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The development of small specimen mechanical test techniques
327
Journal of Nuclear Materials 117 (1983) 327-339 North-Holland Publishing Company
THE DEVELOPMENT G.E.
OF SMALL SPECIMEN
MECHANICAL
TEST TECHNIQUES
LUCAS
Depariment of Chemical and Nuclear Engineering, Uniuersiiy of California, Santa Barbara, CA 93106, USA
The current program plan for the development of materials for fusion reactors requires testing candidate materials in both fission reactors and high energy neutron sources. Because of the volume limitations of available facilities, both current and near term, and because of the relatively large number of materials and test conditions that will need to be explored, it is essential that test techniques be developed to extract mechanical property information from small volume specimens. A variety of such test techniques are under development at the University of California, Santa Barbara. These include instrumented microhardness, bulge, shear punch, indentation creep and load relaxation and miniaturized fracture tests for obtaining strength, ductility, time-dependent flow, and fracture behavior information on specimens as small as TEM discs.
1. Introduction The current program plan for the development of materials for fusion reactors requires testing candidate materials in both fission reactors and high energy neutron sources. The data so obtained are needed for the selection of candidate materials and, ultimately, the design of reactor components. However, irradiation volumes of available facilities, both current and near term, are limited, especially in comparison to the relatively large numbers of candidate materials, metallurgical conditions, test conditions and properties being considered. This is a constraint of the problem which will simply not vanish in the early phases of alloy development. Consequently, it is essential that test techniques be developed to extract mechanical property information from small volume specimens. Given the need for small specimens, it is quickly recognized that there are additional advantages to diminished specimen volumes. For example, the reduction of dose with specimen mass can simplify and economize testing. Moreover, small test heats of alloys can be divided into many more small samples for subsequent testing over a larger range of test conditions than would be possible if large conventional samples were used. This is certainly an attraction in any alloy development effort. Finally, temperature control considerations may preclude the use of anything but small specimens for reactor irradiations in which gamma heating is large. Miniaturization of conventional mechanical property specimens has thus received considerable attention. For instance, tensile samples have been scaled down to small wire [ 1,2] and foil geometries [3]; and fracture, 0022-3115/83/0000-0000/$03.00
0 1983 North-Holland
fatigue, and fatigue crack propagation specimens have been miniaturized to small disc [4], hourglass [5] and coupon [6] geometries, respectively. Conventional “small specimen” techniques, such as microhardness (71, are being applied to small specimens like transmission electron microscopy (TEM) discs which are widely used in the alloy development effort. In addition, much effort has been put into devising new test techniques. For instance, the “disc bend” tests are being developed to extract ductility information from TEM discs [8,9]. Concurrent with these developments have been the efforts at the University of California, Santa Barbara (UCSB) to develop novel techniques to extract mechanical property information from small specimens [lo- 151. These techniques include miniaturization of conventional samples, the development of new specimen geometries, and the application of new techniques to existing specimen geometries, such as the TEM disc. It is the purpose of this paper to review these efforts and to describe recent advances in the more developed techniques.
2. Review of test techniques
A list of the small specimen test techniques under development at UCSB is given in table 1. The basic approach used in each case has been to initially develop the technique on relatively large specimens, and to scale the test down to smaller sample geometries if the initial results are promising. The techniques listed in table 1 are at all stages of development, and they are listed with
G.E. Lucas / Small specimen mechanical test techniques
328
Table 1 Small specimen test techniques under development at UCSB
W
Instrumented microhardness Shear punch Bulge Indentation creep/load relaxation Subsize fracture/fatigue
\
I-
the most developed techniques discussed below in that order. 2.1. Instrumented
at the top.
They
are
ct = PI&
1.0 I)=
1.07+0.53ln+ 2.8 i
(1)
+I1 1<$127 +> 27
(3)
(4)
SPECIMEN
-c&&&f: I I I vd
microhardness
The instrumented microhardness test is based on the indentation of a sample surface by a spherical indenter. The test has the advantages of the standard microhardness test in that it is relatively simple and inexpensive to perform and only a small region of the sample surface is “damaged” for each indentation. Therefore, the sample can be reused in subsequent irradiation or post-irradiation conditioning (e.g., aging) studies. The test has the additional advantage over the conventional microhardness test of providing more extensive flow property information. This comes about in the following way. As shown in fig. 1, a spherical penetrator of diameter D under a load W penetrates the surface of a sample a distance h until a mean pressure P,,, builds up between the surface and the penetrator to resist further penetration. When the penetrator is removed, elastic recovery occurs primarily in the direction of the load axis; and a partly spherical indentation of chordal diameter d is left in the material. Increasing penetration ( hp) corresponds to increasing effective plastic strain in the material in the vicinity of the penetration (plastic zone) which increases the flow stress of the material. This, in combination with an increase in the interface between indenter and sample, requires an increasing load W to effect the deformation. Quantitatively, an effective flow stress a, and plastic strain c,, are related to the identation parameters in the following semi-empirical way [ 13,17,18]:
D *----+j
I
I I -----+I
I
AFTER LOADING
Fig. 1. Schematic illustration of the ball indentation process and relevant geometric parameters.
fp = 0.2d/D,
(5)
where E is the modulus of elasticity of the test material. Hence, data from a single penetration can be used in eqs. (l)-(5) to predict a point on the ut-ep curve of the test material. By cyclically penetrating the sample with known increasing loads and determining d after each penetration, a number of different points on the u,-c,, curve can be predicted from data taken at a single penetration location; and from these data a ut-cP relationship can be derived Of course, once this constitutive equation is derived, such engineering parameters as yield stress, strain hardening exponent and ultimate tensile strength can be predicted. This approach was initially applied to rather large samples using an adapted Instrot? testing machine [ 131. In these tests Wand h, were determined by monitoring the load on the indenter with the testing machine load cell and the displacement of the indenter relative to the specimen with a linear variable differential transformer (LVDT). Because of specimen and machine compliance, h, was determined by the relative displacement of the
G.E. Lucas / Small specimen mechanical test techniques
indenter at zero load after a complete load cycle. Sets of W and h, values were determined by cycling the load between zero and increasingly larger maximum values of W at the same indentation location. Values of h, were used to determine d through a combined elasticity and trigonometric analysis, and W and d were used to determine 0, and ep as described above. Based on the initial success of these tests, a scaled-down version of this “instrumented hardness” tester was built to perform microhardness tests (111. However, considerable difficulty was encountered measuring h,, primarily because of difficulty in determining h at zero load (i.e., locating the exact surface of the specimen or the exact point of contact between indenter and surface). This resulted in an uncertainty in measuring h, of 0.25 pm. While there was evidence that this could be improved somewhat with a considerably more sophisticated test apparatus [19], it appeared that even then the resulting uncertainty in calculating d from h, would still be larger than could be achieved by measuring d directly by optical or other means. Consequently, the effort was shifted to measuring d optically in a standard microhardness tests. Subsequently, a Tukon@ microhardness tester has been fitted with interchangeable spherical penetrators having diameters 0.25 mm, 0.76 mm, and 1.52 mm, and it has been modified to achieve dead weight loads up to 10 kg (spherical penetrators produce smaller indentations per unit load than the conventional pyramidal penetrators). The chordal diameter is measured optically after each penetration with a filar eyepiece, and the microhardness tester has been fine-tuned so the subsequent penetration is made at the same location as the previous one (only at higher load). The eyepiece can be used in conjunction with a drum potentiometer and scalar to produce a calibrated digital readout of d. Both d and W can be conveniently entered into a computer data bank at an adjacent terminal, and the data converted to a,+, curves with associated software. Tests are currently all conducted at room temperature. An example of the results obtained on a 0.5 mm thick SAE 1018 steel coupon is shown in fig. 2. Here the predicted u,-eP points are compared to the u,-er curve obtained from conventional tensile tests of the same material. Agreement is reasonable, and similar results have been obtained for a range of materials (e.g. brass, aluminum, austenitic stainless steel). However, the instrumented microhardness test is not without its limitations. As in standard microhardness testing, it has been found that the penetration diameter should not exceed l/2 the sample thickness and that the penetration depth should not exceed l/10 the sam-
0.001
329
0.01 STRAIN. cp
Fig. 2. Comparison of microhardness-derived stress-strain with uniaxial tensile data of an SAE 1018 steel.
