⻠  ⟵࿕૕ਛߩⴣ᠄ᵄߩ⑼ቇ౉㐷 ጊ 㓷 ⧷દ⮮ᔘ࠹ࠢࡁ࠰࡝ࡘ࡯࡚ࠪࡦ࠭ ᩣ  ‫ޥ‬100-6080᧲੩ㇺජઍ↰඙㔰߇㑐 3-2-5㔰߇㑐ࡆ࡞ 

Introductory Shock Wave Science in Solids
KATAYAMA Masahide(Received October 13, 2009)
Key words: condensed matter (phase), elastic precursor, HEL, hugoniot, impact dynamics, shock impedance, shock wave, taylor test

1. ✜   ⸒ᧄⓂߢߪ㨬࿕૕ਛߩⴣ᠄ᵄ‫ޠ‬ߦߟ޿ߡ⼏⺰ߔࠆ㧚ߣߎࠈ߇㧘ᐢㄉ⧞╙౐ߦࠃࠆߣ㧘ⴣ᠄ᵄߣߪ㧘㨬ⓨ᳇ߩࠃ߁ߥ࿶❗ᕈᵹ૕ߩਛߢ㧘㖸ㅦࠍ⿥߃ࠆㅦߐߢવࠊࠆᒝ޿࿶ജᄌൻߩᵄ㧚ಽൻߔࠆߩߢߪߥߊ㧘ߘࠇࠄࠍ⛔৻⊛ߦขࠅᛒ߁㨬ㅪ⛯૕ജቇ㨭ߣߒߡᝒ߃ࠆߩ߇᦭ല߆ߟലᨐ⊛ߢ޽ࠆ㧚ߎߩㅪ⛯૕ߣ޿߁᭎ᔨߪ㧘ᢙቇၮ␆⺰ߩㅪ⛯ᕈߦ⿠Ḯ߇޽ࠅ㧘ㅪ⛯૕ࠍ޿ߊࠄ⚦ಽൻߒߡ߽ਇㅪ⛯ᕈ߇⃻ࠇߥ޿ࠃ߁ߥᇦ૕ࠍ઒ቯߔࠆ߽ߩߢ޽ࠆ㧚ߘߩ೨㕙ߦ࿶ജ࡮᷷ᐲ࡮ኒᐲ߇ᕆỗߦᄌൻߔࠆਇㅪ⛯㕙߇࿕૕ߣᵹ૕ߩ඙೎ߪ㧘ᔕജߣ߭ߕߺߩߖࠎᢿᚑಽ㨯஍Ꮕᚑߢ߈ࠆ㧚῜⊒ߦ઻߁࿶❗ᵄ㧘ㆫ㖸ㅦߢ㘧ⴕߔࠆ⠢߆ࠄ⊒↢ಽߩ᦭ή㧘᧚ᢱᒝᐲߩ᦭ήߦ޽ࠆ㧚ߐࠄߦ឵⸒ߔࠇ߫㧘ᓟߔࠆᵄߥߤߪߘߩ଀㧚㨭ߣ޽ࠅ㧘ⴣ᠄ᵄߩ⊒↢ߪ޽ߚ߆߽᳇

ㅀߩ᭴ᚑೣ constitutive equation ߇᦭ᗧ߆ุ߆ߦ޽ࠆ㧚ㅪ⛯૕ਛߦ㒢ࠄࠇࠆ߆ߩࠃ߁ߦ⷗߃ࠆ㧚ࠗࡦ࠲࡯ࡀ࠶࠻਄ߩ⊖૕ജቇߦ߅޿ߡߪ㧘࿕૕ߣᵹ૕ߩਔᣇߦኻߒߡ㧘ห৻ߩ㧘⑼੐ౖߢ޽ࠆᣣᧄ⺆ “Wikipedia”߽㧘2009 ᐕ 10 ᦬ᤨὐߢi)ㅪ⛯ߩᑼ㧘ii)ㆇേᣇ⒟ᑼ㧘iii)ࠛࡀ࡞ࠡ࡯ߩᑼߩਃߟߩၮ

ߪ㧘㨬ⴣ᠄ᵄ㨭ߪ᳇૕ਛ㧘ਥߦⓨ᳇ਛߦ⊒↢ߔࠆߣㅀߴߡ޿

␆ᑼ߇┙ߡࠄࠇࠆ㧚ߎࠇࠄߩᑼߪ㧘ߘࠇߙࠇ㧘⾰㊂㧘ㆇേࠆ㧚ߘࠇߦኻߒߡ㧘⧷⺆

㊂㧘ࠛࡀ࡞ࠡ࡯ߩฦ଻ሽೣߦ⋧ᒰߔࠆ㧚ߎߩ߁ߜ㧘ㆇേᣇ⒟“Wikipedia”ߢߪ㧘᣿⏕ߦ“solid,liquid or gas”ਛࠍવ᠞ߔࠆߣ⸃⺑ߒߡ޿ࠆ㧚ᑼߩߺ߇ࡌࠢ࠻࡞ᣇ⒟ᑼߢ޽ࠆ߇㧚ⓨ㑆ࠍ 1㨪3 ߩ޿ߕࠇߩ

ᣣᧄߦ߅ߌࠆߎߩ⺋⻪ߪ㧘࿶❗ᕈߩዊߐߥ࿕૕߇᦭ᗧߥ

ᰴరࠍ઒ቯߒߡ߽㧘ࠬࠞ࡜࡯ᣇ⒟ᑼߩᢙߦኻߒᄌᢙߩᢙ߇

࿶❗ࠍⵍࠆࠃ߁ߥᭂ߼ߡᄢ߈ߥജࠍᕆỗߦ૞↪ߐࠇࠆࠃ߁

৻ߟᄙߊߎࠇࠄߩၮ␆ᑼߛߌߢߪ⸃ߌߥ޿㧚ߒ߆ߒ㧘ߎࠇߥ⃻⽎ࠍ⚻㛎ߔࠆߎߣ߇ዋߥ޿ߎߣߦේ࿃߇޽ࠆࠃ߁ߦᕁ

ࠄߩၮ␆ᑼߦ฽߹ࠇࠆਃߟߩ⁁ᘒᄌᢙߢ⸥ㅀߒߚ㧘ߘߩㅪࠊࠇࠆ㧚߽߁ ৻ߟߩේ࿃ߣߒߡߪ㧘࿕૕ਛߦ⊒↢ߒߚⴣ᠄⛯૕‛⾰ߩ․ᕈࠍⷙቯߔࠆ⁁ᘒᣇ⒟ᑼ equation of sate:ᵄࠍੱ㑆ߩ੖ᗵߢᝒ߃ࠆߎߣ߇࿎㔍ߢ޽ࠆߎߣ߽⠨߃ࠄࠇ

EOS ࠍㅪ┙ߐߖࠆߎߣߦࠃߞߡ⸃ߊߎߣ߇ߢ߈ࠆ㧚ᾲജࠆ㧚ߘࠇߦኻߒߡ㧘੹ߪ⚻㛎ߔࠆߎߣ߇⒘ߦߥߞߚ߇㧘╩ቇߦࠃࠇ߫㧘ᾲജቇ⊛⁁ᘒ㊂ߪ㧘10 ⒳એ਄ቯ⟵ߔࠆߎߣ⠪߇ሶଏߩ㗃ߩ 1960 ᐕઍೋ߼㗃߹ߢߪ㧘ࠫࠚ࠶࠻ᯏ߇ૐⓨߢ㖸ㅦࠍ⿥߃ࠆࠃ߁ߥ㘧ⴕᴺࠍណࠆߎߣߦࠃߞߡ⊒↢ߒߚ߇ߢ߈ࠆ߇㧘⁛┙ߦᄌൻߔࠆߩߪੑߟߩߺߢ޽ࠆ㧚ㅢᏱ㧘ⴣ᠄⸃ᨆᴺߢߪ㧘ኒᐲ U ߣන૏⾰㊂ᒰࠅߩᲧౝㇱࠛࡀ࡞ߣᕁࠊࠇࠆᄢ߈ߥ㖸 ࠰࠾࠶ࠢࡉ࡯ࡓ ࠍ⡞ߊߎߣ߇ߒ߫ߒ

ࠡ࡯ E ࠍ⁛┙ᄌᢙߣߒߡ࿶ജ P ࠍᓥዻᄌᢙߣߔࠆ߫޽ߞߚ㧚ᒰᤨߩᄙߊߩ৻⥸ߩᄢੱ߽ߘߩේ࿃ࠍ⍮ߞߡ߅Pࠅ㧘߶߷ᱜߒ޿⺑᣿ࠍฃߌߚࠃ߁ߦ⸥ᙘߒߡ޿ࠆ㧚࿕૕‛⾰ߦኻߒߡ߽࿶ജࠍቯ⟵ߔࠆߎߣߦࠃࠅ㧘࿶ജߣᔕᧄⓂߢߪ㧘࿕૕ߣᵹ૕ࠍ✚⒓ߔࠆ↪⺆ߢ޽ࠆ㨬ಝ❗૕㨭ਛߦ⊒↢ߔࠆⴣ᠄ᵄߦ㑐ߒ㧘․ߦ࿕૕ߦὶὐࠍᒰߡߡ⼏⺰ߔf U , E ߣ޿߁ᒻߩ⁁ᘒᣇ⒟ᑼ߇ណ↪ߐࠇࠆ㧚ߎߩߚ߼㧘ജ߇⋧੕ߦ෻ᤋߐߖࠄࠇࠆ㧚ߔߥࠊߜ㧘࿶߇ਥᔕജᚑಽ
V i ߩᐔဋ୯ : V 0 1 3 V 1  V 2  V 3 ߣ p V 0 ߥࠆ㑐

