Materials Science and Engineering A 528 (2011) 1636–1640
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Materials Science and Engineering A
journal homepage: www.elsevier.com/locate/msea
Assessment of tearing resistance of ductile metals: Using a new concept of
tearing toughness
C.H. Li, Q.Q. Duan, Z.F. Zhang ∗
Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China
a r t i c l e
i n f o
Article history:
Received 4 August 2010
Received in revised form 22 October 2010
Accepted 3 November 2010
Keywords:
Low-carbon steel
Tearing test
Tearing toughness
Strength
Elongation
a b s t r a c t
Tensile and three-leg trousers tearing tests of the cold-rolled 20 steel sheets heat-treated at different
temperatures were investigated. A concept of tearing toughness is proposed for the first time to evaluate
the resistance to crack propagation, and to reflect the comprehensive properties of strength and ductility
of ductile metallic materials. The present results show that the tearing process is steady, and the tearing
toughness is dependent on the microstructures and tensile properties of the 20 steel sheets.
© 2010 Elsevier B.V. All rights reserved.
1. Introduction
The mechanical properties of ductile metallic materials are successfully assessed most often by means of uniaxial tensile test
[1]. Throughout history there has been a never-ending effort to
develop materials with better mechanical properties [2]: higher
strength or better ductility; and in engineering applications, the
strength is, without doubt, an important parameter [3]. However,
the increase in the strength is usually accompanied with a loss of
ductility, of which the trade-off between strength and ductility has
made great trouble for the selection among various engineering
materials, because the strength is by no means the only important
one and usually a material must provide comprehensive properties [3,4]. How does the strength match the ductility becomes the
key of the problem, and this indicates that the mechanical properties of materials should be evaluated more rationally. On the other
hand, for high-strength or brittle metals, the fracture toughness
(KIC ) has been widely employed to characterize their properties
[5–7]; and yet for those ductile metals, the fracture processes are
more complex and strongly depend on the specimen geometry and
loading configuration [5,6]. Undoubtedly, the fracture toughness is
invalid to evaluate the toughness of ductile materials; besides, for
these thin sheets of ductile metals conventional testing geometries
are difficult to use [8]. These give rise to an interesting question:
how the fracture work or resistance to crack propagation can be
measured in fracture process of ductile metallic materials?
∗ Corresponding author. Tel.: +86 24 23971043.
E-mail address: [email protected] (Z.F. Zhang).
0921-5093/$ – see front matter © 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.msea.2010.11.013
In addition to the tensile and fracture toughness tests, there is
another mechanical testing method, which is called as tearing test
with various loading formats (uniaxial, biaxial, or multiple) [9–13]
and different specimen shapes (deeply double edge notched, deeply
center notched, or deeply single edge notched) [6] using for thin
sheet of ductile materials, correspondingly, a series of assessment
parameters have been proposed and used [5,7,9,12,14–20]. Of these
parameters, the fracture work per unit area dissipated in the fracture area zone that was called specific essential work of fracture
(we ) proposed by Mai and Cotterel [5–7] was took as a material
constant, which could be obtained by extrapolating the linear relationship between the total specific fracture work and the ligament
length to zero ligament. Taking account of the differences in local
sheet curvature at the tear tip, Muscat-Fenech and Atkins [15,16,21]
expanded Mai and Cotterell’s work, they analyzed the elastic, rigidlinear, and elastoplastic conditions of tearing of the sheet materials
in detail, and proposed the parameter of fracture toughness R to
express the specific work of fracture per unit area, and modified
Mai and Cotterell’s linear straight relationship using the trousers
tearing test which was first developed by Rivlin and Thomas [22].
