Thermally Induced Grinding Damage in Superalloy Materials

J. A. Kovach, Eaton Corporation, Cleveland, Ohio; S. Malkin ( I ) , Univ. of Massachusetts a t Amherst Received on January 28.1988

ABSTRACT:

This paper i s concerned w i t h thermal damage developed d u r i n g convent ional g r i n d i n g opera t ions employed i n t h e f i n i s h i n g o f cast equiaxed nickel-based supera l loy components. were u t i l i z e d t o i d e n t i f y t h e modes o f s u p e r a l l o y g r i n d i n g danage developed under abusive g r i n d i n g c o n d i t i o n s and the t h r e s h o l d parameters respons ib le f o r t h e onset o f sur face i n t e g r i t y degradation. element analyses compared f a v o r a b l y w i t h those measured by X-ray d i f f r a c t i o n techniques. mic rocrack ing i n Rene-77 and 8-1900 a l l o y s i s n o t caused by r e s i d u a l s t resses alone b u t enhanced by the onset o f c o n s t i t u t i onal 1 i q u a t i on.

Laboratory exper imenta t ion coupled w i t h f i n i t e element process models

The r e s u l t s a l s o i n d i c a t e t h a t Residual s t resses p r e d i c t e d by f i n i t e

KEY W OROS :

sur face gr ind ing , r e s i d u a l stress, superal loy, g r i n d i n g damage, f i n i t e element modeling, c o n s t i t u t i o n a l l i q u a t i o n

1.0 INTRODUCTION

Improving metal removal processes associated w i t h t h e manufacture o f many supera l loy aerospace components can be q u i t e cha l leng ing due t o t h e e x t r a o r d i n a r y mechanical p roper ty and performance requirements o f t h e workpiece m a t e r i a l . The c h a r a c t e r i s t i c s which make these m a t e r i a l s d e s i r a b l e f rom a produc t performance standpoint u s u a l l y render them f a r f rom i d e a l i n t e n s o f manu- f a c t u r i n g processabi 1 i t y .

Many researchers [3,14,18,24.26,33,36] have i n v e s t i g a t e d t h e convent ional g r i n d i n g process as a p p l i e d t o the g r i n d i n g o f f e r - rous a l loys . p a r t i t i o n " . s p e c i f i c a l l y t h e a c t u a l g r i n d i n g energy e n t e r i n g t h e workpiece as heat, governs t h e process from a c r i t i c a l maximum temperature s tandpo in t . Salmon C321 e t a l . C341 have shown t h a t superal l o y g r i n d i n g p r o d u c t i v i t y c o u l d be d r a m a t i c a l l y increased by u t i l i z i n g f u l l depth o r creep feed sur face g r i n d i n g t e c h - niques. Although t h e creep feed process can o f f e r s u b s t a n t i a l p r o d u c t i v i t y improvements, t h e process i s geared toward heavy stock removal opera t ions . With advancements i n near n e t shape component manufactur ing technologies, a d d i t i o n a l emphasis has r e c e n t l y been placed upon improv ing supera l loy g r i n d i n g produc- t i v i t y through convent iona l g r i n d i n g techniques u t i l i z i n g moderate s tock removal rates. Based upon t h e above manufactur ing t h r u s t s , t h e o b j e c t i v e of t h i s program was t o u t i l i z e l a b o r a t o r y exper imenta t ion coupled w i t h f i n i t e element process models t o i d e n t i f y t h e modes o f s u p e r a l l o y g r i n d i n g damage developed under abusive g r i n d i n g c o n d i t i o n s and determine t h e t h r e s h o l d parameters respons ib le f o r t h e onset o f sur face i n t e g r i t y degradat ion.

M a l k i n [ l 8 l has shown t h a t t h e " g r i n d i n g energy

2.0 TECHNICAL APPROACH

For t h e purposes o f t h i s i n v e s t i g a t i o n , two c a s t equiaxed n i c k e l - based supera l loys , 8-1900 and Rene-77. were studied. Al though these a l l o y s do n o t represent t h e s t a t e o f t h e a r t i n a i r c r a f t engine t u r b i n e b lade m a t e r i a l s , they are c u r r e n t l y among t h e most w i d e l y used. I n i t i a l l y . t h e supera l loy c h i p fo rmat ion energy was determined u s i n g two types o f Norton g r i n d i n g wheels (32A 46H 8VBE and 53A 801 8VJN). i n g sur face damage. an a d d i t i o n a l s e r i e s o f t e s t s was conducted u s i n g cons iderab ly harder wheels (M and N grade) and more abusive dress ing parameters.

Laboratory g r i n d i n g t e s t s were performed on a f u l l y instrumented Brown & Sharpe sur face gr inder . To determine t h e c h i p fo rmat ion energy, a procedure s i m i l a r t o t h a t presented i n E14.18-211 was employed. I n a d d i t i o n t o de termin ing c h i p fo rmat ion energy and bas ic supera l loy g r i n d i n g behavior, t h e above t e s t s were a l s o used t o i d e n t i f y c o n d i t i o n s which produced sur face d i s c o n t i n u - i t i e s (microcracking). t h e specimen was examined f o r sur face d i s c o n t i n u i t i e s t o d e t e r - mine the na ture and l o c a t i o n o f any microcracks r e l a t i v e t o t h e supera l loy mic ros t ruc ture . a c i d etches, o p t i c a l microscopy. and scanning e l e c t r o n microscopy were used t o e v a l u a t e t h e f i n l s h e d sur face o f t h e ground super- a l l o y specimen.

