F R O M ABROAD

MEASUREMENT OF THE HARDNESS OF SINTERED MATERIALS

D. Argir

The hardness of s intered mate r ia l s , in contrast to that of bulk mater ia ls , is not related to other physi- cal and mechanical charac te r i s t i c s (tensile, bend, and impact strengths) [1]. However, hardness provides a very effective and convenient measure of densification, the degree of sintering, heat t reatment , and other physical and mechanical charac te r i s t i c s , and is also important in studies of both the powder metal lurgical p rocess as a whole and its individual elements.

Hardness measurements per formed on sintered par ts having a uniform part ic le size distribution and a homogeneous composition and s t ruc ture show that the surface hardness differs f r o m that determined within the part even after the most careful sintering and heat t reatment . This difference is caused by s t ruc - tural changes induced by concentrat ions of forces (compaction forces , fr ict ional forces between the par t ic les and the die set, f r ict ional forces between the par t ic les themselves , etc.) in cer ta in zones of compacts. When a nonuniform work-hardening is not rel ieved by heat t reatment , it too affects the result ing density.

By measur ing the hardness HB (Brinell hardness) on the plane faces of a cylindrical specimen, pe r - pendicular to the direction of compaction, it is possible to obtain a hardness vs radius plot, as shown in Fig. l a and b.

The hardness H B of a mater ia l represen ts its res i s tance (in k g / m m 2) to surface indentation and, fo r an end face of a cyl indrical specimen, can therefore be expressed as a function of the radius:

where p is the radius of a point of hardness H B.

The surface dS (Fig: 2) has the a rea

and is acted upon by the force dF:

Then the surface S lying between R 1 and R 2

withstands the force F:

H s = g s (~), (1)

dS ~-- 2 ~ . do (2)

dF : Hz~ (Q). dS. (3)

S ~ 2 (R2 - - R~) (2')

R~

F = S HB (@ dS. (4) R~

It may b~ assumed that the hardness is a l inear function of the radius (relative deviations from lin- ear i ty a re in pract ice small). Then

where HB1 and HB2 are the hardness values corresponding to the radii R l and R 2.

Engineering Institute, Cluj, Rumania. Transla ted from Poroshkovaya Metallurgiya, No. 7, (91), pp. 101-104, July, 1970. Original ar t ic le submitted August 14, 1969.

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a b

F i g . 1 Fig. 2

, eCe

Fig. 3

2 I

Fig . 4 Fig. 5

LZ~ R ~j

F i g . 6

TABLE 1

Diameter of l Br~aei1 sphere, mm

1.25 '

r

2.50

Indentations

Number Figure Number Figure

0 - - 5

Specimen diameter, mm

5- -10 10--15

2 5

15--25

The l o c a t i o n s of i n de n t a t i ons a r e m a r k e d wi th • in the f i g u r e s .

F r o m Eqs . (4) and (6) it fo l lows tha t

[ +

so that the m e a n h a r d n e s s HBm of the who le s u r f a c e S is

H B - - He, ( 1 i-IBm = HB, + 2 R; - - R1 3

In t he c a s e of c y l i n d r i c a l s p e c i m e n s ,

R I-.~0; HB,~HBo;

and the e x p r e s s i o n (7) b e c o m e s t r a n s f o r m e d into

HB, , - H & / I Ru a _ R ~ I '~w 2 i a 2RqJ ' (6)

R2--Rt I RI �9 (7) R ~ 2 - - R~ 2

R 2 = R; HB, = HB e, (8)

1 HB. * = -~ (tI~. + 2H B). (9)

This relationship shows that, for each indentation in the center, two peripheral indentations are necessary.

The effect of the peripheral hardness on the mean value is twice that of the central hardness. If this pro- portion is not observed, a mean value is obtained.

When the diameter of a cylindrical specimen is too small to permit hardness measurements in the

center and on the periplhery, measurements should be performed on the circle corresponding to. the mean hardness. The radius of this circle is determined from Eqs. (5) and (9):

2 R.., = T R . (10)

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For determing the mean hardness , it is, of course, neces sa ry to pe r fo rm severa l indentations. If the hardness values HB0 , measured once in the center, and HBe 1 and HBe2, measured twice on the per iphery at d iametr ica l ly opposed points, a re such that

tIB. 4= lIB., =/= HBe' (11)

the expression for the mean hardness will have the form

1 H Bm := "~ (H B, Jr H Be ' -~- H Be ). (12)

This satisfies the principle, expressed by Eq. (9), that in mean hardness determination two indentations on the per iphery correspond to a single indentation in the center .

When a large blank (Fig. 3) is available permit t ing a number of indentations, the mean hardness is determined using the relationship

1 (H + 3 H s + 2 H ) (13) HB,,, ~ --6- Bo B~ �9

C O N C L U S I O N S

1. The hardness of plane surfaces is not a constant magnitude, but a l inear function of the radius. The following relat ionships may apply:

HB0 ~ HBe . (14)

2. The mean hardness of a surface is determined as the mean of values obtained at all points.

3. When a hardness determination is based on only a few indentations, made in the center and on the per iphery, the mean value HBm is given by the expression

1 HBm -- 3n (n'HBo + 2nH~o), (15)

where n is the number of indentations, equal to 1, 2, 3, etc.

4. The mean hardness cor responds to the hardness measured on a c i rc le with the radius calculated f rom Eq. (10).

5. When the size of the specimen enables the number of indentations to be increased, the latter can be positioned as shown in Fig. 3, and the mean hardness is then given by the expression

H~, -- ~-~ (n. Hp. + 3nil z + 2nHB). (16)

6. F r o m what has been said above it follows that the number and location of indentations required for the determinat ion of t h e m e a n hardness of round surfaces should be chosen in accordance with the data listed in Table 1 (Figs. 4-6).

L I T E R A T U R E C I T E D

1. D . R . Kiefer and D. W. Hotop, Metalurgie des Poudres , Dunod, Par i s (1947).

610