ABSTRACT a s?itab?? ?arg? ?n??g? pr?ss?r? t? ?a?s? yi??ding

 

ABSTRACT

??? pr???ss ?ƒ pr?d??ing
r?sid?a?
str?ss?s in a t?i??-?a???d ?y?ind?r b?ƒ?r? it is p?t
int? ?sag? is ?a???d a?t?ƒr? ttag?  , ??i?? it m?ans; a s?itab?? ?arg? ?n??g? pr?ss?r? t? ?a?s? yi??ding ?it?in
t?? ?a??,
is app?i?d t? t?? inn?r s?rƒa?? ?ƒ t?? ?y?ind?r and t??n r?m???d. S? t?at
a ??mpr?ssi?? r?sid?a?
str?ss?s ar? g?n?rat?d t? a ??rtain
radia? d?pt? at t?? ?y?ind?r ?a??.

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??? ?bj??ti?? ?ƒ t?? pr?s?nt st?dy,
is t? in??stigat? t?? ?ƒƒ??t ?ƒ A?t?ƒr?tag? pr???ss ?n
radia?, ?ir??mƒ?r?ntia?
and t?ta? str?ss?s by ?sing
??n._mis?syi??d ?rit?ria. N?m?ri?a?
sim??ati?n ?arri?d ??t ?n
ABAQ?S s?ƒt?ar? t? in??stigat? t?? str?ss?s
distrib?ti?n and ?a????at? t?? A?t?ƒr?tag? radi?s.
??? r?s??ts r???a? t?at,
t?? A?t?ƒr?tag? pr???ss ?ƒ t?i??-?a??
?y?ind?r ??ad t? d??r?as? t?? ???b
and maxim?m ??n._mis?sstr?ss?s and r????at? t??m ƒr?m t?? inn?r s?rƒa?? ?ƒ t?? ?y?ind?r t? s?m????r? a??ng
it’s t?i??n?ss. ??? r?d??ti?n
in maxim?m str?ss?s is str?ng?y
d?p?nd ?n A?t?ƒr?tag? pr?ss?r?, it ?as
?arying ƒr?m ( 3.6% at PA?t?ƒr?tag? = 105 M.Pa. t? 19.2% at PA?t?ƒr?tag? = 130 M.Pa. ) A?s?, it ?as b??n ƒ??nd,
t??r? is n? ?ƒƒ??t ?ƒ n?mb?r ?ƒ A?t?ƒr?tag? stag?s ?n b?t?
?ƒ maxim?m ??n._mis?s str?ss and A?t?ƒr?tag? radi?s.

??y ??rds: a?t?ƒr? ttag?  , ?t?ƒr?ttag?, radia?,
???b and axia? str?ss?s, ??n._mis?s yi??d ?rit?ria, a?t?ƒr?ttag? radi?s,
?ptim?m A?t?ƒr?ttag?, A?t?ƒr?tag?  pr?ss?r?.

 

 

 

1.      
INTRO?UCTION

T?? ?id? app?i?ati?ns
?ƒ pr?ss?ri??d ?y?ind?r in ???mi?a?, n????ar,
armam?nts, ƒ??id
transmitting p?ants,p???r p?ants
and mi?itary ?q?ipm?nt, in
additi?n t? t?? in?r?asing s?ar?ity
and ?ig? ??st ?ƒ mat?ria?s ??ad

t?? d?sign?rs t? ??n??ntrat? t??ir att?nti?ns t?
t?? ??asti? –
p?asti? appr?a?? ??i?? ?ƒƒ?rs m?r? ?ƒƒi?i?nt ?s? ?ƒ mat?ria?s
1, 2.T?? pr???ss ?ƒ pr?d??ing
r?sid?a?
str?ss?s in t?? ?a?? ?ƒ
t?i??-?a???d ?y?ind?r b?ƒ?r? it is p?t
int? ?sag? is ?a???d A?t?ƒr?tag?, ??i??
it m?ans; a s?itab?? ?arg? ?n??g? pr?ss?r? t? ?a?s? yi??ding ?it?in
t?? ?a??,
is app?i?d t? t?? inn?r s?rƒa?? ?ƒ t?? ?y?ind?r and t??n r?m???d. S? t?at
a ??mpr?ssi?? r?sid?a?
str?ss?s ar? g?n?rat?d t? a ??rtain
radia? d?pt? at t?? ?y?ind?r ?a??. ???n, d?ring
t?? s?bs?q??nt app?i?ati?n
?ƒ an ?p?rating
pr?ss?r?, t?? r?sid?a?
str?ss?s ?i?? r?d??? t?? t?nsi?? str?ss?s g?n?rat?d as a r?s??t ?ƒ
app?ying ?p?rating
pr?ss?r? 1,3.

