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Low cycle fatigue damage and critical crack length affecting loss of fracture ductility
Accepted Manuscript Low Cycle Fatigue Damage and Critical Crack Length Affecting Loss of Fracture Ductility Yukitaka Murakami, Md. Shafiul Ferdous, Chobin Makabe PII: DOI: Reference:
S0142-1123(15)00155-3 http://dx.doi.org/10.1016/j.ijfatigue.2015.05.006 JIJF 3596
To appear in:
International Journal of Fatigue
Received Date: Revised Date: Accepted Date:
18 December 2014 7 May 2015 10 May 2015
Please cite this article as: Murakami, Y., Shafiul Ferdous, Md., Makabe, C., Low Cycle Fatigue Damage and Critical Crack Length Affecting Loss of Fracture Ductility, International Journal of Fatigue (2015), doi: http://dx.doi.org/ 10.1016/j.ijfatigue.2015.05.006
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Low Cycle Fatigue Damage and Critical Crack Length Affecting Loss of Fracture Ductility Yukitaka Murakamia, Md. Shafiul Ferdousb, Chobin Makabeb a
Kyushu University, 744 Moto-oka, Nishi-ku, Fukuoka, 819-0395, Japan e-mail: [email protected]
b
University of the Ryukyus, 1 Senbaru, Nishihara, Okinawa, 903-0213, Japan Tel: +81 98 895 8605 e-mail: [email protected], [email protected]
Abstract
The role of small cracks on fatigue life and loss of ductility are discussed to understand the reality of fatigue
damage in low cycle fatigue. The series of low cycle fatigue tests were carried out paying attention to the role of
small cracks and their influence on ductility loss. These tests showed that the fatigue lives were pronouncedly
extended by removing surface cracks. Also, it was quantified that the loss of fracture ductility was correlated with
crack length but not with the number of fatigue cycles. From those results, it is concluded that the behavior of
small cracks is crucial to explain the mechanism of low cycle fatigue damage rather than the crack initiation
process and change in bulk material properties.
Keywords: Low cycle fatigue, Surface cracks, Fatigue life, Crack initiation, Crack growth, Fracture ductility,
Fatigue damage
1. Introduction
It is well known in low cycle fatigue that the relationship between cyclic plastic strain range and number
of cycle to failure is expressed as:
∆εp Nfα =C
(1)
where ∆εp is the cyclic plastic strain range, Nf is the number of cycles to failure, and C and α are material
constants. Equation (1) was proposed by Coffin [1]. Another similar equation was also proposed by Manson [2].
This relationship is well known as the Coffin-Manson law.
Coffin [3] proposed that the value of C in Eq. (1) can be correlated with fracture ductility (or fracture
strain) εf in static tensile test as given by:
C=0.5εf : here εf = ln A0/A= ln[1/(1-ψ)]
(2)
where Ao is the initial area of cross-section of specimen, A is the area of the minimum cross-section after tensile
fracture, and ψ is the reduction of area. It has been discussed if the constant C can be correlated with material
ductility or not. After the early work by Coffin [3], similar tests were conducted by other researchers and similar
conclusions were derived. These discussions have led many researchers to a misconception of fatigue damage. A
typical misconception is that low cycle fatigue damage is thought to be the weakening or losing the bulk strength
of a material due to an irreversible slip in crystals or plastic strain cycling due to microstructural changes such as
dislocation structures. However, Murakami and Miller [4] showed concrete evidence that the fatigue life is
determined by the behavior of surface cracks rather than the accumulation of cyclic strain and change in material
bulk qualities. They discussed fatigue damage from the viewpoint of small cracks growth during total fatigue life
and pointed out that the very ambiguous term “fatigue damage accumulation” often leads researchers to the
misconception.
As reported first by Kikukawa et al. [5], the fatigue failure life Nf can be extended if the surface layer of a
specimen is removed during fatigue testing, though cyclic strain hardening or softening occurs in the bulk material.
Their work also suggested that attention should be paid to the condition of the surface layer of a specimen to
understand the true meaning of fatigue damage. It has been more clearly shown by Murakami et al. [4, 6, 7] that
the presence of small cracks in the surface layer has a direct correlation with fatigue damage. They showed that
the low cycle fatigue process is mostly (nearly 100%) dominated by the small crack growth process.
Regarding crack initiation mechanism, it is crucially important to note that cracks in low cycle fatigue do
not necessarily initiate along persistent slip bands, though the fatigue crack initiation mechanism has been
discussed very often based on the model of persistent slip bands [8-12]. In low cycle fatigue of 70/30 brass, 100%
of cracks initiate at grain boundaries [6] and in low cycle fatigue of a 0.45%C steel, cracks mostly initiate from
cracked pearlites almost from the first cycle [7]. In the case of present study of a 0.15%C steel, cracks mainly
initiated from grain boundary of ferrite as shown in Appendix. In our experiences based on precise observations
on many materials, it is rather rare that cracks initiating from persistent slip bands lead to final fatigue fracture.
Thus, according to the observations, the Palmgren-Miner rule [13, 14] in low cycle fatigue can be
interpreted from the viewpoint of the small crack growth behaviour under various stress or strain amplitudes [4, 7].
Furthermore, it was shown that the loss of fracture ductility during fatigue cycle is related not to the history of
strain cycles but to the length of surface cracks. Following the previous works, more precise experimental studies
were carried out in details to confirm that fatigue life can be extended by removing surface cracks, and that loss of
fracture ductility during fatigue cycling is caused by presence of surface cracks. From these results, it is concluded
in this paper that the discussion of low cycle fatigue damage based on surface cracks is most crucial to understand
the reality of fatigue damage in a low cycle fatigue regime.
When very large plastic strain is repeated, local necking occurs in specimen and fatigue life becomes
shorter than 100 cycles [5, 15]. In such cases, internal voids are nucleated in specimen under tri-axial tensile stress
and the final fracture is originated from the core part of specimens. The present paper does not treat such an
exceptional case of very low cycle fatigue.
2. Material and experimental procedure
The material used for test specimens was a round bar of 0.15% carbon steel. Pieces of bar were annealed
at 900ºC for 1 hr and then machined on a lathe. The chemical composition and mechanical properties of this
material are shown in Table 1. Figure 1 shows the shape and dimensions of the specimen. In some specimens, a
partial notch or a hole was introduced on the surface of specimens. The partial shallow notch shown in Fig. 1(b)
was introduced to localize the location of crack initiation to a small area for easiness of observation of crack
initiation and growth compared to a completely smooth specimen. But comparing the fatigue lives with those of
smooth specimens, the specimen with the shallow partial notch can be approximately regarded as a kind of
smooth specimen.
Table 1. Chemical composition and mechanical properties of material (σS; Yield stress [MPa],
σB; Ultimate tensile strength [MPa], ψ; Reduction of area [%])
Fig. 1 Geometry and dimensions of the specimen and notches (in mm), (a) Specimen, (b) Partial notch, (c) Hole
The specimens having an artificial small hole with fewer fatigue cycles were used to compare fracture
ductility with the smooth specimens or specimens with partially notched specimens having small cracks after
longer fatigue cycles. Hereinafter, specimens with a partial notch are called “partially notched specimen”.
Specimens having a hole are called “holed specimen”.
Push-pull low cycle fatigue tests were carried out by strain control technique with 0.1Hz of cyclic
frequency. A clip gage of 10mm in length was set in the test section of the specimen. The strain was defined as the
nominal strain based on the gage length of 10 mm in all specimens used. As shown in Fig. 1, the size of partial
notch is very shallow and small. The maximum projection area An of partial notch in tensile direction is about 0.38 mm2. Since the cross-sectional area Ao of test section of smooth specimen is about 78.54 mm2, the ratio of
minimum cross section of the partially notched specimen to the smooth specimen (Ao –An) /Ao is 0.995. Also, the
stress concentration factor of the partial notch is about 1.06. In fact, as shown in later, the experimental results
showed that the fatigue life of the partially notched specimen was almost the same as that of smooth specimens
when the nominal strain was used.