Based on the method above, it is wondered whether or not the
tearing test method can be utilized to evaluate the resistance to
crack propagation or to measure the toughness of ductile materials, and can be applied for characterization of mechanical property
of materials in the engineering application. In this study, we chose
the typical engineering material—low carbon steel 20 steel as our
ductile material, used the three-leg trousers tearing test, to tear the
thin 20 steel sheets heat-treated at different temperatures. For the
first time, a new parameter, tearing toughness , is defined to represent the fracture work dissipated per unit area of a tearing crack in
C.H. Li et al. / Materials Science and Engineering A 528 (2011) 1636–1640
1637
evaluating the resistance to the crack propagation of ductile materials. It is interesting to find that the tearing toughness of the 20
steel is not a material constant, and varies with its microstructure
and tensile strength.
2. Experimental procedure
Cold-rolled 20 steel sheet with compositions of C (0.17–0.23%),
Si (0.17–0.37%), Mn (0.35–0.65), Cr (≤0.25%), Ni (0.30%), Cu (0.25%)
was used in this study. Both of the specimens for tensile and
three-leg trousers tearing tests were cut along the rolling direction. The gauge section of tensile specimens has dimensions of
16 mm × 3 mm × 3 mm and the three-leg trousers tearing specimens were cut from the 20 steel sheets to have dimensions of
40 mm × 20 mm × 0.5 mm. With an interval of 8 mm, two initial
notches of 20 mm in length were cut on one of the short edges of the
thin sheets for tearing, as shown in Fig. 1(a). Some tensile and tearing specimens were quenched at 920 ◦ C, then, tempered at 200 ◦ C,
400 ◦ C, 600 ◦ C, and 700 ◦ C for 2 h, respectively. Their microstructures were observed by LEXT OLS4000 Measuring Laser Confocal
Microscope. The tensile tests were performed at a constant strain
rate of 5 × 10−4 s−1 , and the tearing tests were conducted at a constant displacement rate of 1 mm/min with an Instron-8871 testing
machine. Before mounting the tearing specimen, the center leg and
the other two-edged legs of the specimens were bent opposite to
the suitable direction to fit the testing machine. The microstructures of the 20 steel performed on the fracture surfaces of the torn
specimens (shown in Fig. 1(b)) were observed by Supra 35 scanning
electron microscope (SEM).
3. Experimental results
Fig. 1. Typical tearing specimen (a) and the final tearing fracture (b).
Microstructures of the 20 steel sheet heat-treated at different
temperatures are shown in Fig. 2. Microstructure of the speci-
Fig. 2. Microstructures of the 20 steel sheet heat-treated at different temperatures: (a) RT, (b) 200 ◦ C, (c) 400 ◦ C and (d) 700 ◦ C.
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C.H. Li et al. / Materials Science and Engineering A 528 (2011) 1636–1640
Fig. 3. (a) Tensile stress–strain curves and (b) relationship between strength and
elongation of 20 steel specimens heat-treated at different temperatures.
mens which were quenched at 920 ◦ C first, and then tempered
at 200 ◦ C (Fig. 2(b)), 400 ◦ C (Fig. 2(c)), 700 ◦ C (Fig. 2(d)) respectively, are completely different from the cold-rolled one (Fig. 2(a)).
With increasing the tempering temperature, the microstructures
undergo the room temperature structure, tempered martensite,
trooatite to sorbite, which should directly affect the corresponding
mechanical properties of the 20 steel sheet heat-treated at different
temperatures (shown in Fig. 3(a)).
The tensile stress–strain curves of the 20 steel sheets heattreated at different temperatures are shown in Fig. 3(a). It can be
seen that the cold-rolled sheet (sample A) has the lowest tensile
strength of about 440 MPa and a total elongation of about 40%. The
tensile strength of the sheets quenched at 920 ◦ C first and then tempered at 200 ◦ C (sample B) is as high as ∼1200 MPa, when the steel
sheet was quenched at 920 ◦ C and tempered at 700 ◦ C (sample E),
its tensile strength drops to about 480 MPa; meanwhile the elongation rises from 13% for sample B to 31% for sample E. Perfectly,
metals are expected to be processed as the trend of strengthening
and toughening as the dash line shown in Fig. 3(b), and in engineering applications a material could provide a better comprehensive
property of high strength and good ductility [3,4]. Considering the
relationship between the strength and elongation of all the samples, the 20 steel displays the typical trade-off rule again, i.e. higher
strength with lower elongation, or lower strength with better elongation, as shown in Fig. 3(b). According to the present results,
obviously, it is difficult to select the material state with an excellent combination between strength and elongation of the 20 steel
sheets. To solve the problem, the tearing test is expected to provide
new method to the toughness of the ductile materials.
