日本機械学会北海道支部シニア会
2018 年度

シニア会総会および交流会議事録

2018 年度シニア会総会および交流会は 2019 年 3 月 12 日以下のように実施された。

Ⅰ. 2018 年度シニア会総会

司会

杉

山

委員長、小

林

副委員長

開催日時：2018 年 3 月 12 日（火） 13:10-13:40
開催場所：北海道大学工学部 A 棟 4 階

A4-63 室

出 席 者：13 名（杉山弘、小林道明、近久武美、三浦展義、豊田国昭、臺丸谷政志、
疋田弘光、石坂淳二、後藤正芳、小野信市、岸浪紘機、二俣正美、猪狩昌和

敬称略）＜審議事項＞
1. 2018 年度活動報告

資料１に基づき杉山委員長から報告があり、異議なく承認された。
１．北海道学生会第 47 回学生員卒業研究発表講演会への参加・協力
２．2017 年度第５回運営委員会の開催
３．2017 年度シニア会総会および交流会の開催
４．2018 年度第 1 回シニア会運営委員会（メール審議）
５．第５回「科学と技術に関する公開講座」の開催
６．2018 ものづくり基礎技術セミナーの開催
７．2018 年度第 1 回企業見学会・交流会の企画と開催（中止）
８．工場見学とものづくり基礎技術セミナーの開催
９．第６回「科学と技術に関する公開講座」の開催
10．日本機械学会北海道支部第 56 回講演会への参加・協力
11．2018 年度（平成 30 年度）日本機械学会北海道支部賞「中堅技術者貢献賞」の推薦依頼文書の発送
12．道南地区におけるシニア会懇談会・懇親会の開催
13．道東地区におけるシニア会懇談会・懇親会の開催
14．2018 年度第２回シニア会運営委員会（メール審議）

2. 2018 年度活動決算報告

資料 2 に基づき小林副委員長から計上予算 450,000 円、

支出 211,350 円の内訳説明と残余 238,650 円を支部に返却したとの報告があり、異議なく承認された。
3. 2019 年度活動計画

資料 3 に基づき杉山委員長から報告があり、異議なく承認された。
（１）企業見学会・交流会の開催（2 回程度）
（２）高校生・小中学生等に対する理工学支援（啓蒙・啓発）活動〇高校生を含む一般社会人を対象とした「科学と技術に関する公開講座」〇小中学生を対象とした理科授業の支援活動

北海道は面積的に広大であるので、３地区、すなわち道央地区、道南地区、道東・道北地区で、それぞれ 1～２件程度実施する。
（３）ものづくり人材育成支援
具体的には、ものづくり技術セミナーの開催（一般社団法人 北海道機械工業会などとの共催で実施する）（４）日本機械学会北海道支部行事に対する協力・支援〇道支部学生員卒業研究発表会への協力・支援〇道支部講演会への協力・支援〇道支部賞（中堅技術者貢献賞）選考に関する協力・支援(５) シニア会運営委員会と総会・交流会の開催〇メールによる運営委員会（メール審議）を数回実施する。
〇運営委員全員が一同に会する運営委員会、およびシニア会員全員が参加できるシニア総会・交流会は、1 回程度、札幌で開催する。
4. 2019 年度活動予算

資料 4 に基づき小林副委員長から 2018 年度計上予算から一万円増の 460,000 円の予算計上とその内訳説明があり、異議なく承認された。

Ⅱ. 2018 年度シニア会交流会

司会

杉

山

委員長

開催日時：2018 年 3 月 12 日（火） 13:45-15:45
開催場所：北海道大学工学部 A 棟 4 階

A4-63 室

出 席 者：13 名（杉山弘、小林道明、近久武美、三浦展義、豊田国昭、臺丸谷政志、
疋田弘光、石坂淳二、後藤正芳、小野信市、岸浪紘機、二俣正美、猪狩昌和

敬称略）

ARTICLE IN PRESSARTICLE IN PRESS[m5G;January 2, 2019;15:19]

M. Kobayashi / International Journal of Solids and Structures xxx (xxxx) xxx[m5G;January 2, 2019;15:19]

le fracture
progress Journal
char- of Solids
2. Theoretical
Kobayashi/ Internationaland Structures formulationxxx (xxxx) xxx of crack propagation as shock wave