The total cyclic strain range ∆εt was set at a constant value during the test. The observations of crack
initiation and growth were performed by the replica method. In some tests, the specimen surface was carefully
removed by using a lathe and emery-paper once or several times by interrupting the test after a determined
number of stress cycles. The fatigue lives were compared with the ones without surface removal. The crack
growth behaviors under some testing conditions were compared. The tensile fracture ductility εf (Eq. (2)) was measured by tensile tests for the fatigue specimens. The relationships between the fracture ductility εf and number
of cycles N or length of main crack l were compared with holed specimens and partially notched specimens.
3. Experimental results and discussion
3.1 Extension of fatigue life by removing surface layer
Figure 2 shows the relationship between cyclic plastic strain range ∆εp and number of cycles to failure Nf.
The circular symbols show the data for the ordinary low cycle fatigue test using partially notched specimens
without interrupting the test until final failure. The data are almost the same as for the life of the smooth specimen
denoted by a solid circular symbol. The triangular symbols show data for the specimens whose surface layer was
removed after interrupting the previous fatigue test before failure. In these cases, the length l of existing cracks
was checked before surface removal. In Fig. 2, the numbers associated with the triangular symbols show the
number of times of surface removal. The arrows associated with the triangular symbols show the data in which the
test was stopped before specimen failure. Although the values of total strain range ∆εt were kept constant, plastic strain range ∆εp varied due to cyclic hardening or softening. Therefore, the values of ∆εp are shown by the values
at Nf/2 of partially notched specimens. The first removal of surface layer was carried out when the number of
cycles N was reached about Nf/2 of partially notched specimen. After the surface removal, the test was continued
until the specimen was broken. As shown in Fig. 3 (a), the third and fourth surface removal was carried out every defined number of cycles (Nf/2). The depth of removal layer was 0.2mm. Figure 3 (a) shows the examples of
variation of stress range for ∆εt =0.0139 or 0.0161 (∆εp =0.0111 or 0.0132). Figure 3 (b) shows the surface conditions just before the third time surface removal with ∆εp =0.0132. In this example, the total number of
applied cycles N was 6x103 cycles (Nf of partially notched specimen ≅ 4.5x103) and there were some small cracks
within notched area. Cracks of 0.1 mm - 0.2 mm in length were observed before surface removal.
Fig. 2 Relationship between plastic strain range ∆εp and the number of cycles to failure Nf .
Fig. 3 Examples of variations in the stress range and observation of cracks: (a) Variations in the stress
range. The arrows show the cycles where the cracked surface layer was removed, (b) Surface conditions
just before the third time surface removal
The Coffin-Manson law for the ordinary low cycle fatigue test without surface removal is expressed by
∆εp Nf0.4 =0.33
(3)
When the surface layer of the specimen with ∆εp = 0.0132 was removed four times, the fatigue life Nf
was extended more than twice compared to the case without surface removal. As shown later and in the previous
studies by Murakami et al. [4,6,7], when the crack length reached 1 mm, the relative number of cycles N/Nf was
more than 0.8. Thus, it should be noted that if a crack is visible to the good naked eyes, the specimen will break
with additional small cycles. Considering the experimental fact, the surface layer of the specimens with triangular
symbols in Fig. 2 was removed at the cycle N before the main crack length reached 0.2 mm. Since it is very
difficult to observe the entire specimen surface, only the main crack nucleating from the partial notch was
measured during the tests by the replica method. In the case of triangular symbol associated with an asterisk (*) in
Fig. 2, another crack which was overlooked grew from outside the partial notch, and its length became longer than
1mm. From SEM (Scanning Electron Microscope) observation, it was revealed that there existed an exceptionally
large material defect at the crack origin as shown in Fig. A1of Appendix. The final length of crack which initiated
from outside of the partial notch in this fatigue test was 1.7mm at N/Nf=0.90. The test for the specimen with * was
stopped at N/Nf=0.9 and it was used to measure the ductility loss as shown later in Figs. 8 and 9. After this
experience, the surface layer was removed carefully not only inside the partial notch but also over all surface of
the specimen. Except for the data with * in Fig. 2, all the surface cracks were removed when the following fatigue
tests were continued.
Extension of fatigue life by removing small surface cracks indicates that low cycle fatigue life is
controlled by surface conditions, more concretely by small surface cracks. Considering that the low cycle fatigue
process is mostly (nearly 100%) dominated by a small crack growth process, we can conclude that the reality of
fatigue damage is the existence of small cracks and not overall microstructural changes such as dislocation
structures or void nucleation during fatigue cycles as also pointed out by Feltner and Beardmore [16]. Feltner and
Laird [17] and Laird [18] pointed out that in fatigue under step loading fatigue a specific dislocation structure
under a strain amplitude is developed, and another specific dislocation structure is developed in the next strain
step and then again the first dislocation structure is recovered after switching the strain amplitude from the second
strain amplitude to the first strain amplitude regardless of the accumulation of number of cycles. This important
experiment made clear that dislocation structures themselves do not directly reflect the degree of fatigue damage.
3.2 Cause of ductility loss during fatigue cycle
3.2.1 Surface crack and fracture behavior in tensile test
Murakami et al. [4, 6] showed that the fracture ductility during fatigue cycles of 70/30 brass had a good
correlation with the length of crack, regardless of fatigue cycles. A series of experiments were carried out in this
study to confirm their conclusion by using a 0.15% carbon steel. Partially notched specimens with and without
surface removal, and holed specimens were used for the measurement of ductility loss in the tensile test.
Figure 4 shows the relationship between the crack length l and relative number of cycles N/Nf, where the
value of Nf for the data of partially notched specimens is employed as the scale for fatigue cycles. The crack
length l of holed specimens is defined by including the diameter of hole. Naturally, the holed specimen having a
hole with d=h =0.2mm, had fewer cycles to produce a crack of the same length compared to partially notched
specimens. Figure 4 indicates that the crack growth rate is not so much different between the holed specimens and
partially notched specimens. The crack growth curve for the specimen with h=d/2=0.05mm shows almost the
same tendency as that for partially notched specimens. This means that the crack growth rate is not affected by the
accumulation of strain cycles, i.e. so-called “fatigue damage” as referred to by many researchers when the applied
strain conditions are the same.
As shown in Fig. 4 (b), the tendency of crack growth is clearer in the relationship between ln l and N/Nf.
It means that the small crack growth law is approximated by
ln l = C1 + C2 N/Nf
(4)
where, C1 and C2 are constants determined by experimental conditions. We obtain the following relation by
differentiating of Eq. (4)
dl/dN = C2 l / Nf
(5)
Thus, the crack growth rate dl/dN is proportional to crack length l, and this relationship is evaluated by Fig. 4. The
crack growth rate in the present study is represented by the parameters of crack length and fatigue life Nf, in
dependent of types of specimens used.
Figure 5 shows examples of observation of crack growth. In the case of the partially notched specimen,
locally dense slip bands and crack initiation were observed. In the case of the holed specimen, the crack emanated
from hole and its growth followed. By comparison of Figs. 5 (b) and (c), regardless hole sizes, the surface
conditions (roughness and slip patterns) in the vicinity of the crack tip looks similar. As shown by Murakami et al.