Under ac tua l p r o d u c t i o n cond i t ions , i f a c rack g r e a t e r t h a n 0.38mm i n l e n g t h i s de tec ted v i a FPI techniques, t h e p a r t i s considered d e f e c t i v e . t h i s study lead t o a w ider g r i n d i n g c rack s e v e r i t y range than normal, and as such t h e standard b i n a r y (i.e., good/bad) p ro- d u c t i o n acceptance c r i t e r i o n was expanded. An a r b i t r a r y rank ing scale, rang ing f r o m 1 t o 10, was u t i l i z e d t o b e t t e r d i s t i n g u i s h between t h e s e v e r i t y of t h e de fec ts and the c o n d i t i o n s which produced them. A r a n k i n g o f 1 was assigned when t h e ground sur face d isp layed no s igns o f any defects. assigned when l i n e a r sur face i n d i c a t i o n s having a l e n g t h o f 0 . 3 b s t a r t e d t o appear ( i . e . , t h e t h r e s h o l d f o r p r o d u c t i o n r e j e c t i o n ) . very severe c rack ing (many cracks over 0 . 3 8 n i n l e n g t h ) . The remaining rankings were assigned by d i r e c t s ide-by-side

To increase t h e l i k e l i h o o d o f generat-

A t t h e conc lus ion o f each g r i n d i n g t e s t ,

Fluorescent dye penetrants, Molybdic

However, t h e use o f t h e harder wheels i n

A rank ing o f 5 was

A rank o f 10 was assigned when t h e sur face d isp layed

comparison o f t h e ground specimen surfaces. l a b o r a t o r y supera l loy specimens were analyzed through t h e use o f X-ray d i f f r a c t i o n techniques t o i d e n t i f y t h e corresponding sur face r e s i d u a l stresses.

The s u p e r a l l o y g r i n d i n g temperature p r o f i l e was developed u s i n g ANSYS, a la rge-sca le , general-purpose f i n i t e element model ing program. Rev is ion 4.1 and 4.2 o f t h e program were u t i l i z e d on a OEC VAX 11/780 and VAX 8600, r e s p e c t i v e l y . The b a s i c FEA model cons is ted o f a nov ing band heat source hav ing un i fo rm i n t e n s i t y . Inputs t o t h e program i n c l u d e d temperature dependent thermal and mechanical m a t e r i a l p r o p e r t i e s , convec t ive c o o l l n g , con tac t l e n g t h cons idera t ions , and g r i n d i n g c o n d i t i o n s which caused surface damage d u r l n g t h e l a b o r a t o r y exper imentat ion. Tempera- t u r e dependent m a t e r i a l p r o p e r t y data was u t i l i z e d from C8.14.23. 27,351.

A two-dimensional g r i d was cons t ruc ted u s i n g ANSYS STIF55 thermal elements. T h i s element has f o u r nodes and s i n g l e degree o f freedom, temperature, a t each node and i s a p p l i c a b l e f o r use i n a two-dimensional , s teady-s ta te o r t r a n s i e n t thermal ana lys is . Another key f e a t u r e o f t h e element i s t h a t i t can be d i r e c t l y rep laced w i t h an e q u i v a l e n t s t r u c t u r a l element (STIF42) f o r use i n a subsequent s t r e s s ana lys is . A f t e r a few i n i t i a l at tempts, an element s i z e o f 0.254mm square was chosen f o r use i n t h e area under t h e band source. Element s i z e was se lec ted based upon s o l u t i o n accuracy and computing t ime t r a d e o f f s . The heat source was "stepped" through a d i s t a n c e o f t h r e e band widths a t a r a t e e q u i v a l e n t t o t h e workpiece v e l o c i t y . s ides, except t h e upper surface, were f i x e d and i n s u l a t e d .

A n o n l i n e a r e l a s t i c / p l a s t i c FEA s tudy was conducted t o determine t h e e f f e c t s o f un load ing upon c o o l i n g and t o develop t h e r e s u l t - i n g r e s i d u a l s t r e s s d i s t r i b u t i o n s under t h r e s h o l d g r i n d i n g damage c o n d i t i o n s . As t h e workpiece cooled. t h e m a t e r i a l was e l a s t i c - a l l y unloaded through a maximum s t r e s s range equal t o t w i c e t h e y i e l d s t r e s s . I n t h i s fash ion , t h e r e s i d u a l s t r e s s f i e l d cou ld a l s o be pred ic ted . The workpiece m a t e r i a l was modeled u s i n g c l a s s i c a l b i l i n e a r k inemat ic hardening C131 behavior w i t h mater- i a l da ta f o r f i v e temperatures. With t h i s assumption, ANSYS can accept temperature dependent y i e l d p o i n t s o c c u r r i n g a t var ious l e v e l s o f s t r a i n . Required m a t e r i a l data a t i n t e r m e d i a t e tenper - a tu res was determined by ANSYS through l i n e a r i n t e r p o l a t i o n . Y i e l d i n g was based upon t h e Yon Mises y i e l d c r i t e r i o n . Since t h e developed temperature d i s t r i b u t i o n i s extremely sha l low compared t o t h e b u l k o f t h e workpiece, a c o n d i t i o n o f p lane s t r a i n was assumed f o r a l l o f t h e s t r e s s analyses.

3.0 MATERIAL and SURFACE INTEGRITY CONSIOERATIONS

I n genera l , supera l loy m a t e r i a l s must m a i n t a i n h i g h s t r e n g t h l e v e l s a t e leva ted o p e r a t i n g temperatures. s t r e n g t h a t e levated temperature, t h e m a t e r i a l s must a l s o e x h i b i t good r e s i s t a n c e t o o x i d a t i o n and h o t cor ros ion . Adequate d u c t i l - i t y t o t o l e r a t e creep deformat ion and enhance low-cyc le f a t i g u e behavior i s a1 s o requ i red . Furthermore, good impact s t rength , c a s t a b i l i t y , low d e n s i t y , and m i c r o s t r u c t u r a l s t a b i l i t y p rov ide obvious advantages. Low thermal expansion and h i g h thermal c o n d u c t i v i t y a r e d e s i r a b l e t o minimize t h e e f f e c t s o f thermal stresses. Unfor tunate ly , t h e thermal c o n d u c t i v i t y o f many super- a l l o y s i s o n l y 10% - 30% t h a t o f steel . Moreover, t h e thermal behav io ra l p r o p e r t i e s o f Rene-77 can vary s i g n i f i c a n t l y w i t h temperature. Both the thermal c o n d u c t i v i t y and s p e c i f i c heat inc rease w i t h temperature w h i l e t h e thermal d i f f u s i v i t y tends t o peak a t approximately 787'C.