1. 話 題 提 供 「 衝 撃 波 理 論 に よ る 破 壊 現 象 の 解 明

ructure of damage/failure
ed by discontinuity levels
fracture progress charplacement were analyzed.
ucture of damage/failure
fracture modes are anad by discontinuity levels
ity bands determined byacement were analyzed.
e crack opens and proparacture modes are anay bands determined byempirically that phenomcrack opens and propan (AE) and so forth caused
y wave (soliton), however,
mpirically that phenomlly the long-period pulse
AE) and so forth causeds of the 2016 Kumamotowave(soliton),however,rn
Iburi
Earthquakeat they the long-period pulseof thestudied
2016 Kumamoto
icallythe dynamIburi Earthquakeat thegeneous
media anddis-

– Solitary pulse wave

In this paper, only outline of the theoretical formulation of the
2. Theoretical formulation of crack propagation as shock wave
proposed micro-crack evolution equation is presented. The detailsof the formulation are given in the previous papers (Kobayashi,
In this paper, only outline of the theoretical formulation of the2012, 2017a,b).
proposed micro-crack evolution equation is presented. The detailsof the formulation are given in the previous papers (Kobayashi,
2.1. Micro-crack evolution equation and crack opening criterion
2012, 2017a,b).

radiated by crack propagation as shock wave -」（小林シニア会員）
初めに波動の基本的事項について群速度、位相速度、加速度波および衝撃波についての解説があり、衝撃波状態においては波頭で生じる加速度波速度の不連続によThe jump in a function of across a discontinuity band is defined
2.1. Micro-crack evolution equationand crack opening criterion
by the limiting values of f + and f − ahead of and behind the dis-

りひずみの不連続、すなわちマイクロ・クラック発生条件についての説明がなされ
continuity band, respectively, as follows:
The jump in a function of across a discontinuity band is defined+−= f limiting−f[ f ]thebyvalues of f and f ahead of and behind the(1)disた。ついで、加速度波がCut-off された場合に不連続面が発生し、それによりひず+−continuity
band,
as follows:
Based onthe respectively,
shock wave theory,
i.e., [ẍ] ̸= 0 and [x˙ ] ̸= 0, and

