Mechanical Properties Of Materials (farsi) 2t5c1r

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‫ ‬ ‫ﻣﻘﺪﻣﻪ‪5 .......................................................................................................... .‬‬ ‫ﺳﺮﻓﺼﻞ ﻫﺎي درس ‪ ..........................................................................................‬‬ ‫ﻛﺘﺎب ﻫﺎي ﻣﺮﺟﻊ ‪ ............................................................................................‬‬ ‫‪-1‬ارﺗﺒﺎط ﺳﺎﺧﺘﺎر و ﺧﻮاص ﻣﻮاد ‪ ............................................................................‬‬ ‫‪ -2‬ﺧﻮاص ﻣﻮاد ‪ ..............................................................................................‬‬ ‫‪ -3‬ﺗﺎﺛﻴﺮ ﺳﺎﺧﺘﺎر ﺑﺮ ﺧﻮاص ﻣﻜﺎﻧﻴﻜﻲ ‪ .......................................................................‬‬ ‫‪ -4‬ﺗﺎﺛﻴﺮ ﺑﺎﻧﺪﻫﺎي اﺗﻤﻲ ‪ ......................................................................................‬‬ ‫‪ -5‬ﺗﺎﺛﻴﺮ ﺷﺒﻜﻪ ﻫﺎي ﺑﻠﻮري ‪ .................................................................................‬‬ ‫‪ -6‬ﺗﺎﺛﻴﺮ ﭼﻨﺪ ﺑﻠﻮري و اﻟﻴﺎف ‪ ................................................................................‬‬ ‫‪ -7‬ﺗﺎﺛﻴﺮ ﻓﺎزﻫﺎ و ﺗﻮزﻳﻊ آﻧﻬﺎ ‪ ...............................................................................‬‬ ‫‪ -8‬ﻣﻔﻬﻮم ﺗﻨﺶ و ﻛﺮﻧﺶ ‪ ..................................................................................‬‬ ‫‪ -9‬ﻣﻔﻬﻮم ﻛﺮﻧﺶ ‪ ..........................................................................................‬‬ ‫ﻓﺼﻞ اول ‪16........................................................................................................‬‬ ‫‪ -1‬ﺗﺴﺖ ﻫﺎي ﻣﻜﺎﻧﻴﻜﻲ ‪ ...................................................................................‬‬ ‫‪ -2‬ﺗﺴﺖ ﻛﺸﺶ )‪ ................................................................... (Tension Test‬‬ ‫‪ -3‬ﺗﻌﺮﻳﻒ ﺗﻨﺶ و ﻛﺮﻧﺶ ‪ .................................................................................‬‬ ‫‪ -4‬اﻧﻮاع ﻣﻨﺤﻨﻲ ﻫﺎي ﺗﻨﺶ – ﻛﺮﻧﺶ ‪ ....................................................................‬‬ ‫‪ -1-4‬رﻓﺘﺎر ﻛﺸﺴﺎن‪ :‬ﻧﻮع ‪20 ............................................................................ 1‬‬ ‫‪- 2-4‬رﻓﺘﺎر اﻻﺳﺘﻴﻜﻲ – ﭘﻼﺳﺘﻴﻜﻲ ﻫﻤﮕﻦ ‪ :‬ﻧﻮع ‪22 ................................................ 2‬‬ ‫‪ -1-2-‬ﺳﻄﻮح اﺳﺘﺤﻜﺎم در ﻣﻮاد‪25.......................................................................................................‬‬ ‫‪ -2-2-4‬ﻧﺎﭘﺎﻳﺪاري ﭘﻼﺳﺘﻴﻜﻲ و ﮔﻠﻮﻳﻲ ﺷﺪن‪28....................................................................................‬‬ ‫‪ -3-2-4‬ﻣﻘﺪار ﻛﺮﻧﺶ ﻳﻜﻨﻮاﺧﺖ‪30..........................................................................................................‬‬ ‫‪ -4-2-4‬ﭼﻘﺮﻣﮕﻲ‪ ،‬ﺗﺎﻓﻨﺲ‪34.....................................................................................................................‬‬ ‫‪ -3-4‬رﻓﺘﺎر اﻻﺳﺘﻴﻜﻲ – ﭘﻼﺳﺘﻴﻜﻲ ﻧﺎﻫﻤﮕﻦ‪ :‬ﻧﻮع ‪36 ................................................ 3‬‬ ‫‪ -4-4‬رﻓﺘﺎر اﻻﺳﺘﻴﻜﻲ‪ -‬ﭘﻼﺳﺘﻴﻜﻲ ﻧﺎﻫﻤﮕﻦ ‪ -‬ﭘﻼﺳﺘﻴﻜﻲ ﻫﻤﮕﻦ ‪ :‬ﻧﻮع ‪37 ..........................4‬‬ ‫‪ -5-4‬رﻓﺘﺎر اﻻﺳﺘﻴﻜﻲ – ﭘﻼﺳﺘﻴﻜﻲ ﻧﺎﻫﻤﮕﻦ ‪ :‬ﻧﻮع ‪38 ............................................... 5‬‬ ‫‪ -6-4‬رﻓﺘﺎر ﻛﺸﺸﻲ ﻣﻮاد ﻣﺮﻛﺐ ) ‪39 ............................ (composite materials‬‬ ‫‪ -1-6-4‬آﻧﺎﻟﻴﺰ ﻛﺮﻧﺶ ﺛﺎﺑﺖ در ﻣﻮاد ﻣﺮﻛﺐ ﺑﺎ اﻟﻴﺎف ﺑﻠﻨﺪ‪41.................................................................‬‬ ‫‪ -2-6-4‬ﻧﻤﻮدار ﺗﻨﺶ‪-‬ﻛﺮﻧﺶ ﻣﺎده ﻣﺮﻛﺐ ﺑﺎ اﻟﻴﺎف ﭘﻴﻮﺳﺘﻪ‪42.............................................................‬‬ ‫‪ -5‬آزﻣﺎﻳﺶ ﻓﺸﺎر )‪43 ............................................................(Compression test‬‬ ‫‪ -6‬آزﻣﺎﻳﺶ ﺳﺨﺘﻲ )‪46 ............................................................. ( Hardness Test‬‬ ‫‪ -1-6‬اﻧﻮاع ﺗﺴﺖ ﺳﺨﺘﻲ‪ :‬ﺳﺨﺘﻲ اﻻﺳﺘﻴﻚ و ﺳﺨﺘﻲ ﭘﻼﺳﺘﻴﻚ ‪46 ...................................‬‬ ‫‪2‬‬

‫‪ -2-6‬روش ﻫﺎي اﻧﺪازه ﮔﻴﺮي ﺳﺨﺘﻲ‪46 ................................................................ :‬‬ ‫‪ -3-6‬دﻗﺖ در اﻧﺪازه ﮔﻴﺮي ﻋﺪد ﺳﺨﺘﻲ ‪51 ............................................................‬‬ ‫‪ -7‬ﺗﺴﺖ ﺿﺮﺑﻪ )‪52 ...................................................................... ( Impact Test‬‬ ‫‪ -8‬آزﻣﺎﻳﺶ ﺧﺰش )‪53 ..................................................................... (Creep Test‬‬ ‫‪ -9‬آزﻣﺎﻳﺶ ﺧﺴﺘﮕﻲ )‪57 ................................................................(Fatigue Test‬‬ ‫‪ -10‬آزﻣﺎﻳﺶ ﻣﻘﺎوﻣﺖ ﺳﺎﻳﺸﻲ )‪60 .......................................................... (wear test‬‬ ‫‪ -1-10‬ﺳﺎﻳﺶ ﻣﺎﻟﺸﻲ ) رﻓﺖ و ﺑﺮﮔﺸﺘﻲ ( )‪60 .................................... (sliding wear‬‬ ‫‪ -2-10‬ﺳﺎﻳﺶ ﭘﻴﻦ روي دﻳﺴﻚ ‪60 ............................................... (pin on disk):‬‬ ‫‪ -3-10‬ﺳﺎﻳﺶ رﻓﺘﮕﻲ )‪61 .......................................................... (erosion wear‬‬ ‫ﻓﺼﻞ دوم ‪62 ......................................................................................................‬‬ ‫‪ -1‬ﺧﻮاص ﻛﺸﺴﺎن )‪ ........................................................ (Elastic properties‬‬ ‫‪ - 2‬رﻓﺘﺎر اﺗﻤﻲ ﺗﻐﻴﻴﺮ ﺷﻜﻞ ﻛﺸﺴﺎن ‪65 ..................................................................‬‬ ‫‪ -3‬اﺛﺮ دﻣﺎ و ﻧﺮخ ﻛﺮﻧﺶ روي رﻓﺘﺎر ﻛﺸﺸﻲ ‪69 .............................................................‬‬ ‫‪m‬‬

‫‪ -4‬ﻣﺤﺎﺳﺒﻪ ‪ m‬در راﺑﻄﻪ ‪ .................................................................... σ = Bε o‬‬ ‫‪ - 5‬ﺗﺌﻮري ﻫﺎي ﺷﻜﺴﺖ و ﺗﺴﻠﻴﻢ ‪ ........................................................................‬‬ ‫ﻓﺼﻞ ﺳﻮم‪ :‬ﻣﺒﺎﻧﻲ ﺗﺌﻮري ﻧﺎﺑﺠﺎﻳﻲ ‪77.........................................................................‬‬ ‫‪ -1‬ﻧﻘﺺ ﻫﺎي ﺷﺒﻜﻪ اي ‪ ...................................................................................‬‬ ‫‪ -2‬اﺳﺘﺤﻜﺎم ﺑﻠﻮرﻫﺎي ﻛﺎﻣﻞ ‪ ...............................................................................‬‬ ‫‪ -3‬ﺗﻮﺟﻴﻪ وﺟﻮدي ﻧﻘﺺ ﻫﺎي ﺷﺒﻜﻪ اي‪ :‬ﻧﺎﺑﺠﺎﺋﻲ ﻫﺎ ‪ ....................................................‬‬ ‫‪ -4‬ﻣﻘﺎوﻣﺖ ﺷﺒﻜﻪ در ﺑﺮاﺑﺮ ﺣﺮﻛﺖ ﻧﺎﺑﺠﺎﺋﻲ‪ :‬ﺗﻨﺶ ﭘﻴﺮﻟﺰ)‪ ................................... (Peierls‬‬ ‫‪ -5‬ﻫﻨﺪﺳﻪ ﻧﺎﺑﺠﺎﺋﻲ ﻫﺎ ‪ .....................................................................................‬‬ ‫‪ -6‬ﺣﺮﻛﺖ ﻧﺎﺑﺠﺎﺋﻲ ﻫﺎ ‪ .....................................................................................‬‬ ‫‪ -7‬ﻣﺸﺎﻫﺪه ﻧﺎﺑﺠﺎﺋﻲ ﻫﺎ‪ ................................................................................... :‬‬ ‫‪ -8‬ﺧﻮاص اﻻﺳﺘﻴﻜﻲ ﻧﺎﺑﺠﺎﻳﻲ ﻫﺎ ‪ .........................................................................‬‬ ‫‪ -1-8‬اﻧﺮژي ﻛﺮﻧﺶ اﻻﺳﺘﻴﻜﻲ‪96 ........................................................................ .‬‬ ‫‪ -2-8‬ﺧﺎﺻﻴﺖ اﻻﺳﺘﻴﻜﻲ دﻳﮕﺮ ﻳﻚ ﻧﺎﺑﺠﺎﻳﻲ‪ ،‬ﻛﺸﺶ ﺧﻄﻲ ‪97 .........................................‬‬ ‫‪ -9‬ﻧﺎﺑﺠﺎﻳﻲ ﻫﺎي ﺟﺰﺋﻲ ‪ ...................................................................................‬‬ ‫ ‪ ..................................................................................................................‬‬ ‫‪ -١١‬ﺗﻜﺜﻴﺮ ﻧﺎﺑﺠﺎﻳﻲ‪104..........................................................................................................................................‬‬ ‫‪ -12‬اﺛﺮ ﺑﺎﺷﻴﻨﮕﺮ )‪ ........................................................ (Bauschinger effect‬‬ ‫‪ -13‬اﺛﺮ ﭘﻴﺮ ﻛﺮﻧﺸﻲ )‪ ............................................................... (Strain aging‬‬ ‫ﻓﺼﻞ ﭼﻬﺎرم ﻣﻜﺎﻧﻴﺰم ﻫﺎي ﺗﻐﻴﻴﺮ ﺷﻜﻞ ﭘﻼﺳﺘﻴﻚ در ﺟﺎﻣﺪات ﺑﻠﻮري ‪109 .............................‬‬ ‫‪ -1‬ﻟﻐﺰش ‪ ................................................................................................‬‬ ‫‪ -2‬ﺑﻠﻮرﺷﻨﺎﺳﻲ ﻟﻐﺰش ‪ ...................................................................................‬‬ ‫‪ -3‬ﻫﻨﺪﺳﻪ ﻟﻐﺰش ‪ ........................................................................................‬‬ ‫‪3‬‬

‫‪ -4‬ﺑﺎﻓﺘﻬﺎي ﺑﻠﻮري ) ﺟﻬﺎت ﺗﺮﺟﻴﺤﻲ ﻳﺎ ‪119 ..................................................(Texture‬‬ ‫‪ -5‬ﺗﻐﻴﻴﺮ ﺷﻜﻞ دو ﻗﻠﻮﻳﻲ )‪ – (Twinning‬ﺗﻐﻴﻴﺮ ﺷﻜﻞ ﺗﻮﺳﻂ ﻣﻜﺎﻧﻴﺰم دوﻗﻠﻮﻳﻲ ﺷﺪن ‪120 ........‬‬ ‫‪ -1-5‬ﻣﻘﺎﻳﺴﻪ ﺗﻐﻴﻴﺮ ﺷﻜﻞ ﻫﺎي ﻟﻐﺰش و دوﻗﻠﻮﻳﻲ‪120.........................................................................‬‬ ‫‪ -1-1-5‬ﺗﻔﺎوت ﻫﺎي دوﻗﻠﻮﻳﻲ و ﻟﻐﺰش‪124............................................................................................‬‬ ‫‪-6‬ﻟﻐﺰش ﻣﺮز داﻧﻪ اي و ﺧﺰش ﻧﻔﻮذي ‪126 .................................................................‬‬ ‫ﻓﺼﻞ ﭘﻨﺠﻢ‪129 ...................................................................................................‬‬ ‫ﻣﻜﺎ ﻧﻴﺰم ﻫﺎي اﺳﺘﺤﻜﺎم دﻫﻲ ﺟﺎﻣﺪات ‪129 ....................................................................‬‬ ‫‪-1‬ﻛﺮﻧﺶ ﺳﺨﺘﻲ ﺗﻮﺳﻂ ﻛﺎر ﺳﺮد‪129 ......................................................................‬‬ ‫‪ - 2-1‬ﺑﺎزﻳﺎﺑﻲ وﺗﺒﻠﻮرﻣﺠﺪد ‪134 .........................................................................‬‬ ‫‪ -2‬ﺳﺨﺖ ﮔﺮداﻧﻲ ﻣﺤﻠﻮل ﺟﺎﻣﺪ ‪136 .......................................................................‬‬ ‫‪ -1-2‬ﻋﻮاﻣﻞ ﻣﻮﺛﺮ در اﻓﺰاﻳﺶ اﺳﺘﺤﻜﺎم ﺑﻪ وﺳﻴﻠﻪ ﻣﺤﻠﻮل ﺟﺎﻣﺪ ‪139 ..................................‬‬ ‫‪ -3‬ﺳﺨﺖ ﮔﺮداﻧﻲ رﺳﻮﺑﻲ )ﭘﻴﺮ ﺳﺨﺘﻲ( ‪142 ..............................................................‬‬ ‫‪ -4‬ﺳﺨﺖ ﮔﺮداﻧﻲ رﻳﺰ داﻧﻪ اي ‪146 ..........................................................................‬‬ ‫‪ -5‬ﺳﺨﺖ ﮔﺮداﻧﻲ ﻣﺎرﺗﻨﺰﻳﺘﻲ ‪150 ..........................................................................‬‬ ‫‪ -6‬ﺳﺨﺖ ﮔﺮداﻧﻲ ﺑﺎ ﻣﻮاد ﺗﻘﻮﻳﺖ ﻛﻨﻨﺪه ) ﻣﻮاد ﻣﺮﻛﺐ ( ‪153 ..............................................‬‬ ‫‪ -1- 6‬واﻛﻨﺶ ﻫﺎي ﺷﻴﻤﻴﺎﻳﻲ ﺑﻴﻦ ﻣﺎده ﺗﻘﻮﻳﺖ ﻛﻨﻨﺪه و زﻣﻴﻨﻪ ﻓﻠﺰي ‪155 ..........................‬‬ ‫‪ -2- 6‬اﺳﺘﺤﻜﺎم ﻛﺎﻣﭙﻮزﻳﺖ ﻫﺎي زﻣﻴﻨﻪ ﻓﻠﺰي ﺗﻘﻮﻳﺖ ﺷﺪه ﺑﺎ ذرات ‪155 ..............................‬‬ ‫‪ -3- 6‬اﺳﺘﺤﻜﺎم ﺑﺨﺸﻲ ﻧﺎﺷﻲ از اﻧﺘﻘﺎل ﺑﺎر از زﻣﻴﻨﻪ ﺑﻪ ذرات ﺗﻘﻮﻳﺖ ﻛﻨﻨﺪه ‪156 ....................‬‬

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A "B C5 $# ; &>? (!3 . 7 (!3 B -5E 2 / 'E 82 .D !@ O( >& f = ' .$+' Èa = O( Dk O' ]^ +D6 ' o*' + . >!. ' d' ) )=& . >!. ' nDi )k - 3$+' H* 6S AX+' ' . .% s ^ ]j( . nO& A% 3]M 3i 3 <.X + O' 1O( .' * i _!( c* ' $+ . a+ [+ 1 W_! ";o .DM ',- !K& ! d' 6S 0% ADS 1 ]j( )* DM ! c= 0PV O' ' At . ' $6= :!' .M

3M 0% . v Q N-- B' M 1. ! !K& $%& ' ! d' )* SO' .M A' )'' 9 1 ]j( + wQ . )g'' 7 * . 7D& W6X )'' 10

G / G>2 H I .F ]!E%& . !- ' /

% Dk .

%. 3 % >&

2 & R.' .D1 N^ z, y, x <ja (Triaxial)

% )+ <j E*

1. ! $%& $+' 25 <GQ/

1% $6= )+ ' 6S 31. ! +D6

1 $P . (Uniaxial)

% >& 1

',-

.M fa^ NS G' !!\& 3. ! R5"' K' )GQ/ ]M !!\& 2!Dr51 .DM .M AX+' (e, ε ) 7 * O' Rb !!\& = ) . (σ ) 7D& O' . ! )* $+' & R'. xQ+ 5" . ! )rDk :nQ8 xQ+ . ! $5@/ m O' $+' <V" 7D& : G>2 K5J2 (+5 )τ M 7D& 3M xQ+ 95 . ! )rDk . σ (R ) 5" 7D& M nQ8 .M A! $+ )!.' Rb ) . ! R5"' K' AM ' Rb !!\& H!@8& O' 7 * : G K5J2 . - )g'' `G& 2' O' ^! <!g_= ADS S ]M 3 !- ' / F ^^* . ! $%& A nQ8 xQ+ ' )GQ/ -' :% C5 # G>2 H I )* (M D 5&' 1 O' 1. ! 2') DD* $.8 NS ]8 E' 1. ! 3() :$+' O <j RG& 2' C.C nQ8 > .M ' / RG& A+ <j

9 (!3

11

F= ∫ σdA

()

A

(M !\ Q' M '& ) M $K . $'D σ )rDk .$+' xQ+ P'. . ! σ σ=

F A

(3)

', .

F = σ ∫ dA = σA

( )

M ( n N&! ) 3(Pa) R+4 (SI) EE5' 2! '+' H@!+ 7D& P'. P'. . 2' ]V& .M A' N^ psi )* $+' n yD' 4 NS P'. 4.' H@!+ : $+' ]8 <j 1MPa =145 psi

. 1 Pa =145×10-6 psi

.( ]M )' N^ N'& O <j ' 1 7D& 3 % Dk 1. ! . & E* $P 1% '' τ ( +5 ) M . σ ( R ) 5" 1 )X )Q8 > 7D& .M fa^ <ja )* $+' 2' ID 3 σ yy

j' $;" O'

y $6= 5" )%Xi . y $6= 5" 7D& . $6= R.' $;" ) M y % 5" )%Xi . x $6= M 7D& ID τ xy O' . ()%Xi W. $;" )* DS $+ &%Xi 3( <ja 1% !!\& ) <ja 1% [a' 2' . 5" 1 7D& . Ei' <%Xi ' <%Xi 2' .' =. 6S M 7D& )r!1 <%Xi . )* - !*& .D- (Principal Stress) Ei' 1 7D& ' <%Xi $;" ' ^( 1 7D& . $Vo ''' / <j ' ^^* 1 7D& . $+' τ = 0 Ei' . )%Xi ) M = 7D& )X )* + ID ]M ) )=& .D1 N^ XD ]M A' N^ )%Xi )+ ', 3D@1 zD H1 ]8 <%Xi Nk ' .()%Xi 1 7D&

cG D ) A {'_=' Nk ( b O' .1 71* ) ' 1 7D& )* M )( - I O' W'* 1 RP 3^ k D ', 3' ' / )+!4 B!% > ( ]M A' N^ 12

)! . 2' O' .X! |X&' NS N. A {_= 1 7 k & M Xi z, y, x 1% =. '& ]8@ )X 7M B8( 3B' M 2' τ zy = τ yz , τ zx = τ xz , τ xy = τ yx )* M τ yz , τ xz , τ xy M )X )+ . σ zz , σ yy , σ xx

.M

5" )X )+ ]M )* M )M'

: (!3 [M Xi z % RP ^ k D M dz, dy, dx AO'' ) . >k* cG -' : <VK']

(τ

yx

, dydz)dx = τ xy (dx.dz ) dy → 2 2

).'O H1 )* ) H/ . =

τ yx = τ xy

1% 2! )Q' . <ja

$.8 1 [* <VK' ) .M ]iP z′, y′, x′

1% !!\& O' AX+'

= 1% O B'. (O@ θ (xj

σ x' =

σx +σy

σ y' = τ x′y ′ =

2

σx +σy 2

σ y −σ x 2

+

−

σx −σy 2

σx −σy 2

cos 2θ + τ xy sin 2θ

()

cos 2θ − τ xy sin 2θ

() ()

sin 2θ + τ xy cos 2θ

: M )! )Q' O' M Xi )%Xi NS .τ x′y ′ )* Ei' 1 7D& )V+% ' τ x ' y ' = 0 → tan 2θ =

2τ xy

()

σ x −σ y 13

:M )V+% O <j Ei' 1 7D& |( B'. θ '8 2' N' ' / σ 1 = σ max =

σ 2 = σ min

σx +σ y 2

 σ − σ y +  x  2

2   2  + τ xy   

2  σ x + σ y  σ x − σ y  2  + τ xy  = −  2  2  

1

2

() 1

2

()

. 1' H5_* NS .τ xy )* ' =. H1 ' )%Xi τ max

 σ x − σ y = ±  2 

2    + τ xy 2   

1/ 2

()

H5_* 5" 7D& )* ) Ei' 1 )%Xi ) $V@ ◦ ).'O M 7D& H5_* )%Xi .$+' )( - ' / ('

: G H I .L 25 ]M !!\& 2' . D1 ]M !!\& !- ' /

',- $%& )* /. = '

. ! )* D1 H@= )!.' G' O . - )!.' $P ) = . ! 2M' O' G $+' _!k ";* = ' N@^* W ( !!\& .M A! N@^* >!+?' ( M :,P .$+' O! (strain gauge ^ * }!- D ) w!/ '_' . ]+. ) NS !- AO'' ' . A ) (∆l ) Rb !!\& $V@ .' Q "V 8& $V@ 5"' . ! Rb !!\& N@^* )EP . mm/mm <j ' $+' P'. N. '8 > )* .D +D6 7 * ' lo )!.' Rb 7 * c= )* M H* nQ8 xQ+ 3 Rb 7'_(' )EP 2' .M T'_- in/in N+'4 c # 7 * . 2' 2! $V@ .M (z . y ";o ) 1% $6= XD . D1' XD ez . ey . $Vo ex = ν=

∆l lo

M x $6= . ! )rDk .$+' ' / ( ~? )

− e y − ez = ex ex

()

14

.$+'

',- )I% 1 )GQ/ Rb l )* M ( G ε t = ln

l lo

<j 8!8P 7 *

8!8P 7D& . F Ao +D6 7D& 3 ε 8!8P 7 * 3e +D6 7 * ^! <!g_= ' >!+;4 . >!+?' ( + . ! 1 $@& 7a 6S B'. . F/A .M 0%

ε t = ln

l lo

( )

15

/ () !! $' M2 . :DM O 1 $@& ]M ! 1 $@& $@& – T_ $@& – ) # $@& – 7r!4 $@& – a+ $@& ^( $@& – 7^* $@& .7+ $@& – @ 2!!G& ^( . 7^* 7OS D* ]5%& ' $K

. ! > ' )* A > '&

a+ 7OS %Q+ Hg' >!+;4 ]M !!\& ' A $.8 1-S . - ' ) # . S ',- B' M A > YD(& 2!!G& ' ) # 7OS .S $+ .D* fa^

',- ' <' P )= . NO K' T_ 7OS . !- ' / AX+'

.D* 2!!G& .D& ',- B' M ' A > !X 5" Rb @ 7OS

(Tension Test) GN M2 .4 . !- ' / O' ! d' ^! NS )* $+' ' A+ "V@ $@& 7^* $@& '+' NS 2 (. G . !- W' Èa 1'+' wQ ! 1 7OS "?5G )5 '+' 2' wVb .M AX+' DIN '+' O' 4.' .M ASTM E8-69 G+ M = ' )!6& $.% -' ' .M )+ fa^ G' ' )'+' 1 1 |.

