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ﺖﺤﺗ ﻲﻣﻮﻴﻨﻴﻣﻮﻟآ كزﺎﻧ راﺪﺟ
هﺪﻨﺒﺴﭼ نﺎﻤﻟا زا هدﺎﻔﺘﺳا ﺎﺑ يزﺎﮔ ﻦﺸﻴﻧﻮﺗد يراﺬﮔرﺎﺑ
سرﺪﻣ ﺖﻴﺑﺮﺗ ناﺮﻬﺗ ،
ناﺮﻬﺗ ،
mmirzaei@modares.ac.ir
ﺖﺳا هﺪﺷ ﻪﺘﺧادﺮﭘ يزﺎﮔ ﻦﺸﻴﻧﻮﺗد يراﺬﮔرﺎﺑ ﺖﺤﺗ كزﺎﻧ راﺪﺟ ﻪﻧاﻮﺘﺳا ﻚﻳ رد كﺮﺗ ﺪﺷر .
تﻼﻜﺸﻣ ﻪﺑ ﻪﺟﻮﺗ ﺎﺑ
ﺖﺳا هﺪﺷ هدﺎﻔﺘﺳا ﻖﻴﻘﺤﺗ ﻦﻳا رد دوﺪﺤﻣ نﺎﻤﻟا شور زا ،ﻪﻟ .
ﻞﺣ ﺎﺑ كﺮﺤﺘﻣ رﺎﺑ زا ﻲﺷﺎﻧ تﺎﺷﺎﻌﺗرا
ﺖﻬﺟ ﺶﻳاﺪﺟ لﺪﻣ
يزﺎﺳ هﺪﺷ هدﺎﻔﺘﺳا كﺮﺗ ﺪﺷر
ﺖﺳا ﻪﺘﻓﺮﮔ راﺮﻗ ﻞﻴﻠﺤﺗ درﻮﻣ و هﺪﺷ ﻪﺴﻳﺎﻘﻣ ﻪﺘﻓﺮﮔ مﺎﺠﻧا .
Crack growth modeling
gaseous detonation loading using cohesive element
1- M.Sc. Student of Aerospace 2- Assoc. Prof. of Aerospace
* P.O.B.
Abstract-This paper reports the finite element modeling of axial crack growth in a thin aluminum tube under gaseous detonation loading. The finite element method was used to handle the movi
of the problem. The simulation results were compared with the experimental results reported in the literature and also with the results obtained from an analytical model. Moreover, the cohesive element with tr
used for the crack growth modeling. The final part of the paper is devoted to comparisons between the numerical crack growth simulations obtained from the current work and the numerical results based on the CTOA criteria
previously reported in the literature. The very good agreement between the two methods was indicative of the robustness of the implemented procedures.
Keywords: Moving load, Finite Element M
هرود 12 هرﺎﻤﺷ 3 رﻮﻳﺮﻬﺷ 1391 ص ص 95 - 102
ﻧاﻮﺘﺳا رد كﺮﺗ ﺪﺷر ﺔ
ﺖﺤﺗ ﻲﻣﻮﻴﻨﻴﻣﻮﻟآ كزﺎﻧ راﺪﺟ
هﺪﻨﺒﺴﭼ نﺎﻤﻟا زا هدﺎﻔﺘﺳا ﺎﺑ يزﺎﮔ ﻦﺸﻴﻧﻮﺗد يراﺬﮔرﺎﺑ
نﺎﻜﻠﻣ ﺪﻤﺤﻣ ﻲﺋازﺮﻴﻣ ﺪﻴﺠﻣ ،1
2
*
1 - ﺎﻀﻓاﻮﻫ ﻲﺳﺪﻨﻬﻣ ﺪﺷرا ﻲﺳﺎﻨﺷرﺎﻛ يﻮﺠﺸﻧاد ،
هﺎﮕﺸﻧاد سرﺪﻣ ﺖﻴﺑﺮﺗ
2 - ﻲﺳﺪﻨﻬﻣ رﺎﻴﺸﻧاد ﺎﻀﻓاﻮﻫ
سرﺪﻣ ﺖﻴﺑﺮﺗ هﺎﮕﺸﻧاد ، ناﺮﻬﺗ ،
* ،ناﺮﻬﺗ ﻲﺘﺴﭘ قوﺪﻨﺻ 143
- 14115
، mmirzaei@modares.ac.ir
يزﺎﺳ ﺖﺳا هﺪﺷ ﻪﺘﺧادﺮﭘ يزﺎﮔ ﻦﺸﻴﻧﻮﺗد يراﺬﮔرﺎﺑ ﺖﺤﺗ كزﺎﻧ راﺪﺟ ﻪﻧاﻮﺘﺳا ﻚﻳ رد كﺮﺗ ﺪﺷر
ﺴﻣ ندﻮﺑ ﻲﻄﺧﺮﻴﻏ و كﺮﺤﺘﻣ رﺎﺑ ﺄ
ﺖﺳا هﺪﺷ هدﺎﻔﺘﺳا ﻖﻴﻘﺤﺗ ﻦﻳا رد دوﺪﺤﻣ نﺎﻤﻟا شور زا ،ﻪﻟ
هﺪﺷ ﻲﺑﺎﻳزرا و ﻪﺴﻳﺎﻘﻣ ﻲﻫﺎﮕﺸﻳﺎﻣزآ ﺞﻳﺎﺘﻧ و ﻲﻠﻴﻠﺤﺗ زا و
ﺶﺸﻛ ﻲﺑاﺮﺧ رﺎﻴﻌﻣ ﺎﺑ هﺪﻨﺒﺴﭼ نﺎﻤﻟا -
ﺖﻬﺟ ﺶﻳاﺪﺟ
ﻳﺎﭘ ﺮﺑ ﻪﻛ ﻲﻠﺒﻗ ﺞﻳﺎﺘﻧ ﺎﺑ هﺪﻣآ ﺖﺳﺪﺑ ﺞﻳﺎﺘﻧ ﺔ
ﻣ كﺮﺗ كﻮﻧ ﻲﻧاﺮﺤﺑ ﻪﻳواز ﺪﺷر رﺎﻴﻌ ﺖﺳا ﻪﺘﻓﺮﮔ راﺮﻗ ﻞﻴﻠﺤﺗ درﻮﻣ و هﺪﺷ ﻪﺴﻳﺎﻘﻣ ﻪﺘﻓﺮﮔ مﺎﺠﻧا
دوﺪﺤﻣ نﺎﻤﻟا شور
، رﺎﺸﻓ ﺖﺤﺗ نزﺎﺨﻣ .
growth modeling for a thin aluminum tube under gaseous detonation loading using cohesive element
M. Malekan1, M. Mirzaei2*
M.Sc. Student of Aerospace Engineering, Tarbiat Modares University., Tehran Prof. of Aerospace Engineering, Tarbiat Modares University, Tehran
P.O.B. 14115-143 Tehran, Iran. mmirzaei@modares.ac.ir
This paper reports the finite element modeling of axial crack growth in a thin aluminum tube under gaseous detonation loading. The finite element method was used to handle the moving load and also the nonlinear characteristics of the problem. The simulation results were compared with the experimental results reported in the literature and also with the results obtained from an analytical model. Moreover, the cohesive element with tr
used for the crack growth modeling. The final part of the paper is devoted to comparisons between the numerical crack growth simulations obtained from the current work and the numerical results based on the CTOA criteria
previously reported in the literature. The very good agreement between the two methods was indicative of the of the implemented procedures.
Method, Pressure Vessels.