み速度の不連続が不連続面に沿って生じ、そこで局所変形が生じることの理論的背f ] =equationf + − f −of motion, the following equation can be obtained(1)[thealong the intersection line between two stationary discontinuityẍ] ̸=vanishing
Basedon the1 shock
theory, i.e.,
0 and [x˙ ]velocity
̸= 0, andbands,
labeledand 2,wave
characterizedby [thens, hence found existencetheequationof acceleration
motion, the wave
following
equationcan1 beobtainedally
studiedthealong
dynamconditionof an
as shown
in Fig.
basedont waves
(CFW)
the
along
the intersection
line between
stationary
eneousmedia
and wave
disthe proposed
theory of ultrasonicwavetwovelocities
underdiscontinuity
the plastic
than theRayleighbands,
labeled1 and 2,1982,
characterized
by thevelocity
foundstudied
existence
deformation(Kobayashi,
1987, 1998a,b
and vanishing2010; Kobayashi) hencenumericallythecondition
waves(CFW) alongthe
et al., 2003of). an acceleration wave as shown in Fig. 1 based onallheterogeneities(asperthe proposed theory of ultrasonic wave velocities under the plastic
hantheof Rayleigheffects
persistentwaveCFW.
! "δ [ε] δV̄(Kobayashi,
deformation
1982,
1987,
numerically
the
2V̄
+
0 1998a,b and 2010; Kobayashi(2)
PMMA werestudied
experimen[ε] + V 2 (∇ε)+ =δt2003δ).tetal.,lFineberg
heterogeneities(asperet al. (2003) andwhere ε , V and V̄ are! theof theoreticallypersistent CFW.
tfectswaves
pre" strain,+ the acceleration wave velocity andδ [ε] δV̄
the
.
2the
+ of[εV 2 (front∇ε )at =time
0 t and reference coordinate x(2)V̄ velocity
MMA
wereexperimen] +shocknd
crack
generation
weret
Ifδt ε280is δover
the threshold value [ε ]thand becomes finite,
nebergal. (2003)sodaandy in theet tempered
M. Kobayashi / International Journal of Solids and Structures 121 (2017) 275–288
where, Vtheandnonlinear
strain, theequation
acceleration
velocity ofandEq. (2) εis
underwave
the relation
waves
theoretically
preeedphotography
togetherδV̄ εare theδdifferentialV2: −V̄ · [ε2of[V 1] velocity=]V. the shockthecoordinate x.
+ front
ε +atVtime(∇tε and) − =reference0
ni crack
et al.,generation
1992). Recently,dwereStaget [ε]ththresholdδatt t = t0 Eq.value[ε ] δ=the(2) is[deduced
the following
IfSupposing
ε is overε ]th andtobecomes
finite,lly
the excitationin realized
the tempered
sodaRiccati
forfor strain(∇ε the) − jump
1 equation
δV[ε ] as⎫follows:Eq.
(2) equationis the nonlinear
differential
under the relation oflksolitons by a geometric
2 ⎧d photography
together[ε ] =V ⎨exp(−$ ⋅t ) − 1⎬[V ] = −V̄ · [#ε ]. δV / δtonlinearnanosecond
and
et al., 1992). Recently,⎩ + 2V δt⎭
δ:[ε ]
δV̄
−
2
Stage
2
Supposing
[
ε
]
=
[
ε
]
at
t
=
t
Eq.
(2)
is
2
+
−
2
·
V
∇ε
ε
+
∇ε )+ [ε ]2to=the
0 following
(3)
V̄
V̄
V̄
)0 [ ](deducedy realized the excitationth (δt
2 # δt 2+!
−V [εstrain[ V] =for] , the above+ 2V
Based onthe relation: theis obtained[V ] and
Riccatiequationjump[ε ] equation
as follows:
lse
wave byreleasedby the"V $ = [V ] for
solitonsa geometricas the following Riccati #equation. mthe crackas shock wave
Although Eq. (3) is nonlinear $equation, the exact solution can
nlinearnanosecond
and
δ
δV̄
[ε ]
+
+
bands, is obtained sponta2be+ as follows:− 2V̄ · V − (∇ε ) [ε ] + V̄ 2 (∇ε ) [ε ]2 = 0(3)V̄ obtained
δ
t
δ
t
waves
(CFW).
The
solitarye wave released by the2[ε ]th(4.1)[ε ] =
d basedproposedthecrackonas theshock
wave
Althoughis (nonlineart − t0 ) + 2equation, the exact solution canV̄ · (∇εEq.
]th ×)+ [ε(3)rifiedtobesoliton.
In
thends, is obtained spontabe obtained as follows:in whichIf [theε ] = denominatorthe0 Eq. (4.1) becomes zero, then thee in (CFW).
the inhomogeneous[ε ]th at t=t
0 andofT=t-t
aves
The solitary2[ε ]thstrainjump[
ε]becomes
infinite
within the finite time and the colaintobelargest
and
the
ε
=
(4.1)
[
]
based on the proposed+# ∂u &u+−εu]− × (t[u−] )+lapse/fracture
the displacement
small,
waveveε ]2→ ∞ of thenu] ≠ 0 jumplim )is [happened= lim byt0occurrenceth[ε ] ≡ % V̄ (· =(∇ε[[fied tothe
be shocksoliton.
In the
ΔX→0
ΔX→0
$ '
ΔX
ΔX
[u]If̸=∂X
0 as denominatorfollows:
hevelocities,
theof the Eq. (4.1) becomes zero, then thein surrounding
the inhomogeneous
M. Kobayashi, Verificationof crack opening criterion deduced by newly derived micro-crackmaybestablypropagating%&strainjump[ε ] becomes
infinite
withinVol.
the finite time and the coln to be largest and theevolution
equation ∂, International
Journaluu+ of−Solids
u− and Structures[u] 106-107 (2017), 139-151. 
f-focusing
just likeasvethelapse/fracture
happened by=occurrence
displacement=islimlim, [ofε ]the→∞then [u] ̸= 0jump
mall,
the shockwave[ε ] =
Fig. 8. Precisely estimated yielding stress$x → 0$ x → 0 $x
∂asx6.follows:$xand, in the case of crack√ σ y of A533B steel in the case of the crack
Diagram of driving force and fracture resistance to crack growth of Maraging[u] ̸= 0Fig.
e surrounding velocities,
opening direction θ = π /4 and α = 1/ 2 under the plane stress.
mogeneous media characsteel 300 ksi(450 °C 3 h tempering) in the case of crack opening direction θ = π /4√
(4.2)
y be stably propagating%and α&= 1/ 2 under theplane stress.
allest and the surroundu+ − u−∂u[u ]focusing just like as the==thelimlim→ ∞infinite
then [u]at̸=the0strain jump [=ε] issettled, by[ε ] Therefore,[ε ]being
e crack center velocity is$
x→0$
x → 0 $x∂x$x
nd, in the case of crack
Hierarchicaland/or failure level
crack
tip in thisdamage
paper.
hence the crack propagaogeneous media charac(4.2)
structure
top just like as the ductile
lest and the surround2.2. Shock wave solution derived by Eq. (3)down at the crack center
Therefore,
thestrain
jump
[
ε
]
is
settledby
being
infiniteatthecrack center velocity is
crack tip in this paper.
ence the crack propagaEq. (3) canCrackbe rearranged
cal formulation of crack⎡u ⎤ ≠ 0as follows:⎡ε ⎤ → ∞
⎣ ⎦
⎣ ⎦
%
&
p just like as the ductile
he proposed micro-crack
and/or∂ε wave∂ V̄solution derived by Eq.2 (3)22.2. Shockown at the crack center2V̄+ εvoid − 2V̄ · V · ε on· ∇ε+ V̄ · ε · ∇εa point
∂ t nucleation
∂t
us media is performed in
Eq. (3)' can(2 be rearranged as+follows:
al formulation of crack+