' . lo d = 4 o

' )'+'

1 )5

' lo d Q/ ) Rb $V@ )* M o

. $+' )5 )!.' nQ8 xQ+ Ao )* lo

Ao

= 4.5

Rb !!\& )5 3. ! R5"' O' G .M [a' lo N'DG n= Rb > 3)5 Rb '' )5 > 3 ]M . 71* Ao NS )!.' nQ8 xQ+ N_51 .M l NS Rb . 1 .D* )g'' ' R.' do . lo 8 R.= . 1 N^ ' 7^*

16

GN M2 $ % % –= (!3

GN G5EB # % $>NO J . /&

Q/ (d) mm 12.5 8.75 6.25 4.0 2.50

n= Rb(l) (in)

mm

(0.5) (0.345) (0.25) (0.16) (0.1)

50 35 25 16 10

(in) (2.0) (1.375) (1.0) (0.63) (0.394)

$G+. . -. 3' !+?' d' ) U 56 <";b' N'& 3$@& 1 ]* $VK O' ID ) ..S $+ ( YD(& ) 8k . ^^* 1 W%+' . H!E@& 3!+;4 ]M !!\& )g'' ]j( 2' 7 * – 7D& '5 2Dk 3^^* ',- ' ^^* ( n= + .DM ' <.X ]M !!\& d' ! )* M 1'

<\ )* $+' c+D 3 ' 7 * – 7D& ( 0% O' ]V/ P G / G>2 K5J2 .7 +D6 )( P A @- b ) )* `G& 2!.' .M ` G& 8!8P . +D6 7 * . 7D& : O' D&V" - AX+' F Ao

( )

li − lo lo

()

( σ e )+D6 7D& =. ! / )!.' nQ8 xQ+ = (e)+D6 7 *=Rb !!\& /)!.' Rb =

)I% 1 . ! R5"' K' K Rb = li )!.' Rb = lo 17

: M ` G& <i 2' ) 8!8P 7 * . 7D& 8!8P 7D& = . ! / )I% 1 nQ8 xQ+= 8!8P 7 *= ln

‫طوله در ھر لحظه‬ ‫اوليه‬ ‫طول‬

= ln

F Ai li lo

() ()

:$M N'& $K HP C ( ' )'+' 1 )5 ' ()

Ao lo = Al

. - K Q/ 71* 0" )!.' n= Rb b O' 1 ', Q AO'' ) $'D b ) F ^^* R5"' K' (yD' ) 5!E! Rb ) )5 > -' O' . l / lo = 1.1 Nk . 1' -_ +D6 7D& O' 8!8P 7D& 3M A!^* 5!E! / 8!8P 7D& . B'. ) )=& . A f =

Ao )! Ao / Af = 1.1 H' () )Q' 1. 1

σ e σ t = 1.1

O' $@&V"

$+ <i 2' ) +D6 . 8!8P 6^D& 2! )Q' 3 () . () . ( )
F l     l  = σ e . l l  = σ e .(1 + e Ao  o   o

)

()

: )* M U E* Rb !!\& 2( - I :M # )* ! I ' P A+ Ro > N'D" ) : O' D&V" ]M !!\& 6^ * . 3+D6 7 * 9+' .M ]!S )EP . 2! .

(l2 − l1 ) / l1

(l1 − lo ) / lo

n5= 3 : b O' .S 5 $+ ) (l2 − lo ) / lo DG g6 7 *3 {_= . 2' N * n5= :2' D .S $+ ) $+ )! 8!8P 6^ * N * l ln  1  l0

 l  + ln  2  l1 

 l  = ln  2   l0

  = ε t 

4 Q NO. ) $%& 5!+ / ' Q/ (yD' ) 5!+ Rb ) )E! > )V+% ' O ' 3 71* + / ) Q/ -' . !- ' / (4 ) 2&! :!D* : )E! g6 Rb (a : H' ( )G O' ) A0l0 = Af l f Nk A lf =  0  Af 

 l0 = π (0.25)2 / π (0.22 )2 × 25 ⇒ l f = 32.3  4 4 

5!+ : )E! 2' 8!8P 7 * . 7D& (b

σt =

F 4500 = Af π 2.2 × 10 − 3 4

ε t = ln

(

lf l0

= ln

)

2

= 1185MPa (172000 psi )

32.3 = 0.256 ‫يا‬ 25

25.6%

+D6 7 * . 7D& (c F 4500 = = 917 MPa A0 π 2.5 ×10 −3 2 4 l f − l0 32.3 − 25 29.2% e= = = 0.292 l0 25

σe =

(

)

19

G – G>2 $' >R> S .9 :,P _! Rb !!\& 3. ! :,P )* $+' ( N@^* ( : S .MN # # . -9 . - )!.' G' ) )GQ/ . M : - N! !+?' D( ' )G > )E!+ # . . ! /. :M )M A. O <i ) ( ))G ( )

σ = Ee

7D& = σ = F / A

: )* =

7 * = e = x / l ()!@!+?' R. ‚ R. ) c+D& $K = E c+D 6^ * . 1 7D& )*D* N! ' A O' Q' M – s1 N/ W ) ( ) )G .M )! ]M AM A' N^ 7 * – 7D& '5 . .$+' AM A' N^ R.= Èa' ' ‚ R. 8 1. ! W%+' 6&.X& ) U E h_ 6&.X& 2' Ei' $E" .M . 65&' 6 2! 5&' 2!

S G.G>2 # # . D(!3

20

&> !T .4 /& ' !+ )= A

<'_E(

E(GPa)

G(GPa)

v

Aluminum

W!D!S

70.3

26.1

0.345

Cium

W!*

49.9

19.2

0.300

Chromium

W *

279.1

115.4

0.210

Copper

Y

129.8

43.3

0.343

Gold

;b

78.0

27.0

0.44

Iron

21S

211.4

81.6

0.293

H_!D

44.7

17.3

0.291

]!

199.5

76.0

0.312

W!!

104.9

37.5

0.397

A 8

82.7

30.3

0.367

Tantalum

W&

185.7

69.2

0.342

Titanium

W!!&

115.7

43.8

0.321

Tungsten

2@D&

411.0

160.6

0.280

Vanadium

W'.

127.6

46.7

0.365

Magnesium Nickel Niobium Silver

' pG ' !+ )= A

_E( !~ '

E(GPa)

G(GPa)

v

W!D!S !@*' ≈ 415

-

95' ≈ 965 )^!M 80.1

-

-

31.5

0.27

-

-

-

-

2E!&' E4 0.4-1.3

-

-

R@ * ]! E4 2.4-3.4

-

-

Polypropylene

2!E!4. 4 E4 1.1-1.6

-

-

Polystyrene

2 !+' E4 2.7-4.2

-

-

Aluminum Oxide(fully dense) Diamond Glass(heavy flint)

NE 1.2-2.9

Nylon 66 Polycarbonate

<D * E4 2.4

Polyethylene(high density) Poly methyl methacrylate

21

_&'* 73.1 N!E!+ !* ≈ 470 534.4 2@D& !*

Quartz(fused) Silicon carbide Tungsten carbide

31.2

0.170

-

-

219.0

0.22

.$+' AM A' v M G ]j( 5&' 2! 1. ! W%+' ) )=& ' N@^* (

(Resiliency) VW2# ;U - . .9 [,= !+?' ',- B' M $%& '& )* $+' ' '8 O' +!8 A "&' R.

O )!P O' "&' R. 3 ` G& 2' ) D .D* 'OS ' S ]* b ) 1 2M' . D* :M !- AO'' ]M D%D 1 2

"&' R. = R = σ max ε max

( ) !+?' B' M ' o*'P 7D& = σ max : )* = !+?' 7 * P = ε max

R=

2 σ max

( )

2E

: ( ) )G O'

? ' [,= !+?' $5@/ B8( )*M )M' m!P' A > ) +D6 v b > -' W%+' )* 1' NS M [a' )* V+D A 3 ( ! D( > D ) S * ) .M )M' D!g4 ‚ R. ' ? H!E@&

4 S : YZ' !XO – !T # #- 4.9 cE~' 7 * – 7D& '5 3 M )M' ' ,4 $^- – Hg' ]M !!\& '& A > /. >k* 6^ * ' )^ !+?' )!P _! D' .S L '5 ]M ' H!D!

22

!+;4 ]M !!\& ' A ^'_(' $.8 ! )* + o*'P 7D& > ) '5 .$+' :. G [ G W ) )* DS ( M ^!

.YZ' CXO (!3 ]2 < ' % CT # # \ 4 S # # .F (!3 $+' 25 3 o*'P & H!E@& L. M O'3 ( True)G/'. 7 * – 7D& D%D O' ' )!P : - N! (Hollomon)21 ) [@D & ' )Q' σ = Kε n

( ) 8!8P 7D& = σ 8!8P !+;4 7 * = ε a+ * a+ 7 * c # = n ' 8!8P 7 * 8!8P 7D& ' 3A $K = K

.D* N! ' ^! ]M !!\& ' $.8 ' A '& 3 na+ 7 * c # '8 )* M Xi 1 75 ' RS A' !+?' ( )* M ' $+' 25 n 3$6 'G& ' a+ 7 * c # O' a' 8 .1 75 ' RS A' !+;4 A > <!E5" ) n 8 )* !D* )=& ) .' AM A' ( ) R.= +D6

_E(

1!S O'

AM +* $P . -_ AM ]!S B' M ' ' E* b ) 3D+@P ! & $+ 5 ,~*

. 8!8P 7 * c@P 8!8P 7D& H+ n 8 .(Dk*

3 ]M .S $+ n c!M $+' B > 3M x!%i wEQ b ) ( ) )G -' .DS 23

$. ]/ )8QD )+ )* - )=& .1 N^ ' 8!8P 7 * . 7D& 5 '5 ' n '8 3N' c!M )* >!+;4 )8QD "6 . >!+;4 >!+?' O 3>!+?' )8QD 3D@1 .1 < &>? [ G 5^ .7 /& < Material N_ ‚O ?( Stainless steel

[ # 5^ Strain-Hardening Coefficient, n 0.45-0.55

} Brass Y Copper

0.35-0.4

W!D!S Aluminum 21S Iron

0.15-0.25

0.3-0.35 0.05-0.15

(

__ H > B) n YJ2 / G – G>2 5#Z G5 – L (!3 . 7'_(' 3 E )VM D!G 1 g s %& 71* . W%+' xQ+ 71* n .M 1' )X- ^! 1 g ]j( A $!i 2'

24

# H!R ` . .4.9 .DD* ` G& W%+' vQ+ 2Dk )* $+' R5G ' ^^* ( 2!!G& ID ) ]5" ( ) )G wQ $+' c+D 7 * 7D& NS O )* $+' ^D& '8 3>2 &a : K $^- ]* b ) ]M !!\& 6^ * NS O )* $+' ^D& '8 3!T &a : , . . ,4

!~ ' !+?' ( '& _E( > ' . ' "++' $!5* . 2' 3+D6 ' ^! .1 N^ ' Q )Q' H* 6^ * . 1 75 ' & )Q' > ( )G ) b ' U .M &"V 8& !+?' P .M N^ ' ,4 $^- !+;4 ]M !!\& L. M )* ^D& '8 3 (σ y ) d;M2 H!R : c .M 2!!G& a+ ) $!5* 2' .1 '+' $@& T. 3H!E@& W%+' 2!!G&

' 51 RV/ ]/ T. > ) N!+

'

:S $+ O T. ) H!E@& W%+' '8 .$+' AM ( G ( ASTME8-69 ) .$+' AM A' N^ ]M )* )rS D ) +D6 7 * – 7D& '5 2!!G& – ( '8 > ) {'V O' )* A!^* 7 * – 7D& '5 !+?' $5@/ O' B > ( ( %/ / RV/ ]/ 8 ) M )M' )Ei( fa^ )Q8 ) M 2!G 7 * – 7D& '5 . O' B nb8& ]% H!E@& W%+' (

$@(S %/ H!E@& W%+' "?5G ' '8 2' 3M )X- ? )* Q51 (A .D 3D* ]5%& '! A )* +D6 7D& o*' P (B )Q8 ) 3 (σ u ) NN H!R : 3 - ` G& )!.' nQ8 xQ+ $P@ H!@8& o*' P . ! 2 : < .M ]iP 25

.' AM .S - . R.'= +D6 ' O' 'G& ' ^^* d' O' ' )"5 d' 75 . ^(

1 $@& ', .$+' ]^ 7^* $@& W' 1 >!' +

'

.M !- AO'' 6S %+'

-f2 (R # NN d;M2 H!R .&> G – G>2 >R> _ (!3 . 3 K5J2 j &1 E %;k %_/4 $E g / G – G>2 >R> [> &> $ NN - 9 /& Material A

Treatment <!E5"

1015

As-rolled =

1340 1340 1340 4340 4340 4340 301

= Q+T(205◦c) Q+T(425◦c) Q+T(650◦c) Q+T(205◦c) Q+T(425◦c) Q+T(650◦c) Annealed

Yield Tensile Elongation Reduction strength strength in 5-cm in Area (MPa) (MPa) gage(%) (1/28cm W%+' W%+' Rb O' diameter) 71* H!E@& ^^*

+ nQ8 xQ+ % % Steel Alloys $T $'"B 315 420 39 61 415 725 20 40 585

965

12

17

1590 1150 620 1675 1365 855 275

1810 1260 800 1875 1470 965 725

11 14 22 10 10 19 55

35 51 66 38 44 60 -

26

304 310 316 403 410 431 AFC-77

plate = = = Annealed bar = = Variable

60 50 55 35 35 20 10-26

32-74

PH 15-7Mo

=

2-35

-

Ti-5Al-2/5Sn Ti-5Al-1Mo1V Ti-6Al-4V Ti-13v -11 Cr -3Al

Annealed Duplex annealed Annealed Solution+age

240 565 310 655 250 565 275 515 275 515 655 860 5608351605 2140 3808951450 1515 Titanium Alloys 2 $'"B 805 950

860 1000

16 15

40 28

925 1205

995 1275

14 8

30 -

9-12

-

4-9

-

4-6

-

Magnesium Alloys d56> $'"B AZ31B

ZK60A

103220 125 Extruded bar 185290195 295 Artificially 215295aged 260 315 Aluminum Alloys H > B $'"B

-T31, -T351

250

360

17

-T3

345

485

18

-T6, -T651

395

475

10

-T6, -T651

415

485

13

-T4, -T451

145

240

23

-T73

475

530

11

-T6

505

570

11

-T73

415

505

11

-T6

540

605

11

AZ80A

Annealed

Plastics ' CXO 27

ABS Acetal poly(tetrafluorethylene) poly(vinylidene floride) Nylon 66 Polycarbonate Polyethylene Polystyrene Polysulfone

Medium impact Homopolymer -

-

46

6-14

-

-

69 14-48

25-75 100-450

-

-

-

35-48

100-300

-

Low density -

-

59-83 55-69 7-21 41-54

60-300 130 50-800 1.5-2.4

-

-

-

-

50-1000

-

[> $! !R .5 /&

<

W%+'

W%+'

W%+'

‚ R.

^(

^^*

^5

[GPa( 10 4 psi)]

[MPa(ksi)] [MPa(ksi)] [MPa(ksi)] Alumina(85%dense)

1620(235)

125(18)

295(42.5)

220(32)

Alumina(99/8%dense)

2760(400)

205(30)

345(60)

385(56)

Alumina silicate

275(40)

17(2.5)

62(9)

55(8)

Transformation

1760(255)

350(51)

635(92)

200(29)

1860(270)

-

690(100)

205(30)

138(20)

24(3.5)

69(10)

115(17)

3450(500)

-

860(125)

-

toughened zirconia Partially stabilized zirconia+9%MgO Cast Si3N4 Hot-Pressed Si3N4

&3 5 ;l / !XO $# &5O .4.4.9 ' ++' 6&.X& 37^* $@& O' AS $+ 8!8P . +D6 7 * – 7D& 1 D%D +D6 7D& )* P .' AM A' N^ () ]M )* Q51 3DD* MS 71* $@M & YZ+ .( ]M B)Q8) + o*'P ) o*'P . ! 28

U +D6 D%D :' %' .D* Gi $@M & )+!4 b ) 8!8P 7D& 3 W%+' NS )* P . (&3 m5 ;l <&5&O)G# !+;4 N;!+ L. M ) $+' .$+' AM ` G& (σ u ) ^^* > ) 7D& /. . ! I ' O n/. c!& & )I% > ' 3L# 2' s ' 1' |X&' Ô' )5 $5@/ 2 X!G# !+;4 ]M !!\& 3+ ' % '8 0" ^^*

',- $%& G# Rb O' 2' 3n= Rb '' = > .('

= 1 O' &? )Q8 2' 8!8P G# 7D& 2' D .M xQ+ 71*

_* 5 <M ) )!P 2' (#' ]M !!\& W5& 3)! .M n= Rb '' 2' 3RP 6 3 ' ^! ' .M RS A' !+;4 A P 2!Dk > .M c a& ' ' S )! . D* $a+ 7 * ' A 3G# !+;4 ]M !!\&

^! !+;4 ]M !!\& !&

' 5"' 7D& 3)EP 2' .D* .8

$a+ 7 * A A. D' . 7'_(' n= Rb '' `!G# )Q8 2!. $'D b ) n= Rb 34+. * 9!8 > . )'' DS ( . M )*.S ) ) . 71* $'D b ) _! nQ8 xQ+ $P@ . M A!^* )* + ' )Q8 3. ! 7'_(' (.M $K HP DS ( > !+;4 ]M !!\& ( ]M B )Q8 ) . 2! O' A a+ 7 * $!( z S 7D& ' O 3 - _* 5 E- )!P ^! !+;4 ]M !!\& 3 o*'P . ! 2' . ! :,P )! 5"' . ! -' P . 7'_(' 3xQ+ 71* )+!4 b ) . - A4 E- )!P N6- 3 71* E- )!P O' m Ô' )5 !+?' NM E- O' G )5 . ._ . ! 3 $+' AM ` G& Ao )4 +D6 7D& Nk nQ8 xQ+ 71* )E!+ 3._ . ! 3 )@8 .M 1' ._ 7D& > )V+% 0"

!!\& .. ? NM E- O' G P 8!8P 7D& )* b ) - N' V= ' )I% NS O' G . )5 Rb $'D <j E- )Q8 & H!E@& )Q8 O' >!+;4 ]M 29

G )+ 7D& c= )* M (E- ) G# <j . $'D !~ <j . -

>!5 G # & .7.4.9 7 * )* B & A $5@/ .$+' $5@/ . ]M >+;4 ]M !!\& 3 ]M ) )=& _* 5 ^! . $'D !~ 7 * )* C & B $5@/ . $+' )5 Rb $'D .$+' E- )8QD H1. ]* 7 * H1 11- 2!88% 3^^* )GQ/ Rb '' Rb O' !!\& ) )@ !*& .DD* T'_- ' 3 G# NM E- O' ]V/ ) $+' U )* 3$'D 7 * 3M H* n= Rb /. .$M' 1' @ $@& )E! n= Rb ) ]* 7 * )* * 7 * 8 3)! .',- ^! !K& NM E- DS ( 0% Rb O' ) ).M T'_- ]* 7 * H1 . )GQ/ G' H1 ]! 2' ) .$( 1' 7'_(' ]* (M )G=' R.=

$'D Rb O' '8 )* $+' [EQ 3+D6 )GQ/ > A AX+' I )Q8 O' 7 * '8 )* ' N^ N'& .+ o*'P ) ' G# NM E- L. M O' ]V/ .' UV&' a+ 7 * c # '8 $'D F = σ .A dF = σdA + Adσ dF = o

( )

:(' |X&' o*'P . ! NM E- )D' .S dσ

dA A

: )!

Adl + ldA = 0

)Q' O'

− dA dl = A l

σ

=−

30

: M )! B'. 2' c!* & O' 3 σ=

dl = dε Nk l

dσ dε

( )

)Q' D_= . ( ) 21 )Q' O' AX+' Kε n = Knε n −1

: 2' D ( )

n=ε

a+ 7 * c # " I O' E- '4 )Q8 8!8P !+;4 7 * ', .$+' ' '5 . ' .$+' f!a^& ]/ P' +D6 σ − ε D%D B E- )Q8 .DD* 2!!G& ' S ]V/ `G& O' AX+' )* $+' fa^ 8!8P „a^ ' (. ! H5_* ) E- )Q8 8!8P 7D& 3 σtu N'& . )Q' O' . D@1 .@ dσ dε DG '5 c!M . σ )!g= 3 σ − ε 8!8P '5 2M' .5 8!8P σ − ε D%D NM E- )Q8 3($+' n 2@' ) O! ) M ε = n )' )Q8 .DD… fa^ ' =. E- )Q8 O' G . ]V/ 8!8P . +D6 7 * . 7D& 2! _! B'. . D@1 |i NM E- )Q8 & B'. 2' O' pG .' :M N! i <j )… * ` G& O <j . r ' nQ8 xQ+ 71* N'& r=

Ao − A Ao

( )

:M ]iP O )Q' . 3 1 7 * `G& . . )Q' O' AX+' e=

r . 1− r

ε = ln

1 1− r

(†‡)

.M AX+' ' N' ]M 0% B'. 2' O'

31

M AX+' ε = ln

Ao )Q' O' $@M )Q8 7 * dja . 3E- )Q8 O' G Af

!!\& ' AD5 . $+' G# NM E- O' G Rb !!\& Nk ε = ln

lf O' ) . lo

$@M )Q8 )GQ/ G' Af . lf ). 7 * )V+% ' V . M 5 Rb .(D@1 6 .( ]M ) ' =. E- _ % )+ 7D& $P 3E- 6^ * A.;" A 7D& <M ) A .DS = N+'4 K' O' (σ t ) # " . (σ r ) "GM 6^D& .D* ]G& ' h_ G# 6b O' & M A!^* N. ) $+' ]5 E- )!P 3 ($+' ^! NS A ) D* ) & ' 5* E! 6^D& 3E- )8QD . A Nk ) ' E- NM w!5" )* ^^* 6^D& N * '. 1 CV8' 2!Dk ' P' 2' . * D1' $.8 3O'' !&

.% ' )* AM E- )!P N! % )+ ^^* 7D& nO&

(!3 .D* ]5" E- )!P O ]M !!\& N *

<i ) )( ]!E8& )!P A ]M !!\& O' & D* ]5" % )+ 7D& N'! )! 7'_(' % 7D& 3!+;4 ]M !!\& )'' ' .S ]5" ) !-E= !+;4 32

R'.O L. M 0" E- )!P N! % )+ ^^* 7D& B' M 3' % ' )Q8 H1 . A * M 3AS = _ 1 A XP . AM RG( $@M 1 W_! 3 - nQ8 xQ+ )* DD* !& 5"' 7D& % 5" @ s & > . A * b. a ' )%Xi '' M DS ( YZ+ 6 $@M .D1 71* ' K ) *.* $@M xQ+ 3]*DS ( 2' .(' |X&' 7D& % ) $V@ )= ).'O ' A ' ' )!P 3'' ..S = ' ( ) ]M AM A' N^ (f/[ .H A' )!P 3 - !& W'S . '4 s & M ((!' )8QD W ) ) )5 B+. . !- ]M 6 $@M :i M 1 >k* &+ ! )* M g6!-S + > ]M (!' )8QD ""GM .M 1 RX O' AM AS 7^* $@&

(a) : !M N. ^^* )E! > f/[ .H )5 3W $@M 1z . 4 (!3 .b. a $5@/ (b)3 W= $5@/

33

(b) $@M 1z Yˆ" (a) : M )V . "GM 3(!' wbD $@M 1z . 7 (!3 .)8QD j& 75

(A> 2 ) Z? .9.4.9 ( M

!- AO''

' ) $@M ' 7.8 3A H6 $!i

' ) 8k A )!P D* [,= 5*

' )* H!g- & '

