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WEARA STUDY OF EROSI ON PHENOMENA PART I I (Received August z-4, 1962) SUMMARY I n Part I of this work (Wear, 6 (1963) 5-2~) it was stated that erosion consists of twa types of wear: deformation and c&t@ w&r. For the former a fonnuta was derived containing two con&~&s expressing the influence of tht ~~~a~~~ properties of the eroded substance, I n this part, equations are deduced for cutting wear, containing tvro new constants: C, whici represents the hardnem of the eroded substance, and p, which describes the plaatic_eI asti~ behaviour of the material. The combination of the two types of wear is discussed and the equations are shown to agre% with the results of experiments on hard and brittle, and on soft and ductile mate&& Several erosion phenomena are explained by the furmuI ae, and indications are given for pre- venting or reducing erosion in practice. ZUSAMMBNFASSUNG I m ewten Teil dieser Arbeit wurde dargelegt, dass Erosion zwei Typen des Verschleisses umfasst, die auf Verformung bsw. Schnittwirkung zuriickzufiihren sind. Fiir den Verschleies infolge Verformung wurde eine Forrnel mit zwei Konstanten abgeleitet, die den Einfluas der mechanischen Eigeaschsften des erodierten Materiales mm Ausdruck bringen, Im vor~~nd~n Teil wertaen G~e~hun~e~ fur den S~n~~ve~cblei~ abgeleitet, in denen zwei neue Konstanten auftreten: C, die die Htie dee ercdierten Ma-toriaks urn&z&, und e, die sein plastisch-elaatfsche VerhaRen beschreibt. Die Kombination der beidc?n Verschleisstypen wird besprochen und es wird gezeigt, dass die Gleichuagen mit den Ergebnissen van Versuchen an harten sprlJ den und an w&hen zahen Materi- alien im Ginklang sind. Einige Erosionserscheiaungen werden an Hand der Gleichungen erkhirt. M& & m& men zur Verh~~~~~ oder Ve~ind~~~~~ von Eroeion in der Raxis werden angegeben. I . I NTRQDUCTI ON (For a complete list of symbols see Part I .) I n the first part of this publication1 it was stated that in erosion two types of wear are inx~lved, tix. wear due to repeated def#~ation (WO) and cutting wear (WC), For d~fo~at~on wear the fol~#~~ equation was found: w _ tM [Vsinu - KID n- 0) E 170 J . <;. ,\ . 13I’rTElt in which l+L) = umt~ volume loss. iZf z total mass of impinging particles, 1’ = pdrtkk velocity, ix = impact angle, li = maximum particle velocity at which the collision still is purely elastic and F = the energy needed to remove a unit volume of material from the body by deformation wear (deformation wear factor). In the case of brittle subst~~es such as glass and cements a good correlation could be shown to exist between experimental and calculated dependence of wear on particle velocity and 31. Ductile materials such as most metals are also liable to de- formation wear, but since cutting wear occurs simultaneously this type of wear must be considered first. Cutting wear exists if particles strike a body at an acute angle, scratching out some material from the surface. This scratching is highly influenced by the velocity and the impact angle of the particle. Now the particle velocity can be resolved into two components, one normal to the body surface (VJ and another parallel to it (V,,). As a result of T/ , the particle @nedrates into the body, while F’#gives the particle its s~~~~~~~ actian. As long as V, does not exceed K no damage occurs as a result of V ,t, for a movement along the surface is ac~ornpa~~d by a corr~spon~n~ muvement of the stress concentrations, the greatest stress nowhere exceeding the elastic load limit yr . If, however, V, exceeds K, plastic deformation occurs and as a result of I/ , the body is subjected to a shearing load over an area equal to the vertical cross section of that part of the particle which has ~~etrated into the body, causing a scratch. In this scratching and deformation energy is expended, which is supplied by the inertia of the particle, resulting in a decrease of both the vertical and horizonta1 velocity components. Now there are two possibilities: (a} the particle still has a horizontal velocity component (us) when it leaves the body surface, (bf the horizontal velocity component becomes zero during the collision. In case (a) the energy absorbed in the process of scratching is in which nz = mass of the particle. The quantity of energy needed to scratch out a unit volume from a surface de~nds on the mechanical properties of the body {assuming that the particle is not