0.1 data
ple thickness. These limitations result in an upper limit on the magnitude of c,, which can be measured, or alternately in a lower limit on the thickness of the sample which can be used. A lower limit on the magnitude of cP is imposed by the scale of the microstructure and resolving power of the optical system for shallow indents (small d/D). It has been found, for instance, that eqs. (l)-(5) break down when the penetrator intersects less than about 5 grains (the largest microstructural unit observed in materials investigated to date) at the surface. Considering these limitations, an approximately optimum specimen geometry has been selected as a 3 mm diameter disc (TEM disc), 0.5 mm in thickness; with this thickness and the available penetrators on the Tukor? microhardness tester, a,-r, data can be obtained for the strain range l-10%. This is usually adequate to establish a constitutive relationship. It should also be noted that for materials with little tensile ductility (i.e. cP < lo%), effective a,-~, data can be obtained with the instrumented microhardness test for strains greater than the tensile ductility, because the stress state during testing is largely compressive; this may ultimately have some advantage in testing highly irradiated materials. While the early work in instrumented microhardness testing has focused on predicting the ut-eP curve, more recent work has addressed the possibility of extracting flow mechanism and flow distribution information from the geometry of an indentation. In particular, Haggag and Lucas [20] observed that in mild steels which exhibited Ltiders strain c,_ when tested in tension, the degree of pile-up around a spherical indentation increased with the magnitude of cL. Moreover, the lip of the pile-up became irregular when the steel exhibited Ltiders strain, in agreement with results of Underwood
330
G.E. Lucas / Small specimen mechanical test techniques
[21]. Representative results obtained with optical interferometry are shown in fig. 3. These interferographs were obtained with mon~hromatic red light; the differential elevation between two fringes is 322 nm. The
,>,\,,/ REFfRENCEjSURFIICE (
nested fringes at the lip of the indentation are indicative of an irregular lip. Since Liiders deformation is one type of localized flow, the above results suggested that the localized flow manifested in irradiated material might give rise to similar irregular indentation lip geometries. Consequently, a systematic study has been undertaken to investigate the possible correlation between indentation geometry and flow dist~bution. To date the results have been difficult to interpret, but there appears to be a relationship between the coarseness of slip exhibited during plastic deformation and the regularity of the indentation lip geometry as observed by optical interferometry. Some preliminary results which support this are given in fig. 4. The micrographs in figs. 4a and b were obtained by differential interference microscopy and figs. 4c and d by monochromatic optical interferometry. Figs. 4a and c show that copper-beryllium (Cu-2 Be) which exhibits relatively course slip around the indentation also exhibits an irregular Iip (nested fringes) around the indentation. The A6 tool steel as shown in figs. 4b and d on the other hand, exhibits relatively fine slip and a regular lip. The regularity of the lip, observed in interferometry is, of course, a function of the elevation resolution, so that the material exhibiting fine slip may actually have a fine-scale lip irregularity. Nonetheless, a relationship between flow distribution and lip geometry appears to exist, and may prove to be useful in monitoring plastic flow characteristics. In addition the optical techniques of characterizing this behavior are adaptable to microhardness testers, thereby providing the potential for an integral test system for flow property determination and flow characterization. 2.2. The shear punch test While potential mation, directly). hardness gated to
the instrumented microhardness test has the to provide strength and work hardening inforit does not provide ductility data (at least * Consequently, to complement the microtest, several test techniques have been investidirectly measure ductility, and primarily failure
* Certainly, Boklen (221 and others [23] have demonstrated that indentation lip geometry can be empirically correlated with the uniform tensile efongation of the test material, and the relationship between Ltiders strain and lip geometry previously discussed supports such a relationship. However, Fig. 3. Profilometer traces and optical interferographs of indentations made at 9.07 kg on a 1015 steel with (a) cL = 0.881, (b)
it is difficult to obtain failure ductility information directly from hardness tests, at least in metals, since metals do not generally fail in the vicinity of the indentation.
G. E. Lucas / Small specimen mechanical
331
test techniques
Fig. 4. Comparison of indentations made in a Cu-2 Be alloy, solution treated at 800°C and aged 1 h at 330°C to RC 38 (a and c); and an A6 tool steel, solution treated at 730°C and furnace cooled to RC 21 (b and d). The top micrographs (a and b) were obtained by differential interference microscopy. The lower micrographs (c and d) were obtained by optical interferometry.
These have been besed to a large extent on tests used in the sheet metal forming industry. One of these, the shear punch test, has also the potential to provide strength and work hardening information. The shear punch test apparatus is shown schematically in fig. 5, and a photograph of the actual apparatus is given in fig. 6. It consists of an upper and lower die and a cylindrical punch. In testing, a thin sheet sample is held between the two dies and a hole is punched from the sample by driving the cylindrical punch through it. The upper and lower dies have concentric, hardened steel bushings. The upper bushing serves as a guide for the punch; and the lower bushing and punch act as the two blades in shearing the disc from the sample. To provide useful information from the shear punch test, the test apparatus is mounted in an MTS” hydraulic testing machine, and the hydraulic ram is used to
ductility.
push the punch through the sample. Both the load on the punch and the punch displacement are continuously monitored during the test by means of a load cell in series with the load train and a displacement transducer
Lower
\ Specimen
Die Displacement Transducer Arm u
Fig. 5. Schematic illustration of the shear punch test apparatus.
G.E. Lucas / Small specimen mechanical test techniques
332
Fig. 6. Photograph of the shear mm diameter punch.
punch test apparatus with a 1
on the hydraulic ram, respectively. Alternately, a displacement transducer can be placed below the sample within the lower bushing, so that specimen displacement can be monitored directly; however, the results obtained with the two displacement monitoring techniques do not differ significantly, and the former is the easier technique to employ. Consequently, most results to date have been obtained by monitoring hydraulic ram displacement. A typical load-displacement curve obtained in such a test is shown in fig. 7. The curve has many of the features of a load-displacement curve obtained in a conventional tensile test. That is, it exhibits an initial, nearly linear portion; a subsequent deviation from linearity and non-linear increase of load with displacement; a maximum load; and a decrease in load with
displacement until a final drop in load signals completion of the punching process. Indeed, with an early version of the shear punch tests apparatus employing a 6.35 mm diameter punch these features of the load displacement curve were successfully correlated with uniaxial test data for materials with a wide range of strengths and ductilities. Specifically, PY (defined in fig. 7) was found to empirically correlate with the uniaxial yield strength of the materials investigated; P,,,, with the ultimate tensile strength; d, with the uniform elongation; and d, with the total ductility (details are given below). Moreover, the features of the deformation process during punching support this correlation. Experimental analysis of the punch test has shown that essentially all deformation takes place in an annular region or process zone 20-50 pm wide, corresponding to the tolerance between the punch and lower die. For loads greater than Py, permanent deformation occurs here. Subsequent deformation in the zone is a combination of shear, bending and tension, with the “thickness” of the sample continuously decreasing. Apparently, at P,,, the decrease in thickness is no longer offset by work hardening in the process zone, and the sample deforms and ultimately fails by shear linkage of microvoids under falling load. Based on experience with the 6.35 mm diameter punch attempts were made to scale tbe test down to permit smaller samples to be tested. An apparatus was built to use a 3 mm diameter punch and one to use a 1 mm diameter punch. In theory, then, the 3 mm shear punch tester could be used to obtain mechanical property information during a TEM disc blanking operation and the 1 mm shear punch tester could be used on TEM discs themselves. Photographs representing this progression are shown in figs. 8a and 8b. The data obtained in both the 3 mm and the 1 mm version have also correlated quite successfully with corresponding tensile properties. Summary examples are given in figs. 9 and 10. In fig. 9, the uniaxial yield stress ay obtained in tests on samples of aluminum, copper, yellow brass, SAE 1015 steel, AISI 304 stainless steel, and four pressure vessel steels are compared to the values of a;ff obtained in shear punch tests on the same material. The value of O;effis defined by P-C
+ff_-y --
OY
: / df
i d” DISPLACEMENT
Fig. 7. Typical load-displacement punch test.
(0,
curve obtained in the shear
-
2lrrt
where F = punch friction, r = punch radius and t = sample thickness. The punch friction F can be obtained either directly from the load displacement curve (i.e., the load required to push the punch through the guide hole) or from the
G. E. Lucas /
Small specimen mechanical test techniques
333
While there is again a reasonable correlation between the two quantities for each type of tester, it is clearly not a linear relation as it was for yield stress and uJff. But it is important to note that there may be some advantage to this non-linearity. For instance, in the range of small total ductilities (the regime of interest for irradiated metals) the variation of eFff (d,) with uniaxial total ductility should be large; thus the shear punch test may have enhanced sensitivity in the measurement of small total ductilities as compared with other test techniques. Some shear punch testing of irradiated metals has already been performed, and representative results are shown in table 2. The data give clear indication of radiation hardening. The changes in shear punch yield load are in good agreement with changes observed in the diamond pyramid hardness (DPH), DPH being a good indicator of yield strength changes in these steels for this regime of radiation damage [24]. Moreover, the maximum load P,,,,, (and thus ultimate tensile strength) increases with radiation, albeit to a lesser extent. It should be noted that there is considerably more difficulty in determining Py than Pm._, especially in hardened materials where the deviation from linearity is much more subtle. Hence, the uncertaintly in the values of APJP, listed in table 2 is larger than that for Finally, consistent with the other data is AP,,,/P,,,. an indicated reduction in ductility (d,) with irradiation. Like the microhardness test the shear punch test has both advantages and disadvantages. The chief advantages over the microhardness test are that it provides ductility as well as strength information; and because the shear punch test “samples” a much larger volume fraction of the test specimen (in the process zone), it is Fig. 8. (a) Photograph illustrating the different size discs punched from a sheet sample as the shear punch apparatus was scaled down. The largest disc is 6.35 mm in diameter and the
smallest 1 mm; (b) Photograph illustrating a 1 mm disc punched from a TEM disc specimen.
Table 2 Change in properties of several pressure vessel steels and welds after irradiation to 1 x lOI n/cm2 (E, > 1 MeV) at 55O’C and 7 x lOI n/cm2.s (E n > 1 MeV) Property
intersection of the linear regression line of Py vs uy with the Py axis (at aY = 0). Both values are approximately equal. Thus, fig. 9 not only indicates the good correlation between yield stress and P,, but the validity of the punch size and sample thickness scaling laws used in eq.