' A .M

' 3!M N. ^^* )E! > ' .$M' 1' m!P' O ' 8 ) $@M :M AO 9P 7 * – 7D& D%D O )!P O' $@M εf

' / HP = ∫o σdε 34

( )

) 3S $+ ]M !!\& W%+' O' EQ c!* & o*'P 8k 32' D O ' [,= ) )* ( !5 D )O ,4 ]M B8( ) . ()^!M D )O W%+' .( ]M ) ' m!P' $@M ' ‫الف‬

‫ب‬

!+;4 N;!+ H%@ A ' A 37 * – 7D& 1'5(K – ]M . W%+' O' )D!6 c!* & A C . O ,4 :QG' . W%+' H* A B 3( &)H* ]M A' 51 & . W A 7 *7D& Š1 '5 (, \ o*'P 8k ' ,4 :QG' .$@M )5

35

7 S :YZ' !XO – !T # # .7.9

+ > )* * 1' !& ' ^ * – 7D& '5 37OS )5 > 3</.' 1() ]M AM A' N^ 3 ( 2!Dk > .DS = N@^* A.% O' G )' ' )' 7 * – 7D& ( .M A 251 $'D !~ ]M !!\& ! (H)H*' R-'_1 <'_E( ) /. .(' |X&' <.X B' M . ]/'P $%& '' T_\ O' V!* & )* ' ]5& 3M '. . ! n!+. "V@ A.% $G!Vb ) .D ]M !!\& !+;4 <i ) '_ wbD NM E/. . T_\ <%Xi .($+' AM 0% ADS Rj( <!g_= <'_E( !+;4 ]M !!\& <i ) 2 * ]M BCC 21S 1!S 2!Dr51 ' )' 7 * – 7D& 1'5 .$+' AM A 3Al w!/ = 6E% . = RE% U )* M (Portevin-Le chatelier))!E&M 2&4 K' ) U |( ( ' )VM 1 g (solute)AM ]P H&' (vacancy) 1= 6^D*'. ) .M

!+;4 N;!+ A' 51 ) !+?' ( ! 7 *– 7D& ( W+ L . : (!3 AM ]P H&' – !K& E/ . ‹!+;4 ]M !!\& '& ( 2' .251 !~ X! |X&'

36

9 S : YZ' !XO . YZ' !XO .!T # # .9.9 )5 )D' O' G 3D1S !~ 1!S O' 'G& . BCC 21S )4 1!S O' E! N6- ( ]M ) M ',- 3/( H!E@& )Q8 W ) 3 A )Q8 & !+?' YZ+ A )* $+' AM A1^ .(D!g4 H!E@& )Q8 ) D* $(' B )Q8 ) 7D& .(Luder) 3 ( ]M ) .S = ' G# ]M !!\& .M T'_- D!g4 H!E@& )Q8 '8 ""'.P /( H!E@& .$+' AM A _! $?'* . ' pG D!4 . ? H!E@& (

]M !!\& . )!.' >!+?' wbD 2! > 251 !~ ]M !!\& )!P . = (!3 D!g4 H!E@& )Q8 ) . A(' |X&' A g" O' G . D* $(' B

A+ D * ?( ÔS )5 AM ]!^& ( ) ]M !!\& 1 . D (!3 37

: S : YZ' !XO – !T # # .:.9 )!P .M A @ *

1 5!E4 O'

'G& ]M !!\& $+' 25 HD4 L (

(a ]M ) 3$+' NS c/G $(' . /( H!E@& )Q8 '' W6k L ( )^ . )!.' $(' 3L# 2' .(' |X&' H!E@& 3 5!E4 )!.' @ * + 2@M 3'' . - 0" ' ]M !!\& 2 ^! )!P )5 E* NM !X+ b ) 1 +?' 1 7 * ^! .DM (>!+? ) 1 +?' 31 >!+;4 O' L 2M' O' G K ]M !!\& y!1 32' D .D@1 Q !~ ' N@^* . ,4 $^- ]* NM @ ) $+' U '' >!+? )!@!+?' .. ( b ]M ) 1'a / 3 3 g_= AM A!^* 6&i ) NM mG . }* 1 $!G/ O' ]M 5!E4 1 A !O . ! 7'_(' .$+' 2!g4 >!+?' R. )!P $+' h_ !+?' ]M !!\& '8 )! )! . - ' A !O N. $D'* 1 $.8 c= 1 A !O NM @ O' G .(b]M )M h_ 1 7 * A a+ n + 7'_(' 0" 1 !O NM $+' $P )* D1 N^ . - )XMS $P ) A. 1 !O 3M )M' /. .M A' x!= & H1 . H1

. 3 5 M5 $';O # "T J : S G – G>2 # # (a) F (!3 NO+ . )!.' + M4 H1 O' 2! $/ .D* N! ' ^* + 3D%D ]/'P )Q8 )r!1 ]M >!+? )!@!+?' (b) . ' $6= ";* H%@ A > <i ) A. 2( . - )!.' )Q8 ) 2M' O' G D%D .M 5 $(' 38

(composite materials ) NN # # .=.9 1 7D& D'&

(A) & ' H%@ ' )* H!D! 3 () ]M ) )G='

(C) ,4 ]M 3W ' .' .%

,4 ]M . DD* ]5%& $@M O' ]V/ ' -_

.' 5* ]5%& $!( z ' D1 N^ 6=& ]/ !+;4 N;!+ ' 3D1 N^ ' gDo+' ,4 ]M . W%+' . 1 5* "V@ G!Vb ' 3)k 6!+;4 3Ro

' .D5 )g'' N_51 ' 1 -. 2' D'&

G c* '

3' g? W%+' )* )^!M . !'S :!' ' 6=& ]/ ,4 ]M )* D!G +D6 )M' O W%+' H1 . (*

,4 ]M H1 )* M !& V* ' & M $8&

.DD* $/ <.X '_=' AX+' ' _E( 1!S ' 2!Dk .( R.= )DM NS O( Dk UEa AD1 ]!^& '_=' d' ! c* A > 7 * – 7D& ( . . L O' bEa D ) D* MS ' V* ( $+' 25 7 * – 7D& D%D .M

,4 ]M ' ' MPa O' 7! ^^… W%+' )*

' )^!M :!' 3Ro

' .(

) NE 3]8 .D1 N^ ' L 7 * – 7D& ( 3 .S H1' ( .% ) ^^* W%+' 31 N^ ' L )( ]G& ( ( +D6 >!+;4 & O' ' )5 % /. )* H!D! () R.= O' . % O' 7! '8 ) b O' . MPA '8 ) ' . a+ . W%+' 3 - )(#' NE )D!O ) ' )^!M :!' O' 5P . 71* )V& ,4 ]M )!P 3D 7'_(' c!& &

39

[ <&3 o;M / NN .= /& <

Nylon 66+25v/o Epoxy resin+60v/o Polyester resin+50 v/o aligned glass fibers Polyester resin+20 v/o random glass fibers Epoxy+ 50v/o Boron fibers Epoxy + 72 v/o S- glass 2024Al+25 v/o SiC

p5 /& [GPa(106psi)

NN HR [GPa(ksi)]

% f 5E

14(2)

0.2(29)

2.2

220(32) 38(5.5)

1.4(200) 0.75(110)

0.8 1.8

8.5(1.2)

0.11(16)

2

200(29.2)

1.4(200)

-

60.7 (8.8)

1.3(187)

-

124-162(1825)

0.53-0.64(77-93)

≤1

415-485(6070) 125(18) 380(55) 390(57) 250(36) 76(11) 85(12) 485(70) 380(55)

7.0-21.0(10003000) 2.8-3.6(400-520) 3.4(500) 2.2(320) 2.7(390) 1.4-2.5(200-360) 4.5(650) 20.7(3000) 1.4(200)

Reinforcement 5 2 \<&>> Al2O3 whiskers Aramid (Kevlar 49) Boron Carbon fiber, Type I Carbon fiber, Type II E glass S glass SiC whiskers Si3N4 whiskers

40

2-3 0.5 1.0 2-3 -

&>; @ # 8 G 6B -. .=.9 V@ 5P 1 @* 3ADD* $8& 1O( . )D!O d' ) c* A > 7 * – 7D& ( .' @ 7D& R5"' $6= ) $V@ :!' $6= . :!' wEQ Rb 36S Rb DG ) ' )+!4 :!' )D' C ( ' AM $8& A > W%+' _!S ''

-' .^! )'' D@1 5"' 7D& O' . ' $'D W%+' 3(' AM A!^* )5 ]* A ) 5"' 3DD* ( !+?' <i ) O( . 1 . DM A!V@k )D!O ) ";* :!' :M 1' nO& O <i ) :!' 1% $6= c* Pc=Pf+Pm

( ) : )* = : c!& & ) )D!O . :!' 3c* A )E!+ AM ]5%& = Pc,f,m :2' D . DM )^ O( . 6^ * 3( -O+ )wQ& N … A.S ' (

)

εc = εm = ε f

: )* 1 )! $K 7 * B' M 3(

) )G O' ( )

σ c Ac = σ f A f + σ m Am

: )* = .c!& & ) )D!O . :!' 3c* A W%+' = σ c , f ,m .c!& & ) )D!O . :!' 3c* A nQ8 xQ+ $P@ = Ac , f ,m :$+' RG (V f ,m ) O( 5P @* )+!4 O( > %Q+ @* Nk Af Ac

= Vf

,

Am = Vm Ac

( ) :2' D ( )

σ c = σ f V f + σ mVm = σ f V f + σ m (1 − V f )

s1 N/ O' ( )

σ c = E f ε f V f + E m ε mVm 41

:. ( )

Ec = E f V f + EmVm

: 2!Dr51 Pf Pm

=

E f ε f Vf Ef Vf . . . = E m ε m V m E m Vm

( )

NS 5P 1 @* . ‚ 6. ) c* A )D!O . :!' ) AM nO& 3 ( ) )G O' ‚ 6. $V@ /. DD* ]5%& ' 5"' ^! :!' 32' D .' @ O( . .M h_ O( . 5P 1 @* . :!' – )D!O P O' 5"' 7D& )* DDM /. . ' $'D <%+' :!' )D' C ( !+?' 7 * 7D& '5 . Èa wbD +

>!+?' P )D!O . :!' – I )8QD $+' A!+ σ mu ) ' AM >!+;4 )8QD '. )D!O . >!+?' P :!' – II )8QD .$+' >!+;4 )8QD )D!O . AM )@M :!' – III )8QD

42

W%+' 7D& o*'P σ mu . σ uf . < σ − ε # # q[N %> % . L (!3 )D!O H!E@& 7D& σ my . (DDˆ^)D+ σ uf ) :!' /. )D!O 7D& σ m' 3)D!O . :!'

(Compression test) #N G5EB.: 6S xQ+ . >k* !@ 1 s & =. ba 2' .DDM 7^* "V~ 3 & ' ^^* W%+' . D' O' .M 9 .O $@M ) D . AM O ^^* B' M )* M . ^^* W%+' ( ) ]M .$+' ^! 6S $.8 ^( . ! $%& )!P .$+' H* 6S .1 N^ ' 2 . @* Nk 3 & A . ^(

.Y / $M &? \2 < / #N / GN HR .4_ (3 43

NM E- A4 ', .M A._(' NS nQ8 xQ+ ) ' AM & H* )5 Rb 3^( 7OS ' <;^ . 1 $.% ^( 7OS W . N@ ' ( b O' ' .1 5 Œ )5 95& xQ+ sQi' ' $EG 2' . 1'a ND!5b' ]/ ^( $@& <";b' )* 5 $* P sQi' $EG A+ )5 95& 6' . .M A+ >( 7OS $%& G )+ 1 7D& A )8QD 2' .M ' (Dead Zone) A )8QD . . DD* ) )!P 2' . $+'

% >& 1 7D& 36' . O' &. wbD )!P 3S =

( )]ˆM .M P(Barreling) NM ' )^ A4 . A' ]ˆM !!\& P'

#N M2 # &3 $ %N <&5&O / < %> .4 (3 )GQ/ ]* . ',- !K& H1 . )GQ/ + . O' A wbD 3M >k* 1 )5 Rb -' '& 6 'OS )8QD 3M 5* 'OS )8QD ) A )8QD $V@ 8k 1 .$+' & $a+ ..S $+ "5!8@ ^( $@& N'& 5 ' σ − ε D%D . D' O' .D* $* P )+ H@= > O' ' )'+' )5 'G& -' )* M A1^ <i 2' ) sQi' =. N@ . ! $%& 6S . M hn , ......, h2 , h1 ' . !\ 6S LX&' ' M d o 6S )51 Q/ )* 2' ) 2'. 1 N^ ^! 7 * 3 &DE )5 .D1 5 N^ N@ 7 * 3 !- ' / F 5* 6' . sQi' !K& . $+' H* NS 'OS )8QD ) A )8QD $V@ )* $+' $E" .M _! (Buckling) 75* N' M O E! )5 Rb -' ( b O' .M 6D^!4 T. O' N'& 3.S $+ ' σ − ε '5 . A * K' ' sQi' N'_! )D' ' 1 Rb )5 + Dk 3T. 2' . ( ]ˆM ) * AX+' (Cook-Lark) s?s*

44

.... F3 , F2 , F1 $K 1. ! ',- $%& 1 )5 O' + 1 . AM )!6& N@ Q/ . !\ . - H+ (r) 6S nQ8 xQ+ !!\& i . d h '5 3 + 1 ' . !- ' / .

r#T – r 2 s/# .44 (3 O' .$+' AM :,P sQi' K' )* * C ( N'& 3( 5* d h ) M DE !@ )GQ/ Rb -' d h

AS $+ 1'5 -' . 2' O' .M w8% → o . h → ∞ {'O C ( 2' e& d h

' sQi' N. B' M r % 1 ]% 3M N. → o $5@ ? ]M 1 )Q' O' YZ+ . r ∗ D* fa^ 1 − r∗ F

K' )* 5 H+ ' 8!8P σ − ε D%D N'& ', .$+' )V+% ]/ σ = H1 8!8P A

7D& . * )V+% ' 8!8P 7 * N'& ε = ln

( )

.$+' AM :,P NS sQi' sQi' K' P & N'& )5 + . [ 7!4 . c+D D~. )* $+' *t ]/ . * H* '

45

( Hardness Test) [ G5EB .= ‫ ﺳﻄﺢ‬$.8 3! d' A- O' .$+' <.X Èa ' (' A- O' a+ ` G& A! a+ 3AD1 T ' )E!+. . A. . ( ' )V5+ ' 5g' ]ˆM !!\& ]8 .M CXO [ / CT [ :[ M2 S . .= $+' !- AO'' !G 3>!+?' ]ˆM !!\& ]8 $.8 ' pG :CT [ 1 >!+? D .M v Q 6S 1!S . <'_E( dja <'= :CXO [

:[ $l <E & $' s/# .4.= .N1+ O' AX+' (Scratch Test) T' $@& : `' )V5+ O' AX+' (Indentation Test) - A. . ( $@& : [ AÔS O' m . NG ' a+ !- AO'' ' ^! )* (Mohs)T' $@& AX+' ' AM D A A & > O' )* <.X 1 a+ N1+ " A O' 3. NS a+ N'_! ADD* 2!!G& O'D! B ' ' A )* 1 N1+ 2' O' W'* 1 ( R.= ) M .M (") 95' 6S 2 & $a+ . (" ) >& 6S 2 & W .$+' A

46

* [ .D /& [

53 2 Mg[Si4O10](OH)2

H

CaSO4.2H2O

CaCO3

$!@E…

CaF2

$E(

Ca[PO4]3(F , C1)

$!&4S

K[Si3AlO8]

SiO2

_&'…

SiAl2F2O4

O4&

Al2O3

C

‹& y-

Z+ E(

W.'… 95'

.M !- AO'' A. . ( ' )V5+ ' A $.8 N'_! 3CXO a+ 7OS

!- AO'' ' .M )+ $a+ A O' ]M b. a . 1 3 ' )E- + )V5+ 7OS ^! .D@1 R.' 95' . 2@D& !* )V5+ 3AM $a+ ?( )5 a+

!K & . 1 ^( 2!G NO < ) )5 xQ+ ' )V5+ @1S ) . ! 3'+' 1 .M A ( . ( <j xQ+ . )VD+ :M )V+% O '+' T. Dk O' a+ " (Brinell) ]D a+ (Vickers) O . a+ (Knoop) Ž a+ _

(Rockwell) R*' a+ (Shore) M 3 >!+?' a+

47

xQ+

. (. ( V= xQ+ . ! H!@8& O' a+ " 3 '

1 T.

.M )V+% "&' ";* ' ' T. .' Y" $V@ (. ( w5" a+ " T. 'OS U8+ )GQ/ xQ+ . LX&' O' k* )O. T. 2' .M 1 >!+? D .D* 2!!G& ' >!+?' a+ N'_! 3 $^- LX&' .M [& 4 ? ) .D* '8 . )V5+ G' . ]M 3YD= I O' D+ a+ Èa

1 T. 3

]M

.' AM A' N^ )b )Q' . AM R5"' . ! 1 NS O' W'* 1 O' AX+' A.% . ' AM )@8 H1 1 T. 2' H1 ]M .' AM )g'' +D6 1 )5 a+ . YD= ) )=&

W> [ $' s/# .47 (3

48

[ &V K;[ 5 %M5 .49 (3

) R*' . O . 3]D T. )VD+ AO'' Nk . * )=& & ) a+ $@& W' ', 3$+' h_ E! (N. ! P ) 1!S +. ! G' )@8 ( 5!E! P a+ !- AO'' :1 )rDk .M !- AO'' B+ a+ 3T. Dk 2' T. O' 3M . ! <+ . )D!O . [+ s ^ ]j( 3)'O D d U8 . * AX+' (microhardness) Ž a+ _ AO'' 3 ^! 5D-_ . Ž+. ! O 3 d (. ( G' a+ $@& W' .M )V+% a+ " ]M AM )g'' B'. O' AX+' YZ+ . M !-

49

)V+% 6S B+ . 3^! W' )Q8 )+ 7OS ]/'P 3 !- AO'' $/ ' G!Vb .' (D) )5k+ Q/ . "' . ! '8 .M .M AX+' ( 5* P ) W - i Dk P H* 1. ! O' a+ _ $@& )* $+' W -E!* i Dk 1. ! 3 5!E! Q/ ) ' )5k+ ]D 7OS )!P LD !@ R*' T. .M $K P

D2

$V@ )* M [a' b (P) . ! . ..

L 1 !G 2' O' W'* 1 <.X& .M A' N^ ... RC, RB, RA 1!G . $+' ' ' W5& a+ N'& .M M '. 6S ) )* 5"' 1. ! . A.. ( ' R*' . ]D 1 T. a+ RG 8 ]M . * !- AO'' 1!G 2' O' .D! )'' ( . ( <. . )V5+ O ' A.% )5 xQ+ 3a+ 7OS )* S O' AO'' W. ]% [a' 3 - $a+ * "G!Vb . M >!+;4 ]M !!\& k .^ ' Q & $( - )Ei( EV/ !- AO'' ]% O' . 5 $/ !-

)* E'" . 2' O' . A * N@ ]M !!\& ' A a+ 1 7OS ^! ) .',! K' _! a+ 7OS . 3DM ',- !K& N@ ]M !!\& . 7^* $@& ' =. ' ! W%+' . a+ 2! V+D )Q' > . 2' O' . (7 * Œ ";o .$+' O <j )Q' 1"' O' P1 P = 22 2 D1 D2

50

" ' .P O' )5 $a# N'& 1 ]( . sO 1 )5 ' .',- K' AM !- AO'' a+ A- )!& . * AX+' a+ _ 7OS O' )Ei( )5 'OS )V O' ( ( . ( Q/ ) d ' ' / .P !- AO'' ]% .M )M' M d ' ]/'P 1 !- AO'' ]% 2! )Ei(

a+ O' 5* 3)'+' ";o 3'D%' 1 xQ+ . a+ .M :i . _!5& )5 xQ+ .M !- AO'' :i xQ+ ) $V@ a+ " . 5 a+ * ' ' ) # . ! ' O . - '. @1S ) . ! .M )V+% G/'. '8 O' ^! . * $P O' $+' 25 G ** O' G ?(

1 A. . ( )D' ) )=&

. - „G& ', 3D1 ]M !!\& NM . AM m 51

( Impact Test) %^ M2 .D '8 . D* + ' ^! 7 * Œ . ' ) # 1. ! K' $%& ' ( 3) # $@& .D* 2!!G& ' S . ! > )E!+ )5 $@M ' WO? ' 5G 1 7OS '+' A+ ' .' AM )+ <.X 1 ' ) # 1 A+ . !' +

1 )5

' 5*

' A+ .D* '. )GQ/ )

' R. '&

.' =. _! h_ . H!a# <GQ/ ' -_ 1 A+ 2!Dr51 D'& )* D@1 cG 5!E! ×× G' ) &GQ/ "" . (4M $@& ) 8(' <j ( )]M

%^ M2 <Z .4= (3 NS ) . AM 1 2!G LX&' O' R.4 > . !- ' / 8(' A= )5 4M T. . . R.4 W = O' AX+' .D* $* P ? $5+ ) 3D^ ' S )rDk . 5 '. ) # )5 !M =. . - )V+% $@M AM [,= ' 36 . )!.' 1 LX&' <.X&

^ 3) # 7OS .O+ & ]5% ' & $@M ) ]5& 3NS s 7D& _* 5& ' . . & A- O' Èa ' )@8 ' 7OS 2' 2!Dr51 .$+' (s & ) !M ) A $!+@P 52

2' O' 3D* !!\& <' P )= +D6 ' ( )* S O' . . N W WD )* M AX+' & ) N@ $P O' R8' <' P )= 2!!G& )= > W'* 1 . AM )!6& 4M )5

' 7OS

O 'G& 3ID 2 .$+' :. G NDT

M $@M ) D )* 6S B+& AM [,= ' . !- ' / ) # 7OS <' P . - H!+ & <' P )= ]8 (CVN) AM [,= ' '5 YZ+ . - 2!!G& .$+' ]!V/ 2' O' '5 ( )]M

NDT & ) W O' $@ˆM R8' )Q8 2!!G& . – ) # ' '5 .4D (3

<' P )= W5& 3N@ ' .DDM 5* ' 1 <' P )= W5& ";* & ' . N@ "V@ 1 2!g4 1 <' P )= AX+' ' ' 2' D1 N^ & ( 2!g4 1 <' P )= + 1 [S 1 ^* pG $@M .M )( - V (NDT) R8' <' P )= O' & .$+' AM T'_- A4 2' b )

(Creep Test) s6 G5EB .F NO $M,- . <' P )= K' (h_ ) H* 1. ! !K& $%& ' ' ( 3T_ 7OS ' &'t 1 '4 . NO 3<' P )= 3. ! O' G& 7 * $P 2' . D* + 53

k 3A NO $M,- . $K 7D& > P )* $+' AM A . ε = f (σ ,T , t , m) M O' *P 3 Q!% <' P )= N. / Rb 1 A/ <;( . 2!O 7' . - ]M !!\& O' 5* 1 <' P )= N@' 5" A&* 1 NO .M $G!Vb A4 2' 

N'Dk T_ O' M ]M !!\&  Τh = 

Τ ΤM

  2E… wEQ 

)4 <'_E( [.t )Q8 i

v Q 56 . fM <j A4 2' 3 &" T_ 7OS )Q . M B' M 31 A^?4 !5!M 1 *S 1 ) . {'_=' . 2!& 1 A 4 AD <GQ/ A4 k )* !- ' / )+ Dk 6O < ) . ! $%& . ? <' P )= . * . - „G& c a& . $@M )- 1 O' ]V/ . 2' O' . M D1' T_ . AM )!6& =

1'+' wQ I <GQ/ O' 1 )5 3T_ 7OS

!!\& . !- ' / ? 1 <' P )= $K 7D& . $K . ! $%& 37^* 1 A+ 3T_ '+' D%D .M H+ )b 1'5 . AM !- AO'' NO )GQ/ Rb ( ]M ) M A' N^ NO 7 *

s6 M2 # & # – 4F (3

54

:D1 N^ ' Rb 7'_(' )EP 6k ""?5G )* ()K) '4 $P T_ )8QD

(steady state)

$+' )GQ/

R'.O + ) )GQ/ ]M !!\& $" + AD1 N^ )* ( 2!+ ) '4 $P T_ )8QD .S $+ (tr ) -4 NO NS 6' )* (Tertiary) $+' <' P )= .

',- B' M $%& '

+ _ <' !!\& O' M 3|( Rb <' !!\&

1DS ( YZ+ . )!.' T_ ]P' a+ * ' . 1 $* P . $+' ?