An i n i t i a l bench t e s t was conducted t o c o r r e l a t e crack l o c a t i o n s developed under r a p i d h e a t i n g and c o o l i n g w i t h those observed i n abusive superal l o y g r i n d i n g experiments. Several Rene-77 and 8-1900 specimens were instrumented w i t h a microthermocouple b u r i e d t o w i t h i n 0.3&rm from t h e surface. Then, us ing an oxyace- t y l e n e t o r c h . the t e s t specimen sur face was r a p i d l y heated t o approx imate ly 1093'C f o l l o w e d by a r a p i d quench i n a bath o f room temperature g r i n d i n g f l u i d . The t e s t was repeated us ing a maxi- mum measured temperature o f 787'C. The sur faces o f a l l specimens

Subsequently. t h e

It was assumed t h a t a l l

Aside from h i g h

Annals of the ClRP Vol. 37/1/1988 309

were subsequently examined u s i n g o p t i c a l and scanning e l e c t r o n microscopy. Using t h e 1093'C t e s t cond i t ions , microcracks were developed a t t h e g r a i n boundaries and assumed a s i m i l a r , b u t more severe, appearance t o those observed under abusive g r i n d i n g cond i t ions . The Rene-77 cracks developed under t h e 787'C maximum temperature t e s t cond i t ions , on the o ther hand. were q u i t e l i n e a r , very sha l low and e x i s t e d o n l y a t t h e gama/gamna pr ime in te r faces . T h i s evidence tends t o agree w i t h s t r e s s r u p t u r e data and emphasizes t h a t t h e i n t e r g r a n u l a r cracks observed under abusive g r i n d i n g c o n d i t i o n s are generated a t e leva ted tempera- tures.

The s i m i l a r i t i e s i d e n t i f i e d between t h e m i c r o f i ssures ( g r a i n boundary c racks) developpd under abusive g r i n d i n g c o n d i t i o n s and those generated through the use t h e above heatlquench t e s t man- da te f u r t h e r d iscuss ion . I t must be r e a l i z e d t h a t i n each case the workpiece was sub jec ted t o h i g h temperatures and r a p i d h e a t i n g and coo l ing . Under such r a p i d heat ing and coo l ing , t h e m a t e r i a l behavior i s cons iderab ly d i f f e r e n t f rom t h a t developed under slow s teady-s ta te heat ing. As i n d i c a t e d i n C11,14,15,17, 28,30.35,37,381 r a p i d o r non-equ i l ib r ium heat ing can induce l o c a l i z e d m e l t i n g i n t h e supera l loy , known as c o n s t i t u t i o n a l l i q u a t i o n , p r i o r t o ac tua l b u l k m e l t i n g o f t h e m a t e r i a l .

To generate performance data necessary f o r understanding super- a l l o y behavior under such r a p i d h e a t i n g and coo l ing , welding researchers developed s p e c i a l i z e d t e s t s [8,17] capable o f estab- l i s h i n g u l t i m a t e s t r e n g t h and d u c t i l i t y da ta u s i n g heat ing o r c o o l i n g r a t e s up t o 5538'C/sec. O f t h e a v a i l a b l e h o t d u c t i l i t y data, the l a r g e s t percentage was generated on a Gleeble t e s t machine [8] us ing supera l loys t h a t a r e commonly welded. F igure 1 schemat ica l l y i l l u s t r a t e s t y p i c a l s u p e r a l l o y h o t d u c t i l i t y da ta es tab l i shed on such a machine. It has been g e n e r a l l y shown tha t , i n c r a c k - s e n s i t i v e a l loys , the g r a i n boundar ies o r i n t e r d e n d r i t i c regions may s t a r t t o l i q u a t e upon r a p i d heat ing , forming f i l m s and a r a p i d l o s s o f d u c t i l i t y . S l i g h t a d d i t i o n a l heat ing beyond t h e onset o f t h i s l i q u a t i o n can d r a m a t i c a l l y reduce t h e d u c t i l i t y upon c o o l i n g [8,2B,30,35,37,38]. As F i g u r e 1 i n d i c a t e s , a 2Z'C increase beyond 1150'C r e s u l t s i n a very l a r g e n i l d u c t i l i t y reg ion [ d e l t a TNDT] upon coo l ing . Note t h a t some extremely crack s e n s i t i v e a l l o y s can exper ience an a d d i t i o n a l l o s s i n d u c t i l i t y as the a l l o y c o o l s down through t h e i n i t i a l d u c t i l i t y r e d u c t i o n reg ion C351. i n d i c a t e t h a t Rene-77 behaves i n a fash ion comparable t o t h a t presented i n t h e upper p o r t i o n o f F ig . 1. Consequently, peak g r i n d i n g temperatures c l o s e t o 1149'C c o u l d induce c o n s t i t u t i o n a l l i q u a t i o n and g r i n d i n g cracks.

Hot d u c t i l i t y da ta presented i n C8.27.301 tends t o

t -HEATING

-- I I '

TMELT

1 \ \

1 I - A T ~ ~ - = ~ 788

TEMPERANRE (OC)

Typ ica l Hot D u c t i l i t y Curves f o r Cast N i c k e l -Based Supera l loys .

