Study on crack branching control technology that contributes to the improvement ofarrest property of steel plates
厚鋼板アレスト特性改善に寄与するき裂分岐制御技術の探索
研究代表者 東京大学大学院工学系研究科 准教授 川畑 友弥
1. Introduction
Currently, steel materials are widely used for transportation and energy storage aswell as in large structures for buildings and civil engineering. In recent years, from theviewpoint of construction cost, the sizes of structures have remarkably increased, andthe thickness and strength of the steel plates used have correspondingly increased. In
general, the toughness of steel materials with the same microstructure decreases withincreasing plate thickness, and the risk of brittle fracture increases [1]. It has beenthought crack branch can enhance the crack arrest property. However, no actualtechnology in steel structural field was proposed so far.
Crack branches from brittle fracture are also seen in daily life. When a crack
propagates through a material, crack branching and bending sometimes occur. For
example, when the windshield of an automobile is destroyed, many branches appear
along with the crack propagation; the number of branches is remarkably high as thebranches are used for absorbing energy, so it is conceivable that the crack branchinghas propagation arresting effects. Does the amount of energy dissipated increase dueto the microbranches of the crack, decreasing the driving force, or does the driving
force of each crack tip decrease since the two cracks propagate in parallel? Is it a
combination of these two ideas? The conclusion is not clear. As a first step, we hope tounderstand the mechanical factors that dominate the fracture surface irregularities
and crack branches.
In the present study, to clarify the mechanism of the crack branching phenomenon
during fast crack propagation, we observe the relationship between the roughness ofthe fracture surface and the driving force and, in particular, the cause of the branching
phenomenon particular to steel is examined.
2. Brittle crack branching by large-scale wide plate testing and fracture surface
roughness
To realize long-distance brittle crack propagation, where reaching a crack
branching condition is possible, ESSO tests have been conducted under constant low
temperature using a 10 MN large-scale test machine, as is shown in Fig. 1. For details,－ 49 －

please refer to our recent paper [2]. A normalized steel plate (N30; YS416MPa,
TS541MPa, vTrs-10deg.C) for a welding
structure has been used as a test specimen.
In the tests, two types of test specimens
have been prepared as is shown in Table 1.
The first type of test specimen comprised
entirely N30 (#5), and the other type of test
specimen was a sandwich structure (#3)
where the hard part consisted of high-Ni
Fig. 1 Ten MN tension testingmachine used for wide plate tests

steel to increase the plastic constraint, andthe N30 zone was only 10 mm. Both parts

Table 1 Test conditions#

Homogenous/Soft welded
jointPart A#3

Soft weldedjoint

High-nickel
steel#5 Homogenous

Part B

Experimental
conditions,
Gross
Width
Material[mm] stress/Temperature
N30

20

N30

300 MPa/-100°C
300 MPa/-100°C

have been joined by EBW (Electron Beam Welding).
Both test piece outlines are shown in Fig. 2. Tensile stress has been applied fromboth ends through pins. In the tests, after controlling the temperature at a constant-100 °C, such as the usual ESSO test, a uniform tensile stress of 300 MPa was applied,
and then, a crack has been artificially generated with blows from an air gun. To
minimize the impact of the blows, we have used an impact energy as small as possible.

(a) #3Fig. 2 Configuration of specimens－ 50 －(b) #5

As a result of the tests,
both specimens have shown
clear branching of the brittle
crack.

Fig.

fracture

3

shows

the

appearance

andfracture surface observation
results.

Aroundtheclear

crack branching position, thefracturesurfaceroughnesschanges drastically for both
specimens.

The

first

branching points occur at a
crack length of 80 mm for # 3
and 160 mm for # 5.
Fig. 4 shows the crack(a) Specimen #3(b) Specimen #5
Fig. 3 Fracture appearance, fracture surface andcrack branching position

propagation speed transition andthe crack branching position. The
propagation speed at the time ofcrack

propagationisapproximately 800 m/s, which ismuch lower than the theoreticalvalue from the elastic fracture
mechanics

described

intheprevious section. As is confirmedby the visual observation of theroughness of the fractured surface,Fig. 4 Crack velocity and crack branchingposition

the surface is smooth up to the branching position, and the roughness dramaticallyincreases in the vicinity of the crack branching.
For an objective evaluation, the roughness is quantified. Fig. 5 shows the plots ofthe fracture surface roughness measured using a laser displacement metre(OPTEX-FA Co.; CD1-100N). The laser displacement metre irradiates a target areawith laser light (the spot diameter of the focal area is 1 mm × 1.5 mm), and the
distance to the target area can be precisely measured by the measurement of the time
taken to receive the reflected light. The data measured are used as a roughness index
by calculating the standard deviation in that region for each 5 mm width of the crack.
The plots show that the fracture surface irregularities are conspicuous, after the crack－ 51 －

branch point is confirmed visually.