1

)Q8 [!" tX 2!Dr51 . + O' 6S :,P . c!* & . 1 nb8 T_\ ]!V/ O' O . 7 * N'_! (/ TM " + . M ' O o

 

_* 5 . E- A4 c= 3)GQ/ Rb !!\& K' K nQ8 xQ+ NM H* . )VM 1 f8 . R'.O ) . !- ._( a+ * Œ NM W Œ . AM G# <j ]M !!\& NM .M D )GQ/ -4 .$+' )@'. 5"'

. ! ) H1 . <' P )= ) H1 M_ ( 3M *t ";V/ )* Q51

$" + ', . AM O 1DS ( 7'_(' . ! W%+' 71* c= 3<' P )= 7'_(' . 5* NO Rb !!\& 7'_(' c= 3. ! 7'_(' )* $+' G!Vb . 7'_(' T_ 1'5 3`' ]M ' AM A' N^ ( )]M 1( 2' . - 7 * Œ 7'_(' 3 [ ]M )!P ' AM H+ $K 7D& . Èa

1 <' P )= M_

.' AM H+ $K <' P )= . Èa 1 7D& M_ 1'5

55

' M_ ( <' P )= . 7D& !K& . 4L(!3

1'5 YZ+ . A * 2!!G& Èa 1 7D& ' ' (tr ) -4 NO N'& 1'5 2' O' .( ]M 3 5 H+ ' - A4 NO c@P 7D&

] !' ' <' P )= Dk AM R5"' 7D& c@P - A4 NO .( 7_)(!3 B' M )* S O' .M )( - +D6 <GQ/ !X 5" D! 7!4 ' 1'5 2' 7OS O+ )!VM ', 3^* Rb R+ Dk O' ^! . " N'& σ − tr '5 O' AX+' . ? . * )V+% t r , Τ,σ 2! > '4 B'. O' 56

ΤΜ O' ^! ) ?

1 <' P )= N@ ]M !!\& 1 W_! )* $+' *t ) WO?

1 <' P )= .D* | ( (/ TM O' 5* ) 2!g4 1 <' P )= 1 W_! (/ $6= 6S 2( - ' / . 1 H&' $* P tX 31 g . M_\ 1 ]M !!\& A.;" 3"'

&"?5G 1 )' O W%+' .M N@ ]M !!\& c= 3( ' _\ H1 . 1 )' 3. ! !K& $%& . $+' 5* )' ]' O' 3( / TM O'

(Fatigue Test) ZM G5EB .L

K' <GQ/ 5" .M + .D& . !\

',- $%& ' ( 37OS 2'

7OS <";b' ', .$+' (2*+ ) $K ',- B' M 6S 5" O' & A&*3 [.D ',- !\ ',- B' M '& 5 S $+ $K "V@ ',- B' M )* 7^* .M )( 2!M '. <GQ/ D ' * . + !\ 1. ! * . Y. + <GQ/ pG .M !\ 6S ]' ^( )* ^( $%& NOa .
^ k – ^5 7D& $%& @ 7OS A+ . 7 (3

57

' / ^( . ^^* 1 7D& $%& )5 xQ+ 2!g4 . " )Q8 1 ^D& $!G/ 3)= T - . !- 3M A' N^ O <j )* $+' ^( ) 7^* O' 7D& !!\& ]* . > AD1 N^ .. ( )]ˆM

$'Dˆ [.D 7D& ]ˆ!+ – (74) (3 D^ & .S W'. )GQ/ )* 1. 'G& 3fa^ ^5 . ! {'O 3@ 7OS . - )V+% M ' xQ+

. )* (S) H5_* 7D& .M

!- AO'' (N)

H+

'5 . AM 2!!G& $@M 1. 'G& . M ' & Èa 1 7D& ' 7OS .$+' :. G // '5 . S-N D%D ) )* -

(b) W!D!S . (a) ?( ' S-N '5 – 77 (3

.D1 N^ '

AM A' N^ 58

1'5 O' 3Èa ' "?5G

$+' 25 .MV @ 7OS )!VM $+' 2ˆ5 ',- 3<GQ/ O' !@ * B' M

K' D HID ',- . N@ !~ ^( – ^^* 3 !\ ^^* B' M A'51 )GQ/ ( ]M ) .M ( ... 5!4'1 31 ]4 ) +D6 1 AO+

t/I $' ( ] G>2 $'# . 79 (!3

. )5 Q+ B' M )E5S O' .DM ',- !K& @ 7OS } . -- ]'" 1 f8 3&' P <!E5" O' 5@4

1 7D& 3 D!M O' M %Q+

1 s & pP

.DM Q!% - B' M . ! 1DS ( . - )a O' ]iP ' )VM c= A 1 B!% O' AX+' W" . ^( 5@4 ^( R5"' 3%Q+ 1 s & :,P . %Q+ 1 T' 3^^* 5@4 1 7D& 3]8 . - <GQ/ @ 5" 7'_(' . - <GQ/ 5" 71* c= A 1 B!%

59

(wear test) N5 / G5EB . _ 2' .M 6S xQ+ O' A (NM AD* ) NM H* ]8 ' $.8 3^+ $.8 "' 1z 3M ( & )$a+ E! A -' .$+' )@'. NS YD(& ) H1 . A a+ ) H1 $!i +S ) NS xQ+ O' A 3 ) # K' ' 3' O $.8 A.. ( . AD+ tX ]8 <'t 3Y . W!D!S W <'_E( D 3M W . MV $a+ A -' ( b O' .M AD*

-' )k - ) M H* ^+ $.8 ', . A!+ ' S xQ+ 3 6S 95& <GQ/ . AD+ YD(& . a+ c!* & ', .(M A!+ NS xQ+ & $+' O!

O

' 3M O YD(&

7+ '8 D'& _! Q!% ]'" . - 1' c+D ^+ $.8 c= 3c+D D~. O' . (M :i )M '

5*

O O' <GQ/ xQ+ )rDk .DM K

. - 7+ 71* c= 35 5* ' 95& <GQ/ xQ+ NM !- )* M AX+' .M A!g+ 5*. AM H* 95& xQ+ & M AX+' 2~. O' D!M <GQ/ ^! 7OS N4 )GQ/ NO. 71* 6S W5& )* 3 !- W' . )5 7OS 2' .M !- AO'' NS NO. 71* . 1 W' I 1

(pin on disk): CM5 $/# YO G5 .4. _ NO . 'G& {'O' ) . 1 W' '. $* P (n= ) AD+ 1 2!4 ]8 )5 .M !- AO'' NO. 71* 3 I

60

(erosion wear) Z # G5 .7. _ <'t . (' |X&' $G!Vb )rS )!VM .M !- AO'' xQ+ > . AD+ <'t !K&
O+ )!VM

' 7OS 2' .D+ ' N@1* xQ+ = .. NG . O.^*

<j )GQ/ 37OS 2' . ]ˆM 3$+' )+ . !+? Œ k T. 31 7OS 2' O'

'. !+? Œ k > >5* ) )+ <'t . )( - ' / A= |. <j . cG > .M !- AO'' )GQ/ NO. 71* 6' .D+ ' S . AM A! . A!M4 NS .

)+ˆ!+? Œ k 7+ $@& 5 .7: (3

xQ+ N'& * $a+ &' P <!E5" . $a+ 1 )? 1 7M4 1 T. R5"' .' 7'_(' ' ^+ $.8 . * $a+ ' <GQ/ =

61

H/ ()

(Elastic properties) MN . 37D& )* D1 3' 2' 7D& )E!+. ) AS = 7 * 3= ' N@^* ]M !!\& ' . $+' Q 3' O' 7 * . 7D& 2! )Q' .. 2! O' ";* M )M' 2' 32!Dr51 .M U = 5&' 1!4 L . + ) )* $+' Q !~ +?' $6= ) d AM * ' 1E >& . ' @ <' P ) 37 * – 7D& 2! )Q' .$+' U _! (' -@ * . 1 . HP !!\& 3]M !!\& 3<' P )= !!\& 5"' 7D& > !K& $%& 3' )51 M A' AO=' A ) )* D1 3AS = HP !!\& ]M !!\& -' .D1 ' .M A! N@^* ]M !!\& 3 M ,4 $^- ";* 3 - )!.' <' P )= ) &

!~ ' )* &i 3$+' Q "" 3N@^* A.% 7 * – 7D& 2! )Q' 3 E ' D%D . .D1 N^ O' Q !~ N@^* ( "?5G 3 8EP 1 R E .$+' AM A' N^ ]M 7 * c@P (σ ) 7D&

N4 ^ 3D%D 1

. A )Q8 3Q !~ ([) . Q N@^* ( ( `' ) ]M .$+' N@^* )!P

62

2' .$+' A 35&' DV 3' ( 1 A' )- 1 O' & 2!^!4 3Q )!@!+?' ) I !+?' cg' # O' . )X- 2a+ 4+. * 9!8 7 * . 7D& 2! c+D& O' 6D& ) I )Q' 3)5 ' . * 2!!G& ' 6S N'& 37^… $@& D 1 7OS )* D* AX+' E c+D& $K )* $+' σ = Eε (`' ]ˆM ) ^^* 7 * 7D& D%D Q 7a

' .M 2!!G& _!

'

1 T. )E!+. ) $+' 25 ‚ R. '8 .$+' ‚ R.

:YZ+ 3M E ‚ R. . 3 ρ k ' A !+?' ($K ) c # L 2Dk : O' D&V" . D1 B H1 ) ' 6S 3$'K 2' )* $+' ^ * . 7D& E=

G=

K=

σ ε

()

τ γ

‚ R.

( )

σ Hyd

M R.

( )

∆V V0

5P R.

7D& σ Hyd 3$+' M 7D& 3 τ 3$+' ^( 7^* % >& 7D& 3 σ 3? 1 )G

@* ∆V V . M 7 * γ 3$+' 5G 7 * ε 3$+' 0

^( ^^* >!&+'.!1

L'' 2! +D1 )Q' .3 3 1 ]M .$+' CV8' U@V' O' AS $+ ) 5P .D1 N^ ' ? )G )+ AM x ^& 7 * . 7D& ^^* Š. ! )rDk .D υ N+'4 c # '

% 7 * ) # " 7 * $V@

. D1' XD ex . ey . $Vo ez 3 M z $6= ν=

− ey ez

=

63

− ex ez

nE# cG > DG 3)!.' ]M ^ 2!k B UQ 3 ^^* % >& 7D& ]M .$+' lo

. (D* 5 !!\& 3 )Q8 ) )Q8 > O' 1 -. 3NS )* ) 251 ' ' 3 )!@!+?' $K 6k O' $K . 1 -' ($+' N@ + )51 )Q8 > 1 -. 3NS )* ) @51 ..S $+ ) N'& ' $K . 3H!M )M' ' ν . K 3 G 3 E >!+?' K=

E 3(1 − 2v )

()

G=

E 2(1 + v )

()

v=

E −1 2G

() .$+' )G O' ]M 6D& )G

7D& N >k* . ' N Ž. &._' C ( ) . ( ]M) >!+?' ŠG 7D& $P :$M N'& ' O B'. . .S = $6= 7 *3 Š5" 7D& 1 3Š5" ε x = 1 [σ x − υ(σ y + σ z )] E 1 ε y = E [σ y − υ(σ x + σ z )] ε z = 1 [σ z − υ(σ x + σ y )] E

64

)!.' ]M ^ 32!k )Q8 UQ 33 G – 3 G>2 &>' % # - 7F (!3 AM A' N^ )* )S 3= H@= 7 k > ) .$+' lo nE# Rb cG > 7D& N. .1 Œ _! $+'

3cG :' b' 2!k )Q8 UQ 3dWa ]2 Ma \C2 /#&' G>2. 7L (!3 .$+' )!.' 7D& N. cG AO'' ^

MN (3 ]2 2 # # - 4 2' O' ˆ )… 3M N! r 6S 7'= )Ei( c@P $+' 25 H&' $X= > V ]!@4 ' M 9 – N.… )Q' 3 1 )Q' L

65

V=

−A B + m rn r

()

D@1 )b N'& m . n . D@1 )G(' . )t= ' ' c+D& $'K 3c!& & ) B . A )* ' H&' . N! = )G(' . )t= . ! DS .D1 N^ r c@P ' V <' !!\& )* ..S $+ O T. ) ]!@4 ' )Q' O' N'& F=

− ∂V − nA mB = n +1 + m +1 ∂r r r

.M m+1=M . F=

() n+1=N

−a b + rN rM

, mB=b

3 nA=a

-'

()

]M '' 1z ) )* . 1 )G (9 – N* 1 D%D ) 1 D%D H!+ & )Ei( 3)D!5* ]!@4

'

' r '8 .$+' AM A' N^ ]M 3D@1 @

3+ 1 = )= > . 3$+' Xi 3D‘S

. ! d0 . $+' H&' . 2! 3 d0 3G&

' '= H&' $X= > ( 31 D%D 2' )k -' .DD* ]5" & A * RG( ' AD1 $^- 1. ! )VM > ) 3'OS H&' > )* M A1^ P 3( 2!51 D51 31 x!#& ) YZ+ . ( 71* 3]!@4 ' ) ' =. )t= . ! > $@a 3M >_ 3 E ) H1 )G(' . )t= 1. ! d0 )Ei( (+ )D!5* > ) 3]!@4 ' ) + Xi .D+ RG& 1 H&' N' $^- ' 3 )G(' . ! > M A' 71* ^! 35&' 2! )Ei( )* &i ]M & ' 7' - 3 E + > 1 H&' 2' D . * 1' ]5" 36S G& )Ei( )

!!\& O' M 4+. * N@^* 7 * 3 ! ) )@51 1 H&' )Q' ' D!G 2!! g_= !!\& $+' ' 3+' >

l − lo 4+. * 7 * $+' 5&' )Ei( lo

3 E ‚ R. )* ' N^ N'& +S ) 2' D 3+' NS $+' ' 3 2a+ ) do )Q8 9 N*

66

d − do 5&' 2! )Ei( do

. ! D%D c!M $+' c+D

) 3 E ' N@^* 7 * G!Vb A.% . do 9 – N* ]!@4 D%D D%' .. &' ( i ± . ! D%D _ !@ )- ) )* )S 7D& 3E5" i8 )51

1 O' < 2

∂F 95 N'& ]M )* )51 2' D ∂r

' )* $+' MS .$+' wVQD H1 7 * O' )!P 2' .$+' 7 * O' Q n& D* N! )!@!+?' ) I

( [) . ' (`' ) @ '. (Condon-Morse) *# – & $' >R> . 9_ (!3 .D1 N^ r 1 H&' g'= )Ei( c@P ' . !

67

N@^* 7 * A.% 3NS 95 . 1. ! DS D%D 3 E <'= . 9 (!3 3$+' wVQD .$@' 7 * c+D N'& ' 7D& N@^* A.% 2' D Q !~ . Q )!@!+?' $+' 25 1 5!E4 )^!M D 3 E !~ = ' O' '5 .M A' v M DM L O' )… 6S 7^… $@& '5 ;V/ .D1 N^ O' .M A ]ˆM 1 +?'

.^( . 7^* 1 +?' N@^* ( O' ' )5. 94 (!3 68

74 ]/ 6S 9 – N* ]!@4 D%D ]M c@P ' &' P . ! d' pG DM D! Š1 !4 </ ) 513 ‚ R. . (α) NS &' P U@V' ( 3A > [.t <' P )= 9N* ]!@4 Š ' w5" /. )* M A' N^ ]M .' @ A NS &' P U@V' c # (O'- <'_E( . 1 = . *' M' Š1 !4 D) $+' O .$+' ? NS ‚ R. . O [.t <' P )= 3$+' >k*

]M ) ‚ R. . (α) NS &' P U@V' ( 3A > [.t <' P )= . 97 (!3 3$+' U R'- w5" ) 5!8@ [.t <' P )= .$+' U 9N* ]!@4 D%D U D%D N8& )= ) &' P U@V' c # ( . R'- )& D%D LGM ‚ R. .$+'

NN # # $/# G u / 8 .7 <' !!\& A' 51 ) </.' ^! 3 K' 2' Nk . ',! !K& ' ^^… ( 7 … Œ . > ' E* N;!+ D%D .' O! ^! 0% 3$+' A ,4 ]M . W%+' 56 o

2' '8 .( ]M ) .$( 1' 71* 3 ε 7 * Œ 71* . (T) 7'_(' 2!G A $V@ !' + ' . (Mo, W, Cr, Fe D ) BCC <'_E( .D* !!\& A L <' !!\& 69

o

5!E4 <'= . ' ^! $!+@P T . ε ) (Ni. Au, Cu, Al D ) FCC <'_E( )

' A > E* ( )* !M* 2!88% O' 'G& 3N!+ Rb .' 9 @P A. b ) . 7 * Œ 3 7 * ) 8!8P 7D& @'. ! )* DD* ` G& E* $P )G c@P :M )G <i ) 7 * Œ . 8!8P 7D& 2! )Q' .M om

()

σ = Bε

o

8!8P 7D& = σ 3A $K = B 37 * Œ = ε 37 * Œ $!+@P *( = m : )* = NS )* d B' M $%& .D* !!\& / . / 2! . $+' H* m <'_E( ^!

'

!!\& ( A' 51 ) ' ' )IP; ]/ 7 * Œ $!+@P )= $+' 25 A 3$+' m > 0 / 3 )^ A 7 * Œ – 7D& ( 3 m=1 )* = .P .1 N^ !+;4 |( ]M 3* B' M )GQ/ $G!Vb ) )@ .M 3 ' =. D&! O@. N;!+ A' 51 ) )* )rS .D* !!\& ' O' ^! $+' 25 7 * Œ Œ . - 2!G T_ . -4 7D& ( A ( 310-3/S O' 5* 32!g4 7 * Œ 71* $@M ' . D* ) & ' ' ) # B' M A 3 105/S . 103/S 2! 7 * 1 . D(' |X&' 105/S O' ^! 7 * 1 $" + >!@ B' M .D^ $+' 25 . )(

) # . O ' . </ <'X' 3>M [& 4 ) # D Q' M . ' *M $P c@P ' ' d' & ' AM W' 1 7M* .' =. 1 )D!X+ 6D+ [6M o

.DD* fa^ . 2!G 3M ]M ' ε

. T . 1 )* 1 '4 .

70

G V (b) / (a) E J2 >V % d;M2 H!R ]2 99 (!3

AM A.S R.= NS A.% . $+' !\ ! Èa 1 7OS 7 * Œ ?i' :$+'

K;[ $' M2 # G u </&R .F /& S-1 \ G u 10-8-10-15

G5EB S T_ $@&

10-5-10-1 -1

10 -10

$" + H* 7^* $@&

2

n + 7^* $@&

102-104

) # $@&

104-108

X' $@&

$" + N!^* $" + v -' .DM O <j 8!8P . +D6 ’% O' 7 * Œ ` G& :M A+ >(

eo = o

de d (l − lo ) / lo 1 dl v = = = dt dt lo dt lo

()

dε d [ln( l / lo )] 1 dl v = = = dt dt l dt l

( )

ε =

71

o

' 3$+' !\ l Nk $@! $K ε 8!8P 7 * Œ )* M A )Q' . 2' )@8 : * '!4 .D' 2! _! ' )Q' N'! .$+' $K +D6 7 * Œ o

v l de 1 de e ε= = o = = l l dt 1 + e dt 1 + e o

o

ε=

eo 1+ e

( )

o

)* M AX+' 1+ O' )* $+' WO? 35 $K ε )* M O! 7^* 7OS -' . 7'_(' H1 A+ N!^* $" + 3)5 Rb 7'_('

m

σ = Bε o % # # m %1R .9

)= O' $+' G& m .M h_ 1 ]M !!\& . N' ]M )Q' m '8 $!51' .$+' )( - ' / )=& NS )V+% . 2' O' .7 * Œ 2!Dr51 . <' P $+ ( ) )Q' 3 w^ YZ+ . M )( - H )Q' 2!( b O' m )V+% ' S  ∂ log σ m= o  ∂ log ε 

   ≈  ∆ log σ o   ε ,T  ∆ log ε

  = log σ 2 − log σ 1 = log(σ 2 / σ 1 ) . .  o o o o ε ,T log ε 2 − log ε1 log (ε 2 / ε 1 )

()

/. . L. M ε1o Œ 7^* 7OS )* !- W' !+;4 4+ B' M NS ) )* D* ]! ‹ A!^* )!.' Rb ' .P & )GQ/ . (' 5 |X&' E- A4 . A O $'D >k* )' G' -' ]5" . $@' )' 2! T_\ ^! 3$P 2' ]M !!\& W_! .M c+ D 7 * Œ . ( 0/7 Tm O' ^! ) ? 1 <' P )= . ( N. ! O' 5* ) M

4+ ]M !!\& B' M . + H5_* ) ' m '8 N'& (M fa^ 7OS )* ) 72

W5& . M A &'t $!i > m )* $M' )=& )V' . 5 ,4 N' ' >!+;4 ? AM *t B' M N'& ' m '8 )k - 3' ' NM >!+;4 4+ $!E/ ' .' 7'_(' :M )'' O ]!E%& 3 !+;4 ( m '8 K' N' N^ ' .M 5 P NM E- n/'. MV nQ8 xQ+ O' G& 3NO nQ8 xQ+ <' !!\& -' :' N^ N'& O <i ) ' L# 2' om

σ = Bε

om F = σ = Bε A

1

F m ε =   . 1A B o

o

ε= o dA P − = Aε =   dt K

1

m

A

m −1

m

( )

1

m

1 dl − 1 dA = dt l A dt

()

( ) ( )

( b O'

. )Q' .@& O'

)* M A3 () ]M 3M H+ m Èa 8 ' A c@P dA dt <' !!\& -' nQ8 xQ+ 71* Œ ";* m=1 P . $+' )@'. A ) 5* dA dt M ^! m )k 1 nQ8 xQ+ <' !!\& )* $+' W6X 2' ) ˆ_!( I O' 2' .$@! )@'. A ) . $K .(' 5 |X&' E- A4 3M $'D -' NO ) $V@

73

m K;[ 5 / -f o Ma - o ]2 u .9: (3 o

A )* &O ε $%& .$+' ' / dσ dε = σ )Q' E- )Q8 )* M A ";V/ ( b O' o

M O E! ε -' ' .(' !& ) E- A4 . 1'

dσ > σ M $a+ dε

( h_ m n/'. . ) >!+;4 4+ ( ', 3M .% >!+;4 ( . AM & & A o

.1 N^ Èa 1 ε

o

' ' m '8 ]M .M P ε O' i A.%

o

ε Ma m t ]2 .9= (3

74

d;M2 / M!3 $' $# v2 . : )k )* ' x!#& R5=' ) N'& 3M 2!G +D6 ' <.X ^^* ( )D' O' G 6e& 3)M,- N!+ .. * ) $@M D! 7!4

' $+' 25 A ^^* (

> $@M Re@ 7D& B' M )* D@1 '+' W6X 2' .' AM 2!G G $@M 3M ]M ' V!* & 1 )* ' )GQ/ $@M Re@ 2!Dr51 . '+' ^^* )5 N! e& 2' .M $@M e& 2 & N+S M 3 o*'P 5" 7D& e& .M

^! (σ u )

^( ^^* % W%+' O' AM R5"' ^( ^^* 7D& /. )* D*

N^ ' L ( )* g6SD & ' ' ";* e& 2' .(' |X&' $@M 3 - |X&' /. $@M )* D* N! (Tresca)+ & e& 3W. e& .$+' c+D 3D1 : - ^! % >& ^^* $@& H!E@& M W%+' O' o*'P M 7D& )* (' τ max =

σ1 − σ 3

()

2

o*'P M 7D& = τ max .Ei' ^^* 6^D& 2 k* . 2 -_ = σ 3 ‫ و‬σ 1 W%+' ', .DM (σ 2 = σ 3 = 0) . $+' = σ 1 B8( % >& ',- B' M ' 8QD ! 3!2 $# v2 .$+' 7^* $@& H!E@& W%+' `j ' H!E@& M

e& 31 )g'' (D1 N^ ' II L )* 6S D ) ,4 ]M ' H!E@& UV&' )4 )* M (Von Mises)E6 / d;M2 $# v2 o*'P [,= ' DV (' |X&' /. H!E@& )* M C ( 3 e& 2' .' ' / G/'. $@& 1 A' 6 ]5%& ' % Dk ',- )* ' )GQ/ ,= ' ^^* $@& ,= ' )* .($+' A^ '. ]!E%& . )_& 2' HP !!\& A' 51 ) !+?' ') M ' 3D* ]5%& ' % Dk ',- )* {_= )GQ/ > (ασ 2 / E ) [,= −

' 2!!G& '

.$( - I ' σ RG 7D& > )* $+' c+D 3D*

75

−

σ=

[

2 (σ 2 − σ 1 )2 + (σ 3 − σ 1 )2 + (σ 3 − σ 2 )2 2

]

1

()

2

: )* = 2!Dr51 '& RG 7D& .DM (principal stresses) Ei' 1 7D& = σ 1 , σ 2 , σ 3 :M A' x!#& H1 5" )%Xi )+ . A'. M . ^^* 1 7D& c@P −

σ=

[

2 (σ x − σ y )2 + (σ y − σ z )2 + (σ z − σ x )2 + 6 τ 2 xy + τ 2 yz + τ 2 xz 2

(

)]

1

2

() −

',- )5 > H!E@& .M ' % >& ^^* $@& > H!E@& W%+' σ -' .M D! 7!4 % Dk AM

76

H () 5W $# v2 1 6S ' )VM 1 f8 . D@! ]* <j G!Vb = ' o*' $ %!13 $' q . (R@ * E4 ) E Dk ' o*' . A _! E >& ' )* M )X- ";V/ .' =. H1 O' 1 )' O B+& )* M E >& > )' 1 )* G 1 )' O' ]^ . D@1 .M '= :M D H!@8& O <j ' )VM 1 f8 $ % $' q – K 1 H&' -' .DMV ( ]M ) A.' )VM AM 2!!G& 1 $!G/ 1 H&' pG $+' 25 2!^ 2!