e character
proposedofmicro-crack
the solitary

gy and acceleration; thenmediais isconcluded
performed
wave
to in
be

haracterof theofsolitary
the suggestion
the nuandpaper
acceleration;thenhis
to be available
wave
arizedisinconcluded
Section 5. to be

景の説明があった。加速度波の Cut-off 条件を求めるために加速度波速度の応力依存性については音弾性理論に基づき、塑性変形については放射線損傷と同様に塑性

変形によって生じる点欠陥の影響を考慮し定式化がなされていることの説明と氏が定式化した理論の実証実験結果についての例示および水素脆性機構（水素助長局

所塑性変形理論）における空孔生成と超音波速度変化の関連性についての海外の研究紹介があった。また、加速度波速度の Cut-off 条件を用いて方位の異なる２つの[][] [ ]
不連続面が発生した時に不連続面の交差線上において衝撃波状態が生じひずみの[ ]不連続が発生、その状況を持ってマイクロ・クラック発生条件としている。また、
マイクロ・クラック発展方程式としての非線形 Riccati 方程式を導出し、その厳密解から分母が有限時間でゼロ、すなわちひずみが無限大になった時に変位に不連続が生じ、これを破壊開始条件としている。これら“ひずみ速度”、“ひずみ”および“変位”の不連続発生条件を用いて破壊に至る損傷過程の階層性を図１に示す４段階に分類し、加速度波速度算出アルゴリズムを結晶塑性有限要素法に組み込み要素ごとに図１の損傷過程を判定し、破壊に至る損傷の進展状況のシミュレーションと純アルミ単結晶による実証実験結果による検証と破壊進行が２つの不連続面のい()% = V̄ 2 ε− [∇ε] + 2V̄ 2 (∇ε ) ε− [ε] − 2V̄ [V ]ε+&(∇ε )∂ε − ∂ V̄−nucleation ⎡ε ⎤ ≠ 0 2 on2a line2−2+ε− 2V̄ · V · ε ·⎣∇εV̄Micro-crack⎦ + V̄ · ε · ∇ε(5)∂V̄t · V · ∂εt [∇ε]−+' − (2 ε = 0, 2ε = ε+and
By considering[V ] = −V̄ · [ε ] = −V̄ ·+ε at the2+
localization
=Deformationε⎡⎣ε−!⎤⎦[beε≠] obtained
−
εfrom
V̄
V̄ (∇ε ) canV̄ [Va ]plane[∇ε] + 2equation(∇εEq.
) (5).
0 2on
crack
tip, εthe following−2V̄ · V∂−V̄ · ε− [∇ε](5)∂ε⎡ ⎤ ⎡ε ⎤==0⎡u ⎤ = 0
2V̄ Continuous+ε− 2V̄ · V · ε · ∇ε − V̄ 2 · ⎣εε!2⎦· =∇ε(6)⎣ ⎦ ⎣ ⎦
∂ t considering∂ t deformationBy
ε − = 0, ε + = ε and [Vin]a=whole−V̄ · body[ε ] = −V̄ · ε at thecrack tip, the following equation can be obtained from Eq. (5).

7. Diagram ofasdriving
force
and fracture
resistanceJournal
to crack ofgrowthof D6AC
Solitary
pulse ofwave
by crackFig.
propagation
shock
wave,
International
Solidshesuggestion
theradiatednu√θ = π /4 and α = 1/ 2 under the∂ε alloy ∂steelV̄ in the case of crack opening2direction
jsolstr.2018.12.022
2s paper to be available
2V̄+ε− 2V̄ · V · ε · ∇ε − V̄ · ε · ∇ε = 0(6)∂ t plane ∂stress.
t 図 1
zed in Section 5.