ADPH DPH
(6). In fig. 10, the total uniaxial ductility for the materials listed above is plotted against EF”, where c;” is defined by d cff = r
Ef
t ’
(7)
Apmax Pmax Ad, dr
change
Alloy A302B
A533
Weld
Weld
(A)
(B)
(C)
(D)
0.21
0.27
0.22
0.27
0.25
0.33
0.23
0.32
0.12
0.14
0.11
0.12
- 0.07
- 0.08
- 0.08
-0.16
G.E. Lucas / Small specimen mechanical test techniques
334
LEGEND Sample Thickness (mm) .5 .5 .5 .25 Punch Diameter (mm) , 3 6.3 1
MATERIAL “y;;;zL
800
STRESS, q WW
600
0
200
400
600
800
Copper
0
v
Aluminum
0
0
Brass
0
0
0
Mild Steel
rl
!?I
0
Alloy Steel
0
Stainless Steel
A
A
A
t
1000
fYyeff (MPa) Fig. 9. Comparison
of the uniaxial
yield stress I+ obtained
for a range of materials
with the normalized
yield load o;ff obtained
from
different shear punch tests on the same materials.
LEGEND s.4 ENGINEERING STRAIN TO FAILURE,
Vti
,3
MATERtAL
;#?I
,2 _
8b * z ,#,#
ef .l -
0 00
Specimen Thickness (mm) .5 .5 .5 .25 Punch Diameter (mm) , 3 6.3 1
Copper Aluminum
v
v
0
0
Brass
0
0
0
Mild Steel
8
II
0
A
A
A
Alloy Steel Stainless Steel
0
0
.2
I
I
/
.4
.6 eff Ef
.8
1.0
Fig. 10. Comparison of the normalized displacement to failure obtained the uniaxial failure strains obtained on the same materials.
considerably less sensitive to the scale of the microstructure and sample preparation than the microhardness test. The major disadvantages are that the test can be * and that the stress and deformation states destructive; in the process zone are highly complex, thus making physically based correlations of the data rather than simple empirical correlations most difficult. Nonetheless, the shear punch test has many attractions and its * If a 1 mm hole is punched hand, it is a “productive” TEM disc blanking.
4
from a TEM disc; on the other test if used in conjection with
from different
shear punch
tests on a range of materials
development will continue to be pursued in mechanical testing of small irradiated
with
for application samples.
2.3. The bulge test Another test technique which has been under development is the bulge test. Like the shear punch test, the bulge test was originally envisioned as a means of obtaining ductility information and thus as a complementary test to the microhardness test. To date it has only been developed for relatively large specimens (2 cm x 2 cm x 0.5 mm thick); however, it has served as a
G. E. Lucas / Small specimen mechanical test techniques
useful means of the investigating the basic mechanisms contributing to “ductility”, and the necessary experience and understanding to scale the test down to smaller sample sizes has been gained. The bulge test is based on an approach used in metal sheet forming analyses [25]. A schematic of the apparatus is given in fig. 11. Like the shear punch test apparatus, the bulge test apparatus consists of an upper and lower die and a punch; however, the punch in this case is spherically tipped. A sheet metal sample is clamped between the dies, and the punch is forced into it, causing the sample to bulge and ultimately fail. The upper die features a hardened steel guide bushing for the punch and the lower die has a shouldered hole into which the sample is bulged. With proper lubrication the sample can be made to fail at the center of the bulge where the stress state is approximately balanced biaxial tension. As in the shear punch test, the apparatus can be mounted in an MTS and a load-displacement curve generated during the bulging operation. However, in this case the specimen deformation is not restricted to a localized process zone but is spread out over the whole region of the sample that is not clamped. In addition the stress and the deformation states change with radial position from the bulge center. Hence, the load-displacement curve appears very compliant, and information about the deformation state at any one point in the sample cannot be obtained directly from the curve. While analytical solutions of the stress and deformation states in a bulge sample have been attempted [26], the best descriptions have been obtained by finite element analysis [27]. The problem of describing the stress and deformation history of the bulge sample is analogous to that encountered in disc bend testing [8,9], although the boundary conditions differ. Finite element analyses of the bulge test have been particularly useful in investigating the onset of plastic instability as a function of stress state [27]; this is just one of several important “ductility” parameters.
l-7
Punch
Fig. 11. Schematic
illustration
of the bulge test apparatus.
335
To date the finite element methods have not yet been applied to obtain ductility information from the loaddisplacement curves generated with this particular version of the bulge test. However, total ductility (failure strain) has been obtained directly by gridding the sample surfaces. Square grids with a 0.25 mm mesh have been photo-etched onto each sample and lacquer-enhanced [15]. By measuring grids in the vicinity of the crack before and after the sample has deformed to failure, surface strains at failure can be determined. Moreover, the samples have been sectioned after failure and through-thickness strains determined by optical measurements. These data then provide a complete characterization of the deformation state at failure. This approach to obtaining ductility data is in itself useful, in that ductility is measured for a stress state (balanced biaxial tension) which is a better approximation of that anticipated in a fusion reactor first wall than uniaxial tension. However, to date the technique has had utility in studying the effect of stress state on ductility as well. Specifically, an investigation was undertaken in which the principal strains to failure were measured in a set of materials (the same set used in shear punch testing, less the pressure vessel steels). This was done both for the case of balanced biaxial tension (bulge test) and uniaxial tension. These data were then used to evaluate the various ductile failure criteria which have been developed to account for stress state effects [28-311. The biaxial and uniaxial data were best related by the model of Ghosh [31], which is based on the assumption that ductile failure occurs by the growth and shear linkage of microvoids; mathematically the criterion reduces to af(a+
l)=K,,
(8)
where a = a,/az; u,, u2 = principal stresses for a planar stress state and K,, = failure parameter, which is a material constant. In theory, once K,, is known, the principal strains at failure (ductility) can be determined for any planar stress state by tracking the deformation history of the specimen with an appropriate constitutive relation and flow rule rule until eq. (8) is satisfied. As shown in fig. 12, the approach worked quite well for the materials investigated here. Using values of K,, determined in uniaxial tension tests, principal strains to failure were predicted for balanced biaxial tension and were found to be in fairly good agreement with actual biaxial data obtained in the bulge test. Hence, the bulge test has the advantage over the shear punch test that the stress and deformation state are more amenable to analytic description; it has there-
G.E. Lucas / Small specimen mechanical test techniques
336
2.4. Indentation
loo-
80 -
I
0
I
20
I
I
40 PREDICTED
I
Ii
I
80
80
I
I
100
E,f (%)
Fig. 12. Comparison of measured and predicted to failure. The 45” line represents a perfect fit.
biaxial
strains
fore been more useful thus far for fundamental studies of ductility. Also, like the shear punch test, a relatively large fraction of the specimen is “sampled” making the test less sensitive to specimen preparation. However, the bulge test is potentially more difficult to conduct on a small scale than the shear punch test. Scaling studies on relatively large (cm x cm) coupon samples indicate that samples must have a width-to-thickness ratio greater than 30 and a width greater than 3 times the hole diameter for there to be sufficient material to keep the sample clamped in place during bulging. This suggests that tests would be feasible for 0.75 cm X 0.75 cm X 0.025 cm thick samples - of the order of TEM discs in size - and a 0.25 cm diameter punch. However, for such small samples, gridding may be impractical; instead, techniques such as through-thickness strain measurement at the failure site by optical (e.g. jewellers microscope) or other means might be used. For such an approach, the assumption would have to be made that surface strains were equal to one half the thickness strain, which is usually a good approximation for fee or bee metals. In addition, without a finite element or equivalent analysis, other flow property information such as strength could not be obtained from the bulge test. Nonetheless, this test may prove to be quite valuable in producing fundamental fracture information, such to the failure as K,,, which may be more pertinent analysis of thin walled structures like the fusion reactor first wall than fracture mechanics parameters like K,, 1321.
creep and load relaxation
The tests described thus far have addressed only the time-independent deformation behavior of materials. However, the time-dependent deformation behavior is also important. Consequently, some effort has gone into developing a test which measures this response. The test is based on the approach shown schematically in fig. 13. A flat cylindrical indenter of diameter D is placed on the sample surface. If a constant load is placed on the indenter at a sufficiently high homologous temperature, the material beneath the indenter will creep and the vertical displacement of the indenter can be monitored as a function of time; this procedure is referred to as indentation or impression creep. Alternately, the vertical displacement can be fixed, and the load as a function of time an be monitored; this is referred to as indentation load relaxation. Chu and Li’{33] have investigated indentation creep in several mater&g and suggest that the load and indentation rate are rel&dto an effective stress u and strain rate (, respectively. For the regime of power law creep the relationship is (J = PI&J i:=Ajl/D,
(9) (10)
where # and A are constants and P,,, is again the mean pressure between the indenter and the sample surface as defined in eq. (2). At UCSB the applicability of these expressions to indentation load relaxation as well as indentation creep have been investigated. Samples of lead have been tested at room temperature by conventional creep and load relaxation and by indentation creep and load relaxation techniques. Indentation tests were performed with a compression cage which transmitted a tensile load on the pull rods of the cage as a compressive load between a cylindrical indenter and the test sample (2.5 cm diam-
SPECIMEN
Fig. 13. Schematic illustration of the approach tation creep and load relaxation.