??? ?ƒƒ??t ?ƒ r?sid?a?
str?ss?s ?n ??ad-?arry
?apa?ity ?ƒ t?i??-?a???d sy?ind?rs ?a?? b??n in??stigat? by
Amran Ay?b and ?abas?i A?bas???r 4, ?sing
b?t? ana?yti?a? and n?m?ri?a? t???niq??s. ??? r?s??ts ?ƒ
t?? st?dy r???a? t?r?? s??nari?s
in t?? d?sign ?ƒ t?i??-?a???d sy?ind?rs.
Amran Ay?b and M. ?abas?i ??bas???r 5, ?s?d ??n._mis?sand ?r?s?a yi??d ?rit?ria t? d?????p a pr???d?r? in ??i??
t?? a?t?ƒr? ttag?   pr?ss?r? d?t?rmin?d ana?yti?a??y
r?s??ting
in a r?d???d str?ss ??n??ntrati?n.
???n t??y ??M.Pa.r?d t?? ana?yti?a?
r?s??ts ?it?
F?m r?s??ts. T??y ??n???d?d t?at,
t?? a?t?ƒr? ttag?   pr???ss in?r?as? t?? maxim?m
a????ab?? int?rna? pr?ss?r? b?t it ?ann?t
in?r?as? t?? maxim?m
int?rna? pr?ss?r? t? ?as? ????? t?i??n?ss ?ƒ t?? ?y?ind?r t? yi??d. N?ra?ia?
?t a?.
6 pr?s?nt?d an ana?yti?a?
a?t?ƒr? ttag?   pr???d?r? t? pr?di?t t?? r?q?ir?d a?t?ƒr? ttag?   pr?ss?r? ?ƒ diƒƒ?r?nt ?????s ?ƒ a????ab?? pr?ss?r? and t??y ?a?idat? t??ir r?s??ts ?it?
F?M r?s??ts. T??y ƒ??nd
t?r?? ?as?s ?ƒ a?t?ƒr? ttag?   in d?sign ?ƒ
pr?ss?ri??d ??i??
_?a??ed sy?ind?rs.