[4, 7], the Palmgren-Miner rule [13, 14] can be applied to the crack growth behavior when the applied stress level
was switched during low cycle fatigue test. The applicability of the Palmgren-Miner rule is justified by the crack
growth law expressed by Eq. (5). According to the investigation of Murakami et al. [4, 7], the prior fatigue history
in front of the main crack, where the crack has not yet grown, has no effect on the subsequent crack growth. This
is consistent with the applicability of the Palmgren-Miner rule and Feltner et al’s studies and Laird’s study on
dislocation structure [16 -18].
Fig. 4 Crack growth curves (∆εp=0.0132, Nf=4510 and ∆εp=0.009, Nf=13990): (a) l vs. N/Nf, (b) ln l vs. N/Nf Fig.5 Observation of crack growth: (a) Partially notched specimen (∆εp=0.009) , (a1) N=6300, l=0.2mm, (a2) N=10100, l=1.01mm : (b) Holed specimen (d= h= 0.2 mm, ∆εp=0.0132),
(b1) N=1000, l=0.48mm, (b2)
N=1900, l=1.4mm: (c) Holed specimen (d/2=h=0.05mm, ∆εp=0.0132), (c1) N=3100, l=0.38mm, (c2)
N=4080, l=1.9mm
Now, the residual ductility is compared on holed specimens and smooth specimens as a function of
applied strain cycles and that of crack length.
The tensile tests were carried out on fatigued specimens and nonfatigued specimens by interrupting the
fatigue test. Figure 6 shows the tensile stress – elongation δ curves. The elongation was measured between the
grip ends of the testing machine. The open circles show the curve of nonfatigued specimen before the fatigue test.
The fracture morphology was affected by the cyclic conditions and the types of the specimens. The final
fracture stresses were also affected by the fracture mode. As shown later, the final ductile fractures were either
cup-and-cone type or shear fracture from the surface layer. In cases where the fracture mode was cup-and-cone,
the nominal fracture stress was higher than in the cases of shear fracture.
Figure 7 shows an example of the crack deformation and extension during tensile test of fatigued
specimen with l=1.6mm after fatigue test.
Fig. 6 Results of tensile tests (l denotes the length of main surface crack when tensile test was started)
Fig. 7 Crack deformation and extension during tensile test of fatigued specimen with l=1.6mm after fatigue test
with ∆εp=0.01.
3.2.2 Relationship between the length of surface crack and the fracture ductility
In order to understand the effect of a surface crack on fatigue life in a low cycle regime, the results of the
previous studies on 70/30 brass [4, 7] were discussed together with the results of 0.15% carbon steel of the present
study.
Figure 8 shows the relationship between the fracture ductility εf and the relative numbers of cycles N/Nf, where fracture ductility εf was defined by Eq. (2). The fatigue crack length l at the moment of tensile tests is
associated with the data points in Fig. 8. Figure 8 (a) shows the results of 0.15% carbon steel and Fig. 8 (b) those
of 70/30 brass. Figure 9 shows the relationship between the fracture ductility εf and the fatigue crack length l at
the moment of tensile tests. Figure 9 (a) shows the results of 0.15% carbon steel and Fig. 9 (b) those of 70/30
brass. In these figures, the curves A, B and C summarized the data separately as follows.
A: The partially notched specimens of 0.15 % carbon steel and those of the smooth specimens of 70/30
brass after fatigue test.
B: The specimens whose surface layer was removed after fatigue test.
C. The specimens containing fatigue crack emanating from artificial hole.
Fig. 8 Relationship between fracture strain εf and relative number of cycles N/Nf . The numbers associated with
the data points denote the crack length l at the moment of tensile test. Nf is the fatigue life of partially notched
specimens; (a) 0.15% carbon steel (The meaning of the mark * is explained in Fig. 2), (b) 70/30 brass
Fig. 9 Variations in fracture ductility εf as a function of the length of surface crack l; (a) 0.15% carbon steel
(* see Fig. 2), (b) 70/30 brass
In Fig. 8, the fracture ductility εf is plotted all together for the partially notched specimens (or smooth
specimens) and holed specimens in terms of fatigue cycles N/Nf. However, the series of the data A, B and C are
separately plotted and a unique curve cannot be obtained. The fracture ductility of holed specimens shown by
curve C decreases in the early stages of N/Nf, compared with the case of partially notched specimens or smooth
specimens shown by curve A. The ductility of fatigued specimens whose surface cracks were perfectly removed
from the surface layer remained almost at the same value as the initial ductility.
If the fracture ductility εf is plotted in terms of crack length as in Fig. 9, all the data of partially notched
specimens and holed specimens can be summarized uniquely regardless of the number of fatigue cycles N/Nf. In
other words, this means that the fracture ductility εf after fatigue cycles cannot be used as the parameter to express
the microstructual change of the bulk materials based on the number of applied cycles or history of applied strain.
Thus, the fracture ductility or residual ductility has a strong correlation with crack length l regardless of
fatigue cycles. At the same time, we can conclude that the change in microstructural quality such as dislocation
structure after fatigue cycles has no substantial relationship with the variations in fracture ductility. Also, it is not
reasonable to say that the changes in the material qualities after low cycle fatigue test are related to the variations
in fracture ductility εf. Thus, the reality of fatigue damage of low cycle fatigue is the existence of small fatigue
cracks.
In addition to the above findings, it is found that there is a critical crack length lc for the drastic decrease
in ductility due to surface crack growth by unstable shear fracture mode. From Fig. 9, the size of lc for 70/30 brass
is 0.4 mm and that for 0.15 % carbon steel is 0.8 mm. These values may be used as the criterion for the analysis of
ductile fracture.
Fig. 10 Morphologies of fracture surface after tensile tests in the case of 70/30 brass (∆εp = 0.0254);
(a) Cup and cone type fracture; (a1) Nonfatigued specimen, (a2) l = 0.1 mm ,
(b)
Smooth specimen; broken by shear mode; (b1) l = 0.8 mm, (b2) l = 1.6 mm,
(c)
Hold specimen (d = 0.2mm), (c1) l = 0.86 mm, (c2) l = 1.6 mm
Fig. 11 Morphologies of fracture surface after tensile tests in the case of 0.15% carbon steel (∆εp = 0.0132);
(a) Specimen after surface removal with l=0mm, (b) Partially notched specimen with l=1.21mm,
(c) Partially notched specimen with l=1.7mm, (d) Holed specimen (d = 0.2mm) with l=1.4mm
Figure 10 shows the fracture surfaces after tensile tests for 70/30 brass. Figure 11 shows those for
0.15% carbon steel. The original fracture pattern for the nonfatigued specimen without a notch or defect is a cup
and cone pattern, where the tensile fracture originated from voids nucleating dimples in the central part of the
specimen. As shown in Figs. 10 and 11, this pattern was observed in the cases of nonfatigued specimens and
specimens with very small cracks whose length was shorter than 0.8mm for 0.15 % carbon steel and shorter than
0.4mm for 70/30 brass. The same fracture pattern was also observed on the specimen with surface removal, ie.
l=0mm as shown in Fig. 11 (a).
The shear type fracture occurs from the surface fatigue crack if the crack length is longer than the
critical length. As shown in Figs. 10 (c) and 11 (d), the appearance of shear type fracture is clearer in the cases of
holed specimens, because there is only one leading crack initiating from hole-edges. In the case of Fig. 11 (b), the
fracture started from both from internal voids and surface fatigue crack. However, the final fracture mode is shear
type. In Figs. 10 and 11, the start of shear fracture was a fatigue crack. Thus, the loss of fracture ductility is related
to the fracture modes. When the fracture started unstably from fatigue crack or surface crack by shear mode, the
ductility loss is pronounced. It was confirmed from the fracture surface that the critical crack length lc for unstable
shear fracture in 0.15 % carbon steel is approximately lc=0.8mm which is longer than the value for that in
annealed 70/30 brass, i.e. lc=0.4mm.
