繰返し荷重を受けるコンクリートの損傷機構と力学的挙動に関する基礎的研究(梗概)

(1)

Lig.,,{},].,2

tOT",'.'.2i.gli.S.tE".eft"A'l}f"Nd.F,o,",7t'J".c.tLo.",?n,g,kn,eering

z",R,,ee##mk'Lm,as,lfft{L=$,

DAMAGE

MECHANISMS

AND

MECHANICAL

BEHAVIOUR

OF

CONCRETE

UNDER

CYCLIC

LOADS

by

HIROZO

MIHASHI"

and

MASANORI

IZUMI",

Members

of

A.

I.

J. lntroductjon

Concrete

is

undoubtedly one of

the

cemmonest and most

important

structural

materials.

In

spite

of

a

huge

amount of effort

to

study

its

strength

properties,

the

fracture

_process

and

the

mechanism of nonlinear

behavieur

under cyclic

loads

are

far

from

being

as

fully

understood as

those

fer

metals

and

_polymers

(Yoshimoto,

Ogino

and

Kawakami,

1972;Stroven,

1979;Weigler

and

Klausen,

1979).

Unfortunately

it

is

hardly

possible

to

observe

directly

the

cracking

inside

of

concrete

materials under

loads,

so

far.

Since

concrete

is

a

brittle

material with

a

very

heterogeneous

microstructure,

the

mechanical

pToperties

are

quite

different

from

those

of metallic mateTials.

Moreover,

the

mechanical

behaviourhighly

depends

on

the

experimental cendition such as

the

type

of

loacling,

the

temperature,

the

humidity

and so on.

Although

many researchers

have

studied

the

dynamic

fatigue

of

concrete

materials, most of

thern

use experimental approaches

tb

know

the

widely scattered relation

between

the

maximum

loacl

and

the

fatigue

life.

Recently

the

results of some experimental studies

_presented

the

deformation

_properties

of

concrete

materials under cyclic

loads

(Sparks

and

Menzies,

1973

;

Tokumitsu

and

Matsushita,

1979

;

Cornelissen

and

Timrners,

1981).

They

pointed

out

that

there

was a strong relation

between

the

fatigue

life

and

strain

rate,

Moreover

Cornelissen

and

Timmers

carried out

the

fatigue

test

under

tension-compression

cyclic

loads.

It

might

be

one of

the

most

important

findings

in

their

work

that

the

slope of

the

relatien

between

lnN

and

ln

_o

in

the

case of

tension-compression

cyclic

loads

is

about

twice

steeper

than

that

in

the

case

of

tension-tension

cyclic

loads

;

where

IV

is

the

mean value of

fatigue

life

and

_o

is

the

ratio of

the

maximum stress

to

the

strength,

The

micromechanism

of

fatigue

damage

and

deformation,

however,

is

still ambigous

and

there

are no

_generally

accepted

theoretical

models

to

describe

such a comprehensive

behaviour.

In

order

to

_predict

the

mechanical

behaviour

and

the

life

time

of

concrete

structure under cyclic

loads,

some

theoretical

model

based

on

the

fundamental

_properties

of

the

rnaterial should

be

developed.

Recently,

the

authors

have

_presented

a stochastic

theory

for

the

fatigue

of concrete

(Mihashi

and

Wittmann,

1980

;

Mihashi

and

Izumi,

1980),

The

non-fractuTe

_probability

P(N)

and

the

fatigue

life

N

were

_given

by

eq.

(

1 )

and

eq.{2) respectively,

P{N)=exp(-AafiN)-･--･･--･-･･････---･･･････-････････････-･･････-･･-･･-･･････'-''-･････････-･･-･･-･･--･･･････-･-･･･(1)

iKi'`=Al.n"''''"''-''"''"''"''''''''''''''''-''''-'-'''''''''''''''''''''-''''''''''''''m-'''''''''''''"''-'-''''-'''-''''(2)

These

theoretical

results were

in

_good

agreement with

_{publisheddata.}

They

have

also analyzed

the

experimental results

of

Cornelissen

and

Timmers

by

means

of

fracture

mechanics and

discussed

the

mechanism of

fatigue

_process

(Mihashi

and

Izumi,

_l984).

The

purpose

of

this

_paper

is

to

_present

an

theoretical

medel

to

link

the

_probable

mechanism of

fatigue

processes

of concrete

to

the

macroscopic

behaviour

undeT

cyclic

loads.