for both inden-
G. E. Lucas / Small specimen mechanical test techniques
eter by 2.5 cm thick) within the cage. Indentation creep tests were performed by fixing the cage in the load train of a conventional creep frame; and indentation load relaxation tests were performed by placing the cage in an Instrone testing machine. Standard techniques of displacement and load monitoring were used in each case. The conventional creep and load relaxation data were used to establish a constitutive relationship for the test material at room temperature, and it was found that both the indentation creep data and the indentation load relaxation data fit the corresponding conventional data for values of A = 1 and # = 5.33. Representative results are given in fig. 14. While the indentation approach holds some promise of extracting time-dependent constitutive behavior from small samples, scaling the test down from its present size will not be without certain difficulties. The primary reason for this is that in the time-dependent regime the effective plastic zone beneath the indenter is considerably larger than it is for time-independent (hardness) testing. Consequently, it has been recommended that specimen thickness-to-indenter-diameter ratios be greater than 50 [33] for valid indentation creep testing. This would mean for TEM discs 0.5 mm in thickness, indenter diameters would have to be 10 pm. Not only
0 Standard creep 0 Indentation creep
33-i
would this make the test experimentally difficult, but the results would be even more sensitive to specimen preparation and scale of the specimen microstructure than the microhardness test discussed previously. Similar constraints for indentation load relaxation have yet to be determined. However, indentation load relaxation tests may have an additional difficulty imposed by temperature control. Analysis suggests that the temperature control required for indentation load relaxation tests is 1 to 2 orders of magnitude greater than that for standard load relaxation tests, depending on the assumed test geometries. For a given achievable temperature control, then, the minimum resolvable strain rates would be 1 to 2 orders of magnitude greater for indentation load relaxation tests. For instance, for constant temperature environments used in high resolution stress relaxation experiments (AT 5 0.1 “C), resolvable strain rates are of the order lo-’ s-‘. For the same temperature control, resolvable effective strain rates in indentation load relaxation experiments could be expected to be no better than 10-6-10-7 SK’. If the test techniques are scaled down to reasonably small sizes, their utility would most likely be in the post-irradiation testing of materials, as the apparatus for testing (compression cage) is too bulky for practical in-reactor operation. In addition, there might be some limited application to irradiation creep testing in front of neutron sources. However, because of the specimen thickness/indenter diameter .constraints mentioned above, other test techniques for extracting post-irradiation time-dependent flow properties, such as modified versions of the shear punch or bulge test, might hold greater promise for small specimen sizes. 2.5. Subsire fracture tests
LOG STRESS (MPa) Fig. 14. Steady-state creep rates as a function of applied stress at room temperature. Data are obtained from both conventional and indentation creep tests.
Development of subsize fracture specimens and techniques to test these specimens has been in progress although the results so far are limited. Nonetheless, it is worth noting here the directions being taken for completeness of the discussion. Subsize Charpy-V-Notch (CVN) specimens (3.33 mm x 3.33 mm x 16.7 mm) have been developed for the purpose of tracking the shift in ductile-brittle transition temperature (DBTT) in ferritic steels subject to neutron irradiation. The approach is derived from previous work by Myers et al. [34]. An example of the specimen compared to a standard CVN specimen is given in fig. 15. Although it is not expected that the subsize specimen will provide direct engineering data, potentially it can be used to monitor radiation effects in ferritics (or tempered martensitics) and provide basic fracture infor-
G.E. Lucas / Small specimen mechanrcal test techniques
338
approximates conditions (stress state and geometry) ticipated in first wall structures.
an-
3. Summary
Fig. 15. Photographs illustrating Charpy-V-Notch specimens.
the
scale
of
the
subsize
mation. These would have great utility in fundamental studies. Subsize bend bars (0.1 T and 0.2 T) have also been developed and are shown in fig. 16. These are being used in studies to evaluate the appropriateness of various fracture parameters in relatively thin structures. Finally, efforts have been initiated to develop a cyclic bulge test for the investigation of the propagation of small cracks and part-through cracks under fatigue conditions. The technique takes advantage of the bulge test geometry to investigate fatigue crack propagation in thin samples under biaxial conditions. Not only is the test potentially applicable to small specimens, but it
A variety of test techniques have been and continue to be investigated for the extraction of mechanical properties from small specimens. Each technique has its own set of advantages and disadvantages; and therefore each may be applicable in different circumstances. The instrumented microhardness test can be used to determine an effective stress-strain relationship over a strain range 1- 10%~from spherical indentations on samples as small as TEM discs. In addition there is some potential that flow distribution information can be obtained from a characterization of the indentation geometry. The major disadvantage of the instrumented microhardness test is that, like microhardness in general, the results are sensitive to specimen preparation and the scale of the microstructure. The shear punch test can be used to obtain both strength and ductility information from specimens as small as TEM discs. Moreover, the technique “samples” a larger volume of the test specimen, and is therefore less sensitive to the scale of the microstructure than the microhardness test. The shear punch test can be applied either as a productive test (TEM disc blanking) or a destructive test (TEM disc testing). However, the stress and deformation paths in the process zone are highly complex and not easily analyzed; therefore data interpretation has been strictly empirical to date. Like the shear punch test, the bulge test can be used to obtain ductility information. It has been particularly useful in evaluating ductile failure criteria, of which the criterion of Ghosh [31] best fits the data. The ductile fracture parameter K,, so obtained may have relevance to the failure analysis of thin-walled structures. The indentation creep and load-relaxation tests can potentially be used to determine post-irradiation constitutive behavior of materials. However, the tests may have constraints on the ratio of specimen thickness to indenter diameter and temperature control which limit their scalability. Finally, several approaches to small specimen fracture and fatigue testing are under development. The specimens under investigation, in addition to being small, may provide data more pertinent to fusion first wall structures than their conventional counterparts.
339
G. E. Lucas / SmaN specimen mechanical test techniques
Acknowledgements The author wishes to express his thanks to G.R. Odette for his many creative suggestions and helpful discussions and to J.W. She&herd for his talents in implementing many of the test techniques described here. The author also acknowledges the support of the Office of Fusion Energy, Department of Energy (Contract No. DE-AM03-76SF0034) and the Electric Power Research Institute (Contact No. RP-1021-7) for this work.
[12] G.E. Lucas and F. Haggag, DOE/ER-OO46/6 (1981) 105. [ 131 P. Au, G.E. Lucas, J.W. She&herd, G.R. Odette, in: Nondestructive Evaluation in the Nuclear Industry (ASM, Metals Park, Ohio, 1981) p. 597. 1141 G.E. Lucas and N.F. Panayotou, J. Nucl. Mater. 103/104 (1981) 1527. [ 151 M. Dooley, G.E. Lucas and J.W. Sheckherd, J. Nucl. Mater. 103/104 (1981) 1533. [16] GE. Lucas and C. Pendleton, J. Nucl. Mater. 103/104 (1981) 1539. [l7] D. Tabor, The Hardness of Metals (Clarendon Press, Oxford, 1951). [ 181 H.A. Francis, fl91 M. Nishibori (1972) 750.
References [l] N.F. Panayotou, R.J. Puigh and E.K. Gpperman, J. Nucl. Mater. 103/104 (1981) 1523. [2] E.R. Bradley and R.H. Jones, J. Nucl. Mater. 103/104 (1981) 901. [3] J.A. Horak, Oak Ridge National Laboratory, ORNL-5082 (1975) 40. [4] F.H. Huang and G.L. Wire, J. Nucl. Mater. 103/104 (1981) 1511. (51 M.L. Grossbeck and KC. Liu, J. Nucl. Mater. 103/104 (1981) 853. [6] R.J. P&h, R.E. Batter, A.M. Ermi and B.A. Chin, J. Nucl. Mater. 103/104 (1981) 1501. [7] N.F. Panayotou, J. Nucl. Mater. 108/109 (1982) 456. [S] F.H. Huang, M.L. Hamilton, G.L. Wire, Nucl. Technol. 57 (1982) 234. [9] M.P. Mar&an, AS. Argon and O.K. Harling, J. Nucl. Mater. 103/104 (1981) 1545. [IO] G.E. Lucas, P. Au, J.W. Sheckerd and G.R. Odette, DOE/ET-0065/S (1979) 199. [ll] G.E. Lucas, G.R. Odette, W. She&herd, C. Pendleton, F. Haggag, M. Dooley, W. Server and P. McConnel, DOE/ET-0046,‘4 (198 1) 45.
Trans. ASME (1976) 272. and K. Kinosita, Japan. J. Appl.
Phys.
II
[20] F.M. Haggag and G.E. Lucas, Trans. ANS 39 (1981) 431. [21] J.H. Underwood, Proe. Sot. Exp. Stress Anal. 30 (1973) 1. 1221 R. Boklen, in: The Science of Hardness Testing and its Appiications, Eds. H. Westbrook and H. Conrad (ASM, Metals Park, OH, 1973) p. 109. [23] K. Furuya and J. Moteff, Met. Trans. 124 (1981) 1303. 1241J.F. Mancuso, J.A. Spitznagel, R.P. Shogan and J.R. Holland, ASTM-STP-725 (1981) 38. 1251 S.P. Keeler and W.A. Backofen, Trans. ASM 56 (1963) 25. 1261N.M. Wang, J. Appl. Mech. (1970) 431. 1271 A.K. Ghosh and S.S. Hecker, Met. Trans. 6A (1975) 1065. [281 V. Weiss, Proc. Third Int. Conf. Mech. Behavior of Mater., Kyoto, Japan 91971) 458. Behavior of Engineering Materials 1291 J. Marin, Mechanical (Prentice Hall, London, 1963). in: Ductility (ASM, Metals Park, Ohio, (301 M.G. Cockcroft, 1968). 1311 A.K. Ghosh, Met. Trans. 7A (1976) 523. and W. Server, J. 1321 G.R. Odette, R.O. Ritchie, P. McConnd Nucl. Mater. 103/104 91981) 149. [331 S.N.G. Chu and J.C.M. Li, J. Mat. Sci. 12 (1977) 2200. 1341 H.P. Myers, M. Grounes and N.E. Hannerz, Proc. 3rd Int. Conf. on Peaceful Use of At. Energy, Geneva (1964) p. 240, 266.
