Ductile Fracture of Steel Sheets under Dynamic Membrane Loading

Ductile Fracture of Steel Sheets under Dynamic Membrane Loading

Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 197 (2017) 185 – 195 +.-#! / !"  - +&  ,$ ( +$...

534KB Sizes 1 Downloads 35 Views

Available online at www.sciencedirect.com

ScienceDirect Procedia Engineering 197 (2017) 185 – 195

+.-#! / !"  - +&  ,$ ( +$ -

+$ ,$ ( 0 0" $  +&  -%  ' 1$ 1$% 2232 + - %22 - $ ' "%2   4 0 5%2            !"# $  & '   $( ) ) *  *+$ , * +   $(   $$* !"# $ $ ,    ($ -  ) ) -   ($    % $

$./+$ , * +   $(    $$* !"# $ $ , %

 ,$      $ %   (    $  (   (    $"        " !" "   %       $%6    %&  $ " "  ""  !" ((      !"  "   %       $ 7   2       8$%7    !"$2 "      " & $ ( " "    $   ,    $  ( "    $ " "     '0+.9# !"  %"$ ( "    $ " 5"& & ($   %  " "  ( $    "   !"    : %& "  2 "$    (    !" ((  " (  $ ($  $ %&  " 7    $ (  $ ( " 7   "    0 ,$ 1 +$ ,$; 0 ': ; ,    # &

    )  & $$   %   &   ($ 0 7    2 ""  2 " $  <2 =    ( = ,$ ( " & (   (  %&  :  )    2 " " 7"%  ? <= "" $    "  %  "

3 *  $" !@AB B   C   1*) * )% 2  ($

1877-7058 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the International Conference on Dynamic Fracture of Ductile Materials

doi:10.1016/j.proeng.2017.08.095

186

Gaute Gruben / Procedia Engineering 197 (2017) 185 – 195

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

7    $     "?  $"  "2 + >

+' <=2       "? $    "2 + B

- <C= E 7      $ F2 BF   C F  "   ( %"  !" $"  &   &  G/ -    $  ( G> -       ( G 2 " "    &   &  G

-    $  ( G/ -  G        , %" 2   ($  " " ' ?( ((    " (      $ & ,  $ $ 2 "     "  $     G    G B  ($ ( " $"   "   2 & !         $    5?  % $
  

2     (  ( 7&  -  ($  ( %" 2 ""     ( I ( " $ "    I ( "    4)   J$   & $ "    $2 $          (  "        (   " (  " $( ( "   "  ,      "  ( "      &2 " ,  % " "  2 & 0 2 0

  0  !"    "    $ (   ! $ " $(  ( 2    &  "  $2  ,     2           &  " $$   % "   2     ,      !"  $( ( "   &  "  ?     $  " $ %     "$      +)* (
187

Gaute Gruben / Procedia Engineering 197 (2017) 185 – 195

 2 " " 0

  " 0            8$%7   2 &

,    0"  ( 7  $2 %  &2  $ ( 8$  2  $ ( &      & "     $ "



!" 8$   ( $       /    "&$  "  "  & (  ?92  ,   ! $   (  & ( "  !" (   " "    $ %& "  " 2 "     G  ( "   "  "  (  (  5: ( " $"    B 5: ( "    !" (   $ ( "   "  ,   !" &    $ $   $$ 


  4      4 42 )     2 )     )

  

"  M / ?  "  ( " &   " %? ( "  2   4 M / ?  "  ( " $ "   " (   ( "   ,   " " (  $ ( " & 



     0$  ( "    $ " "    (     '0+.9# !"    : %& N&"?!& "   "    " : (    " $     

188

Gaute Gruben / Procedia Engineering 197 (2017) 185 – 195

(      "$ " " "?  ( " 1$'   8$$ # %$ &      $ %&   "  %    %? "        " "  "? 2  ,  2   %& (7 " $  ( "   "       "  ,  % !" $ "   : %& "7"   "  "   : (   ) " 8$ $ 2    ( %& %    ( /       " %? ( " $ "  ) " 8$  &2   $  (    $  %   % $  "  $   % ?     ) "  ( " &  2 " &   "     $2 "$  $      " 7  2  ,  

,    -" (  (7 %  %? % -" ( 0  2 " "  (7 (    (   ?  1& (  & , 

8#$

)

 $  * !" 5"& & ($ 
 9  



 

 







        /      / 





/

"    7     " :8  ($   " & $( '    5(    $ ( N** 2   " $  ($  $% ( "    !" (   (  





'  B  '





"   "   & 2 ;      2 2/     " ? "  2 '  " 

/

 (  '2 '      ;  7   '    

  " 8$  8$     ""    6$  " " 8$     '   '

   !"     '   "  ($  ( "   !"    "  !%  !%  -  ( "   <=

-

 <-= ; <-= 

>

+'

/

 