Fig. 9. Diagram of driving force and fracture resistance to crack√ growth of A533B
steel in the case of crack opening direction θ = π /4 and α = 1/ 2 under the planestress.

olitary pulse wave radiated by crack propagation
as shockwave,
Internationalof Solids
Therefore, basedon Eq.
(23),
Eqs (14)–(17)Journal
are available
andthen the proposed crack opening criterion is applicable to the crack
olstr.2018.12.022

253 MPa m1/2 ,growth process. From Eq. (20) and J = ɡIc
Jpl is as follows:! c "2KIc

図2the over-estimated fracture toughness raised fromthe experimental one misleads us to the dangerous side assessment because the critical crack length of the crack opening becomes the dangerous side of a = 2.6 mm under the raised fracture
toughness 253 MPa m1/2 from a = 0.84 mm under the experimental
one 56.4 MPa m1/2 . More detailed discussion to estimate the frac-== 2 km2x = 4 km!
ε0namely(9)(z )! · exp(λ/η ),η = x − V̄ · tts,!
!
− 7×10. (11)
W=
MPa
∙m
which
εand
and ε + arezero
and going to infinity at η = 0, re!
erationwave
velocityV.
! the fracture toughness
ctively; λ is a parameter determined by

Aelastic= 0.0975×= 77 kmand !
moduli E, ν !as described in the next Section 3. Sub分）
uting
Eq.
(9)
exact
solutionof the shock wave==
2 intokmEq. (8.1)!the
2x
(17)
! =
=A!2
km
2x
=
4 4km
!km
!
=!77
km
V̄=is 0.0975×
city
obtained as follows:＊未選別デ

ollows:! !"×!
!
"#$2 1.74 m
=
=
ε
2
λ
!"#
0
る
− ! !! !+
λ/η )
(10)
V̄0 · exp(18)!!
! 2 · exp(2(9)η
134!
M. Kobayashi / International Journal of Solids and Structures 163 (2019) 130–138
ずれかでありカオス発生メカニズムの一つである２分岐特性を有することの説明
x
=
=
2
km
2xrange=is4(2)km!
!
g
toinfinity
at
η
=
0,
reV̄
The velocity
in
η
being
negative
approaching to
!
があった。
!
!"×!
xp
(−=
ε02 and/2 )fracture
under =
η →1.74−∞ andutionsbythetoughness
mclearly corresponds to the shock"#!"×!
続いて、提案の破壊開始条件から導出した破壊靭性値から算定される破壊エネル!
!!
!
!
velocityon its amplitude. The other hand, the ve! !
are!depending=
1.74
m
necasesthenextSection3. Subx==
2km
2x! =non-zero
4 kmvalue!
ギーと破壊プロセス・ゾーン面積の関係式を用いて原子炉圧力容器材料である
V̄
ty!!
in
η
being
positive
range is approaching!
!
hesolitary! ! !!!
olutionof the
shock
wave
m
zero
under
η →A533B∞
which
is supposed to be the velocity of
スチールについて塑性変形によるエネルギー消費も考慮した破壊靭性とクラ
etal
mate-

ashi / International Journal of Solids and Structures 163 (2019) 130–138

135

solitary
pulse !"×!
wave radiated by the crack propagation as shock
タ
ng
1.

に関して図
!and
= inック長=a later.
1.74 m 2 に示すダイアグラムを求め、平面応力状態下の表面クラック$evelocities
described
detail!"#!! ! !