2. ㅪ⛯૕ജቇߦࠃࠆቯᑼൻ

ଥ*1ߦ޽ࠆߣ઒ቯߔࠇ߫㧘ోᔕജ࠹ࡦ࠰࡞ V ij 㧘஍Ꮕᔕജ࠹
ࡦ࠰࡞ W ij ߅ࠃ߮࿶ജߩ㑆ߦߪ㧘 V ij W ij  PG ij ߥࠆ㑐ଥ߇ᚑࠆߎߣߦߔࠆ㧚┙ߔࠆ ߚߛߒ㧘 G ij ߪ Kronecker ߩ࠺࡞࠲ 㧚ߎߩࠃ߁ߦ⴫৻⥸ߦ㧘࿕૕ਛߦⴣ᠄ᵄ߇↢ߓࠆࠃ߁ߥࠛࡀ࡞ࠡ࡯ኒᐲߔߎߣߦࠃߞߡ㧘ᵹ૕ߪ஍Ꮕᔕജᚑಽ߇ߔߴߡ 0 ߩ⁁ᘒߣߩᄢ߈ߥജ߇૞↪ߔࠆ⃻⽎ߢߪ㧘ߒ߫ߒ߫ᶧൻ߿᳇ൻ㧘ߐߒߡ࿕૕ߣห᭽ߦขࠅᛒ߁ߎߣ߇ߢ߈㧘ㅒߦ㧘࿕૕ߦኻߒࠄߦߪ㧘ࡊ࡜࠭ࡑൻߩࠃ߁ߥ⋧ᄌൻࠍ↢ߓࠆ㧚ߎߩࠃ߁ߦ㧘ߡ߽࿶ജࠍዉ౉ߔࠆߎߣ߇ߢ߈ᾲജቇߣߩ࡝ࡦࠢ߇น⢻ߦⴣ᠄໧㗴ߦ߅޿ߡߪ㧘ኻ⽎ߣߔࠆ‛ℂ♽ߦ‛⾰ߩ 3 ⋧߇ᷙߥࠆ㧚߹ߚ㧘ౝㇱࠛࡀ࡞ࠡ࡯ߪ࿕૕‛⾰ߩ஍Ꮕ߭ߕߺᚑಽ࿷ߒ㧘ߒ߆߽ⶄ㔀ߦ㑐ଥߒว߁ߩ߇৻⥸ߢ޽ࠆ㧚ߘߩߚ߼㧘ߚߣ߃߫㧘㨬ᵹ૕ജቇ㨭ࠍ㨬᳇૕ߩജቇ㨭ߣ㨬ᶧ૕ߩജቇ㨭ߦ⚦*1 ࿶ജߪ࿶❗߇ᱜ㧘ᔕജߪᒁᒛ߇ᱜࠍ઒ቯߔࠆ㧚ߩჇಽߣߒߡߩ㕖นㅒߥ႟ᕈ߭ߕߺࠛࡀ࡞ࠡ࡯㧘߅ࠃ߮นㅒߥࠛࡀ࡞ࠡ࡯ߢ޽ࠆᾲജቇ⊛઀੐ߩ๺ߣߒߡ⹏ଔߐࠇࠆ㧚࿕૕‛⾰ߦኻߒߡߪ㧘஍Ꮕᚑಽࠍ⹏ଔߔࠆߚ߼ߦ㧘⁁ᘒᣇ⒟ᑼߛߌߢߪߥߊ㧘ᔕജ㧙߭ߕߺ㑐ଥߦઍ⴫ߐࠇࠆ᭴ᚑೣ߇ㅪ┙ߒߡ⸃߆ࠇࠆ㧚․ߦ㧘ⴣ᠄ജ߇ᄢ߈ߥ໧㗴ߢߪ㧘࿕૕‛⾰ߦ߅޿ߡ߽஍ᏅᚑಽߦᲧߴߡ㕒᳓࿶ᚑಽ߇ථ⿧ߔࠆ

૕ߩㆇേ㊂ᄌൻߦ╬ߒ޿ߚ߼㧘51 5 0U1 U  u 1 u 1  U0Uu 0        ( 2 )ߎߎߢ㧘◲නߩߚ߼ⴣ᠄೨ߩᵹㅦࠍ 0 ߣߒ u0 = 0 㧘ᑼ(1)ࠍ↪޿ߡ U0 ࠍᶖ෰ߔࠆߣᑼ(3)ࠍᓧࠆ㧚

51 5 0U0Uu 1              (3)ߚ߼ᵹ૕⊛᜼േࠍ␜ߔߎߣߦߥࠆ㧚ߐࠄߦ㧘ജቇ♽ߦ߅ߌࠆࠛࡀ࡞ࠡ࡯଻ሽೣߪ㧘ోࠛࡀ࡞ࠡ࡯
3. ⴣ᠄ᵄߩၮ␆ℂ⺰ౝㇱࠛࡀ࡞ࠡ࡯ߣㆇേࠛࡀ࡞ࠡ࡯ߩ๺ ߣᄖㇱ߆ࠄߩ઀

3.1 ଻ሽೣߣࠫࡖࡦࡊ᧦ઙⴣ᠄ᵄߩ෩ኒߥቯ⟵ߦߟ޿ߡߪ⦡‫߇ࠆ޽߇⺰⼏ߥޘ‬㧘ߎߎߢߪ㧘ㅪ⛯૕ߣߒߡߩ޽ࠆᇦ⾰߇ᕆỗߥ࿶❗ࠍฃߌߚ⚿੐㊂ߩ᝼ฃߩ๺߇଻ሽߔࠆߎߣࠍᗧ๧ߒߡ޿ࠆ㧚't ߩ㑆ߦⴣ᠄ᵄ㕙߇⒖േߔࠆో૕Ⓧߩᇦ⾰߇ೋᦼߦ߽ߞߡ޿ࠆౝㇱࠛࡀ࡞ࠡ࡯ߪ㧘ߘߩೋᦼߩᲧౝㇱࠛࡀ࡞ࠡ࡯ E 0 ࠍ↪޿ߡ㧘ᨐ㧘ᇦ⾰ਛߦ⊒↢ߒߚᡓੂ߇޽ࠆㅦᐲ ૏⋧ㅦᐲ ߢવ᠞ߔU 0U 't u E 0 ߢ⴫ࠊߐࠇࠆ㧚৻ᣇ㧘ߘߩ㑆ߦߘߩᇦ⾰ߦኻߒࠆࡈࡠࡦ࠻ 㕙 ߩ೨ᓟߢኒᐲ㧘࿶ജ㧘᷷ᐲߥߤߩ‛ℂ㊂߇ߡࡇࠬ࠻ࡦ߇ⴕ߁઀੐㊂ߪ 5 1 u u 1't ߢ޽ࠆ㧚ߘࠇߦኻߒߡ㧘ਇㅪ⛯ߦᄌൻߔࠆ⃻⽎ߢ޽ࠆߣ⠨߃ࠆ㧚ߎߩ㕙ߩ೨ᓟߢ߽⾰㊂㧘ㆇേ㊂㧘ࠛࡀ࡞ࠡ࡯ߩฦ଻ሽೣ

't ᓟߦ߅ߌࠆหᇦ⾰ߩౝㇱࠛࡀ࡞ࠡ࡯ߪ㧘ⴣ᠄ᓟߩᲧౝㇱࠛࡀ࡞ࠡ࡯ E1 ࠍ↪޿ߡ㧘 U0U 't u E1 ߢ⴫ߐࠇ㧘ߘߩㇱಽ߇ᚑࠅ┙ߟ߽ߩߣߔࠆ㧚࿑䋱ߪ㧘න૏ᢿ㕙Ⓧߩ೰ߥ౞▤ਛ߇ᜬߟㆇേࠛࡀ࡞ࠡ࡯ߪ㧘  u U0U 't u u 1 2 ߢ޽ࠆ߆ࠄ㧘ߩᇦ⾰߇೰ߥࡇࠬ࠻ࡦߦࠃߞߡᏀ߆ࠄฝᣇะߦⴣ᠄ജࠍട

ࠛࡀ࡞ࠡ࡯଻ሽᑼߪᑼ(4)ߩࠃ߁ߦ⴫ߐࠇࠆ㧚
1
U0U 'tE 0  5 1u 1't U0U 'tE1  U0U 'tu 12(4)2
ᑼ(4)߆ࠄᑼ(1)ߣ(3)ࠍ↪޿ߡ U ߣ u1 ࠍᶖ෰ߔࠆߣ㧘ᑼ(5)ߩ

߃ࠄࠇߚ೨ᓟߩ᭽ሶࠍ␜ߒߡ޿ࠆ㧚ߚߛߒ㧘◲නߩߚ߼㧘౞▤ਛߩᇦ⾰ߪᵹ૕⊛ߥ 1 ᰴర⊛ቯᏱᵹࠇߢ޽ࠅ㧘ゲᣇะએᄖߩㅦᐲᚑಽߪߥ޿߽ߩߣ઒ቯߔࠆ㧚߹ߚ㧘એਅߢߪᐳᮡ♽ࠍⓨ㑆ߦ࿕ቯߔࠆ Euler ᐳᮡ♽ࠍㆡ↪ߔࠆ߽ߩߣߔࠆ㧚ᤨೞ t 0 ߦࡇࠬ࠻ࡦߪㅦᐲ u1 ߢേ߈ᆎ߼㧘t 0  't ߦߪೋᦼߩHugoniot ࠛࡀ࡞ࠡ࡯ᑼߣ๭߫ࠇࠆ㊀ⷐߥᑼ߇ዉ߆ࠇࠆ㧚૏⟎߆ࠄ u1't ߩ〒㔌߹ߢ⒖േߔࠆ㧚ೋᦼߩ⁁ᘒߩᇦ⾰ߣ࿶(5)❗ߐࠇߚᇦ⾰ߩ㑆ߩਇㅪ⛯㕙ߪࡇࠬ࠻ࡦߦవⴕߔࠆᵄߣߒ
ߡવ᠞ߔࠆߚ߼㧘ߘߩ૏⋧ㅦᐲ U ߪ u1 ࠃࠅ߽ㅦߊ㧘ࡇࠬ࠻