Very Crack S e n s i t i v e A l l o y I n d i c a t i n g Add i t io f la l D u c t i l i t y Loss on Cool ing a t ?80 .

It was i n t e r e s t i n g t o no te t h a t t h e c h i p s generated d u r i n g non- abusive g r i n d i n g tended t o resemble ac tua l m i l l i n g c h i p s o r s t e e l wool. Po l i shed and etched lOOOx cross sec t ions taken t h r o u g h t h e non-abusive c h i p s showed ex is tence o f t h e gamma prime phase. The abus ive ly produced c h i p s , on the o t h e r hand, always appeared h i g h l y d i s t o r t e d and e x h i b i t e d very l i t t l e evidence o f t h e gamma pr ime phase i n t h e lOOOx cross sect ions. As given i n C351, t h e s o l u t i o n temperature f o r these a l l o y s i s approximately 1162- 1191'C. produced ch ips showed l i t t l e evidence o f gamma prime, t h e c h i p i t s e l f probably reached t h e s o l u t i o n temperature. R e a l i z i n g t h a t t h e maximum sur face temperature i s lower than t h e c h i p tempera- t u r e C5,6,18,191, i t appears u n l i k e l y t h a t sur face temperatures much beyond 1162'C should have been achieved, e s p e c i a l l y under i i i a rg ina l l y abusive g r i n d i n g cond i t ions . For t h e case o f fe r rous a l l o y g r i n d i n g c201, c h i p examinat ion can be mis lead ing because smal l , h o t ch ips may undergo a r a p i d exothermic r e a c t i o n ( b u r n ) r e s u l t i n g i n a shape o r s t r u c t u r a l change. However, s i n c e t h e h igh temperature o x i d a t i o n r e s i s t a n c e o f supera l loys i s f a r super io r t o s t e e l s , t h e p r o b a b i l i t y o f c h i p i g n i t i o n i s reduced. Fur ther , on the e x p l o s i b i l i t y index f o r powdered metals c121, n i c k e l i s f a r lower than i r o n , a l s o c o n f i r m i n g t h e reduced l i k e l i h o o d o f burning. Thus, it i s f e l t t h a t va luab le in fo rma- t i o n i s a v a i l a b l e f rom t h e supera l loy g r i n d i n g chips.

Based upon the combined r e s u l t s o f t h e abusive g r i n d i n g t e s t s , c h i p morphology s tud ies , r a p i d heat/quench bench t e s t s , and Gleeble h o t d u c t i l i t y da ta presented above, i t appears as i f t h e abusive g r i n d i n g zone temperature t h r e s h o l d should be i n t h e v i c i n i t y o f 1037-1149'C f o r Rene-77.

Since t h e c ross sec t ions taken through t h e a b u s i v e l y

4.0 FINITE ELEMENT TEMPERATURE CALCULATIONS

To c a l c u l a t e t h e g r i n d i n g temperature p r o f i l e developed i n t h e workpiece, the p o r t i o n of t h e g r i n d i n g energy which a c t u a l l y heats the workpiece (U study i t was assumed tW8fkthe g r i n d i n g energy cou ld be p a r t i - t i o n e d [14,18-22] i n t h e form:

) must f i r s t be determined. For t h i s

' t o t a l ' s l ide "chip ' 'plow

where t h e p o r t i o n o f the s p e c i f i c g r i n d i n g energy e n t e r i n g t h e workpiece, Uw k , was i n i t i a l l y based upon r e s u l t s ob ta ined i n [18,20,22]. 96 these works, v i r t u a l l y a l l o f t h e s l i d i n g and plowing energy were considered t o e n t e r t h e workpiece as h e a t , w h i l e about 45% o f t h e c h i p fo rmat ion energy was c a r r i e d away w i t h the chips. Thus,

uwork = ' t o t a l - m45uchip

Utotal = FtVs/bQw' where;

Assuming t h a t approximately 45% of t h e s p e c i f i c c h i p f o r m a t i o n energy i s c a r r i e d o f f w i t h t h e chip, t h e balance o f t h e g r i n d i n g energy ( U ) was then u t i l i z e d i n t h e f i n i t e element c a l c u l a - t i o n s . S!g%quently, u s i n g h igh temperature supera l loy thermal p r o p e r t i e s and t h e r e l a t i o n s h i p s determined by Boothroyd C Z l and Dawson C41, t h e f r a c t i o n of g r i n d i n g energy e n t e r i n g t h e work- p iece was reca lcu la ted . o f t h e c h i p format ion energy can be c a r r i e d away w i t h t h e ch ip . Or, a l t e r n a t i v e l y s ta ted :

This approach showed t h a t as much as 94%

'work = ' to ta l - '94uchip I t i s f e l t t h a t t h e increased energy c a r r i e d away w i t h t h e c h i p i s p r i m a r i l y due t o t h e increased ch ip / rake face f r i c t i o n a l i n t e r a c t i o n s and t h e poor thermal d i f f u s i v i t y o f supera l loys compared t o s tee l . Assuming t h a t 100% o f t h e energy developed from t h e ch ip / rake face f r i c t i o n a l i n t e r a c t i o n i s c a r r i e d away w i t h t h e c h i p , a l a r g e p o r t i o n (approx imate ly 85%) o f t h e energy developed i n t h e pr imary shear p lane s t i l l goes o f f w i t h t h e c h i p owing t o t h e low thermal d i f f u s i v i t y . Consequently, a l l o f t h e f o l l o w i n g analyses w i l l be conducted u s i n g 94% as t h e amount o f Uchip c a r r i e d o f f w i t h t h e ch ip .