destroyed). We call this quantity the cutting wear factor, e, The volume cut from the body surface by one particle equals: In case (bf it can be expected that: (3) Wuw, 6 {196$ 169-190 EROSI ON PHENOMENA We shall see later that sometimes a correction must forces set up in a direction parallel to the surface. be applied for elastic reaction In the following an expression will be deduced for v,a in eqn. (2) and for the correc- tion in eqn, fsf . II. CUTTI NG WEAR EQUATI ON WHEN VI $ 0 To arrive at an expression for pii we consider a plastic4astic collision at an acute angle, assuming the particle to be spherical. This is an arbitrary assumption which, however, approximates practice very nearly, as can be made plausible by the following argument. The particles involved in erosion are small and generally have rounded edges. The probability that such a particle strikes a surface with an edge or a plane surface is very small in comparison with the probability that it strikes the body with a point, I t can be easily calculated that the depth to which a sphere with a density of 4 gfj cm3 and a velocity of wz. 100 mjsec penetrates into, for example, low-carbon steel is at most ~/I O of the particle radius. This means that in actual practice only the rounded part of the point of a non-spherical particle penetrates into the surface. Therefore we may assume that such a particle is a sphere with a radius equal to the radius of curvature (r] of the point and a density which is {A/r}3 times as large as the actual density, if the volume of the particte equals 4/a&a (see Fig. I ). Ra AVERAGE RAMuS r =APPARENT RACKS Fig. I. Apparent specific gravity is (R/r)3 x real specific gravity. We suppose that the area subjected to a horizontal shearing load is at every instant A, then the energy required to displace the particle a distance db in horizontal direction is : AA he, which equals so Since the depth of penetmti~n of the particle is small in relation to its ~arn~ter zR it follows that where H has the same significance as in Part I. 17’ J. G. A. BITTER Substitution in eqn. (5) gives or 1’ * ito) - (71 where V,,(&} = horizontal velocity component at the beginning of the collision, V,(it,) = y,, = horizontal velocity component at the end of the collision. No allowance is made for friction, which might, for instance, impart a certain energy of rotation to the par&&, However, for the size of particles involved in erosion this energy proves to be ne~li~ble~ as has been shown also by FINN~E~. A collision can be split up into two periods, the first period ending at the moment the vertical velocity component has just become zero, and the second period during which the particle is pressed out of the body again by the elastic reaction forces set up in the particle and body during collision. The first part of the first period is purely elastic. In this part no erosion occurs, so we can leave it out of con~deration. Far the duration af the plastic-efastic part of the first period ANDREW@ derives: 6, - to = (4 + f!} I/- & in which 6 is a correction for elastic defo~ation. 6 appears to be neg~gibly small, so that we can ignore it and write instead the equation for a purely plastic collision : where For the penetration depth ANDKEW~ derives: H = H,., sin I*(6 - to]] Substitution in eqn. (7) and graphical integration gives : where V,(&f = horizontal velocity component at the end of the first period of the collision. During the second period the particle continues its cutting action. The elastic reac- tion forces, however, press the particle out of the surface and decrease the penetra- W*ar, 6 {u&3] i6g-rgo EROSION PHENOMENA I 73 tion depth, which according to Part I is at the beginning of the second period given by: @ mrx = H m”r + h*r Since cutting only occurs if y is exceeded h,r has to remain constant. Therefore H,,, decreases to zero, hcl remaining unchanged; when H has become zero bet decreases, being zero when the particle leaves the body. Also in the elastic part of the second period no erosion occurs. This picture is correct as long as the direction of movement of the particle does not coincide with the tangent to the edge of the indentation at that instant. It can be argued that in ignoring this phenomenon only a slight error is introduced. According to Part 11 the force on the area subjected to plastic and elastic deformation equals 3~~~2y and the force on the only elastically deformed area equals lrre2 %y. So the total force on the contact area during the first part of the second period equals at any instant : from which follows: d V, 2izRy H 9&?yhet -ze dl +------ (111 m m Since during the first part of the second period H decreases to zero, h,r remaining constant, we may put Multiplication of eqn. (~2) and eqn. (II) gives an expression which on integration gives : Using eqn. (12) the decrease of the horizontal velocity component during the second period can be written as: V,(h) - V,(h) = dv,, = _ I Hmmx dvl dH H=o dt V, Elimination of dV,/db and VL with the aid of eqns. (6) and (13) and transformation of H to xHmsx produces: .