E1  E 0§ 1 1·1P1  P 0 ¨  ¸2
© U0 U1 ¹

ᑼ(1), (3), (5)ߩ 3 ଻ሽೣࠍ⴫ߔᑼࠍ Rankine-Hugoniot ߩᑼߣࡦ߇⒖േߔࠆ㑆ߦ U 't ߛߌฝߦ⒖േߔࠆ㧚ᧂ࿶❗ߩᇦ⾰ߩ
ኒᐲࠍ U0 ߣߔࠆߣ㧘ਇㅪ⛯㕙ߣࡇࠬ࠻ࡦ㑆ߩ࿶❗ࠍฃߌߚ✚⒓ߔࠆ㧚

ᇦ⾰ߩ✚⾰㊂ߪ㧘࿶❗೨ߩᇦ⾰ࠍၮḰߦߔࠆߣ U0U 't ߢ޽ᶖ෰ߔࠆߣᑼ(6)߇ᓧࠄࠇࠆ㧚ࠅ㧘࿶❗ᓟߩᇦ⾰ࠍၮḰߦߔࠆߣ U1 U  u 1 't ߢ޽ࠆ㧚⾰㊂଻ሽೣ߆ࠄ㧘ߎࠇࠄߩ⾰㊂ߪ╬ߒߊ㧘ਔ⾰㊂ࠍ 't ߢ㒰ߒߡᑼ(1)ࠍᓧࠆ㧚U0U

U1 U  u1            (1)ߣߎࠈߢ㧘ߎߩᧂ࿶❗ߩᇦ⾰ࠍ㨬ᣂ㔐㨭ߦ㧘ࡇࠬ࠻ࡦࠍ㨬㒰㔐ེ㨭ߦ⷗┙ߡࠆߣ࿶❗ᓟߩᇦ⾰ߪ㨬᛼ߒ࿕߼ࠄࠇߚ㔐㨭ߦ ৻ᣇ㧘⾰㊂ߣㆇേ㊂ߩ଻ሽೣࠍ⴫ߔᑼ(1)ߣ(3)߆ࠄ u1 ࠍ
P1  P0
V1  V 0

 U0U2         (6)ߚߛߒ㧘V ߪ V { 1 U ߢቯ⟵ߐࠇࠆᲧኈⓍߢ޽ࠆ㧚੹㧘 P, Vᐔ㕙ߢ P1 , V1 ࠍᄌᢙߣ⠨߃ࠆߣ㧘ᑼ(6)ߪ௑߈߇⽶ߩ⋥✢ߩᣇ⒟ᑼࠍ⴫ߔ㧚ߎߩ⋥✢ߪ Rayleigh ✢ߣ๭߫ࠇ㧘⾰㊂ߣㆇ
േ㊂ߩ଻ሽ߇ᚑࠅ┙ߟᵹࠇߩᄌൻߪߎߩ⋥✢਄ࠍ⒖േߔࠆ㧚ᑼ(6)߆ࠄ Rayleigh ✢ߪ⽶ߩ௑߈ࠍᜬߟߎߣߦᵈᗧߔࠆ㧚⋧ᒰߒ㧘ⴣ᠄ᵄ㕙ߪ㔐߇ᰴ╙ߦ᛼ߒ࿕߼ࠄࠇߡ޿ߊᦨ೨㕙3.2 Hugoniot ߩ⁁ᘒᣇ⒟ᑼ

ࠍᗧ๧ߔࠆߎߣߦߥࠆ㧚ߘߩߚ߼㧘ߎߩࡕ࠺࡞ߪ㧘ߒ߫ߒ೨㗄ߢ␜ߒߚᑼ(1)㨪(6)ߢߪ㧘2 ┨ߢㅀߴߚၮ␆ᑼߦ⃻ࠇࠆᄌᢙߦᲧߴߡ㧘ⴣ᠄ᵄ㕙ߩ⒖േㅦᐲߢ޽ࠆ૏⋧ㅦᐲ U ߫㧘“snow plow” 㔐ហ߈ ࡕ࠺࡞ߣ๭߫ࠇࠆ㧚৻ᣇ㧘ㆇേ㊂ᣇ⒟ᑼ ㆇേ㊂଻ሽೣ ࠍᤨ㑆Ⓧಽߒߚᑼ߆

߇Ⴧ߃ߡ߅ࠅ㧘‛ℂ㊂ࠍ᳿ቯߔࠆߚ߼ߦߪᣇ⒟ᑼߩᢙ߇⿷

ࠄ㧘޽ࠆᤨ㑆ߩ㑆ߦ‛૕ߦ૞↪ߒߚജⓍߪ㧘૞↪೨ᓟߩ‛ࠅߥ޿㧚2 ▵ߢㅀߴߚⴣ᠄ᵄ㕙ࠍ઒ቯߒߥ޿ᣇ⒟ᑼ♽ߢߪ㧘
ㆇേ㊂଻ሽᑼ߆ࠄᵄേᣇ⒟ᑼ߇ዉ಴ߢ߈㧘ߘߩ࿕᦭୯ߣߒ
ߡ㖸ㅦ߇⹏ଔߢ߈ࠆ㧚ߎߩ૏⋧ㅦᐲߢ޽ࠆ㖸ㅦ߇ᇦ⾰ਛߩu1ᡓੂߩવ᠞ࠍᓞㅦߔࠆ㧚ߘࠇߦኻߒߡ㧘એ਄ߩᣇ⒟ᑼ♽ߢ

P0, 0, E0, u0(u0 = 0)
u tu1

ⴣ᠄೨

U tu1

P1,1, E1ⴣ᠄ᓟ೰ო䊏䉴䊃䊮䈮䉋䉎Ꮐ䈎䉌ฝ䈻䈱ⴣ᠄
ⴣ
᠄
ᵄ
㕙

U

ⴣ᠄೨
P0, 0, E0, u0(u0 = 0)࿑ 㪈㩷 ೰䈭䊏䉴䊃䊮䈮䉋䈦䈩㚟േ䈘䉏䈢ⴣ᠄ᵄ㕙䈱᭽ሶߪ㧘ᣂߚߥ૏⋧ㅦᐲࠍ઒ቯߔࠆߎߣߦࠃࠅ㧘ߘߩⴣ᠄ᵄ㕙೨ᓟߢ‛ℂ㊂ߩਇㅪ⛯ᕈࠍ⴫⃻ߒߚ⸶ߢ޽ࠆ㧚ⴣ᠄ᵄ⎇ⓥ
ߩಽ㊁ߢߪ㧘ߎߩ૏⋧ㅦᐲ U ࠍⴣ᠄ᵄㅦᐲߣ๭ࠎߢㅢᏱU S ߢ⴫ߒ㧘ᵹㅦ u 1 ࠍ☸ሶㅦᐲߣ๭ࠎߢ u p ߢ⴫ߔ㧚ⴣ᠄࿶❗⎇ⓥߪᩭ౓ེ㐿⊒ࠍ⋡⊛ߣߒߡ 1940 ᐕઍߦ☨࿖ߢᆎ߹ࠅ㧘╙ 2 ᰴᄢᚢᓟߪᒰᤨߩ࠰ࡆࠛ࠻߇ടࠊߞߡ㧘1950 ᐕઍߦᧄᩰൻߔࠆߎߣߦࠃߞߡ㧘ℂ⺰⎇ⓥߣߣ߽ߦ⤘ᄢߥᢙߩ⹜㛎߇ታᣉߐࠇߚ㧚ߘߩ⚿ᨐߣߒߡ㧘ᢙ⊖ߩ‛⾰ߦኻߒߡ U S ߣ u p ߩ㑐ଥ߇᳞߼ࠄࠇ㧘ߘߩ⿠Ḯߩᓸᅱߐߦ

