SCIENTIFIC

SOME

BASES

OF POWDER

METALLURGY

P R O B L E M S OF P O W D E R C O M P A C T I N G G . A. M e e r s o n Moscow Red Labor Flag Order Institute of Steel and Alloys Translated from Poroshkovaya Metallurgiya, No. 5 (11), pp. 8-14, September-October, 1962 Original article submitted November 10, 1961

The theory of powder compacting has been under development for many years already. However, contradictions, and sometimes even errors, are encountered in several cases. Some problems needing a more correct, or more accurate treatment in the Soviet engineering !tterature are discussed in the present paper. B r i q u e t D e n s i t y as a F u n c t i o n of the Compacting Pressure The first relationship between the briquet density and the compacting pressure, which relationship is the most extensively used in this country, was proposed by M. Yu. Bal'shin [1]:

log p = - c~(i~-- 1) + c

(1)

In the literature of the last few years [3, 4] investigators reasoning in line with the present author [2] have made critical remarks on the foundation of equation (1) and on the correctness of its derivation. However, the papers cited criticize only M. Yu. Bal'shin's extension of Hooke's law to plastic deformation of powder particles. This extension, which is based on the assumption that the particles are not hardened during compacting, might be used to simplify the primary calculations, but also other assumptions are made in the derivation of equation (1). The reader need be reminded only of the basis of this derivation. Starting from Hooke's law

d~D_ =_

_

S

(2)

E dlz ho

it is supposed that the compacting of a powder satisfies the analogous law

S

(s)

h0

where dp/S c represents the pressure increment per 1 cm 2 of the overall briquet cross section divided by the original "contact cross section" Sc; dh/h 0 is the relative reduction of the briquet height; Sc = 2 represents the projection of the contact regions between two transverse particle layers on the plane of the briquet cross section. Further, in paper [1] it is taken to be "practically convenient" to refer dh not to the initial briquet height h0, but to its height limit h c corresponding to zero porosity:

dp Sc

.

K" dh

.

.

. hc

.... .q K a?,

(4)

where/3 represents the relative volume defined as h/h c. Moreover, particle hardening is excluded: :

~c--= COl]St,

Sc where o

C

(5)

is the stress at the particle contact points and approximately equals Meyer's m e t a l hardness,

315

Substituting (5) in (4) and integrating, we obtain equation (1) logp=--a([3--1)

+

where p represents the compacting pressure without allowance being made for the loss by external friction; c = log Pmax (Pmax is the pressure corresponding to zero porosity). This derivation not only neglects particle hardening and extends Hooke's law to plastic particle deformation, but also tacitly introduces the following assumptions. The transition from (2) to (3) implies that the elastic deformation law of a solid nonporous m e t a l is extended to the deformation of pores (the decrease in height dh is due only to reduction of the pore volume). However, Hooke's law specifies elastic deformation with a uniform stress distribution over the entire volume of a compact metal, while neither the type of deformation nor the nature of Ehe stress distribution are changed. In equations (3) and (4), dh is related to extreme conditions: either to h 0 of loosely poured powder with high porosity and negligible contact between the particles, or to h c of the nonporous metal. As the degree of compacting increases with the reduction in height from h 0 to h c, the number of contacts, the porosity, the type of interaction and the arrangement of the particles, the nature and the degree of their deformation and stress distribution over the entire powder volume change markedly. Hence, any intermediate state of the briquet differs noticeably both from the original state with h 0 and from the final state with h c. Consequently, if dh is referred to h 0, or to h c, the description will not be quite correct. It is more correct to refer dh to h at the given degree of compacting, i.e., to take h as a variable. Then, instead of equations (3) and (4), we have df

i~ dh - -

Sc

h

iz -d> -.