! 長さについて! !
2a=0.46mm 以上の潜在クラックの存在でその後の負荷でクラックは発e4width of
Solitary
pulse wave
radiated (10)by crack
propagation as shock wave
達し、2a=234mm
で一気に破壊が進展する脆性破壊が生じることを予測している。一velocity isFig. 4. Shock wave velocities of metal material cases.
!"×!
方、平面ひずみ状態下の内部クラックについては更に厳しい
2a=94mm で脆性破壊がlseexamine
width the physical!"#Tocharacter of the velocity V̄ under
!!
!
!
!
!
!
to of the shock wave caused byorangeownis approaching
生じ安全側の評価からはこの値を用いるべきであるとしている。ところで、2015年∞its, supposing
that
the amplitudedlatter.
crack
propagationto
disturbed
from ε to ε (1 + &), the follow-30 年経過したティアンジュ原発２号
corresponds
the
shock
2 is
月ベルギー連邦原子力管理庁は運転開始から
in thearematerialcases
are calculated byorder approximate
equationsobtainedfrom Eq.
(8.1)which.
e.firstThe
other propagation
hand,
the
ve- ceramic
機とドール原発３号機で原子炉圧力容器内側に多数のクラックが見つかり、その最
Eq.
under
*0pulsebeing
Fig. 8. Shock wave velocities of ceramic material cases.
Fig. 12. (18)Comparisonsof the solitary
waves and1.
its velocities V̄ /V̄ underε = distributions
ε =waves
0.008 and λ =68.11
nm with0.16 and= 68.11
nm in cases.
AISI4340 steel% Fig. 5. non-zero&
Strainandsolitarypulse
of λmetal
material
proachingvalue
大長が
2a=180mm
であるが安全性が確保されているので運転継続をすることを公表∂ε∂Zp<L±^hÔV̄Fig. 1+ V̄ 2 + ε2 case. The= 0relation between the solitary pulse(11)waves and its velocities
15 Nm
∂η
∂η
sed
velocityof 10. As seen from Fig. 10 it is clear that the pulse
wavetove-be theareshown in Fig.
したがドイツとルクセンブルグの運転停止と詳細な検査の要求に応じ運転を停止
ting in ceramic materials.
and 8propagation, re- ∂ε widthof thesolitary pulse waveof Alumina case is extremely
rack
shock
することになった。上述の図2 の予想では表面クラック長
2a=180mmnarは危機的状況
∂ &as
=
1
+
&
+
ε
(12)
)
(
d by crack ∂η row∂ηand its velocity is accelerated very rapidly.
に近く、現状の破壊力学によれば安全側の判断によりクラック長 2a=94mm で運転を!

=

= 1.74 m0

Ic0!! = 0.003

0Ic!! = 0.15

From Eqs. (9)–(12)停止すべきであるとの説明がなされた。
the following equation regarding to the disbance& is obtained
as follows:
propagation
as shockwave
Riccati 方程式を用いて伝搬するクラック先端のひずみ&! 1 + ∆ ' % 最後に、導出した非線形&(∂+ ε2 4 log & 2 とひずみ伝搬に伴い放出されるパルス波の解を求めこれが実験で観測された破壊+ ε2 = 0(13)∂ηW(joule)V̄ underof theM velocity
時にクラックとともに伝搬するパルス波であり、ソリトンであることを明らかにし
Numericalof homogeneousmedia
he shocksimulation
wave
causedby 年の熊本地震および昨年の胆振東部地震で観測された長周期パている。また、2016
log W = 4.8 + 1.5M
εEstimation
to ε (1 +),ルス波との関連性についてマグニチュードから求めた破壊エネルギーから破壊靭
the λfollowof &parameter
based on fracture toughness KIc and
M =7W
moduli E, ν frometicobtained
Eq. (8.1).
性値を算定し、岩石の物性値を用いて算定したパルス波と西原村で観測された地震
w!! = 0.15!"

w

Fig. 13. The whole wave shapes propagating in metal materials.

Fig. 23）を行い、先端の波形は地表地震断層に伴うクラック先端ひFig. 6. Solitary波との比較検討（図pulse waves and its velocities propagating
in metal materials.
case is obtained
as follows:
Tovelocities
considerthe steelfracturepropertyof each materials undertheV̄ /V̄ calculated
Fig. 9.
Strain distributions and its solitary pulse wave of ceramic material cases.
!
eing 34.055 nm, 136.22 nm
ε0 ! MPa ∙ m
K !" = 72.1×10
#
ε
·
d
η
=
3
.
13
+
380
nm
(20)
(
)
merical simulation it is necessary
todetermine the parameter λ22+I!!" = 7.45×10!(11)
MPa
∙ mε0
: elastic
Seismogram of the 2016 Kumamoto
ed on the fractureHere,toughnessKandmoduliE, νof. 4. Discussions
the dependenceI of the accelerationand thevelocity
Earthquake observedat Nishihara
W = 2×10!" joule (Nm)0I!! = 0.003