The c h i p fo rmat ion energy was then determined using an energy p a r t i t i o n approach C14.18-221. Wi th t h i s approach, t h e c h i p fo rmat ion energy, U , was then found t o be 1.6. J/m3 u s i n g t h e 32A 46H 8VBE whsbi! w h i l e with t h e 53A 801 8VjN wheel, t h e c h i p fo rmat ion energy was i d e n t i f i e d as 24.2 J/m , o r a p p r o x i - mately 1.75 t imes g r e a t e r than expected from t h e approx imat ion based upon en tha lpy cons idera t ions C3.18.211. For t h e purposes o f th is3paper a l l c a l c u l a t i o n s were conducted us ing a Uchip o f 24.2 J/m . A s s t a t e d p r e v i o u s l y , t h e f i n i t e element approach was u t i l i z e d i n t h i s i n v e s t i g a t i o n so t h a t t h e combined e f f e c t s o f temperature dependent m a t e r i a l p r o p e r t i e s and convec t ive c o o l i n g c o u l d be simultaneously considered. Unfor tunate ly , de termina t ion o f t h e ac tua l convec t ive f i l m c o e f f i c i e n t and g r i n d i n g arc l e n g t h o f con tac t i s an extremely d i f f i c u l t task. Therefore, t o i d e n t i f y an upper bound f o r t h e convec t ive f i l m c o e f f i c i e n t s , i n i t i a l a t t e n t i o n was focused on de termin ing t h c magnitude o f convec t ive c o o l i n g necessary t o achieve rea l i s t i c maximum sur face tempera- t u r e s w h i l e assuming a contac t l e n g t h equal t o t h e geometr ic contac t leng th . Under these cond i t ions , a convect ive f i l m

FIGURE .1

31 0

c o e f f i c i e n t g r e a t e r than 68100 J/m'-sec-'K was requ i red i n t h e FEA analyses t o c o n f i n e t h e maximum sur face temperature below 1149'C.

I n [33] Sauer t r i e d t o determine t h e maximum hc a v a i l a b l e f rom several g r i n d i n g f l u i d s . H is r e s u l t s , based upon t e s t s conducted ou ts ide t h e work zone, i n d i c a t e d t h a t hc values up t o 9420 J/m'- fec-'K might be obtained. A p o s s i b l e maximum o f 17025 J/m'-sec-

Oesruisseaux [5] i n d i c a t e d t h a t convec t ive heat t r a n s f e r coef- f i c i e n t s up t o hc = 50000 J/m'-sec-'K cou ld p o s s i b l y occur, bu t would be d i f f i c u l t t o o b t a i n under " p r a c t i c a l " g r i n d i n g pro- cesses.

Several rcscarchcrs [1,7,10,29,32,34,40] have suggested t h a t t h e creep feed o r f u l l depth g r i n d i n g process i s l i m i t e d by a burn- o u t heat f l u x , o r t h e maximum heat f l u x which can be convected away by t h e coo lan t . The burn-out heat f l u x , being comparable t o t h a t observed i n t h e burn-out o f heat exchangers, reaches a maximum a t t h e peak o f t h e nuc lea te b o i l i n g regime. However, even though b o i l i n g i s one o f t h e most comnon heat t r a n s f e r phenomena, i t i s a l s o one o f t h e most perp lex ing . The pub l ished l i t e r a t u r e on b o i l i n g approaches 2000 papers. With t h i s i n mind, d i f f i c u l t i e s assoc ia ted w i t h i d e n t i f i c a t i o n o f t h e g r i n d i n g zone hc become i n c r e a s i n g l y apparent. Nevertheless, assuming pool b o i l i n g f o r water on a c lean metal surface, a maximum repor ted convect ive heat t r a n s f e r c o e f f i c i e n t o f 40000 J/m'-sec-'K can occur i n t h e nuc lea te b o i l i n g regime C391.

I n l i g h t o f t h e above d iscuss ions , i t appears r e a l i s t i c t h a t g r i n d i n g zone convec t ive heat t r a n s f e r c o e f f i c i e n t s on t h e order o f 40000 J/m'-sec-'K cou ld e x i s t under c o n d i t i o n s o f nuc lea te b o i l i n g . However, r e c a l l f rom t h e prev ious FEA analyses t h a t f i l m c o e f f i c i e n t s l a r g e r than 68100 J/m'-sec-'K would be requ i red t o achieve r e a l i s t i c g r i n d i n g zone temperatures under abusive g r i n d i n g cond i t ions . convect ive heat t r a n s f e r c o e f f i c i e n t s a r e generated i n t h e g r i n d - i n g zone o r t h a t t h e ac tua l con tac t l e n g t h i s f a r g r e a t e r than t h e geometric contac t leng th .

I n an at tempt t o b racket t h e e f f e c t s o f increased contac t l e n g t h alone, t h e above analyses were then repeated w h i l e assuming no convec t ive coo l ing . Ma in ta in ing a cons tan t t o t a l power i n p u t o f 8683 J/sec, t h e u n i t heat f l u x was reduced accord ing ly as t h e contac t l e n g t h was increased. Using t h e geometric contac t l e n g t h (lc=2.54mn), a maximum sur face temperature o f 1659'C was ca lcu- l a t e d . By doub l ing t h e contac t l e n g t h (lc=5.Omn), t h e maximum sur face temperature was reduced t o 1368'C. t imes the geometr ic c o n t a c t l e n g t h (lc=7.62mn), t h e c a l c u l a t e d maximum sur face temperature reached 121O'C (see Fig. 2).

K was a l l u d e d t o , however, f o r some water-based coolants.