(a)(b)
Fig. 5 Surface roughness measurement results by laser displacement metreTo

investigate

thelocal critical conditions of
the crack branches, FEM
analysis is carried out.

(a) Overview

The model and sizes used
are shown in Fig. 6. The
finite element length in
the

crack

propagation

direction and longitudinal
direction is set at 200 μm,
whichachieves

both

accuracy in the stress(b) Enlarged
view of crack
propagationarea
Fig. 6 Overview of FEM model for simulation

distribution evaluation and reasonable calculation costs. For the analysis, thestress-strain relationship obtained from the low-temperature high-speed tensile
testing is used. To further realize actual mechanical conditions, the strength change inthe heat affected zone from EBW welding is modelled. The increase of the strength in
the heat affected zone is quantified by proportional calculations using the hardness
tests. The crack tip shape is determined so that the stress intensity factor obtained
from the stress values extracted from the elastically deformed region among the 20
elements in front of the crack tip is constant in the plate thickness direction.
First, the validity of the circumferential stress criterion introduced by theoretical
dynamic fracture mechanics [3] is examined for various crack length conditions. The
circumferential stresses are calculated by the nodal stress data at the nearest (≒200～
400 μm from the crack tip) nodes. However, the maximum circumferential stress is－ 52 －

observed at the zero-degree position like the static LEFM solution as is shown in Fig. 7.
Only small increases in the circumferential stresses at non-zero degrees are observed
compared with the LEFM solution. Thus, explaining the branching behaviour by thechange of circumferential stress distributions is difficult.
In the present study, considering that crack branching perhaps occurs in markedly
plastically deformed areas, the maximum principal stress at the crack tip and thestress triaxiality η are focused. The calculation results are shown in Fig. 8. Comparedwith the crack branching position in the experiment, the limit condition for crack
branching is both σ1>1500 MPa and t η>1.4. Again, these stresses must be focused sothat branching does not occur in steel under the conditions of crack propagation speed
shown from the theoretical solution by Yoffé [3]. We consider the micro mechanism
corresponding to this focussing later. In addition, we confirmed the change in energy
flux which is suggested by Nishioka et al. [4] does not develop into branchingconditions.

(a) Specimen #3(b) Specimen #5

2
1.9
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1

crack branchingcondition

a=60mma=80mma=100mma=120mma=140mmfar from thecrack tip

a=160mmnear thecrack tip0

specimen #3(soft welded joint)
1E+09

2E+09

Stress triaxiality, ηStress triaxiality, ηFig. 7 Calculation of circumferential stress variation
2
1.9
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1

crack branchingcondition

a=60mma=80mma=100mma=120mma=140mma=160mmfar from thecrack tipnear thecrack tip0

specimen #5(homogenous)
1E+09

2E+09

Max principal stress, σ1 [Pa]Max principal stress, σ1 [Pa](c) Specimen #3(d) Specimen #5

Fig. 8 Increase of stress triaxiality and max principal stress under crack propagation－ 53 －

3. Small-scale brittle crack propagation test and fracture surface roughness
For the purpose of
establishing

a

more

accurate and simpler
test method, we havedevelopedaedge-notched(SENT)

singletensiontest.

A

schematic of the test
piece is shown in Fig. 9.

Fig. 9 Overview of SENT specimen

The thickness of theevaluation area of thespecimen is 10 mm. For
thisexperiment,

SM490A steel is used,which is the same kind
of

steel

with

same

strength level as thatused in Section 2. After
uniform tensile stressisapplied,brittlecracking is realized at
an arbitrary time by
the secondary loading.