*,*d.V v, It11 - v,(k) = 98 (14) I - x * + 418 Summation of eqns. (IO) and (14) gives the total decrease of the horizontal velocity Wear, 6 (1963) K&P-rgo I74 J. G. A. KITTER component during collision : in which f(x) represents the integral from eqn. (14). In this expression we first eliminate h,l and Hmax. According to eqn. (~za) in part I : According to eqns. (II) and (13) of Part I we have: “liyH mbr~ = ~eH,,,z = f(V, -- K)a = t(V sina -- K)a (171 m From eqns. (16) and (17) it then follows that t V sina H msx = t K II hcJ (18) By elimination of H,,, with the aid of eqn. (18) it can be found by graphical integra- tion using different values for h,JHma, that for eqn. (IS) can, with sufficient accuracy, be written as where I Vsina: - K] [Psincr - o.gKJ V,/(h) -’ V,(b) = ZC@ ..L-- (19) 1-V msinn In practice, where V sin&/K: is generally much higher than, say, 1.5, this equation may be written as: v, (fo) ~ v,, (fz) = ZC@ (V sincx - K)s liv-sin a (2 1) Weau, 6 (1963) 169-190 EROSION PHENOMENA 17.5 Since V,,(S) = Y COSLX it follows from eqn. (21) that: V,,(h) = vcosa - 2Cp (V sina - K)a i Vsi noc So the energy expended by a tm(Va COSMI C - v,yt ,)) = particle in scratching is 2mC( V sin oc - K)l C(V sina - K)* jV’siG Q Vcosa - [ j /V sina ’ 1 Replacing m by the total mass of the impinging particles h4 and dividing the equation by the cutting wear factor e we find the cutting wear WC~ expressed as units volume loss : III. CUTTING WEAR EQUATION WHEN v”r BECOMES ZERO The horizontal velocity component may become zero during the first period, during the second period or in the boundary case at the end of the first period. Let us consider the last case more closely. As long as the particle still has a hori- zontal velocity component its retardation in horizontal direction is at any instant: rA ‘lar,Ht - a ‘/+‘2RH=l % I =-= -= m m wl where t represents the strength of the material in this direction, which can at most reach the value y. Since the highest value H can reach is I/IO R, the maximum retardation in a hori- zontal direction is : l ati I mar = 4/aJ i o.o02 Ray m The vertical retardation then, according to eqn. (II), equals: or anRHy o.znR9 Ia,1 > II_ = ~ m m So the ratio a ,, mLX to a, has the maximum value : a,mar dV,/dt ~ ~ < 0.094 a, d Y,/dt Weau, 6 (1963) 169-190 I 7h J . C;. A. BITTER Since it was supposed that L’,, and V,. became zero at the same time (at the end of the first period) it follows that at any previous instant Therefore if the horizontal velocity of the particle is to become zero during the first period of the collision the impact angle must be larger than 84.“5 (max. 90”). This means that in actual erosion and in erosion experiments this velocity will not become zero during the first period. If the horizontal motion of the particle were arrested exactly at the end of the first period (so VA = o and If,, = o when H = Hms,) the energy absorbed by elastic d~fo~~tion of the area subject to shear would be restored to the particle, If we again put t equal to y, and the horizontal compression equal to t&s*, the energy restored to the particle in a horizontal direction is Elimination of kd and H,,, produces If the horizontal velocity of the particle should become zero sooner (in the first period) or later {in the second period} the area subject to shear and hence its eta&k energy would be smaller. Therefore: The energy absorbed for cutting wear equals: tm (P CO@& - v,*(t,)) SO +snv~ COSZU 3 &n{V cos~u - V,/‘(b) 2 @z[V”” eosa?x - Kl[V sina - fqais] I=4 For calculating the cutting wear we shall use the right-hand term of eqn. (24). For a total mass M of the impinging particles we again find the cutting wear WCS expressed in units volume loss by dividing the absorbed energy by e : ‘EVct = tM[V~cos"a - Xl(l'Sin& - rr)Jy 125) e -,- * Analysis of this horizontal elastic compression shows it to be smaller than &a, which was derived for vertical compression. EROSION PHENOMENA 177 IV. DISCUSSION OF THE FORMULAR We now have three equations ex~~g ercsion, Y.