لﺪﻣ يزﺎﺳ
ﻧاﻮﺘﺳا رد كﺮﺗ ﺪﺷر
هﺪﻨﺒﺴﭼ نﺎﻤﻟا زا هدﺎﻔﺘﺳا ﺎﺑ يزﺎﮔ ﻦﺸﻴﻧﻮﺗد يراﺬﮔرﺎﺑ
هﺪﻴﻜﭼ - ﻪﺑ ﻪﻟﺎﻘﻣ ﻦﻳا رد لﺪﻣ
يزﺎﺳ
زا ﻲﺷﺎﻧ لﺎﻤﻋا ﺴﻣ ندﻮﺑ ﻲﻄﺧﺮﻴﻏ و كﺮﺤﺘﻣ رﺎﺑ
هﺪﺷ ﻲﺑﺎﻳزرا و ﻪﺴﻳﺎﻘﻣ ﻲﻫﺎﮕﺸﻳﺎﻣزآ ﺞﻳﺎﺘﻧ و ﻲﻠﻴﻠﺤﺗ ﺖﺳا . ﻳﺎﭘ ﺮﺑ ﻪﻛ ﻲﻠﺒﻗ ﺞﻳﺎﺘﻧ ﺎﺑ هﺪﻣآ ﺖﺳﺪﺑ ﺞﻳﺎﺘﻧ
ﺪﻴﻠﻛ نﺎﮔژاو : كﺮﺤﺘﻣ رﺎﺑ
، دوﺪﺤﻣ نﺎﻤﻟا شور
thin aluminum tube under gaseous detonation loading using cohesive element
, Tehran, Iran , Iran
This paper reports the finite element modeling of axial crack growth in a thin aluminum tube under gaseous ng load and also the nonlinear characteristics of the problem. The simulation results were compared with the experimental results reported in the literature and also with the results obtained from an analytical model. Moreover, the cohesive element with traction-separation law was used for the crack growth modeling. The final part of the paper is devoted to comparisons between the numerical crack growth simulations obtained from the current work and the numerical results based on the CTOA criteria that were previously reported in the literature. The very good agreement between the two methods was indicative of the
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ﻪﻣﺪﻘﻣ
ﺮﺘﺸﻴﺑ هﺪﺷ مﺎﺠﻧا تﺎﻘﻴﻘﺤﺗ رد
ﻪﻨﻴﻣز ﻚﻴﻧﺎﻜﻣ ﺖﺴﻜﺷ ﻪﻧاﻮﺘﺳا
كزﺎﻧ راﺪﺟ ﺎﺸﻓ ﺖﺤﺗ
،ﻲﻠﺧاد ر يراﺬﮔرﺎﺑ ﺎﺑ
يﺎﻫ ﻪﺒﺷ و ﻚﻴﺗﺎﺘﺳا
ﺎﻳ ﻲﮕﺘﺴﺧ ﻲﻣ ﻂﺒﺗﺮﻣ ﺪﻨﺷﺎﺑ
1]
، 2 .[
ﺖﺴﻜﺷ كزﺎﻧ راﺪﺟ ﻪﻧاﻮﺘﺳا
يراﺬﮔرﺎﺑ ﺖﺤﺗ ﻪﻟﻮﻟ ﺖﺴﻜﺷ زا هﺪﻤﻋ ﻞﻴﻟد ود ﻪﺑ ﻦﺸﻴﻧﻮﺗد ﺖﺤﺗ ﻪﺒﺷ ﻲﻣ ﺰﻳﺎﻤﺘﻣ ﻚﻴﺗﺎﺘﺳا ﺪﺷﺎﺑ
. ،لوا جاﻮﻣا ﻲﺸﻤﺧ زا ﻲﺷﺎﻧ رﻮﺒﻋ
ﺎﻫرﺎﺑ ﻲﻣ ﺪﻧاﻮﺗ ﻪﺑ ﻪﺘﺴﺑاو ﺎﻬﻧآ ﻪﻨﻣاد ﻪﻛ هﺪﺷ ﻲﻧﺎﺳﻮﻧ ﺶﻧﺮﻛ ﺚﻋﺎﺑ
و هدﻮﺑ رﺎﺑ رﻮﺒﻋ ﺖﻋﺮﺳ ﻲﻣ
راﺪﻘﻣ زا ﺮﺘﮔرﺰﺑ ﺮﺑاﺮﺑ ﻦﻳﺪﻨﭼ ﺪﻧاﻮﺗ
ﺶﻴﭘ ﺪﺷﺎﺑ ﻲﻜﻴﺗﺎﺘﺳا نﻮﻴﺳﻻﻮﻣﺮﻓ ﻂﺳﻮﺗ هﺪﺷ ﻲﻨﻴﺑ .
د مو ،
ﺎﻫﺮﺘﻣارﺎﭘ ي ﺖﺴﻜﺷ ﻲﻜﻴﻣﺎﻨﻳد ﻲﻣ
ﺪﻧاﻮﺗ ﻛ
ًﻼﻣﺎ توﺎﻔﺘﻣ زا ﻞﻜﺷ
ﻚﻴﺗﺎﺘﺳا لدﺎﻌﻣ
ﺪﻨﺷﺎﺑ . ﺦﺳﺎﭘ هزﻮﺣ رد ﻲﻔﻠﺘﺨﻣ تﺎﻌﻟﺎﻄﻣ
هزﺎﺳ ﻪﺘﺳﻮﭘ يا ﻪﺘﻓﺮﮔ مﺎﺠﻧا ﻦﺸﻴﻧﻮﺗد و كﻮﺷ يراﺬﮔرﺎﺑ ﻪﺑ ﺎﻫ
ﺖﺳا 3]
- 9 .[
و ﻪﺘﻓﺮﮕﻧ ﺮﻈﻧرد ار كﺮﺗ تﺎﻌﻟﺎﻄﻣ ﻦﻳا ﺪﻨﭼﺮﻫ
ﻧ ﻲﺳرﺮﺑ ار ﺖﺴﻜﺷ ﺮﻜ
هد ﺪﻧا . لﺎﺳ رد 2004 ﻲﻫﺎﮕﺸﻳﺎﻣزآ ﻪﻌﻟﺎﻄﻣ
يور ﺮﺑ ﻲﻌﻣﺎﺟ ﺖﺴﻜﺷ
ﻦﺸﻴﻧﻮﺗد ﺖﺤﺗ كزﺎﻧ راﺪﺟ ﻪﻧاﻮﺘﺳا
ﻂﺳﻮﺗ يزﺎﮔ واﺎﭼ
و
1دﺮﭙﺷ ﺖﻓﺮﮔ مﺎﺠﻧا 1]
، 2 .[
ﻪﻴﺒﺷ هزﺎﺳ ﻞﺑﺎﻘﺘﻣ ﺮﺛا يزﺎﺳ -
راﺪﺟ ﻪﻧاﻮﺘﺳا ﺖﺴﻜﺷ رد لﺎﻴﺳ
ﻂﺳﻮﺗ ﻦﺸﻴﻧﻮﺗد و كﻮﺷ رﺎﺑ ﺖﺤﺗ كزﺎﻧ كاﺮﻴﺳ
رد نارﺎﻜﻤﻫ2
لﺎﺳ 2006 10]
ﺖﻓﺮﮔ مﺎﺠﻧا [
. ﻪﻴﺒﺷ ﺎﻬﻧآ ﺶﻨﻜﻤﻫﺮﺑ يزﺎﺳ
هزﺎﺳ - ﻚﻴﺘﺳﻼﭘﻮﻜﺴﻳو ﻞﻜﺷ ﺮﻴﻴﻐﺗ و گرﺰﺑ دﺎﻌﺑا رد لﺎﻴﺳ
ﻪﻧاﻮﺘﺳا ﻲﻫﺎﮕﺸﻳﺎﻣزآ ﺖﺴﻜﺷ واﺎﭼ
و دﺮﭙﺷ 11]
زا و ﺪﻧداد مﺎﺠﻧا[
ﺖﺴﻜﺷ ﻲﮕﻣﺮﻘﭼ )
KIC
( ﻪﺤﻔﺻ ﺶﻧﺮﻛ ﺖﻟﺎﺣ رد ﻚﻴﺗﺎﺘﺳا يا
ﺪﻧدﺮﻛ هدﺎﻔﺘﺳا هﺪﻨﺒﺴﭼ يﺎﻬﻧﺎﻤﻟا صاﻮﺧ ندروآ ﺖﺳﺪﺑ ياﺮﺑ .
رد
هداد ﺎﺑ ﺎﻬﻧآ ﺞﻳﺎﺘﻧ ﺖﻳﺎﻬﻧ يﺎﻫ
واﺎﭼ و دﺮﭙﺷ هزاﺪﻧا صﻮﺼﺧ رد
ﺖﺷاﺪﻧ ﻖﺑﺎﻄﺗ ﺖﻋﺮﺳ و كﺮﺗ ﺪﺷر .
كﺮﺗ ﺪﺷر ﺖﻋﺮﺳ ﻦﻴﻨﭽﻤﻫ
ار 3 - 2 ﺪﻧدروآ ﺖﺳﺪﺑ نآ ﻲﻫﺎﮕﺸﻳﺎﻣزآ راﺪﻘﻣ ﺮﺑاﺮﺑ 12]
.[
ﻲﺋازﺮﻴﻣ لﺎﺳ رد نارﺎﻜﻤﻫ و 2005
13]
ﻲﻠﻴﻠﺤﺗ ﻞﺣ [
رد و ﻲﻠﺧاد ﻦﺸﻴﻧﻮﺗد يراﺬﮔرﺎﺑ ﻪﺑ ﻚﻴﺘﺳﻻا كزﺎﻧ راﺪﺟ ﻪﻧاﻮﺘﺳا ،ﻪﻣادا ﻲﺋازﺮﻴﻣ لﺎﺳ رد نارﺎﻜﻤﻫ و 2006
14]
و ﻞﻴﻠﺤﺗ ﻞﺣ [
ﻦﺸﻴﻧﻮﺗد يراﺬﮔرﺎﺑ ﻪﺑ ﻚﻴﻣﺎﻨﻳدﻮﺘﺳﻻا كزﺎﻧ راﺪﺟ ﻪﻧاﻮﺘﺳا يدﺪﻋ ﺪﻧداد ﻪﺋارا ار ﻲﻠﺧاد .
ﻲﺋازﺮﻴﻣ و ﻲﻤﻳﺮﻛ ﺎﺳ رد ل 2006 15]
ﻪﺑ[
ﻪﻧاﻮﺘﺳا رد كﺮﺗ ﺪﺷر ﻲﺳرﺮﺑ رﻮﻈﻨﻣ زا ﻦﺸﻴﻧﻮﺗد يراﺬﮔرﺎﺑ ﺖﺤﺗ
رﺎﻴﻌﻣ كﻮﻧ ﻲﮔﺪﺷزﺎﺑ
3كﺮﺗ (CTOA) ا
ﺪﻧدﺮﻛ هدﺎﻔﺘﺳ .