Probable

Mechanism

of

Fatigue

Proeess

Since

concrete

is

a

brittle

material with

the

extremely

heterogeneous

structure,

the

fractu[e

and

fatigue

properties

are

dominated

by

the

internal

structure.

The

fatigue

_process

may

be

subdivided

inte

three

stages

as

follows:1).

i

Ecole

Pelytechnique

Federal

de

Lausanne,

Labo.

Mat.

Construction,

Chemin

de

Bellerive

32,

CH-loo7

Lausanne,

Switzerland,

--

Tohoku

University,

Dept,

of

Architecture,

Sendai

980,

Manuscript

received

April

l,

1985

(2)

Crack

initiation

around

larger

aggregates,

being

arrested

by

the

neighbouring aggregates

;

2).

Damage

accumulation

in

the

matrix and

interfaces

;3),

Unstable

crack extension

to

cause

fracture.

The

first

stage

is

constituted

by

the

following

mechanism,

Stress

is

hightly

concentrated

in

the

vicinity

of

the

aggregates

and

there

is

a

_porous

and

weak system on

the

interface.

Accordingly

cracks

initiate

even under a

low

stress.

However,

these

cracks

immediately

come

across

ottier

aggregates

and

are arrested

by

them

because

of

high

toughness

of aggregates

(Fig.1).

On

the

other

hand,

the

matrix system

is

a comparatively

homogeneous

solid

but

a

kind

of composite materials

including

micropores.

Therefore

_the

damage

of

the

system

is

successively accumulated under a cyclic

load.

The

mechanism _of

the

damage

_was _studied

experimentally

by

Yoshimoto

and

his

co-workers

(197Z).

According

to

his

study,

the

damage

may

be

due

to

the

accumulation of microcracks

(boid-cracks)

in

the

_paste,

AfteJ

a certain amount of

the

accumulation of

damage,

the

fracture

toughness

of

the

matrix may

be

decreased.

As

the

result of

that,

thg

arrested cracks will

be

extended and mutually connected.

In

other words,

the

speimen

may

be

fractured

when

the

damage

on

the

second stage

is

aceumulated

enough

to

allow arrested cracks

to

_propagate

in

an unstable manner.

Therefore

the

fatigue

_life

may

be

closely related

to

the

rate of

the

damage

accumulation,

In

the

case of

tension-compression

cyclic

loads,

the

_possibility

to

transient

into

the

third

stage may

be

increased.

Because

the

vicinity of crack

tips

are

thrust

in

the

Mode

_]

and

Mode

M

under

compressive

loads

and

vertical

bond

cracks are also created

linking

the

horizo'ntal

tensile

cracks.

Deformation

due

,to

Crack

lnitiation

at

the

First

Stage

It

is

supposed

that

the

increase

of

deformation

in

stage

1 is

due

to

the

accumulation of mesocracking which

takes

place

in

succession

from

the

weakest region such as

interfaces.

According

to

the

elements

of

Linear

Fracture

Mechanics,

the

deformation

in

the

_y

direction

on

the

_point

P(x,

_y>

<Fig.

2)

is

given

by

eq.

(

3 )

in

the

case

of

_plane

straln.

'v==

2K6

_vlZIJ

sinl(x+i-2

cosg)･--･--･-･---･-･--･-･･-･--･---･-･---･-(3)

where x

is

equal

to

(3-4

v) and

G

is.

the

stiear modutus.

The

displacernent

on

the

center

of

the

crack

surface

:

T

is

t

obtained

from

eq.<3) as

follows:

le(1-v}

ac･--t---･---L-･-･---･---(4)

T=

±

G

The

strain

due

to

a single crack

initiation

may

be

clescribed

by

eq.

(

s

).

2Vi}'(1-.)

'

･

qc-･---k-""""'-H--"H"H"H"'"-"""""H'"'""'"'

5

eo=

aG

S[HEmaTI[

DESCRIPTION

OF

FAILURE

PROCESS

accuttu1

O

,

ef dama brtgewh.S

1iS

V

eggr stress stress

TENSILE

FRACTURE

cpeck

O

ttt..t

o'

stress

:,r:::t.,.

<

er

ka;

vi

wG4i

:

astress

eecumuletionfd g

hts,

kii

,

: i'b sttess

COMPRESSIVE

FRACTVRE

D'i"i'''

･=

_,,･ostress

Fig.