the solitary pulse wave on ε 0 is negligible as shown in Fig. 12.
!!! ! ! !
!
solitarypulse
the shock wave!!andrelatedA=! wave24-32! ∙ The
20 −value
8! of ε 0 is the amplitude!! =of0.003= 0.15!"#!
ost same in spite of
to a total energy of the solitary pulse wave released by the shock
sted that the accelerwave. Under constant! valueof λIc the released!rateof the energy! = 0.003! = 0.15
n its pulse width deand the acceleration of the solitary pulse wave characterized by!
!
= 0.0975energy∙
m! =are220almost
km! same. Therefore, it is recognized from
adiationfrom A =its0.22×10
pulse width!
! 1+∆
te of an energy; theFigs. 11 and 12 that the increased pulse width of the solitary pulse
lse width of the soliwave caused by the increase of the value of ε 0 under its same aca mass of a particle
celeration due to the!same
1 +value∆ of λIc as shown in Fig. 12 corresomething analogous
sponds to gathering of the unit solitary pulse waves determined byrs induced by a highthe value of λIc as shown in Fig. 11.
er laser and observed
Accordingly in this Section the solitary character of the crackt al., 1980).
front solitary pulse wave is examined due to its energy and accelPeriod, sec
the comparisons oferation and then in this point of view the solitary pulse wave isV̄ /V̄0 calculated unconcluded to be soliton.
se of ε 0 = 0.16 andFigs. 13 and 14 show the whole wave shapes, ε (1 + #), cong. 12 the dependence
sisted by the shock wave and the solitary pulse wave propagatve on ε 0 in AISI4340
ing the metal and ceramic materials, respectively. To easily and

! 1+∆

0.15

(12)

tion regarding to the dis4

(13)

4

Fig. 3図 3

4

us medialFig. 7. Strain distributions of ceramic material cases.

: Seismogram of the 2018 Hokkaido Iburi Eastern
Earthquake observed at Mukawa

4.1. Homogeneous case of ε ≡ ε (η) and # ≡ #(η)
In AISI4340 steel case Fig. 11 shows the comparisons of
the solitary pulse waves and its velocities V̄ calculated underλIc = 68.11 nm and ε 0 = 0.008 with those of λIc being 34.055 nm,
136.22 nm and ε 0 = 0.008. From Fig. 11 the dependence of the total energy of the solitary pulse wave on λIc is obtained as follows:!

#ε · dη = 0.046 · λIc + 1.52 (nm )(19)Under the same value of ε 0 , the total energy caused by the fracture is depending on only λIc . The pulse width of the solitary pulse
図 4wave is closely related to the sharpness of the shock wave causedby the fracture, because its sharpness is dependent on the value of
λIc as shown by Figs. 5 and 9.
Fig. 11 also shows that the pulse width of the solitary pulse
wave is narrower, then its acceleration becomes larger; due topposingTthat theof the shock wave caused by! amplitudeT
log W = 4.8 + 1.5M
εpropagationisdisturbed
fromε
to ε (1 +), the λfollow3.1. Estimationof &parameter
based on fracture toughness KIc and
−
2
η
M
=7
W
cosh η · e(8.2)
elastic
moduli E, ν from Eq. (8.1).
rder
approximate equations
are obtained!! = 0.15!"202cosh2w

Fig. 13. The whole wave shapes propagating in metal materials.

1 + ∆ distance from the 4nity at! faraway
W = 2×10!" joule (Nm)Fig. 2
Fig. 6. Solitary pulse waves and its velocities propagating in metal materials.
case is obtained
as follows:
solution is non-realistic.
Tovelocities
considerthe steelfracturepropertyof each materials undertheFig. 11. Comparisons of the solitary pulse waves and its
V̄ /V̄ calculated
Fig. 9.
Strain distributions!
under λ = 68.11 nm and ε = 0.008 with those W
of λ being 34.055 nm, 136.22 nm
ε0 ! MPa ∙ m
K = 72.1×10
2#it
ε · disη =necessary
3.13 !"
+ 380
nm
(20)
(
)
crack
opening
[u]
̸
=
0
due
to
numerical
simulation
todeterminetheparameterλ= 0.008
in AISI4340
steel case.
and ε
2
2+
=0
2+
I
!!" = 7.45×10!(11)
MPa
∙ mε0
:
Seismogram of the 2016 Kumamotostrain at the crack tip propagatbased on the fractureHere,toughness
KI ofandelastic
moduliE, νof. 4. Discussions
the dependence
the accelerationand thevelocity
Earthquake observedat Nishihara