(4a)

~

Substituting (5) in (4a) and integrating between the boundaries p and Pmax, we get

10gp = - - m log [~~-!ogpmax-

(6)

Here it is supposed that m = const, i.e., o c = const. In the derivation of equation (6) only a single provisional assumption is made, whereas the derivation of equation (1) shows several other flaws, so that the latter equation cannot be considered as well-founded. In practice, the experimental data of some materials in particular those of nonplasttc substances are sometimes found to obey equation (1) satisfactorily. This is the case if, within the density limits, both a semtlogartthmtc and a logarithmic plot can be satisfactorily approximated by straight lines. Moreover, besides particle hardening tending to produce a concave downwards bend in the curves corresponding to equations (1) and (6), physical factors tending to produce a bend in the opposite direction are sometimes encountered; the two tendencies may compensate each other in a given section of the curve. The motivation in papers [3, 4] where it was stated that equation (1) "much better describes the briquet density as a function of the pressure in the case of hard and brittle powders, since their disintegration more closely resembles elastic deformation" cannot be considered as correct. This formulation suggests that in the case of such materials the derivation of the equation can be taken to rest on a sound basis, notwithstanding that equation (1) has no sound basis, not only because it starts from Hooke's law, but also for other reasons. The above derivation of equation (6) was given in paper [1]. However, this equation can be derived in other ways, using very few provisional assumptions. We shall compare the increase in relative briquet density with the increase in density of a cross section. The relative density

h

d

tends to unity as the porosity approaches zero (7 represents the briquet density; d the specific weight of the metal; B the relative volume).

316

In a loosely poured powder, usually a ~ 0.15-0.3 and 8 = 3-6. We.shall express the degree of compacting of a briquet cross section as the ratio of the "contact cross section" to the entire cross section; Sc/Sbr. Like I~- and 8, this ratio tends to unity with increasing degree of compacting. However, in the original powders the Sc/Sbr ratio may be of the order of 10 -a or smaller. Consequently, the Sc/Sbr ratio rises much more with the degree of compacting than does 8. With an accuracy sufficing for practical purposes, this may be expressed in the general form

SC

--

1

t~r/z ~

__

S br

(7)

~m

We shall provisionally assume that no hardening occurs

P -

~-~ a c =

-

const.

(8)

S e

Substituting (8) in (7), we obtain

p

1

O~C

~m

(9)

or log p = - m log 8 + log Pmax' i.e., equation (6). In paper [5] it has been established that E'

=-- E~"

-~

E - -,~Z ~

~

(10)

where E' and E represent the elasticity moduli of the briquet and the nonporous metal, respectively; & and 8 are the relative density and the relative volume, Taking into account that

~

Sbr

(11)

and substituting (!1) in (10), we get equation (7) which, as shown above, yields the fundamental equation (6) when it ts assumed that o c = const. Consequently, equation (6) can be derived in three ways, which confirms its soundness. The present paper discusses only data from the Soviet literature, but honesty forces us to admit that a relationship analogous to equation (6) has been established also in foreign papers [16, 17]. If it is assumed that o c = const and the data are plotted in the coordinates log p versus l o g 8 , equation (6) predicts a straight line, whereas equation (1) predicts a straight line in the coordinates log p versus 8 - 1 ; the factor m characterizing the powder compressibility is found from the slope of the straight line. When powders of brittle materials whose particles show no hardening upon deformation are compressed and the briquet is thin, i.e., when external friction has only a slight effect, then, a linear log p versus log g curve (and sometimes even a linear log p versus 13 curve in a restricted range of 8 values) ls often found. This behavior is reported for borldes in the paper [6]. However, the view expressed there, viz. that such a linear relationship holds also for the compacting of metal powders, is generally untrue. When powders of ductile metals are compressed the deforming particles harden, so that the log p versus log 8 curve usually bends downward, i.e., log p rises faster than log 8 falts. It may also happen that the log p versus log ;3 curve bends upwards, t.e., log p rises more slowly than log ;3 fails (if the particles are covered by compact and tough oxide layers) [7]. It is owing to the combined action of the various factors that in a given range of 8 values a linear relationship of log p versus iog 8 holds even for ductile metals. The actual magnitude of e c at given p and ;3 ls estimated from the intercept of the tangent to the log p versus log ;3 curve with the axis of ordinates tn a given point (according to [1] this also holds for a curve of log p