&Z, : wo= tM(V &a - K)s & Wcn - tM[ vn cosp @G - KI(V sina - K)8!g] -- e The total wear at every instant equals: Wb + wcn (26) The equations are valid if V sina >, K. If OE < cc0 eqn. (22) must be used and if iy 2 1yg eqn. (25) is valid, LWO being the impact angle at wl-&h the horizontal velocity eompon~nt has just become zero when the particle leaves the body. An interesting study on cutting wear of free-moving particles has been published by FINNIE~ and we shall first compare his formulae with ours. Assuming the erosive particles to be sharp-edged and rigid and the eroded body to be purely plastic he deduced in the case that ey 2 CTO WCS = MI/P CO.5~& 6w (271 in which: ‘v, = ratio of length to depth of the scratch formed, Y = constant horizontal pressure between particle and eroded body* By neglecting Kl and putting Q = 3~ eqn. (25) can be made identical with eqn. (27). If the normal veIocity component of the particle has become zero before the hori- zontal velocity component, the particle is pressed out of the body again by the elastic reaction forces, while it still continues its cutting action. Since FINNIE neglects these forces he cannot take this effect into account in his calculations. To overcome this difficulty he assumes the time of the second period of the scion to be equal to the time of the first period, using A~DREws’~ time formula for a purely plastic collision of a sphere on a flat body. In other words, although FINNIE considers sharp edged particIes he solves his equation for spherical particles. In this way he finds for o( 6 a~: MV= WC1 = - klpy 6 -sin*a k 1 in which: k = ratio of vertical to horizontal force component, 178 J. G. A. BITTER FINNIE has to introduce the arbitrary values y and K since he does not take into account the elastic properties of the colliding particles. y and k are not constant but depend strongly on impact angle. y decreases with increasingn because then the ratio of the horizontal to vertical velocity component decreases. For the same reason k increases with increasing impact angle. At the impact angle a~ both cutting wear equations are valid. FINNIlE deduced that tan cxo = k/6, so m should depend only on k. From a consideration of eqns. (22) and (25), assuming V so large that K and KI are negligible, it follows that or (29) In the case of metals e does not vary much as can be concluded from Table I, so y influences iy~ very strongly. This is shown also in Fig. 2, which expresses 010 as a function of y. VELOCITY* IO4cm& p* 2. lOa qi cm/cm’ 1to’,1 gf/td\ zo- 16- 6- 4- PO w 40 50 6C 70 % Fig. 2. Influence of y on iy0. If Q is assumed to be proportional to y, eqn. (29) transforms to In this case LYO would be nearly constant, as was stated by FINNIE. If the particles are sharp-edged the apparent density of the particles becomes larger and according to eqn. (29) 1x0 becomes larger as was also observed by FINNIE. Wear. 6 (rg63) 169-190 EROSION PHENOMENA 179 According to FI NNI E’S equation it is the material strength y that determines the energy absorption during cutting. A material under load, however, deforms elastic~y {brittle substan~es~ or elastic- ally and plasticahy (ductile substances). So the energy absorption is equal to the integrated product of stress and strain, which is represented by e. Figure 3 shows schematically the relation between the strength, the strain and e both for a hard and brittle material and for a soft and ductile material. From this figure we conclude that it is quite possible for a substance with a higher strength to have a lower value of e. Fig. 3. Relation between the strength ductility and Q of a hard and brittle and a soft and ductile material. A phenomenon which is not explained by FI NNI E’S equations is the attack at high impact angles ; in his theory it should be zero at 90”. Even very soft metals, however, such as aluminium, show noticeable. attack at go”. FI NNI E explains this by assuming that the surface becomes rough, the roughness being proportional to the impact angle. Erosion tests at the KoninklijkejShell-laboratorium, Amsterdam, showed surface roughness to be a function of mechanical properties, partide size and impact angle. Aluminium and silver, for example, &owed a larger surface roughening