Th is tends t o imp ly t h a t e i t h e r l a r g e r

F i n a l l y , a t t h r e e

TEMPERATURE DISTRIBUTION( 'C)

R ENE - 7 7, vy =. I 5 2 0 m / s . c , I = 7.62 m m, 0 = 4 4 .85 J / s e c -m m2

Ab .254mm TEMPERATURE RANGE KEY:

MX= IZIO'C MN= 20.9'C

@ 170.6 0 2;::; @ 1078.3

8 ;:;:; 0 @ 1210

The above a n a l y s i s i n d i c a t e s t h a t , i n o rder t o achieve r e a l i s t i c supera l loy g r i n d i n g zone temperatures, w h i l e n e g l e c t i n g convec- t i v e c o o l i n g w i t h i n t h e wheel/workpiece i n t e r f a c e , t h e a c t u a l con tac t l e n g t h would have t o be over t h r e e t imes as l a r g e as t h e geometric contac t l e n g t h under t h i s p a r t i c u l a r se t o f g r i n d i n g cond i t ions .

To add a d d i t i o n a l complex i ty t o t h e problem, t h e d i f f i c u l t y assoc ia ted w i t h t h e development o f accura te m a t e r i a l da ta should be emphasized. Using abusive g r i n d i n g c o n d i t i o n s i d e n t i f i e d a t .1524 m/sec as i n p u t t o t h e FEA program t h e sur face temperature developed a t a node was p l o t t e d as a f u n c t i o n o f t ime. quent ly , t h e p l o t was d i f f e r e n t i a t e d w i t h respec t t o t i m e t o o b t a i n t h e sur face h e a t i n g and c o o l i n g ra tes . Depending upon t h e maximm temperature and convect ive f i l m c o e f f i c i e n t , t h e h e a t i n g r a t e s ranged from 120,000 -200.000'C/sec, w h i l e t h e c o o l i n g r a t e s were between 56,000 -111,111'C/sec. Unfor tunate ly , even u t i l i z - i n g t h e s p e c i a l i z e d Gleeble t e s t r i g developed f o r s u p e r a l l o y welding s imu la t ion , a maximum heat ing o r c o o l i n g r a t e o f o n l y 5600'C/sec i s t y p i c a l l y obtained. What must be r e a l i z e d i n a l l o f these cases i s t h a t t h e heat ing and c o o l i n g r a t e s a r e ex- t remely r a p i d and, as such, f r u s t r a t e at tempts t o a c c u r a t e l y p r e d i c t superal l o y g r i n d i n g performance based upon s tandard m a t e r i a l t e s t i n g procedures.

Subse-

6.0 FINITE ELEMENT STRESS CALCULATIONS

The r e s u l t s o f t h e non l inear FEA s t u d i e s conducted i n t h i s inves- t i g a t i o n are summarized i n Table 1. The i n i t i a l n o n l i n e a r ana ly - s i s (model 1) was conducted us ing abusive g r i n d i n g c o n d i t i o n s (rank 7+) as i n p u t . Th is model used a heat f l u x o f 44.85 J/mm'- sec w i t h a contac t l e n g t h equal t o t h r e e t imes the geometr ic contac t l e n g t h and convect ive c o o l i n g o f hc = 4500 J/m'-sec-'K o u t s i d e t h e heat source were used. As shown i n Table 1 and F igure 2, t h e maximum sur face temperature reached 121O'C under these rank 7+ abusive g r i n d i n g c o n d i t i o n s . s u l t i n g Sx s t r e s s p r o f i l e (see Fig. 3) shows t h a t a maximum r e s i d u a l t e n s i l e s t r e s s o f 815 MPa e x i s t s on t h e surface, and as Fig. 2 shows, t h e model has cooled down t o approximately 260'C a t t h i s p o i n t . Note t h a t t h e maximum compressive s t r e s s o f 763 MPa i s developed a t t h e l e a d i n g edge o f t h e heat source. T h i s ana ly - s i s a l s o showed t h a t t h e Sz s t r e s s d i s t r i b u t i o n (normal t o t h e heat band mot ion) i s very s i m i l a r t o t h e Sx d i s t r i b u t i o n , except t h a t t h e r e s i d u a l s t resses were s l i g h t l y l a r g e r owing t o t h e p l a i n s t r a i n assumption.

It i s i n t e r e s t i n g t o no te t h a t cons iderab le v e r t i c a l s u r f a c e displacements can a r i s e f rom l o c a l i z e d thermal expansion. The prev ious ANSYS p l o t s (Figs. 2 1 3) schemat ica l l y i l l u s t r a t e d

A p l o t o f t h e re -

TABLE 1

COMPARISON OF NONLINEAR FINITE ELEMENT RESIDUAL STRESS ANALYSES

MODEL NUMBER

1

2

3

4

5

6

WORKPIECE VELOCITY

CONTACT UNIT HEAT LENGTH FLUX (mm)

.1524 7.62 44.85

(J/mm * - sec )

.1524 7.62 27.8

.1524 2.54 73.6

.1524 2.54 134.6

.1524 2.54 73.6

.0508 2.54 40.9

MOOEL NUMBER

MAXlMUM MAX. SURFACE MAX. RESIDUAL TEMPERATURE DISPLACEMENT STRESS, SxR

( 'C) (mn) (MPa)

1 1210 .02616 815

2 861 .01422 80 7

3 1132 .01338 821

4 1116 .01303 865

5 1132 .02288 82 1

6 1119 .03175 670 FIGURE 2

31 1

STRESS DISTRIBUTION(Sx) SURFACE DISPLACEMENT(Uy 1

RE N E - 7 7, v W . I 52 O m / 8 a 5 . I = 7.62 m m , 0 = 4 4 . 85 J / (I e c - mrnz RENE-77. vw = . I 5 2 0 m / ~ mc , Ic -7.62mm. O = 4 4.85 J / s c - mmz

1- UNIFORM

0

I 1 !;.-. , ., .. .. , .. . -. - . . . : .. ,' .-.I.. .. . .. :. ,. .. . , . . .