₁

Schernatic

Description

of

PTobable

Mechanlsm

of

Fatigue

Process

of

Concrete.

.-tttttttt-tttt-tttttt-t-tt-t-(

)

where

a

is

the

distance

between

marked

points.

Since

the

strain

is

caused

by

cracking,

the

increasing

rate of

the

strain may

be

_proportional

to

the

_probabitity

of

the

crack

initiati6n

:

Lafi

(Mihashi

and

Wittmann,

1980);L

is

a

_parameter

of

the

internal

structure and environmental

conditions.

Moreover,

the

magnitude of

the

strain may

be

controled

by

the

number

of

cracks

and

a

fi

y

P

{x,y)

'

V

r

e

x

o

v

---

2c

-y

U

a

(3)

Crack.-III-their

length.

The

number of

crack

initiation

may

be

dependent

on

the

non-fracture

_probability

which

decreases

as

the

number

of

loading

cycles:IV

inereases.

From

the

consideration mentioned above,

the

following

equations are obtained.

Ei==eoLtafiexp(-AiafiN)･-･-･･-･･･････--･･･-･･･-･････････-･････････-･-･････-r･･･--･-･t････-･･･-･･--･-･････-･････-･･･-(6>

Ei=E;lll'n-exp{-Aia"N}･･･････-･･･-･-･･･-･--･･････････-･･･-･･･････-''････--'H''''''H''H''H''H''-H'･-''-''"(7>

Deformation

Due

to

Damage

Accumulation

at

the

Second

Stage

After

most of weaker regions

highly

concentrated with stress release

the

strain energy

by

cracking,

the

damage

accumulation

_process

may

becomedominant.

The

strain rate

ef

the

damage

accumulationprocess

may

be

supposed

to

be

_given

by

eq.(8).

Et=hoills''''''-'''-'--''''''-'''''''"'''"'-'''--'''''''-'''H''-'''''''''H''''''H'''''''H''"''''''"'''''''''''H''-'''H'(8)

where

h,

is

a material censtant,

i

is

the

mean value of

the

strain

increase

_per

one

loading

cycle and

_#.

is

the

probability

to

cause

the

strain

increase

_per

one

loading

cycle.

Since

the

strain

increase'

is

due

to

microcracking

(boid-crack)

(Yoshimoto

et al.,

1972),

the

strain-increase-probability may

be

_proportional

to

the

micro-crack-initiatien-probability,

Provided

microcracking

is

a

kind

of rate

process

dependent

on stress, eq.

<

g

)

is

obtained

(YokoborL

l974;Mihashi

and

Wittmann,

1980).

p.oc

".

:LzaS

'"'''-''-'-'''-'-"'"-''-''"'''--,.-,--,,H,･,.,.,-,,.,.,,-,,"''",.-.'--,,.,.,.,,,.,--,,-.,--,.,(

9 )

where

_",

means

the

microcrack-initiation-probability under stress a;e

is

a material constant affected

by

the

temperature

and

the

humidity,

and a

is

the

maximum stress.

Substituting

eq.

(

9 )

into

eq.

(

8 ),

the

following

equation

are obtained.

E,=h,iL,ae･･-･･････････----･･-･･-･･-･--･･-････････-････････････-････････････-･--･･･-･･t････････････････-･･-････-････(lo)

et=koiLta"N"''''''""''"''-'''''''''''"'''-''"''''''t･-'･-･･'･････-･･････････････-･'･･'･･-･･-･･-･--･･･-･･-･--･-･(11)

Defermation

due

te

Unstabte

Crack

Propagation

Since

the

matrix

and

interfaces

are

damaged

with

the

accumulation

of

microcracks,

the

fracture

toughness

of

the

system may

be

decreased

after

the

second

stage.

According

to

fracture

mechanics,

the

catastrophic

fracture

occurs

when

the

fracture

mechanical

pararneter

such

as

the

fracture

toughness

reaches

a

certain

critical

value,

Since

the

stabil'ity of crack

_propagation

is

proportional

to

the

remained

teughne$s

Qf

the

system,

the

probability

for

the

system

to

reach

the

critical

condition

may

be

in

inverse

proportion

to

the

survival

probability

at

_the

secend

stage.

Supposing

that

the

unstable crack

length

is

_proportional

to

the

kth

_power

of

N,

the

following

equations are obtained.