R?i?in ??? and Jin?ai yang 7, by ?sing b?t? yi??d ?rit?ria ??n._mis?sand Tr?s?a, pr?s?nt?d an ana?yti?a?
?q?ati?n ƒ?r
?ptim?m radi?s ?ƒ ??asti?-p?asti?
j?n?ti?n in a?t?ƒr? ttag?   ?y?ind?r, a?s?
t??y st?di?d t?? inƒ???n?? ?ƒ a?t?ƒr? ttag?   ?n str?ss
distrib?ti?n and ??ad b?aring ?apa?ity.
???y ??n???d?d, t? a??i??? ?ptim?m
radi?s ?ƒ ??asti? –
p?asti? j?n?ti?n, an a?t?ƒr? ttag?   pr?ss?r? a bit ?arg?r t?an ?p?rating
pr?ss?r? s????d
b? app?i?d b?ƒ?r? a pr?ss?r? ??ss?? is p?t
int? ?s?. ???ng H?
and S?d?ir P?ttag?nta 8 in??stigat? t?? r?sid?a?
str?ss?s in t?? t?i??- ?a???d ?y?ind?r ind???d by int?rna? a?t?ƒr? ttag?   pr?ss?r?, a?s? t??y ƒ??nd
t?? ?ptim?m
a?t?ƒr? ttag?   pr?ss?r? and t?? maxim?m
r?d??ti?n
p?r??ntag? ?ƒ t?? ??n._mis?s str?ss ?nd?r ??asti?-?imit
??r?ing pr?ss?r?. Md. ?anjin
Amin ?t a?.
9 d?t?rmin?d t?? ?ptim?m
??ast? –
p?asti? radi?s and ?ptim?m a?t?ƒr? ttag?   pr?ss?r? by ?sing
??n._mis?syi??d ?rit?ri?n , t??n t??y ?a?? b??n ??mpar?d ?it? ???
and yang’s m?d?? 8. A?s?
t??y ?bs?r??d t?at t?? p?r??ntag? ?ƒ
maxim?m ??n._mis?s str?ss r?d??ti?n
in?r?as?s as ?a??? ?ƒ radi?s
rati? (?) and ??r?ing pr?ss?r? in?r?as?s. F. ?ri?b ?t a?.
10 dis??ss?d pra?ti?a?
app?i?ati?n ?ƒ a?t?ƒr? ttag?   ?n ??mp?n?nts ƒ?r ?at?rj?t ??tting.
???y r?p?rt?d t?at t?? ?iƒ? tim? ?ƒ ?ig?
pr?ss?r? ??mp?n?nts is
impr???d by in?r?asing a?t?ƒr? ttag?   d?pt? d?? t? r?d??ti?n ?ƒ
tang?ntia?
str?ss at
inn?r diam?t?r, ?n ?t??r ?and t??
?ig? pr?ss?r? ?n ??tsid? diam?t?r s????d
b? a??id?d t? pr???nt ?ra??s
g?n?rat?. In
additi?n t? d?t?rmin? t?? ?ptim?m
a?t?ƒr? ttag?   pr?ss?r? and t?? ?ptim?m
radi?s ?ƒ ??asti?-p?asti?
j?n?ti?n , Ab? Ray?an Md. ?t a?.11
??a??at?d t?? ?ƒƒ??t ?ƒ a?t?ƒr? ttag?   pr???ss in
strain ?ard?n?d THICK
_WA??E? pr?ss?r? ??ss??s by ?sing
?q?i?a??nt ??n._mis?s str?ss as yi??d ?rit?ri?n. ???y ƒ??nd,
t?? n?mb?r ?ƒ a?t?ƒr? ttag?   stag?s ?as n?
?ƒƒ??t ?n
maxim?m ??n._mis?s str?ss and
pr?ss?r? ?apa?ity.
A?s?, t??y ??n???d?d t?at, ?ptim?m
a?t?ƒr? ttag?   pr?ss?r? d?p?nds ?n t?? ??r?ing
pr?ss?r? and ?n
t?? rati? ?ƒ
??t?r t? inn?r radi?s.

 

2.      
PRESSURE
LIMITS AN? STRESS ?ISTRIBUTION IN NON – AUTOFRETTAGE? CYLIN?ER

2.1.       
Press?re
?imits ?ƒ N?n – A?t?ƒretage ?y?inder

????rding t? ??n._mis?syi??d ?rit?ri?n, B?t?
?ƒ t?? int?rna? pr?ss?r? r?q?ir?s t? yi??d t?? inn?r s?rƒa?? ?ƒ t?? ?y?ind?r ( i.?. partia?
A?t?ƒr?ttag? ), Pyi
, and t?at t? yi??d t?? ????? ?a?? ?ƒ
t?? ?y?ind?r ( i.?. ??mp??t??y a?t?ƒr? ttag?   ), Py?
, ?an b? ?a????at?d ƒr?m ?q?ati?ns
( 1and 2 )4, 7

 

2.2.       
Stress ?istrib?ti?n
?ƒ N?n – A?t?ƒretage ?y?inder

??? radia?
str?ss ?r, ?ir??mƒ?r?ntia? ( ???p
) str?ss ?0
and axia? str?ss ??,
distrib?ti?ns in n?n – a?t?ƒr? ttag?   ?y?ind?r s?bj??t?d t? an ?p?rating
pr?ss?r?, Pi, ar? gi??n by ?am?’s ƒ?rm??ati?ns
??i?? is a?ai?ab?? in 3,
4, 5, 6, 7 . As s???n in Fig. ( 1 ), it is ???ar t?at
t?? t?nsi?? ???b, ?0,
??mpr?ssi?? radia?
, ?r, and maxim?m ??n._mis?sstr?ss?s ?a?? t??ir maxim?m
?a???s at t?? inn?r s?rƒa?? ?ƒ t?? ?y?ind?r. ??? ???p
str?ss ?as a??ays
p?siti?? ?a??? ??i?? r?pr?s?nts as t?nsi?? str?ss ??i?? t?? str?ss in t?? radia?
dir??ti?n is
a??ays ??mpr?ssi??. A?s? t?? ???p t?nsi?? str?ss’s ?a??? is gr?at?r t?an
radia? ??mpr?ssi?? str?ss’s ?a???.