than glass, I n all cases ma~mum surface roughness occurred between an impact angle of 40’ and 60”. So we must conclude that a more important phenomenon exists, which is the earlier mentioned wear due to repeated deformation [I V,). Figures 4 and 5 show the total wear curves of a soft and ductile material and of a hard and brittle one under the same conditions. As soon as V sin ac reaches K wear occurs. The hard substance has a higher f(-value, so the impact angle at which wear just starts is larger. Owing to the greater brittleness E is lower, r~~tiu~ in a steeper curve for deformation wear. Cutting wear also starts when V sin OL = K. For the soft material MI is smaller (in this case I S”), so cutting wear up to 15~ is determined by eqn. (22). In this region cutting wear is very high since C, which Wear, 6 (x963) x49-rgo 180 J . G. A. RI TTER is inversely proportional with y 5/d, is relatively large. Above 15” cutting wear is limited by the kinetic energy of the particle, so eqn. (~5) must be applied. For the hard substance 1~0 is much higher (60”) as could be expected from Fig. Z. Now C is smaller giving less cutting wear. IMPINGEMENT ANGLE Fig. 4. Erosion of a soft and ductile material. Oo 60 75 90 lMPlNGEMENT ANGLE Fig. 5. Erosion of a hard and brittle material. At a > 6o”, eqn. (25) must be used since the kinetic energy of the particles limits the attack. According to eqn. (25) cutting wear becomes zero at an impact angle LYL that is lower than 90~. This is caused by the second term in eqn. (~5)~and is due to the simplifications introduced. Without simplifications cutting wear would foI low the dashed curve in Figs. 4 and 5. A negligible error is introduced in this way. The total wear curve which is found by summation of WD and WC has in the case of soft and ductile materials a maximum at lower impact angles, whereas the hard and brittle materials show a maximum at higher impact angles and may even have two maxima. A totally brittle substance such as glass shows a maximum at 90’ (ref. I ). V. CORRELATI ON WI TH EXPERI MENTS I n the vacuum free-falling apparatus1 experiments were carried out on annealed aluminium test plates (99.9% Al) at different impact angles at a par&al velocity of I O mlsec. I n each experiment 50 kg of cast iron spheres (300 p diameter) were used. The results are shown in Fig. 6. As the Vickers hardness was 31 kg/mm2 the calculated K value was negligibly small. From the results at 30~and 60” impact angle E and Q were calculated (see Table I ). By extrapolating the WC% curve ix0 was found to be cu. 15~. Using eqn. (27) C Wear, 6 (1963) 169-190 M e t a l A l u m i n i u m A l u m i n i u m C O p p S A E - 1 0 5 5 s t e e l ( a s r c c c i v c d ) S A E - 1 0 5 5 S t C C l ( f u l l y h a n k l I e d ) A b Y U S i V t X c a s t i r o n w e t i s i h c u l l c a r b i d e s s i l i c o n c a r b i d e s s i l i c o n c a r b i d e 3 s i l i c m c a r b i d e s W e i g h t o f a b r a s i v e s c a d t . ? x f 5 0 k g 2 3 g 5 3 I ? 5 3 g T A B L E I E R O S I O N C O N S T A N T S F O R S E V E R M . M E T A L S I O ’ 1 0 . 5 2 . 7 9 5 . 1 3 . x 3 . I 1 5 ” 2 I a 0 7 * 1 0 1 5 - S I . 2 9 4 , 3 3 . 8 3 . 1 I Z O z g 1 . 0 7 - 1 0 4 6 . 4 2 . 2 8 2 . 1 9 6 . 6 6 . 3 r 3 O : 1 . 0 7 . 1 0 4 4 J 2 . 2 5 0 . 7 1 1 6 . 2 2 0 2 5 O F 1 , 0 7 . I O Q I . 4 3 I . 5 9 0 . 2 8 3 5 6 0 5 0 ° I82 J , G. A. UITTER could be calculated, from which the ~{.cL curve could be determined using eqn. (22). From C it follows that y = $3 kg/mm2, which is quite close to the Yickers hardntlss. The curve shows a good fit with test results. Fig. 6. Erosion of aluminium. U, Test results. - , Values used for catculating curves. Particle velocity: IO mjsec. Abrasives: cast iron pellets (0 3oop) Fig. 7. Erosion of aluminium. x , Test results. - , Values used for catculating curves. Particle velocity: 107 mjsec. Abrasives: silicon carbides (60 mesh). FINNIE~ carried out experiments on aluminium, copper and SAE-1055 steel in the <‘as received” condition and after full hardening. In each experiment he used only 2353 g of silicon carbides as abrasives at a velocity of 107 mjsec. The measured hardness is given in Table I. His test results on aluminium are shown in Fig 7. To calculate C the same y value was choosen as in our own experiment since the hardness was the same. From the results at 30’ and 90’ impact angle E and e were calculated (Table I), which were nearly half of those found in the