Journal of Structural Engineering Vol. 67A (March 2021) JSCE

Investigation on low cycle fatigue crack propagation in steel

under fully random variable amplitude loading

Arief Panjaitan*, Kazuo Tateishi†, Masaru Shimizu**, Takeshi Hanji**

*Doctoral Course Student, Dept. of Civil Eng., Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603 †,** Dr. of Eng., Dept. of Civil Eng., Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603

Low cycle fatigue is a failure mode which is possibly caused by random large strains such as

seismic motion. To examine the effects, this study elaborated crack propagation behavior in

steel under random amplitude loading. Firstly, study on crack growth rate under constant

amplitude conditions was conducted to obtain basic characteristics. Next, several patterns of

random amplitude loading were applied. It is discovered that crack growth accelerated when

amplitude decreased from high to low levels at tensile portions, compared to that in constant

amplitude conditions. Prediction model was constructed with establishing relationship

between cyclic J-integral range and crack growth rate and confirmed to give good estimation.

Keywords: low cycle fatigue, random variable amplitude loading, crack growth rate, cyclic

J-integral range.

1. INTRODUCTION

Low cycle fatigue (LCF) crack is a typical crack which

propagates under a small number of loading repetitions.

Murakami et al.1) identified that crack initiation life of LCF is very

small and most of total life is spent in crack propagation phase.

Correspondingly, crack propagation life should be accurately

estimated for preventing LCF failure.

Random large plastic strain experiences amplitude

changeability from high to low or low to high levels, but number

of studies evaluating the effects of those amplitude alterations to

the crack growth are very limited. In high cycle fatigue (HCF),

several studies have been undertaken to evaluate crack

propagation behavior when one or more overloads were put in

steady cycles2,3). These studies confirmed that crack growth rates

of steady cycles behind overload were less than constant cycles

without overload.

Past studies4,5) also revealed crack propagation behavior from

hole in tubular specimens subjected to cyclic torsional loading

and identified that cyclic J-integral was an appropriate parameter

to estimate crack growth.

At the past study, low cycle fatigue crack behavior in steel

under multiaxial loading was also investigated6). Examinations

were done with developing correlation between two LCF life

values from experiment and analytical study. Equivalent strain

parameter resulted from analytical study was confirmed to give

good estimation indicated by fatigue life distributed within narrow

band in relationship of estimated-experimental fatigue life.

At the past research work, Tateishi and Hanji7) introduced low

cycle fatigue strength curves for plain steel material, deposit metal

and heat affected zone (HAZ), which were based on local strain

amplitude at a cracking point. Accordingly, relationships between

local strain amplitude and LCF life were presented in this study.

Dong et al.8) tested CT specimen made of Q345 steel under

constant amplitude conditions and discovered linear relationship

between crack growth rate and the cyclic crack tip opening

displacement (ΔCTOD).

Morrisey et al.9) investigated influence of frequency and stress

ratio in HCF. The test showed that the fatigue life increases with

increasing frequency at low stress ratio. As stress ratio is increased,

this trend keep continues at high frequency but this frequency

effect was gradually dissappeared at the lower frequencies.

Shahani et al.10) evaluated fatigue crack growth rate behavior

under variable stress ratio and proposed four prediction models

that contained some parameters, i.e., cyclic J-integral, crack tip

opening displacement, crack mouth opening displacement and

stress intensity factor, to estimate crack growth rate.

Dougherty et al.11) established a finite element model for

simulating plasticity induced crack closure. Stationary crack and

propagating finite element models assumed in FE models revealed

† Corresponding author

E-mail: tateishi@civil.nagoya-u.ac.jp

-174-

that plasticity-induced crack closure produces a significant amount

of crack tip shielding and reduced the strain range experienced at

the crack tip due to closure effects.

Gonzales-Herrera and Zapatero12) evaluated CT alumunium

specimen model tri-dimensionally with considering different

specimen thickness and stress range. This study discovered that

crack closure and crack opening mechanism caused abrupt

transition contour of deformation at the external side of the crack

tip on the specimen slice model. This contour area was identified

has similar size with other specimen regardless the thickness.

Relied on this study, in 2D model, this significant abruption can

not be identified.

Terao et al.13,14) tested CT specimen made of steel and deposit

metal under constant amplitude conditions and examined crack

propagation rate. Besides, the difference of cyclic mean

displacement was also considered. This study demonstrated good

relationship between crack growth rate and cyclic J-integral range.

