On the fatigue damage of standing wire ropes multiple step testing loading

16 PtT E2

ARCHIEF

PAPERS

OF

Lab.

y.

Scheepsbouwumk

Technische Hogeschool

DeIfL

No. 63

SHIP RESEARCH INSTITUTE

On the Fatigue Damage of Standing Wire Ropes Multiple

Step Testing Loading

By

Takahisa OTSURU, Jlisao IIAYASHI, Shoju OKADA, Yoshihisa TANAKA and Isao UENO

December 1980

Ship Research Institute

MULTIPLE STEP TESTING LOADING*

By

Takahisa OTSURU* Hisao HAYASHI* * *,

Yoshihisa TANAKA** and Jsao

* Received on August30, 1980.

** Oceanographical Engineering Diviion.

Oceanographical Engineering Division, Dead in October, 1979. Ship Structure Division.

Shoju OKADA**,

UENÓ****

SUMMARY

The authors have investigated applicability of the linear cumulative damage theories or Miner's rule to fàtigue of whe rope for these several years. In the present paper the authors refer to applicability of the rule to standing rope subjected to cyclic tensile load.

In fatigue tests the rope specimens of 20 ilim in diameter, 7X7

con-struction and 31.3 ton of breaking load, were subjected to sinusoidal wave formed cyclic load in _{a horizontal type 50 toñ long spañ low cycle fatigue}

testing machine where cyclic tensile stress level was varied in stepwise from two to four steps, in both step-up and step-down mañner. Test results were analysed by calculating the cumulative cycle ratio

Those test resúlts show that, strictly speaking, Miner's rule does Ììot hold for fatigue of standing rope, however, for the Purpose of design regu-lation the rule is fit for úse on condition that appropriate safety factor is taken into consideration.

L INTRODUCTION

Wire ropes for ocean development (hereinafter referred

_{to as rope or}

ropes) are generally classified into

_{running ropes which are simultaneously}

subjected to a primary bending stress and tensile stress at the same time,

and standing ropes which are mainly subjected to

_{a tensile stress}

_The

authors carried out systematic experiments

_{on the fatigue damage of}

running ropes under the two conditions; firstly, the static

_{tensile stress}

level is changed while keeping the repeated primary bending stress

con-stant, and, secondly, the repeated primary bending stress

_{is changed while}

keeping the static tensile stress level constant

The results of those

ex-periments were reported in the previous papers'

4)

No systematic research

on the fatigue damage resulting from stress variation in either running

or standing ropes has been reported in overseas countries

_{In the ex}

periment covered by this report, the cyclic tensile stress level in a stand

ing rope was varied in stepwise in both step-up and

_{step-down manner,}

2

were then reviewed to - see whether Miner's rule (the cornulative cycle

ratio method) can be applied to ropes or not

The cumulative cycle ratiO methöd is

;-Suppose that n1 cycles of stress is imposed on a specimen at a stress

level c where expected fatigue life is N1 based on S -

N curve.

Then,

fatigue damage can be expressed in terms of cycle ratio,

n1/N1, as D1 =

f(n1/N)

Likewise, n cycles of stress is imposed on another specimen at

another stress level, c, the fatigue damage is D1

=f(n1/N1)

It is assumed

that fatigue damages are the same if the cycle ratios are

the same

Then,

n1 = N1 njN1 is the conversion

formula from the damage at stress level i

to that of stress level o

Summing cycle ratios n1/N1 for all stress levels,

failure criterion is given as follows;

=1.

When the above rule holds, the fatigue life under multiple

step stress

repetition can be estimated

In many cases, however, results of

experi-ments have not confirmed the rule

In this experiment the authors tried

to clarify the adaptability of the rule to

repeated tensile fatigue of ropes.

2. METHOD OF THE EXPERIMENT

The fatigue test and static breaking test were conducte4 in a

hori-zOntal 50 ton long.span low cycle fatigue testing machine.

Fig. 1 outlines

the equipment used for the experiment, and Photo 1

shows its appearance

of this equipment

Load was picked up with a load cell and

elongation

was measured with a displacement gauge

Load and elongation were

recorded with an X Y recorder

Gauge points were marked on each end

of every specimen, and distance between these two gauge

points was

I

Cotheto Meter

Test Rope

Cometo Meter _x-Y

Recorder

Fig. 1. Schematic Drawing of Fatigue Testing Machine. Dato Recorder

CyLinder :!