4. Conclusions
The roles of cracks and fatigue damage in the process of low cycle fatigue were discussed based on the
experiments focusing on small cracks and also based on previous studies. The conclusions can be summarized as
follows.
(1) Removing small surface cracks extends fatigue life and recovers material ductility regardless of
change in the bulk material properties during fatigue cycles.
(2) The loss of fracture ductility εf is caused by the existance of small surface cracks. The ductility loss
can be uniquely correlated with crack length but not with number of fatigue cycles N.
(3) There is a critical crack size lc for the drastic decrease in ductility due to unstable shear fracture.
lc=0.8mm for the low carbon steel used in this research and lc=0.4mm for annealed 70/30 brass.
(4) It is misconceptions to correlate changes in microstructural material properties such as dislocation
structure and energy dissipation ability to fatigue damage. The reality of low cycle fatigue damage is the existence
of small cracks. The geometrical dimension of cracks is the most important factor for the discussion of fatigue
damage.
Appendix
Figure A1 shows examples of crack initiation sites (∆εp =0.0132). Figure A1(a) shows that most of
cracks intiated from ferrite grain boundries. Figure A1(b) shows the fracture surface in the vicinity of the fatigue
crack initiation from an exceptionally large defect contained in the material.
Fig. A1 Examples of crack initiation site, (a) Crack initiation mostly at ferrite grain boundaries, (b) The site
of crack initiation from an exceptionally large defect which was conatined in the specimen from the begining
(This specimen corresponds to the data with symbol * in Fig. 2.)
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Table1
Chemical composition [wt, %] C
Si
0.15
0.30
Mn 0.50
Mechanical properties [MPa, %]
P
S
Cr
Ni
Cu
Fe
σS
σB
ψ
0.013
0.013
0.19
0.05
0.14
Bal.
283
449
60
Fig. 1
(a)
(b)
(c)
Fig. 2
4x10
-2
Plastic strain range ∆εp
∆εpNf0.40= 0.33 1*
10-2
f=0.1Hz 3
4 1
3
Smooth specimen No surface layer removal Surface layer removal Partially notched specimen No surface layer removal Surface layer removal Numbers associated to symbols are number of removal Arrows show the non-broken specimens * Larger crack initiated from outside partial notch
10-3 103
104
Number of cycles to failure Nf
4x10 4
Fig. 3
Stress range ∆σ, MPa
750
600 Arrows show the cycles where the cracked surface layer was removed
450
300 0
Partially notched specimen ∆εp=0.0111, ∆εt=0.0139 ∆εp=0.0132, ∆εt=0.0161
5000
10000
Number of cycles N (a)
(b)
15000
Fig. 4
Crack length l, mm
3
2
Holed specimen Partially notched specimen d/2=h=0.05mm ∆εp= 0.0090 ∆εp= 0.0132 ∆εp= 0.0132 d=h=0.2mm ∆εp= 0.0132
Approximated curve of shifting the original data of
1
0 0
0.2
0.4
0.6
0.8
1
Relative number of cycles, N/Nf (a)
Crack length l, mm
Partially notched specimen ∆εp= 0.0090 ∆εp= 0.0132
100
Approximated curve of shifting the original data of
10-1 Holed specimen d/2=h=0.05mm ∆εp= 0.0132 d=h=0.2mm ∆εp= 0.0132
10-2 0
0.2
0.4
0.6
0.8
Relative number of cycles, N/Nf (b)
1
Fig. 5
(a1)
(a2)
(b1)
(b2)
(c1)
(c2)
Fig. 6
550 Nonfatigued specimen
∆εp=0.0132
Stress σ, MPa
450
300 Fatigued specimen Partially notched specimen l=1.7mm (Fatigue cycle N/Nf=2.17, Surface layer was removed 4 times at every 1/2Nf cycles) l=0.8mm (Fatigue cycle N/Nf=0.67, Ordinary fatigue test, No surface removal) Holed specimen, d=h=0.2mm l=0.4mm (Fatigue cycle N/Nf=0.16) l=1.4mm (Fatigue cycle N/Nf=0.42)
150
0
0
1
2
3
4
Elongation δ, mm
5
6
7
Fig. 7
Fig. 8
l=0.4mm
1 0.3mm
0.8mm
∆εp=0.0132 ∆σ=597MPa
0mm
Fracture ductility ε f
3 0.75
1.21mm
A C
0.5
B 4
1*
1.4mm
1.7mm
1.7mm
1.9mm Initial ductility
Smooth specimen Surface layer removal Holed specimen d/2=h=0.05mm d=h=0.2mm
notched specimen 0.25 Partially No surface layer removal Surface layer removal (Numbers associated to symbols are number of removal)
0 0
0.5
1
1.5
2
2.5
Relative number of cycles N/Nf
(a)
l=0.12mm
l=0.46mm
l=0.0mm
1.5
Fracture ductility ε f
B
l=0.125mm
l=0.5mm
1 l=0.85mm
l=0.92mm
C
Initial ductility Plain specimen, Cracked ∆εp=0.0104, ∆σ=471MPa 0.5 ∆εp=0.0254, ∆σ=541MPa Holed specimen, Cracked ∆εp=0.0254, ∆σ=541MPa Plain specimen, Crack removed ∆εp=0.0254, ∆σ=541MPa ∆εp=0.0104, ∆σ=471MPa
0 0
l=0.8mm
l=1.6mm
0.2
0.4
0.6
0.8
Relative number of cycles N/Nf
(b)
l=1.58mm
A
l=1.6mm
1
Fig. 9 1
Fracture ductility ε f
∆εp=0.0132 ∆σ=597MPa
0.75 3 A, B and C
4 1*
0.5
Initial ductility Smooth specimen Partially notched specimen Surface layer 0.25 No surface layer removal removal Surface layer removal Holed specimen (Numbers associated to symbols d/2=h=0.05mm are number of removal) d=h=0.2mm
0 0
0.5
1
1.5
2
Crack length l, mm
(a)
Fracture ductility ε f
1.5
C
1
A Initial ductility Plain specimen, Cracked ∆εp=0.0104, ∆σ=471MPa ∆εp=0.0254, ∆σ=541MPa Holed specimen, Cracked ∆εp=0.0254, ∆σ=541MPa
0.5
0
0
0.5
1 Crack length l, mm
(b)
1.5
2
Fig. 10
Top view (a1)
Top view (a2)
Top view
Top view
View from inclined direction (b1)
View from inclined direction (b2)
Top view
Top view
View from inclined direction (c1)
View from inclined direction (c2)
Fig. 11
View from inclined direction
Top view (a)
View from inclined direction
Top view (b)
View from inclined direction
Top view (c)
View from inclined direction
Top view (d)
Appendix A1
(a)
(a)
(b)
JIJF 3596
Captions of Table and Figures
Table 1. Chemical composition and mechanical properties of material (σS; Yield stress [MPa], σB; Ultimate tensile strength [MPa], ψ; Reduction of area [%])
Fig. 1 Geometry and dimensions of the specimen and notches (in mm): (a) Specimen, (b) Partial notch, (c) Hole
Fig. 2 Relationship between plastic strain range ∆εp and the number of cycles to failure Nf
Fig. 3 Examples of variations in the stress range and observation of cracks: (a) Variations in the stress range. The
arrows show the cycles where the cracked surface layer was removed, (b) Surface conditions just before the third
time surface removal
Fig. 4 Crack growth curves (∆εp=0.0132, Nf=4510 and ∆εp=0.009, Nf=13990): (a) l vs. N/Nf, (b) ln l vs. N/Nf Fig.5 Observation of crack growth: (a) Partially notched specimen (∆εp=0.009), (a1) N=6300, l=0.2mm, (a2) N=10100, l=1.01mm; (b) Holed specimen (d= h= 0.2 mm, ∆εp=0.0132), (b1) N=1000, l=0.48mm, (b2) N=1900, l=1.4mm; (c) Holed specimen (d/2=h=0.05mm, ∆εp =0.0132), (c1) N=3100, l=0.38mm,
(c2) N=4080, l=1.9mm
Fig. 6 Results of tensile tests (l denotes the length of main surface crack when tensile test was started)
Fig. 7 Crack deformation and extension during tensile test of fatigued specimen with l=1.6mm after fatigue test
with ∆εp=0.01 Fig. 8 Relationship between fracture strain εf and relative number of cycles N/Nf . The numbers associated with the
data points denote the crack length l at the moment of tensile test. Nf is the fatigue life of partially notched
specimens: (a) 0.15% carbon steel (The meaning of the mark * is explained in Fig. 2), (b) 70/30 brass
Fig. 9 Variations in fracture ductility εf as a function of the length of surface crack l: (a) 0.15% carbon steel
(* see Fig. 2), (b) 70/30 brass