Hanji et al.15) examined LCF crack propagation rate tendency

under constant amplitude loading and established estimation

model by acknowledging cyclic J-integral range (ΔJ) parameter.

This study also utilized ΔJ to reveal crack growth behavior in a

corner welded joints.

In this study, evaluation was firstly conducted on crack growth

under constant amplitude conditions to obtain rigorous formula to

estimate crack propagation. Next, crack growth rates under

random loading particularly when the amplitudes at the tensile

portions were changed, were evaluated to provide prediction

model.

2. EXPERIMENTAL PROGRAM

This study tested compact tension (CT) specimen as shown in

Fig.1. The dimension was established referring to ASTM Standard

E1820-03116) and mechanical properties obtained from mill sheet

are shown in Table 1. At the both sides of specimen, sides grooves

were introduced to ensure the crack propagation path as straight as

possible.

In experiment, each specimen was loaded under displacement

control. Five test specimens were prepared for the test where one

specimen was subjected to one test case. To measure crack tip

opening displacement (CTOD) in each cycle, a clip gauge was

installed to the specimen. The test set up is shown in Fig.2(a). In

the test, loading speed ranged from 0.001 to 0.05 mm/s was

applied. Crack propagation was observed at each peak cycle by a

high-resolution microscope as shown in Fig.2(b). The loading was

continued until crack propagation performed insignificant rate. In

this study, crack propagation rate is defined as the difference

between crack length at the observed cycle to crack length at the

one cycle previously.

The test employed tw o loading history types, i.e., constant and

random variable amplitude loadings. Detail information of the

loading schematics will be described later in each chapter.

(a) Specimen

(b) Detail of side groove

Fig. 1 Specimen (unit: mm)

Table 1 Mechanical properties of steel

Steel

type

Yield

stress

(N/mm2)

Tensile

strength

(N/mm2)

Elongation

(%)

SS400 296 431 32

(a) Test set up

(b) Digital image of crack

Fig. 2 Testing program and the observation

-175-

3. FINITE ELEMENT ANALYSIS

Finite element analysis (FEA) was utilized to compute cyclic

J-integral range (ΔJ). Theoretically, ΔJ (N/mm) is defined as :

∆𝐽 = ∫ (𝑊′𝑑𝑦 − ∆𝑇𝜕∆𝑢

𝜕𝑥𝑑𝑠)

𝛤

𝑊′ = ∫ ∆𝜎𝑖𝑗 . 𝑑∆𝜀𝑖𝑗

∆𝜀𝑖𝑗

0

where W’ is the range of strain energy density, ΔT is the range of

traction vector, Δu, ∆σij, and Δεij are the ranges of displacement

vector, stress, and strain in the loading process, respectively.

Fig.3 shows a quarter of specimen modelled in FE. This model

was established with symmetric supports assigned at the thickness

center (XY-plane). Table 1 expresses the material model where

kinematic hardening rule based on true stress strain with Et/E

=0.0034 (E and Et are the first slope initial elastic and the second

slope of plastic phase), was applied.

Prior to the loading employment, several FE models with

different crack lengths, 8 to 56 mm, at 8 mm intervals were initially

provided. Fig. 3 examples 3D-specimen model with 8 mm-long

crack. In this figure, rigid connection was assigned to connect the

loading point and the specimen. Next, the cyclic loading was

applied to the pin center. Analysis by Abaqus standard module

was performed until 1.5 cycles to obtain the ΔJ. The crack closure

was ensured with arranging rigid contact elements and locating

them below the model.

Fluctuation ranging from the minimum to the maximum load

in loading process was utilized to compute the ΔJ, as shown in

Fig.4. The figure also describes the different loading portions to

compute ΔJ. Fig. 4(a) outlines the loading process from 0-CTOD

to tensile-CTOD and Fig. 4(b) illustrates the process from

compressive-CTOD to tensile-CTOD. The loading processes

presented in such figures were utilized to calculate ΔJ at the

different averages of CTOD.

At the past research work, the ΔJ independency to the

integration paths and loading cycles was clarified by Panjaitan et

al.17). Such study tested specimens which is identical to this present

study’s specimen, under the LCF constant amplitude loading. The

test discovered un-obvious differences of ΔJ value regardless the

integration paths and loading cycles which were addressed to the

independency of ΔJ. Since the equivalency of ΔJs had been

proven on the considered paths and loading cycles, to ensure

reliability of the results, 6th-integration path at 1.0 to 1.5-loading

cycle was chosen to compute the ΔJ in this present study.