1 H&' DM AM = -' . (vacancy) = 6& 6S ) 3DM cg~ ";* DM ',- !K& ' d' )!E* ' )Q8 1 f8 .D- (interstitial)

$' q – , (dislocation) g 6S ) "P;Qi' )* A * Q f8 ' 35&' <%Xi O' 5@/ NV v M )'' 3',- ' ! ( O !K& 1 g )* S O' .M )X' $@M . a+ 7 * 3>!+;4 ]M !!\& )* M 1' A . 3M )g'' 6S O' E* . 1' 1 g ( ) )@'.

:$ %RIk $' q – c AS = 1 s ^ ]j( . ]* = ' ) $V@ 5&' <%Xi N!k A% 5I .D ' )%Xi f8 ' (1 )' O D ) ]* 1E Èa 1 $5@/ 2!

77

:Wa $' q . O 'G& n5& O' )* D 5P f8 ' 1 s & . 1 A XP D G )+ 1 c!" .DS = ' )Q8 f8 Œ 1 g dja . E 1 f8 $* P )E!+. ) O~S 3 E ' >!+;4 ]M !!\& 1 g 2! O' M 3 ^! N@ ]M !!\&

' WO? 7D& 7'_(' .1

1E = 1 g .D (a+ 7 * ) a+* ' A4 2' )* $+' !@

!!\& . ! * )E!+. ) 6S ' 3DM 5' WD1 M 1Q )! $+' 25 .DS = ^! N'_! ) ]M )+D1 3g

=. x!=& D 1 L# . M RV 1 g 0% )''

3g )_& 3 :' b'

1 7D& 3g >!+?'

' 3)!@' 3O - ' 3g

.M A' v M ... . 1 g )!.' $!G/ O' 1 H&' = c= 3E > N. )%Xi > . τ M 7D& * . $+' N@^* 7 * 3M >k* g= -' .M A ]M )* )S 3M 6S AO'' ) g= -' . . - G& . EV/ 1 $!G/ ) 1 H&' 37D& 2M' ' / '4 $!G/ 1 H&' 3D* = b 4 O' 7! 1 $!G/ ' 1 H&' )* M O ' .M 1' )VM &' !!\& c= * )'' . !-

( $'# ; H!R .4 '' 1E W%+' . AM 0% ]* 1E W%+' '' 3g $= )!=& ' .M )@8 )VM f8 g= 0" )* ! I 2!G E )%Xi > ' 5&' 6* P 3L# 2' v M ' ) )* M V A H&' -' .( ]M ) - D!g4 )5! ) $V@ cG > ? )5! .X! |X&' T_\ )%Xi . 65&' W5& N_51 R8' 3. N ) B H&' . B N 78

1!4 D ) T_\ )%Xi '' 5&' 2! 1!4 W5& N_51 -4 3 L# 2' Nk ]M . 1' h_ E! D' ' WO? 7D& 3' '(A !~ . C-C` . B-B` . A-A` R . P U8 O' D&V" @ * )VM G& 5&'

6!G/ )* 1 N^ `' –

' '4 )5! RG& . $+' o*'P Q )Q8 ' R . P 2! .P'. b ' ' )Ei( 2! 1!4 $Ej ) `' ]M AM A' N^ ' '5 w!/ ]M .1 75 +D!+ m > )!VM E! . M fa^ 9 –N* '5 B+& )* $+' )@'. 5&' .$+' AM AX+' NS O' ]!E%& . )_& 2' . M m!P' g. ! ) R . P D G& 6!G/ _ = 1 T_\ )%Xi . 65&' N' ' / F=- )* = M ` G& )Q8 NS (`' ]M ) ' D%D c!M )E!+ )* ' $+' : b ) . ! 3 ( 0 < x N' ' / 2

' 3Ro ' dE/dx

.D* $Xa P RG& ]% ) $^- ) H&' ]5& & $+' WO? _! . ! D%D 2' D $+' $Vo )Q8 1 ' D%D c!M Q. P 2! )* !D* )=& R T= RG& N ) )* 1' H&' 3

b b < x 3L# 2' O' !-E= ' D%D 32' D .$+' XD ' D%D c!M 3 R . Q 2! )!P .' ) 2*+ b ) R .M XD _! )!P 2' . ! O' [.D <i ) T_\ )%Xi . 65&' $* P ' WO? M 7D& )* $+' 2M. ? 0% O' ) $+' 25 M 7D& 32' D .D* !!\&

3b b . o*'P '8 & R, Q, P Xi 4 4

!!\& )VM +D!+ <i ) ' )* C ( 2' )4 )* M A' x!#& O !+;4 N;!+ .D* $* P τ m 5"' M 7D& b )

b O' ^! AO'' ) ( 47 ]M 4

: - ` G& s1 N/ $+' 25 M 7D& 3 !+?' 6^ * ' τ =G γ

( ) :M AO c 8& >k* 8 ' $+' 25 M 7 *

γ≈

x a

( ) : )* = T_\ <%Xi 2! )Ei( =a

:H' >k* 6^ * ' sin G

2πx 2πx ≈ c 8& . ( ) . ( ) . ( )
x 2πx ≈ τm a b

() :H' N * c&

τm ≈

G 2πa

()

O ]M ) ( ) )G 2' D 3 ' '8 I O' DG $+' a )V& O' b 31E ^! ' .M )M A. $+' 25 τm ≈

G 2π

()

80

W%+' '8 3 ' D%D ]M "ija 3)( * ) _!S 2' )* c 8& $E" ) .$+' c 8& > () )G O' τ m 3 τ exp N'& ( b O' .1 ' /

8 . () )G O' AS $+

G A.% ' τ m 3 & w!/ &V+% 30

e& M 1 T.

e& W%+' $( - AO'' AÔS ' G/'. W%+'

MS ' AM )g'' () R.= Èa ' 6@ * >& ' 1ÔS M W%+' O' "' o*' τ m τ $V@ . ' =. 1ÔS . exp

e& 8 2! -_

6&.X& )* $+'

.$+' 21S ' . × .P A 8 ' $V@ 2' $+' ^! 6&.X& 2' Re@ ( ) )G )4 AM W' <V+% )Q' $/ V5* 3>M N. . * )g'' NS ' x!#& . $M',- [@P ) ' 6&.X& 2' 3)E .$@! h_

!!\& cG (`') .YJ s6] %RIk C5 & # ;k J! C5 a .9D (!3 > V@ R8' 5 )( T_\ cG ([) 3AM D! 7!4 T_\ )%Xi )(! ]M T_\ )%Xi '' 1!4 AD1 N^ H&' N (m) 3cG $5@/ .(A-A`, B-B`, C-C`, D-D`)

81

%!= & 6 .)VM H&' N ' !!\& (`')3 %!13 C5 />2 ;) .9F (!3 .)VM N! 1 H&' . 5"' . ! !!\& ([) 3 ]/'P ' D@1 R . P U8 H&' .$+' o*'P

(2n − 1)b ....., 5b , 3b , b U8 . Xi G& N . ! 4

4

4 4

K;[ # N5EB / $# v2 d;M2 $' H!R – L /& A

e& 7D& G / 2π

τ exp AM !- AO'' 7D&

τm

τ exp

Gpa

106 psi

MPa

psi

Silver

12.6

1.83

0.37

55

≈ 3× 104

Aluminum

11.3

1.64

0.78

115

≈ 1× 10 4

Copper

19.6

2.84

0.49

70

≈ 4 × 10 4

Nickel

32

4.64

3.2 − 7.35

465 − 1,065

≈ 1× 10 4

Iron

33.9

4.92

27.5

3,990

≈ 1× 103

Molybdenum 54.1

7.85

71.6

10,385

≈ 8× 102

Niobium

16.6

2.41

33.3

4,830

≈ 5× 10 2

Cium

9. 9

1.44

0.57

85

≈ 2 × 104

Magnesium

7

1.02

0.39

55

≈ 2 × 104

(Basal Slip) 82

Magnesium

7

1.02

39.2

5,685

≈ 2 × 104

16.9

2.45

13.7

1,985

≈ 1× 103

49.3

7.15

13.7

200

≈ 4 × 104

49.3

7.15

52

7,540

≈ 1× 103

(Prism Slip) Titanium (Prism Slip) Berylium (Basal Slip) Berylium (Prism Slip)

= ) . A \2 E ^ %RIk d C5 &3 # / E 3 $ %!13 q .9L (!3 ` G& A )%Xi H! )V N'D" ) B .!D* )=& A !~ . C’, C, B’, B <%Xi N8 .M XX’ (#' )& > ]M XCC’YX’ O - ' .$+' AM ' xW :$ %!13 $' q $ / % 2 7 =. )-'= b ) (Polanyi) "' .% )%Xi H! D!g4 )V ) >_ . . 1 H&' ) T_\ )%Xi . 5&' !4 $@M !4 $@M 3D* $* P R@ * N! O' B /. .( B W ) ) M G5= )+ <i ) ) . (' |X&' . ' & >& $* P )^ $* P 2' W%+' . e& H!E@& W%+' 2! h_ 6&.X& ', ( ]M ) D* $* P E= $5+ ( ) )G N $+ )* $+' G!Vb .D' 1E 1 g =. ' 1ÔS 1E . 7OS W' 3$+' m!P' )rS * 2'

' . !- ' / ^! !g&

.M )!6& AÔS O @. W ) – E* 1E 2!Dk .D@1 g N. . ]* O' AM )V+%

e& 8 )* AM )g'' () R.= R.' !~

1E 2' W%+'

' 3M A.% 1O @. ' τ m τ $V@ .' _ $8Q ( ) )G exp ( R.= ) O' ^! ]* 1E ' $V@ 2' )!P $+' / 21S

.D* $* P E N! O' )* D1 1 g [EQ 1 N .:_ (!3 84

E ) M 7D& R5"' K' s P .: (!3 ' ) .$+' E ]* N_51 $* P D51 g V" O' M E g6 $!G#. )* !D* )=& .!D* )=& (m) ]* O -

('E!M5/ ) xW /& '# ; N5EB / $# v2 H!R . _ /& e& 7D&(G/2 π )

AM !- AO'' 7D&

τm

τ exp

<

GPa

106 psi

GPa

106 psi

Copper

19.1

2.77

3.0

0.44

≈6

Nickel

33.4

4.84

3.9

0.57

≈ 8.5

Iron

31.8

4.61

13

1.89

≈ 2.5

B4C

71.6

10.4

6.7

0.98

≈ 10.5

SiC

132.1

19.2

11

1.60

≈ 12

Al2O3

65.3

9.47

19

2.76

≈ 3.5

C

156.0

22.6

21

3.05

≈7

85

(Peierls)6O G>2 :xW a # %!13 / .9 )* AM 0" . A * )XMS ' )VM 365&' (#' )%Xi H! NM '. )* $+' x#'. () ]M O' '' 65&' 3Ro ' .R@ * "V 8& <6= W5& !4 1. ! /. H* H . FCC . 3 BCC

1E _ !4 7D& )* M A 3$+' AM $( H*' 1+ 1E D ) M ' $6= "'M

!4

1. ! /. 3]8 .$+'

.$+' h_ _ !4 7D& 3($?'.*

' xW %&>' .: 2!G ' )(! T_\ . )( T_\ 65@/ 2! O )* $+' )VM Q f8 3 > .r!4 . ' )V g 3' AM A' f!a^& <.X L . 1E .D* . - ` G& ( ) ]M AM A' N^ 365&' (#' )%Xi H! )V )E!+ ' )V UQ -+

' "?5G ' .' AM A' N^ ]M A+ L .

.DD* H!+ & ' 1 )@1 . $+' AS ]M )S D D1 N^ →

$6= . AO'' )* (!D!V ' ]M ) .M b NS O - ' 3 > 1 -. O' 86

> O' .( ]M ) M AX+' O - ' O' 3O - ' 2!!G& ' .D* fa^ ' T_\ .M H+ RP ' > .@ '8 ) y . x 1% '' . A * L. M )Q8 .D- O - ' ' ' ADD* ]!5& ' 3 wVQD L. M )Q8 ) N4 )rDk

)* ' )^ .yO xW (, / $ %1 5W (K \< $' 5W %&>' .:4 (!3 ◦ .$+' AM◦ A' N^ _! . 1 g N' N^ ' "?5G

.yO 5W C5 (, / $ %1 5W C5 (K \El # & / # .:7(!3 3' NM )@ +* O - '

AO'' ) 3 B . H&' ) H&' ' > 2' D

> 3O - ' .M )@ . ]* 3H+ E > 1 H&' . 3D51 ' > )* &i .M ` H1 @ 3A * . A * T_\

)!P 3)VM )* ' O 3$+' ]* 5&' 87

)Ei(

B )* 1 N^ 3( [ . `' ]M ) r!4 .

' )V $* P +

B 3]! 2!51 ) .$+' E A . A * T_\ 1 7a 2! O ^ 3 3E N. B .1 ]!^& )@ ' 3E N. . D* nQ/ ' E xQ+ @ )a!S 3 U8 . r!4 1= 3M ' )V 6D& 31 N O' $+' 25 B 5" ' )V > O - ' .D- 0 ;[ 5W NS ) )* . 1 O' ' (UEa ) )a!S > 3O - ' .$+' B O' r!4 ' . $+' . ]M 3O+ ).'O > B

UEa . r!4 3 ' )V g $* P 75 . ]M

B b 3 ' )V g ' .$+' g B ) $V@ NS $6= 3b H6 cEQ )* )%Xi > ) ' )V g $* P K' !+;4 N;!+ 3R5G b ) .$+' 5" g 3)%Xi 2' ) . - .% 3$+' AM ` G& TO - ' . g B )E!+ )%Xi 2' .(' |X&' b O - ' $6= )^!51 T_\ .M )X- s6] %RIk 88

' xW a .= )V > .DD* $* P 5&' k . )Ei( 2 -_ <%Xi T_\ 1 g 7M_\ R5G )%Xi O' m * P )* M )M' _! 8 N. $* P )* $+' / ' ) (vacancy)1 = 6& tX Ro b ) 365&' O' ` > :,P '& L# 2' .M

)%Xi ) )%Xi > O' 3 g Jk 3$+' <' P AM RG( DS ( > 3 = tX Nk .D* Jk B )* r!4 .M A [.t )Q8 `j >_ . 3 &"5 ) r!4 > $* P 3n/'. .$+' b $* P .' ' )V g ) $V@ ^! s %& r!4 g 32' D . - .% $+' (cross slip) -f s6] W ) D' ( )%Xi ) T_\ )%Xi > O' r!4 g r!4 g 3>!+;4 ]M !!\& L. M .$+' AM A' 75 ]M )* !- W' )E!+ )%Xi 2' . $* P )'' -' .D* $* P ( `' ]M ) A )%Xi . XY N !!\& RG )%Xi ) '& r!4 g 3[+ At > D 3 - `/ G' T_\ 3A !!\& O - ' Nk . ([ ]M ) 1 )'' 7* P ) . B )%Xi D 31 )%Xi . $+' 25 r!4 g $* P .(' |X&' )%Xi . . $6= N51 89

( m ]M ) . - A )%Xi ) )K nb8 T_\ DS ( > )E!+ . )'' B .$+' AS () R.= r!4 . ' )V g 2! ++' 6&.X& O' ' )i;.

$* P )* 1 AO=' )* ' )V g ) ' m2 tX ]M xW Jk .:: (!3 .1 W' )%Xi ) )%Xi > O' ' Gi

.$Z5 % 1M M5 E MU C5 5W E 3 AB yO 5W . := (!3 .M b O' AB )* !D* )=&

90

(c) B %RIk (,) A %RIk (K ) . XY yO 5W C5 -f s6] .:D (!3 .A %RIk

' xW t)[N .

/& xW t)[N

xW S ' )V

T_\ $6=

r!4 b O'

b O'

b 5"

b O'

b )@8 g $* P $6=

b O'

b 5"

T_\ )%Xi O' m g $* P DS (

Gi

nb8 T_\

b . g B 2! )Q'

:' xW <&'N .D . M O 6S G' ' O .$+' A' 51 &;^ 1E 1 H!8@ A1^ E AM ]8!i xQ+ !5!M “' 3w( >!D& > .DM 5 $. ]/

Ž+. !

wbD ) $V@ xQ+ . g ' 4 1 )@1 ]% 3“' <M w!/ R D* .$+' * >P G 1 A XP ]!^& 3)! . !- ' / !5!M A )E5P <M ) 3 5"' 7D& K' )GQ ' >!D& 2' .( ]M )$+' g > ) U > 1 )* M 91

. 7D& K' $%& $!G/ !!\& )* P A XP 1 )* * 2!!G& N'& N * “' ' NO $M,- >P A XP . 2! )Ei( ) 1 $* P )Ei( 2M' .1 75 ' s % g . * [@P ' $* P $" + N'& 37OS NO . ( * . ' Ž+. ! 6S H!8@ 7OS ]M 1 g )GQ

' & R.' >!D&

3<GQ 2' AX+' 1 )5 3' 5* tX </ 1 N. ' Nk .M V" .DM ' .P 0.1 − 0.2 µm .P . sO E! 1 )? ) $V@ ' AM 7a4 . ' LGM !@ NM=. 3D@1

' )VM f8 1 Nk

.j& 31 N. ' T' 4 B' M ) )@ 3)! .D1 !!\& ]* R@ * > T !@ `' ]M )* )rS D 3 XD A!+ UQ ]o 1 3cE~' . - !& G & ? O' . ' ' / d )%Xi > '' g 1 . - 1z 3$+' AM A' N^ B AM j& Rb B8( ADD* A1^ 3)! . ([ ]M ) T @- )/. 2!g4 1 g ]M )%Xi ).'O . )/. $a# ) G/'. Rb )* D! )%Xi

. ' g .' @

A' 51 ) W'* 1 3d &5# x ; <&3 ;k %RIk $/# $# Ca $' <Ia .:F (!3 ]M ) O 'G& !-' / 3 * >P A XP 5 B .M A'a > .1 N^ ' ).'O H* 1O

92

' )%Xi 1 7'S (`') ./! z !/! g 2 ' 5W <&'N .:L (!3 )%Xi . $!G/ AD1 N^ '5 ([) 18Cr-8Ni ‚O # ?( 1 .)5 T_\ N'& d

1 >!D& O' AX+' . . ' Ž+. ! B+& 1 A1^ .5 2!!G& ' 6S O - ' . L )E5= O' 6S <!ij

' 5W !T .F > RP )XMS )VM A' 51 ) !+?' 7D& N'! > 3. I' )* Q51 .' x!#& N'& +S ) ' r!4 > RP )( T @- 1 7D& .' =. .(`' ]M )

93

r!4 RP !+?' 1 XMS .=_ (!3

<i ) VQ/ <ja γ θz M ^ * 3 ([ 60 ]M ) ' )'+' {_= N' T @- O' :$+' O γ θz =

b 2πr

() :$+' O _ Xi ) r /. 3 τ θz 7D& )* 1 N^ () )G (5-10A◦) '8 ) g _* O' ro .% )Ei( > 3$+' 8QD !~ L# 2' Nk .M <ja .D- )@1 ' A.% 2' .$@! |i () )G NS )* ' =. . ) 7D& N'! . 5" 7D& '_=' :DM O 6&i ) 1 7D& 2' 2_&* <ja

) 2π (1 − υ )(x + y ) (x − y ) Gby =+ 2π (1 − υ )(x + y ) Gbx (x − y ) =τ = 2π (1 − υ )(x + y )

σ xx = − σ yy τ xy

(

Gby 3x 2 + y 2

yx

2

2 2

2

2

2

2 2

2

2

2

2 2

()

σ zz = υ (σ xx + σ yy ) τ xz = τ zx = τ yz = τ zy = 0

.$+' N+'4 $V@ υ |( B'. (x=0) ' )V ? $+ ' f ^( )!P > 3() ]M () )G )@8 T_\ )%Xi '' .H! (#' )%Xi H! D!g4 )V O ' f ^^* )!P > . 7D& N'! 3 RP 6!G/ W5& ' .M f M L O' 7D& 3(y=0) .M M '_=' . ^^* 3 ^( '_=' ]M

95

.$ %1 5W C5 a !T G>2 & .= (!3

.M > !+?' $!i !T G $" . .F :M A' O <i ) '8 2' 3r!4 A+ $P ' dE 1 1 = τγ = Gγ 2 dv 2 2 dE G  b  = dv 2  2πr 

H!' ]V/ O'

2

:$M N'& )Q' O' .

` G& (r1) R@ * . ! 1O & (r0) )@1 m )!P ' ' )* !D* )=& (.!D!V ' ]M ) $+' AM .$+' l RQ )'+' {_= P'. HP )* dv = 2πrdr.l 2!Dr51 lGb 2 dr dE = . 4π r

()

1 r1 Gb 2 .l dr Gb 2l r Ε screw = .∫ . = . ln 1 r 0 2 2π r 4π r0

( )

:$+' O ' 96

A' O 8 2! NS ' 3' r!4 '_=' H1 . ' )V '_=' H1 3UEa > Nk .M ( ) . ( )
() : )* g= Rb = l g 1 ' = Ε . / & / 2! 8 +D1 *( = ∝

1' |X&' H*' <6= "?5G T_\ )* $+' 2' () & ( ) .+ T'8 2 5* ) ' & $+' >k* O - ' )!= 3(' .' AM )g'' ]j( 1E L'' AM A' x!= & T_\ <6= |X&' 2!G 7D*'. > S )* DD* 2!G ' Q' M 2!Dr51() & ( )
−

−

)* 1' [EQ &i ^D*'. 2!Dk >3 b1 = b 2 + b3 $" . ! (' 1' : 3M )!.' ' O' 5* (Rj% ) 6 ' ∝ Gb12l >∝ Gb12l + ∝ Gb32l

b12 > b22 + b32

:1 g N@ Rb ' . G 4. &._' !~ <' K' O' ID( i )* .M )_& ' > &

O' $* P ' WO? . ! . GN \5W C5 Z5 !T k .4.F .DM )VM N! )Q' O' AX+' .M ` G& O & D* ]5" Q 7^* ..S 2!g4 ' R@ * E* ' N'DG .D5 '. . ! D'& b $;" . 6S :' b' 7D& AOP ) )=& 3' N@ $;" O - 1' )* r!4 1 3 O' 1 $P ' Ro [,= ' 51 DM )M' à Hg;" 3O - 1' /. . DD* n( ' 51 .' Y" c+D& . 2! )Ei( . ! AO'' 3$P . 1 .DD* 1 7'S D'& )^ ' )V 1 E !+?' ' N * H* ' 3)! H* ).'O )' O ) . ' )( - ' /

?

5" <j )*D1 ]!^&

'4

.M )G=' HD4 ]j( ]M ) . (low angle boundary) D(. G

x6 $' 5W .L )* 3M )_& b3. b2 . ) b1 )D' R5P' 3M AM' ]V/ 7a )* Q51 ' @ 2' ) 3M A' (partial dislocations) g_= 1 N'D" ) cE~' !+?'

' O' 5* b3. b2 g_=

1 !+?'

6 ' L5 S )*

|i NO H1 O )Q' . )* (' 1' |X&' /. )_& 3( ) )G O' . ! $+'b1 :DM −

Gb12 > Gb 22 + Gb 32

.