Fig. 10 Fracture appearance and fracture surface after
SENT test

The test is carried out at temperature of -100 °C under load stress of 300 MPa. The
temperature control is carried out in a spray-type cooling chamber, and the test is
carried out after holding the temperature in the range of ±2 °C for 10 minutes or longer.
The appearance and fracture surface of the specimen after the test are shown in Fig.
10. The cracks that have propagated are very straight, and no clear branching isobserved in this test.
The fracture surfaces of this test tend to have less unevenness in the roughness
than those of the ESSO test described in the previous section, and detailed analysis isdifficult with the same laser displacement gauge. Therefore, we have obtainedroughness data from stereo images taken with a scanning electron microscope (SEM).
In this method, the height of the specimen surface is calculated from a pair of stereo－ 54 －

images acquired by SEM. The height information is obtained by photographing two
inclined images and calculating the height by using the inclination angle. The principleof stereo photography is shown in Fig. 11.

Fig. 11 General explanation of the principle ofthree-dimensional stereoscopic photography
A summary of the fracture

1.1

surface roughness data obtained is
becomeslengthremarkable
of

70

mm

at

crack

and

then

0.9

Ra [mm]shown in Fig. 12. The roughness

1

0.3

part of Fig. 12 and the roughness

does the crack propagation speed.
This decrease results from thestress relaxation due to the longcrack

propagation

under

displacement control test.

the

0

20

40

60

80

100

2500

Crack velocity, v [m/s]photography decreases, and so

x65 2mm from the surface
x65 3mm from the surface
x65 5mm from the surface
x100 5mm from the surface

Distance from the top of the specimen [mm]are correlated. Additionally, atthe three-dimensional stereoscopic

0.6
0.4

speed history shown in the lower

the roughness data obtained by

0.7
0.5

decreases. The crack propagation

crack lengths greater than 70 mm,

0.8

2000
1500
1000
500
0

SM490A, SENT,
0

0.02

0.04

, 300MPa
0.06

0.08

Crack length , a [m]Fig. 12 Surface roughness acquired by SEM
stereo photography and correlation
with the crack velocity record－ 55 －

To obtain the detailed
stressdata

runningaroundcrack,

theFEM

analysis is carried out withappropriatematerial

constant input. The change
in the crack tip stress fieldobtained by FEM analysis
is shown in Fig. 13. Crack
branching is not observed in
this

test

piece,

possibly

the

crack

becausebranchingcondition

Fig. 13 Increase in the stress triaxiality and max
principal stress under crack propagation(SENT, -100 C) with the crack velocity recordsuggested in the previous section is not satisfied. However, the stress field clearly rises
as the crack progresses even if crack branching is not realized. As the main stress andthe triaxiality increase, the roughness of the fracture surface first increases, and there
may be a case where the stress finally reaches the branching condition at certain otherconditions (e.g., a much lower temperature, thicker specimen, or side grooved
specimen).
Microcracks possibly occur at a position distant from the crack tip due to the
expansion of the high stress region [5], where certain brittle phase particles may work
as triggers for the initiation of
microcracks,andcleavagefacet planes with a large angle
from the main fracture plane
are chosen due to the rise in
the stress triaxiality, as isschematically shown in Fig.
14. Thus, microcracks occur
and propagate in the directionof this angle, which explains
the increase in the roughnessofthe

However,

fractureforsurface.

macroscopic

crack branches and stable
growth,microcracks

Fig. 14 Schematic explanation of the microscopic
mechanism for the increase in the fracture surface
roughness under high stress and stress triaxiality
conditions

must－ 56 －

develop individually, for which criteria exist. Further detailed and quantitative
examination is needed to understand the whole mechanism for crack branching
behaviour in polycrystalline steel.
4. Conclusion
In this study, to clarify the mechanism of crack branching during brittle crack
propagation, we have observed the relationship between the roughness of the fracturesurface and the driving force and have discussed the cause of the particular branching
phenomenon for steel.
The fracture surface roughness increases due to the crack propagation driving force,
especially with increases in both the maximum principal stress and stress triaxiality,and branching is estimated to occur when both criteria are satisfied. This estimation
has been validated by two different experiments using ordinary structural steel.
Microcracks in the high stress and high triaxiality region are more likely to begenerated at different angles from the main fracture surface plane at positions
separate from the crack tip. An increase in the crack propagation speed seems tocorrespond to an increase in the roughness in the SENT test. However, the increase in
the propagation speed is not necessarily the direct cause for the increase in thefracture surface roughness but it is one of the results of the increase in the driving
force, at least in steel. We think that the crack branching condition for steel, that is
likely to occur at very low crack propagation speed, can be determined by local
conditions, due to inhomogeneous microstructures.
ACKNOWLEDGEMENT
The authors of this work would like to express their gratitude to the JFE 21stCentury Foundation. This work was supported by the Technical Research Aid of JFE
21st Century Foundation.
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