Fig.5 examples an integration path for an 8 mm-long crack to

compute ΔJ. For other crack lengths, the similar rectangle path to

that for 8 mm-long crack was taken out and then placed at to the

designated tip position with the same path arrangement.

Fixed crack length (ranging from 8 to 56 mm) and fixed

constant CTOD (ranging from -1.5 to 2.5 mm) were considered to

compute the ΔJ. At the following steps, the ΔJ was characterized

by linearly interpolating from two nearest points of the crack

length. Fig.6 depicts the results in which ΔJs perform declining

manner with the increasing crack length due to displacement-

(1)

(2)

Fig. 3 3D-specimen model with 8 mm-long crack (unit: mm)

(a) 0-CTOD to tensile CTOD

(b) Compressive-CTOD to tensile-CTOD

Fig. 4 Fluctuation range where ΔJ was defined

Cyclic Displacement

Crack

surface

Ligament

Side groove

X

Y

Crack surface Ligament

Crack tip

Rigid contact element

X Y

Rigid connection between pin

center and CT specimen

8

0.5

1.0

Sym. supports

-176-

controlled conditions.

4. CONSTANT AMPLITUDE LOADING (CA)

In this schematics, two CTODs were applied, CA-1 and CA-

2, with the maximum CTODs were 1.0 mm and 0.5 mm,

respectively and the minimum CTOD was set to be 0 mm.

Fig.7 clarified the accuracy of the analysis to interpret the test

results with comparing load-CTOD relationships. In such figures,

several crack lengths, i.e., 0, 10, 20 mm, were employed to confirm

the validity of the analysis since those crack lengths were also

presented from the experiment. CA-1 for 1.5 cycles was then

simulated to the specimen model and the analysis’s load-CTOD

was verified to the test result at the same crack length. As shown

in Fig. 7, the good agreement between analysis and test result is

indicated in which the maximum and the minimum loading point

are almost equivalent even though the closure is unidentified in

analysis. Since the ΔJ was principally computed from minimum

to the maximum loading point for considered loading cycle, the

closure effect at the unloading can be considered to be negligible.

Fig.8 shows cumulative plots of the relationship between crack

growth rate and ΔJ obtained in this study and the past study15). It is

noticed the crack growth rates are distributed within narrow band.

Regression line then is constructed to describe crack growth rate

and ΔJ relationship as:

𝑑𝑎

𝑑𝑁= 1.74 × 10−6. ∆𝐽2.00

The Eq.(3) is applied in random amplitude loading and its

(a) 0 mm-long crack

(b) 10 mm-long crack

(c) 20 mm-long crack

Fig. 7 Comparison of load-CTOD hysteresis loop

Fig. 8 ΔJ-crack growth rate relationships under

constant amplitude loadings

Fig. 5 Example of integration path for 8 mm-long crack (unit:

mm)

Fig. 6 ΔJ-crack length relationships

(3)

-177-

utilization will be explained later in the next chapter.

5. RANDOM VARIABLE AMPLITUDE LOADING (RA)

5.1 CTOD Amplitudes in RA

The CTOD amplitudes were obtained by arranging each peak

CTOD in range within 0 to 300-level, in which 0-levels refers to

minimum CTOD and 300-level is addressed to maximum CTOD.

5.2 Load Cases

Three different maximum to minimum range of CTOD are

applied: RA-1, RA-2, and RA-3, with range values of 0.5 to 1.5

mm, 0.5 to 2.0 mm, and -1.5 to 2.5 mm for random amplitude

loadings, as shown in Fig.9. All CTOD amplitudes are un-

repetitive to obtain characteristics of fully random. The RA-1 and

RA-2 are employed to provide loading histories with different

maximum to minimum range of CTOD. Both have positive

maximum CTODs and 0 mm-minimum CTODs. In the RA-3, the

maximum CTODs are positive and the minimum CTOD are

negative to provide a loading history with a different average of

CTOD. Besides, the RA-3 is also a random loading with the

largest maximum to minimum range of CTOD than that of RA-1

and RA-2.

5.3 Crack Propagation Behavior

Crack propagation behaviors under RA are illustrated in Fig.