Journal of Nuclear Materials 117 (1983) 327-339 North-Holland Publishing Company
THE DEVELOPMENT G.E.
OF SMALL SPECIMEN
MECHANICAL
TEST TECHNIQUES
LUCAS
Depariment of Chemical and Nuclear Engineering, Uniuersiiy of California, Santa Barbara, CA 93106, USA
The current program plan for the development of materials for fusion reactors requires testing candidate materials in both fission reactors and high energy neutron sources. Because of the volume limitations of available facilities, both current and near term, and because of the relatively large number of materials and test conditions that will need to be explored, it is essential that test techniques be developed to extract mechanical property information from small volume specimens. A variety of such test techniques are under development at the University of California, Santa Barbara. These include instrumented microhardness, bulge, shear punch, indentation creep and load relaxation and miniaturized fracture tests for obtaining strength, ductility, time-dependent flow, and fracture behavior information on specimens as small as TEM discs.
1. Introduction The current program plan for the development of materials for fusion reactors requires testing candidate materials in both fission reactors and high energy neutron sources. The data so obtained are needed for the selection of candidate materials and, ultimately, the design of reactor components. However, irradiation volumes of available facilities, both current and near term, are limited, especially in comparison to the relatively large numbers of candidate materials, metallurgical conditions, test conditions and properties being considered. This is a constraint of the problem which will simply not vanish in the early phases of alloy development. Consequently, it is essential that test techniques be developed to extract mechanical property information from small volume specimens. Given the need for small specimens, it is quickly recognized that there are additional advantages to diminished specimen volumes. For example, the reduction of dose with specimen mass can simplify and economize testing. Moreover, small test heats of alloys can be divided into many more small samples for subsequent testing over a larger range of test conditions than would be possible if large conventional samples were used. This is certainly an attraction in any alloy development effort. Finally, temperature control considerations may preclude the use of anything but small specimens for reactor irradiations in which gamma heating is large. Miniaturization of conventional mechanical property specimens has thus received considerable attention. For instance, tensile samples have been scaled down to small wire [ 1,2] and foil geometries [3]; and fracture, 0022-3115/83/0000-0000/$03.00
0 1983 North-Holland
fatigue, and fatigue crack propagation specimens have been miniaturized to small disc [4], hourglass [5] and coupon [6] geometries, respectively. Conventional “small specimen” techniques, such as microhardness (71, are being applied to small specimens like transmission electron microscopy (TEM) discs which are widely used in the alloy development effort. In addition, much effort has been put into devising new test techniques. For instance, the “disc bend” tests are being developed to extract ductility information from TEM discs [8,9]. Concurrent with these developments have been the efforts at the University of California, Santa Barbara (UCSB) to develop novel techniques to extract mechanical property information from small specimens [lo- 151. These techniques include miniaturization of conventional samples, the development of new specimen geometries, and the application of new techniques to existing specimen geometries, such as the TEM disc. It is the purpose of this paper to review these efforts and to describe recent advances in the more developed techniques.
2. Review of test techniques
A list of the small specimen test techniques under development at UCSB is given in table 1. The basic approach used in each case has been to initially develop the technique on relatively large specimens, and to scale the test down to smaller sample geometries if the initial results are promising. The techniques listed in table 1 are at all stages of development, and they are listed with
G.E. Lucas / Small specimen mechanical test techniques
328
Table 1 Small specimen test techniques under development at UCSB
W
Instrumented microhardness Shear punch Bulge Indentation creep/load relaxation Subsize fracture/fatigue
\
I-
the most developed techniques discussed below in that order. 2.1. Instrumented
at the top.
They
are
ct = PI&
1.0 I)=
1.07+0.53ln+ 2.8 i
(1)
+I1 1<$127 +> 27
(3)
(4)
SPECIMEN
-c&&&f: I I I vd
microhardness
The instrumented microhardness test is based on the indentation of a sample surface by a spherical indenter. The test has the advantages of the standard microhardness test in that it is relatively simple and inexpensive to perform and only a small region of the sample surface is “damaged” for each indentation. Therefore, the sample can be reused in subsequent irradiation or post-irradiation conditioning (e.g., aging) studies. The test has the additional advantage over the conventional microhardness test of providing more extensive flow property information. This comes about in the following way. As shown in fig. 1, a spherical penetrator of diameter D under a load W penetrates the surface of a sample a distance h until a mean pressure P,,, builds up between the surface and the penetrator to resist further penetration. When the penetrator is removed, elastic recovery occurs primarily in the direction of the load axis; and a partly spherical indentation of chordal diameter d is left in the material. Increasing penetration ( hp) corresponds to increasing effective plastic strain in the material in the vicinity of the penetration (plastic zone) which increases the flow stress of the material. This, in combination with an increase in the interface between indenter and sample, requires an increasing load W to effect the deformation. Quantitatively, an effective flow stress a, and plastic strain c,, are related to the identation parameters in the following semi-empirical way [ 13,17,18]:
D *----+j
I
I I -----+I
I
AFTER LOADING
Fig. 1. Schematic illustration of the ball indentation process and relevant geometric parameters.
fp = 0.2d/D,
(5)
where E is the modulus of elasticity of the test material. Hence, data from a single penetration can be used in eqs. (l)-(5) to predict a point on the ut-ep curve of the test material. By cyclically penetrating the sample with known increasing loads and determining d after each penetration, a number of different points on the u,-c,, curve can be predicted from data taken at a single penetration location; and from these data a ut-cP relationship can be derived Of course, once this constitutive equation is derived, such engineering parameters as yield stress, strain hardening exponent and ultimate tensile strength can be predicted. This approach was initially applied to rather large samples using an adapted Instrot? testing machine [ 131. In these tests Wand h, were determined by monitoring the load on the indenter with the testing machine load cell and the displacement of the indenter relative to the specimen with a linear variable differential transformer (LVDT). Because of specimen and machine compliance, h, was determined by the relative displacement of the
G.E. Lucas / Small specimen mechanical test techniques
indenter at zero load after a complete load cycle. Sets of W and h, values were determined by cycling the load between zero and increasingly larger maximum values of W at the same indentation location. Values of h, were used to determine d through a combined elasticity and trigonometric analysis, and W and d were used to determine 0, and ep as described above. Based on the initial success of these tests, a scaled-down version of this “instrumented hardness” tester was built to perform microhardness tests (111. However, considerable difficulty was encountered measuring h,, primarily because of difficulty in determining h at zero load (i.e., locating the exact surface of the specimen or the exact point of contact between indenter and surface). This resulted in an uncertainty in measuring h, of 0.25 pm. While there was evidence that this could be improved somewhat with a considerably more sophisticated test apparatus [19], it appeared that even then the resulting uncertainty in calculating d from h, would still be larger than could be achieved by measuring d directly by optical or other means. Consequently, the effort was shifted to measuring d optically in a standard microhardness tests. Subsequently, a Tukon@ microhardness tester has been fitted with interchangeable spherical penetrators having diameters 0.25 mm, 0.76 mm, and 1.52 mm, and it has been modified to achieve dead weight loads up to 10 kg (spherical penetrators produce smaller indentations per unit load than the conventional pyramidal penetrators). The chordal diameter is measured optically after each penetration with a filar eyepiece, and the microhardness tester has been fine-tuned so the subsequent penetration is made at the same location as the previous one (only at higher load). The eyepiece can be used in conjunction with a drum potentiometer and scalar to produce a calibrated digital readout of d. Both d and W can be conveniently entered into a computer data bank at an adjacent terminal, and the data converted to a,+, curves with associated software. Tests are currently all conducted at room temperature. An example of the results obtained on a 0.5 mm thick SAE 1018 steel coupon is shown in fig. 2. Here the predicted u,-eP points are compared to the u,-er curve obtained from conventional tensile tests of the same material. Agreement is reasonable, and similar results have been obtained for a range of materials (e.g. brass, aluminum, austenitic stainless steel). However, the instrumented microhardness test is not without its limitations. As in standard microhardness testing, it has been found that the penetration diameter should not exceed l/2 the sample thickness and that the penetration depth should not exceed l/10 the sam-
0.001
329
0.01 STRAIN. cp
Fig. 2. Comparison of microhardness-derived stress-strain with uniaxial tensile data of an SAE 1018 steel.