ﻦﻳا ﺎﺑ
1. Chao & Shepherd 2. Cirak
3. Crack Tip Opening Displacement
ﻲﺘﻟﺎﺣ رد ار كﺮﺗ ﺪﺷر ناﺰﻴﻣ شور زا ﻪﺤﻔﺻ ﻚﻳ رد كﺮﺗ ﻪﻛ
ﻲﻣ ﺪﺷر هﺪﺷ ﺺﺨﺸﻣ ﺶﻴﭘ ر ﺞﻳﺎﺘﻧ و ﺪﻧدﻮﻤﻧ ﻪﺒﺳﺎﺤﻣ ،ﺪﻨﻛ
ﺎﺑ ا
ﺞﻳﺎﺘﻧ واﺎﭼ و دﺮﭙﺷ 11]
ﻪﺴﻳﺎﻘﻣ [
ﺮﻛ ﺪﻧد . ﻚﻳ ﺖﺴﻜﺷ ﺰﻴﻟﺎﻧآ
ﻂﺳﻮﺗ هﺪﺷ ﺮﺠﻔﻨﻣ يزﺎﮔ لﻮﺴﭙﻛ ﻲﺋازﺮﻴﻣ
لﺎﺳ رد 2008 16] [
ﻪﻴﺒﺷ و ﻂﺳﻮﺗ هﺪﺷ ﺮﺠﻔﻨﻣ لﻮﺴﭙﻛ ﻦﻳا دوﺪﺤﻣ نﺎﻤﻟا يزﺎﺳ
ﻲﺋازﺮﻴﻣ لﺎﺳ رد نارﺎﻜﻤﻫ و 2008
17]
تﺎﻌﻟﺎﻄﻣ ﺮﮕﻳد ﻪﻠﻤﺟ زا[
ﻲﻣ ﻪﻨﻴﻣز ﻦﻳا رد ﻪﺘﻓﺮﮔ ترﻮﺻ ﺪﻨﺷﺎﺑ
ﻪﻛ ﻪﺑ دﻮﺧ ﻪﻟﺎﻘﻣ رد
و و ﺖﺴﻜﺷ ﺖﻠﻋ ﻲﺳرﺮﺑ زﺎﮔ ياراد رﺪﻨﻠﻴﺳ ﻚﻳ ﻲﮔﺪﻧﺎﻣا
ﻪﺘﺧادﺮﭘ نژورﺪﻴﻫ ﺪﻧا
. ﻲﻣ نﺎﺸﻧ ﻖﻴﻘﺤﺗ ﻦﻳا ﻪﺠﻴﺘﻧ رد ﺪﻫد
جاﻮﻣا ﻂﺳﻮﺗ كﺮﺗ ﺪﺷر ﻦﺸﻴﻧﻮﺗد يراﺬﮔرﺎﺑ زا ﻲﺻﺎﺧ هدوﺪﺤﻣ هزﺎﺳ و هﺪﺷ لﺮﺘﻨﻛ يا ﻪﺑ
ترﻮﺻ ﻲﻣ ﻲﺑوﺎﻨﺗ ﺪﺷﺎﺑ
.
ﻪﻟﺎﻘﻣ ﻦﻳا فﺪﻫ لﺪﻣ
يزﺎﺳ ﻦﺸﻴﻧﻮﺗد ﺖﺤﺗ ﺖﺴﻜﺷ يدﺪﻋ
ﺎﺑ نآ ﻪﺴﻳﺎﻘﻣ و كزﺎﻧ راﺪﺟ ﻪﻧاﻮﺘﺳا ﻚﻳ زا هﺪﻣآ ﺖﺳﺪﺑ ﺞﻳﺎﺘﻧ
ﻲﺋازﺮﻴﻣ و ﻲﻤﻳﺮﻛ لﺎﺳ رد 2006 15]
ﻲﻣ[
ﺪﺷﺎﺑ .
2 - يراﺬﮔرﺎﺑ تﻻدﺎﻌﻣ و ﻲﻫﺎﮕﺸﻳﺎﻣزآ تﺎﻌﻟﺎﻄﻣ
يزﺎﮔ ﻦﺸﻴﻧﻮﺗد
جﻮﻣ ﻦﺸﻴﻧﻮﺗد داﻮﻣ قاﺮﺘﺣا زا ﻲﺷﺎﻧ تﻮﺻ ياروﺎﻣ جﻮﻣ ﻚﻳ
و جﻮﻣ ﻪﻬﺒﺟ يﻮﻠﺟ رد كﺎﺷ جﻮﻣ ﻚﻳ ﻞﻣﺎﺷ ﻪﻛ ﺖﺳا ﻲﻨﺘﺧﻮﺳ ﺶﻨﻛاو ﻪﻘﻄﻨﻣ ﻚﻳ ﻲﻣ ﻪﻬﺒﺟ ﺖﺸﭘ رد
ﻪﺑ ﻪﻛ ﺪﺷﺎﺑ ﺎﺑ تﺪﺷ
هﺪﺷ ﻞﭘﻮﻛ ﺮﮕﻳﺪﻜﻳ ﺪﻧا
. جاﻮﻣا ﻦﺸﻴﻧﻮﺗد رﺎﺸﻓ و ﺖﻋﺮﺳ ياراد
ﻦﻤﭘﺎﭼ مﺎﻧ ﻪﺑ ﻲﺼﺨﺸﻣ -
ﻲﻣ ﺖﻛوژ ﺮﺘﻣارﺎﭘ ود ﻦﻳا ﻪﻛ ﺪﻨﺷﺎﺑ
ﺖﺧﻮﺳ طﻮﻠﺨﻣ يﺎﻫﺪﺻرد ﻪﺑ ﻲﮕﺘﺴﺑ -
دراد اﻮﻫ . رد رﺎﺸﻓ ﻞﻴﻓوﺮﭘ
زا ﻪﻄﻘﻧ ﻚﻳ ﻪﻧاﻮﺘﺳا
ﻞﻜﺷ ﻖﺑﺎﻄﻣ نﺎﻣز لﻮﻃ رد 1
ﻣ ﻲ ﺪﺷﺎﺑ .
نﺎﻣز (ms)
ﻞﻜﺷ 1 ﻦﺸﻴﻧﻮﺗد جﻮﻣ ﻲﻌﻗاو ﻞﻴﻓوﺮﭘ )
هزاﺪﻧا رد هﺪﺷ يﺮﻴﮔ
هﺎﮕﺸﻳﺎﻣزآ ( هﺪﻳا لدﺎﻌﻣ و نآ لآ
1] [
هزاﺪﻧا هﺪﺷ يﺮﻴﮔ
ﻪﺑ ﻦﻴﻤﺨﺗ ترﻮﺻ ﻲﺸﻫﺎﻛ ﻲﻳﺎﻤﻧ ﻊﺑﺎﺗ
رﺎﺸﻓ(MPa)
[ Downloaded from mme.modares.ac.ir on 2022-10-31 ]
ﻲﻣ ﻪﻈﺣﻼﻣ ﻪﻛ ﻪﻧﻮﮕﻧﺎﻤﻫ ﻮﺷ
ﻞﻴﻟد ﻪﺑ ﻲﻌﻗاو ﺖﻟﺎﺣ رد ،د
هزاﺪﻧا رﻮﺴﻨﺳ ﻪﺑ دﻮﺧ ﻪﺑﻮﻧ ﻪﺑ ﻪﻛ هزﺎﺳ تﺎﺷﺎﻌﺗرا ﻲﻣ ﻞﻘﺘﻨﻣ يﺮﻴﮔ
-
ﻮﺷ رﺎﺸﻓ ﻞﻴﻓوﺮﭘ رد ،د هزاﺪﻧا
ﻲﻣ هﺪﻳد ﻲﺗﺎﺷﺎﻌﺗرا ،هﺪﺷ يﺮﻴﮔ دﻮﺷ
.
ﻪﺑ ﺶﻴﭘ رﻮﻈﻨﻣ هﺪﻳا لﺪﻣ ﻚﻳ زا ،ﻞﻴﻠﺤﺗ نﺪﺷ هﺪﻴﭽﻴﭘ زا يﺮﻴﮔ
لآ
رﺎﺸﻓ ﻞﻴﻓوﺮﭘ ياﺮﺑ )
تﺎﺷﺎﻌﺗرا ﻦﺘﻓﺮﮔ ﺮﻈﻧ رد نوﺪﺑ (
هدﺎﻔﺘﺳا
ﻲﻣ ﻮﺷ د . زا ﻪﻈﺤﻟ ﻚﻳ رد ﻦﺸﻴﻧﻮﺗد جﻮﻣ زا ﻲﺷﺎﻧ رﺎﺸﻓ ﻞﻴﻓوﺮﭘ
ﻞﻜﺷ رد ﻪﻧاﻮﺘﺳا لﻮﻃ رد نﺎﻣز 2
ﺖﺳا هﺪﺷ هداد نﺎﺸﻧ .
ﮕﻨﻫ ﻲﻣﺎ جﻮﻣ ﻪﻛ ﻦﺸﻴﻧﻮﺗد رد
ﻪﻧاﻮﺘﺳا ﻲﻣ ﺖﻛﺮﺣ ﻪﺳ ،ﺪﻨﻛ
رد توﺎﻔﺘﻣ يﺎﻫرﺎﺸﻓ ﺎﺑ ﻪﻘﻄﻨﻣ ﻪﻧاﻮﺘﺳا
ﻲﻣ دﺎﺠﻳا ﻮﺷ د:
1 - ياراد ﻪﻛ جﻮﻣ ﻪﻬﺒﺟ يﻮﻠﺟ رد اﻮﻫ و ﺖﺧﻮﺳ ﻞﻣﺎﺷ ﻪﻘﻄﻨﻣ
ﻪﻴﻟوا رﺎﺸﻓ
P1
ﺖﺳا .