10. The figure indicates that RA experiences faster crack

propagation correlated to the larger maximum to minimum range

of CTOD rather than average of CTOD. As shown in figure, under

RA-3, the crack grows at the fastest than that under RA-1 and RA-

2, which is indicated by longest crack length that it achieves than

that under RA-1 and RA-2, at the same number of cycles.

In this present study, it is supposed that the crack growth rate

(a) RA-1

(b) RA-2

`

(c) RA-3

Fig. 9 Loading patterns of random variable amplitude

-178-

is governed by a combination between the previous and the current

loading amplitudes. Therefore, a new parameter of ΔJ ratio,

ΔJi/ΔJi-1, which is the ratio of ΔJ for an observed cycle to ΔJ at one

cycle before the observed cycle, is introduced.

Fig.11 shows relationships between the crack growth rate and

the ΔJ under random variable amplitude loading where the

relationships are individually presented for the ΔJ ratio equal to or

larger than 1.0 and for the ΔJ ratio less than 1.0. The test result

obtained at the ΔJ ratio higher than 1.0 express a similar pattern to

those observed under constant amplitude loadings for all cases of

random amplitudes loading as shown in Fig.11(a). In figure, the

variation in crack growth rates is indicated in which it may come

from material constant, dimensions, test set-up, crack

measurement error and estimation error. To confirm the possible

variation, acceptable region is calculated from test results of

constant amplitude loading and described as (-2D to +2D, D:

standard deviation) in Fig.11. In Fig.11(a), the random loading

plots are located in -2D to 2D band. Therefore, the variation of

crack growth rate for ΔJ ratio higher than 1.0 was considered

similar with the case of constant amplitude loading. On the

contrary, as shown in Fig.11(b), at the ΔJ ratio less than 1.0, crack

growth rate performs a trend which is remarkably different than

that in constant amplitude loadings. Most of the test results are

distributed above the regression curve, particularly in the relatively

high ΔJ region. Thus, utilization of constant amplitude regression

curve results a smaller estimation for the crack growth rate when

the amplitudes are reduced from high to low levels. Besides, Fig.

11(b) also expresses that several plots are also located out of the

domain of standard deviation (-2D to +2D) in which it means the

variation is not equivalent to that under constant amplitude loading.

The phenomenon observed in Fig.11(a) is supposed to be

caused by insignificant contribution of plastic zone at the end of

low amplitude loading employment. When the amplitude is

increased for the following step, remained plastic zone which is

presumed smaller than that under high amplitude leads to give

equivalent crack growth manner to that under constant amplitude

conditions. The specimen behavior illustrated in Fig.11(b) is

highly expected by the remained plasticity area at the end of high

amplitude loading employment. In such process, a drop of the

amplitude is supposed to leave wider plastic zone than that under

low amplitude. Accordingly, that wider plasticity area is possible

to accelerate the crack growth. Those two phenomena are

hypothetically provided and need to be clarified for the future

research work.

5.4 Amplification Factor

In order to simulate accelerated crack growth behavior due to

variable amplitude loadings application such as random loading, a

correction factor named ‘amplification factor (AF)’ is introduced

in this study. The AF is defined as the ratio of crack growth rate

under variable amplitude to constant amplitude loading as:

(a) ΔJ ratio ≥ 1

(b) ΔJ ratio < 1

Fig. 11 ΔJ-crack growth rate relationships under constant and

random amplitude loadings

Fig. 10 Crack propagation rate behavior under random variable

amplitude loadings

-179-

AF =(𝑑𝑎 𝑑𝑁⁄ )

𝑣𝑎𝑟

(𝑑𝑎 𝑑𝑁⁄ )𝑐𝑜𝑛𝑠𝑡

where (da/dN)var is the crack growth rate under variable amplitude

loading, (da/dN)const is the crack growth rate obtained from the

regression curve presented in Eq. (3).

The AFs were noticeably to be influenced by the ΔJ ratio.

Hence, relationship between AF and ΔJ ratio are presented in

Fig.12. When the amplitude increases from low to high level, the

AF is almost 1.0 constantly as shown in Fig.11(a). This means that

the effect can be disregarded when the ΔJ ratio is larger than 1.0.

On the contrary, as shown in Fig.12(b), when the amplitude is

reduced from high to low level, AF tends to increase with the

decrease of the ΔJ ratio. The figure also indicates that the AFs are

widely scattered even though the ΔJ ratios are nearly equal.