& ∂ε
ε
∂η

0

Ic

Ic

0

0

4

I

the solitary pulse wave on ε 0 is negligible as shown in Fig. 12.
!!! ! ! !
!
some calculations of a force acting to the solitarypulse
the shock wave!!andrelatedA=! wave24-32! ∙ The
20 −value
8! of ε 0 is the amplitude!! =of0.003= 0.15!"#!
under same value of ε 0 the force is almost same in spite of
to a total energy of the solitary pulse wave released by the shockdifferent values of λIc . Therefore, it is suggested that the accelerwave. Under constant! valueof λIc the released!rateof the energy! = 0.003! = 0.15
ation of the solitary pulse wave depends on its pulse width deand the acceleration of the solitary pulse wave characterized by!
!
= 0.0975energy∙
m! =are220almost
km! same. Therefore, it is recognized fromtermined by λIc which closely related to a Aradiationfrom A =its0.22×10
pulse width!
! 1+∆
crack propagation, especially the released rate of an energy; theFigs. 11 and 12 that the increased pulse width of the solitary pulse
released unit energy characterized by the pulse width of the soliwave caused by the increase of the value of ε 0 under its same actary pulse wave may be recognized such as a mass of a particle
celeration due to the!same
1 +value∆ of λIc as shown in Fig. 12 correjust like solitons. This phenomenon may be something analogous
sponds to gathering of the unit solitary pulse waves determined by
to optical solitons propagating in optical fibers induced by a highthe value of λIc as shown in Fig. 11.
power and narrowing mode-locked color-center laser
Accordingly in this Section the solitary character of the crack
2 and observed
at certain critical power levels (Mollenauer et al., 1980).
front solitary pulse wave is examined due to its energy and accelPeriod, secRegarding with another parameter ε 0 the comparisons oferation and then in this point of view the solitary pulse wave isthe solitary pulse waves and its velocities V̄ /V̄0 calculated unconcluded to be soliton.
der ε 0 =0.008 and λIc =68.11 nm with those of ε 0 = 0.16 andFigs. 13 and 14 show the whole wave shapes, ε (1 + #), conλIc =68.11 nm are shown in Fig. 12. From Fig. 12 the dependence
sisted by the shock wave and the solitary pulse wave propagatof the total energy of the solitary pulse wave on ε 0 in AISI4340
ing the metal and ceramic materials, respectively. To easily and!! = 0.003

%

4

S

S

! 1+∆

4.1. Homogeneous case
∂ε
∂&
3T
0.003
0.15
+ &)
+ ε ずみであることを示した。
(12)
In AISI4340 steel
the solitary pulse wa∂η∂ηこれらの地震は内陸で発生する活断層型地震でそのメカニズムと考えられていλ = 68.11 nm and ε =Ic

qs. (9)–(12) the following equation regarding to the dis4
3 4!
& is obtained asfollows:
様な破壊エネルギーと破壊プロセス
・ゾーン面積の関係を図 4 に示すように得られ、0136.22 nm and ε 0 = 0.
るダイラタンシィモデルにおける破砕帯生成に伴うエネルギーを考慮して図 2 と同
tal energy of the solita#ε · dη = 0.046 · λ
Δ!
' %
&(
∂
活動した断層面積が220km
で最大すべり量を2m,少なくとも地震発生
10
日前には震Under the same val
log T
& 2S
+ ε2 S=0(13)
4ture is depending on o
源近くで応力低下が生じ音速が増加したことを推定できる。
ηwave is closely related

Fig. 34
図 5 は昨年の胆振東部地震においcal simulationof homogeneous mediaて鵡川町で観測された地震波形であS

lFig. 7. Strain distributions of ceramic material cases.

り、胆振東部地震では地表地震断層

tion of parameter λ based on fracture toughness KIc andが現れず、断層が地中で止まったとI4
3
3
duli E, νT: Seismogram of the 2018 Hokkaido Iburi Eastern
Earthquake observed at Mukawaby the fracture, becaus
λIc as shown by Figs. 5
Fig. 11 also shows
wave is narrower, the

考えられている。従って、図 5 に見Sられるようにクラック先端のひずみ

sider the fracture property of each materials under theは観測されずパルス波のみが観測さ
simulation it is necessary to determine the parameter λれたと考えられ長周期パルス波発生
hetoughness
KI andelastic moduli E, ν .
, E.,fracture
et. al., Nature
410 (2001),
68-71.
メカニズムは熊本地震と同じであると結論付けている。
J. Ceram. Soc. Japan
100 (1992), 1440-1443.

Fig.図
4 5

t. Jour. of Solids and 話題提供後、交流会参加者一同から現在取り組んでいる仕事、趣味および関心
Structures 163 (2019), 130-138.
事の紹介があり、参加者一同会して記念撮影した。

I