2 - رﺎﺸﻓ ﻦﻳﺮﺘﺸﻴﺑ ياراد ﻪﻛ جﻮﻣ ﻪﻬﺒﺟ ﻪﻴﺣﺎﻧ
P2
ﻲﻣ ﺪﺷﺎﺑ .
3 - رﺎﺸﻓ ياراد ﻪﻛ جﻮﻣ ﻪﻬﺒﺟ ﺖﺸﭘ ﻪﻘﻄﻨﻣ
P3
ﺖﺳا .
طﻮﻠﺨﻣ ﻪﻜﻨﻳا ﻪﺑ ﻪﺟﻮﺗ ﺎﺑ يﺎﻫ
ﻖﻴﻘﺤﺗ ﻦﻳا رد هﺪﺷ هدﺎﻔﺘﺳا
ﻪﺑ ﻪﻧﻮﮔ ﻲﻣ يا رد ،دراد نرﺎﻘﺘﻣ ًﺎﺒﻳﺮﻘﺗ ﻲﺘﻟﺎﺣ جﻮﻣ ﻪﻬﺒﺟ ﻪﻛ ﺪﻨﺷﺎﺑ
ﻪﻴﺒﺷ ﺖﺳا هﺪﺷ ﻪﺘﻓﺮﮔ ﺮﻈﻧ رد نرﺎﻘﺗ ﻦﻳا ﺰﻴﻧ جﻮﻣ ﻪﻬﺒﺟ يزﺎﺳ .
ﻞﻜﺷ ﻪﺑ ﻪﺟﻮﺗ ﺎﺑ 1
ﻲﻣ ﺮﺑ ﻪﻟﻮﻟ ﻞﺧاد رد ار رﺎﺸﻓ ﻞﻴﻓوﺮﭘ ناﻮﺗ
نﺎﻜﻣ و نﺎﻣز يﺎﻫﺮﺘﻣارﺎﭘ ﺐﺴﺣ ﻪﺑ
ترﻮﺻ ﻂﺑاور ) 1 ( و ) 2 (
ﺖﺷﻮﻧ 9]
:[
1 2 1 2 3
( ) ( ) ( ) ( )
1 ( ) 0
t atm T
cj
P t P P P P P P e
H x V t x L
−
= − + − + −
× − − < < (1)
[ ]
1 2 1 2 3
( ) ( ) ( ) ( )
1 ( ) 0
x L V T
atm cj
P x P P P P P P e
H x L x L
− −
×
= − + − + −
× − − < < (2)
ﻞﻜﺷ 2 ﻪﻧاﻮﺘﺳا لﻮﻃ رد نﺎﻣز زا ﻪﻈﺤﻟ ﻚﻳ رد رﺎﺸﻓ ﻞﻴﻓوﺮﭘ 9]
[
ﻂﺑاور رد )
1 ( و ) 2 P1( ،ﻪﻴﻟوا رﺎﺸﻓ P2
،ﻢﻤﻳﺰﻛﺎﻣ رﺎﺸﻓ P3
رﺎﺸﻓ
،ﻲﻳﺎﻬﻧ وt ،نﺎﻜﻣ و نﺎﻣز يﺎﻫﺮﺘﻣارﺎﭘx ،ﻲﻳﺎﻤﻧ ﺶﻫﺎﻛ ﺐﻳﺮﺿT
Vcj
جﻮﻣ ﻲﻧﺎﺸﻴﭘ ﺖﻋﺮﺳ )
ﻦﻤﭘﺎﭼ ﺖﻋﺮﺳ -
ﺖﻛوژ ( ﻊﺑﺎﺗ ، فﺮﻌﻣH
و ﺪﺣاو ﻪﻠﭘ ﻊﺑﺎﺗ ﻲﻣ ﻪﻧاﻮﺘﺳا لﻮﻃ ﺰﻴﻧL
ﺪﻨﺷﺎﺑ .
3 - ﻪﻴﺒﺷ رد يزﺎﮔ ﻦﺸﻴﻧﻮﺗد يراﺬﮔرﺎﺑ يزﺎﺳ
كزﺎﻧ راﺪﺟ ﻪﻧاﻮﺘﺳا
هزﺎﺳ ﺦﺳﺎﭘ ﺶﺨﺑ ﻦﻳا رد يا
ﻪﺑ كﺮﺗ نوﺪﺑ كزﺎﻧ راﺪﺟ ﻪﻧاﻮﺘﺳا ﻚﻳ
ﺖﺳا هﺪﺷ ﻪﺋارا يزﺎﮔ ﻦﺸﻴﻧﻮﺗد يراﺬﮔرﺎﺑ .
ﻪﺑ ﻪﻴﺒﺷ رﻮﻈﻨﻣ يزﺎﺳ
ﻊﺟﺮﻣ رد ﻪﺘﻓﺮﮔ ترﻮﺻ ﻲﺑﺮﺠﺗ ﺶﻳﺎﻣزآ يراﺬﮔرﺎﺑ 1]
راﺮﻗ ﺮﻈﻧﺪﻣ[
ﺖﺳا ﻪﺘﻓﺮﮔ .
ﻞﻜﺷ رد ﻪﻛ ﻪﻧﻮﮕﻧﺎﻤﻫ 3
ﻲﻣ هﺪﻫﺎﺸﻣ ﻢﺘﺴﻴﺳ ،دﻮﺷ
درﻮﻣ ﻲﻠﺻا ﻪﻧاﻮﺘﺳا ﻪﻛ ﺖﺳا هﺪﺷ ﻞﻴﻜﺸﺗ ﻪﻧاﻮﺘﺳا ﻪﺳ زا ﺶﻳﺎﻣزآ ﻲﻣ مود ﻪﻧاﻮﺘﺳا ،ﻲﺳرﺮﺑ ﺪﺷﺎﺑ
. ﻪﻟﻮﻟ ﻲﻣﺎﻤﺗ ﺲﻨﺟ ﺎﻫ
AL 6061-
درﻮﻣ ﻲﻠﺻا ﻪﻧاﻮﺘﺳا ﻲﺳﺪﻨﻫ و يدﺎﻣ تﺎﺼﺨﺸﻣ ﻪﻛ هدﻮﺑ T6 لوﺪﺟ رد ﺶﻳﺎﻣزآ 1
ﺖﺳا هﺪﺷ هدروآ .
ﺗ ﻦﻴﺗوﺮﺑﺎﺳ نﺮﺗﺮﻓ ﺖﺤ
VDLOAD مﺮﻧ
سﻮﻛﺎﺑآ راﺰﻓا ياﺮﺑ1
ﻪﻴﺒﺷ ﻲﻧﺎﻣز هزﺎﺑ ياﺮﺑ و هﺪﺷ ﻲﺴﻳﻮﻧزﺎﺑ ﻦﺸﻴﻧﻮﺗد يراﺬﮔرﺎﺑ يزﺎﺳ
7ms / 4 ﻪﻴﺒﺷ زﺎﺳ ﺖﺳا هﺪﺷ اﺮﺟا ي .
هدﺎﻔﺘﺳا درﻮﻣ يﺎﻫﺮﺘﻣارﺎﭘ
لوﺪﺟ سﺎﺳا ﺮﺑ يراﺬﮔرﺎﺑ ﺪﻛ رد 2
ﻲﻣ ﺪﻨﺷﺎﺑ .
لوﺪﺟ 1 كزﺎﻧ راﺪﺟ ﻪﻧاﻮﺘﺳا ﻲﺳﺪﻨﻫ و يدﺎﻣ تﺎﺼﺨﺸﻣ 1]
[
ௗMPa ௧MPa
ν E (N/m2) (kg/mρ 3)
276 310
33 / 0 109
× 69 2780
Rout(m) Rin(m)
L (m) h (mm) (ﺖﻣﺎﺨﺿ)
02064 / 0 01975 / 0 610 / 0 89
/ 0
لوﺪﺟ 2 يراﺬﮔرﺎﺑ تﺎﺼﺨﺸﻣ 1]
[
Vcj(m/s) T (ms)
P3(MPa) P2(MPa)
P1(MPa)
2365 / 0 15 / 0 5 / 0 6/
2 0
لﺪﻣ ﺖﺧﺎﺳ ياﺮﺑ ﻪﻧاﻮﺘﺳا
هدﺎﻔﺘﺳا ﻲﻟﻮﻃ نرﺎﻘﺗ زا ﺷ
ﻲﻤﻴﻧ و هﺪ
ﺖﺳا هﺪﺷ لﺪﻣ نآ زا .
نﺎﻤﻟا داﺪﻌﺗ ﻲﻟﻮﻃ يﺎﺘﺳار رد ﺎﻫ
350 رد ،
ﺖﻣﺎﺨﺿ يﺎﺘﺳار 3
ﻲﻄﻴﺤﻣ يﺎﺘﺳار رد و 30
ﺪﺷ ﻪﺘﻓﺮﮔ ﺮﻈﻧرد .