એ਄ߩࠃ߁ߥቯᑼൻߦࠃࠅ㧘ⴣ᠄ᵄߩવ᠞ㆊ⒟ߣ࿶ജ
⹏ଔࠍਛᔃߣߒߚ࿕૕ߣᶧ૕‛⾰ߩⴣ᠄․ᕈࠍᮨᡆߔࠆ

߽߆߆ࠊࠄߕߘߩᄙߊ߇౏㐿ߐࠇߡ߈ߚ㧚ታ㛎ᣇᴺߣߒߡߎߣ߇น⢻ߦߥࠆ㧚࿶ജ୯ߣߒߡߪ㧘100 GPa ⒟ᐲ߹ߢㆡ

ߪ㧘῜⮎ࠍ૶߁ᣇᴺ㧘2 Ბᑼシࠟࠬ㌂ߥߤ⿥㜞ㅦടㅦⵝ⟎↪น⢻ߢ޽ࠆ㧚ߚߛߒ㧘⋧ォ⒖߿⋧ᄌൻ߇↢ߓࠆࠃ߁ߥ႐

ࠍ૶߁ᣇᴺ㧘ᩭታ㛎ߥߤ߇↪޿ࠄࠇߡ߈ߚ㧚ઍ⴫⊛ߥ࠺࡯วߪㆡ↪㒢⇇ߣߥࠆ㧚࿑䋲(a)ߦ㧘2024Al ว㊄ߦኻߒߡ㧘Los࠲ߣߒߡߪ㧘Los Alamos ࿖┙⎇ⓥᚲ 1)㧘Lawrence Livermore࿖┙⎇ⓥᚲ 2)㧘☨࿖ⓨァ⎇ⓥᚲ 3)㧘ࡠࠪࠕ ࡠࠪࠕᩭ࠮ࡦAlamos ࿖┙⎇ⓥᚲߢขᓧߐࠇߚ U S  u p 㑐ଥߩታ㛎୯ 1)ࠍ
ࡊࡠ࠶࠻ߒߚࠣ࡜ࡈࠍ␜ߔ㧚☸ሶㅦᐲߩჇടߣߣ߽ߦⴣ᠄࠲࡯࡮ోࡠࠪࠕታ㛎‛ℂቇ⎇ⓥᚲ: RFNC-VNIIEF 4)㨬޿ߕࠇᵄㅦᐲ߇Ⴧടߔࠆߎߣߦᵈᗧߔࠆ㧚ߩ႐ว߽⃻⚵❱ฬ㨭ߥߤߩᯏ㑐߆ࠄ౏㐿ߐࠇߚ߽ߩ߇޽ࠆ㧚࿑䋲(b)ߪ㧘Hugoniot ࿶ജߣᲧኈⓍߩ㑐ଥ Hugoniot ࿶❗ᦛ✢ ࠍ㧘╬ࠛࡦ࠻ࡠࡇ࡯߅ࠃ߮╬᷷ᦛ✢ߣหߓ P , V ᐔ㕙ߦឬ޿ߚᮨᑼ࿑ߢ޽ࠆ߇㧘╬᷷ㆊ⒟㧘╬ࠛࡦ࠻ࡠࡇ࡯ㆊ⒟ߘߩᚑᨐߦࠃࠆߣ㧘߶ߣࠎߤߩ࿕૕ߣᶧ૕‛⾰ߦኻߒߡ㧘USc0  su p              ( 7 )ࠃࠅ߽ⴣ᠄࿶❗ㆊ⒟ߩᣇ߇ᄢ߈ߥ࿶ജࠍ↢ߓࠆߎߣࠍ␜ߒߥࠆ✢ဳ㑐ଥ߇߆ߥࠅ⦟޿♖ᐲߢᚑࠅ┙ߟ㧚ߚߛߒ㧘 c0 ߪߡ޿ࠆ㧚࿑ਛἯ⦡ߢႣࠅߟ߱ߒߚ㕙Ⓧ߇⚐☴ߦⴣ᠄࿶❗ߦࡃ࡞ࠢ㖸ㅦߣ๭߫ࠇ㧘㕒⊛ߥ╬ࠛࡦ࠻ࡠࡇ࡯ㆊ⒟ߩ૕Ⓧᒢࠃࠆౝㇱࠛࡀ࡞ࠡ࡯਄᣹ಽࠍ⴫ߒߡ޿ࠆ㧚ߎߩ࿑ߢᵈᗧߔ

K U ߥࠆ㑐ଥ߇޽ࠆߩߦ

ߴ߈ߪ㧘╬᷷㧘╬ࠛࡦ࠻ࡠࡇ࡯ߩਔㆊ⒟ߩ႐วߦߪ㧘࿶❗㨯ኻߒߡ㧘 s ߪήᰴరߩଥᢙߢ޽ࠆ㧚ߣߎࠈߢ㧘⾰㊂଻ሽೣߩᑼ(1)ࠍ U S , u p , V ࠍ↪޿ߡᄌᒻ⤘ᒛᤨߩ⁁ᘒ㊂ߪߘࠇߙࠇߩ✢਄ࠍㅪ⛯⊛ߦᄌൻߔࠆߩߦᕈ₸ K

V dP dV S ߣ c0ߔࠆߣ㧘 V1 V01  u p U S ߣߥࠅ㧘ߐࠄߦ㧘 K { 1  V1 V0 ߣ߅ߊߣ㧘ᑼ(7)߆ࠄ u pc0K 1  sK , U S

c0 1  sK ߣ޿߁㑐ଥ߇ᓧࠄࠇࠆ㧚 P00 ߩ઒ቯߩਅ㧘ߎࠇࠄੑߟߩ㑐ଥᑼኻߒߡ㧘ⴣ᠄࿶❗ㆊ⒟ߩ႐วߦߪ㧘0ψ1 ߩᄌൻߪ㧘޽ߊ߹ߢ߽ Rayleigh ✢਄ࠍᄌൻߒ㧘Hugoniot ࿶❗ᦛ✢਄ࠍᄌൻߔࠆߩߢߪߥ޿ߣ޿߁ߎߣߢ޽ࠆ㧚ߔߥࠊߜ㧘Hugoniot ࿶❗
ᦛ✢ߪ޽ࠆ‛⾰߇ขࠅᓧࠆ࿶❗⁁ᘒߩ゠〔ߦㆊ߉ߥ޿㧚឵⸒ߔࠇ߫㧘0ψ1 ߩᄌൻߩ࿶❗ㆊ⒟ߢߪ㧘Rayleigh ✢਄ߩ 0

ࠍㆇേ㊂଻ሽೣߩᑼ(3)ߦઍ౉ߔࠆߎߣߦࠃࠅ㧘ᑼ(7)ߦ␜ߒ

ߣ 1 ߩ㑆ߩછᗧߩὐ A ߩ⁁ᘒߦߪߥࠅᓧࠆ߇㧘Hugoniotߚ✢ဳߩ Hugoniot 㑐ଥߦၮߠ޿ߚ࿶ജ⹏ଔᑼ(8)ࠍᓧࠆ㧚ߎߩ࿶ജࠍ Hugoniot ߩⴣ᠄࿶ജ PH ߣ๭߮㧘ᑼ(8)ࠍⴣ᠄

࿶❗ᦛ✢਄ߩ⁁ᘒࠍߣࠆߎߣߪߥ޿㧚ߚߛߒ㧘޿ߞߚࠎ㧘1ᵄߩ⁁ᘒᣇ⒟ᑼ EOS: equation of state ߣ๭߱㧚ജ✭๺ߔࠆ႐วߦߪ㧘⁁ᘒ 1 ࠍㅢࠆ╬ࠛࡦ࠻ࡠࡇ࡯ᦛ✢ߦ

PHU 0c02K  sK2            (8)ߩ⁁ᘒ߹ߢⴣ᠄࿶❗ߐࠇߚᓟߦᏗ⭯ ⤘ᒛ ᵄࠍ↢ߓߡ࿶ᴪߞߡ࿶ജᷫ⴮߇↢ߓࠆ㧚ߥ߅㧘ᑼ(8)ߪኒᐲߦߩߺଐሽߔࠆ⁁ᘒᣇ⒟ᑼߢ޽ࠆ߇㧘* { V wP wE V ߢቯ⟵ߐࠇࠆ Grüneisen ቯᢙࠍ↪޿ߡ㧘ౝㇱࠛࡀ࡞ࠡ࡯ଐሽᕈࠍᜬߞߚ⁁ᘒᣇ⒟ᑼߦ᜛ᒛߔࠆߎߣ߇ߢ ߈ ࠆ 㧚 ߎ ߩ ⁁ ᘒ ᣇ ⒟ ᑼ ߪ 㧘 Mie-Grüneisen ဳ ߩ ⴣ ᠄Hugoniot ߩ⁁ᘒᣇ⒟ᑼߣ๭߫ࠇ㧘ⴣ᠄ಽ㊁ߢᐢߊㆡ↪ߐࠇߡ޿ࠆ߇㧘ߎߎߢߪ⚕ᢙߩ೙⚂ߩߚ߼⹦⚦ߥ⺑᣿ߪഀᗲߔࠆ㧚
3.3 ജቇ⊛ࠗࡦࡇ࡯࠳ࡦࠬ
એ਄ߦ߅޿ߡߪ㧘‛⾰ߩᒝᐲߦ⌕⋡ߒߡ㧘ᵹ૕ ᶧ⋧ߣ᳇(a)㩷2024 Al ߦኻߔࠆ Hugoniot 㑐ଥ 1㧕

⋧ ߣ࿕૕ ࿕⋧ ߣ޿߁ಽ㘃ᴺ߇᦭ലߢ޽ࠆߎߣࠍㅀߴߚ㧚৻ᣇ㧘ኒᐲ㧘㖸ㅦ߇㧘ߘࠇߙࠇ㧘 U , c ߩㅪ⛯૕߇㧘ೋㅦᐲ
uimp ߢ೰ო ߦⴣ⓭ ߔࠆ㓙 ߦⴣ⓭ 㕙ߢ⊒ ↢ߔࠆ ⴣ⓭࿶ ജPimp ߪ㧘ㆇേ㊂଻ሽೣ߆ࠄᑼ(9)ߣߥࠆ㧚Pimp

U cuimp(9)ߘࠇߦኻߒߡ㧘ⴣ᠄ᵄ߇⊒↢ߔࠆ໧㗴ߢߪ㧘ᑼ(3)ߢ P0
ߣߒߡ㧘 Pimp

0

UU S uimp ߣߥࠆ㧚ߎࠇࠄߩᑼߩฝㄝߩㅪ⛯૕ߩ ‛ ᕈ ߦ ଐ ሽ ߔ ࠆ ㊂ 㧘 U c , UU S ࠍ 㧘 ߘ ࠇ ߙ ࠇ 㧘 㖸 㗀ࠗࡦࡇ࡯࠳ࡦࠬ*2 acoustic impedance 㧘ⴣ᠄ࠗࡦࡇ࡯࠳ࡦ
ࠬ shock impedance ߣ๭߮㧘࿶ജߦኻߔࠆㅪ⛯૕ߩᗵᐲࠍ⴫ߔ‛ℂ㊂ ‛ᕈ୯ ߢ޽ࠆߣ⷗ߥߒᓧࠆ㧚೨ㅀߒߚࠃ߁ߦ㧘*2 㩷 (b)㩷P-V ࿶❗ᦛ✢ߩᲧセ࿑䋲 ✢ဳ Hugoniot 㑐ଥ䈫 Hugoniot ࿶❗ᦛ✢㩷ࠗࡦࡇ࡯࠳ࡦࠬߪ㧘㔚⏛᳇ቇߦ߅޿ߡߪ੤ᵹ࿁〝╬ߩᛶ᛫ߦ⋧ᒰߔࠆ‛ℂ㊂ߢ޽ࠆ㧚ߘߩࠕ࠽ࡠࠫ࡯߆ࠄജቇಽ㊁ߢ߽㧘ᧄ᧪ߪᵄߩㅘㆊߣ෻኿ࠍᡰ㈩ߔࠆ‛ℂ㊂ߣߒߡቯ⟵ߐࠇ㧘ߎࠇࠄࠍ✚⒓ߒߡജቇ⊛ࠗࡦࡇ࡯࠳ࡦࠬߣ๭߫ࠇࠆ㧚S = d /ddS /d < 0Ყ଀㒢ᐲC(ᔕജ ( )ᔕജ ( )

㪅a㪅a < 㪅b < 㪅c

㪅c㪅b

¥S

S = d /d = const.