317

versus 8 ). Hence. the way in which, and the extent to which, the log p versus log B curve deviates from a straight line permit relating the compressibility of the various powders to their properties and of analyzing their behavior during compacting. In paper [5] allowance was m a d e for the effect of particle hardening (without external friction), and the following relationship was proposed for the degree of briquet cqmpacting as a function of the pressure:

(12)

I

.,

where Pc [s a constant representing the c r i t i c a l creep stress of the c o m p l e t e l y hardened metal; h 0 and 7 0 are the height and the density of the powder before compressing; h is the briquet height at p; 7 m is the specific weight of the m e t a l . Rearranging equation (12), we get the following relationship:

F ~c

[(7) ] i '] [S~--I]

-=Pc

1

'

(13)

~n

~0 where 80 and B represent the r e l a t i v e volumes of the original powder and of the briquet at p, respectively. According to e x p e r i m e n t a l data [5], the exponent n in several metals (Fe, Cu, Ni, Co, Sn, Pb) is m 4. Hence, the fraction 1/B n is small ( ~ 0.001-0.01) and the denominator in the right-hand side of equation (13) can be taken equal to unity to an accuracy of 0.1-1%. Then

[1

ll (14)

Assuming Pc = const, considering that B0 = constant for a given powder, and using the designation Pc/Sn = K, we find P --~ K ~ ' P c

~n

(15)

or

log

(p+K) ~ - -

,z log } + l o g 2 c ,

(16)

Consequently, transformation of equation (12) where hardening is taken into account leads to equation (16), which differs from the above derived "ideal" equation (6) in that log (p + K) in the left-hand side of (16) replaces log p. The r e l a t i v e magnitude of K decreases with rising 1~. The following remarks should be made on the bases underlying the derivation of equation (12). In paper [5] the stresses generated in the briquet during compression are expressed as follows"

P, G i 2 - SZ )

where Pz is the load applied (kg); Sz represents the m e t a l l i c part of the briquet cross section equalling Sbr" -~; Sbr is the total briquet cross section; O- is the r e l a t i v e density (in the paper cited referred to as "the compactness factor" designated by a z, which is considered to be a new concept). Actually, however, the load is transmitted from one particle to another via the contact regions the stresses of which (according to M. u Bal'shin) ~c = Pz/S c exceed Oiz, since "the contact cross section" Sc is much smaller