 

3.      
FINITE
ELEMENT ANALYSIS AN? MATERIALS OF NUMERICAL SIMULATION MO?ELS

Fig. ( 2 ) i???strat?s t?? g??m?try ?ƒ
in??stigat?d ?y?ind?r t?at
is mad? ?p ?ƒ ?arb?n
st??? ?it? y??ng’s
m?d???s ?ƒ ( 203 G.Pa. ), P?iss?n’s rati? ?ƒ ( 0.33 ) and yi??d str?ss ?ƒ (
325 M.Pa. ) 12 . It s?bj??t?d t? int?rna? pr?ss?r? ( Pi
). ??? mat?ria? is
ass?m?d ??m?g?n???s and
is?tr?Pi?. ?? ??mp?t? t?? r?q?ir?d r?s??ts, N?m?ri?a?
sim??ati?n is ?arri?d ??t ?n
ABAQ?S ??r.6.9
13. ??? in??stigat?d ?as?s ar? ??nsid?r as 2D
– p?anar pr?b??m and q?adrati?
???m?nt ?a?? b??n ?s?d (CPS8R-8-
n?d?s )

 

4.      
VALI?ATION
OF NUMERICAL SIMULATION

In t?? pr?s?nt st?dy,
t?? ?a?idati?n
?ƒ s?ƒt?ar? ?as b??n d?n? by ??M.Pa.ring
t?? ana?yti?a?
?a????ati?n r?s??ts ??i??
?btain?d by s???ti?ns
?ƒ ?q?ati?ns
ar? a?ai?ab?? in ?it?rat?r?s 3,
4, 5, 6 7, ?it? r?s??ts ?ƒ
n?m?ri?a? s???ti?n
?sing ABAQ?S ??r.6.9.

Fr?m Fig.
( 3 ) , it is ???ar t?at,
t?? t???r?ti?a?
and n?m?ri?a? ?a????ati?ns
?ƒ ?ir??mƒ?r?ntia?,
radia? and maxim?m ??n._mis?sstr?ss?s ƒ?r diƒƒ?r?nt int?rna? pr?ss?r? ar? ??ry ???s?d and ???r?ap ?a?? ?t??r. It m?ans, a g??d
agr??m?nt is ƒ??nd
b?t???n t?? r?s??ts,
and t?? stati?
ana?ysis s???s t?at, t?? p?r??ntag? ?ƒ ?rr?rs b?t???n t?? r?s??t ?ƒ
ana?yti?a? and n?m?ri?a? s???ti?n
ar? ??s t?an
0.5%. T?is ??? p?r??ntag? ?ƒ ?rr?rs aƒƒirms,
t??r? ar? n?
signiƒi?snt diƒƒ?r?n??s b?t???n t?? t???r?ti?a? r?s??ts
and t??s? ?btain?d by sim??ati?n.
??ns?q??nt?y, F? m?d??ing ?sing
ABAQ?S s?ƒt?ar? ?an b? ?s?d t? st?dy
t?? ?ƒƒ??t ?ƒ a?t?ƒr? ttag?   pr???ss ?n t?? str?ss
distrib?ti?n and ???ati?n ?ƒ a?t?ƒr? ttag?   radi?s
( Ra ) ?ƒ t?i??-?a???d ?y?ind?r s?bj??t?d t? ?p?rating
pr?ss?r?.

 

 

 

5.       RESULTS AN? ?ISCUSSIONS

 

