. Green and B. B. Hundy, Inelastic plastic yielding in notch bend tests. J. Mech. Phys. Solids 4(3), 9, 128-144 (1956). W. L. Server, General yielding of Charpy V-notch and precracked Charpy specimens. J. Engng Mafer. Technol. 100, 183-188 (1978). W. L. Server, Impact three-point bend testing for notched and precracked specimens. J. Testing Eualn 6,29-34 (1978). ASTM E 23, Standard methods for notched bar impact testing of metallic materials. Annual Book of ASTM Standards, Part 10 (1980). K. G. Samuel, Effects of thermal ageing on the mechanical properties of AISI 316 stainless steel. M.S. thesis, Indian Institute of Technology, Madras (1984). C. Albertini, M. Montaglani, R. Cenerini and S. Curiori, Dynamic mechanical properties of austenitic stainless steels-fitting of experimental data on constitutive equations. Proc. of Seventh Int. Conf, on Structural Mechanics in Reactor Technology (7th SMIRT), Vol. L., Paper No. L2/4, pp. 53-62. North-Holland Physics, Amsterdam (1983). 171J. W. Sheckherd, M. Kangilaski and A. A. Bauer, Impact properties of shock-strengthened type 316 stainless steel. Instrumented Impact Testing, ASTM STP 563, 118-132 (1974). 1810. K. Chopra and H. M. Chung, Aging degradation of cast stainless steels: effects on mechanical properties. Proc. of Third International Symposium on Environmental Degradation of Materials in Nuclear Power Systems-Water Reactors (Edited by G. J. Theus and J. R. Weeks), pp. 737-748. The Metallurgical Society, Warrendale, PA (1988).

191 G. E. Lucas, G. R. Odette, J. W. Sheckherd and M. R. Krishnadev, Recent progress in subsized Charpy impact specimen testing for fusion reactor materials development. Fusion Technol. 10, 728-733 (1986). no1 D. M. Norris, Jr., Computer simulation of the Charpy V-notch toughness test. Engng Fracture Mech. 11, 261-264 (1979). (Received 10 April 1991)