318

than Sz, especially at the start of the compression. For example, in a loosely poured powder & ~ 0.2-0.4, and, consequently, Sz, will be rather high ( 20-40~ of Sbr), whereas the a c t u a l area of particle contact wiI1 be negligibly s m a l l (S c ls some powers of ten smaller than Sz). Then, Sc rises rapidly during compacting and, as compression proceeds, S c and Sz draw gradually nearer to each other and finally tend to Sbr, when the density approaches zero. Hence, equation (12) and relationship (16), derived above, can be considered as a p p r o x i m a t e formulas valid only for their dense briquets (at .9 values above, say, 70%). However, equations (12) and (16) differ from r e l a t i o n ship (6) in that the former make allowance for particle hardening during compression. It would evidently be much more appropriate to derive an equation analogous to relationship (12) by starting from the stress per unit "contact cross section," and not from the stress per unit of " m e t a l l i c cross section. ~ The physical meaning and the magnitudes of the constants K and n in equation (16) and the dependence of these constants on the properties of the m e t a l powder also require a further theoretical and e x p e r i m e n t a l analysis for the various metats and other powders. Hence, it is to be specified to what extent and under what conditions the premises on which the derivation of equation (12) is based are a p p l i c a b l e , or when these premises a/re to be corrected. It can be expected in particular that in tests extended over a. broad range of conditions, the exponefit _n for various powders will vary much more than was found in paper [5]. All the above considerations refer to cases where external friction can be neglected; in practice it is n o r m a l l y endeavored to establish this condition. Attempts at making allowance for the effect of external friction considerably c o m p l i c a t e the corresponding relationships. Finally, one general feature common to a l l qualitative relationships proposed by the various authors for the briquet density as a function of the compacting pressure should be pointed out: all these relationships are of the continuous type. This is contradicted by the hypothesis [8] that in the first stage of compacting the particles are displaced without deformation, and that in the second stage where the porosity is still high, the particles are neither displaced nor deformed, but show only "elastic resistance," while the pressure rises without compacting the briquet. Finally, in the third stage, compacting is assumed to occur by plastic deformation, or by crushing of the brittle particles. In paper [8] it is stated that the second stage is the more noticeable the higher the stability against compression and the higher the elasticity modulus of the m a t e r i a l but, meanwhile, the reservation is m a d e that "in the overwhelming majority of powders applied in practice the second stage is almost i m p e r c e p t i b l e or does not occur at all." The latter remark has no sound foundation and is contradicted by the above discussion, for, materials having a high compression resistance and high elasticity modules are very extensively used in powder compression (refractory metals, solid alloys, carbides, borides, siltcides, oxides etc.). Since, according to [8], the second stage should be the most noticeable during compression of such materials, the question arises why "in the overwhelming majority of powders, the second stage is i m p e r c e p t i b l e , " and why the authors did not produce any examples from the extensive p r a c t i c e of compacting hard and brittle powders, which might confirm the existence of the second stage. Also false is the statement that c o m p a c t packing of the particles can be achieved in the i n i t i a l , c o m p a c t i n g stage without any deformation being involved. Actually, the relative displacement of the particles even in the initial compacting stage leads to elastic and plastic deformation, or to disintegration of the protuberances and indentations by which the particles contact. The particles cannot be displaced without deformation of these p r o j e c tions~ Further deformation affects ever deeper p a r t i c l e layers. The relative displacement gradually slows down, particle deformation increases, and all these phenomena are superimposed continuously. Practice and the theor e t i c a l considerations of various authors have shown that as the pressure is being increased c o m p a c t i n g goes on without interruption or slowdown. Shear Stress Coefficient, tion and Extrusion Force

Compression

Force

Consumed

in S u r m o u n t i n g

External

Frtc-

The shear stress coefficient g depends on Poisson's modulus v of the m e t a l [1]

Psh

"~

Pax

1 -- v

319

However, M, Yu. Bal'shin [1] believes that the shear stress coefficient decreases proportionally to the lowering of the relative density

where g' and g are the shear stress coefficients of the briquet and the nonporous m e t a l , respectively. This assumption was also m a d e in paper [9]. Actually, however, the presence of pores does not lead to a partial loss in pressure to the side wall, but the stress is solely redistributed (concentrated) near the region where powder particles touch the mould. This also happens on the contact surface between the briquet and the die. Hence, under the conditions of elastic equilibrium, g m a y change as a function o f f ) a n d I~, if u changes. According to e x p e r i m e n t a l data reported in papers [18, 19], a n o t i c e a b l e variation o f g with p (and, consequently, with l~) was not observed. In paper [10] it is shown that the shear stress is larger the higher the powder dispersion, the simpler the shape of the p a r t i c l e surface, the larger the coefficient of external friction against the mould wall. However, it is not e x plained there how these factors affect the elastic force equilibrium established after the advance of the die has stopped. The factors pointed out in [10] have no effect on the derivation of the relationship g = v / 1 - u . Experiments done by A. Ya. Artamonov and V. I. Danilenko [20] showed that v decreases to some extent with &, but this does not result in a linear relationship U = g&. The above considerations are important for the construction of moulds, since an incorrect m i n i m i z a t i o n of the shear stress coefficient results in a wrong estimate of the mould strength required. Consequently, in computations of the compression force consumed by external friction (the shear stress coefficient enters into these calculations) it is incorrect to assume that the latter coefficient decreases proportionally to ~ [1]. The compression force consumed in surmounting the external friction [1, 3, 4, 11, 20] is often expressed as follows: . X ~ o n ~ Psh "l~ = P ' ~ - ' ~ ' F s h