vacuum free-falling apparatus. This is possibly due to the sharp-edged particles FINNXE used. Recalling that the particle velocity in FINNIE’S experiments was more than ten times as high, we may conclude that the velocity dependence of erosion expressed in the formulae is confirmed. As the total mass of the impinging particles in our experiments was nearly a thousand times as high as in FINNIE’S it follows that the proportionality with total mass of abrasives is confirmed also. The theoretical curves for the other metals tested by FINNIE were also calculated in the way described above (see Figs. 8, g and IO). In general, a good correlation is found with test results. Table I gives the experi- mental constants of these metals. From the constants C, y was calculated; its value was nearly equal to the Vickers hardness, except for SAE-1055 steel for which y is somewhat lower, both in the “as received” and in the fully hardened condition. From the K value of low carbon steel1 determined in rebound tests a much higher y was found than in a Vickers hardness test, which was attributed to the dynamic Wear, 6 (1963) 169m~r90 EROSION PHENOMENA 183 character of the experiment. The same effect can be expected in cutting wear, but under these cmditions the metal is loaded in shear, so that destruction ~lcurs at Khmer stresses~ The rek&iv&y low y for the hard SAE steels is explained by the fact Fig. 8. Erosion of copper. m, Test results. -$ Fig. 9. Erosion of SAE-1055 steel (fully harden- Values used for cakuiating curves. Particle ed). x I Test results. -, Values used for calcul- velocity: 107 m&c. Abrakes: diem carbides a&g curves. Partkle vefocity: re7 m&ee. (Go mesh) t Abrahs: silicon carbides (60 mesh). IMmNGEmT M~QL~ a Fig. IO. Ermian of SAlGras~ steel (as received). 0. Test results. - , Values used Em calculating curves. Particle velocity: 107 m/ sw Abrasives: silicon carbides (60 mesh). 184 J , G. A. BITTER that these metals show less deformation hardening than the soft aluminium and copper, so that in dynamic tests a lower strength is found alsol. From the foregoing it may be concluded that eqn. (zo), giving C is confirmed by experiments. It further follows that Q does not vary much for the different metals. As was already explained in Fig. 3, it is not surprising that the Q for the brittle full) hardened SAE-1055 steels is lower than for the softer and more ductile copper and SAE-1055 steel in the “as received” condition. The E of this steel is also lower, which confirms the theory’. VI. CORRELATION OF THE EQUATIONS WITH EROSION IN PRACTICE The equations provide an explanation for the wide divergence of the results of erosion experiments of various authors: particle velocity plays a much larger role in deter- mining the type and extent of wear than was realized. In Fig. II wear due to repeated deformation is expressed depending, respectively, on particle velocity of a soft and ductile material (small K, large E) and a hard and brittle material (large K, small E). It is seen that at low particle velocity the hard substance shows less erosion since K has a large influence. At high velocities the EP” 360. Jrno- 280. 240. 200. tm- Fig. I I. Influence of velocity on deformation wear. Weav. 6 (1963) dg-~ga EROSION PHENOMENA x85 reverse is true since K is now negligible, whereas e has a large influence. The same is true in the case of cutting wear although this is more complicated. A phenomenon which is explained by the equations is the formation of particularly shaped grooves if erosive particles impinge on bent surfaces. Figure 12 shows the calculated attack of a bend of a transport tube’ of erosive particles after different exposure times. The bend is worn out in such a way that the slope of the upstream part of the groove formed is about equal to the original direction of the particles, the other part being about perpendicular to it. .Fig. 12. Attack of a bend in a transport line by erosive particles calculated for different exposure times. This form of attack, called gouging, has been succesfully imitated in an erosion test apparatus. Figure x3 shows steel specimens tested for 15, 30 and 60 min at an impact angle of x5”. In practice, this type of attack always occurs in bent catalyst transport lines, cyclones etc. Figures 14 and 15 show cross sections of bepds in small catalyst transport lines. Another clear example of this gouging effect is represented in Figs. z6a, b, c, which show