Fig. 4(a) shows the tearing load–displacement curves of the
specimens heat-treated at different temperatures. For all the sam-
Fig.
4. (a)
Tearing
load–displacement
curves
and
(b)
tearing
load/thickness–displacement curves of 20 steel heat-treated at different temperatures; (c) relationship curve between tearing toughness and tempering temperature
of 20 steel.
ples, the applied load increases sharply with the displacement up
to the peak point, then starts to drop gradually to a steady value.
The steady tearing load of the specimen C quenched at 920 ◦ C and
then tempered at 400 ◦ C is the highest, and the steady tearing load
of the cold-rolled specimen A is the lowest. For the other specimens
tempered at different temperatures, their steady tearing loads are
nearly the same to each other and are hard to be distinguished
from the curves (not shown in Fig. 4(a)). Then their thicknesses
are considered to normalize the tearing properties, and the results
are shown in Fig. 4(b). It can be seen that the normalized tearing
loads of all the samples display obvious differences, and there is an
increasing trend from samples A, B and C. The normalized tearing
loads of the samples D and E are between those of samples A and C.
The tearing fractographies of the 20 steel specimens heat-treated at
different temperatures are shown in Fig. 5. No matter how different
the heat-treating conditions of the 20 steel are, it is seen that there
C.H. Li et al. / Materials Science and Engineering A 528 (2011) 1636–1640
1639
Fig. 5. SEM fractographies of the torn 20 steel sheets heat-treated at different temperatures: (a) RT, (b) 200 ◦ C, (c) 400 ◦ C and (d) 700 ◦ C.
are many shearing dimples on all the fractographies without any
different zone. This indicates the steady tearing of the specimen,
which is consistent with the applied stable load shown in Fig. 4(a).
All the tearing load–displacement curves in Fig. 4(a) have the
same feature: the applied tearing load first reaches to a peak value
Fmax , and then slightly drops to a stable value Fs and the curves
nearly become horizontal, as illustrated in Fig. 6(a), showing a
steady tearing process after the initiation of the tearing crack.
Therefore, it can be concluded that the tearing crack is hard to initiate, and much more tearing energy on the notches is required
prior to the stable propagation. However, once the tearing crack
starts to propagate, the applied load (or the normalized tearing
load) nearly maintains the constant value, indicating that the critical tearing work to the crack propagation can be regarded as a
material parameter.
In the present tearing test, a material parameter is proposed to
describe the toughness or to measure the resistance to crack propagation of ductile materials. The tearing load–displacement curves
in Fig. 4(a) show that the applied load nearly maintains constant
value during the propagation of a tearing crack for each sample.
The balance load Fs will correspond to the plastic work dissipated
on the cracking surface to resist the steady propagation of the tearing crack. During the tearing process, if taking into account the
energy dissipated on the per unit area of the tearing crack, a new
parameter can be defined as, i.e. tearing toughness (), which is the
resistance of steady propagating crack of materials. Therefore, the
tearing toughness for the three-leg specimens can be described as
=
W
Fs
Fs l
=
=
2A
2t
2tl
(1)
where, W is the total work performed on the propagated crack, A
is the total area of the propagated crack, 2 stands for two cracks
for each specimen, Fs is the applied stable load, l is the propagation
displacement of a tearing crack, t is the thickness of sheet. Thus, the
tearing toughness can also be described as
l
=
0
(Fs /2t) dx
l
.