-=p.~.p..~.Dh,

(17)

where APcons(kg ) is the compression force consumed by external friction; Psh(kg) is the load applied to the side surface; p ( k g / c m 2) is the pressure on the upper end of the briquet; I~ is the friction coefficient of the powder; D and h are the diameter and the height of the briquet. Relationship (17) will not be fulfilled, if v , and consequently, g too, vary with p (and with I}). However, in this case, where the product g 9 g enters into the relationship, it follows, for e x a m p l e from data in [21], where was found to depend slightly on p, that, nevertheless, the product ~ 9 ~ does not vary with p. Hence, from this point of view, equations (~17)-(20) r e m a i n valid, According to relationship (17) the fraction of the compression force consumed by external friction is given by:

2~Pcons__ P ' ; , ' t ~'lt D . h p ~f) ~ ~"

s

4~.-1~ 9 _ h . D

(18)

Substitution of the final values of APcons and _h_in equations (17) and (18) does not yield correct results, since a constant and exaggerated value of the parameter p (which exceeds the average of p over the briquet) is employed. Considering the compression force consumed by external friction serves a useful purpose only i f the value of APcons is a p p r e c i a b l e , but, then, the a x i a l Kress and the shear stress vary considerably with the height in the briquet. Hence, the above relationship should first be applied to an infiniteIy thin briquet layer dh in which p can be taken as constant: aPcor2~ p . ~ . p,. ~ . D . d h ___ . 4 . ~ . p, . d h

p tt.)

r:D ~ 4

(19)

D

9 - - -

Integrating (19), we obtain

Po

P;~

h

(20)

320

where P0 and Ph represent the force on the upper and lower ends, respectively, so that

~Pcon~ Po

;'~

Relationships similar to (19) and (20) have been derived in paper [1], but these contain the "reduced height" h e corresponding to zero porosity, and not the a c t u a l height h. This difference is due to the fact that the derivation of the former relationships starts from the assumption t h a i t h e shear stress coefficient decreases linearly with ~ , which, as proved above, is wrong. In the papers [1, 3, 4] it [s r e p e a t e d l y stated that the force spent in extruding the briquet from the mould after compression (Pext) is equal, or close, to the force consumed by external friction (&Peons)" This is only possible if / the shear stress remains unchanged after the load has been relieved from the die, i.e., if the briquet does not elongate in the mould as a result of elastic aftereffects. Perhaps this condition is nearly fulfilled in ductile meta!s of low hardness whose particles create larger contact surfaces during compression and strongly adhere to each other and to irregularities of the mould wails. At the same time, the low hardness of the m e t a l resutts in small tensions in the contact regions, which reduces the action of the elastic a f t e r e f f e c t . . T h e elastic aftereffect is also reduced when fine powders are compressed, since their particles adhere more strongly in the briquet. It should be noted that this is contradicted by statements in the papers [10, 11]. In paper [5] it has been shown that noticeable deviations from the above "ideal" conditions are found even in a ratherductiIe m e t a l of average hardness, e.g., in iron. During compression of iron powder it was established that after the load had been taken from the die, the shear stress decreased by 1 5 - 3 0 5 , and the extrusion force Pext fell below &Pcons. In this paper the briquet was found to elongate by 1-1.3% in the mould, owing to elastic aftereffects after the load had been removed. A study on the behavior of powders of hard metals, carbides, oxides revealed stilt greater differences between Pext and &Pcons- In paper [12] it has been shown that during compression of the refractory (WC + Co) powders whose adherence is r e l a t i v e l y low and whose contact stresses generated by compression are high an enhanced elastic aftereffect is noted; owing to this, the extrusion force drops by 2-2.5 times below ~Pcons" Consequently, the customary assumption that Pext ~ LXPcons is generally incorrect. Accordingly, the relationship often encountered in the literature [1, 3, 4, 11]