Therefore, not only the ΔJ ratio but other parameter, such as an

absolute ΔJ, is required to estimate the AF.

Based on the relationships between AF and ΔJ ratio, a formula

to estimate the AF is introduced as follows:

AF =

{

(787

𝛥𝐽𝑖)0.4

+ 1.8 (1 −∆𝐽𝑖∆𝐽𝑖−1

)2.5

+ 0.5…Δ𝐽𝑖

Δ𝐽𝑖−1

< 1

1.0 …Δ𝐽𝑖

Δ𝐽𝑖−1

≥ 1

where ΔJi is the ΔJ at the current cycle (N/mm) and ΔJi /ΔJi-1 is the

ΔJ ratio.

Estimated AF for the ΔJ ratio larger than 1.0 is 1.0 constantly

as shown in Fig. 12(a). Estimated AF for the ΔJ ratio less than 1.0

is evaluated from Fig.12(b). Two parameters, absolute ΔJ and ΔJ

ratio are involved in this estimation model. The power equation is

selected as the estimation formula for ΔJ ratio less than 1.0 to avoid

the value equal to zero or negative in the AFs. In such process, by

conducting regression analysis relied on AFs scatter, the

coefficients for ΔJ ratio and ΔJ in Eq.(5) are obtained.

Accordingly, the power for each parameter is firstly

determined and by employing regression the coefficients

then are solved. However, the estimated AF for the ΔJ ratio

less than 1.0 is only matched with the test although the unit is

different.

Validity of the Eq. (5) was confirmed with providing

comparison of the crack growth rate as expressed in Fig.13.

This figure describes the test results in vertical axis and

estimation by the regression line in Eq. (3) and the AF in

Eq. (5) in its horizontal axis. In figure, the regression line

is established with involving quite wide range of high

crack propagation rates (distributed over than 1.2

mm/cycle), so that the proposed AF may lead to contribute

a small difference of estimation results in crack

(a) ΔJ ratio ≥ 1

(b) ΔJ ratio < 1

Fig. 12 AF-ΔJ ratio relationships under random amplitude

loadings

Fig. 13 Crack growth rate comparison between test result and

estimated value (unit: mm/cycle)

(4)

(5)

-180-

propagation, particularly at high crack growth rate region.

As shown in Fig. 13, the estimation accuracy of crack

growth rate expresses variation. Meanwhile, number of

repetitions is relatively small in the data with large

estimation error. Then the crack length can be estimated

accurately as shown in Fig. 15, even if there are these

variations.

5.5 Crack Propagation Analysis

The crack propagation analyses are carried out with presenting

the relationships between the crack length and number of cycles

for all random loading cases as shown in Fig.14. In the figures, an

estimation curve disregarding the AF is drawn together. It can be

obtained that the disregard estimates shorter crack length.

Meanwhile, the consideration of the AF can drastically improve

the accuracy, and, the crack length curves indicate very close

pattern to the test results.

As shown in Fig. 12 and Fig. 13, the estimation accuracy of

AF and crack growth rate shows variation. In addition, as

described in section 5.3, there are variations in the relationship

between the crack growth rate and ΔJ even if the amplitude is

constant. Meanwhile, number of repetitions is relatively small in

the data with large estimation error. Then the crack length can be

estimated accurately as shown in Fig. 15, even if there are these

variations.

According to the similiarity between estimation model that

considers AF and the test obtained from load cases, it also

confirmed that consideration of AF can be utilized in different

types of random amplitude loadings, regardless the magnitude of

CTOD and the average of CTOD.

6. CONCLUSIONS

Investigations on LCF crack propagation under random

variable amplitude loading using experiments and analytical

studies were carried out in this study. The results are as follows:

1) A decrease of the amplitude from high to low levels in

random amplitude loading accelerated the crack growth than

that observed in constant amplitude loading.

2) When the amplitudes were increased from low to high levels,

the crack growth rate was similar to those observed under

constant amplitude loading.

3) Utilization of a correction factor expressed as the ratio of the

crack growth rate under variable amplitude loading

conditions to that under constant amplitude loading

conditions, can improve the accuracy of the estimated crack

growth rate to be similar to test result.

4) The formula introduced in this study to estimate crack growth

under random amplitude loading is considered acceptable,

regardless of CTOD magnitude and average CTOD, as

presented by close pattern between estimation and test result.