2 V2(1

-

.*)

e3=

dG

aVMexp(Asa"N)=kiblVitexp(Aia"N)･-･･-････････････-･･････････-･･････-･"･････････-･･････C12)

e,=2V2i'

IG-

"') ai

(A,a"lv

lt+hN h")exp

(A,a"lv}-･-･･･-･''H''---'''-'''H''-''''''''H'--'''-'''''''-''H'-'--'H-''(13)

=hia(AsaSNk+hNk'i}exp(A,aSN)

Discussion

Since

the

strain rate and strain under cyclic

loads

are obtained as

the

summation of

those

on

three

stages,

the

following

equations are ebtained.

i:Il++Eii++ee'

,S+e.,

l'

''"'''

''"

''''-'''''

'''''-''-''

'''''H'''''-'''''''''''''-

'''H

'''''''

''

₍₁₄₎

where s.t means

the

elastic strain under

the

maximum stress.

The

fatigue

life

under

cyclic

loads

is

the

maximum stress

level

as

follows

from

eq.(2).

InN=-filnn+consL-･･･-･･･････--･･･-･･･-･･･--･--･-･-･･-･･･-･･-･--･･････-･-･･････--･･-･･･-･-･･･-･･-･･･--･--･･(15)

On

the

other

hand,

eq,(10)

is

rewritten as

follows:

ln

Et=ln

AelAN

=B

ln

_ij+consL

･･････････････････-･･-･･･-･･･-････-･･･-･･･-･･･-･･･････--･-････････-･･-･･････--･--･･･(16)

The

values

of

fi

calculated

from

the

experimental

results

by

Cornelissen

and

Timmers

are

as

follows

(Mihashi

and

Izumi,

1984):

fi=IZ.9

for

wet condition

fi=11.2

for

dry

condition

(4)

-112-e:e:l40

120w:.100･:

80se

60:'E

4oa

2o

10xmicrostrain

rnicrestrain

--

_e. E:

l40

120-XIOOtr.Edi

soLes2

6oo='E

40ben

20 O

O.2

O.4 .

0.6 ･

O.S

1.0 Nermalized

Cyclic

Number

:

NXN

(a)

Influence

of the

Hllmidity.

Fig.3

Theoretical

Re$ults

'

These

values are

_quite

close

to

those

obtained

from

a

Fig,3:

shows,some examples of

the

theoretically

mentioned

different

values of

B

for

the

di

fatigue

deformation

_properties

is

represented

in

Fig.3<a).

It

ef

10xmicrostrain

microstarin

O

O.2

O.4 Normal,ized

(b)

Influence

Fatigue

Process,

cyeli'cof

the

O.6

O.8 Number

:

N/N

Stress

Levet.

LO

completely

different

test

(Mihashi

and

Wittmann,

1980),

simulated results according

to

eq.(14), using

the

above

fferent

environmental

conditions.

The

influence

of

the'

humidity

on

the

is

simulated

that

the

shape ef

the

deformation

eurves seems

to

be

almost

same

but

the

wet

condition

causes a

larger

deformation

than

the

dTy

condition

for

the

same stress

level

:

o.

The

influence

of

the

stress

level

en

the

fatigue

deformation

_properties

can

be

also

described

by

this

model as shown

in

Fig.3(b),

It

is

well simuiated

that

a

larger

stress

level

_gives

a

lhrger

deformation

though

the

whole

fatigue

deformation

_prQperties

are not so much

changed

in

this

calculated

range.

These

theoretical

_predictiens

are

in

good

agreement with

the

experimental

data

published

by

Cornelissen

and

Timmers

(1981)

as

shown

in

Fig.

4. It

means

that

the

_present

theoretical

model

based

on

the

probable

mechanism can

_predict

reasonably

the

mechanical

behaviour

of concrete under cyclic

ioad$.

The

corresponding strain rates calculated

by

eq.

<14)

are also

shown

in

Fig.

3. These

changing

_processes

of strain rates are very

important

to

rnonitor

the

safety of

the

system

because

the

final

fatigue

life

is

dominated

by

the

unstable crack

_propagation

through

the

system.