~Xt ~ '~JDCOI'IT~L.~op .ys h is wrong, or cannot be extended to powders of hard and brittle materials; moreover, it is incorrect to use ]~ in the righthand side of this equation, i.e., to substitute there the pressure applied to the upper briquet end by means of the die (the explanation has been given above). Nonuniform Distribution of the Density Over the Briquet Volume Although this question has been discussed repeatedly, there still appear statements [8, 10, 13, 14] to the effect that not only external friction, but also mutual friction, of the particles cause the density distribution, and hence, the pressure in the briquet to be nonuniform. We shall discuss the experiments described in paper [12]. The load on the die P was divided into two parts: Pl spent in compacting the powder and P2 spent in external friction. Tempered steel balls were placed under the lower die and under the lower end of the mould. The magnitudes of Pl and P2 (P = Pl + P2) were determined by measuring the size of the holes impressed by these balls in iron underlayers of known hardness. Improvement of the quality of the mould surface and also improved lubrication m a y m i n i m i z e Pz; if P2 tends to zero, then Pl tends to P. If it were possible to e l i m i n a t e external friction c o m p l e t e l y , then, the pressure under the lower end of the briquet would be equal to the total load P. Consequently, friction between the powder particles does not result in a drop in pressure and density over the height in the briquet. This means that to attain a given density in the compression of various briquets of different height from the same powder one and the same pressure is required, regardless of the briquet height. Of course, the higher the friction between the particles and the higher their resistance to deformation, the higher will be the pressure required for attaining a given density. However, different briquet heights do not require different compacting pressures (as measured after the movement of the die has stopped) but require different compression energies spent during the m o v e m e n t of the die. Th~is energy is given by:

321

h ?

W =-- j p d / , , U

where p is the compacting pressure (for a briquet cross section equal to 1 cm2), rising as the die moves forward and being a function of h; h is the distance covered by the die. In the analogous formula in paper [1], p was taken to be a function of the briquet height and not of the path covered by the die; however, this is incorrect, since the energy of a variable force must be expressed as the sum of increments of the force multiplied by the path covered. In paper [15] it was pointed out that, besides the effect of external friction, increased compacting of the outer briquet layers adjoining the wails of the mould and the die may cause a nonuniform density distribution in the briquet under the influence of the mould wails. This view arose in connection with the observation that sometimes more dense "nuggets" form in sintered ware during the production of hard cement alloys. However, the explanation must be sought in the conditions of sintertng and the phenomenon does not prove that th e compacting effect is to be ascribed to the mould wails. From the above view it would follow that the pressure transmitted to the die wails via the powder is strengthened in an inconceivable way near any mould wall (for example, near the lower wall), which is impossible. Beside nonuniform compacting under the influence of external friction, an increase in density of the outer briquet layers near curved surface regions is sometimes observed. This is due to the "arch" effect in the stress dis~ibution near curved surface regions. Experiments of B. A. Berok and L. P. Monakhova [2], who observed some compacting of the outer layers in cylindrical briquets of copper powder (over a certain range of briquet diameters) compressed in a rubber jacket by means of hydrostatic compression, may serve as a proof that the "arch" phenomenon does exist beside the effect of external friction. SUMMARY From an analysis of several fundamental questions in the theory of powder compacting and from a discussion of the Soviet literature on this subject the following conclusions can be drawn: 1. The semilogarithmic relationship between the briquet density and the compacting pressure: logp=--u(13--

l) + c

as is used extensively [1], has been derived by starting from not quite sound assumptions. It is more reasonable to apply [1, 2] the relationship logp=--m

l o g [5+c,

which in the present paper has been derived in three different ways. If powders of ductile metals are compressed, corrections are to be introduced to make allowance fo~ particle hardening during compression; this usually leads to a rise of the coefficients m and c with increasing compacting of the briquet. The recently proposed [5] relationship which makes allowance for particle hardening and not for external friction can be transformed into log(p+K)