Fig. 10 Morphologies of fracture surface after tensile tests in the case of 70/30 brass (∆εp = 0.0254): (a) Cup and
cone type fracture; (a1) Nonfatigued specimen, (a2) l = 0.1 mm , (b) Smooth specimen; broken by shear mode;
(b1) l = 0.8 mm, (b2) l = 1.6 mm; (c) Holed specimen (d = 0.2mm), (c1) l = 0.86 mm, (c2) l = 1.6 mm
Fig. 11 Morphologies of fracture surface after tensile tests in the case of 0.15% carbon steel (∆εp = 0.0132):
(a) Specimen after surface removal with l=0mm, (b) Partially notched specimen with l=1.21mm, (c) Partially
notched specimen with l=1.7mm, (d) Holed specimen (d = 0.2mm) with l=1.4mm
Fig. A1 Examples of crack initiation site: (a) Crack initiation mostly at ferrite grain boundaries, (b) The site of
crack initiation from an exceptionally large defect which was contained in the specimen from the begining (This
specimen corresponds to the data with symbol * in Fig. 2.)
Highlights 1. The main damage which affects fatigue life is initiation and growth of cracks. 2. The fatigue life was extended by removing small cracks. 3. There is a critical length of fatigue crack which causes the loss of ductility. 4. The loss of fracture ductility is related to the fracture types in tensile tests.
S0142-1123(15)00155-3 http://dx.doi.org/10.1016/j.ijfatigue.2015.05.006 JIJF 3596
To appear in:
International Journal of Fatigue
Received Date: Revised Date: Accepted Date:
18 December 2014 7 May 2015 10 May 2015
Please cite this article as: Murakami, Y., Shafiul Ferdous, Md., Makabe, C., Low Cycle Fatigue Damage and Critical Crack Length Affecting Loss of Fracture Ductility, International Journal of Fatigue (2015), doi: http://dx.doi.org/ 10.1016/j.ijfatigue.2015.05.006
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Low Cycle Fatigue Damage and Critical Crack Length Affecting Loss of Fracture Ductility Yukitaka Murakamia, Md. Shafiul Ferdousb, Chobin Makabeb a
Kyushu University, 744 Moto-oka, Nishi-ku, Fukuoka, 819-0395, Japan e-mail: [email protected]
b
University of the Ryukyus, 1 Senbaru, Nishihara, Okinawa, 903-0213, Japan Tel: +81 98 895 8605 e-mail: [email protected], [email protected]
Abstract
The role of small cracks on fatigue life and loss of ductility are discussed to understand the reality of fatigue
damage in low cycle fatigue. The series of low cycle fatigue tests were carried out paying attention to the role of
small cracks and their influence on ductility loss. These tests showed that the fatigue lives were pronouncedly
extended by removing surface cracks. Also, it was quantified that the loss of fracture ductility was correlated with
crack length but not with the number of fatigue cycles. From those results, it is concluded that the behavior of
small cracks is crucial to explain the mechanism of low cycle fatigue damage rather than the crack initiation
process and change in bulk material properties.
Keywords: Low cycle fatigue, Surface cracks, Fatigue life, Crack initiation, Crack growth, Fracture ductility,
Fatigue damage
1. Introduction
It is well known in low cycle fatigue that the relationship between cyclic plastic strain range and number
of cycle to failure is expressed as:
∆εp Nfα =C
(1)
where ∆εp is the cyclic plastic strain range, Nf is the number of cycles to failure, and C and α are material
constants. Equation (1) was proposed by Coffin [1]. Another similar equation was also proposed by Manson [2].
This relationship is well known as the Coffin-Manson law.
Coffin [3] proposed that the value of C in Eq. (1) can be correlated with fracture ductility (or fracture
strain) εf in static tensile test as given by:
C=0.5εf : here εf = ln A0/A= ln[1/(1-ψ)]
(2)
where Ao is the initial area of cross-section of specimen, A is the area of the minimum cross-section after tensile
fracture, and ψ is the reduction of area. It has been discussed if the constant C can be correlated with material
ductility or not. After the early work by Coffin [3], similar tests were conducted by other researchers and similar
conclusions were derived. These discussions have led many researchers to a misconception of fatigue damage. A
typical misconception is that low cycle fatigue damage is thought to be the weakening or losing the bulk strength
of a material due to an irreversible slip in crystals or plastic strain cycling due to microstructural changes such as
dislocation structures. However, Murakami and Miller [4] showed concrete evidence that the fatigue life is
determined by the behavior of surface cracks rather than the accumulation of cyclic strain and change in material
bulk qualities. They discussed fatigue damage from the viewpoint of small cracks growth during total fatigue life
and pointed out that the very ambiguous term “fatigue damage accumulation” often leads researchers to the
misconception.
As reported first by Kikukawa et al. [5], the fatigue failure life Nf can be extended if the surface layer of a
specimen is removed during fatigue testing, though cyclic strain hardening or softening occurs in the bulk material.
Their work also suggested that attention should be paid to the condition of the surface layer of a specimen to
understand the true meaning of fatigue damage. It has been more clearly shown by Murakami et al. [4, 6, 7] that
the presence of small cracks in the surface layer has a direct correlation with fatigue damage. They showed that
the low cycle fatigue process is mostly (nearly 100%) dominated by the small crack growth process.
Regarding crack initiation mechanism, it is crucially important to note that cracks in low cycle fatigue do
not necessarily initiate along persistent slip bands, though the fatigue crack initiation mechanism has been
discussed very often based on the model of persistent slip bands [8-12]. In low cycle fatigue of 70/30 brass, 100%
of cracks initiate at grain boundaries [6] and in low cycle fatigue of a 0.45%C steel, cracks mostly initiate from
cracked pearlites almost from the first cycle [7]. In the case of present study of a 0.15%C steel, cracks mainly
initiated from grain boundary of ferrite as shown in Appendix. In our experiences based on precise observations
on many materials, it is rather rare that cracks initiating from persistent slip bands lead to final fatigue fracture.
Thus, according to the observations, the Palmgren-Miner rule [13, 14] in low cycle fatigue can be
interpreted from the viewpoint of the small crack growth behaviour under various stress or strain amplitudes [4, 7].
Furthermore, it was shown that the loss of fracture ductility during fatigue cycle is related not to the history of
strain cycles but to the length of surface cracks. Following the previous works, more precise experimental studies
were carried out in details to confirm that fatigue life can be extended by removing surface cracks, and that loss of
fracture ductility during fatigue cycling is caused by presence of surface cracks. From these results, it is concluded
in this paper that the discussion of low cycle fatigue damage based on surface cracks is most crucial to understand
the reality of fatigue damage in a low cycle fatigue regime.