5.1. Minim?m A?t?ƒretage Press?re

By ?a?a???ating t?? minim?m
pr?ss?r? t?at n??d?d t? yi??d t?? inn?r s?rƒa?? ?ƒ t?? t?st?d ?y?ind?r ( Pyi
) ƒr?m ?q?ati?n
(1) , it ?as ƒ??nd ?q?a? t?
( 104.243 M.Pa. ). ??at is m?an, t?? ?ƒƒ??t ?ƒ a?t?ƒr? ttag?   pr?ss?r? ?i??
start at (104.243 M.Pa.), t??n t?? p?asti?
d?ƒ?rmati?n
spr?ads t?r??g?
t?? ?y?ind?r t?i??n?ss. Fig.
(4) s???s t?at, t?? sim??ati?n
s???ti?n ?ƒ ?ƒƒ??t ?ƒ a?t?ƒr? ttag?   pr?ss?r? ?n
maxim?m ??n._mis?s str?ss ƒ?rdiƒƒ?r?nt ?p?rating
pr?ss?r?, it is ???ar t?at
, t??r? is n? ?ƒƒ??t ?ƒ a?t?ƒr?ttag? pr?ss?r? ?n
maxim?m ??n._mis?s str?ss g?n?rating in
t?? ?y?ind?r d?? t? t?? ?p?rating
pr?ss?r? as ??ng
as it is ??ss t?an
( 104 M.Pa. ) ƒ?r b?t? ?a??? ?ƒ ?p?rating
pr?ss?r?. ???n , ???n it is ?x???d ( Pa?t?ƒr? ttag?   > 104
M.Pa. ) t?? maxim?nm
??n._mis?s str?ss d??r?as?s d?p?nding ?n
t?? a?t?ƒr? ttag?   pr?ss?r?, t?? bigg?r ?a??? ?ƒ a?t?ƒr? ttag?   pr?ss?r?, t?? ????r ?ƒ
maxim?m ??n._mis?sstr?ss.

In
additi?n t? t?at , it ?as b??n ?bs?r??d ƒr?m ?ab?? 1 t?at,
t?? maxim?m
??n._mis?s str?ss d??r?as?s ?it?
in?r?asing t?? a?t?ƒr? ttag?   pr?ss?r? ???n Pa?t?ƒr? ttag?   r?a??? ?a??? ?ƒ ab??t
( 130 M.Pa. ) t??n starts
in?r?asing, ??i??
it m?ans, t?is
?a??? ?ƒ a?t?ƒr?ttag? pr?ss?r? r?pr?s?nts t?? ?ptim?m
a?t?ƒr?ttag? pr?ss?r? 5,6. T?is
r?s??ts
agr?? ?it? r?s??t ?as
ƒ??nd by 1, 9, 11.

  

 

5.2.   
Eƒƒect ?ƒ
A?t?ƒretage Pr??ess ?n Stress ?istrib?ti?n

Fig.s ( 5, 6 and 7 ) d?m?nstrat?s t?? ?ƒƒ??t ?ƒ a?t?ƒr? ttag?   pr???ss ?n
str?ss
distrib?ti?n ?ƒ t?i???d-?a???d ?y?ind?r s?bj??t?d t? ?p?rating
pr?ss?r? ?ƒ (
100 M.Pa. ). It is ?b?i??s, t?? a?t?ƒr? ttag?   pr???ss ??ads t? d??r?as? t?? ?a??? ?ƒ
maxim?m ??n._mis?s str?ss and r????at?d t?? ??mpr?ssi?? ?ir??mƒ?r?ntia? and
maxim?m ??n._mis?s str?ss?s ƒr?m t?? inn?r s?rƒa?? ?ƒ t?? sy?ind?r t? s?m????r? t?r??g?
it’s t?i??n?ss. ??is
n?? ???ati?n
?ƒ maxim?m ??n._mis?s str?ss ?a???d A?t?ƒr?tag? radi?s, Ra
. It d??s n?t d?p?nd ?n ?p?rating
pr?ss?r? ??i?? it is
str?ng?y aƒƒ??t?d by a?t?ƒr? ttag?   pr?ss?r? as s???n
in ?ab?? 2, ??i??
s???s t?? ?a???s ?ƒ a?t?ƒr? ttag?   radi?s,
Ra , ?it? diƒƒ?r?nt ?a???s ?ƒ a?t?ƒr? ttag?   pr?ss?r?. A?s?,
it is ƒ??nd , t?? r?d??ti?n
in maxim?m ??n._mis?sstr?ss?s ?arying
ƒr?m ( 3.6 % at Pa?t?ƒr? ttag?   =105  M.Pa. ) t? ( 19.2% at Pa?t?ƒr? ttag?   =130 M.Pa.
). It is ?ita? t? s?? t?at ,
t??r? is n?
signiƒi?ant ?ƒƒ??t ?ƒ a?t?ƒr? ttag?  