Ii Hdrau1ic ControL Unit Uni t

Photo. 1. Testing Apparatus.

measuzed by using cathetometers, and then true elongation of the

rope

eliminated elongation of socketing metal could be measured.

The rope specimen was 20 mm in diameter, 1000

mm in length and of

7x7 construction. Table 1 shows the chemical composition of the wire

and Table 2 shows the static tensile test results of the

ropes.

In the

fatigue tests, cycling rate was 30 c.p.m. and load

wave form was sinusoidal.

The minimum load was consistently set at 1 ton, and the maximum load

was set at four levels; 10.0, 12.5, 15.0 and 17.5 ton, which correspond to

the maximum stress levels of

ci1, ci2, o and o, respectively.

The S N curve

was determined by single stage fatigue tests at the four levels. On the

basis of the SN curve, determined

were following programs of the

two-step, three-step and four-step tests which have both step-up and step-down

type of the loading;

Table 2. Static Tensile Test Results

Construe-tion Galvanize Lay

Rope diameter (mm) Breaking load (ton) Elon-gation (%) Tensile strength of elemental wire (kg/mm2) Standard Actual 7x7 _{no grease}Zn Ordinary (Z) 20 20.3 31.3 3.3 173

Table 1. Chemical Composition of Material

Material Chemical composition (%)

C Mn Si P S

C o 20 E o 10

for two step tests,

for three step tests añd

for four step tests.

p

_ail-A _C24O4

+

- - -,:1 -4 - --4

q2 __O34,_O4

--4

*- --4

01

23*r-°4

F'rom the above experiments, cycle ratio,

rtjN1,

at each stress level

and cumulative cycle ratio,

n1/N1, Was determined for each specimen..

3

EXPERIMENT RESULTS AND DISCUSSION

The basic SN curve is shown in Fig. 2

Thé abscisa indicates the

number of cycles to failure and the ordinate the maximum load of the

cycle

Babbitt metal (20% tin and 80% lead) was used for

both ends of

the specimen as a socketing metal

Failure of wire in socketing metal,

so called "failure at grips", which has

been one of the problems in this

type of experiment, was almost prevented and, accordingly, results of the

experiment show fairly small scatter.

Table 3 summarizes the results.

10 os

i0

Number of Cycles to FQiture (N)

Fig. 2. Stress Levels of Fatigue Tèsts and the Basic SN

Cüre.

Table 3. Stress Level o -and Broken Cycles N for Original SN Curve

i Wife hope 7x7 2Qmrn

Fre.05Hz

Mhimurn Lood i ton O Non pretersion eprétencr(32°/0U.TS) V

-'

.

(10.0 toñ) (12.5 ton) (15.0 ton) (17.5 ton)

u1=51. 8 c2=64.8 (13=77.7 (74=90.7

Ñ1=2,S94 Ñ2=82,89 N3=29,901 Ñ4 =15,547

o

I.

lo

a

o

J

o

J

15 o I-5

a

2

Ii

11LIiUl

o-i ff111

JlI

Ill

Îï:rt

11I1I

11:EE

l:9

IE1EII

i

mo O o' 0

.5

10 15 20 ELongation (mm)

Fig. 4. Histeresis Loops in a Step-down Test.

O, o2, o and a4 indicate each maximum load divided by the cross-sectional

area of the rope.

During experiments, "failure at grips" occurred in about

10% of the total specimens.

Deta of these 10% were entirely eliminated.

The fact that 90% of the specimens were broken at the middle part shows

that the present experiments were very successful as this type of fatigue

tests of wire ropes.

Examples of hysteresis loops recorded in the X Y recorder in terms

of elongation, on the abscissas, and load, on the ordinates, are shown in

Figs. 3 and 4.

Fig. 3 shows loops of a four step test of step-up type of

Cycim ltumber of brokene1eonta]. virem

16,000 2 20000 4 22,000 6 25,300 10 26,000 20 0 5 10 15 20 25 ELongation (mm)

6

loading (the specimen was subjected to n1

=

1/4 N1 cycles of stress at the

c level, n,

=

1/4 N, cycles at c, n,

=

1/4 N3 cycles at a3 and then cyclic

stress at ¿74

level until failrue,) and Fig. 4 that of a three step test of

step-down type of loading (the specimen was subjected to n,

=

1/3 N4 cycles

of stress at o. level, n3 =

1/3 N3 cycles at o, and then cyclic stress at a,

level until failure).

In those figures cyclic creep behaviour of the rope

is clearly observed.