−

−

b1 = b 2 + b3

$6= b1 ]* )* ' N^ N'& 3R > N'D" ) FCC )VM O' AX+' . - )_& < 110 > H*' . $+' C ) . B ) A O' T_\ )%Xi

. 65&' $* P )* M A `' ]M O' .M 5 3 [110] $6= 3AC H*' $6= "5!8@

98

A i% b3. b2 E*M 6g_= (,) . (E*M ) g_= . ]* !@ \(K ) ]M ?( (H1 ) >_ UQ 1 ) 7D!k f8 1' (c) . A 7D!k f8 )!P ADD* ]j g_= 1 )E!+ 6' f8.2!g4 7D!k f8 ' 18Cr-8Ni ‚O # D@1 ! 1E/. 3sO A!+ 1 .' AM

99

6S W'* 1 ) )* M )_& BC . AB g_= . ) AC ]* .M )X- (shockly) E*M _= :M )g'' O )_& 2' Ro ' a −  a  −  a − −  1 01 211 + 11 2 → 2   6   6  

() ' )G O' 2 2 a2 (1 + 1) > a [4 + 1 + 1] + a [1 + 1 + 4] 4 36 36

a2 a2 > 2 3

W5& G DG .$+' AM ID( i !+?' T R. 4. &._' !~ )- 1 3$6+ ' .$+' AM C ( N@ <6= ' g 7D*'. 2' N'& . *1' $( ^!4 AM A' N^ $6= 7D*'. 32' D ) A!V@k 3)V' ) ‚4 ‚D!4 1 Ž& O' H*' )/. > -' . * YP ' A+ 7OS W' > ' )/. 2' .M FCCE () )%Xi 1 H&' ' R 3M )!6& (H1 )=& .!'_\E H*' <6= O' O' 364& O' )^ )/. > . ' S G . '6 $+ 2! 6- Rb h'O ‚O ]M ) 51 . )* D1 x!= & 1 )/. )* * !1' $E" ) .D@1 < 112 > <6= ]5& 3' N@

O' 6- 2' 3FCC )VM ._\E W. )/.

' '_=' 3g_= 1 )* $!G/'. 2' . ^ *

64&

' 71*

]M A $P@ )* _= . '= '8 .DD* n( ' 51 )* $M' D1' @ 3(' |X&' b3 . b2 2! )* 1 H&' N!k HI $Ej ) 3$+' AM A' N^ [62 )* cG Q/ '' 3FCC L O' 7D!k HI !!\& 0" _= 1 2' $* P .' ABC BC <j G# XMS > ) 3ABCABCABC DG 3$+' [111] $6= AM A' N^ m ]M (stacking fault) 7D!k f8 O' 1 )5 . - 3ABC

100

γA <j NS

' )* - H@!+ ]* ' 2( " 3FCC R@ * > ' .' .$+' xQ+ P'. 7D!k f8 ' γ )*M A' N^

O - ' '_=' )G(' . ! 2! RG& ! _= . 2! G& )Ei( 32' D .M NS A' 51 7D!k f8 ' . N@ $;" 7D!k f8 ' 9G b ) _= . 2! )Ei( 3 (Cottrel) R &* I wVb :M A' O <i ) . D* !!\& (SFE) d=

Gb2b3 2πγ

() : )* g= g_= 1 O - 1' 3b3. b2 . g_= . 2! )Ei( 3d 7D!k f8 ' 3 γ . M R. 3G

' a' 8 . ' @ N^V!* & ) 1!S . 1E (SFE) 7D!k f8 ' '8 .' AS R.= 1!S . Èa iD" ' a' 8 .D&.X _! f <'_E( $V@ "'M SFE )* ' A' N^ N' . (Thornton)N & 3Y )4 1!S

O & "?5G SFE 3$+'

(

)

e > 1 / 1 /. )* D( 6S .$+' )@'. e H&' ) N. ' atom a

. 71* 20 mmJ 2

FCC t 6; $ [> &? q $5" . 4 /& t 6; }

&? q $" mJ/m2=ergs/cm2

‚O # ?(

A 8

;b

Y

]!

W!D!S

101

!K& a+ 7 * '8 )* M 5 W' H1 )_& 3M O SFE '8 /. .',- .5 a+ 7 * ' H1 1 :Z5&!5 5W # . _ . )K

1O( <'t 3)'O D G' ) $* P !@ /. 1

' W'* 1 )T_\ )%Xi . n > ]8 DE5 . M `/ 3DD* ' / R.' + $^4 O 'G& -' . ]M 3(pile up)DD* n5& ( P'. O - 1 .. O' )* 5 (Back Pressure)

^- 7D& > ' n5& 2' 3 !-

n5& '' -_ 7D& _* 5& 3. I' )* Q51 .D* !-E= !@ NS ^! nb8&.M ' O' pG 9.O $@M 0" '& )* S = 1 .M H6 AO'' N51 ) _! <.X T_\ <%Xi . s % 1

T # % E C5 ( # dM / $/# (pile up) 5W -W2 . =7 (!3

(γ = 35 mJ m ) 2

pE &^

.$+' AM A' N^ 64 ]M <.X ' )V . nb8& 0" AB nb8& 35" H1 . O - 1' )* = 3`' $P ' AB 3b1 O - ' XY 3 : b O' . - XY Rb 71* 3$+' b2 3PP` O - ' .' b1 ' b )* D* !& ' PP`(h= ) )E4 > . PP` )E4 3 b2 O - ' XY 3AM A' N^ [ ]M )* Q51

102

r!4 L O' )E4 3$+' PP` )E4 O' AB b2 O - ' Nk .D* !& AB .$+' r!4 L O' _! XY QQ` )E4 3)^ b ) .M $* P NMpP 3)! .' ' )V L ) $V@ ^! s %& QQ` . —PP` r!4 1 )E4 > nb8& 3AM A' N^ `' ]M )* Q51 ..D* 5 `/ ' E* XY r!4 QQ` W ) )E4 . AB ' )V PP’ )E4 3r!4 . ' )V . PP` )* M A 3' T D51 O - ' 3)E4 1 Nk . * 1' !& D@1 ' )V L O' 1 )E4 . 1 QQ` '& 5 )* $+' ' )V )E4 =. ba r!4 1 $* P ' AM ' $.% .D* $* P 3$+' AM ` G& b2 . QQ` )E4 )E!+ )* )rSO' !~ ' )%Xi 1 .

PP` ' )V (jog) )E4 > . 5" O - 1' (`') .$ %1 5W / -f2 .=9 (!3 ' QQ` . PP` r!4 )E4 . . DO' O - 1' ( [) .DD* !& AB 1 .DD* !&

103

' )V )E4 . ]!^& ' AB

' )V (`') XY yO 5W -f2 .=: (!3

.1 ]M ' QQ` . PP` ' )V )E4 . )* AB r!4 ([) . QQ` . PP` .DD* `/ ' N^* P r!4 1 ' )V 1 )E4 5W Q!2 .

]M) $+' N ]/ Ž+. ! > x#'. b ) E xQ+ . T_\ <' K' Nk )5 O - ' Nk .DM )M' 1µm .P DE 6S 3(G ]j( T_\ 1' . ! G' T_\ )E4 !& ' 3$+' 5!+ ×10-8 & )V& O' > ' 7D& $%& E N@ $;" O 1 Nk .DM )M' =. "V 8& = 1 ' . $+' [EQ <M ) L# 2' 3 !- ' / T_\ )%Xi > . . !- W' a@ (back pressure) ^- 7D& $E" ) T_\ )%Xi N51 .

104

) AM ]!S $P O' 1 )!@' )* 1 N^ . ' 1 Ž+. ! 1 Y" W_! > .$+' )( 7'_(' 1011-1012 ) 104-105 /cm2 O' AM + * $P > 3R 2' .$+' (Frank-Read) – >' ( nVD 9+' 7'_(' ' RV/ `/ 1 )E!+ . <'t = 1 H&' )E!+ B O' )GQ/ .( ]M ) M

.5 V" τ M 7D& $%& C . B n . O' )* '. Š1 . ! 75 == (!3

BC )GQ/ M F = τ.b.l '. Š. ! 3 - R5"' E ) τ M 7D& > -' :$M N'& . - H R LGM ()

τ.b.l = 2T sin θ

71* P & {D%' LGM )!P 7'_(' 35"' 7D& 7'_(' NM H 3)Q8 2' .( [ ]M ) - ( l ) 1 n 2! )Ei( Rb `j ' R )!= & !& ' WO? 7D& .(m ]M) D* . ) NM H ) L. M . M '4 )8EP :(T=Gb2 )D' ) )=& ) $+' O <i ) '4 2' ()

τ ≈ 2Gb / l

$+' a+ [+ )Q' ) :. G )Q' 2'

105

Hg;" r!4 . )8QD . 2' Nk 3M A!^* N. ! ) C`. C )8EP 3$6 L# 2' )D' O' G .( ]M ) 3M :,P "6 . [,= ' 51 DM à 3',- / R.' D ' AB )GQ/ N51 . M H!8@ ABC s . )8EP 3(' |X&' .( A ]M ) $+' AM ' )!.' O - ' N51 (#' )8EP > ' 1 ]!^& ' )K )8EP > & - H A. '& AB )GQ/ 3 ^! 7D& R5"' K' R5"' )'' . T @- . D* $* P N. ! ) "GM <i ) '' )8EP )!P 7D& )E!+ )* g= & .D* !& )8EP .% 'G& '& nVD 2' 3M 7D& . - `/ 1 )8EP n5& )E!+ AM !& (back pressure) NO Y4 1

.$+' AM AO )+ 3)( T_\ )!P . !o& ' &5# – C nVD .=D (!3 τ ≈ 2Gb / l 7D& )* + /. )8EP '4 )Q8

106

‫‪ -12‬اﺛﺮ ﺑﺎﺷﻴﻨﮕﺮ )‪(Bauschinger effect‬‬ ‫اﮔﺮ ﻧﻤﻮﻧﻪاي در ﺗﺴﺖ ﻛﺸﺶ ﺗﻐﻴﻴﺮ ﺷﻜﻞ داده ﺷﻮد )ﻗﺒﻞ از ﻧﻘﻄﻪ ﮔﻠﻮﻳﻲ( و ﺳﭙﺲ ﺗﺤﺖ ﺗﺴﺖ ﻓﺸﺎر‬ ‫ﻗﺮار ﮔﻴﺮد‪ ،‬ﻣﺸﺎﻫﺪه ﻣﻲﺷﻮد ﻛﻪ اﺳﺘﺤﻜﺎم ﺗﺴﻠﻴﻢ در ﺣﺎﻟﺖ ﻓﺸﺎر ﻛﻤﺘﺮ از اﺳﺘﺤﻜﺎم ﺗﺴﻠﻴﻢ ﻛﺸﺸﻲ اوﻟﻴﻪ‬ ‫آن ﻣﺎده اﺳﺖ ‪،‬ﺷﻜﻞ ‪ . 68‬دﻟﻴﻞ اﻳﻦ ﭘﺪﻳﺪه‪ ،‬اﻳﻦ اﺳﺖ ﻛﻪ در اﺛﺮ ﺗﻐﻴﻴﺮ ﺷﻜﻞ ﻛﺸﺸﻲ‪ ،‬ﺗﻌﺪاد زﻳﺎدي‬ ‫ﻧﺎﺑﺠﺎﻳﻲ در ﭘﺸﺖ ﻣﻮاﻧﻊ ﺗﺠﻤﻊ ﻛﺮده )‪ (Pile up‬و ﺑﺎﻋﺚ ﺑﻪ وﺟﻮد آﻣﺪن ﺗﻨﺶﻫﺎي ﺑﺮﮔﺸﺘﻲ ﺑﺮ ﺧﻼف‬ ‫ﺟﻬﺖ ﺗﻨﺶ اﻋﻤﺎﻟﻲ ﻣﻲﺷﻮﻧﺪ‪ .‬وﻗﺘﻲ ﺟﻬﺖ اﻋﻤﺎل ﻧﻴﺮو ﺑﻪ ﻓﺸﺎر ﺗﺒﺪﻳﻞ ﺷﻮد‪ ،‬اﻳﻦ ﺗﻨﺶﻫﺎي ﺑﺮﮔﺸﺘﻲ ﺑﻪ‬ ‫ﻛﺎﻫﺶ ﺗﻨﺶ ﻓﺸﺎري ﻣﻨﺠﺮ ﻣﻲﺷﻮد‪.‬‬

‫ﺷﻜﻞ ‪ .68‬ﻧﻤﺎﻳﺶ اﺛﺮ ﺑﺎﺷﻴﻨﮕﺮ‬

‫‪ -13‬اﺛﺮ ﭘﻴﺮ ﻛﺮﻧﺸﻲ )‪(Strain aging‬‬ ‫‪. 71* NS '7k . 7'_(' A W%+' NS b )* $+' &!E5" ^ * !4‬‬ ‫‪A5 ' (E- )Q8 O' ]V/) >!+;4 W ( !!\& '8 R5"' O' G ' ')GQ/ )kNDk‬‬

‫; ‪.P &' P )= $"+ Dk‬‬ ‫) ‪” o O+ !4) !- ' / A* & ' . (Y )Q8‬‬ ‫ & =) ‪^D& >!+;4 ]M !!\& 3 !- ' / 7^* $%& '” )5 . (' -+‬‬ ‫‪107‬‬

P' O
1H&' tX 3( 2' $E" .(' |X&' )!.' H!E@& )Q8 O' &?

]M .(R &* X@5&') M 1NS (]X/) N * 2*+ . O+ !4 b 1

(y) )Q8 ^ * !4 ( 75 . ]M

108

H#? ()

$# ; t & # CXO (!3 ]2 $' H6!

DS ( 3M .% T_\ )* D1 .1 Œ T_\ )E!+ E ' ]M !!\& ]M !!\& $" + . T $' # $# ; &>? ' .D* $ ]M !!\& E/. . !- W' tX T_ . ' )' O T_\ )E!+. ) ]M !!\& 3H* .M A' x!#& ' 2' O' W'* 1 O s6] . $* P i <%Xi '' T_\ )E!+ >!+;4 ]M !!\& )* M A ]V/ ]j( .(' |X&' ) $V@ E $5@/ > V@ O - ' Rb O' p AO'' ) E = NS = 0" 3T_\ D sE $Ej 2' .( ]M ) 3M A (slip band)T_\ 1' <i ) xQ+ . )* M (b)

. # ; E 5W n c/ % 0 s6] E <&B # .D_ (!3

109

E <%Xi . n!+. b ) T_\ 3)VM $.8 N51 3_ !4 7D& N * ]/'P '

^ )* (' 1' |X&' H*' $6= T_\ 3A.;" ) .(' |X&' 5&' k o*'P ' 2 & H* 6= 3)! . (b 2 & A&*) G& 5&' $!G/ . 2! )Ei( 2 & A&* .$+' M A

O' ‹ UQ O'

' )+ E xQ+

. 3A ]ˆM !!\& O' Y4 .(]ˆM)

5&' 1 )%Xi = )= K' T_\ UQ 2' )… M A 3 &? 1 5D-_

!!\&

)'' 32!4 1 .$+' H&' ‹ Q/ ' 6S 2!

)Ei( . AS =

<%Xi . )E D@! )!.' T_\ <%Xi . DS = )* AO& T_\ UQ3 ]ˆM back-) NO Y4 1 7D& b ) 1 ^D& AOP )… Nk . M 1z = . )'' = <%Xi . ]M !!\& ', 3A * $a+ ' = .. ( pressure 1' T_\ UQ3? 1 .(]ˆM)D@1 >_ H1 ) T_\ UQ . DO' 4!4 3 T_\ UQ O' . 1 Œ 5… T_\ 1' 2! . M _… 5 $M (slipT_\ ' N51 )… .S = E xQ+ ' )E4 . A!+ xQ+ ) . A … $… P ( )]ˆM 3DM band)

H > B– A"B# o $/# s6] 0 . D (3 110

T_\ 1 ' . UQ .D4 (3 BCCE )… &i 3D@1 H!8@ <i ) H . FCC 3RG( T_\ 1+' . 1 )%Xi . M 5 ' A.

1E T_\ UQ

)%Xi ‹ . D@1 ]ˆM =

fa^3 T. . )E!+. ) . 1 Œ T_\3 1+' . 1 )%Xi NS )… D@1 1 )%Xi . M . $+' fa^ NS $6= )… E xQ+ .3 T_\ UQ

).'O !- AO''

.E 7 … ]… T_\ $6= . T_\ )%Xi . = )= ]… N' UV&' 1E . FCC , BCC, H 1_E(

' AM A1^ T_\ 1 $6= . 1 )%Xi

T_\ 3 NS )… $+' ' )%Xi 3AM A.S )%Xi 2!@a . ' AM A.S ( )]M FCC ]!ˆ^& ' T_\ H@!+ 3 )%Xi NS T_\ $6= . T_\

)%Xi c!… & . $+' AM A O

)! T_\ )… S O' . $+' E +' 2 & A ^(3 T_\ +' 3 $P 1 . 1 )=& . DD… $… P3 ' 2 5… 3 1 H@!+ 2' 1 3 $+1 $… P 1 g Y43 $+' c+D NS O - ' ., 3 g $… P ' WO? ' )ˆD' ) O! 3$… P ' ' 7D& 2 5… 3D@1E <6= 2 & A ^( ' .$+' O _! 6S

+' 3 6S O - ' )…

)Ei(. D@1 E )%Xi 2 & H…' 3 T_\

1 )%Xi .'

. $+' WO? & O M 7D& 3 H… 5&' )!@' )%Xi . T_\

111

G# 1 7D& b ) " 3n/'. .' ^! ,4 ]M 3BCC 1 )VM .' ^! s % 1 . 5* _ !4 7D& ' O ' ^! ,4 ]M 3 FCC .$@! +S * 3 H' %!= & T_\ 1 H@!+ D! 7!4 <%Xi 36S 2! )Ei( 2 ^! )!@' o*'P <%Xi NS )*_ !4 7D& 0% 9+' R-'_1 1E RG( T_\ <%Xi )* $M' I' $+' 25 3D@1 %!= & T_\ 112

^D <%Xi 3M (1/633) RS A' '8 O' 5* C a $V@ -' .DD* !!\& C a $V@ . - & H*' 3A"/ )%Xi ) $V@ 5&' I O' 2' .( ]M ) 3M A' x!= & < 1120 > $6= . {1010} . T_\ 3$P 2' ' 5 x!%i W! H_!D 3$V* . $+' $+ W!!& . H!* O <'_E( ' cEQ .' A * @= _E( )+ 2' T_\ ( ' ' <%!#& 2!88% .( R.= ) 3M . ' )* Q51 3$+' %!= & T_\ )%Xi A"/ )%Xi 3

C > 1 / 633 /. 3 : b O' a

<6= . <%Xi V@ 5&' 1 )!@' $!51' . 0% 3D' & .$+' AM A' N^ H!* . G@ T_\ H@!+ N'D" ) '& )* )%Xi . $6= O' d c!* & > 2!!G& E . AM :QG 3D* ]5"

I O' ' D@1 8QD k I O' !' +

1E T_\

1 H@!+ O' d &V!* &

1E !&+'. ' 1 7D51 3$?'.* 1E / ' $6= 1!4 <' K' T_\ 1 H@!+ 'G& 3DEQ ' I O' 5&' <* P 2!Dk > Nk . - H@!+ .("V@ 1 _ ) M .% 6S ,4 ]M D ) ' 2' G@ ]M .' AM

.S - () R.= caD !' +

1E AM T'_- T_\

]M !!\& > ]M E* 251 7 * > ]5%& T' '& ) 2!Dr51 A >

1

,4

)* ' N' /. L# 2' )* ' N^ (Von Mises)E6 / .' @ 3 E A'a > [@P ) 7 * ]8@ {_= 1 )* H!1 AO=' -' .^ RG( ]8@ T_\ H@!+ 3RP 1 ) .M A' f!a^& NS D ) H@!+ 3( ]M ) M )M',- T_\ H@!+ H@!+ 'G& 2' D 3 ε xx + ε yy + ε zz = 0 )* $+' $K HP DS ( > >!+;4 ]M !!\& !& ' EM !!\& )* $@S ]8@ T_\ H@!+ > . 71* ) ]8@ T_\ 1 . - !& ' T_\ 1 H@!+ c!* & 1 )E!+ )* D* ' A"/ T_\ H@!+ O' .M ]^ R- '_1 ' ]8@ T_\ H@!+ 2!!G& T_\ H@!+ . B8( 3)^ b ) .DE8@ 6S 113

&. B8( 3 < 1120 > {0001} (basal)

- .M A' f!a^& ^D T_\ H@!+ O' D'& < 1120 > {1010} ]8@ ^D f!a^& ]* T_\ H@!+ O' $+' 25 < 1120 > {1010} 1 ]8@ T_\ H@!+ )k .

' A"/ T_\ H@!+ . N_51 ]5" )E!+ D'& ]iP 1 ]M !!\& 3M A' 'G& A.;" .$+' m!P' _! 5D4 T_\ H@!+ > 3)! 3 - !&

^D

,4 ]M x!#& ' C $6= (#' T_\ 3(!D!V ' G 7a ) ]M !!\& E/. .$+' WO? R-'_1 +D6 1!S AM A1^

114

H . BCC, FCC $' # ; # { s6] $M .D7 (!3

115

l 6Z' $'# ; # J s6] tRIk . 7 /&

6;

C/a1M

tRIk s6]

Be Ti

1.568 1.587

Zr

1.593

Mg Co Zn Cd

1.623 1.623 1.856 1.886

{0001}  −  10 1 0   −   10 1 0   {0001} {0001} {0001} {0001}

[> $! # <&3 <&'N s6] $M . 9 /&

<

# ; S

J 36] dM

Diamond cubic

{111} p 110 f

NaCl, LiF, MgO

Rock salt

CsCl

Cesium Chloride Fluorite

{110} p 11 0 f {110} p 001 f

C, Ge, Si

CaF2, UO2, ThO2 TiO2

Rutile

MgAl2O4

Spinel

Al2O3

Hexagonal

−

−

−

{001} p 11 0 f −

{101} p 101 f {111}

−

p 110 f −

{0001} p 112 0 f s6] %&>' 7

)%Xi . RG( M 7D& )* (' |X&' /. E >& > >!+;4 ]M !!\& L. M $P@ )* M A () ]M O' .+ ' % '8 > ) T_\ $6= . )!.' T_\ :$+' O & )5 nQ8 xQ+ $P@ =Ao :$+' O <i ) T_\ $6= )%Xi 2' . . ! )X 32' A.;" Ps=P cos λ

( ) T_\ $6= . . ! 2! ).'O = λ .

% . ! = P

:$+' O !+;4 ]M !!\& .+ M R@ * >& > H!E@& W%+'

M5 # s6] / s6] %RIk $l <&>' N H l5 .D9 (!3 $# |l# # R % 1M

117

*( 2 -_ )* (' 1' |X&' M_\ H@!+ NS . H!E@& )* H!D! ( ) )G O' T_\ $P D ) 3DM 9 + H@!+ 'G& B8( -' 3)! .M )M' ' $!5M' H@!+ V@ $6= <M ) '& H!E@&

' WO?

. ! 3H!*.

. <'_E( A"/

.D* !!\& ($!5M' *( DG ) T_\ :' v M O <j N'& )I% ) )I% ' T_\ )+D1 A ]M O' .(' /X&' )k 3D* H!E@& ) L. M E >& > /. )* ! I |X&' . O 1 <* N * = )^ L# 2' ([ ]M ) _\E 37^* A+ 1 A !- )E!+ ^^* )5 > E <%Xi V= $* P 2!Dk Nk ' ).'O )* M V T_\ <%Xi 3($+' $K 7^* A+ % Nk ) 3M `/ .(m ]M ) .D r xi > xo f 7 k $%& n= Rb B+. E <%Xi )* ' A' N^ x & 4 w b O' <GQ ' / N_51 75 . 7 k $%& 37^* A+ 1 A !- 6' _ . !- ' / . !-

118

!!\& O' G ([) . ]M !!\& O' ]V/ (`') .M5 s6] %RIk $l .D: (!3 $* P ) $V@ R@ * <GQ/ )* = A !- O' AS = $.% N. ]M

5 A !- O' AS = $.% ]M !!\& O' G (m) . M_\ 7 k N. ' DD* . K nQ8 T_\ )%Xi 7 k (Texture 5 R2 t ) $# ; $ .9 ' / )^ !- $6= $%& )' 'G& 3E Dk > )* * j& N'& 3]V/ 7a O' 1^( )E!+ 2!G )' > )VM A.

!- $6= 3. I' )* Q51 . !

Dk > E 6( T @- DS ( . M !-E= )+!4 1 )' : b O' 5"' .D* A!r!4 ' E 3$+' AM A' N^ R.= 1!S . <'_E( O' 'G& ' )5 1 H!+ 1 $(

K 1*( N'D" ) g_= 1 n!+. $* P . 3! NM E/. 3nb8 T_\ . .' AM 6D^!4 1 |. . 5!+ 1 $( T @-

119

[> &> $'"B # # $' . : /& "B FCC ‚O # ?( A 8 } W!D!S ]! Y BCC 3W& 3NV! 32@D& 321S

Rolling Texture#

(110)112 + (110)[001] −

  − − − (123)412 + (146)211 + (112)111      

(001)110to(111)110 + (112)110to(111)211 −

−



H H_!D 3$V*( c a = 1.633 ) . 3W!* c a > 1.633





−





−







(001)2110 −−

  (0001) plane tilted ± 20-25◦ from rolling plane about a [1010] transverse direction

axis W! 3H!* O 3W!!& c a < 1.633

(0001) plane titled ± 30-40◦ from rolling plane about a [1010] rolling direction axis.