=-n

log [ 3 + c

However, the original formula, as proposed in [5], was based on a too low estimate of the stresses in the briquet (i.e., was referred to unit area of " m e t a l l i c cross section," instead of unit area of "contact cross section"). Hence, the transformed equation must be considered as an approximate formula, obviously, solely valid for relatively high densities. Further corrections must be introduced if the relationship is employed over a broad range of pressures. The physical meaning and the magnitude of the constants K and h__in this relationship require further analysis. 2. The assumption in [8, 9] that the briquet density rises step-wise with a temporary stand-still of the compacting in the middle of the process is not well-founded. 3. The shear stress coefficient ~ = u / 1 - u does not vary proportionally to the relative density. Although some variation of u with p is observed (especially at high p), the product g 9 g nevertheless remains constant.

322

4. The extensively employed [1, 3, 4, 11] relationships characterizing the compression force consumed in surmounting external friction

2~Pcon~ P" ~'i~" =" Dh and

Peons_ 4 . t ~ P

/z -D

are incorrect, since they contain the final values of the parameters &Pcons and h__,and a constant, too high value of 1~ is employed, whereas, actually, P varies with the briquet height. The following formula will be more accurate

lnP0 r'r'i~

inP0

in p 1 "

~.~.l_t " k D '

where /xPcons = P0-Ph; P0 and Ph are the forces on the upper and the !ower ends of the briquet.

J

5. The extrusion force is, genera!ly, not equal to the compression force consumed by externa! friction: Pext 2~Pcons. In brittle, hard materials, Pext may be severaltimes lower than &Peons" The relationship encountered in [1, 3, 4] Pext -~ &~ons~ >" ~ .]2, Fsh where Fsh represents the area of the side surface, is incorrect both for the above reason and because a constant, too high value of p is employed. 6. The statement that friction between the powder particles is one of the causes of the nonuniform density in the briquet [8, 10, 18, 14] is to be definitely rejected. The hypothesis [15] that the mould walls exert a direct compacting effect must also be rejected. External friction is the cause of the density gradient in definite directions in the briquet, in the limit case of no externa] friction, compression of a given powder to briquets of various heights and a given density requires an identical prestZ

sure but different compression energies (proportional to the briquet height: W = f

pdh, where t~ is a function of the

to

0 die displacement h, but, unlike sometimes stated in the literature, not a function of the briquet height). LITERATURE

CITED

1. M. Yu. Bal'shin, Powder Metal Working tin Russian], Metallurgizdat, Moscow (1948). 2. G. A. Meerson, Powder Metallurgy, Collection edited by the Research Institute of Automobile Industry and by the Committee on Powder Metallurgy [in Russian], No. 3, (1956), p. 8. 8. G. V. Samsonov and S. Ya. Plotkin, Manufacture of Iron Powder [in Russian], Metallurgizdat, Moscow (1957)o 4. N. F. Vyazntkov and S. S. Ermakov, Application of Powder Metallurgy Products in Industry [in Russian], Mashgtz, Moscow (1960)o 8. G. M. Zhdanovtch, Some Problems in the Theory on the Compression of Metal Powders and Their Mixtures [in Russian], Izdat Belorusskogo politekhnicheskogo instituta (1960). 6. G. V. Samsonov and M. S. Koval'chenko, Poroshkovaya metallurgiya, No. 1, 20 (1961). 7. G. A. Meerson and A. F. Islankina, Atomnaya ~nergiya, No. 8 (1960). 8. V. S. Rakovskii, O. V. Samsonov, and I. Io Ot'khov, Principles of the Manufacture of Solids Alioys [tn Russian], Metallurgtzdat, Moscow (1960). 9. V. S. Rakovskli, Corrects in Mechanical Engineering [in Russian], Mashgiz, Moscow (194,8). 10. V. S. Rakovski[, Introduction into the Theory of Powder Metal Working [ in Russian], Oborongiz, Moscow (1988). 11. S. Ya. Plotkin and O. V. Samsonov, Vestnik mashinostroentya, 39, 5, 53 (1959). 12. A. G. Samotlov, Powder Metallurgy, Collection edited by the Research Institute of Automobile Industry and by the Committee on Powder Metallurgy tin Russian], No. 4 (1956), p. 22.