1. ABAQUS
هﺪﻨﻫد ﺶﻨﻛاو يﺎﻫ
ﻲﻃﺎﺴﺒﻧا جﻮﻣ ﻦﻛﺎﺳ تﻻﻮﺼﺤﻣ
ﻦﻛﺎﺳ
ﻪﻠﺻﺎﻓ
رﺎﺠﻔﻧا
رﺎﺸﻓ P3
P2= Pcj
P1
Vcj
[ Downloaded from mme.modares.ac.ir on 2022-10-31 ]
ﻞﻜﺷ 3 كزﺎﻧ راﺪﺟ ﻪﻧاﻮﺘﺳا ﻪﺑ طﻮﺑﺮﻣ ﺶﻳﺎﻣزآ ﻢﺘﺴﻴﺳ 1]
[
ﺑ ا ﻪ ًﺎﻌﻤﺟ دوﺪﺤﻣ نﺎﻤﻟا لﺪﻣ رد ﺐﻴﺗﺮﺗ ﻦﻳ 31500
و نﺎﻤﻟا
43524 ﺖﻓر رﺎﻜﺑ هﺮﮔ .
نﺎﻤﻟا نﺎﻤﻟا ﺰﻴﻧ هدﺎﻔﺘﺳا درﻮﻣ يﺎﻫ يﺎﻫ
ﻲﺒﻌﻜﻣ 8 هﺮﮔ ﻲﻣ يا هﺮﮔ و ﺪﺷﺎﺑ نآ رد ﺶﻧﺮﻛ ﻪﭽﺨﻳرﺎﺗ ﻪﻛ يا
ﻪﺒﺳﺎﺤﻣ هﺪﺷ ﻪﻠﺻﺎﻓ رد 2822m
/ 0 ﻪﻟﻮﻟ ﭗﭼ ﺖﻤﺳ يدورو زا
دراد راﺮﻗ . ،يزﺮﻣ ﻂﻳاﺮﺷ ياﺮﺑ ﻪﻴﻜﺗ
هﺎﮔ ﺮﺳود يﺎﻫ ﻪﻧاﻮﺘﺳا
ناﻮﻨﻋ ﻪﺑ
ﻪﻴﻜﺗ هﺎﮔ يﺎﻫ ﺑ ﺰﻴﻧ نرﺎﻘﺗ ﻪﺤﻔﺻ و هﺪﺷ ﻪﺘﻓﺮﮔ ﺮﻈﻧرد هدﺎﺳ ﻪ
ﺖﻠﻋ
ﻒﺼﻧ ندﺮﻛ لﺪﻣ ﻪﻧاﻮﺘﺳا
ﺪﻴﻘﻣ نرﺎﻘﺗ رﻮﺤﻣ ﺮﺑ دﻮﻤﻋ يﺎﺘﺳار رد
ﺖﺳا هﺪﺷ )
ﻞﻜﺷ 4 (.
ﻪﻠﺻﺎﻓ رد ﻲﻄﻴﺤﻣ ﺶﻧﺮﻛ 2822m
/ 0 ﭗﭼ ﺖﻤﺳ يدورو زا
و ﻲﺑﺮﺠﺗ ﺞﻳﺎﺘﻧ هاﺮﻤﻫ ﻪﺑ ﻪﻧاﻮﺘﺳا ﻞﻜﺷ رد ﻲﻠﻴﻠﺤﺗ
5 ﺖﺳا هﺪﺷ هدروآ .
نﺎﻤﻫ ﻲﻣ هﺪﻫﺎﺸﻣ ﻪﻛ ﻪﻧﻮﮔ ﻖﺑﺎﻄﺗ زا ﺞﻳﺎﺘﻧ دﻮﺷ
ﻲﺑﻮﺧ رﺎﻴﺴﺑ
درﻮﺧﺮﺑ را ﺪﻧ . ندﻮﺑ ﺮﻔﺻ ،قﻮﻓ ﺞﻳﺎﺘﻧ ﻦﻴﺑ رد ﺮﻛذ ﻞﺑﺎﻗ توﺎﻔﺗ ﺎﻬﻨﺗ
ﻲﻣ ﻲﻠﻴﻠﺤﺗ ﻞﺣ رد ﻂﺳﻮﺘﻣ ﺶﻧﺮﻛ ﻞﻴﻟد ﻪﺑ ﺮﻣا ﻦﻳا ﻪﻛ ﺪﺷﺎﺑ
ﻲﻣ رﻮﻛﺬﻣ ﻞﺣ رد ﻲﻳﺎﻬﻧ رﺎﺸﻓ راﺪﻘﻣ ندﻮﺑ ﺮﻔﺻ ﺪﺷﺎﺑ
.
ﻞﻜﺷ 4 يزﺮﻣ ﻂﻳاﺮﺷ ﺮﻈﻧﺪﻣ
ياﺮﺑ ﻪﻧاﻮﺘﺳا كزﺎﻧ راﺪﺟ
4 - لﺪﻣ كﺮﺗ ﺪﺷر يزﺎﺳ
ﻚﻳ ﺰﻴﻟﺎﻧآ ﻪﺑ ﺶﺨﺑ ﻦﻳا رد ﻪﻧاﻮﺘﺳا
كزﺎﻧ راﺪﺟ ﻪﻴﻟوا كﺮﺗ ياراد
ﻦﺸﻴﻧﻮﺗد يراﺬﮔرﺎﺑ ﺖﺤﺗ يزﺎﮔ
ﻲﻣ ﻪﺘﺧادﺮﭘ دﻮﺷ
. اﺪﺘﺑا رد
درﻮﻣ رد يﺮﺼﺘﺨﻣ ﺢﻴﺿﻮﺗ ﻪﻛ هﺪﻨﺒﺴﭼ نﺎﻤﻟا
رد لﺪﻣ يزﺎﺳ
ﺲﭙﺳ ،ﺪﺷ ﺪﻫاﻮﺧ هداد ﺢﻴﺿﻮﺗ هﺪﺷ هدﺎﻔﺘﺳا نآ زا كﺮﺗ ﺪﺷر صﻮﺼﺧ رد لﺪﻣ
يزﺎﺳ رد كﺮﺗ ﻪﻧاﻮﺘﺳا هداد ﺢﻴﺿﻮﺗ ﻲﻣ
دﻮﺷ .
4 - 1 - لﺪﻣ يزﺎﺳ هﺪﻨﺒﺴﭼ نﺎﻤﻟا زا هدﺎﻔﺘﺳا ﺎﺑ كﺮﺗ ﺪﺷر
ﺖﻴﻠﺑﺎﻗ زا ﻲﻜﻳ هدﺎﻔﺘﺳا ﻖﻴﻘﺤﺗ ﻦﻳا رد ﻪﻛ هﺪﻨﺒﺴﭼ نﺎﻤﻟا يﺎﻫ
نﺎﻜﻣا ،هﺪﺷ لﺪﻣ
يزﺎﺳ ﻲﺠﻳرﺪﺗ ﺐﻴﺳآ ﻲﮔﺪﻧﺎﻣاو و1
ﻪﻳﻻ رد2
-
هﺪﻨﺒﺴﭼ يﺎﻫ ﻲﻨﺘﺒﻣ
ﺮﺑ ﺦﺳﺎﭘ ﺶﺸﻛ - ﺶﻳاﺪﺟ ﺖﺳا . شور
ﺐﻴﺳآ ﻪﻳﺎﭘ ﺮﺑ ﺦﺳﺎﭘ ﺶﺸﻛ - ﺶﻳاﺪﺟ ﺐﻴﻛﺮﺗ زا هدﺎﻔﺘﺳا هزﺎﺟا
ﺑ ﺐﻴﺳآ مﺰﻴﻧﺎﻜﻣ ﻦﻳﺪﻨﭼ ﻪ
يور ﺮﺑ نﺎﻣﺰﻤﻫ ترﻮﺻ ﻚﻳ
ار هدﺎﻣ
ﻲﻣ ﺪﻫد . ﻲﻣ ءﺰﺟ ﻪﺳ ﻞﻣﺎﺷ ﻲﮔﺪﻧﺎﻣاو مﺰﻴﻧﺎﻜﻣ ﺮﻫ ﺪﺷﺎﺑ
: رﺎﻴﻌﻣ
داد لﺎﻘﺘﻧا بﺎﺨﺘﻧا و ﺐﻴﺳآ ﺪﺷر نﻮﻧﺎﻗ ،ﺐﻴﺳآ عوﺮﺷ نﺎﻤﻟا ن
) ﺎﻳ
ندﺮﻛ فﺬﺣ
3( ﻞﻣﺎﻛ ﺐﻴﺳآ ﺖﻟﺎﺣ ﻪﺑ نﺪﻴﺳر مﺎﮕﻨﻫ رد .