࿑䋳㩷 ࿕૕䈱ᔕജ㧙䈵䈝䉂㑐ଥ㩷࿑䋴㩷 ࿕૕䈱ᔕജ䋭૕Ⓧ㑐ଥ䈫࿕૕ਛ䉕વ᠞䈜䉎ᵄ䈱᭴ㅧⴣ᠄໧㗴ߦ߅޿ߡߪ㧘࿶ജߪᦨ߽㊀ⷐߥ‛ℂ㊂ߢ޽ࠅ㧘ߎ

㐳䈘: 100 mm㪃㩷⋥ᓘ: 40 mmߩⷰὐ߆ࠄߪ㧘⹏ଔ‛⾰ߩኒᐲߣ㖸ㅦ㧘߭޿ߡߪࠗࡦࡇ࡯࠳ࡦࠬ߇ᡰ㈩࿃ሶߢ޽ࠆߣ޿߁ߎߣߦߥࠆ㧚ߎߩߚ߼㧘ኒ*3ᐲߣ㖸ㅦ߇Ყセ⊛ㄭ޿୯ ࠍ߽ߞߡ޿ࠆ࿕⋧ߣᶧ⋧ࠍ߹ߣ

2024-T351Al
S: ᒢ႟ᕈ૕
F: ᵹ૕

S: 3 S: 2 S: 1
F: 7 F: 6 F: 6

S: 4
F: 8100 m/s೰ო߼ߡಝ❗⋧ condensed phase ߣ⒓ߒ㧘᳇⋧ߣ඙೎ߔࠆ㧚ⴣ࿁ォኻ⒓ゲ᠄໧㗴ߦ߅޿ߡߪ㧘ᵹ૕ߣ࿕૕ߩ඙೎ߦ߽Ⴧߒߡ㧘ಝ❗⋧࿑䋵㩷 Taylor ⹜㛎ߩ⸃ᨆࡕ࠺࡞ߣᤨೞᱧ಴ജ૏⟎৻ⷩߣ᳇⋧ߣ޿߁඙೎߇㊀ⷐߢ޽ࠆߎߣߦᵈᗧߔࠆ㧚
4. ࿕૕ߩⴣ᠄ᔕ╵ߊߥߊ࿕૕ਛߦᒝ޿ⴣ᠄ᵄ߇↢ߓࠆߎߣࠍ⺑᣿ߢ߈ߥ޿㧚

4.1 ࿕૕ߩᒢ႟ᕈ᜼േ߹ߚ㧘߭ߕߺ߇ᄢ߈ߊߥࠆߣ࿕૕߇⎕უߒ㧘ߖࠎᢿᚑಽ߿

ߎࠇ߹ߢߪ㧘ㅪ⛯૕ߩ߁ߜߢ߽ಝ❗૕ߣ޿߁ⷰὐ߆ࠄⴣ஍Ꮕᚑಽࠍ༚ᄬߔࠆߚ߼㧘߭ߕߺㅦᐲଐሽᕈߦࠃࠆ૏⋧ㅦ

᠄ᵄߩℂ⺰⊛⢛᥊ߦߟ޿ߡ᭎ⷰߒߚ㧚ߒ߆ߒ㧘2 ┨ߦ߅޿ᐲߩჇᄢߦߪ㒢⇇߇޽ࠆߎߣ߇ࠊ߆ࠆ㧚ߡ⸅ࠇߚࠃ߁ߦ㧘ᶧ૕ߪ╬ᣇ⊛ߥ㕒᳓࿶ᚑಽߩߺࠍ᦭ߔࠆ

ߎߩࠃ߁ߦ㧘࿕૕ߩⴣ᠄ᔕ╵ߪᒢ႟ᕈ․ᕈߛߌߢߪ⺑᣿ߩߦኻߒߡ㧘࿕૕ߩ႐วߦߪߖࠎᢿᚑಽ㨯஍Ꮕᚑಽ߇ሽ࿷ߔߢ߈ߕ㧘࿕૕ਛߩోᔕജࠍ㕒᳓࿶ᚑಽߣ஍Ꮕᔕജᚑಽߩ๺ࠆ㧚ߘߩߚ߼㧘ᣇะߏߣߦ⇣ߥߞߚജߩᚑಽࠍ⴫⃻ߔࠆߎߣߒߡቯ⟵ߒ㧘Hugoniot ߩ⁁ᘒᣇ⒟ᑼߣ᭴ᚑೣߩਔᣇࠍㆡߣߩߢ߈ࠆ࠹ࡦ࠰࡞ߦࠃߞߡ⸥ㅀߔࠆᔅⷐ߇޽ࠆ㧚એਅߢ↪ߔࠆߎߣߦࠃߞߡߪߓ߼ߡᮨᡆߔࠆߎߣ߇ߢ߈ࠆ㧚ߪ㧘࿕૕‛⾰ߦ․᦭ߥⴣ᠄ᔕ╵ߦߟ޿ߡㅀߴࠆ߽ߩߣߔࠆ㧚ࠆߣ㧘࿑䋳ߦ␜ߔࠃ߁ߥ 1 ゲߩ⌀ᔕജߣ⌀߭ߕߺߩ㑐ଥ߇࿑䋴ߩᏀ஥ߦ㧘࿕૕ߩᒢ႟ᕈ․ᕈࠍ㧘1 ゲߩᔕജ㧙߭ߕߺ㑐ଥߢߪߥߊ㧘⁁ᘒᣇ⒟ᑼߣหߓ P , V ᐔ㕙ߦ Hugoniotߩ࿶❗ᦛ✢ߣߣ߽ߦឬߊ㧚ห࿑ߦ␜ߒߚࠃ߁ߦ㧘࿕૕ߦⴣ᳞߼ࠄࠇࠆ㧚ߔߥࠊߜ㧘Ყ଀㒢ᐲߦ⥋ࠆ߹ߢߪᔕജ߇ Young᠄࿶❗ࠍട߃ࠆߣ㧘Hugoniot ᒢᕈ㒢⇇ HEL ߣ๭߫ࠇࠆᔕ

₸ࠍᲧ଀ቯᢙߣߒߡ߭ߕߺߦᲧ଀ߒ Hooke ߩᴺೣ 㧘߭ߕജ߹ߢߪᒢᕈ᜼േࠍ␜ߒ㧘ߘߩᓟ႟ᕈᄌᒻࠍ↢ߓࠆ㧚ߎߩߺߩჇᄢߣߣ߽ߦᔕജߩჇട㊂߇ᷫዋߔࠆ㧘޿ࠊࠁࠆടᎿ⎬ൻࠍ␜ߔ㧚࿕૕ߩ᧚ᢱ᜼േ߇㧘ߎߩࠃ߁ߥᔕജ㧙߭ߕߺ࿶❗ᦛ✢ߪ㧘࿑䋲 (b) ߩ࿶❗ᦛ✢߇ᒢᕈಽߛߌ਄ߦࠪࡈ࠻ߒߚ߽ߩߦ⋧ᒰߔࠆ㧚࿑䋴ߩฝ஥ߩ࿑ߪ㧘V E ,㩷 V P ,㩷 V + ,㑐ଥߩߺߦࠃࠆߣߔࠇ߫㧘࿕૕ਛߦⴣ᠄ᵄ߇⊒↢ߔࠆߎߣߣ޿߁ 3 ⒳㘃ߩᔕജߢ࿕૕ࠍ࿶❗ߒߚ㓙ߦ㧘࿕૕ਛࠍવ᠞๟⍮ߩࠃ߁ߦ㧘ᄙߊߩ࿕૕ߦኻߒߡᒁᒛࠅ⹜㛎ࠍታᣉߔߪߥ޿㧚࿑ਛߦ␜ߔࠃ߁ߦ㧘ᇦ⾰ਛࠍવ᠞ߔࠆ૏⋧ㅦᐲߪߔࠆᵄߩ᭽ሶࠍᮨᑼ⊛ߦ␜ߒߚ߽ߩߢ޽ࠆ㧚HEL ࠃࠅ߽ዊC Hߐߥᔕജࠍട߃ߚ႐วߦߪ㧘ᕆፋߥᔕജߩ┙ߜ਄߇ࠅߩᓟ㧘dV d HU ߢ⴫ߐࠇࠆ߇㧘ടᎿ⎬ൻࠍ␜ߔᔕജ㧙߭ߕߺ㑐ଥ߇਄ߦಲߥᒻࠍ␜ߔ㒢ࠅ㧘ᒢᕈၞߢߪ૏⋧ㅦᐲߪ৻ቯ㧘႟ᕈၞߢߪ߭ߕߺߩჇᄢߣߣ߽ߦ૏⋧ㅦᐲߪᷫዋߔࠆߎߣࠍᗧ๧ߒߡ߅ࠅ㧘⽶⩄ߐࠇࠆജߩჇᄢߣߣ߽ߦ૏⋧ㅦᐲ߇Ⴧᄢߔࠆߎߣߪߥߊ࿶❗ᵄࠍᒻᚑߒߥ޿ߚ߼ߢ޽ࠆ㧚ߚߛߒ㧘ห࿑ߦ␜ߔࠃ߁ߦ㧘ᄙߊߩ‛⾰ߢ߭ߕߺㅦᐲߩჇᄢߣߣ߽ߦ㒠ફᔕജ߇Ⴧᄢߔࠆߎߣ߇⍮ࠄࠇߡ߅ࠅ㧘ߘߩലᨐࠍ⠨ᘦߦ౉ࠇࠆߣ૏⋧ㅦᐲߩჇᄢߩน⢻ᕈ߇⠨߃ࠄࠇࠆ㧚ߒ߆ߒߥ߇ࠄ㧘ታ㓙ߦߪ㧘ߘߩലᨐߪߘࠇ߶ߤᄢ߈࿕૕ߩᒢᕈ․ᕈߦᔕߓߚ޽ࠆ৻ቯᤨ㑆㧘౉ജߒߚᔕജ୯ࠍ଻ᜬߒ㧘ߘߩᓟ┙ߜ਄߇ࠅᤨࠃࠅ߽✭߿߆ߦᷫ⴮ߔࠆ 1 ᵄ᭴ㅧࠍ␜ߔ㧚ߘࠇߦኻߒߡ㧘HEL ࠍ⿥߃ࠆࠃ߁ߥᔕജ V P ߢⴣ᠄࿶❗ࠍട߃ߚ႐วߦߪ㧘 V E ߩ႐วߣหߓㅦᐲߢવ᠞ߔࠆᵄߦࠃࠆᕆፋߥᔕജ਄᣹ᓟ㧘޿ߞߚࠎ✭๺ࠍ↢ߓ㧘ౣ߮Ყセ⊛ߥߛࠄ߆ߥᔕജ਄᣹ࠍ␜ߒ㧘޽ࠆᤨ㑆ߘߩࡇ࡯ࠢ
ᔕജ୯ࠍ଻ᜬߒߚᓟߦᷫ⴮ߔࠆ 2 ᵄ᭴ㅧࠍ␜ߔ㧚1 ᵄ⋡ࠍవⴕᒢᕈᵄ Elastic Precursor ߣ๭ࠎߢ޿ࠆ㧚ߐࠄߦᄢ߈ߥ
V H ߢⴣ᠄࿶❗ࠍട߃ࠆߣ㧘ᒢᕈߩᤨߣ㘃ૃߒߚ 1 ᵄ᭴ㅧߩࠃࠅᄢ߈ߥᵄ߇વ᠞ߔࠆ㧚HEL ߪ㧘‛⾰ߦ࿕᦭ߥ୯ߢߪߥߊ㧘⹜㛎ᣇᴺߥߤߦଐ*3 㩷 ᶧ૕ߩ㖸㗀ࠗࡦࡇ࡯࠳ࡦࠬߪ࿕૕ߦᲧߴߡ 1 ᩴ⒟ᐲዊߐ޿ߦ
ㆊ߉ߥ޿ߩߦኻߒ᳇૕ߩ႐วߦߪ 5 ᩴ⒟ᐲ߽ዊߐ޿㧚ሽߒߡᄌൻߔࠆߎߣ߇⍮ࠄࠇߡ޿ࠆ㧚߹ߚ㧘㊄ዻߩ႐วߦ