(2)
According to Eq. (2), the values of the tearing toughness for the
thin 20 steel sheets heat-treated at different temperatures were
calculated and are shown in Fig. 4(c). It is apparent that the tearing
toughness is not a material constant, but strongly depends on the
microstructures and the tensile strength in detail. Fig. 6(b) shows
the dependence of elongation and tearing toughness on the tensile strength, the relationship between elongation and the strength
also shows the typical trade-off rule. With increasing the tensile
strength, the tearing toughness first increases and then gradually
drops, the peak value appears at the point which is consistent with
the result when the temperature changes. For example, the tearing toughness increases from 220 kJ/m2 (for sample A) to a peak
value of about 330 kJ/m2 (for sample C), and then slightly drops to
300 kJ/m2 (for sample B). This indicates that higher tensile strength
or better elongation cannot bring a higher tearing toughness, which
can be regarded as another mechanical parameter affected by the
microstructures.
It is known that high strength is always accompanied with
low ductility for various structural materials [23]. Such contradictory relationship has made great trouble in material research and
engineering because characterizing or optimizing the mechanical
properties of materials becomes a difficult problem. However, the
point of the highest tearing toughness of the 20 steel quenched at
920 ◦ C and tempered at 400 ◦ C has high strength and good ductility
at the same time. It is indicated that the comprehensive properties
of strength and ductility may be characterized by the tearing toughness, which is expected helpfully to optimize mechanical properties
of ductile materials.
For ductile materials, the fracture toughness (KIC ) is not a true
material property unless the sample dimensions are made sufficient large [24]. Moreover, much of plastic flow at the notch or crack
tip is not directly involved in the fracture process [5], and the plastic
work will dissipate around the crack tip and the intrinsic resistance
to the crack propagation of ductile materials cannot be well characterized. From the results above, it is suggested that the tearing
toughness , with a unit of kJ/m2 , which can be defined by the tearing energy per unit area of the propagating crack, could be suitable
for measuring the resistance to the tearing crack propagation for
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C.H. Li et al. / Materials Science and Engineering A 528 (2011) 1636–1640
the principle of tearing toughness will be established and perfected
elsewhere [25].
4. Conclusions
The three-leg trousers tearing test of the 20 steel sheets displays a steady tearing process, which provides us a new approach
to evaluate the fracture resistance of those high-strength ductile
metallic materials. The corresponding parameter, tearing toughness , defined by the tearing energy per unit area of propagating
cracks, reflects the intrinsic resistance to the tearing fracture of
ductile metallic materials. In the present study, the tearing toughness is not a material constant, but shows close relationship to the
microstructure and tensile property. Normally, the higher tearing
toughness represents a better combination of strength and ductility of materials. In order to evaluate the comprehensive property of
strength and ductility for those ductile metals, the tearing test and
the concept of tearing toughness may be useful in the optimized
design of those high-strength ductile metallic materials.
Acknowledgements
The authors are grateful to Dr. J.X. Zhao, Dr. R.T. Qu, and Dr.
X.H. An for sound suggestions and advices. Thanks are also due
to W. Gao for her assistance in the SEM observations. This work
was financially supported by the National Natural Science Foundation of China (NSFC) under grant nos. 50625103 and 50890173,
the National Basic Research Program of China under grant no.
2010CB631006.
References
Fig. 6. (a) Schematic diagram of tearing load–displacement curve; (b) dependence
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load nearly maintains constant, as shown in Fig. 4(a), this indicates
that the dissipated plastic energy per unit area should be materials constant during the steady propagating of a given tearing crack.
The value of the tearing toughness means the average resistance
to a tearing crack, the smaller the tearing toughness is, the easier the sample sheet is torn. Therefore, the parameter of tearing
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Cu–Be alloy, which further indicates that the tearing toughness
also depends on the materials type and microstructures in detail.
For these ductile metals, systematic studies on the tearing tests and
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