ﺮﮔا
،دﻮﺷ لﺪﻣ ﺮﻇﺎﻨﺘﻣ ﺐﻴﺳآ ﺪﺷر لﺪﻣ نوﺪﺑ ﺐﻴﺳآ عوﺮﺷ رﺎﻴﻌﻣ مﺮﻧ راﺰﻓا سﻮﻛﺎﺑآ ﻲﺟوﺮﺧ فاﺪﻫا ياﺮﺑ ﻂﻘﻓ ار ﺐﻴﺳآ ﺪﺷر رﺎﻴﻌﻣ
ﭻﻴﻫ ﺖﻟﺎﺣ ﻦﻳا رد ،دﺮﻛ ﺪﻫاﻮﺧ ﻲﺑﺎﻳزرا يور ﺮﺑ يﺮﻴﺛﺄﺗ ﻪﻧﻮﮔ
ﺖﺷاﺬﮔ ﺪﻫاﻮﺨﻧ هﺪﻨﺒﺴﭼ نﺎﻤﻟا ﺦﺳﺎﭘ )
ﻪﺑ ﻲﺒﻴﺳآ ﭻﻴﻫ ﺮﮕﻳد نﺎﻴﺑ
دﺎﺘﻓا ﺪﻫاﻮﺨﻧ قﺎﻔﺗا .(
1. Progressive Damage 2. Failure
3. Element Demoval (or Deletion)
هرﺎﻤﺷ ﻪﻧاﻮﺘﺳا 3
هرﺎﻤﺷ ﻪﻧاﻮﺘﺳا
1 ﺖﺴﺗ ياﺮﺑ كزﺎﻧ راﺪﺟ ﻪﻟﻮﻟ ﻪﻧﻮﻤﻧ
) هرﺎﻤﺷ ﻪﻧاﻮﺘﺳا 2
(
ﺞﻨﻠﻓ
رﺎﺠﻔﻧا عوﺮﺷ ﻊﺒﻨﻣ ﺞﻨﻠﻓ
رﺎﺠﻔﻧا جﻮﻣ
[ Downloaded from mme.modares.ac.ir on 2022-10-31 ]
نﺎﻣز (ms)
) ﻒﻟا ( ﺶﺧﺮﭼ ﻪﺒﺗﺮﻣ ﻪﺳ هاﺮﻤﻫ ﻪﺑ ﻲﻫﺎﮕﺸﻳﺎﻣزآ ﺞﻳﺎﺘﻧ 90
ﻪﺑ ﺖﺒﺴﻧ ﻪﺟرد
ﻲﻟﻮﻃ رﻮﺤﻣ ]
1 [
نﺎﻣز (ms)
) ب ( ﻪﻠﺻﺎﻓ رد كزﺎﻧ راﺪﺟ ﻪﻧاﻮﺘﺳا ياﺮﺑ نﺎﻣز ﺐﺴﺣ ﺮﺑ ﺶﻧﺮﻛ m
2822 / 0 زا
نآ ﭗﭼ ﺖﻤﺳ
نﺎﻣز (ms)
) ج ( ﻲﻠﻴﻠﺤﺗ ﻞﺣ ﺞﻳﺎﺘﻧ ]
13 [
ﻞﻜﺷ 5 ﺶﻧﺮﻛ ﻪﭽﺨﻳرﺎﺗ
سﺎﺳا ﺮﺑ ﺐﻴﺳآ عوﺮﺷ رﺎﻴﻌﻣ ﻪﻟﺎﻘﻣ ﻦﻳا رد ﻪﻄﺑار
ﺶﺸﻛ - ﺶﻳاﺪﺟ ياﺮﺑ1
هﺪﻨﺒﺴﭼ نﺎﻤﻟا ﻲﻣ
ﺪﺷﺎﺑ . لﺪﻣ زا ﺶﺸﻛ -
ﺶﻳاﺪﺟ ﻲﻣ جاﺮﺨﺘﺳا ﺮﻳز دراﻮﻣ ، ﻮﺷ
د:
1 - رادﻮﻤﻧ ﻲﻠﻛ ﻞﻜﺷ ﺶﺸﻛ
- ﺶﻳاﺪﺟ ) ﻞﻜﺷ 6 ﻲﻳﺎﻤﻧ ﺖﻟﺎﺣ رد (
1. Traction-Separation
2 - ﺮﺘﻣارﺎﭘ راﺪﻘﻣ σc
) هدﺎﻣ ﻲﺸﺸﻛ ﺖﻣوﺎﻘﻣ ﻢﻤﻳﺰﻛﺎﻣ (
و
Gc
) هدﺎﻣ ﻲﺘﻴﻠﻴﺘﻛاد
، رادﻮﻤﻧ ﺮﻳز ﺢﻄﺳ ﺮﮕﻧﺎﻴﺑ ﻲﻣt-δ
ﺪﺷﺎﺑ (.
مﺮﻧ رد هﺪﺷ ﻪﺋارا يﺎﻫرﺎﻴﻌﻣ ﻦﻴﺑ زا راﺰﻓا
سﻮﻛﺎﺑآ ﻪﻳﺎﭘﺮﺑ
ﺶﺸﻛ - ﺐﻴﺳآ عوﺮﺷ رﺎﻴﻌﻣ ﻖﻴﻘﺤﺗ ﻦﻳا رد ،ﺶﻳاﺪﺟ ﻲﻣﺎﻧ ﺶﻨﺗ
ود ناﻮﺗ ﻪﺟرد ﺖﺳا هﺪﺷ ﻪﺘﻓﺮﮔ ﺮﻈﻧرد2
. ضﺮﻓ ﺖﻟﺎﺣ ﻦﻳا رد
ﻲﻣ ﻲﻣ عوﺮﺷ ﻲﻣﺎﮕﻨﻫ ﺐﻴﺳآ ﻪﻛ دﻮﺷ ﺖﺒﺴﻧ ود ناﻮﺗ ﻪﻛ دﻮﺷ
ﻲﻣﺎﻧ ﺶﻨﺗ )
ﺮﻳز رد ﻪﻛ ﻪﻧﻮﮕﻧﺎﻤﻫ ﻒﻳﺮﻌﺗ
هﺪﺷ ( راﺪﻘﻣ ﻪﺑ 1 ﺪﺳﺮﺑ :
) 3 (
2 2 2
0 0 0 1
n s t
n s t
t t t
t t t
+ + =
نآ رد ﻪﻛ
n0
،t
s0
و t
t0
ﻲﻣﺎﻧ ﺶﻨﺗ ﻪﻨﻴﺸﻴﺑ ﺮﻳدﺎﻘﻣ ﺮﮕﻧﺎﻴﺑt
ﻲﻣﺎﮕﻨﻫ ﺑ ﻞﻜﺷ ﺮﻴﻴﻐﺗ ﻪﻛ ﻪ
ﺲﻴﻓﺮﺘﻨﻳا ﺢﻄﺳ ﺮﺑ دﻮﻤﻋ صﺎﺧ ترﻮﺻ
ﺪﺷﺎﺑ ﻲﺷﺮﺑ ﺖﻬﺟ مود و لوا ﺖﻬﺟ رد ﺎﻳ و .
ﺖﻣﻼﻋ ﺮﮕﻧﺎﻴﺑۃ ۄ
ﺖﻛاﺮﺑ يﻻﻮﻛ ﻚﻣ ﺖﺳا نآ ﻲﻟﻮﻤﻌﻣ ﺮﻴﺴﻔﺗ ﺎﺑ3
. ﺖﻛاﺮﺑ ﻚﻣ
يﻻﻮﻛ ياﺮﺑ ﺮﺛا رد ﺐﻴﺳآ عوﺮﺷ زا يﺮﻴﮔﻮﻠﺟ ﻞﻜﺷ ﺮﻴﻴﻐﺗ
يﺎﻫ
يرﺎﺸﻓ ﺶﻨﺗ ﺎﻳ و ﺺﻟﺎﺧ يرﺎﺸﻓ ﺖﺳا هﺪﺷ هدﺎﻔﺘﺳا
.
ياﺮﺑ ﻊﺑﺎﺗ ﺖﻟﺎﺣ مﺮﻧ ،ﻲﻳﺎﻤﻧ
راﺰﻓا سﻮﻛﺎﺑآ ،ﺐﻴﺳآ ﺮﻴﻐﺘﻣ ﺪﺷر
ﻲﻣ هدﺎﻔﺘﺳا ار ،D ﻪﻛ ﺪﻨﻛ
ﻪﺑ ترﻮﺻ ﺮﻳز ﻪﺻﻼﺧ ﺖﺳا هﺪﺷ :
) 4
0 (
0
mf m
eff c
D T d
G G
δ δ
= δ
∫
−ﻪﻄﺑار رد )
4
eff ( و T δ ﻪﺑ ﺮﺛﺆﻣ ﻲﻳﺎﺠﺑﺎﺟ و ﺮﺛﺆﻣ ﺶﺸﻛ ﺐﻴﺗﺮﺗ
ﻲﻣ ﺪﻨﺷﺎﺑ
0 . ﻲﻣ ﺐﻴﺳآ عوﺮﺷ رد ﻚﻴﺘﺳﻻا يژﺮﻧا G
ﺪﺷﺎﺑ . ﻦﻳا رد
ﺖﻟﺎﺣ ﺢﻄﺳ ﺐﻴﺳآ عوﺮﺷ زا ﺲﭘ ًارﻮﻓ ﺖﺳا ﻦﻜﻤﻣ ﺶﺸﻛ
ﺪﺑﺎﻴﻧ ﺶﻫﺎﻛ .