B

-





B

' <  =

; <-=



;/ <-=

/

 

 

/B

/B





>



 







C

>

B

C

/





>









B

>

189

Gaute Gruben / Procedia Engineering 197 (2017) 185 – 195

87 

$ !" (  $ ( " & $   %         " 7  %&  " (   "   ( "     & 8  ) " 8$ $ 2 "   ( %    $ "   "   ( "   $ "   !" $ ( $   &      " " 7  $  "  ,     ,  2   " $    8$  $ " %   ( "  !"      "      "     $  "  ; "2 "  : 2   "   :   "  ( "   $    " $& ( "  ( " ,  /   " "  : "$ % %  $ " (($ ? "    " 0 2 %$ "  "$ " "?  ? $    "   " "   :2  "  ,  /%

,  /  )$ "   :   " ( " 0     ( ($ + >

+' % * ( "?  ( 0  B

-   " "  

  !" ($     " $& "$ " "  ( "  $  !" ( ($  2 " NH5  2    " ? 2   : " " " "?   "  (   "  !"    7& ? " ( "&   $  !"    2 " *?('"  2  "       ($   %    $  !" ( "&  $  (  "     $$ " " 8$     !" "   %   : "&      ( " %  2 2  :  %  " " "   (  !"  $  ( " ( "&    "  ( " " %  "" &  ( %&      (  ($ ) " ( 2 %(   ( " "     "    " % $ !#<= $ !" NH5  =  "         " N H 
        (      '



190

Gaute Gruben / Procedia Engineering 197 (2017) 185 – 195

 

 



   





(    

>

"      "  $ (  ( " 5  (        !" NH5     %& "  %"$ ( "        %  4   ( " NH5   " "        $2 "$     8$  & !$ $( >  $ !" *?('"  *'
<   7  2    '  <





" <  " ($  ,$ $ " < " "  $ < 2   " ($     %" "  7&   " '  # "     &   2  %  %  $ $     7 2 (     $ 7    !8  $ ?

$  $  !"  : "& 0'!    ( " %   "  ) "   $&2  " %  " (  &  $ %& O < =   - (   $  $   %  " "   % %&  (  ( " 1$ 2 " " & ($     

  9  /   (    9 " 9     9       "  9  " 8$    (  %& 8/2   " (  ( " 72 " 8$   ( ( 



%& 8B2     " & !"  9   9 ( " 1$   ? ( ! 
9     9    !" (  " $&  (      &    "  %  #  $     
$ )

$$(  ( )   H" " NH5  8$  ( % 2 " *?('" *'    "  : "& 0'! 8$  % "     7  ! "  2 " *'    " 0'!  % (  8$ $ 7    <= !" %   %  +)*  & ( " 8$     !"  (   $ %   JB +)*  
191

Gaute Gruben / Procedia Engineering 197 (2017) 185 – 195

+ >

+'   " + B

-2 & ! %  $ %  % " *'    " 0'!2 " ($  <     $ 8  $  "   ( " %  ( "  :  &



,  B  '   %( ($      ( "   !"    (  " &      !"  $   " ((  "   %    $ ( "   !"     "   ( "    2 " "    "   (   " ($      " *'   0'! % 

,   " " ($  (  %& " % ($  ( " $"   "    ( "           /  *& " NH5   &    ($  " " "  2 7     8$%7         /  9%& "  ( " ($ $   ( " *'    " 5  ( " NH5      /  /  ( %"  !" 0'! $    " NH5  (          /  / 2 %$ (    % ($   (    B $  "  %& ( " $ &   $&   $    7&





,   ,$  (  %& " NH5  2 " *?('"    "  : "& ( " $" (   "    "  "

192

Gaute Gruben / Procedia Engineering 197 (2017) 185 – 195



,  >  (     0 2 0

  0    " $ "        ( ($ ( 8$  + >

+' $  !"  ( "        (  "  "   

  ) " $ ( " $ " 2 "   " "     2 (     "   2   (2   "  " (       ( "       " ($  #  72 "  ( "     " 8$ $  ( " $"   "  ,  > !"  ($     " "  ( " 8$    "  ,   ) "  ( " $" 2  "      ( ($ !" NH5   "    " " 0'!2 ""       " " *'   , "   2 " NH5     ( " 0   0

2 "" & ? 2 %$    ( " 0   !"   ?& $  " %  ( ?  " 7    "  ?"  ( "  !" *'    " 0'!  "    ($ ( " 0  2    "& $  " ($  " 0   !"  ( ($  " 0  ( " + B

-   ?&  ?  " (     ""   %  $ & "  ( ( "   , " 0

 2 " *'  $&  "    ($2 " " 0'!  &  "   !" NH5      " & $  %$ " ($   $  (   & !"    ( ($ ( *'    0'!  "  ,   !"   & "      " 8$ $ ; " *'   "    " " 0'! ( " $"    " 0