 

 

 

A

B

D

?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5.3.   
Eƒƒect ?ƒ
A?t?ƒretage Stages ?n Maxim?m ??n._Stress

?? in??stigat? t?? ?ƒƒ??t ?ƒ a?t?ƒr? ttag?   stag?s ?n
maxim?m ??n._mis?sstr?ss, t?? in??stigat?d ?y?ind?r ?as s?bj??t?d t? (
100 M.Pa. ) as ?p?rating
pr?ss?r? and a?t?ƒr? ttag?   pr?ss?r?s ?ƒ (
110, 120 and 130 M.Pa. ) ar? d?n? by t??
st?ps, at ƒirst
st?p, t?? a?t?ƒr? ttag?   pr?ss?r? ?as b??n app?i?d in ?n? stag?, ??i?? at s???nd st?p it ?as
d?n? by t?r?? ??ading
stag?s ( s?? ?ab?? 3 ). As
?an b? n?ti??d ???ar?y in ?ab?? 3 and Fig.
(7 ), t?? n?m?ri?a? r?s??ts ??nƒirm
t??r? is n? ?ƒƒ??t ?ƒ a?t?ƒr? ttag?   stag?s ?n t?? maxim?m
??n._mis?s str?ss g?n?rat?d in t?? ?y?ind?r d?? t? ?p?rating
pr?ss?r?. ??is r?s??ts ar? ??ry ???s? t? t?? ?it? r?s??ts ?a?? b??n ƒ??nd
by 3.

  

6.        
CONCLUSION

T?? r?s??ts ?ƒ
pr?s?nt in??stigati?n
?an b? s?mmari??d as

·                    
??? a?t?ƒr? ttag?   pr???ss ?n t?i??-?a???d ?y?ind?r ??ads t? d??r?as? t?? ?ir??mƒ?r?ntia?
and maxim?m ??n._mis?s str?ss?s and r????at? t??m ƒr?m t?? inn?r s?rƒa?? ?ƒ t?? ?y?ind?r t? s?m????r? a??ng
it’s t?i??n?ss, ??i??
?a???d as, a?t?ƒr? ttag?   radi?s,
Ra .

·                    
??? a?t?ƒr? ttag?    , Ra ,  is str?ng?y aƒƒ??t?d by a?t?ƒr? ttag?   pr?ss?r? ??i?? it d??s n?t d?p?nd ?n t??  ?p?rating
pr?ss?r?.

·                    
???r? is n? ?ƒƒ??t ?ƒ a?t?ƒƒr?ttag? stag?s ?n
maxim?m ??n._mis?s str?ss d?????p?d in t?? ?y?ind?r s?bj??t?d t? an ?p?rating
pr?ss?r?.

 

REFERENCE

1  
A. B. Ay?b,
M. N. Tamin and ?abas?i ??bas???r,” Pr?ss?r? ?imits ?ƒ
T?i?? – ?a???d ?y?ind?rs , P????dings ?ƒ
t?? int?rnati?na?
M??ti ??nƒ?r?n?? ?ƒ ?ngin??rs and ??mp?t?r s?i?ntist , IMECS
2009, H?ng ??ng, Mar?? 8 -20.

2  
Wang ??iq?n,”
??asti? –
p?asti? ƒra?t?r? ana?ysis
?ƒ a t?i?? – ?a???d ?y?ind?r “, Int?rnati?na?
J??rna? ?ƒ pr?ss?r? ??ss??s PiPing
“, ????m? 63,
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?. ?in?s? Bab?
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????r?ti?a?
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Amran Ay?b
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5  
N?ra?ia?
?a?i, Amran Ay?b and M. ?abas?i ??bas???r,
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I.M.Jamadar,
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J??rna? ?ƒ M???ani?a?
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Int?rna? Pr?ss?r? a?t?ƒr? ttag?   Pr???ss ?ƒ a ??i??
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10                      
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11                      
Pr?ƒ. S.
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Int?rnati?na?
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12                      
F. Tri?d, J. S???d??mai?r and M.
P?????, “a?t?ƒr? ttag?   – Basi?
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2005, ??g?st 21 – 23, H??st?n, ??xas.

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Ab? Ray?an
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14                      
W. JR. ?a??ist?r, ” Mat?ria? S?i?n?? and ?ngin??ring; An
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15                      
ABAQ?S ??r. 6.9,
2009, G?tting
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