When very large plastic strain is repeated, local necking occurs in specimen and fatigue life becomes
shorter than 100 cycles [5, 15]. In such cases, internal voids are nucleated in specimen under tri-axial tensile stress
and the final fracture is originated from the core part of specimens. The present paper does not treat such an
exceptional case of very low cycle fatigue.
2. Material and experimental procedure
The material used for test specimens was a round bar of 0.15% carbon steel. Pieces of bar were annealed
at 900ºC for 1 hr and then machined on a lathe. The chemical composition and mechanical properties of this
material are shown in Table 1. Figure 1 shows the shape and dimensions of the specimen. In some specimens, a
partial notch or a hole was introduced on the surface of specimens. The partial shallow notch shown in Fig. 1(b)
was introduced to localize the location of crack initiation to a small area for easiness of observation of crack
initiation and growth compared to a completely smooth specimen. But comparing the fatigue lives with those of
smooth specimens, the specimen with the shallow partial notch can be approximately regarded as a kind of
smooth specimen.
Table 1. Chemical composition and mechanical properties of material (σS; Yield stress [MPa],
σB; Ultimate tensile strength [MPa], ψ; Reduction of area [%])
Fig. 1 Geometry and dimensions of the specimen and notches (in mm), (a) Specimen, (b) Partial notch, (c) Hole
The specimens having an artificial small hole with fewer fatigue cycles were used to compare fracture
ductility with the smooth specimens or specimens with partially notched specimens having small cracks after
longer fatigue cycles. Hereinafter, specimens with a partial notch are called “partially notched specimen”.
Specimens having a hole are called “holed specimen”.
Push-pull low cycle fatigue tests were carried out by strain control technique with 0.1Hz of cyclic
frequency. A clip gage of 10mm in length was set in the test section of the specimen. The strain was defined as the
nominal strain based on the gage length of 10 mm in all specimens used. As shown in Fig. 1, the size of partial
notch is very shallow and small. The maximum projection area An of partial notch in tensile direction is about 0.38 mm2. Since the cross-sectional area Ao of test section of smooth specimen is about 78.54 mm2, the ratio of
minimum cross section of the partially notched specimen to the smooth specimen (Ao –An) /Ao is 0.995. Also, the
stress concentration factor of the partial notch is about 1.06. In fact, as shown in later, the experimental results
showed that the fatigue life of the partially notched specimen was almost the same as that of smooth specimens
when the nominal strain was used.
The total cyclic strain range ∆εt was set at a constant value during the test. The observations of crack
initiation and growth were performed by the replica method. In some tests, the specimen surface was carefully
removed by using a lathe and emery-paper once or several times by interrupting the test after a determined
number of stress cycles. The fatigue lives were compared with the ones without surface removal. The crack
growth behaviors under some testing conditions were compared. The tensile fracture ductility εf (Eq. (2)) was measured by tensile tests for the fatigue specimens. The relationships between the fracture ductility εf and number
of cycles N or length of main crack l were compared with holed specimens and partially notched specimens.
3. Experimental results and discussion
3.1 Extension of fatigue life by removing surface layer
Figure 2 shows the relationship between cyclic plastic strain range ∆εp and number of cycles to failure Nf.
The circular symbols show the data for the ordinary low cycle fatigue test using partially notched specimens
without interrupting the test until final failure. The data are almost the same as for the life of the smooth specimen
denoted by a solid circular symbol. The triangular symbols show data for the specimens whose surface layer was
removed after interrupting the previous fatigue test before failure. In these cases, the length l of existing cracks
was checked before surface removal. In Fig. 2, the numbers associated with the triangular symbols show the
number of times of surface removal. The arrows associated with the triangular symbols show the data in which the
test was stopped before specimen failure. Although the values of total strain range ∆εt were kept constant, plastic strain range ∆εp varied due to cyclic hardening or softening. Therefore, the values of ∆εp are shown by the values
at Nf/2 of partially notched specimens. The first removal of surface layer was carried out when the number of
cycles N was reached about Nf/2 of partially notched specimen. After the surface removal, the test was continued
until the specimen was broken. As shown in Fig. 3 (a), the third and fourth surface removal was carried out every defined number of cycles (Nf/2). The depth of removal layer was 0.2mm. Figure 3 (a) shows the examples of
variation of stress range for ∆εt =0.0139 or 0.0161 (∆εp =0.0111 or 0.0132). Figure 3 (b) shows the surface conditions just before the third time surface removal with ∆εp =0.0132. In this example, the total number of
applied cycles N was 6x103 cycles (Nf of partially notched specimen ≅ 4.5x103) and there were some small cracks
within notched area. Cracks of 0.1 mm - 0.2 mm in length were observed before surface removal.
Fig. 2 Relationship between plastic strain range ∆εp and the number of cycles to failure Nf .
Fig. 3 Examples of variations in the stress range and observation of cracks: (a) Variations in the stress
range. The arrows show the cycles where the cracked surface layer was removed, (b) Surface conditions
just before the third time surface removal
The Coffin-Manson law for the ordinary low cycle fatigue test without surface removal is expressed by
∆εp Nf0.4 =0.33
(3)
When the surface layer of the specimen with ∆εp = 0.0132 was removed four times, the fatigue life Nf
was extended more than twice compared to the case without surface removal. As shown later and in the previous
studies by Murakami et al. [4,6,7], when the crack length reached 1 mm, the relative number of cycles N/Nf was
more than 0.8. Thus, it should be noted that if a crack is visible to the good naked eyes, the specimen will break
with additional small cycles. Considering the experimental fact, the surface layer of the specimens with triangular
symbols in Fig. 2 was removed at the cycle N before the main crack length reached 0.2 mm. Since it is very
difficult to observe the entire specimen surface, only the main crack nucleating from the partial notch was
measured during the tests by the replica method. In the case of triangular symbol associated with an asterisk (*) in
Fig. 2, another crack which was overlooked grew from outside the partial notch, and its length became longer than
1mm. From SEM (Scanning Electron Microscope) observation, it was revealed that there existed an exceptionally
large material defect at the crack origin as shown in Fig. A1of Appendix. The final length of crack which initiated
from outside of the partial notch in this fatigue test was 1.7mm at N/Nf=0.90. The test for the specimen with * was
stopped at N/Nf=0.9 and it was used to measure the ductility loss as shown later in Figs. 8 and 9. After this
experience, the surface layer was removed carefully not only inside the partial notch but also over all surface of
the specimen. Except for the data with * in Fig. 2, all the surface cracks were removed when the following fatigue
tests were continued.
Extension of fatigue life by removing small surface cracks indicates that low cycle fatigue life is
controlled by surface conditions, more concretely by small surface cracks. Considering that the low cycle fatigue
process is mostly (nearly 100%) dominated by a small crack growth process, we can conclude that the reality of
fatigue damage is the existence of small cracks and not overall microstructural changes such as dislocation
structures or void nucleation during fatigue cycles as also pointed out by Feltner and Beardmore [16]. Feltner and
Laird [17] and Laird [18] pointed out that in fatigue under step loading fatigue a specific dislocation structure
under a strain amplitude is developed, and another specific dislocation structure is developed in the next strain
step and then again the first dislocation structure is recovered after switching the strain amplitude from the second
strain amplitude to the first strain amplitude regardless of the accumulation of number of cycles. This important
experiment made clear that dislocation structures themselves do not directly reflect the degree of fatigue damage.