According

te

these

theoretical

_predictions,

the

changing

behavieur

Qf

the

strain rate at

the

final

stage ef wet specimen

is

not so much sensitive as

microstrain ILO

120

100

80

=

'E

3 fio

en to ru

o

Fig.4

al

a2,

ol

oA

os

Noumalized･

Cyclic

Fatigue

Property

after

Timmersl}

ofi

e,7

o,s

os

to

Number

: NXN

Cornellssen

and

v-Lrv,-vU-aec=.zaben

logL,esec

-5

-6

-7

-E

-9

-IO

-11

Fig.5

(E

per

second)

presenttheory

'

sN1sl)

empiricalformula ]1odrying Ns

tensien-tensionosealed

tension-compressionAdrying

_hLx

O

l

₂₃₄

56

7 logi,N

Fntigue'Life

Relation

between

the

_Straia

_Rale

at

the

Second

Stag'e

and

FatigueLife

_{[ExperimeEtal}

Results

were obtained

by

(5)

that

of

dry

specimens.

The

behaviour

on

a

low

stress

level

is

also

not

sensitive

in

comparison

with

that

on

a

high

stress

level.

Therefore

the

target

to

be

controlled

should

be

very

carefully

fixed

when

the

system

is

monitored

by

the

unsensitive

_parametet

Comparing

eq.

{15)

with

eq.

(16),

the

following

relation

is

obtained.

InNoc-lnet-･---･･---･--･---･･----･---･---･---<17)

that

is

N=ipl,-i･･-･･-･･･-･･･････--･･･-･･-･･--･-････-･･･-･･-･･-････-･･･-･･･-･･--･･･-･･･-･･･-･･･-･･･････-･･-･･･--･-･･･-･････--･･(18)

where

e

is

arnaterial constant.

Therefore

it

is

expected

to

estimate

the

fatigue

life

by

monitoring

the

strain rate at

the

second stage.

The

comparison of eq.

(17)

with

the

experimental results

by

Cornelissen

and

Timmers

is

shown

in

Fig.s

and one can

find

the

_geod

agreement,

This

tendency

was also

_presented

for

the

compressive

fatigue

test

by

Sparks

and

Menzies

(1973).

Concluding

Remarks

In

order

to

investigate

the

mechanism

of

the

nonlinear mechanical

behaviour

of concrete under cyclic

loads,

the

fatigue

_process

should

be

subdivided

into

three

stages.

At

the

first

stage,

the

strain energy accumulated

by

the

locally

concentrated stress around

fatal

material

defects

such as

larger

aggregates and shrinkage cracks

is

easily released

by

rnesocracking.

However,

these

cracks are

arrested

by

other

aggregates

or with

the

change

of

the

stress

field

at

the

crack

tip.

The

crack

initiation

_process

occurs successively

throughout

the

specimen and continues until

the

saturated stable condition,

The

strain

is

widely scattered

because

the

crack

initiation

and arrest

process

is

highly

influenced

by

the

_geometric

_properties

and arrangement

of

aggregates.

Undoutedly

it

is

necessary

_to

study

theoretically

the

cracking

_process

at

the

first

stage

by

means of computer simulation

in

a random media with compesite structures.

At

the

second stage, microcracks

(boid-cracks)

initiate

in

the

rnatrix

becau$e

of

the

heterogeneity

in

the

matrix

itself.

Since

these

cracks are

_gradually

accumulated

in

the

matrix.

the

fatigue

_proeess

at

the

second

stage

may

be

supposed

to

be

a

kind

of rate

_process

dependent

on stress.

Therefore

the

strain

rate may

be

_preportional

to

_L,afi.

The

fatigue

process

at

the

third

stage may

be

due

to

the

extension of a critical crack which

links

mesocracks occurred on

the

first

stage.

Since

the

stress

intensity

factor

increases

with

the

crack extension,

the

most critical crack

extension

may

dominate

the

rnechanical

behaviour.

Since

the

fatigue

life

may

be

in

inverse

_proportion

to

the

strain rate of

the

second stage,

it

will

be

_possible

to

predict

the

fatigue

life

by

monitoring

the

strain rate at

the

second stage.

Acknowledgement

The

authors are very

_grateful

to

Dr,

Cornelissen

at

Delft

University

of

Technology

in

the

Netherlands

for

offering

the

results of

his

experimental research about

the

fatigue

of

_plain

concrete.

Reterences

1)

CoTnelis$en,

H.A.W.

and

G. Timmers.

{1981),

Fatigue

of

PLain

Concrete

in

Uniaxial

Tension

and

in

Alternating

Tensien-Cornpression

Experiment

and

Results,

Stevin

Report

5-81-7,

Detfle

Uhitersity

of

7lechnoftrg),,

Dqpt,

of

Cien'l

Engineering;

7VLe

Nbtherlands.

2)

Mihashi,

H.

and

M. Izumi.

"980).