&3 5 ;U/ H6! g 2 (!3 ]2 – (Twinning) 5 ;U / (!3 ]2 .: ˜XP

' ]8@ T_\ H@!+ ]/'P N_51 ]5" 3M N! ]V/ 7a )* Q51

$@M 0" * 2' * .M WO? E Dk = >

1 )' O +!4

]M !!\& 3M )M' ]8@ T_\ H@!+ (* 'G& E Dk > -' . - 9.O ' WO? (#' ]M !!\& 1 H@! . - RG( <'_E( O' pG $+' 25 E/. $+' AM E/. D- /. ' E > ..S H1' ( ' A'a ]M !!!\& > N.S = E/. )%Xi ) 39G' E )%Xi .M 7a ' )D!gS j& 3NS )VM O' 7a > )* .M E/. $6= . )%Xi O' ]^ E/. H@!+ > .$+' :. G

5 ;U / / s6] $;!3 ]2 %M5 .: 1DS ( 2' O' AS = ]M !!\& 3 AM E/. . )( T_\ E > 2! <.X& 2 &MS . > 3M T_\ )%Xi >'' A+ M R8' > ]M T_\ )!P .M

120

)( - ' / 251 M 7 * > $%& )* $+' E H@= > O' ' )!P ]M !!\& E/ .( ]M )<.X $6= ' $+' H@= + )^ )EiP + )b ) $+'

cG ( `') .!XO (!3 ]2 E <&B ;k J! # (!3 ]2 D= (!3 $6= A. 5 AM E/. cG (m)3 nb )E4 )( T_\ cG ( [ ) 3m="' N. DV+D E/. )%Xi O' )Ei( 1 g= .E/. N! ! W' O - ' 2Dk '8 ) $* P T_\ 3M N! ]j( )* Q51 3)!.' <6= ) $V@ γ M 7 * '8 ) <%Xi 7 k O' E/ . ]M !!\& 3' . ! 1 = )* M A m ]M O' 3n/'. .M M 3E/ . )%Xi RP

& w!/ 7OS .$+' c+D E/ . )%Xi O' T' )Ei( "5!8@ 3E/. N! )%Xi 0" NM E/. DS ( )* M A 3 VG )VM > NM E/. 1 = 2' $!G/ ' )D!gS j& 3E/ . 7a 5&' 1 $!G/ )b ) AM )VM 7 k ]^ E/ . H@!+ _! D' .( ]M ) 3D1 75 ' A^ E/ . 7a 1 AM )g'' () R.= E/ . 1 H@!+ pG .M E/. $6= . E/ . )%Xi O' .'

121

' AM E/. 1E ! )8QD . # 6 < / J! # ; # &3 ;U/ .DD (!3 .' AM fa^ _! E/ . $6= . )%Xi .1 N^

5 ;U / $' / %RIk . = /& 5 ;U / 3 G

5 ;U / / %RIk

# ;

0/707

(111)[112]

FCC

0/707

(112)[111]

BCC

Cd, 0/171

 −  − − 101 2  1011   

H

Zn, 0/139 Mg, 0/129 Ti,

./189

)5 > )( ]M !!\& xQ+ )* - MS /. ]M !!\& W_! . 2' 1 <.X& .(]M ) . !- ' / 7OS NM * ]8!i O' G N. - N5 (A SFE ) )@ ) $+' = UQ ) : b . E/. 1 .T_\ K' : b . 4+. ! j& !!\& )r!1 )* - 0" E/. N! )VM A. 122

!- $6= ' O M 5 A ]M

N * “' . N' ]8!i O' G . - [&O Ž+. ! ' M 1 +" O' xQ+ ) DM A' 51 )VM A. !- $6= 6S ' O D / E/. 1 B8( 3)5 A. .( . [ 6EM ) 6EM ) ]M !!\& O' ]iP 1E/. 2! )* $+' c+D 3H. 7!4 ^! )S O' ]V/ .HM ]g/ f!a^& ( . m 6EM ) ]!S 1E/. . ( [ . `' :(]M !!\& )! E/. . ]!S E/ . 3$+' = E/ . L . n/'. ' AS = >!+;4 ]M !!\& )! 3 . _E( O' )GQ/ > ]M !!\& 1E/. .' )M' =. >!+;4 ]M !!\& O' ]V/ )5 ]!S 1E/. )!P 3=

1 )' M . EV& A' 51 ) } EV/ &' P <!E5" 2!P ]!S 1E/.

c!& & j8 3=

1 )' = 7D!k HI >

!- ]M 2!P .' )( - ]M

]!S 1E/. !- ]M ) 7D51 2' 3(7D!k f8 D )) S = )!.' N!k ] B AM A' N^

' )%Xi N!k f8 3Ro

' . - H

' )%Xi. )* !D* )=& 2!Dr51 ..S = ' E/ . O > 3ABCABC/BACBA ' ( SF ) 7D!k f8 > 3c!& & 2' .' )^ ' ' / E/ . )%Xi : b . )* .( B ⁄ B DG ) .S = .M 5 ]!^& ]!S 1 E/. 35/ 1 )' ]V/ O' ( SF ) 7D!k f8 =. N. A $+' " .M 3' @ ]M !!\& '8 ) 2!Dr51 7D!k f8 R5P' Nk .(O SF R5P' ) ' ]M !!\& )D!^!4 ' ' )^ 3AM EV& A > AM $( ]!S 1 E/. 'G& ..S H1' ( A

123

: DM O ' / ) s6] . 5 ;U / $ ' t/I2 . . .: A * T_\ 7a )* &i 3$+' )!.' )VM )D!gS j& 3E > )( E/. 7a ( .$+' )!.' E D51 +' '' 3E > )* &i 3$+' E O' ]* sE > ' 3M = >

'' 3T_\ (

.$+' $'D M 7 * > 3E/. 3E/. T

+' )* P 3M XD $Vo $+' 25 3T_\

+' (

.D* E/. j& ' )* '8 ) $+' .%

' . 3M ^! + I ) 3T_\ )@8 E/ . ' WO? 7D& ( 36=& NM b ) 3E/ . )"M' ' WO? 7D& .$+' 9@P 5* 3<' P )= .$+' NS O~S ' WO? 7D& O' 5* 5 A1^ N * “' . . 2! O' T_\ <' K' )5 xQ+ N * 7!4 ( N * “' . 3. 2! O' )5 xQ+ N * 7!4 )k - 3E/. <' K' . .M .M 1z E/ . $6= .

)%Xi 2 & R.' 3H R-'_1 H*' +

1_E(

Rb - @- . NM A ^( c= E/ . S )* L# 2' 3M 101 2  1011 −



−−





3/

O' -_ c/a $V@ Zn . Cd .M 2!!G& c/a $V@ )E!+. ) 3M c %

!!\& 3 c/a=1/633 )* D1 .(' |X&' E/ . 3M A ^( c% $6= )* D1 c % $6= )* D1 Mg . Be D c/a<1/633 1E . $+' Xi E/ . W ( .( ]M ) M E/ . k 3M A!^* $+' N5 NS E/. <6= . <%Xi )* 1 N^ ' R-'_1 E > '' ]M c/a 1E . ' AM E/ . k ^( 7D& $%& )* 3 O' -_ c/a 1E YZ+ . .' AM E/. k ^^* 7D& $%& )* 3 O' & >k*

124

. AM ]8!i 7!4 O' (Zn) . (`') .!+;4 ]M !!\& O' M %Q+ <' K' .DF (!3 1 . ($+' . 2!g4 ) uk . ? O' <' K' ) T_\ UQ AD1 N^ 3)( ]M !!\& ' E/. 1 B8( )* AM “' . ]8!i ' (`') D51 ([) . (8(' h_ ) E/.

! ) H!8@ T_\ UQ AD1 N^ )( ]M !!\& . ]8!i ]V/ O' } (m) .1 N^ )* “' . AM ]8!i . (m) D () . = ]V/ O' ]!S 1E/. . (2!g4 N!k f8 ' .1 N^ ' ]!S 1E/. B8(

.<.X c/a H ' E/ . .DL(!3 125

$} I s6 / $ % E s6].= DM ‹!+;4 ]ˆM !!\& ' W_! . 3 tX T_ . ' )' O T_\ )… E'" . 71… 7'_(' <'_E( Wˆ%+' M )X- R.' ]j( )… b N51 .5 )i; O <i ) N'& ' - 7'_(' K' Wˆ%+' 71… c= 7'_(' 1 = 6& G& 'G& 7'_(' Gi W_!ˆ ? 1 1 n + $… P ? 1 H&' n + $… P . tX

1 H@!+ NS =. ) . 3 7'_(' <'_E( M_\

1 H@!+ !!\&

.D1 71… _! ' T_\ L. M ' O! 7D& )… = M_\ ' )' O T_\ 1 W_!ˆ NM RG( K' A W ( !!\& 7'_(' 2( -' / AM + … <'_E(3Ro N'D" ) .' ˆ + '4 ' C G )… AM $a+ !4 !S .M $M 1 )' . AM EV& k ? 1 $+ O' + <'t NM $M ' Wˆ%+' .M !4 AO'' O' 7! !- ' / <' P ? 1 AM $a+ [+ 1!S = 1 [+ )… $+' 2ˆ5 32!Dr51 .1 . D1 $+ O' !S Wˆ%+' ˜XP ' S… . M )_& . R;%' k ? 1 + <'t T 1 W_!ˆ NM RG( ( ™' - . N!+'!@…') ? B!% _E( 7D…'. )' O T_\ . D5 $… P H1 ) $V@ D'& E Dk ' 1 )' 3? 1 7 … Œ 71… . 7'_(' . (' |X&' )' O '' )… $+' M D' ( ‹ ' . 7'_(' Œ 1 )'O '' T_\ 3 E Dk ' 32!g4 7 … Œ . ? 1 <' P )= )= )'O Wˆ%+' )… M A (

' )'_ â Wˆ%+' ) G 7a .1

).'O 1 )'O Nk .$+' & ]5% 6S . T_\ . 71… ? 1 <' P 126

' B' M 2' O 7 … 3D1! W' ' T_\ 2 ^! ^^… % ) $V@ )= H1 . )' )+ AM “' . 7!4 xQ+ . T' 'G& ' N'& ' L# 2' .M )!.' $P ) $V@ 3 H1 ) $V@ 1 )' O T_\ $EG T_ O' G )… ' N^ C. B,A .() ]ˆM 3' AM =

% E s6] E 3 YZ' (3 ]2 .F_(3 i N'_! ) )… $+' AM A 2!4 1 7D& f 1_E( . T_ 7OS 71… 7D& 7'_(' i 2' )… 3M M ' )'O T_\ O' $+' 2ˆ5 E… 7 … $K ” V@ '8 7 … ]… ) 3)'O T_\ O' M 7 … $V@ 3]ˆM !!\& Rb . M R D… T_\ 1D' ( B+& ' )'O T_\ )… $+' 2' ]! ) 3N $K 2' .$+'

127

. 3$+' .% )'O T_\ 2' D .$+' 'M 1O nb8& A 3T_\ 2' 2( - = . .M R D… 5G T_\ 1 DS ( 251 ]ˆM !!\& Œ )E!+ . 3$+' O (vacancy) 1= 6& G& $IE~ )… = 3[.t )Q8 ‹_ 1 <' P )=

!!\& tX T_ WD ….O+ ‹ )E!+ $+' 2ˆ5 E Dk ' 3n + 5&' = .T_\ )E!+. ) )ˆD' & DD… '!4 ]ˆM % 5" 1O ) 1 H&' = )E!+. ) E ‹ 3M A ]ˆM )… )51

!@ .1 Rb 7'_(' '& 3% NS O' 1O ) 1= 6& tX N_51 . 3^^… )… $8!8P 2' O' AX+' 3M_\ ]ˆM !!\& O' tX T_ .$+' 1 )' AO'' '8 ) tX D) $+' 5"' 7D& c+D ” 5!8@ 3AM ' ]ˆM !!\&'8 ) . 37 … Œ ‹ Oˆ@. N;!+ N'D" ) 1- ' DS ( 2' 32 D .$+' ,4 f!a^& (&! )Oˆ@. .D E A

3NO ) )@'. 7 … c= ^^… % O' 1O ) 1= 6& < =6 .F (3 M tX T_ . 128

dW>O () t & ' H!R $' H6 ! 0% 2' .$+' AM + <'= 1 W%+' . ' - $a+ 1 T. $5@/ 2' .$+' v Q T_ . @ $.8 7'_(' _! 1- . YD(& 3a+ 3W%+' 7'_('3 .D* O 1= ( ' 56 78 + 3$+' AM *t ]V/ 1 7a )* Q51 `& 3N' ]M 1 T. 3 - )a ) G )EP . !5!M c!* & ) R.' )EP +

!K& $%& 31DS ( 2!Dk ! 1 -. .$+' )@'. &' P <!E5" L'' . M= N-- 1 f8. AD*' 4 1O( 3 _E( )VM 1O( 31 > 31 j $IE~ '8 3)'O 1 n5& ]! ) a+ 7 * 3M AM' 2' O' 7!4 )* )51 .D@1 ' )VM RE%

1!S $+ .$+' 1_E( 1 W%+' 1 T. O' 3N@ ]M !!\& R; :DM O ' / ) 1 W%+' 1 T. .$+' T. 3= 1

+ * B+& a+ 7 *

strain hardening

= RE% O+!S

solid solution hardening

+ ' - $a+

precipitation hardening grain size hardening

' )' _ ' - $a+

martensitic hardening

_D& ' - $a+

reinforcement hardening (c* ' ) ADD* $8& ' ' - $a+ .M A' v M ja Q 1 T. 2' )''

# g 2 [ G. i ) >_ 3 + * 1DS ( . H!+ 7^* 3 ]M 31 ]M 1DS ( ' . ' . AM ).' ' )VM + ' )!8 .M ]V& - ) ( j ' 129

)k 1 . + 1_E( 0.01 − 1.0cal / g >_ ) AM ).' ' '8 31 7'_(' 3AM ).' ' .$+' ^! '8 2' 3M &O _E( !S jD" i . [.t )Q8 $+' 25 . 7'_(' 3 * <' P )= 71* _! . 3LVM' P & _E( 7 * 7'_(' .M E/. . 7D!k f8 Q . ]!^& : i 3AM ).' 1 ' O' !@ )* D1 .M ]V& 1 2! 7D*'. ) 3AM ).' ' A5" 7a 3 ) 3AM ]!S";* $P > O' A . 7'_(' 3n 5!+ ( ρ ) k ., ' M Wˆ%+' 2! Q )Q' ‹ )… $+' A' N^ <GQ ]!S E N.S $… P

' WO? 7D& ) _ !4 7D& ^ τ ° -' .$+' ' / AS 3M (AM ()

τ = τ ° + AGb ρ

‹& ' / / .P 8 $K ‹ A 3O - ' AO'' b3 M R. G )Q' 2 ' AM '

1 k 7'_(' 3a+ 7 … ', .M 31_E( E Dk . E . 7'_(' 3 +…

‹!& 5M Q )… $+' AM N! a+ 7 … `!i& ' ( R ) N-- ….O+ }D4 O' a+ 7 … AM C ( )… $+' (Tylor) E!& O' R 2!.' .$+' AM A.S ]ˆM R5"' ' WO? 7D& )… DG .M ' 1 2! ‹!+?' 7 … 1 AOP 1 )51 )E!+. ) AM ' . 7D& 2!! '8 -_ ) 3A. - N! O' ‹ . ! 1 ` O' )ˆVM |( ‹ NS )… ' N! ' ' (Seeger) W. R .M 1 7D& )… $+' AM C ( D' .' AM ]X/ 2…+ 1 )E!+. ) (pile up) ' AM ' AO& 1 $… P 3 1 ` O' ( backup pressure) NO Y4 1 1 2! N@^… 1 ' 1DS ( 3( Basinski) W+ R .D… ]ˆ^ 1 )E4 A' 51 ) 1 $… P 3(Mott-Hirsch) W6k R .$+' AM A^… j& ) 130

HD4 R .' O!

^! 7D& ) ' AS = ; ” V/ 1 )…

1 & M h_ (… AO'' ) $@ N;!+ 7D& )… $+' AM C ( (Kuhlmann) A 8 Nk .D… H N. ! ) ( ]D= ) A!r!4 H1

1 )ˆVM O' '

) () )Q' wQ . N@ˆ 1 R 2' 1 R ( 3$+' N@ˆ 7! . H… 3AM 1R .' @ k

131

T_\ O' 1 k ρ .[ G & ~>O %M5 .F4 (3 .$+1 ]D= ]… k ρ f 132

. ADD…

N'& ' 7'_(' 2' .D 7'_(' 3 +* 3H!E@& W%+' . a+ 3? 0% wVb .' 75 ]M

# A> 2 / $5|O @J G' / / / d;M2 G>2 G5 6 .F7 (3

!!\& .S = 3($( ) E %!= & $6= . AM O' 1 )' + … 1DS ( ' $'1 )* &i 3.S = ' )!@' _!k 71* 3_E( O + ]M 3 + * K' !5!M ,4 7D*'. A5" 7'_(' . 7'_(' - U@V' . 71* N. AM + * } !S /. {;o .' - 7'_(' ) )* $+' E" 2 & H6

K' s & " )* 1 N^ ' Ej( s & A4 3 !- ' / s!S RE% A!= E* nX& &' P <!E5" )E!+. ) 3M )X- 2' O' 7!4 )* +* [EQ KS .$+' ^D& - 1 W ) 3<' P )= O' A.% )+ 3AM +* A (]!S) &' P <!E5" .M )= O &' P <!E5" .D@1 H1 O' ‹!ˆX& ]/ \% &3# . &W # ;12 35E .1 !!\& 5* !@ '8 ) ' )' + . !- W' [.t )Q8 W+ ‹ O <' P

133

7 * )* 1 N^ Y' & 4

1 7OS .M )!.' $P D51 ' $'1 . 71* )VM &W# ;12/ 5E . 4.

]ˆM !!\& O' ]V/ $!G/ ) $V@ &? E' ' 3 + ]ˆM !!\& O' G <'_E( $+' '4 ˆ!ˆ ’% O' )( ]ˆM !!\& _E( O' ]iP )ˆVM + )… P . '

!!\& 2!P )… ^ … a+ . a+ … A4 2' D .$@! '4 ˆ!D & ’% O'. W A4 W ) E8 A4 W' w b O' '& 31 Œ 2!4 1 + ]ˆM _E( N' <' P 3 . 2' O' .M N' V= 3$+' A' 51 k . 7'S !!\& )… NM ' B' M . m ˆ!ˆ '4 $P O' ' NS N'& 7'_(' . AM A' + ]ˆM !!\& )( ]ˆM !!\& _E( NM W ) D )… 56 1 A4 .5 H1' ( NM W A4 W' ' . D@1 &W # ;12 / 5E 3M . O )rDk .M W' ˆ!D . ˆ!&+' $P '& EV& . O 2!P )rDk . ˆ!&+' EV& . O ' NS M W' ]ˆM !!\& O' G EV& . D ˆ!D EV& . O 3 !- W' ]ˆM !!\& )8QD ]ˆM !!\& !- W' '& + ]ˆM !!\& O' G _E( NM W A4 NS W' )… DS ( š V@ DS ( L )+ ) '& DS ( 2' = 2' .' W ]!S )… 3$+' &' P <!E5" " d' pG <' !!\& ]ˆM .% &3# / &W # ;12 \5E :M H!@8& ˆ O' '_ )' + … K' )… - )=& . 1! N^ ' AM …t )EP )+ ' )' G' . ˆ!ˆ D'& )… DS = = . _ 1 )' EV& )EP . AM ' $6= 1 .DD… M ? 1 <' P )=

134

. EV& 3O O' ]iP . + … K' )' G' . ˆ!ˆ d' !!\& .F9 (3 Èa 1 A.% )' M

3O WD1 .$+' +* O' M AM ).' ' 3 EV& . O ' )* % . ! 1 7 *3DD… $… P (1= 6& ) ' )Q8 1 f8 3&' P <!E5" <' P )= 7'_(' 1 )* 1 Œ ]! 2' ) 3A4 2' .1 Œ 3+ NM 6=. Dk . AM 'OS )* $+1 Gi )E!+. ) .D1 71* ' ' & DD* ' H* ).'O " ( 1O . (G 7a ) 3M ' H… ).'O 1O 6=. Dk )VM ) 3 +* + .1 Œ EV& 3O <' P )= O' &?

1 <' P )=

KS )E!+. ) EV& .$+' AM 'OS 6S 7 * )* M 2_= = 1 )' )E!+. 7'_(' 3( ' 7ˆk) :QG' $!E/ . )( 71* W%+' . a+ 3M fa^ ! . 71* 6=& ]/ b ) 3 EV& DS ( R; 1 )!@' . … I O' .1 7'_(' ' )' AO'' 3&' P <!E5" <' P )= 7'_(' EV& R; 1)' + 3$"+ > < ) NS )* $+' &' P )= EV& <' P )= 3 D 1 !\ ) . $+' A.% >

'' )E $@! $K <' P )= 2' .S 4 = 135

E… Q .' @ NO . <' P )= ) k 32!^!4 +* '8 3c!* & 3)!.' )' AO'' N' <' P .$+' [.t <' P )= / & / A.% EV& <' P )= Wˆ%+' 71… 0" )' M . - )' M c= [.t

)= / O' ^!

)' M 31 " N._(' !K& .1 N^ ' ^( ^ * 1 N'! 3DM R;P 1 H&' O' -_ AM ]P 1 H&' )* &i H&' L 1 =. . ]M 3DS = ^^* 1 N'! M k* H&' -' . M . M $* P n 3AM ]P

|&' <' P )= Y!S Dk $@(S H!E@& 7D& . AM ]P jD" K' P F: (!3

136

Y!S Dk H!E@& 7D& . )VM m="' 5&' LGM K'– F= (!3

' 3(d τ/dc) AM )(#' jD" $IE~ P'. {'O 3H!E@& 7D& 7'_(' Œ )* 1!S )* D1 . !- .P j . !- )E!+. ) $+' 25 DS ( 2' .' @ r!4 1 . (R-' &) 2!^ 2! p( -!r!4 2! 7D*'. ) 31 ' .. _! w!/ =

1 RE%

' 3M 0% ? )* E% ' - $a+

1 H&' 5M -' .M T_\ A'O '& 5&' G# HI 3 ^! $IE~ 3= 6E% )D' H* HI !S M <.X 3. I' )* S 5M O' 3)@51

137

. ! 3D* b ' T_\ )%Xi )* 2!@a .S = (short range order) 78 3)D' H* HI )* $+' O !@ 1 ]M !!\& O' Y4 6D& . D* YP ' A'O ._ H1 ) ' G# HI "?5P' O 1 ]M !!\& .1 $+ O' ' O' 1 H&' )D' 4 HI .$+' <.X 3)D' H* HI (Long range order) )D' 4 HI )VM |( > )! 3DD* R\M' N_! )VM %!= & 1 N 3L >

-' .1 Œ )VM O'

O

1 N

. R\M' 2' .DD* !& (Super lattice)

) HID O( > -' .S = a+ 5* 7'_(' 3M ]* HI c= &' P <!E5" )= &' P <!E5" )E!+. ) YZ+ . S = ?

O' N * + n + )E!+.