3.2 Cause of ductility loss during fatigue cycle
3.2.1 Surface crack and fracture behavior in tensile test
Murakami et al. [4, 6] showed that the fracture ductility during fatigue cycles of 70/30 brass had a good
correlation with the length of crack, regardless of fatigue cycles. A series of experiments were carried out in this
study to confirm their conclusion by using a 0.15% carbon steel. Partially notched specimens with and without
surface removal, and holed specimens were used for the measurement of ductility loss in the tensile test.
Figure 4 shows the relationship between the crack length l and relative number of cycles N/Nf, where the
value of Nf for the data of partially notched specimens is employed as the scale for fatigue cycles. The crack
length l of holed specimens is defined by including the diameter of hole. Naturally, the holed specimen having a
hole with d=h =0.2mm, had fewer cycles to produce a crack of the same length compared to partially notched
specimens. Figure 4 indicates that the crack growth rate is not so much different between the holed specimens and
partially notched specimens. The crack growth curve for the specimen with h=d/2=0.05mm shows almost the
same tendency as that for partially notched specimens. This means that the crack growth rate is not affected by the
accumulation of strain cycles, i.e. so-called “fatigue damage” as referred to by many researchers when the applied
strain conditions are the same.
As shown in Fig. 4 (b), the tendency of crack growth is clearer in the relationship between ln l and N/Nf.
It means that the small crack growth law is approximated by
ln l = C1 + C2 N/Nf
(4)
where, C1 and C2 are constants determined by experimental conditions. We obtain the following relation by
differentiating of Eq. (4)
dl/dN = C2 l / Nf
(5)
Thus, the crack growth rate dl/dN is proportional to crack length l, and this relationship is evaluated by Fig. 4. The
crack growth rate in the present study is represented by the parameters of crack length and fatigue life Nf, in
dependent of types of specimens used.
Figure 5 shows examples of observation of crack growth. In the case of the partially notched specimen,
locally dense slip bands and crack initiation were observed. In the case of the holed specimen, the crack emanated
from hole and its growth followed. By comparison of Figs. 5 (b) and (c), regardless hole sizes, the surface
conditions (roughness and slip patterns) in the vicinity of the crack tip looks similar. As shown by Murakami et al.
[4, 7], the Palmgren-Miner rule [13, 14] can be applied to the crack growth behavior when the applied stress level
was switched during low cycle fatigue test. The applicability of the Palmgren-Miner rule is justified by the crack
growth law expressed by Eq. (5). According to the investigation of Murakami et al. [4, 7], the prior fatigue history
in front of the main crack, where the crack has not yet grown, has no effect on the subsequent crack growth. This
is consistent with the applicability of the Palmgren-Miner rule and Feltner et al’s studies and Laird’s study on
dislocation structure [16 -18].
Fig. 4 Crack growth curves (∆εp=0.0132, Nf=4510 and ∆εp=0.009, Nf=13990): (a) l vs. N/Nf, (b) ln l vs. N/Nf Fig.5 Observation of crack growth: (a) Partially notched specimen (∆εp=0.009) , (a1) N=6300, l=0.2mm, (a2) N=10100, l=1.01mm : (b) Holed specimen (d= h= 0.2 mm, ∆εp=0.0132),
(b1) N=1000, l=0.48mm, (b2)
N=1900, l=1.4mm: (c) Holed specimen (d/2=h=0.05mm, ∆εp=0.0132), (c1) N=3100, l=0.38mm, (c2)
N=4080, l=1.9mm
Now, the residual ductility is compared on holed specimens and smooth specimens as a function of
applied strain cycles and that of crack length.
The tensile tests were carried out on fatigued specimens and nonfatigued specimens by interrupting the
fatigue test. Figure 6 shows the tensile stress – elongation δ curves. The elongation was measured between the
grip ends of the testing machine. The open circles show the curve of nonfatigued specimen before the fatigue test.
The fracture morphology was affected by the cyclic conditions and the types of the specimens. The final
fracture stresses were also affected by the fracture mode. As shown later, the final ductile fractures were either
cup-and-cone type or shear fracture from the surface layer. In cases where the fracture mode was cup-and-cone,
the nominal fracture stress was higher than in the cases of shear fracture.
Figure 7 shows an example of the crack deformation and extension during tensile test of fatigued
specimen with l=1.6mm after fatigue test.
Fig. 6 Results of tensile tests (l denotes the length of main surface crack when tensile test was started)
Fig. 7 Crack deformation and extension during tensile test of fatigued specimen with l=1.6mm after fatigue test
with ∆εp=0.01.
3.2.2 Relationship between the length of surface crack and the fracture ductility
In order to understand the effect of a surface crack on fatigue life in a low cycle regime, the results of the
previous studies on 70/30 brass [4, 7] were discussed together with the results of 0.15% carbon steel of the present
study.
Figure 8 shows the relationship between the fracture ductility εf and the relative numbers of cycles N/Nf, where fracture ductility εf was defined by Eq. (2). The fatigue crack length l at the moment of tensile tests is
associated with the data points in Fig. 8. Figure 8 (a) shows the results of 0.15% carbon steel and Fig. 8 (b) those
of 70/30 brass. Figure 9 shows the relationship between the fracture ductility εf and the fatigue crack length l at
the moment of tensile tests. Figure 9 (a) shows the results of 0.15% carbon steel and Fig. 9 (b) those of 70/30
brass. In these figures, the curves A, B and C summarized the data separately as follows.
A: The partially notched specimens of 0.15 % carbon steel and those of the smooth specimens of 70/30
brass after fatigue test.
B: The specimens whose surface layer was removed after fatigue test.
C. The specimens containing fatigue crack emanating from artificial hole.
Fig. 8 Relationship between fracture strain εf and relative number of cycles N/Nf . The numbers associated with
the data points denote the crack length l at the moment of tensile test. Nf is the fatigue life of partially notched
specimens; (a) 0.15% carbon steel (The meaning of the mark * is explained in Fig. 2), (b) 70/30 brass
Fig. 9 Variations in fracture ductility εf as a function of the length of surface crack l; (a) 0.15% carbon steel
(* see Fig. 2), (b) 70/30 brass
In Fig. 8, the fracture ductility εf is plotted all together for the partially notched specimens (or smooth
specimens) and holed specimens in terms of fatigue cycles N/Nf. However, the series of the data A, B and C are
separately plotted and a unique curve cannot be obtained. The fracture ductility of holed specimens shown by
curve C decreases in the early stages of N/Nf, compared with the case of partially notched specimens or smooth
specimens shown by curve A. The ductility of fatigued specimens whose surface cracks were perfectly removed
from the surface layer remained almost at the same value as the initial ductility.
If the fracture ductility εf is plotted in terms of crack length as in Fig. 9, all the data of partially notched
specimens and holed specimens can be summarized uniquely regardless of the number of fatigue cycles N/Nf. In
other words, this means that the fracture ductility εf after fatigue cycles cannot be used as the parameter to express
the microstructual change of the bulk materials based on the number of applied cycles or history of applied strain.
Thus, the fracture ductility or residual ductility has a strong correlation with crack length l regardless of
fatigue cycles. At the same time, we can conclude that the change in microstructural quality such as dislocation
structure after fatigue cycles has no substantial relationship with the variations in fracture ductility. Also, it is not
reasonable to say that the changes in the material qualities after low cycle fatigue test are related to the variations
in fracture ductility εf. Thus, the reality of fatigue damage of low cycle fatigue is the existence of small fatigue
cracks.
In addition to the above findings, it is found that there is a critical crack length lc for the drastic decrease
in ductility due to surface crack growth by unstable shear fracture mode. From Fig. 9, the size of lc for 70/30 brass
is 0.4 mm and that for 0.15 % carbon steel is 0.8 mm. These values may be used as the criterion for the analysis of
ductile fracture.