 ( "   2 " " *'      ( " 0   0   ( "    *  " 8$  2 "  %" &  ( " $" 2 " "&     ( "    !"    %  (   ( ($  " 0 &

193

Gaute Gruben / Procedia Engineering 197 (2017) 185 – 195

     !" ($  " %  %   ( 8$ $ "  (  $"      "2    ( "  " %   &    "  "  !" $& " " " NH5        ( $ ($ " "  7"%  (  ?"   !" *?('"  2   2   ( "   ( $ ($2 " "       "$   %  !"  :  &     "   $ ($2 %$ 8$ " "      "  $ & %& " (      !  !" $ ( *  ( #  0$$ # & *#0#2 *  ( O"% )  *O)  " "& ?  

,  



O$ ( 8$ 7    $  !"    ( ($  " ( " " ($ 

194

Gaute Gruben / Procedia Engineering 197 (2017) 185 – 195





,   ,  $ ( & 7    $  !"    ( ($  " ( " *?( '" *'    "  : "& 0'!

"  <= ?2 P K    2  ! CC> - ( "    "   "   4   /@  B <= 0  2 N * CC 0" $   ?Q) !"& -  0$$  @ C>  '    "  ( "( "  )    P$  ( -"  0  CC@ > C>  B   %&   ($  " "    $ " #0- !   J$& >@ B <= 1 2 1 - C> # (    &  "  (  "  " O <>= 0$ " 2 ! N   . 2 P H   #  " ( ($  ( "  )    P$  ( & /@ BB  BC <= - 2  # ,2 N&2 92 !??&2 #    #? 2 # 1  B *": ( ($    (  )    P$  ( -"  0  /@ / <= -* ?2 , # C> * ( $ ($ %& " ( " P$  (  "  /@ />// C 4 " $     (   7  ( P$  ( " -"    "& ( 0 @  

Gaute Gruben / Procedia Engineering 197 (2017) 185 – 195 < = O2 P O C !" : (  (  +(2 9"5  $%"  <= N6T?$ 2 4   9 2 '  B ,$ " (  $"  " P$  ( -  !"  & B>@ C  B <= 5$"  2 P H   ! 2 U C 0" %  (      )    P$  ( 0   0$$ @ B B  </= N  2  H C 0$     (   ($@ "  "  " (( ( "& $ *% 2 -2 5 E   <B= N2 .   H:%?2 ! 

B 4 ($ $  " 8$      7&  )    P$  ( -"  0  B>@ C <= N$2 )   ,? 2 P 

 O$$ "   %      "Q 7  )    P$  ( 0   0$$ BB>@ >> <>= -"2 +   % "2 , 

C &   ($ (   %  $        )    P$  ( 0   0$$ B> @ ///B <= 1$% 2 12 U&" ?&2 +2 *$2 !2 O&2 #   '2 41  / +  ( $ ($  (  $"  %&  $  0 BC/@ / <= O"2 * *   -"2 +  > +$ ($ 7  " &    " )    P$  ( & [email protected] //B <C= 12 V   K2 P 

> - ( $ ($ @ 0 (  (    )    P$  ( 0   0$$ B/@  < = N$2 )   ,? 2 P   -"   &  "  ($  ( " '    "     )    P$  ( 0   0$$ B>@ CC/ <= +$  2 -   -"2 +  B (( ( '    ( : (       7 P$  ( " -"    "& ( 0 >>@ /// <= '2 H C> U$" L%   ($W   5$ $ $(  ,W  -  2 K$( $  9? R"( (L "&? # 5    9$ />@ C/C/C </= N2 .   H:%?2 ! 

 #   (  &   ($ " $   '    )    P$  ( & B>@   C> <B= 5 ?2 P H   -? :2 # * C> 4 " "  ( $ ($  " " "  $%6  $7  P$  ( " -"    "& ( 0 B/@ B>C <= P"  2 1 O   *?2 H 5 C ,$ " ( "  $%6  $  2  2 $   $   ,$ -"  @ /B <>= 1$% 2 12 , "2 2 52 4 0   NX?2 !   ,$ " (   $"  $ P$  ( -"   #0 / @  B <= 1$% 2 12 ' "2 -2 , "2    52 4 0  > '&   " " "  "@ # 7    $ $& )    P$  ( )   @ / <= 00#N Y+ >

+'Y O  2  B2 ( "@% N +$+>

+' <C= 00#N Y+ B

-Y O  2  B2 ( "@% N +$+B

- 
/ !" ?? " @ #  (   ( $$    )    P$  ( *""  B@ //C @ BBC

 # &   $  & ( "   %& $   %   )    P$  ( 0   0$$ B@  B  = 52 O C 4   $$  2 "  (   : ?  " " P$  ( " -"    "& ( 0 @ C/    +$&   " ?%& (  P$  ( " ) $ ( - C>@ ///C @ //C

195