ߪ 0.5㨪1 GPa ߩ⒟ᐲߢ㧘㒠ફᔕജߩࠝ࡯࠳ߣหߓߢ޽ࠆ㧚

ᣇ⒟ᑼߩ᧚ᢱ࠺࡯࠲৻ⷩࠍ㧘ߘࠇߙࠇ㧘⴫䋱㧘⴫䋲ߦ␜ߔ㧚ߘࠇߦኻߒߡ㧘࠮࡜ࡒ࠶ࠢࠬߥߤߩ႐วߦߪᢙච GPa ߦ߽࿑䋵ߦ␜ߒߚࠃ߁ߦ㧘⹜㛎૕ࠍ 100×20 ߩ Lagrange ⷐ⚛

㆐ߔࠆ႐ว߇޽ࠆ㧚޽ࠆ઒ቯߩਅߦ㒠ફὐᔕജ V y ࠍ↪޿ߦࠃࠆ 2 ᰴరゲኻ⒓ࡕ࠺࡞ߢᮨᡆߒߚ㧚࿑ਛߦ␜ߒߚ 1㨪8

ߡ㧘V HEL 1  Q 1  Q V y ߣ⹏ଔߐࠇࠆ㧚߹ߚ㧘࿑䋴ߩਔࠣ࡜ࡈߪ㧘ⴣ᠄᳇ൻߩࠃ߁ߥ⋧ᄌൻࠍ↢ߓࠆ႐วߛߌߢߪߩ૏⟎ߪ㧘એਅߢ␜ߔ㨬ᒢ႟ᕈࡕ࠺࡞ S 㨭ߣ㨬ᵹ૕ࡕ࠺࡞ߥߊ㧘หᒻォ⒖ߩࠃ߁ߥ࿕⋧㑆ߩォ⒖ࠍ↢ߓࠆ႐วߦ߽ࠃࠅⶄ㔀ߥᒻ⁁ࠍ␜ߔߎߣߦᵈᗧߔࠆ㧚F 㨭ߩᢙ୯⸃ᨆߦࠃࠆᤨೞᱧߩ಴ജὐࠍᗧ๧ߒߡ޿ࠆ㧚⹜㛎૕ࠍᵹ૕ߣ⷗ߥߒߚߣ߈ߦⴣ⓭㕙ߢ⊒↢ߔࠆ࿶ജߪ㧘ᑼ (9) ߦ㕒⊛⻉㊂㧦 U0u  g/m 3 㧘 c05328 m/s ߣ

4.2 Taylor ⴣ⓭⹜㛎ߩᢙ୯⸃ᨆ

u imp 100 m/s 㧘ࠍઍ౉ߒߡ Pimp 1.484 GPa ߣߥࠆ㧚ߎߩ࿕૕‛⾰ߩⴣ᠄⹜㛎ᴺߣߒߡ㧘1940 ᐕઍߦ⧷࿖ߩ G.I.

୯ߪ࿑䋶(a)ߩᵹ૕ࠍ઒ቯߒߚࠤ࡯ࠬߩ㧘ⴣ⓭㕙ߦធߒߚਛ

Taylor ߦࠃߞߡឭ໒ߐࠇ㧘⃻࿷߽ᮡḰ⊛ߥ⹜㛎ᴺߣߒߡ↪

ᔃゲㄭறߩ಴ജὐ #5 ߦ߅ߌࠆ࿶ജጁᱧߩ⚂ 1㨪3 Ps ߩ޿ࠄࠇߡ޿ࠆ Taylor ⴣ⓭⹜㛎ᴺ Taylor Cylinder Test 7)߇޽㑆ᜬ⛯ߔࠆ࿶ജߣ߶߷৻⥌ߔࠆ߇㧘⹜▚୯ߩᣇ߇⧯ᐓૐ

ࠆ㧚౞ᩇ⁁ߩ࿕૕⹜ᢱߩᐩ㕙ࠍలಽߦ೰ߥოߦⴣ⓭ߐߖࠆ߼ߢ޽ࠆ㧚ᒢ႟ᕈ૕ࠤ࡯ࠬߩⴣ⓭㕙ਛᔃߩ಴ജὐߢ޽ࠆ#1න⚐ߥ⹜㛎ߢ޽ࠆ㧚ߒ߆ߒߥ߇ࠄ㧘ᧄⓂߢߪలಽߦ⼏⺰ࠍߦ߅ߌࠆ 1㨪3 Ps ߩ㑆ߩᜬ⛯࿶ജߪ㧘ᵹ૕ࠤ࡯ࠬߦᲧߴ⚂ዧߊߖߥ޿߶ߤߦ㊀ⷐߥᖱႎࠍᓧࠆߎߣ߇ߢ߈ࠆ㧚⚕ᢙߩ

0.1 GPa ૐߊ⹏ଔߐࠇߡ޿ࠆ㧚ⴣ⓭ᣇะ x ᣇะ ߩု⋥ᔕജᚑಽߢ޽ࠆ V xx ߩᤨೞᱧࠍ࿑䋶(b)ߦ␜ߔ㧚ᒢ႟ᕈ૕ߩ#1 ߦ㑐ଥ਄㧘⹦⚦ߦߟ޿ߡߪઁߩᯏળߦ⼑ࠆ߽ߩߣߔࠆ㧚4.2.1 ⴣ⓭ㅦᐲ 100 m/s ߩ Taylor ⹜㛎߅ߌࠆᔕജᚑಽߩ⛘ኻ୯ߪ㧘వ⒟ߩ࿶ജ୯ࠃࠅ߽ᄢ߈ߊ㧘࿑䋵ߦ␜ߔࠃ߁ߥ㧘⋥ᓘ 40 mm㧘㐳ߐ 100 mm ߩ 2024-⚂ 1.65 GPa ߢ޽ࠆ㧚৻ᣇ㧘ᵹ૕ࠤ࡯ࠬߩᔕജ୯ߩ⛘ኻ୯ߪ

T351Al ⵾ߩ౞ᩇࠍ೰ოߦⴣ⓭ߐߖࠆ໧㗴ߩᢙ୯ታ㛎ࠍᗐ

వ⒟ߩ࿶ജ୯ߣ৻⥌ߒߡ޿ࠆ㧚ߎࠇߪ㧘ᒢ႟ᕈ૕ߩ႐วߦ

ቯߔࠆ㧚⸘▚ߪ 2 ࠤ࡯ࠬታᣉߒ㧘᧚ᢱᒝᐲࠍ⠨ᘦߔࠆࡕ࠺ߪ㧘ⴣ⓭ᣇะߩ஍Ꮕᔕജᚑಽ߇ථ⿧ߒߘߩઁߩᣇะߩᔕജ

࡞ߣ⠨ᘦߒߥ޿ ᵹ૕⊛ ࡕ࠺࡞ߩ 2 ⒳㘃ߢ㧘᧚ᢱᒝᐲࠍ⠨ᚑಽߪߘࠇߦᲧߴߡዊߐߊߥࠆߚ߼㧘ᐔဋ୯ߣߒߡߩ࿶ജ

ᘦߔࠆ႐วߩ᭴ᚑೣߪ Johnson-Cook ߩࡕ࠺࡞ 5)ࠍㆡ↪ߒߚ㧚ߪᵹ૕ࠍ઒ቯߒߚࠤ࡯ࠬࠃࠅ߽ૐߊߥߞߚߚ߼ߢ޽ࠆ㧚ߘߎߩ᭴ᚑೣߢߪ㧘ടᎿ⎬ൻ㧘߭ߕߺㅦᐲଐሽᕈ㧘ᾲエൻ߇ࠇߦኻߒߡ㧘ᵹ૕ࠍ઒ቯߒߚࠤ࡯ࠬߢߪ㧘ర᧪㧘஍Ꮕᚑಽ⠨ᘦߐࠇ㧘ᑼ(10)ߦࠃߞߡ㒠ફᔕജ߇⸘▚ߐࠇࠆ㧚ࠍᜬߚߕ╬ᣇ⊛ߢ޽ࠆߚ߼㧘ゲᣇะߩု⋥ᔕജᚑಽߛߌߢYA  BH