Elongation at failure obtained from Figs. 3 and 4 are

2.2% and 1.8

%,

respectively. On the other hand, elongation at failure

measured with the aid of the cathetometers for eliminating elongation in

socketing metal were 1.6% and 1.2%, respectively.

Number of broken

wires indicated in the figures were counted visually.

In both cases,

elon-gation of the rope sharply increased just after the first failure of elemental

wire until the ropes were fractured completely.

Photo. 2 shows appearances of fractured specimen ropes.

No. i in

the picutre is an example of a specimen of which all strands fractured

at a time by static tensile load, and from No. 2 to No. 5 are

examples

of failure due to fatigue loading.

Photo. 2. Appearances of Fracture Ropes.

Photo. 3 is a microphotograph of the fracture surface of an

elemental

wire by the static tensile test indicating a typical cup-and-cone

shape.

Photo. 4 is an example of the fracture surface of an elemental

wire

resulting from 2-step 2-stage test (a4-a1) and shows that a crack initiated

in the plane of the maximum principal stress.

Tables 4 and 5 summarize the results of the multiple step fatigue

tests.

In these tables, the columns from left to right are the experiment

Photo. 3. Microphotograph of Fracture Surface of Elemental Wire by Static Tensile Load.

Photo. 4. Microphotograph of Fracture Surface of Elemental Wire by Fatigue Load.

at each stress level, and the cumulative cycle ratio.

If Miner's linear

cumulative damage rule holds, the value of the cumulative cycle ratio

should be unity,

njN. =

1.

When

nJN <1, fatigue damage at each

stress level occurs so that the life at the last stress level may be

shor-tened. When

n1/N1>1, the fatigue damage occurs to the contrary.

Figs. 5 a.nd 6 illustrate the test results.

The abscissa indicates the

cumulative cycle ratio and the ordinate indicates the stress level.

The

process of stress variation is also shown.

Fig. 5 is for the step-up tests

and Fig. 6 is for the step-down tests.

In the case of step-up tests,

njN

is larger than unity for all the two, three and four step tests. In the

case of step-down tests,

njN is generally smaller than unity.

However,

when n4/N4=O.25 in the two step test

(a4-i2) and n4/N4=n3/N4=n2/N2=O.1

in the four step test (a4-a3-a2-+a1), in other words, when ropes were

sub-jected to a relatively small number of cycles of high stress at the initial

s

Table 4. Results of Step4Jp Type Fatigue Tests 20mm, 7x7, B.L=31.3ton, A=193mm2

Table 5. Results of SteprDown Type Fatigue Tests 20mm, 7X1, B. L=31.3ton, A193 mm2

-Number of Stress Levéls

A O i D

4-an yce a los

Stress Level a1 (kg/mm2) and

Number of Cycles Cumulatiqe Cycle Ratio

n/N

a=51.8 fl_ c2=64.8 nl -ö3=77.7 na -a4=90.7 n4 1 2 6 7 12 2 n2/N2=0.25 20,717 .14,130 1.20 n1/N1=0.4 133,158 13,415 1.26 n1/N1=0.5 166,447 13,716 1.38

n/Ni=0.5

nilN2=0.75 62,152 4,115 1.01 n1/N1=n3/N2=0.33, 110,965 27,623 16,870 1.23 n2/N2=n3/N3=0.33 27,623 9,961 ni/Ni=na/Ni=n3/Ni=0.25 83,223 20,711 1,475 n1/N1=n2/N2mn3/N30.1 33,289 8,281 2,990 12,425 1.10

-No. Number of Stress Levels

_{and C ele R to}

_{y a i .s}

Stress Level a1 (kg/mm2) and

Numbér öf Cycles Cumulative Cycle Ratio n,jN, a4=90.7 n4 a3=77.7 n3 c=64.8 na a1=51.8 - n1 1 2 5 6 7 8

i

13 2 n4/N4=O.25 3,887 113,380 1.62 n4/N4=Ô;5 7,774 222,730 1.17

''7'

-n4/N4Ò.75 11,660 17,975 0.97 -n4/N4=ns/N2=0.33 . 5,182 9,987 29,531. 27,655 26,488 1.02 1.00 0.99 n3/N3=nilN2O 33 9 987 27,623 g 3,887

1,75

20,717 n4/N4=n3/N=n2/NaÖ.1 1,555 2,990 8,287 no ruPthe

10 b70 (n U) 90 50 90

E::

50-0.2 0.4 0.6 0.8 1 0 1.2 1.4 1.6 1.8 Cumuidtive Cycle Ratio E

fuN;

Fig. 5. Resülts f Step-up Fatigue Tests

100-L

L

I. 'I I i I I I -1

Ö.2 Ö.4 0.6 08 10 1.2 1.4 '. 1.6 1.8'

Cumulative Cycle Ratio E flu/N;

Fig. 6. Results of Stef,-dòwn Fatgüe Tests.

stage,

n1/N was 'much larger than tthity

As a followup an experiment

to certify the "break in effect of ropes" by pretension or over stress load

ing is now under way.