,254mm dk .254mm

VERTICAL NODAL DISPLACEMENT RANGE KEY:

MX= .02616mm MN= -.00034mm

STRESS RANGE KEY:

MX- 815.05 MPa MN= -763.42 MPo

@.00228 @ .02362

0 . 0 2 6 1 6

@ -588.047 @ -61.88 113.508

@ 639.675

B -412.658 @ 288.897 @ 815.05 -237.269 464.224

FIGURE 3 FIGURE 4

these e f f e c t s . The ac tua l sur face displacements (Uy) c a l c u l a t e d by t h e FEA program a r e g i v e n i n F i g u r e 4. A mximum sur face displacement o f 0.029mn was determined near t h e t r a i l i n g edge o f t h e moving band heat source. Obviously, f rom t h e s tandpo in t o f producing p r e c i s i o n ground supera l loy components, l o c a l i z e d sur face s w e l l i n g can promote d i s t o r t e d f i n i s h e d surfaces o r excessive s tock removal. Unfor tunate ly , t h i s sur face s w e l l i n g a lso compl icates c a l c u l a t i o n o f t h e ac tua l con tac t l e n g t h and t h e e f f e c t i v e depth o f c u t used f o r a n a l y t i c a l l y model ing conven- t i o n a l supera l loy g r i n d i n g behavior.

A s i m i l a r non l inear s t r e s s a n a l y s i s was then conducted u s i n g a comparable se t o f c o n d i t i o n s bu t w i t h a reduced heat f l u x input (model 2: 27.8 J/mm'-sec). This a n a l y s i s s imulates Rene-77 g r i n d i n g c o n d i t i o n s i d e n t i f i e d i n t h e l a b o r a t o r y as be ing non- abusive f rom a c r a c k i n g s tandpo in t ( rank 1). a n a l y s i s a r e summarized i n Table 1. Under these nonabusive g r i n d i n g cond i t ions . a maximum sur face temperature o f o n l y 861'C was ca lcu la ted . Note, however, t h a t t h e r e s i d u a l Sx s t resses reached 807 MPa. I n o ther words, t h e r e s i d u a l stresses developed under nonabusive g r i n d i n g c o n d i t i o n s ( rank 1) were w i t h i n 1% o f those developed under abusive c o n d i t i o n s '(rank 7+ c rack ing) . This r a t h e r s u r p r i s i n g r e s u l t r e q u i r e s f u r t h e r discussion.

Since t h e r e s i d u a l s t resses i d e n t i f i e d above f o r t h e abusive and nonabusive g r i n d i n g c o n d i t i o n s a r e e s s e n t i a l l y i d e n t i c a l , i t appears t h a t Rene-77 sur face microcracks are probably n o t formed p u r e l y by t h e r e s i d u a l stresses. It i s be l ieved t h a t t h e deve l - opment o f microcracks d u r i n g the convent ional g r i n d i n g o f Rene-77 must a l s o be due t o t h e c o n s t i t u t i o n a l l i q u a t i o n phenomena d i s - cussed i n Sec t ion 3.0. Recal l t h a t r a p i d h e a t i n g t o temperatures near 1150'C can induce l o c a l i z e d m e l t i n g o f t h e g r a i n boundaries and a dramat ic l o s s i n d u c t i l i t y upon c o o l i n g (see Fig. 1). The n e t r e s u l t i s t h e fo rmat ion o f g r a i n boundary microcracks. as conf i rmed by m e t a l l u r g i c a l analyses. A l t e r n a t i v e l y s ta ted , h i g h s t resses upon c o o l i n g through a reduced s t r e n g t h o r d u c t i l i t y r e g i o n c o u l d enhance t h e occurrence o f microcracking.

To f u r t h e r c o n f i r m these observat ions, t h e Rene-77 specimens, used t o generate t h e g r i n d i n g da ta f o r t h e above models, were then analyzed u s i n g X-ray d i f f r a c t i o n (XRD). techn ique r e a d i l y lends i t s e l f t o t h e i d e n t i f i c a t i o n o f res idua l s t resses developed under machining opera t ions [9,16,311. should be noted, however, t h a t the technique i s best s u i t e d f o r f i n e gra ined m a t e r i a l s . The r e s u l t s o f t h e a n a l y s i s showed t h a t ho th the cracked and uncracked specimens d isp layed n e a r l y iden- t i c a l r e s i d u a l t e n s i l e s t r e s s o f 1124 MPa on the sur face i n t h e l o n g i t u d i n a l o r X d i r e c t i o n . Al though t h e magnitude of t h e measured r e s i d u a l sur face s t r e s s i s l a r g e r t h a n t h a t p r e d i c t e d by

The r e s u l t s o f t h i s

I n general , t h e XRD

I t

t h e FEA ana lys is , i n b o t h cases t h e abusive and nonabus ive ly ground specimens d i s p l a y e d n e a r l y i d e n t i c a l r e s i d u a l s t r e s s l e v e l s .

Attempts t o i d e n t i f y r e s i d u a l s t r e s s l e v e l s below t h e sur face were f a i r l y successful t o depths l e s s than 0.02mm. However, a t depths beyond O.O2m, t h e m a t e r i a l was e s s e n t i a l l y i n i t s o r i g i n a l l a r g e g r a i n c a s t i n g c o n d i t i o n ; thereby, p r e v e n t i n g r e s i d u a l s t r e s s measurement by XRD. The absence o f numerous d i f f r a c t i n g gra ins , r e s u l t i n g from t h e l a r g e c r y s t a l l i n e s t r u c t u r e , p roh i b i t s t h e fo rmat ion o f s u f f i c i e n t l y i n t e n s e d i f f r a c t i o n peaks C311. 0 . 0 l m and 0.02mm below t h e sur face the r e s i d u a l s t resses i n t h e l o n g i t u d i n a l d i r e c t i o n were approximately +745 MPa. These measurements, taken nearer t o t h e convent iona l l a r g e c r y s t a l l i n e g r a i n s t r u c t u r e , a r e i n cons iderab ly good agreement w i t h those i d e n t i f i e d through use o f t h e n o n l i n e a r FEA analysis.