n1  ClnH

*1 Tm     (10)ߪߥߊߔߴߡߩᣇะߩု⋥ᔕജᚑಽ߇࿶ജߣ৻⥌ߔࠆ㧚ਔࠣ࡜ࡈߢ㧘ⴣ⓭㕙߆ࠄ㔌ࠇࠆ߶ߤ㧘ᒢ႟ᕈ૕ߩᣇ߇ᵹߚߛߒ㧘 T{ T  TroomTmelt  Troom 㧘 T ߪ᷷ᐲߢ㧘ਅᷝ૕ࠤ࡯ࠬࠃࠅ߽ᡓੂ߇ᣧߊ೔㆐ߒߡ޿ࠆ㧚ᒢ႟ᕈ૕ਛࠍⴣሼߪቶ᷷ߣⲢὐࠍᗧ๧ߔࠆ ߪ⋧ห᷷ᐲ㧘 H * ߪᱜⷙൻߐࠇ᠄ᵄએᄖߢᦨ߽ᣧߊવ᠞ߔࠆᡓੂߢ޽ࠆ❑ᵄߩવ᠞ㅦᐲ

ߚ߭ߕߺㅦᐲߢ޽ࠆ㧚 A , B ߣ n ߪ㕒⊛ടᎿ⎬ൻ㧘C ߪ߭⹜㛎ߦࠃߞߡ᳿ቯߐࠇࠆ㧚৻ᣇ㧘⁁ᘒᣇ⒟ᑼߦߪ㧘ਔࠤ࡯ࠬߣ߽ߦ㧘 Mie-Grüneisen ဳߩⴣ᠄ Hugoniot ߩ⁁ᘒᣇ⒟ᑼ
ࠍㆡ↪ߒߚ㧚2024-T351A1 ߦኻߒߡㆡ↪ߒߚ᭴ᚑೣߣ⁁ᘒ

Pressure (GPa)ߕߺㅦᐲଐሽᕈ㧘 m ߪᾲエൻߦ㑐ࠊࠆ‛ᕈ୯ߢ޽ࠅ㧘᧚ᢱ
1.8
#5
#1

Elastic
Precursor

1.0

# 1
# 3
# 5
# 7

#7

1.4

# 2
# 4
# 6
# 8
#80.6
#2

#6

#3

2.0

3.0

#40.2

⴫䋱㩷 2024 A1 ߩ᭴ᚑೣ࠺࡯࠲5)-0.2 0.0

Johnson-Cook ߩࡕ࠺࡞

1.0

4.0

5.0

6.0

7.0

8.0

9.0

G : 27.6 Gpa
A : 0.265 Gpa

10.0ᤨ㑆 (ms)-0.6-1.0(a) ࿶ജጁᱧ-1.4

B : 0.426 Gpa-1.8N : 0.34 㧙Vxx (GPa)C : 0.015 㧙
m : 1.0 㧙Tmelt : 775.0 K

1.8
# 1
# 3
# 5
# 7

1.4
1.0

# 2
# 4
# 6
# 8

Elastic
Precursor

0.66)

⴫䋲㩷 2024 A1 ߩ EOS ࠺࡯࠲ 㩷
Mie-Grüneisen ဳ shock
Hugoniot ߩ⁁ᘒᣇ⒟ᑼ
3
U : 2.785 g/cm

c0 :5328 m/s

s : 1.338 㧙*:2.0 㧙Troom : 300.0 K

0.2-0.2 0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

Time (Ps) -0.6-1.0


-1.4
-1.8





(b) V xx ጁᱧ࿑䋶㩷 ⴣ⓭ㅦᐲ 100 m/s ࠤ࡯ࠬߩᤨೞᱧ㩷

10.0

Stress, Pressure (GPa)2.0࿑䋷ߦᒢ႟ᕈࠤ࡯ࠬߩⴣ⓭㕙ߦធߒߚਛᔃゲㄭற #1 ߩ

1.5

PPPVsxx
xx

VsxyxyVsttTT

Vsyyyy࿶ജߣ྾ߟߩᔕജᚑಽߩᤨೞᱧࠍ␜ߔ㧚ߎߩ࿑߆ࠄ㧘ᒢ႟ᕈࠤ࡯ࠬߩⴣ⓭㕙ㄭற #1 ߦ߅ߌࠆᔕജฦᚑಽߣ࿶ജߩ

1.0⛘ኻ୯ߩᦨᄢ୯ߩ㑆ߦߪ V xx ! P ! V yy

0.5

V㫏㫐

0.0
0.0

2.0

4.0

6.0

8.0

10.0

Time (Ps)-0.5

V TT ! V xy ߥࠆ㑐ଥ߇޽ࠆߎߣ߇ࠊ߆ࠆ㧚4.2.2 ⴣ⓭ㅦᐲ 1000 m/s ߩ Taylor ⹜㛎೨㗄 4.2.1 ߣหߓߊ㧘ᒢ႟ᕈ૕ߣᵹ૕ߩੑߟߩࡕ࠺࡞ߦߟ

-1.0VyyVTT߈㧘ⴣ⓭ㅦᐲߩߺ 10 ୚ߦߒߡ 1000 m/s ߣߒߚ⸃ᨆࠍታᣉ-1.5ߒߚ㧚࿑䋸(a)ߦฦ಴ജὐߦ߅ߌࠆ࿶ജߩᤨೞᱧࠍ㧘(b)ߦߪ

ᒢ႟ᕈࠤ࡯ࠬ#1ߩ࿶ജߣฦᔕജᚑಽߩᤨೞᱧ

Vxx-2.0ᒢ႟ᕈ૕ࠤ࡯ࠬߩⴣ⓭㕙ߦធߒߚਛᔃゲㄭற #1 ߩ࿶ജ࿑䋷㩷 ⴣ⓭ㅦᐲ 100 m/s ᒢ႟ᕈࠤ࡯ࠬߩᤨೞᱧ㩷ߣ྾ߟߩᔕജᚑಽߩᤨೞᱧࠍ␜ߔ㧚ᑼ(3), (9)ߩ޿ߕࠇߩᑼ
ߦ᜚ߞߡ߽㧘ⴣ⓭ㅦᐲ߇ 10 ୚ߢ޽ࠆߚ߼ⴣ⓭࿶߽ 10 ୚ߦ

Pressure (GPa)

20.0

#5

ߥࠆߎߣ߇੍᷹ߐࠇࠆ߇㧘࿑䋶(a)ߩ⚿ᨐߣᲧセߔࠆߣ޿ߕ

#6

#1

#7

ࠇߩጁᱧ߽ 10 ୚એ਄ߩᦨᄢ࿶ജ߇⸘▚ߐࠇߡ޿ࠆ㧚ߎࠇߪ㧘

#2
#3

15.0

ⴣ⓭࿶ജ߇ᄢ߈ߊߥࠆߎߣߦࠃߞߡ㧘ⴣ⓭૕߇ⴣ᠄࿶❗ࠍ
# 1
# 3
# 5
# 7

10.0

# 2
# 4
# 6
# 8

ฃߌ㧘૏⋧ㅦᐲ ᵄߩવ᠞ㅦᐲ ߣኒᐲ߇਄᣹ߔࠆߚ߼ߢ޽
#8ࠆߣ⠨߃ࠄࠇࠆ㧚߹ߚ㧘100 m/s ߩࠤ࡯ࠬߢߪ㧘ᒢ႟ᕈ૕ߣ

5.0ᵹ૕ࡕ࠺࡞ߩᦨᄢ࿶ജߩ㑆ߦ⚂ 1 ഀߩᏅ߇ሽ࿷ߒߚߩߦኻ

#4ߒ㧘1000 m/s ߩࠤ࡯ࠬߢߪ߶ߣࠎߤᏅ߇⷗ࠄࠇߥ޿㧚

0.0
0.0

1.0

2.0

3.0

4.0

5.0
#6

-5.0

6.0

7.0

#2

8.0

9.0

10.0

Time (Ps)ห᭽ߦ㧘ᒢ႟ᕈ૕ࠤ࡯ࠬߩⴣ⓭㕙ߦធߒߚਛᔃゲㄭற#1 ߩ࿶ജߣ྾ߟߩᔕജᚑಽߩᤨೞᱧ ࿑䋸(b) ࠍ⷗ࠆߎߣ#3#7(a) ࿶ജጁᱧߦࠃߞߡ㧘ࠃࠅ᣿⏕ߦ⏕⹺࡮ᛠីߔࠆߎߣ߇ߢ߈ࠆ㧚ߔߥ-10.0