the stem of a valve used for dispensing catalyst at a pressure of I atm. Because the valve was not quite closed the catalyst blew at high velocity against its shoulder. Wear, 6 (1963) 169-190 Fig. (b) 1 )iwction of catalyst flow Fig. 14. Cross section of bend in catalyst transport tube oroclcd by catalyst. TVew’, 6 (1963) 16g--rgo EROSI ON PHENOMENA 187 Along the stem the shoulder, which was only 3 mm thick and had a bevelled edge of about 45”‘ was worn away, the outer layer being left intact. Another practical case of erosion is that of the so-called dollar plate. This is a flat plate, placed in front of the outlet of a riser in a gas-solid system, normally exposed to elevated temperatures. The particles impinge perpendicularly on the dollar plate. It was observed that under these conditions mild steel was less attacked than stainless steel. The explanation is believed to be as follows. At the working temperature lattice recovery takes place in the mild steel dollar pIate, which eliminates the plastic de- formation caused by the impin~g particles, This causes the deformation wear factor E to become greater and according to eqn. (I) the wear itself correspondingly smaller. On the other hand, stainless steel, being more heat resistant, needs higher temperature to recover. Finally, we consider the reduction of the erosion of a sand blastingnozzle. Thisnozzle, which was made of carbon steel, showed a heavy attack of the air inlet tube just op- Fig. 15. I nside of bent catalyst transport tubes eroded by catalyst, Wear, 6 (1963) 169-19o 188 posite the inlet of the abrasives which impinge perpendicularly on the air inlet [Fig. 17). After a Week% service a hole was formed. This attack could be reduced by pushing a soft rubber hose round the air inlet tube. The rubber hose has a very low elasticity modulus resulting in a very high K value, decreasing erosion according to eqn. (I). The tube could then be used for more than half a year. The outlet of the nozzle was worn away in nearly two weeks, but in this case rubber did not help: it was attacked heavily. This is due to the fact that now the impact angle is very small so that cutting wear is most important. The resistance of rubber EROSI ON PHENOMENA 189 Fig. 16b. Stem of regulating valve eroded by catalyst. Bottom view of shoulder. Fig. 16c. Stem of regulating valve eroded by catalyst. Top view of shoulder. CERMET NOZZLE Fig. 7 7. Sand-blasting nozzle. to cutting is low. According to eqn. (zz) erosion under these conditions can be reduced by choosing a hard material. Accordingly, a tungsten carbide outlet was installed which has now been in service for several years without presenting any difficulties. Wtw, 6 (1963) 169-190 VII. COMBATING EROSION In systems in which impact angles are small cutting wear prevails. According to etln. (22) it is sufficient to use a hard material. The brittleness of the material has little influence upon cutting wear. Systems where this solution can be applied are risers and straight transport lines. The erosion of bends in transport lines can be reduced by keeping the radius of curvature large while using a hard substance in such a wan that V sin 01 does not far exceed K. The tangential inlet of a cyclone, for example, can be made with a rectangular cross section of small width, so that the impact angk I\ : in the cyclone is small. Hardfacing or covering with a hard concrete will reduce: the erosion in the cyclone considerably. At large impact angles wear due to repeated deformation prevails. In this cast! prevention of erosion is not so simple. At low particle velocities hard materials may bc applied. For the conventional materials of construction the value of h’ is usually not much higher than IO mjsec. An exception is soft rubber which has a larger K value, due to the low modulus of elasticity. Also F is large for this substance, The low service temperature, however, limits its application. At higher temperatures, materials having a low recrystallization temperature can be used, as E is then large due to lattice recovery during impingement. At low im- pact angles cutting wear is very large in these materials. Then heat-resistant materials such as concretes, ceramics or cermets must be used. 1 J . (i. 4. &mm, Went, 6 (1963) 3. 2 I. FINNIE, Wear, 3 (I g6o) 87. 3 J . I ? ANDREWS. PM. &fag., 9 (1930) 593; 8 (1929) 781~ 4 I. FINKIE, personal comnmnication. 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