References

1) Murakami, Y., Harada, S., Tani-ishi, H., Fukushima, Y. &

Endo, T.: Correlations among propagation law of small cracks,

Manson-Coffin law and Miner rule under low-cycle fatigue,

Japan Society of Mechanical Engineers, A49, pp. 1411-1419,

1983. (in Japanese)

2) Ling, M. R., Schijve, J.: The effect of intermediate heat

treatments on overload induced retardation during fatigue crack

growth in an Al-alloy, Fatigue and Fracture Engineering

(a) RA-1

(b) RA-2

(c) RA-3

Fig. 14 Crack propagation analysis results

-181-

Material and Structure, Vol. 15(5), pp. 421–430, 1992.

3) Shercliff, H. R., Fleck N. A.: Effect of specimen geometry on

fatigue crack growth in plane strain-II. Overload response,

Fatigue and Fracture Engineering Material and Structure, Vol.

13(3), pp. 297–310, 1990.

4) Tanaka, K., Takahashi, H., Akiniwa, Y.: Fatigue crack

propagation from a hole in tubular specimens under axial and

torsional loading, International Journal of Fatigue, Vol. 28(4),

pp. 324-334, 2006.

5) Tanaka K, Akiniwa Y, Takahashi A, Mikuriya T.: Fatigue

crack propagation from a hole in thin-walled tubular steel

specimens under torsional-axial loading. Transactions of the

Japan Society of Mechanical Engineers, Vol. 69, pp.1001–

1008, 2003.

6) Itoh, T., Miyazaki, T.: A Damage model for estimating low

cycle fatigue lives under nonproportional multiaxial loading,

European Structural Integrity Society Journal, pp.423-439,

2003.

7) Tateishi, K., Hanji, T. and Minami, K.: A prediction model for

extremely low cycle fatigue life under variable strain amplitude,

Journal of Japan Society of Civil Engineers, No. 773, pp. 149-

158, 2004. (in Japanese)

8) Dong, Q., Yang, P., Xu, G., & Deng, J.: Mechanisms and

modeling of low cycle fatigue crack propagation in a pressure

vessel steel Q345, International Journal of Fatigue, Vol.89,

pp.2-10, 2016.

9) Morrissey, R. J., McDowell, D. L., & Nicholas, T.: Frequency

and stress ratio effects in high cycle fatigue of Ti–6A1–4V,

International Journal of Fatigue, Vol.21(7), pp.679–685, 1999.

10) Shahani, A. R., Kashani, H. M., Rastegar, M., and Dehkordi,

M. B.: An unified model for the fatigue crack growth rate in

variable stress ratio, Fatigue and Fracture Engineering

Materials and Structures, Vol.32(2), pp.105–118, 2009.

11) Dougherty, J. D., Padovan, J., & Srivatsan, T. S.: Fatigue

crack propagation and closure behavior of modified 1070

steel: Finite element study, Engineering Fracture Mechanics,

Vol.56(2), pp.189–212, 1997.

12) Gonzalez-Herrera, A., & Zapatero, J.: Tri-dimensional

numerical modelling of plasticity induced fatigue crack

closure, Engineering Fracture Mechanics, Vol.75(15),

pp.4513–4528, 2008.

13) Terao, N., Hanji, T. and Tateishi, K.: Crack propagation

behaviour of structural steel in extremely low cycle fatigue

region, IABSE Conference NARA, 2015.

14) Terao, N., Hanji, T., Tateishi, K. and Shimizu, M.: A

prediction method for extremely low cycle fatigue crack

propagation of structural steel, Proceedings of the 8th

International Symposium on Steel Structures, pp.387-388,

2015.

15) Hanji, T., Tateishi, K., Terao, N., and Shimizu, M.: Fatigue

crack growth prediction of welded joints in low-cycle fatigue

region, International Journal of Material Joining,

Vol.61(6R), pp.1189-1197, 2017.

16) ASTM E1820-031: Standard Test Method for Measurement

of Fracture Toughness, pp. 1-48, 2008.

17) Panjaitan, A., Masaru, M., Tateishi, K., Hanji, T.: Study on

low cycle fatigue crack propagation under two-steps variable

amplitude, Japanese Society of Steel Construction, Vol.

27(108), pp. 93-103, 2020.

(Received September 15, 2020)

(Accepted February 1, 2021)

-182-