Several a d d i t i o n a l n o n l i n e a r FEA s tud ies , b r i e f l y summarized i n Table 1, were conducted t o examine t h e impact o f con tac t l e n g t h and convec t ive c o o l i n g c o e f f i c i e n t s . surface t r a c t i o n s and reduced heat source v e l o c i t y were a l s o s t u d i e d . Using a contac t l e n g t h equal t o t h e geometric contac t l e n g t h (model 3), t h e t o t a l heat i n p u t was reduced un t i l a maximum temperature o f 1132'C was developed. I n t h i s model, t h e e f f e c t s o f h i g h convec t ive c o o l i n g under t h e heat source were s imulated. Under these cond i t ions , a maximm r e s i d u a l t e n s i l e s t r e s s o f 821 MPa was c a l c u l a t e d i n t h e l o n g i t u d i n a l d i r e c t i o n . Th is s t ress , and t h e m g n i t u d e o f remaining s t resses , were very s i m i l a r t o those developed i n model 1. Thus, u s i n g t h e geometr ic c o n t a c t l e n g t h w i t h a reduced t o t a l heat i n p u t , which i s i n d i c a t i v e o f h i g h convec t ive c o o l i n g i n t h e contac t area, t h e magnitude o f t h e r e s u l t i n g s t resses a r e very s i m i l a r t o those ob ta ined assuming an increased contac t l e n g t h and n o a d d i t i o n a l wheel/workpiece i n t e r - face convec t ive c o o l i n g . Note, however, t h a t the reduced contac t l e n g t h d i d tend t o reduce t h e maximum sur face displacement.

The above model was t h e n mod i f ied t o i n c o r p o r a t e convec t ive c o o l i n g over t h e e n t i r e surface. Th is model (model 4) c o r r e s - ponds t o t h e maximum r e q u i r e d convec t ive c o o l i n g case discussed i n Sec t ion 4.0. Reca l l t h a t , by u s i n g t h e geometric c o n t a c t l e n g t h , convec t ive c o o l i n g o f 68,100 J/rn'-sec-'K over t h e e n t i r e surface, and abusive g r i n d i n g i n p u t data, a maximum sur face temperature o f 1116'C was ca lcu la ted . Under these c o n d i t i o n s , t h e maximum r e s i d u a l Sx sur face t e n s i l e s t r e s s (865 MPa) was w i t h i n approximately 5% o f those c a l c u l a t e d us ing t h e reduced

However, t h e a n a l y s i s d i d show t h a t a t

I n a d d i t i o n , t h e e f f e c t s o f

31 2

heat f l u x model 3. The s l i g h t inc rease i n t e n s i l e r e s i d u a l s t r e s s i s most l i k e l y t h e r e s u l t o f t h e a d d i t i o n a l convec t ive c o o l i n g u t i l i z e d o u t s i d e t h e heat source.

To i n v e s t i g a t e p o s s i b l e e f f e c t s a r i s i n g t h e o v e r a l l mechanical g r i n d i n g loads, sur face t r a c t i o n s were added t o model 3 i n t h e heat band area. The a d d i t i o n a l normal and t a n g e n t i a l loads were comparable t o those developed under abusive g r l n d i n g c o n d i t i o n s . As the model 5 r e s u l t s i n d i c a t e , t h e a d d i t i o n a l sur face t r a c t i o n s had no apprec iab le e f f e c t on t h e r e s i d u a l Sx stress. observat ion was made by Mishra C251 us ing p r i m a r i l y cons tan t mater ia l p roper t ies . Thus, t h e r e s i d u a l s t resses developed under abusive g r i n d i n g c o n d i t i o n s a r e main ly thermal i n o r i g i n . Some- what s u r p r i s i n g l y , however, t h e maximum sur face displacement increased under t h e a d d i t i o n o f t h e sur face loads.

F i n a l l y , u s i n g model 3, t h e moving band v e l o c i t y was then reduced by a f a c t o r o f 3 ( i .e. , Vw = 0.0508 m/sec) w h i l e t h e heat source f l u x was reduced t o 40.9 J/mm'-sec. Under these model 6 cond i - t i o n s , t h e maximum sur face temperature (1118'C) was very c l o s e t o t h a t developed a t t h r e e t imes t h e heat source v e l o c i t y . Note t h a t , a l though t h e temperatures were n e a r l y i d e n t i c a l f o r models 3 and 6 , t h e peak r e s i d u a l S x t e n s i l e s t r e s s was approximately 23% greater u s i n g t h e increased heat source v e l o c i t y c o n d i t i o n s .

I n sumnary, t h e above analyses, coupled w i t h exper imental data, tended t o show t h a t comparable maximum g r i n d i n g zone temperatures may no t n e c e s s a r i l y induce comparable l e v e l s o f g r i n d i n g damage. A l t e r n a t i v e l y , i t was shown t h a t h i g h r e s i d u a l s t resses a lone may n o t cause microcracks i n superal loys. Consequently, i t i s f e l t t h a t the development o f microcracks d u r i n g t h e convent iona l g r i n d i n g o f Rene-77 must a l s o be enhanced by t h e c o n s t i t u t i o n a l l i q u a t i o n phenomena discussed i n Sec t ion 3.0 .

A s i m i l a r

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Welding Research Supplement t o t h e

Mass., Chapter 9.

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