323

13. A. G. Samoilov, Tsvemye m e t a l t y , No. 4 (1946). 14. B. A. Borok and I. I. Ol'khov, Powder Metallurgy [in Russian], Metallurgtzdat, Moscow (1948). 15. V. S. Rakovskii and N. R. Anders, Principles of the Manufacture of Solid Alloys tin Russian], Metallurgizdat,

Moscow (195t). 16. 17. 18. 19. 20.

W. Rutkowski and H. Rutkowska, "Prace Glow," I. Met. 111 (1949). Y. Vacek, ",Hutnicke" Ltsty, 1_~1,No. 8, 456 (1954). V. G. Filtmonov, Vestnik mashinostroeniya, No. 3 (1951). V. N. Goncharova, Zav. lab. No. 5 (1948). I. M. Fedorchenko and R. A. Andrievskii, Principles of Powder Metallurgy [in Russian], Izd. AN Ukr. SSR, Kiev (1961), p. 157. 21. P. Duwez and L. Zwell, "J. Metals. Trans." 1, 2, 187 (1949).

MICROSCOPIC Ya.

PYCNOMETRY

E. G e g u z i n

and

N.

OF SOLIDS

WITH

MICROCAVITIES

N. O v c h a r e n k o

A. M. Gor'kit Khar'kov State University of the Order of the Red Banner of Labor Translated from Poroshkovaya Metallurgiya, No. 5 (11), pp. 15-19,September-October, 1962 Original article submitted February 5, 1962

In the investigation of m a n y processes occurring in metals and alloys, it ts often necessary to perform precision pycnometrtc measurements. In most cases the difference between the a c t u a l pycnometric density (pp) and the x - r a y density (Px) arises due to mtcrocavtties and discontinuities which appear as a result of the spectmen's history. These defects appear [n metals which were subjected to " c y c l i c heat treatment," plastic deformation, radiation, etc., and also in alloys from which the volatile component has been partially removed. An accurate determination of the density of such m a terials is necessary for finding the relative (A) of discontinuities, which is determined by the relationship

Px

(1)

While its principle ts very simple, the ordinary pycnometric method is rather difficult to use in practice, especially if the value of 5 is small. Besides errors which can occur in precision weighing, there m a y also be errors which are due to microscopic air bubbles which adhere to the specimen's surface. Another disadvantage of the pycnometric method consists in the fact that it yields only information on the integral porosity; however, information on the distribution of defects throughout the specimen's volume also is of considerable interest. The method of the s m a l l - a n g l e scattering of x-rays which has been successfully used in recent years by Ya. S. Umanskit and collaborators in investigating submicroscopic cavities is free from these disadvantages [1]. This method yields important information on the size of microcavities and their distribution with respect to size. However, this method entails considerable e x p e r i m e n t a l difficulties, and the thus obtained results cannot always be interpreted in a positive manner. In our article, we would like to draw the reader's attention to the fact that, for the solution of such problems in pycnome,try when A is very small, the ordinary metallographtc method can be used if high-temperature annealing is to be preferred to the metallographic inspection of the spectmen's defects. Fine-dispersion cavities ( ~10 -s cm and less) cannot be resolved by means of the metallographic method and using an optical microscope, and, m o r e over, such cavities, as a rule, are distorted and partially filled as a consequence of polishing in preparing m i c r o scopic sections. However, during the process of high-temperature annealing, diffusion coalescence occurs in a specimen which contains microcavtties of different sizes; in this case, the larger cavities grow diffusively at the expense

324