A

Stochastic

Theory

ferFatigue

FTacture

of

ConcTete,

Thansactiens

of

the.rtipan

Concrete

lhstitute,

Z,

203-210.

･

3)

Mihashi,

H.

and

F.

H. Wittmann.

(19so).

Stochastlc

Approach

to

Study

the

Influence

of

Rate

of

Loading

on

Strength

of

Concrete,

fferon,

zs,

3 4)

Miha$hi,

H.

and

M. Izurni.

(1984).

Deformation

and

Fracture

of

Concrete

under

Cyclic

Loads,

Theeretical

and

ApPlial

haha,iies,

Edt.

by

Japan

National

Committee

for

Theoretical

and

Applied

Mechanics

ScienCe

Council

ofJapan,

University

of

Tokyo

Press,

445-452.

5)

Sparks.

P.R.

and

J.B.

Menzies,

(]973}.

The

Effect

of

Rate

of

Loading

upen

the

Static

and

Fatigue

Strengtli

of

Plain

Concrete

in

Compressien,

Mlag

of

Cbncrete

Research

25,

83,

73-80.

6)

Stroven,

P.,

(1979).

Microeracking

in

_Cencrete

_Subjected

to

Fatigue

Loading,

Ptec,

77}ird

int.

CbnfZ

on

ndechandeal

Behambur

of

Materials,

Cantbridge,

Englanct

3,

141-150.

7)

Tokifmitsu,

Y.

andH.

Mats"shita.

(1979).

Fatigue

Strength

ofPlain

Concrete

under

RepeatedLeading,

thncTeteJburnal,

17,

6,

13-ZZ,

(in

Japanese).

8)

Weigler,

H.

and

D,

Klausen,

(1979).

Fatigue

Behaviour

of

Concrete--Effect

ef

Loading

in

the

Fatigrte

Strength

Range,

BETOATZVZERK+EERTTGI:ELL-TECEUVIK,

4,

214-z2o.

9)

Yokoberi.

T. _{1974),

An

intercEsciplinary

Apmaach

te

FVzrcture

and

Strength

of

bolids,

Iwanarni

Book

Co.,

Cin

Japanese)

(6)

lo)

Yoshimoto,

A.

,

S. Ogino

and

M. Kawakami.

(1972).

Microcracking

Effect

on

Flexural

Strength

of

Concrete

Aftei

Repeated

Loading,

Jbu,mal

ofAmen'can

Concrete

institute,

69,

233-240.

'

Appendix

The

foMowing

notations are used

in

the

present

paper.

A

:

Parameter

to

describe

the environmental condition and alFo

the

frequency

of

the

cyclic

load

(see

Mihashi

and

Wittmann,

･

1980).

Ai,AhA3:the

value ofAat the

ith

stage.

･

a:distance

between

marked

peints,

2c:craek

length.

2i

:

the

initial

yalue of

the

_.equivalent

crack

length

in

the cTitical condition.

G:shearing

modulus.

'

Ki:stress

intensity

factor.

h,ko,ki:material,constants.

･

L

:

_parameter

of the

internal

structure of

the

specimen and

the

environrnental conditien,

L,.L,

:

the

value of

_L

at

the

ith

stage.

'

N:nu'rnber

of

loading

cycles.

1if:the

expected

fatigue

life,

i.e,

the mean value of

the

numbeT of

]oading

cycles

te

collapse

the

specimen.

AN:increment

of

the

cyclic number of

the

toad.

P(N):non-fracture

probability.

i.e.

the

_probability

that

the specimen stiilsuivives afte[

N

cycles of the

lotid.

v:displacement

in

the

_y

direction

on a certain

_point

(x,

_y)

around a crack.

T:displaeement

on

the

center ef

the

crack surface.

P

:

material constant as a

functien

of

the

enyironmental

temperature

and

hurnidity.

i:the

rnean value of the stram increment

_per

ene

loading

cycLe at

the

second stage

(damage

accllmulation

_process).

ee

:

stra･in

due

to

a single crack

initiation.

et,ei,es:strain

due

te

the

mechanism at

the

ith

stage.

'

e,.EhE

:

strain rate

due

to the mecltanism at

the

ith

stage. e.i

:

elastic strain under the maximum stress.

Ae

:

stlain

increment.

n:ratio

of

the

maxirnurn stress to the strength.

k

:

material constant

(=3-4

v}

#.