-.

2 levels -r-O 3 ----X 4 '-ó 2 leveLs

.-o

3 -,-X 4

lo

60

g

40

o

Cycle ratio (°I)

Fig. 7. Rèlation bet*een Cyclè Ratio in the Primary

Stage and Damage Rátio iñ the Primary

Stage D=ln2/N2;

Fig. 7 summarizes the results of the two step two stage tests at stress

levels o

and a

The abscissa indicates the cycle ratio in the pnmary

stage, n,/N1, and the ordinate indicates the damage in the primary stage,

D, expressed in terms of the cycle ratio in the secondary stage, n2/N2, as

follows; D = 1-- n2/N2.

In the case of step-up tests, all experiment points

were below the straight line

n1/N = 1, in other words, the fatigue

damage due to the primary stress was small.

hi the case of step-down

tests,

njN was smaller than unity, for n4/N4= Q.75 and 0.50.

However,

when n4/N4 = 0 25, the rate of damage was minus

This fact means that

the life of rope became longer than that of the virgiìi rope by virtue of

loading in the primary stage.

In other words, appropriate numbei of

cycl-ing of a certain over stress resulted in an increase in the life of the rope

As regards the itifluence of over-stress on fatigue life of rope, H. L.

Smith et al.5> conducted än experiment, using 6 X 19 IWRC ropes, in such

a manner that an over-stress was imposed at the first cycle and every

5000th cycle thereafter, and reported that the fatigue

life

generally

increased.

The authors have been conducting an experiment on the effect of

pre-tensile loading on fatigue life of the rope

The specification of the

rope tests is the same as that of the rope reported herein

Ropes 80 m

long cut from the same reel were subjected to a load of 10 ton, 40% of

the catalogue strength (32% of the actual breaking strength), 3 times for

30 min for every time, and then tested in fatigue, and also under static

load.

In the static breaking test, no effect of preloading was observed.

Fatigue test results with preload are shown in Fig. 2 with solid circles.

All the plotted points are located to the right of the basic SN curve

for virgin ropes, indicating that fatigue lives increased to 15-30% by

virture of pre-tensile loading.

4. CONCLUSION

The cumulative cycle ratio ratio

nJN, of the standing rope

subjected to multi-step repeated tensile load was larger than unity for

up type of loading, and smaller than unity, in most cases, for

step-down type of loading.

These results were different from those of running

rope which are subjected to multi-step tensile load while keeping primary

bending stress level constant.

It is likely that the difference resulted from

the difference in state of stress in state of stress in elemental wires

be-tween standing rope and running rope.

Study of this point is continuing.

In the case of step-down type of loading, the fatigue life of rope

increased when 55% of the breaking strength of the rope (u) was

repeat-edly imposed 10-25% of number of cycles to failure.

It is thought that

this fact resulted from the break-in effect on strands and elemental wires.

By pre-tensile loading of 40% of breaking strength, the fatigue

life of the rope increased to 15-30%.

Strictly speaking Miner's linear cumulative damage rule does not

hold for fatigue in standing ropes, in the case of either up or

step-down type of loading. However, for design purposes, Miner's rule will

fit for use, on condition that an appropriate safety factor is taken into

consideration.

REFERENCES

I. Ueno, T. Kawazura and S. Okada: Collected Papers for the 16th Meeting of the Ship Research Institute, 1970.

I. Ueno, T. Kawazura and S. Okada: Collected Papers for the 19th Meeting of the Ship Research Institute, 1972.

I. Ueno, T. Kawazura and S. Okada: Collected Papers for the 22th Meeting of the Ship Research Institute, 1973.

I. Ueno: Proc. of the 16th Japan Congress on Material Research, 1973. H. L. Smith, F. R. Stonesifer and E. R. Seibert: 10th O.T.C. 3256, 1978. F. R. Stonesifer and H. L. Smith: 11th O.T.C. 3419, 1979.

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