0.1 data
ple thickness. These limitations result in an upper limit on the magnitude of c,, which can be measured, or alternately in a lower limit on the thickness of the sample which can be used. A lower limit on the magnitude of cP is imposed by the scale of the microstructure and resolving power of the optical system for shallow indents (small d/D). It has been found, for instance, that eqs. (l)-(5) break down when the penetrator intersects less than about 5 grains (the largest microstructural unit observed in materials investigated to date) at the surface. Considering these limitations, an approximately optimum specimen geometry has been selected as a 3 mm diameter disc (TEM disc), 0.5 mm in thickness; with this thickness and the available penetrators on the Tukor? microhardness tester, a,-r, data can be obtained for the strain range l-10%. This is usually adequate to establish a constitutive relationship. It should also be noted that for materials with little tensile ductility (i.e. cP < lo%), effective a,-~, data can be obtained with the instrumented microhardness test for strains greater than the tensile ductility, because the stress state during testing is largely compressive; this may ultimately have some advantage in testing highly irradiated materials. While the early work in instrumented microhardness testing has focused on predicting the ut-eP curve, more recent work has addressed the possibility of extracting flow mechanism and flow distribution information from the geometry of an indentation. In particular, Haggag and Lucas [20] observed that in mild steels which exhibited Ltiders strain c,_ when tested in tension, the degree of pile-up around a spherical indentation increased with the magnitude of cL. Moreover, the lip of the pile-up became irregular when the steel exhibited Ltiders strain, in agreement with results of Underwood
330
G.E. Lucas / Small specimen mechanical test techniques
[21]. Representative results obtained with optical interferometry are shown in fig. 3. These interferographs were obtained with mon~hromatic red light; the differential elevation between two fringes is 322 nm. The
,>,\,,/ REFfRENCEjSURFIICE (
nested fringes at the lip of the indentation are indicative of an irregular lip. Since Liiders deformation is one type of localized flow, the above results suggested that the localized flow manifested in irradiated material might give rise to similar irregular indentation lip geometries. Consequently, a systematic study has been undertaken to investigate the possible correlation between indentation geometry and flow dist~bution. To date the results have been difficult to interpret, but there appears to be a relationship between the coarseness of slip exhibited during plastic deformation and the regularity of the indentation lip geometry as observed by optical interferometry. Some preliminary results which support this are given in fig. 4. The micrographs in figs. 4a and b were obtained by differential interference microscopy and figs. 4c and d by monochromatic optical interferometry. Figs. 4a and c show that copper-beryllium (Cu-2 Be) which exhibits relatively course slip around the indentation also exhibits an irregular Iip (nested fringes) around the indentation. The A6 tool steel as shown in figs. 4b and d on the other hand, exhibits relatively fine slip and a regular lip. The regularity of the lip, observed in interferometry is, of course, a function of the elevation resolution, so that the material exhibiting fine slip may actually have a fine-scale lip irregularity. Nonetheless, a relationship between flow distribution and lip geometry appears to exist, and may prove to be useful in monitoring plastic flow characteristics. In addition the optical techniques of characterizing this behavior are adaptable to microhardness testers, thereby providing the potential for an integral test system for flow property determination and flow characterization. 2.2. The shear punch test While potential mation, directly). hardness gated to
the instrumented microhardness test has the to provide strength and work hardening inforit does not provide ductility data (at least * Consequently, to complement the microtest, several test techniques have been investidirectly measure ductility, and primarily failure
* Certainly, Boklen (221 and others [23] have demonstrated that indentation lip geometry can be empirically correlated with the uniform tensile efongation of the test material, and the relationship between Ltiders strain and lip geometry previously discussed supports such a relationship. However, Fig. 3. Profilometer traces and optical interferographs of indentations made at 9.07 kg on a 1015 steel with (a) cL = 0.881, (b)
it is difficult to obtain failure ductility information directly from hardness tests, at least in metals, since metals do not generally fail in the vicinity of the indentation.
G. E. Lucas / Small specimen mechanical
331
test techniques
Fig. 4. Comparison of indentations made in a Cu-2 Be alloy, solution treated at 800°C and aged 1 h at 330°C to RC 38 (a and c); and an A6 tool steel, solution treated at 730°C and furnace cooled to RC 21 (b and d). The top micrographs (a and b) were obtained by differential interference microscopy. The lower micrographs (c and d) were obtained by optical interferometry.
These have been besed to a large extent on tests used in the sheet metal forming industry. One of these, the shear punch test, has also the potential to provide strength and work hardening information. The shear punch test apparatus is shown schematically in fig. 5, and a photograph of the actual apparatus is given in fig. 6. It consists of an upper and lower die and a cylindrical punch. In testing, a thin sheet sample is held between the two dies and a hole is punched from the sample by driving the cylindrical punch through it. The upper and lower dies have concentric, hardened steel bushings. The upper bushing serves as a guide for the punch; and the lower bushing and punch act as the two blades in shearing the disc from the sample. To provide useful information from the shear punch test, the test apparatus is mounted in an MTS” hydraulic testing machine, and the hydraulic ram is used to
ductility.
push the punch through the sample. Both the load on the punch and the punch displacement are continuously monitored during the test by means of a load cell in series with the load train and a displacement transducer
Lower
\ Specimen
Die Displacement Transducer Arm u
Fig. 5. Schematic illustration of the shear punch test apparatus.
G.E. Lucas / Small specimen mechanical test techniques
332
Fig. 6. Photograph of the shear mm diameter punch.
punch test apparatus with a 1
on the hydraulic ram, respectively. Alternately, a displacement transducer can be placed below the sample within the lower bushing, so that specimen displacement can be monitored directly; however, the results obtained with the two displacement monitoring techniques do not differ significantly, and the former is the easier technique to employ. Consequently, most results to date have been obtained by monitoring hydraulic ram displacement. A typical load-displacement curve obtained in such a test is shown in fig. 7. The curve has many of the features of a load-displacement curve obtained in a conventional tensile test. That is, it exhibits an initial, nearly linear portion; a subsequent deviation from linearity and non-linear increase of load with displacement; a maximum load; and a decrease in load with
displacement until a final drop in load signals completion of the punching process. Indeed, with an early version of the shear punch tests apparatus employing a 6.35 mm diameter punch these features of the load displacement curve were successfully correlated with uniaxial test data for materials with a wide range of strengths and ductilities. Specifically, PY (defined in fig. 7) was found to empirically correlate with the uniaxial yield strength of the materials investigated; P,,,, with the ultimate tensile strength; d, with the uniform elongation; and d, with the total ductility (details are given below). Moreover, the features of the deformation process during punching support this correlation. Experimental analysis of the punch test has shown that essentially all deformation takes place in an annular region or process zone 20-50 pm wide, corresponding to the tolerance between the punch and lower die. For loads greater than Py, permanent deformation occurs here. Subsequent deformation in the zone is a combination of shear, bending and tension, with the “thickness” of the sample continuously decreasing. Apparently, at P,,, the decrease in thickness is no longer offset by work hardening in the process zone, and the sample deforms and ultimately fails by shear linkage of microvoids under falling load. Based on experience with the 6.35 mm diameter punch attempts were made to scale tbe test down to permit smaller samples to be tested. An apparatus was built to use a 3 mm diameter punch and one to use a 1 mm diameter punch. In theory, then, the 3 mm shear punch tester could be used to obtain mechanical property information during a TEM disc blanking operation and the 1 mm shear punch tester could be used on TEM discs themselves. Photographs representing this progression are shown in figs. 8a and 8b. The data obtained in both the 3 mm and the 1 mm version have also correlated quite successfully with corresponding tensile properties. Summary examples are given in figs. 9 and 10. In fig. 9, the uniaxial yield stress ay obtained in tests on samples of aluminum, copper, yellow brass, SAE 1015 steel, AISI 304 stainless steel, and four pressure vessel steels are compared to the values of a;ff obtained in shear punch tests on the same material. The value of O;effis defined by P-C
+ff_-y --
OY
: / df
i d” DISPLACEMENT
Fig. 7. Typical load-displacement punch test.
(0,
curve obtained in the shear
-
2lrrt
where F = punch friction, r = punch radius and t = sample thickness. The punch friction F can be obtained either directly from the load displacement curve (i.e., the load required to push the punch through the guide hole) or from the
G. E. Lucas /
Small specimen mechanical test techniques
333
While there is again a reasonable correlation between the two quantities for each type of tester, it is clearly not a linear relation as it was for yield stress and uJff. But it is important to note that there may be some advantage to this non-linearity. For instance, in the range of small total ductilities (the regime of interest for irradiated metals) the variation of eFff (d,) with uniaxial total ductility should be large; thus the shear punch test may have enhanced sensitivity in the measurement of small total ductilities as compared with other test techniques. Some shear punch testing of irradiated metals has already been performed, and representative results are shown in table 2. The data give clear indication of radiation hardening. The changes in shear punch yield load are in good agreement with changes observed in the diamond pyramid hardness (DPH), DPH being a good indicator of yield strength changes in these steels for this regime of radiation damage [24]. Moreover, the maximum load P,,,,, (and thus ultimate tensile strength) increases with radiation, albeit to a lesser extent. It should be noted that there is considerably more difficulty in determining Py than Pm._, especially in hardened materials where the deviation from linearity is much more subtle. Hence, the uncertaintly in the values of APJP, listed in table 2 is larger than that for Finally, consistent with the other data is AP,,,/P,,,. an indicated reduction in ductility (d,) with irradiation. Like the microhardness test the shear punch test has both advantages and disadvantages. The chief advantages over the microhardness test are that it provides ductility as well as strength information; and because the shear punch test “samples” a much larger volume fraction of the test specimen (in the process zone), it is Fig. 8. (a) Photograph illustrating the different size discs punched from a sheet sample as the shear punch apparatus was scaled down. The largest disc is 6.35 mm in diameter and the
smallest 1 mm; (b) Photograph illustrating a 1 mm disc punched from a TEM disc specimen.
Table 2 Change in properties of several pressure vessel steels and welds after irradiation to 1 x lOI n/cm2 (E, > 1 MeV) at 55O’C and 7 x lOI n/cm2.s (E n > 1 MeV) Property
intersection of the linear regression line of Py vs uy with the Py axis (at aY = 0). Both values are approximately equal. Thus, fig. 9 not only indicates the good correlation between yield stress and P,, but the validity of the punch size and sample thickness scaling laws used in eq.