Pressure, Stress (GPa)ࠊߜ㧘ᵹ૕ࠤ࡯ࠬߩⴣ⓭㕙ㄭறߩὐ #5 ߦ߅޿ߡߪ㧘

V xx

20.0
P15.0
10.0

PPVsxxxx

VsxyxyVsttTTPV yy

V TT ! V xy ߩ㑐ଥ߇޽ࠆ㧚߹ߚ㧘ᡓੂߩ೔㆐ᤨ㑆ߦ㑐ߒߡ߽ਔࠤ࡯ࠬߩ㑆ߦ᦭ᗧߥᏅߪߥߊߥߞߡ

Vsyyyy޿ࠆ㧚ߎࠇࠄߩ੐ታߪ㧘2 ┨ߩᦨᓟߩㇱಽߢㅀߴߚ㧘㨬ⴣ᠄ജ߇ᄢ߈ߥ໧㗴ߢߪ㧘࿕૕‛⾰ߦ߅޿ߡ߽஍ᏅᚑಽߦᲧߴ

5.0

Vxy

0.00.0ࠆ㧚㨭ߣ޿߁ߎߣࠍⵣઃߌߡ޿ࠆ㧚ㅒߦ㧘ߘߩࠃ߁ߥ᧦ઙߩ
2.0

4.0

6.0

8.0

Time (Ps)10.0-5.0ਅߢߪ㧘ߚߣ߃᭴ᚑೣࠍήⷞߒߡ߽㧘ߘࠇ߶ߤ⚿ᨐߦߪᖡᓇ㗀ࠍ෸߷ߐߥ޿㧚

-10.0
-15.0

Vxx, Vyy, VTT(b) ᒢ႟ᕈࠤ࡯ࠬ#1ߩ࿶ജߣฦᔕജᚑಽߩᤨೞᱧ

-20.0

࿑䋸㩷 ⴣ⓭ㅦᐲ 1000 m/s ࠤ࡯ࠬߩᤨೞᱧ㩷5. ⚿   ⸒એ਄ߢߪ㧘࿕૕ਛߦ⊒↢ߔࠆⴣ᠄ᵄࠍℂ⸃ߔࠆ਄ߢᔅⷐߥ㧘⥋ᭂ㧘ၮᧄ⊛ߥⷐઙߦߟ޿ߡߩߺㅀߴߚ㧚ࠃࠅ㜞ᐲߥℂ⸃㧘߅ࠃ߮ታ㛎ᴺࠍ฽߻ታ㓙⊛ߥ⍮⼂ߩ⠌ᓧߩߚ߼ߦߪ㧘cl ߪᒢᕈ₸߆ࠄ㧘cl4 ·§¨ K  G ¸ U ߢ⸘▚ߐࠇࠆ ߚߛ3 ¹©

ߒ㧘G ߪᮮᒢᕈ₸ 㧚ߘࠇߦኻߒߡ㧘ᵹ૕ߩ႐วߦߪߖࠎᢿߘࠇߙࠇߩኾ㐷ᦠߦ᜚ࠆᔅⷐ߇޽ࠆ㧚ߒ߆ߒߥ߇ࠄ㧘ᣣᧄ⺆ߢᦠ߆ࠇߚᦠ☋ߪ㕖Ᏹߦዋߥ޿ߩ߇⃻⁁ߢ޽ࠆ㧚╩⠪߇㧘೎ߩᯏળߦ㧘㜞ㅦⴣ᠄⃻⽎ߩߚ߼ߩᢙ୯⸃ᨆᴺߦߟ޿ߡᦠᚑಽ߇ሽ࿷ߒߥ޿ߚ߼㧘ᮮᒢᕈ₸ߦࠃࠆነਈ߇ߥߊ㧘਄ㅀ޿ߚ߽ߩ߇޽ࠆ 7)㧚ߎߩಽ㊁ߪᣣᧄߩᄢቇᢎ⢒߆ࠄ߶߷ቢߩࡃ࡞ࠢ㖸ㅦߢવࠊࠆᵄ߇ⴣ᠄ᵄએᄖߢߪᦨ߽ᣧߊવ᠞ߔోߦᰳ⪭ߒߡ޿ࠆߚ߼㧘ෳ⠨ᢥ₂ߩೋ߼ߩㇱಽߢઍ⴫⊛ߥࠆᡓੂߢ޽ࠆ㧚޿߹㧘2024A1 ߦኻߔࠆ㕒⊛ߥ૕Ⓧᒢᕈ₸ࠍࡃ࡞ࠢ㖸ㅦߣኒᐲ߆ࠄㅒ▚ߔࠆ㧚ߔߥࠊߜ㧘c 0 5328 m/s㧘ෳ⠨࿑ᦠߦߟ޿ߡ߹ߣ߼ߡ⸥ߒߚ㧚ᔅⷐߥ⺒⠪ߪߘߜࠄࠍ
ෳ⠨ߦߒߡ㗂ߌࠇ߫ᐘ޿ߢ޽ࠆ㧚

79.06 GPa

4.2 ▵ߢ␜ߒߚᢙ୯⸃ᨆ଀ߪⴣ᠄⸃ᨆࠦ࡯࠼: AUTODYNࠍᓧࠆ㧚ߒߚ߇ߞߡ㧘 2024A1 ߦኻߔࠆ❑ᵄߩ㖸ㅦߪ㧘ࠍ↪޿ߡ⸘▚ߒߚ߽ߩߢ޽ࠆ߇㧘⃻࿷ߩࡄ࠰ࠦࡦߢߪ㜞‫ޘ‬㧚㧚㧚
1 ಽ⒟ᐲߢ⚳ੌߒߡߒ߹߁੹ߢߪ◲නߥ⸘▚ߢ޽ࠆ㧚ߒ߆

Ucl2.785 u 10 3 kg/m3 ࠍ K

U0c 02 ߦઍ౉ߒߡ㧘K6450 m/s ߣߥࠆ㧚ߘߩ⚿ᨐ㧘 c 0 c l | 1.2 ߣߥࠅ㧘࿑䋶ߩ⚿ᨐߣ╓วߔࠆ㧚ߥ߅㧘(a), (b)ߩࠣ࡜ࡈਛ㧘⍫ශߢ␜ߒߚㇱಽߪ೨ㅀߩవⴕᒢᕈᵄ Elastic Precursor ߩ 2 ᵄ᭴ㅧࠍ␜ߒߡ޿ࠆ߇㧘ᢙ୯ࡕ࠺࡞ߩߚ߼┙ߜ਄߇ࠅ߇㊰ߞߡ޿ࠆ㧚ߚߛߒ㧘࿑䋶ߪᤨೞᱧߢ޽ࠅ㧘࿑䋴ߩฝ஥ߩ࿑ߣߪ⴫␜ᣇᴺ߇⇣ߥࠆ㧚ߒߥ߇ࠄ㧘‛ℂ⊛ߥᗧ๧ߪ᳿ߒߡℴᧃߢߪߥ޿㧚ᧄⓂߢߪ␜ߐߥ߆ߞߚ߇㧘⋧ォ⒖߿⋧ᄌൻࠍ઻߁⃻⽎㧘ߚߣ߃߫㧘㜞಴ജኒᐲߩ࡟࡯ࠩࠍᾖ኿ߔࠆ㓙ߦ↢ߓࠆⴣ᠄᳇ൻ⃻⽎ߥߤ߽ᢙ୯⊛ߦᮨᡆߔࠆߎߣ߇ߢ߈ࠆ㧚߹ߚ㧘⃻࿷ߢߪⶄ㔀ߥ 3 ᰴరᒻ⁁ߩ໧㗴߽߆ߥࠅߩ⒟ᐲ߹ߢ⸃ߌࠆࠃ߁ߦߥߞ⪺ ⠪ ⚫ ੺ߡ߈ߡ޿ࠆ㧚ᯏળࠍᡷ߼ߡ⚫੺ߒߚ޿ߣ⠨߃ߡ޿ࠆ㧚ጊ㓷⧷ෳ ⠨ ᢥ ₂1) Marsh, S.P(Ed).: LASL shock Hugoniot data, University of California Press, Berkeley, (1980).
2) Thiel, M.van.: Compendium of Shock Wave Data, UCRL-50108,
Lawrence Livermore Laboratory, Livermore, (1977).
3) Kohn, B.J.: Compilation of Hugoniot equations of state, AFWL-TR-69-38, Air Force Weapons Laboratory, New Mexico, (1969).
4) Trunin, R.F.: Shock compression of condensed materials, Cambridge
University Press, Cambridge, (1998).
5) Johnson, G.R. and Cook, W.H.: A constitutive model and data formetals subjected to large strains, high strain rates and high temperatures, Proc. 7th Int. Symp. on Ballistics, The Hague, (1983), 541-547.
6) Steinberg, D.J.: Equation of state and strength properties of selectedmaterials, UCRL-MA-106439, Lawrence Livermore National Laboratory, Livermore, (1991).
7)ጊ㓷⧷: ⸘▚ജቇࡂࡦ࠼ࡉ࠶ࠢ ⍫Ꮉరၮ㧘ችፒೣᐘ✬ 㧘ᦺୖᦠᐫ㧘(2007), 443-460㧚

KATAYAMA Masahide
1955 ᐕ 3 ᦬ 8 ᣣ↢㧚1979 ᐕᄢ㒋ᄢቇᎿቇㇱේሶജᎿቇ⑼ත㧚2001 ᐕ᧲ർᄢቇࠃࠅඳ჻ Ꮏቇ ߩቇ૏ ⺰ᢥ ࠍᓧࠆ㧚1979 ᐕ࠮ࡦ࠴ࡘ࡝࡝ࠨ࡯࠴࠮ࡦ࠲ ᩣ⮮ᔘ࠹ࠢࡁ࠰࡝ࡘ࡯࡚ࠪࡦ࠭ ᩣ⃻㧘દ౉␠㧚એᓟ㧘㜞ㅦⴣ⓭߿῜⊒໧㗴ߩᢙ୯⸃ᨆߦ㑐ߔࠆᬺോߦ㑐ਈߔࠆ㧚2006 ᐕࠃࠅ᧲੩Ꮏᬺᄢቇᔕ↪࠮࡜ࡒ࠶ࠢࠬ⎇ⓥᚲߩቴຬᢎ᝼ࠍ౗ോ㧚ᣣᧄⴣ᠄ᵄ⎇ⓥળ㧘ᣣᧄᯏ᪾ቇળ㧘ᣣᧄ႟ᕈടᎿቇળ㧘ᣣᧄ⥶ⓨቝቮቇળ㧘Ἣ⮎ቇળ㧘࿯ᧁቇળ㧘ᣣᧄᑪ▽ቇળ㧘

International Shock Wave Institute㧘Hypervelocity Impact Society ߥߤᚲዻ㧚E-mail: masahide.katayama@ctc-g.co.jp
TEL: (03) 6203-7425, FAX: (03) 3539-5173