:

probability

of microcrack

initiation.

".:probability

te

cau$e

the

strain

increase

_per

one

loading

cycle,

v

:

Poisson's

ratio.

v*

:

apparent

Poisson'$

ratio o.fthe

damaged,

system.

a:the maximum stress of

the

cyclic

load.

(7)

【

論

　

文

1

UDC ：

691 ．

32

日本建築学会構造系謚文報告集第

359

号

・

昭和

60

年 1 月

繰

返

し

荷

重

を

受

ける

コ

ン

ク

リ

ー

ト

の

損

傷機構

と

　　

力学

的

挙動

に

関す

る

基礎的研究（

梗

概

）

　

コンクリ

ー

トは

_最

も

重

要

な

構造材料

の

一

つであり

，

繰

返

し

荷

重

の

_作

用

を

受

けるのが

通例

で

あ

る。

最大荷

重

と

疲

労

寿命

の

関係

については

数多

くの

実験的研

究

によって

長

い問

研究

されているが

，

繰返

し

荷

重による

損傷機構

あるいは

損傷過程

については

未解明

な

部分

がほとんどと

言

えるのが

現状

で

あ

る。

　

本論文

は_，

疲労損傷

のメカニ

ズ

ムを

考察

し

，

その

損傷

過程を表現

し

得

る

理論

モ

デ

ル

を構築

するための

一

つの

_考

え

方を示

そう

と

する

も

ので

あ

る

。

疲労損

傷

過程

を

3

つの

段階

に分

類

して_，

各段階

の

損傷機構

を

破壊

力

学

的視

点

から

考察

する

。

さらに

損傷

モデルに

基

づいた

変

形

理

論

曲

線

を求

め

，

実験結果

と

比

較検討

する

。

　 3

つに

分類

された損傷過程の第

1

段階は

，

クラック

発

生過程

であり，

大

きな

粗

骨

材

や

乾燥収縮

クラックまわりに

生

じた局

所集中応力

によって

蓄

えられたひ

ず

みエ

ネ

ルギ

ー

は

，

ボンドクラックやモルタルクラック

等

のメ

ゾ

レベルのクラック

発生

によって

容易

に

解

放される

。

しかしながら，これらのクラックは

周囲

の

骨

材

や

応力

場

の

変化

によって

伝播を阻止

される

。

このクラック

発生

過

程

は

，

゜ _ス_イ_ス_{運邦工科大学}_ロ

ー

_ザ_{ンヌ}_{校構造材料研究所}

・

_工_博＊＊東北大学

　

教

授

・

工

博

　（昭和 60 年 4 月

1

日原稿受理｝正会員正会員

　和

橋

泉

博

正

三

＊

哲

＊＊

供試体内

の至る

所

で次々と起り局

所的

に

集中

した

高

ひ

ず

みエ

_ネ

ル

ギ

ー

が

解放

される必

要

のなくなるまで

続

く

。

この

段階

のひ

ず

みは

，

その

原因と

なるクラックの

発生

お

よ

び

伝播阻

止過程が粗骨

材

の

幾何学的形状

や

配置

に

強

く

依

存

するために

大

きなバラツ

キ

を

示

す。

　

第

2 段階

においては_，マ

トリ

ックス

部分自身

の

非均質

性

のためにセメントペ

ー

スト

内

に

微細

クラック

（

ボ

イド

クラック

〉

が

生

じる。これらの

微細

クラックはマトリックス

内

にゆっくりと

累

積

されるので

，

第 2

段階

における

疲労損傷過程

は

一

種の応力依存型

速度

過程と

考

えられる。したがって

第

2 段階

のひ

ず

み

速度

は

L2

σ β に比

例

する

も

のと

考

えられる。

　

第

3

段階における

疲

労

損傷

過

程

は

，

第

1 段階

で

発生

したポンドクラックやモルタルクラックを連

結

するクラックの

伸展

に

よ

る

も

の

と考

えられる。クラック

先端

における

応力拡大係数

は

，

クラックの

伸

展

とともに

増大

するので

主要

なクラックの伸展が第

3

段階の

力

学

的挙動

を

支配

す

る。

　

疲労寿命

は

，

第

2 段階

におけるひ

ず

み

速

度

に

反比例

するものと

思

われるので

，

_{第 2 段階}

におけるひ

ず

み

速度を

モニタ

ー

する

事

によって

疲労寿命を予測

する

事

が

可

能

と

考

えられる