ADPH DPH
(6). In fig. 10, the total uniaxial ductility for the materials listed above is plotted against EF”, where c;” is defined by d cff = r
Ef
t ’
(7)
Apmax Pmax Ad, dr
change
Alloy A302B
A533
Weld
Weld
(A)
(B)
(C)
(D)
0.21
0.27
0.22
0.27
0.25
0.33
0.23
0.32
0.12
0.14
0.11
0.12
- 0.07
- 0.08
- 0.08
-0.16
G.E. Lucas / Small specimen mechanical test techniques
334
LEGEND Sample Thickness (mm) .5 .5 .5 .25 Punch Diameter (mm) , 3 6.3 1
MATERIAL “y;;;zL
800
STRESS, q WW
600
0
200
400
600
800
Copper
0
v
Aluminum
0
0
Brass
0
0
0
Mild Steel
rl
!?I
0
Alloy Steel
0
Stainless Steel
A
A
A
t
1000
fYyeff (MPa) Fig. 9. Comparison
of the uniaxial
yield stress I+ obtained
for a range of materials
with the normalized
yield load o;ff obtained
from
different shear punch tests on the same materials.
LEGEND s.4 ENGINEERING STRAIN TO FAILURE,
Vti
,3
MATERtAL
;#?I
,2 _
8b * z ,#,#
ef .l -
0 00
Specimen Thickness (mm) .5 .5 .5 .25 Punch Diameter (mm) , 3 6.3 1
Copper Aluminum
v
v
0
0
Brass
0
0
0
Mild Steel
8
II
0
A
A
A
Alloy Steel Stainless Steel
0
0
.2
I
I
/
.4
.6 eff Ef
.8
1.0
Fig. 10. Comparison of the normalized displacement to failure obtained the uniaxial failure strains obtained on the same materials.
considerably less sensitive to the scale of the microstructure and sample preparation than the microhardness test. The major disadvantages are that the test can be * and that the stress and deformation states destructive; in the process zone are highly complex, thus making physically based correlations of the data rather than simple empirical correlations most difficult. Nonetheless, the shear punch test has many attractions and its * If a 1 mm hole is punched hand, it is a “productive” TEM disc blanking.
4
from a TEM disc; on the other test if used in conjection with
from different
shear punch
tests on a range of materials
development will continue to be pursued in mechanical testing of small irradiated
with
for application samples.
2.3. The bulge test Another test technique which has been under development is the bulge test. Like the shear punch test, the bulge test was originally envisioned as a means of obtaining ductility information and thus as a complementary test to the microhardness test. To date it has only been developed for relatively large specimens (2 cm x 2 cm x 0.5 mm thick); however, it has served as a
G. E. Lucas / Small specimen mechanical test techniques
useful means of the investigating the basic mechanisms contributing to “ductility”, and the necessary experience and understanding to scale the test down to smaller sample sizes has been gained. The bulge test is based on an approach used in metal sheet forming analyses [25]. A schematic of the apparatus is given in fig. 11. Like the shear punch test apparatus, the bulge test apparatus consists of an upper and lower die and a punch; however, the punch in this case is spherically tipped. A sheet metal sample is clamped between the dies, and the punch is forced into it, causing the sample to bulge and ultimately fail. The upper die features a hardened steel guide bushing for the punch and the lower die has a shouldered hole into which the sample is bulged. With proper lubrication the sample can be made to fail at the center of the bulge where the stress state is approximately balanced biaxial tension. As in the shear punch test, the apparatus can be mounted in an MTS and a load-displacement curve generated during the bulging operation. However, in this case the specimen deformation is not restricted to a localized process zone but is spread out over the whole region of the sample that is not clamped. In addition the stress and the deformation states change with radial position from the bulge center. Hence, the load-displacement curve appears very compliant, and information about the deformation state at any one point in the sample cannot be obtained directly from the curve. While analytical solutions of the stress and deformation states in a bulge sample have been attempted [26], the best descriptions have been obtained by finite element analysis [27]. The problem of describing the stress and deformation history of the bulge sample is analogous to that encountered in disc bend testing [8,9], although the boundary conditions differ. Finite element analyses of the bulge test have been particularly useful in investigating the onset of plastic instability as a function of stress state [27]; this is just one of several important “ductility” parameters.
l-7
Punch
Fig. 11. Schematic
illustration
of the bulge test apparatus.
335
To date the finite element methods have not yet been applied to obtain ductility information from the loaddisplacement curves generated with this particular version of the bulge test. However, total ductility (failure strain) has been obtained directly by gridding the sample surfaces. Square grids with a 0.25 mm mesh have been photo-etched onto each sample and lacquer-enhanced [15]. By measuring grids in the vicinity of the crack before and after the sample has deformed to failure, surface strains at failure can be determined. Moreover, the samples have been sectioned after failure and through-thickness strains determined by optical measurements. These data then provide a complete characterization of the deformation state at failure. This approach to obtaining ductility data is in itself useful, in that ductility is measured for a stress state (balanced biaxial tension) which is a better approximation of that anticipated in a fusion reactor first wall than uniaxial tension. However, to date the technique has had utility in studying the effect of stress state on ductility as well. Specifically, an investigation was undertaken in which the principal strains to failure were measured in a set of materials (the same set used in shear punch testing, less the pressure vessel steels). This was done both for the case of balanced biaxial tension (bulge test) and uniaxial tension. These data were then used to evaluate the various ductile failure criteria which have been developed to account for stress state effects [28-311. The biaxial and uniaxial data were best related by the model of Ghosh [31], which is based on the assumption that ductile failure occurs by the growth and shear linkage of microvoids; mathematically the criterion reduces to af(a+
l)=K,,
(8)
where a = a,/az; u,, u2 = principal stresses for a planar stress state and K,, = failure parameter, which is a material constant. In theory, once K,, is known, the principal strains at failure (ductility) can be determined for any planar stress state by tracking the deformation history of the specimen with an appropriate constitutive relation and flow rule rule until eq. (8) is satisfied. As shown in fig. 12, the approach worked quite well for the materials investigated here. Using values of K,, determined in uniaxial tension tests, principal strains to failure were predicted for balanced biaxial tension and were found to be in fairly good agreement with actual biaxial data obtained in the bulge test. Hence, the bulge test has the advantage over the shear punch test that the stress and deformation state are more amenable to analytic description; it has there-
G.E. Lucas / Small specimen mechanical test techniques
336
2.4. Indentation
loo-
80 -
I
0
I
20
I
I
40 PREDICTED
I
Ii
I
80
80
I
I
100
E,f (%)
Fig. 12. Comparison of measured and predicted to failure. The 45” line represents a perfect fit.
biaxial
strains
fore been more useful thus far for fundamental studies of ductility. Also, like the shear punch test, a relatively large fraction of the specimen is “sampled” making the test less sensitive to specimen preparation. However, the bulge test is potentially more difficult to conduct on a small scale than the shear punch test. Scaling studies on relatively large (cm x cm) coupon samples indicate that samples must have a width-to-thickness ratio greater than 30 and a width greater than 3 times the hole diameter for there to be sufficient material to keep the sample clamped in place during bulging. This suggests that tests would be feasible for 0.75 cm X 0.75 cm X 0.025 cm thick samples - of the order of TEM discs in size - and a 0.25 cm diameter punch. However, for such small samples, gridding may be impractical; instead, techniques such as through-thickness strain measurement at the failure site by optical (e.g. jewellers microscope) or other means might be used. For such an approach, the assumption would have to be made that surface strains were equal to one half the thickness strain, which is usually a good approximation for fee or bee metals. In addition, without a finite element or equivalent analysis, other flow property information such as strength could not be obtained from the bulge test. Nonetheless, this test may prove to be quite valuable in producing fundamental fracture information, such to the failure as K,,, which may be more pertinent analysis of thin walled structures like the fusion reactor first wall than fracture mechanics parameters like K,, 1321.
creep and load relaxation
The tests described thus far have addressed only the time-independent deformation behavior of materials. However, the time-dependent deformation behavior is also important. Consequently, some effort has gone into developing a test which measures this response. The test is based on the approach shown schematically in fig. 13. A flat cylindrical indenter of diameter D is placed on the sample surface. If a constant load is placed on the indenter at a sufficiently high homologous temperature, the material beneath the indenter will creep and the vertical displacement of the indenter can be monitored as a function of time; this procedure is referred to as indentation or impression creep. Alternately, the vertical displacement can be fixed, and the load as a function of time an be monitored; this is referred to as indentation load relaxation. Chu and Li’{33] have investigated indentation creep in several mater&g and suggest that the load and indentation rate are rel&dto an effective stress u and strain rate (, respectively. For the regime of power law creep the relationship is (J = PI&J i:=Ajl/D,
(9) (10)
where # and A are constants and P,,, is again the mean pressure between the indenter and the sample surface as defined in eq. (2). At UCSB the applicability of these expressions to indentation load relaxation as well as indentation creep have been investigated. Samples of lead have been tested at room temperature by conventional creep and load relaxation and by indentation creep and load relaxation techniques. Indentation tests were performed with a compression cage which transmitted a tensile load on the pull rods of the cage as a compressive load between a cylindrical indenter and the test sample (2.5 cm diam-
SPECIMEN
Fig. 13. Schematic illustration of the approach tation creep and load relaxation.