.' =. W%+' 6=& NM 7'_(' N' H!E@& 7D& ) 3 K' 2' .$+' AM A' N^ ]M L# 2' .M HID !S O' ^! c&' 5 N. HID P' 2! 3E Dk > 1O 2' .M U (APB) O( S 1O =. .DD* $* P D* 1O 2!Dk !K& $%& 1 .M ]!^& 1 )' O . )' ADD* D*

. ! 2' D 31 7'_(' ' O( S O N'_! 31 T_\ )* SO'

HI . HID + ' 7 *–7D& '5 ]M . 7'_(' ]M !!\& 7'_(' Œ ' 3D@! <.X O HI . HID E ' H!E@& )Q8 .1 N^ ' Ni3 Mn .M HI E NS '8 O' ^! HID E a+ 7 *

138

Ni3 Mn HI . HI +

' 7 * 7D& 1 '5 .FD (!3

& ;R %;/ % HR G5 6 # 8 ( V . .4 W_!ˆ !S NM $a+ 0" AM ]P . (R;P ))D!O O( iD" 2! Èa c' # :;' )8QD ‹ O' ‹ $… P ' (#' … ) O! O' M !K& 2' . M = RE% ]!ˆ^& K' Wˆ%+' 7'_('

. )… H6 ]" Dk O . M )D!O $a+ W . M A' x!#& ',- K' = RE%

Xa / <& 3 (a $' d2 <E & @X – K 3M ^! = RE% ]!ˆ^& K' )ˆVM '4 &V" ) 3M ^! :;' 2' )k 1 . Y ) Èa 5&' AO'' jD" Dk N._(' !K&3Ro N'D" ) . 1' ^! Wˆ%+' M A1^ )… Q51 .$+' AM A' N^ . 1 ]ˆM NS H!E@& Wˆ%+' . 7'_(' !S H!E@& Wˆ%+' 3Y H&' . AM ]P H&' )ˆVM $K 2! :;' 7'_(' .1 N^ ' )VM m="' 5&' AO'' K' _! ]M 139

Xa / <& 3 (a $' d2 1M – , 7D& ]ˆM 2' . $+' AM A' N^ ]ˆM H&' N. ˆ' $V@ <i ) ]" 2' !K& . $+' AM A' N^ H&' N. ˆ' $V@ c@P 3 ja^ )ˆVM $K 3Y 1!S H!E@& Cu% Zn !S ‹ ' . M A' x!#& O Ro H&' ) N. ˆ' $V@ )V+% A%

-' . $+' ' . $!( z . ' Y $!( z .M )V+% O <i ) $V@ 2' N. ˆ' 'G& Y4 . $+' . ) U H&' . Y ) U H&' 3M )( - I H&' ";… ) 3!S 2' H&'N. ˆ' $V@ :)! .×+ × = : $+' ' H&' $!( z 1 .S $+ ) / ) ]5& @ …

1+ .',- !K& _! AM ]P H&' $!;P '8

. $V@ 2'

_E( $+' ^! $!( z '' )… _E( $!;P .NS 71…&' H&' N. ˆ' $V@ 7'_(' . . Y & M ]P Y ^! . Ro ' . $+' ^! ' 5… $!( z )… ]P ]ˆ! ^! $+'

^! $!( z '' )… H!D!S _! ]ˆ!. H!D!S= RE%

‹ ' )… $+' AM fa^ .M ]P H!D!S %/ AO'' ) ]ˆ! ..(%.P)M . ' Yˆ" $V@ $!;P P Wˆ%+' 7'_(' 3AM ]P jD" O' fa^ 5&' i

.fa^ )ˆVM $K Y !S Dk H!E@& 7D& . H&' – N. ˆ' $V@ !K& .FF (3 140

;R/ Xa 3 /& Y @X – c WO? NS $… P ' ^! 7D& )! . ',! K' Q 7^… ]P

1 H&' 2( - ' / K' AS =. ) E'

. :;' 2'

1 7D& )…D( - )! 2!88% .$+'

6S R 9+' . - !S NM $a+ c= '& )D!O 1 H&' ˆ!+?' )ˆVM AM Wˆ%+' "?5G3 )k - . M )V+% O )Q' w!/ RE% ‹ ' τ M H!E@& 7D& .5 D! 7!4 ' ^! 8 )G 2' O' AS $+ ) ( )

2G.ε .c = τ

]P 1 H&' $IE~ c . 3)VM P'. AO'' |VQ' W" ε 3 >!+?' M R. G3 |( )Q' . DM AM

5 $' G> / . .M nO& i b ) !S 2' D D… $.8 ^( ' . ˆ' ' Nk DD… $… P 7^… $%& )P ) ' )V ‹ :' b' ^( $%& )!P O' 1 N. ˆ' N. ˆ'3!( z ‹& R;P ‹ ..S =. ) ' (dipole)ˆ ˆ' VQ/ . ‹ 2' D ' $Vo ‹ )! ' ' ' ( ) ]5& ^! !( z Dk AM ]P H&' ‹ $'1 1 A&… ˆ!&+. ˆ' ‹ 32' D.',-

= ) AM ]P 1 H&'

1 N

$+' / ev .P ˆ!&+. ˆ' . ! 2'.S =. ) 1 . AM ]P 1 H&' 2! .',- K' 1 $… P . )… (Suzuki G> /) 53 $' G> / .< ) 7'= ) ]5& "%!= & AM ]P 1 H&' )… ' N^ (Suzuki)*.O+ W ) 88% AM ]P 1 H&' $IE~ 7'_(' . ' g_= 1 2! (SF) 7D!k f8 wbD

^! g_= 1 2! )Ei( )! . AM 5… (SEF)7D!k f8 '3 f8 )!P

141

2' )… 1' O! ^! 7D& ) . M 1' & ]ˆ^ 1 $… P3 2' D . - .M = RE% ]!ˆ^& K' A Wˆ%+' 7'_(' c=

(Fisher 8 ) $# $' G> / ./ . M ]!ˆ^& HID !~ $'Dˆ <i ) ]… b ) <D = 1 RE% 1' =. ( clustering) NM ' A& <i ) 1= pG . .% <i ) HI P' A- 1!4 'G& 3.% HI )!P ‹ $… P )… ' N^ ( Fisher) ^!( .$M' c=3 71… 2'. 2! O' ' HI &V" ) 1 71… T_\ )%Xi

. ' B

7'_(' . M H@!+ ' 71… 0" A-B 1!4 ' O M H@!+ ' 7'_(' ' WO? ' γ NS )… τ = γ / b $+' ' .% )D' HI 2( 2! O' K' N;!+ 7D& 7'_(' . $+' erg/cm2 .P } dj ' 2'. M .% )D' HI NO H1 .$+' AM A' N^ ]ˆM HID ' N;!+ 7D&

(m[ O) # l [ .7 RE% 3 +* O' M ' - $a+ O' + ' - $a+ 3 !S

1 H@!+ O'

1 RE% D'& 3+ ' - $a+ ) G@ 1!S .$+' &S* )' AO'' . = [+ (M A' <' P) M ]!S ! 2!g4 1 )* D1 . D1 ]!^& = 71* 6S = $!;P )* & )+ &. 1!S .DD* ' ' ' AD*' 4 _ 1 3Al NS )* Y H!D!S H@!+ .D@1 c+D <!E5" 2' ' 71* <' P )= .$+' + ' - $a+ H@!+ O' * ' )5 3$+' Ei' jD" .$+' AM A' N^ uk $5+ O( >& )8QD . Al-Cu

142

O( W' - ( ]M )

Al-Cu H@!+ O( '5 .FL (!3 ) 2' & ' . DD* W - O( >& )!P & ' !S $@a 3a+ [+ <!E5" )* M + $" + ) G&

O(. )!P ) NS O' Y4 . !- <i

O+ 251 & '

1 [+ ]!^& O' 3N * + $" + .M )X- (quench) \€ P;Qi'

&" )+ ]!^& O' ' )! $+' AM A' N^ ]M 2' )* a+ <' !!\& .$+' AM A' N^ .' AM A' v M ]M )* D@1 EV& O(

143

]!^& CuAl 2 G& O( ) N!+ O' 7!4 )* D@1 θ `, GP − 2, GP − 1 ]M 1O( 2' )'' . $+' AM A' N^ )D!O 6S UV&' . 1 [+ 2' )+D1 ]M .M .M 1' A' &%!#&

!4 o C

)* Al-Cu N-- 1!S ' NO a+ <' !!\& .L_ (!3 .' AM $a+

# (c)\ GP − 2 f> (,) \ GP − 1 f> ( K :Al-Cu [ , # . L (!3 θ CuAl2 # () \ θ `

) )* M ^ * 1 N'! . G# m="' 0" H!D!S )D!O 1 [+ 2' ]!^& τ ≈ 2Gb / l a+ [+ )Q' wVb ) D* D* ' 1 $* P . A * ]5" n _ Rb Y 1 M )@V51 ";* )D!O O( 2' .`'– ]M 3DD* [+ H!D!S (100) ˜XP

1

' . 1 H&' LGM 2! :;' ]! ) .(D@1 H1 '' [+ . )D!O <%Xi)

2' .S = wbD 2' ]!^& O V@ N@^* ^ * ' 3)VM @V51 3Y i / . 1!S ' ]M )* D@1 ' )!.' a+ Re@ GP-1 wbD @V51 O' M N@^* N'! .$+' AM A' N^ 3' AM $a+ !4 C o

31 $* P O'

)*

!-E= 6S !K& . )M' T @- H!D!S )VM N. 1 [+ .$+6S G/'. _!( AO'' O' &O

+ ]M >@ [+ > )* 3 [ ]M3 $+' GP-2 )8QD EV& + 2!. 2' .' $a# W @S & . Q/ W @S ) >_ . $+' R-' & @ * .$+' )@V51 $a#

+' . A )@V51 Q/ '' H!D!S )D!O [+

!& M 1 7 * 1 ) $V@ ' ^!

N' !4 )8EP ]!^& O' "5!8@ . $+' GP − 2 + D513 m ]M 3 θ ` + N@^* 1. ! 3)! . A' $+ O' )D!O ' @V51 )* S =. ) 1 [+ .' A ) θ ` + ]!^& 2' D .. 2! O' O )Ei( ADD* ]5" . "GM

+' θ ` M )E!+. ) 3 ]M 3 (θ )CuAl 2 R-' & [+ G& O(

D1 2' D .$+' Al )D!O O' ^! θ + &'t W%+' .S = $a# +' 145

_!k a+ θ AD*' 4 [+ pP 3(over age O !4) M ]!S O !S )* )* DD* M [+ <'t O !4 $P 3RP 1 ) .D* !& H!D!S )D!O ) 71* 2' . * $ 1 $* P )* M 1 [+ 5M 71* c= |( = RE% O' 5* '& (over age) AM !4 ]* !S a+ )* +

P

.M a+ !4 <!E5" O' 7!4 LVM' )* $+' (a+ !4 ) + ' - $a+ H@!+ O' * H@!+ > Al-Cu H@!+ D51 1 H@!+ )51 7! . H* a+ !4 E* ]P' .' | ( 1 H@!+ <!g_=

1 )Ei P W%+' '8 . 1O( L 3NO 3a+ !4 <' P )= 6S 2! <.X& . A .M H@!+

$ % 65# l [ .9 . 1' TO' )' O A. + 3E >& . E Dk ' ]M !!\& 2! )@8 O' 7!4

-' .M ]!^& EV& . +* O' Y4 . 5' O' Y4 $+' 25 _E( > 1 )' O . 1' BV& )5! cE~' .M ' . v b 1 .M A' N^ ]M D51 r!4 1 O' ^'S 3" ( )' O R.' $P â " ( 1 )' O 3E* $P ";5" .M A! (twist boundary)r!4 O > .D@1 r!4 â . }*

146

(tilt boundary) }* 3 H* ).'O " ( O .L4 (!3

(twist boundary) r!4 " ( O .L7 (!3

147

)* D* H!@8& G P' ) ' )VM 3DM O }* O L O' " ( 1 )'O 'G& -' .( polygonization) D- NM 6=. Dk NS ) P;Qi' D) M )= O' -_ 3)@51

1 )'

E 1+' 2! 3wQ& W" )* D1

' 1 )' 2! s ^ xQ+ 3(AM EV& . )( +* 3a ' ^! $P 3' =. 1 )' 2! 5* ' )VM +!4 3 O 2!Dk > .D ;k $ % E .M )M' $a# H&' Dk AO'' ) 6D& O -' P 32' D .D@1 1 )' N. A O' 2 $ U "?5G 1 )' O 3YxO $' t# a %# )* $+' DG 2' ) . 1' ' )' N. <i ) 32!g4 1 1_E( ^! $@M 32!g4 1 <' P )= .. 7!4 ) 1 )' N. 31 )' O '' = ) s & .DD* ]5%& $@M O' 7!4 ' E/100 P ' 1 7D& D'& E Dk 1_E( Œ Š' )'O T_\ )! . .D@1 1 )' N. A O' 2 KJ^ 1 )'O 3T ‚' ‚ c@k H1 Š D@1 1 )' O' & `!G# 1 )' O NS O' &? )* .1 ( ]M ).M A!(equicohesive temperature, ECT ) mZ O d'

+!4 H1 Š 75 . W%+' )' AO'' K' )@8 .L9 (!3 148

) ]! . 1 )* ,4 !K& 1 j . !S iD" )E!+. ) 31 )'O W%+' 1_E( P . DD* & 2!g4 1 )= ' A D'& 31 7'= )- 2' .' S 7'= )' O 7'= .(Hot shortness W - &) DD… & ' ? 1 ' .(‚O # ?( NM 9@P D ) 3D* n @& ' G# - )* $+' 25 1 )' AO'' ) 3)' O > Rb T_\ ' -'O )* $+' AM A & b ) $.8 σ i . & $K > K . )' Q/ d 3M H!E@& 7D& σ y -' .$M' 1' @ :$M N'& 3_E( A. )VM σ y = σ i + Kd

−

1 2

( )

A &'t $.8 O' +!8 N'D" ) σ i 3$+' ( Petch ) €O )G ) W+ )* )G 2' ) )@'. 3*Qi' 7D& 2' .M ( G 3(_ !4 7D& RG) > $* P ' .$+

VG 3( H* ) i Dk P 1 7 * ' 6D& 3a+ 7 * Œ . )' AO'' !K& 1' )' AO'' O' ]8@ "V 8& 3a+ 7 * Œ 3NS O' Y4 .$+' M A Dk P . ‹k… !@ (d) )' AO'' )… /. €O )Q' )… $+' *t ) WO? 5 $+ NS O' 5… €O )Q' )… M ` G& ' % )' AO'' ‹ .$@! |i .M 7 … Œ O' G& . $@! K '8 ' % )' AO'' .M N^ D@1 <.X 1 )' '' )… Y !S Dk ' 7 …7D&

1'5 ]ˆM

.M A 6' Wˆ%+' )' AO'' !K& )… ' AM A'

149

Y 1E Dk . E ‹& ' 7 … 7D&

1'5 .L: (3

56>2# l [ .: 1 H@!+ . $+' tX N. (Displacive) 1. - = 7D*'. > _D& - - . * `/ N * + n + N'& ' tX AM R D* O( $P !!\& > )* 1 Œ $!D+S O( O' $_D& O( 31" + 2' .M <i B' M AM ]!^& $_D& '8 ADD* 2!G 3O )'= AM RG( ' 2' D .$+' H* .$+' AM '

150

3(Ts) $_D& L. M ' % <' P )= ) N!+ . )D!O O( (y*) n + N * + ) $!D+S $P !!\& 3Tf <' P )= ) N!+ . D* NM 1z ) L. M $_D& . ! 7'_(' c= Ts

O ) ^! N * + . V& |( .M ]* $_D&

.D* O ' $_D& O )'= wbD ]!^& 2' D . AM $_D& - - )* %

5 h_ 32 * H* ?( 2 * 21S $_D& (`') .L= (!3 ◦C O ) Fe, 16%Cr, 12%Ni !S N * + n + K' AM ]!^& $_D& ([) . 5 h_ 3 – O( ) )@V51 1O ) .% M 4!4 = )= . ' ]M $_D& 1 )%Xi )* M 251 M ]M !!\& > = ) = 2!@a .( ]M) .S $+ ) 2!. .1 Œ (Habit Plane) B' )%Xi W ) )D!O O( A. )%Xi > <'O' ) 3T_\ :1 Œ O 1* . O+ O' )E!+. ) $+' 5* = )= )* = )= .Fe-Ni H@!+ $_D& D 3E/. . Fe-C H@!+ $_D& D

151

, Fe-Ni-C ,Fe-C ,Fe-Ni 1 H@!+ D !S G 1 H@!+ $_D& - - .1 Œ Co, Zr, Li D f 1_E( 1 H@!+ P . Fe-Mn, Cu-Zn, Au-Cd

(N2 B %;/ % 56>2# %RIk ƒ5 % 5 % / 2 G5 .LD (3 78_ E/ . )E!+ )… )K = ( [ ) 3)!.' = (`' ) 3 H… T_\ )E!+. ) $+' 2ˆ5 3)K = 3$+' AM A' w!VQ& ( micro- twinning ) .(' |X&' _! )D' A1^ .( ]ˆM) M AM ]!S?( )@8 NS O !@ a+ 3$ D& O( -.

' 2Dk A'51 . )( 7'_(' ?( = 2 … i $_D& a+ )… M .$+' AM ]!S ?( a+

152

"V@ 1 7D& $%& )GQ/ )* Q' M D51 ' 2' )*1 N^

_E( )D!O

1 $OZ* ! . _!( d'

. - ' c+D $.8 3? ' . &' P $'1

'' 3 AO+

1!S

O' P' 2' 7+ ) $.8 . X+ 3W%+' .DM $@M @ [ d' .$+' ^! _! 6S AO+ 1!S

153

A5" )+ )+ ) 6S 7a Wˆ%+' O( ]M c@P _E( )D!O 1 $OZ* E* b ) <'t . ˆ@. 3)+!4 :!' AM $8& 1 $OZ* : M D H!@8& .DM $GDi * 2 ^! '' O ]" – W%+' '' <'t AM )+ 1 $OZ* ) $V@ 1 ˆ@. O' AM )+ ' )k -' ^! 3!& 5… )D_1 ) )=& _ <'t ' 3DM 6 &' P '4 . ^! AM $a+ !4 1!S N'& ' <'t AM $8& 1 $OZ* . !- ' / AX+' . ? 1 [+ NM $M R;%' ]^ 3$P 2' )* <.X& 2' 5 )@8 AX+' n!+. A.% > 6' O' N'& )! .' =. W%+' !5^k $(' . * O( 2! )* ,4 <i ' )- ) 1 $OZ* ADD* $8& A . )D!O !S [a' O( . )D!O 2! !5!M -O+ .M )M' =. &' P . !5!M -O+ !' + . _E(

D )* A @- 1 7D*'. O' . AM $+ ]P' b 6S d' . $!1 ˜XP 0" )K OZ* )GQ/ )* _! ' .5 !-E= M $OZ* ! d' $(' ) ' ' A. $!51' O' &' P -O+ 3D* * &' P 1 ]!+ " ) * $6= V+D 1 )D_- ' 6S 1!S . W!!& 3H_!D 3W!D!S - d' 3[

,4 :QG' 3" W%+' ) )=& .$+' )+ 1 $OZ* 154

AX+'

_E( )D!O 1 $OZ* !& NS 1!S . W!D!S O' 3c+D $5!/ . [EQ

. Al-Si-Mg !IDM )M' &' P <!E5" $!E/ )* 1!S N! 2' . - O .' A * cE= ) ' ' A. )=& Al-Cu-Mg 3(TiC ,B4C, WC. SiC) 1!* ]M "&5" 1 $OZ* AX+' 1 ADD* $8& (ZrB2, 1!. 3(ZrO2, BeO. Al2O3)1!@*' 3(AlN, TaN, ZrN, Si3N4) 1 ! !*' 2' N! O' .DM 2@D& . NV! 3$!(' - Nk iD" . TaB2, TiB2) G )= W!!&!* . D!S . ' 1 $OZ*!& ' * 2 ^! H!@!E!+ _E( )D!O 1 $OZ* ]* O' % 3 R+ AM ^D S wVb .' ' / $!51' ) (DRA) )+!4 ADD* $8& !D!S )D!O 1 $OZ* ' ! AM !& .' A' dj'

‫ واﻛﻨﺶ ﻫﺎي ﺷﻴﻤﻴﺎﻳﻲ ﺑﻴﻦ ﻣﺎده ﺗﻘﻮﻳﺖ ﻛﻨﻨﺪه و زﻣﻴﻨﻪ ﻓﻠﺰي‬-1- 6 ' 56 78 !' + <'t AM $8& _E( )D!O 1 $OZ* s ^ ]j( d' > E* b ) .D* X' 8k .

,4 :QG' 3W%+' D ! d' 2!!G&

$8& . )D!O O( 2! !5!M
_E( )D!O 1 $OZ*!& nM ]^

25 _E( )D!O 1 $OZ* .M s ^ ]j( )? > ' ) D )* $+' ADD* ]!^& ? 1 !& 2!P ^! ' M ' * 2!P s ^ ]j( 1 )? $+' . -

‫ اﺳﺘﺤﻜﺎم ﻛﺎﻣﭙﻮزﻳﺖ ﻫﺎي زﻣﻴﻨﻪ ﻓﻠﺰي ﺗﻘﻮﻳﺖ ﺷﺪه ﺑﺎ ذرات‬-2- 6 ADD* $8& O( >5* Ro ' .$+' ',- !K& )D!O ^^* d' . ADD* $8& O( )IP; ]/ b ) Èa 1 O' -_ A @- W!D!S ! d' SiC . Al2O3 L !K& .' AM …t 1 $OZ… 2' ˆ!ˆ d' O' R.= . V6 ' 155

Wˆ%+' (Mg, Cr, Si iD" .P ) !S .$+' )GQ ]/ R.= 2' _! )D!O !S .M H… (YD(&) KIC ' ' Al2O3 % O' 7! 8 V+D â

8 ' 3 ' ' . 2!51 _! $+' & Hˆ%@ !S )… ( Cu,Mn, Si iD" .P) .$+' & !@ ?

SiC ‫ و‬Al2O3 ‫ ﺑﺮﺧﻲ از ﺧﻮاص ﻣﻜﺎﻧﻴﻜﻲ ﻣﻮاد ﻣﺮﻛﺐ آ ﻟﻴﺎژ ﻫﺎي آﻟﻮﻣﻴﻨﻴﻮم ﺑﺎ‬-17 ‫ﺟﺪول‬ " B

6061-0% Al2O3 6061-10% Al2O3 6061-15% Al2O3 6061-20% Al2O3 2014-0% Al2O3 2014-10% Al2O3 2014-15% Al2O3 2014-20% Al2O3 A356-0% SiC A356-10% SiC A356-15% SiC A356-20% SiC

‫اﺳﺘﺤﻜﺎم‬ ‫ﺗﺴﻠﻴﻢ‬

‫اﺳﺘﺤﻜﺎم‬ ‫ﻣﻜﺎﻧﻴﻜﻲ‬

‫( ﺗﻐﻴﻴﺮ‬%) ‫ﻃﻮل‬

‫ﺿﺮﻳﺐ ﻳﺎﻧﮓ‬

‫ ﺗﺎﻓﻨﺲ‬KIC

Gpa

MPa m1/2

MPa 276 297

MPa 310 338

20.0 7.6

69 81

29.7 24.1

386

359

5.4

88

22.0

359

379

2.1

99

21.5

414 483

483 517

13.0 3.3

73 84

25.3 18.0

476

503

2.3

92

18.8

483

503

0.9

101

--

200 283 324 331

276 303 331 352

6.0 0.6 0.3 0.4

75 81 90 97

-----

‫ اﺳﺘﺤﻜﺎم ﺑﺨﺸﻲ ﻧﺎﺷﻲ از اﻧﺘﻘﺎل ﺑﺎر از زﻣﻴﻨﻪ ﺑﻪ ذرات ﺗﻘﻮﻳﺖ ﻛﻨﻨﺪه‬-3- 6 .$+' v Q 1 $OZ* B8( ADD* $8& <'t ) )D!O O' R8' O' M â W%+' a+ [+ 0%V 5P @* O' ^! E! 1 $OZ* <'t 5P @* )* S O' ) 7 * 2!P ' 3)D!O )* $+' $8!8P 2' O' M â W%+' O' 6=& ]/ H6+ 3$+' ]M 3<'t 5P @* ) )* 3$+' R8' W6X 2' .1 R8' ADD* $8& <'t .' @ <'t G )+ HI . <'t +D1 156

3 ?” 5G .$+' ',- !K& _E( )D!O $OZ* W%+' ADD* $8& O( AO'' . 5P @* 2' .M Q b )

_E( )D!O

1 $OZ* ^^… W%+' . ‚ c # !!\&

W%+' . E )* M A1^ ]M 2' .$+' AM A' N^ ]M L# 5P @* 7'_(' ( b O' .D 7'_(' ADD* $8& <'t 5P @* 7'_(' $OZ*

&"# ? 5P 1 @* ,4 ]M 1 ADD* $8& ' O $+' I' _E( )D!O 1 $OZ* ' '* ? $K3)D!O ) $V@ &? 1 & ' d' 3M )( - * ) ?” 5G )* !' + .' )

157

‫اﻟﻒ‬

‫ب‬

‫ﺷﻜﻞ ‪ ) -99‬اﻟﻒ( اﺛﺮ ﻛﺴﺮ ﺣﺠﻤﻲ ﺗﻘﻮﻳﺖ ﻛﻨﻨﺪه ﻫﺎي ‪ SiC ،Al2O3‬و ‪ B‬ﺑﺮ ﺿﺮﻳﺐ ﻳﺎﻧﮓ ﻣﻮاد‬ ‫ﻣﺮﻛﺐ آﻟﻮﻣﻴﻨﻴﻮم ﺑﺎ اﻳﻦ ﻣﻮاد‪) .‬ب( اﺛﺮ ﻛﺴﺮ ﺣﺠﻤﻲ ﺗﻘﻮﻳﺖ ﻛﻨﻨﺪه ﻫﺎ ﺑﺮ اﺳﺘﺤﻜﺎم ﻛﺸﺸﻲ‪ .‬اﻧﺪﻳﺲ ‪p‬‬ ‫ﺑﺮاي ذرات و ‪ c‬ﺑﺮاي اﻟﻴﺎف ﺑﻜﺎر رﻓﺘﻪ اﻧﺪ‪.‬‬ ‫‪158‬‬

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