ﻞﻜﺷ 6 رادﻮﻤﻧ ﺶﺸﻛ - ﺶﻳاﺪﺟ ﻲﻳﺎﻤﻧ ﻊﺑﺎﺗ ﺖﻟﺎﺣ ياﺮﺑ
2. Quads Damage 3. Macaulay
ﻲﻫﺎﮕﺸﻳﺎﻣزآ
دوﺪﺤﻣ نﺎﻤﻟا
ﻲﻠﻴﻠﺤﺗ ﺶﻧﺮﻛﺶﻧﺮﻛ ﺶﻧﺮﻛ
[ Downloaded from mme.modares.ac.ir on 2022-10-31 ]
ﻪﺑ ﺮﻳدﺎﻘﻣ ﻦﻴﻴﻌﺗ ﻪﺑ زﺎﻴﻧ هﺪﻨﺒﺴﭼ نﺎﻤﻟا زا هدﺎﻔﺘﺳا رﻮﻈﻨﻣ
يﺎﻫﺮﺘﻣرﺎﭘ δc
c و ﻲﻣσ ﺪﺷﺎﺑ . يﺎﻫﺮﺘﻣارﺎﭘ δc
c و ﻊﻗاو ردσ
ﻲﻣ هدﺎﻣ ﺖﺴﻜﺷ ﻚﻴﻧﺎﻜﻣ صاﻮﺧ خﺮﻧ رد ﺮﻴﻴﻐﺗ ﺎﺑ و ﺪﻨﺷﺎﺑ
دﺮﻛ ﺪﻫاﻮﺧ ﺮﻴﻴﻐﺗ ﺰﻴﻧ ﺎﻬﻧآ راﺪﻘﻣ ﺎﻣد و ﺖﻣﺎﺨﺿ ،يراﺬﮔرﺎﺑ .
ﻪﺟﻮﺗ ﺎﺑ
ﻂﺳﻮﺗ هﺪﺷ مﺎﺠﻧا يدﺪﻋ تﺎﺒﺳﺎﺤﻣ ﻪﺑ نارﺎﻜﻤﻫ و Li
18]
و [
ﻦﻴﻨﭽﻤﻫ كاﺮﻴﺳ
نارﺎﻜﻤﻫ و 10]
ﻪﺤﻔﺻ ﺶﻨﺗ ﺖﻟﺎﺣ رد [
و يا
مﺮﻧ ﺖﺴﻜﺷ ،1
c 2 ys
σ = σ نآرد ﻪﻛ هدﻮﺑ
σys
ﻢﻴﻠﺴﺗ ﺖﻣوﺎﻘﻣ
رد هدﺎﻔﺘﺳا درﻮﻣ ﻲﻤﺠﺣ هدﺎﻣ لﺪﻣ
يزﺎﺳ ﻲﻣ ﺪﺷﺎﺑ .
راﺪﻘﻣ Γc
ﺤﻟ رد ﻪﻛ ﻪﺘﻜﻧ ﻦﻳا ﻪﺑ ﻪﺟﻮﺗ ﺎﺑ ﻈ
كﺮﺗ ﺪﺷر ﻪ
c Gc
ﻲﻣ Γ = ،ﺪﺷﺎﺑ ﻲﻧاﺮﺤﺑ ناﺰﻴﻣ زا هدﺎﻔﺘﺳا ﺎﺑ ﻪﺋارا CTOA
ﻂﺳﻮﺗ هﺪﺷ ﻲﺋازﺮﻴﻣ
و ﻲﻤﻳﺮﻛ 15]
كﺮﺗ ﺪﺷر عوﺮﺷ ﻪﻈﺤﻟ رد[
ﻲﻣ ﻪﺒﺳﺎﺤﻣ ﻮﺷ
د . لﺪﻣ نﺎﻜﻣ ﺮﻴﻴﻐﺗ ﻪﻳﺎﭘﺮﺑ ﻪﻛ ﻲﻳﺎﻫ يﺎﻫ
كﺮﺗ كﻮﻧ ﻲﮔﺪﺷزﺎﺑ ﻪﻳاوز ﺪﻨﻧﺎﻣ ،ﺖﺳا ﻚﻴﭘﻮﻜﺳوﺮﻛﺎﻣ CTOA
ﺐﺳﺎﻨﻣ رﺎﻴﻌﻣ ﻲﻣ كزﺎﻧ تﺎﻌﻄﻗ رد ﺪﺷر ياﺮﺑ يﺮﺗ
ﺪﺷﺎﺑ . CTOA
ﻲﻣ ار ﻪﺑ ﺮﻳز ﻪﻄﺑار ﺎﺑ ناﻮﺗ دﺮﻛ طﻮﺑﺮﻣCTOD
:
2tan (1 / 2 )
CTOA= − CTOD x (5) نآ رد ﻪﻛ ﻪﻠﺻﺎﻓ x
ﻪﻛ ﺖﺳا يا و CTOA
نآ رد CTOD
ﻲﻣ ﻪﺒﺳﺎﺤﻣ ﺪﻧﻮﺷ
. ﻊﺟﺮﻣ ﻖﺒﻃ 19]
ناﺰﻴﻣ ،[
ﻲﻧاﺮﺤﺑ CTOA
ﺮﺑاﺮﺑ 61 / 4 ناﺰﻴﻣ و ﻪﺟرد نآ ﺎﺑ ﺐﺳﺎﻨﺘﻣx
763mm / 0 ﻲﻣ ﺪﺷﺎﺑ .
ﻪﻄﺑار ﻪﺑ ﻪﺟﻮﺗ ﺎﺑ ﻦﻳاﺮﺑﺎﻨﺑ )
5 ( ناﺰﻴﻣ ﻲﻧاﺮﺤﺑ CTOD
0614mm / 0 ﺪﻣآ ﺪﻫاﻮﺧ ﺖﺳﺪﺑ .
ﻲﻣ ﺮﻳز ﻪﻄﺑار يژﺮﻧا ياﺮﺑ ﺪﻧاﻮﺗ
هدﺎﻔﺘﺳا ﺖﺴﻜﺷ ﻮﺷ
د:
c c ys
G =CTOD ×σ (6)
ﺖﺴﻜﺷ يژﺮﻧا راﺪﻘﻣ ،ﻻﺎﺑ رد هﺪﺷ ﺮﻛذ ﺮﻳدﺎﻘﻣ سﺎﺳا ﺮﺑ
J/m2
16953 ﺎﺑ ﺐﺳﺎﻨﺘﻣ ﻲﻣ ﺖﺳﺪﺑ ﻲﻧاﺮﺤﺑCTOA
ﺪﻳآ .
4 - 2 - ﺞﻳﺎﺘﻧ ﻞﻴﻠﺤﺗ لﺪﻣ
يزﺎﺳ
ياﺮﺑ ﻪﻧاﻮﺘﺳا لوﺪﺟ رد هﺪﺷ ﻪﺋارا كزﺎﻧ راﺪﺟ 1
كﺮﺗ تﺎﺼﺨﺸﻣ و
2a=8.115mm لﺪﻣ
يزﺎﺳ ﺖﺳا ﻪﺘﻓﺮﮔ مﺎﺠﻧا كﺮﺗ ﺪﺷر .
هرﺎﻤﺷ ﺶﻳﺎﻣزآ سﺎﺳا ﺮﺑ يراﺬﮔرﺎﺑ 34
ﻊﺟﺮﻣ 1]
ﻪﻛ ﻪﺘﻓﺮﮔ مﺎﺠﻧا[
لوﺪﺟ رد نآ ﻒﻠﺘﺨﻣ يﺎﻫﺮﺘﻣارﺎﭘ ﺮﻳدﺎﻘﻣ 3
ﺖﺳا هﺪﺷ ﻪﺋارا .
ﻞﻜﺷ رد 7
لﺪﻣ ﺞﻳﺎﺘﻧ ﻲﻤﻳﺮﻛ و ﻲﺋازﺮﻴﻣ يزﺎﺳ
15]
نﺎﺸﻧ [
ﺖﺳا هﺪﺷ هداد .
كﺮﺗ ﺪﺷر رﺎﻴﻌﻣ زا ﺎﻬﻧآ ﻖﻴﻘﺤﺗ ﻦﻳا رد CTOA
ﻲﺗﺎﻘﻴﻘﺤﺗ ﺪﻛ و Warp3D
لﺪﻣ ياﺮﺑ هدﺎﻔﺘﺳا كﺮﺗ ﺪﺷر يزﺎﺳ
ﺪﻧدﺮﻛ 19]
.[
1.Ductile Fracture
ﻪﺑ لﺪﻣ رﻮﻈﻨﻣ هﺪﻨﺒﺴﭼ نﺎﻤﻟا زا هدﺎﻔﺘﺳا ﺎﺑ كﺮﺗ ﺪﺷر يزﺎﺳ
راﺪﻘﻣ
J/m2
16953 ﻪﺑ ﻪﺟﻮﺗ ﺎﺑ ﻲﻧاﺮﺤﺑ ﺖﺴﻜﺷ يژﺮﻧا ياﺮﺑ
راﺪﻘﻣ ﺖﺳا هﺪﺷ ﻪﺘﻓﺮﮔ ﺮﻈﻧ رد ﻲﻧاﺮﺤﺑ CTOA
. ﺖﺳﺪﺑ ﺞﻳﺎﺘﻧ
ﺑ كﺮﺗ ﺪﺷر زا هﺪﻣآ ﻞﻜﺷ رد هﺪﻨﺒﺴﭼ نﺎﻤﻟا زا هدﺎﻔﺘﺳا ﺎ
8 نﺎﺸﻧ
ﺖﺳا هﺪﺷ هداد .