for both inden-
G. E. Lucas / Small specimen mechanical test techniques
eter by 2.5 cm thick) within the cage. Indentation creep tests were performed by fixing the cage in the load train of a conventional creep frame; and indentation load relaxation tests were performed by placing the cage in an Instrone testing machine. Standard techniques of displacement and load monitoring were used in each case. The conventional creep and load relaxation data were used to establish a constitutive relationship for the test material at room temperature, and it was found that both the indentation creep data and the indentation load relaxation data fit the corresponding conventional data for values of A = 1 and # = 5.33. Representative results are given in fig. 14. While the indentation approach holds some promise of extracting time-dependent constitutive behavior from small samples, scaling the test down from its present size will not be without certain difficulties. The primary reason for this is that in the time-dependent regime the effective plastic zone beneath the indenter is considerably larger than it is for time-independent (hardness) testing. Consequently, it has been recommended that specimen thickness-to-indenter-diameter ratios be greater than 50 [33] for valid indentation creep testing. This would mean for TEM discs 0.5 mm in thickness, indenter diameters would have to be 10 pm. Not only
0 Standard creep 0 Indentation creep
33-i
would this make the test experimentally difficult, but the results would be even more sensitive to specimen preparation and scale of the specimen microstructure than the microhardness test discussed previously. Similar constraints for indentation load relaxation have yet to be determined. However, indentation load relaxation tests may have an additional difficulty imposed by temperature control. Analysis suggests that the temperature control required for indentation load relaxation tests is 1 to 2 orders of magnitude greater than that for standard load relaxation tests, depending on the assumed test geometries. For a given achievable temperature control, then, the minimum resolvable strain rates would be 1 to 2 orders of magnitude greater for indentation load relaxation tests. For instance, for constant temperature environments used in high resolution stress relaxation experiments (AT 5 0.1 “C), resolvable strain rates are of the order lo-’ s-‘. For the same temperature control, resolvable effective strain rates in indentation load relaxation experiments could be expected to be no better than 10-6-10-7 SK’. If the test techniques are scaled down to reasonably small sizes, their utility would most likely be in the post-irradiation testing of materials, as the apparatus for testing (compression cage) is too bulky for practical in-reactor operation. In addition, there might be some limited application to irradiation creep testing in front of neutron sources. However, because of the specimen thickness/indenter diameter .constraints mentioned above, other test techniques for extracting post-irradiation time-dependent flow properties, such as modified versions of the shear punch or bulge test, might hold greater promise for small specimen sizes. 2.5. Subsire fracture tests
LOG STRESS (MPa) Fig. 14. Steady-state creep rates as a function of applied stress at room temperature. Data are obtained from both conventional and indentation creep tests.
Development of subsize fracture specimens and techniques to test these specimens has been in progress although the results so far are limited. Nonetheless, it is worth noting here the directions being taken for completeness of the discussion. Subsize Charpy-V-Notch (CVN) specimens (3.33 mm x 3.33 mm x 16.7 mm) have been developed for the purpose of tracking the shift in ductile-brittle transition temperature (DBTT) in ferritic steels subject to neutron irradiation. The approach is derived from previous work by Myers et al. [34]. An example of the specimen compared to a standard CVN specimen is given in fig. 15. Although it is not expected that the subsize specimen will provide direct engineering data, potentially it can be used to monitor radiation effects in ferritics (or tempered martensitics) and provide basic fracture infor-
G.E. Lucas / Small specimen mechanrcal test techniques
338
approximates conditions (stress state and geometry) ticipated in first wall structures.
an-
3. Summary
Fig. 15. Photographs illustrating Charpy-V-Notch specimens.
the
scale
of
the
subsize
mation. These would have great utility in fundamental studies. Subsize bend bars (0.1 T and 0.2 T) have also been developed and are shown in fig. 16. These are being used in studies to evaluate the appropriateness of various fracture parameters in relatively thin structures. Finally, efforts have been initiated to develop a cyclic bulge test for the investigation of the propagation of small cracks and part-through cracks under fatigue conditions. The technique takes advantage of the bulge test geometry to investigate fatigue crack propagation in thin samples under biaxial conditions. Not only is the test potentially applicable to small specimens, but it
A variety of test techniques have been and continue to be investigated for the extraction of mechanical properties from small specimens. Each technique has its own set of advantages and disadvantages; and therefore each may be applicable in different circumstances. The instrumented microhardness test can be used to determine an effective stress-strain relationship over a strain range 1- 10%~from spherical indentations on samples as small as TEM discs. In addition there is some potential that flow distribution information can be obtained from a characterization of the indentation geometry. The major disadvantage of the instrumented microhardness test is that, like microhardness in general, the results are sensitive to specimen preparation and the scale of the microstructure. The shear punch test can be used to obtain both strength and ductility information from specimens as small as TEM discs. Moreover, the technique “samples” a larger volume of the test specimen, and is therefore less sensitive to the scale of the microstructure than the microhardness test. The shear punch test can be applied either as a productive test (TEM disc blanking) or a destructive test (TEM disc testing). However, the stress and deformation paths in the process zone are highly complex and not easily analyzed; therefore data interpretation has been strictly empirical to date. Like the shear punch test, the bulge test can be used to obtain ductility information. It has been particularly useful in evaluating ductile failure criteria, of which the criterion of Ghosh [31] best fits the data. The ductile fracture parameter K,, so obtained may have relevance to the failure analysis of thin-walled structures. The indentation creep and load-relaxation tests can potentially be used to determine post-irradiation constitutive behavior of materials. However, the tests may have constraints on the ratio of specimen thickness to indenter diameter and temperature control which limit their scalability. Finally, several approaches to small specimen fracture and fatigue testing are under development. The specimens under investigation, in addition to being small, may provide data more pertinent to fusion first wall structures than their conventional counterparts.
339
G. E. Lucas / SmaN specimen mechanical test techniques
Acknowledgements The author wishes to express his thanks to G.R. Odette for his many creative suggestions and helpful discussions and to J.W. She&herd for his talents in implementing many of the test techniques described here. The author also acknowledges the support of the Office of Fusion Energy, Department of Energy (Contract No. DE-AM03-76SF0034) and the Electric Power Research Institute (Contact No. RP-1021-7) for this work.
[12] G.E. Lucas and F. Haggag, DOE/ER-OO46/6 (1981) 105. [ 131 P. Au, G.E. Lucas, J.W. She&herd, G.R. Odette, in: Nondestructive Evaluation in the Nuclear Industry (ASM, Metals Park, Ohio, 1981) p. 597. 1141 G.E. Lucas and N.F. Panayotou, J. Nucl. Mater. 103/104 (1981) 1527. [ 151 M. Dooley, G.E. Lucas and J.W. Sheckherd, J. Nucl. Mater. 103/104 (1981) 1533. [16] GE. Lucas and C. Pendleton, J. Nucl. Mater. 103/104 (1981) 1539. [l7] D. Tabor, The Hardness of Metals (Clarendon Press, Oxford, 1951). [ 181 H.A. Francis, fl91 M. Nishibori (1972) 750.
References [l] N.F. Panayotou, R.J. Puigh and E.K. Gpperman, J. Nucl. Mater. 103/104 (1981) 1523. [2] E.R. Bradley and R.H. Jones, J. Nucl. Mater. 103/104 (1981) 901. [3] J.A. Horak, Oak Ridge National Laboratory, ORNL-5082 (1975) 40. [4] F.H. Huang and G.L. Wire, J. Nucl. Mater. 103/104 (1981) 1511. (51 M.L. Grossbeck and KC. Liu, J. Nucl. Mater. 103/104 (1981) 853. [6] R.J. P&h, R.E. Batter, A.M. Ermi and B.A. Chin, J. Nucl. Mater. 103/104 (1981) 1501. [7] N.F. Panayotou, J. Nucl. Mater. 108/109 (1982) 456. [S] F.H. Huang, M.L. Hamilton, G.L. Wire, Nucl. Technol. 57 (1982) 234. [9] M.P. Mar&an, AS. Argon and O.K. Harling, J. Nucl. Mater. 103/104 (1981) 1545. [IO] G.E. Lucas, P. Au, J.W. Sheckerd and G.R. Odette, DOE/ET-0065/S (1979) 199. [ll] G.E. Lucas, G.R. Odette, W. She&herd, C. Pendleton, F. Haggag, M. Dooley, W. Server and P. McConnel, DOE/ET-0046,‘4 (198 1) 45.
Trans. ASME (1976) 272. and K. Kinosita, Japan. J. Appl.
Phys.
II
[20] F.M. Haggag and G.E. Lucas, Trans. ANS 39 (1981) 431. [21] J.H. Underwood, Proe. Sot. Exp. Stress Anal. 30 (1973) 1. 1221 R. Boklen, in: The Science of Hardness Testing and its Appiications, Eds. H. Westbrook and H. Conrad (ASM, Metals Park, OH, 1973) p. 109. [23] K. Furuya and J. Moteff, Met. Trans. 124 (1981) 1303. 1241J.F. Mancuso, J.A. Spitznagel, R.P. Shogan and J.R. Holland, ASTM-STP-725 (1981) 38. 1251 S.P. Keeler and W.A. Backofen, Trans. ASM 56 (1963) 25. 1261N.M. Wang, J. Appl. Mech. (1970) 431. 1271 A.K. Ghosh and S.S. Hecker, Met. Trans. 6A (1975) 1065. [281 V. Weiss, Proc. Third Int. Conf. Mech. Behavior of Mater., Kyoto, Japan 91971) 458. Behavior of Engineering Materials 1291 J. Marin, Mechanical (Prentice Hall, London, 1963). in: Ductility (ASM, Metals Park, Ohio, (301 M.G. Cockcroft, 1968). 1311 A.K. Ghosh, Met. Trans. 7A (1976) 523. and W. Server, J. 1321 G.R. Odette, R.O. Ritchie, P. McConnd Nucl. Mater. 103/104 91981) 149. [331 S.N.G. Chu and J.C.M. Li, J. Mat. Sci. 12 (1977) 2200. 1341 H.P. Myers, M. Grounes and N.E. Hannerz, Proc. 3rd Int. Conf. on Peaceful Use of At. Energy, Geneva (1964) p. 240, 266.