ﻞﻜﺷ ﺔﺴﻳﺎﻘﻣ ﺎﺑ يﺎﻫ
7 و 8 ﻪﻛ دﺮﺑ ﻢﻴﻫاﻮﺧ ﻲﭘ ﻪﺘﻜﻧ ﻦﻳا ﻪﺑ
مﺮﻧ رد هﺪﻨﺒﺴﭼ نﺎﻤﻟا زا هدﺎﻔﺘﺳا زا ﻪﻠﺻﺎﺣ ﺞﻳﺎﺘﻧ ﺎﺑ سﻮﻛﺎﺑآ راﺰﻓا
كﺮﺗ ﺪﺷر رﺎﻴﻌﻣ زا هﺪﻣآ ﺖﺳﺪﺑ ﺞﻳﺎﺘﻧ ﻲﺗﺎﻘﻴﻘﺤﺗ ﺪﻛ ردCTOA
Warp3D ﺪﻧراد ﻲﺑﻮﺧ ﻖﺑﺎﻄﺗ
. ودﺮﻫ رد لﺪﻣ
هﺪﻫﺎﺸﻣ يزﺎﺳ
ﻲﻣ ﻪﻬﺒﺟ زا ﺮﺘﺸﻴﺑ ﻮﻠﺟ ﻪﻬﺒﺟ رد كﺮﺗ ﺪﺷر ﺖﻋﺮﺳ ﻪﻛ دﻮﺷ
ﻲﻣ كﺮﺗ ﺐﻘﻋ ﺪﺷﺎﺑ
.
لوﺪﺟ 3 كﺮﺗ ﺪﺷر يزﺎﺴﻟﺪﻣ ياﺮﺑ يزﺎﮔ ﻦﺸﻴﻧﻮﺗد جﻮﻣ تﺎﺼﺨﺸﻣ ]
1 [
Shot
# L(m) Vcj
(m/s) P1
(MPa) Pcj
(MPa) P3
(MPa) T (ms) 34 0/610 2404 0/18 /61 2 0/15
0.102 , f 0, b 0
t= ms ∆a = ∆ =a
0.223 , f 71.7, b 53.3
t= ms ∆a = ∆ =a
0.287 , f 122.8, b 81.6
t= ms ∆a = ∆ =a
0.414 , f 195.2, b 123.5
t= ms ∆a = ∆ =a
0.541 , f 236.4, b 163.2
t= ms ∆a = ∆ =a
ﻞﻜﺷ 7 ﺞﻳﺎﺘﻧ سﺎﺳاﺮﺑ لوا ﻲﻠﺻا ﺶﻨﺗ ﻊﻳزﻮﺗ لﺪﻣ
يزﺎﺳ ﺎﺑ كﺮﺗ ﺪﺷر
كﺮﺗ ﺪﺷر رﺎﻴﻌﻣ زا هدﺎﻔﺘﺳا CTOA
19] )[ ﺐﺴﺣ ﺮﺑ MPa (
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0.102 , f 0, b 0
t= ms ∆a = ∆ =a
0.223 , f 72.1, b 52.8
t= ms ∆a = ∆ =a
0.287 , f 122.4, b 82.3
t= ms ∆a = ∆ =a
0.414 , f 194.3, b 124.1
t= ms ∆a = ∆ =a
0.541 , f 237.0, b 164.1
t= ms ∆a = ∆ =a
ﻞﻜﺷ 8 ﻊﻳزﻮﺗ ﻨﺗ ﺞﻳﺎﺘﻧ سﺎﺳاﺮﺑ لوا ﻲﻠﺻا ﺶ لﺪﻣ
يزﺎﺳ كﺮﺗ ﺪﺷر
هﺪﻨﺒﺴﭼ نﺎﻤﻟا زا هدﺎﻔﺘﺳا ﺎﺑ )
ﺐﺴﺣ ﺮﺑ (MPa
5 - ﻪﺠﻴﺘﻧ يﺮﻴﮔ
ﻪﺠﻴﺘﻧ يﺮﻴﮔ ﻲﻣ ﺮﺿﺎﺣ ﻖﻴﻘﺤﺗ زا ﺮﻳز يﺎﻫ ﺪﻨﻳآ
:
1 - لﺪﻣ ﻳزﺎﺳ كﺮﺗ ﺪﺷر رﺎﻴﻌﻣ ﻪﻳﺎﭘﺮﺑ ﻪﺘﻓﺮﮔ ترﻮﺻ يﺎﻬ CTOA
ﻲﺗﺎﻘﻴﻘﺤﺗ ﺪﻛ ﻂﺳﻮﺗ Warp3D
و رد هﺪﻨﺒﺴﭼ نﺎﻤﻟا
مﺮﻧ يرﺎﺠﺗ راﺰﻓا سﻮﻛﺎﺑآ
ﻲﻧﺎﺴﻜﻳ ﻦﺸﻴﻧﻮﺗد ﺖﺤﺗ كﺮﺗ ﺪﺷر
ﻲﻣ نﺎﺸﻧ ار ﺪﻨﻫد
. ودﺮﻫ رد لﺪﻣ يزﺎﺳ رد كﺮﺗ ﺪﺷر ﺖﻋﺮﺳ
ﻮﻠﺟ ﻪﻬﺒﺟ رد كﺮﺗ ﺪﺷر ﺖﻋﺮﺳ و هدﻮﺑ توﺎﻔﺘﻣ ﺐﻘﻋ و ﻮﻠﺟ ﻲﻣ ﺮﺘﺸﻴﺑ ﺪﺷﺎﺑ
19]
.[
2 - ﻚﭼﻮﻛ ﻲﻧﺎﻣز هزﺎﺑ رد ﺞﻳﺎﺘﻧ هﺪﻫﺎﺸﻣ ترﻮﺻ رد )
دوﺪﺣ رد
(µs نﺎﻤﻫ ، ﻊﺟاﺮﻣ رد ﻪﻛ ﻪﻧﻮﮔ 16]
، 17 ،ﺖﺳا هﺪﺷ هرﺎﺷا [
و كﺮﺗ ﺪﺷر ﻲﮔﺪﻣآﺮﺑ
يزﺎﮔ ﻦﺸﻴﻧﻮﺗد يراﺬﮔرﺎﺑ ﺖﺤﺗ نآ1
ﻪﺑ ترﻮﺻ ﻲﻣ ﻲﻠﻜﻴﺳ ﺪﺷﺎﺑ
. هدوﺪﺤﻣ رد ،ﺮﮕﻳد ترﺎﺒﻋ ﻪﺑ
هزﺎﺳ جاﻮﻣا ﻂﺳﻮﺗ كﺮﺗ ﺪﺷر ﻦﺸﻴﻧﻮﺗد يراﺬﮔرﺎﺑ زا ﻲﺻﺎﺧ يا
ﻨﻛ ﺑ و هﺪﺷ لﺮﺘ ﻪ
ﻲﻣ ﻲﺑوﺎﻨﺗ ترﻮﺻ ﺪﺷﺎﺑ
. لﺪﻣ يزﺎﺳ ﻲﮔﺪﻣآﺮﺑ
ﻲﻜﻳ ﻲﻣ ﻪﻟﺎﻘﻣ ﻦﻳا زا ﻞﺻﺎﺣ هﺪﻣآ ﺖﺳﺪﺑ ﺞﻳﺎﺘﻧ ﻦﻳﺮﺘﻤﻬﻣ زا -
زا هدﺎﻔﺘﺳا ﺎﺑ ﻪﻛ ﺪﺷﺎﺑ يﺮﻴﮔرﺎﻜﺑ زا ﻞﺻﺎﺣ ﺪﺷر يﻮﮕﻟا
نﺎﻤﻟا
ﺖﺳا ﻪﺘﻓﺮﮔ ترﻮﺻ رﺎﺑ ﻦﻴﻟوا ياﺮﺑ هﺪﻨﺒﺴﭼ .
6 - ﻣ ﺟاﺮ ﻊ
[1] Chao T.W, Gaseous Detonation-Driven Fracture of Tubes, PhD thesis, California Institute of Technology, Pasadena, California, March 2004.
[2] Chao T. and Shepherd J.E., “Detonation Loading of Tubes in the Modified Shear Wave Regime. In Z.
Jiang, editor”, Proceedings of the 24th International Symposium on Shock Waves, volume 2, Springer, 200, pp. 865-870.
[3] Tang, S., “Dynamic Response of a Tube under Moving Pressure”, Proceedings of the American Society of Civil Engineers, Vol. 5., 1965, pp. 97–
122.
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H. Scanlon, editors), Pergamon Press: Oxford, 1965, pp.349–363.
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& Structures, 2006.
[11] Chao T.W, Shepherd J.E. Fracture Response of Externally Flawed Aluminum Cylindrical Shells under Internal Gaseous Detonation Loading.
1.Bulging
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International Journal of Fracture, 134(2) (2005), 59–90.
[12] Deiterding, R., Cirak, F., & Meiron, D. (2006).
Computational Results for the Fracturing Tube Validation Experiment. ASCI/ASAP Research review Caltech,
http://www.cacr.caltech.edu/asc/wiki/pub/Fracturin gTube/WebHome/DetFracSim.ppt
[13] Mirzaei, M., Mazaheri, K., Biglari, H., Analytical Modeling of the Elastic Response of Tubes to Internal Detonation Loading, International Journal of Pressure Vessels and Piping, Vol. 82, No. 12, pp. 883-895, 2005.
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[19] Mirzaei M., Finite Element Analysis of Deformation and Fracture of Cylindrical Tubes under Internal Moving Pressures, In: David Moratal (ed.) Finite Element Analysis, Chapter 21, http://www.intechopen.com, 2010.
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