Fig. 10 Morphologies of fracture surface after tensile tests in the case of 70/30 brass (∆εp = 0.0254);
(a) Cup and cone type fracture; (a1) Nonfatigued specimen, (a2) l = 0.1 mm ,
(b)
Smooth specimen; broken by shear mode; (b1) l = 0.8 mm, (b2) l = 1.6 mm,
(c)
Hold specimen (d = 0.2mm), (c1) l = 0.86 mm, (c2) l = 1.6 mm
Fig. 11 Morphologies of fracture surface after tensile tests in the case of 0.15% carbon steel (∆εp = 0.0132);
(a) Specimen after surface removal with l=0mm, (b) Partially notched specimen with l=1.21mm,
(c) Partially notched specimen with l=1.7mm, (d) Holed specimen (d = 0.2mm) with l=1.4mm
Figure 10 shows the fracture surfaces after tensile tests for 70/30 brass. Figure 11 shows those for
0.15% carbon steel. The original fracture pattern for the nonfatigued specimen without a notch or defect is a cup
and cone pattern, where the tensile fracture originated from voids nucleating dimples in the central part of the
specimen. As shown in Figs. 10 and 11, this pattern was observed in the cases of nonfatigued specimens and
specimens with very small cracks whose length was shorter than 0.8mm for 0.15 % carbon steel and shorter than
0.4mm for 70/30 brass. The same fracture pattern was also observed on the specimen with surface removal, ie.
l=0mm as shown in Fig. 11 (a).
The shear type fracture occurs from the surface fatigue crack if the crack length is longer than the
critical length. As shown in Figs. 10 (c) and 11 (d), the appearance of shear type fracture is clearer in the cases of
holed specimens, because there is only one leading crack initiating from hole-edges. In the case of Fig. 11 (b), the
fracture started from both from internal voids and surface fatigue crack. However, the final fracture mode is shear
type. In Figs. 10 and 11, the start of shear fracture was a fatigue crack. Thus, the loss of fracture ductility is related
to the fracture modes. When the fracture started unstably from fatigue crack or surface crack by shear mode, the
ductility loss is pronounced. It was confirmed from the fracture surface that the critical crack length lc for unstable
shear fracture in 0.15 % carbon steel is approximately lc=0.8mm which is longer than the value for that in
annealed 70/30 brass, i.e. lc=0.4mm.
4. Conclusions
The roles of cracks and fatigue damage in the process of low cycle fatigue were discussed based on the
experiments focusing on small cracks and also based on previous studies. The conclusions can be summarized as
follows.
(1) Removing small surface cracks extends fatigue life and recovers material ductility regardless of
change in the bulk material properties during fatigue cycles.
(2) The loss of fracture ductility εf is caused by the existance of small surface cracks. The ductility loss
can be uniquely correlated with crack length but not with number of fatigue cycles N.
(3) There is a critical crack size lc for the drastic decrease in ductility due to unstable shear fracture.
lc=0.8mm for the low carbon steel used in this research and lc=0.4mm for annealed 70/30 brass.
(4) It is misconceptions to correlate changes in microstructural material properties such as dislocation
structure and energy dissipation ability to fatigue damage. The reality of low cycle fatigue damage is the existence
of small cracks. The geometrical dimension of cracks is the most important factor for the discussion of fatigue
damage.
Appendix
Figure A1 shows examples of crack initiation sites (∆εp =0.0132). Figure A1(a) shows that most of
cracks intiated from ferrite grain boundries. Figure A1(b) shows the fracture surface in the vicinity of the fatigue
crack initiation from an exceptionally large defect contained in the material.
Fig. A1 Examples of crack initiation site, (a) Crack initiation mostly at ferrite grain boundaries, (b) The site
of crack initiation from an exceptionally large defect which was conatined in the specimen from the begining
(This specimen corresponds to the data with symbol * in Fig. 2.)
References
[1] Coffin, Jr. L. F., A Study of the Effects of Cyclic Thermal Stresses on a Ductile Metal, Transactions of
American Society of Mechanical Engineers, 1954, 76, 931-950.
[2] Manson, S. S., Behavior of Materials under Thermal Stress, 1953 and 1954, NACA TN 2933 and NACA TR
1170
[3] Coffin, Jr. L. F., Design Aspects of High-temperature Fatigue with Particular Reference to Thermal Stresses,
Transactions of American Society of Mechanical Engineers, 1956, 78, 527.
[4] Murakami, Y., Miller, K. J., What is Fatigue Damage? A View Point from the Observation of Low Cycle
Fatigue Process, International Journal of Fatigue, 2005, 27, 991-1005.
[5] Kikukawa, M., Ohji, K., Ohkubo, H., Yokoi, T., Morikawa, M., Damage and Recovery from it in Low Cycle
Fatigue, Transactions of Japan Society of Mechanical Engineers, 1972, I 38, 8-15.
[6] Murakami, Y., Makabe, C., Nisitani, H., Effects of Small Cracks on Ductility Loss in Low Cycle Fatigue of
70/30 Brass, Journal of Testing Evaluation, 1989, 17, 20-27.
[7] Murakami, Y., Harada, S., Endo, T., Tani-ishi, H., Fukushima, Y., Correlations among Growth Law of Small
Cracks, Low-Cycle Fatigue Law and Applicability of Miner’s Rule. Engineering Fracture Mechanics, 1983,
18, 909-924.
[8] Winter, A. T., A model for the fatigue of copper at low plastic strain amplitudes, Philosophical Magazine, 1974, 30, 719-738.
[9] Mughrabi, H., Wang, K., Differt, K., Essmann, U., Fatigue Mechanisms, Edited by Lankford, J., Davidson, D.
L., Morris W. L., Wei, R. P., 1983, ASTM STP 811, 5-45.
[10] Lukáš, P., Klesnil, M., J. Krejčí, J., Dislocations and Persistent Slip Bands in Copper Single Crystals Fatigued at Low Stress Amplitude, Physical Status Solids, 1968, 27, 545-558.
[11] Imura, T., Yamamoto, A., Defect, Fracture and Fatigue, Proceedings of the Second International Symposium,
Mont Gabriel, Canada, 1982, 17-21.
[12] Murakami, Y., Mura, T., Kobayashi, M., Change of Dislocation Structures and Macroscopic Conditions from
Initial state to Fatigue Crack nucleation, Basic Questions in Fatigue: Vol. I, Edited by Fong, J. T., Fields, R.
J. , 1988, ASTM STP 924, 39-63.
[13] Palmgren A., Durability of Ball Bearing. ZVDI, 1924, 68, 339-341.
[14] Miner, M. A., Cumulative Damage in Fatigue. Journal of Applied Mechanics, 1945, 12, A159-A164.
[15] Komotori, J., Shimizu, M., Microstructural Effect Controlling Exhaustion of Ductility in Extremely
Low-Cycle Fatigue, Transactions of Japan Society of Mechanical Engineers Ser. A, 1991, 57, 2879-2883.
[16] Feltner, C. E., Beardmore P., Strengthening Mechanism in Fatigue, in Achievement of High Fatigue
Resistance in Metals and Alloys, American Society for Testing and Materials, 1970, ASTM STP 467, 77-112..
[17] Feltner, E., Laird, C., Cyclic Stress-Strain Response of FCC Materials and Alloys-II: Dislocation Structures
and Mechanism. Acta Metallurgica, 1967, 15, 1633-1653.
[18] Laird, C., Cyclic Deformation of Metals and Alloys, Treatise on Materials Science and Technology, 1975, 6,
101-162.
Table1
Chemical composition [wt, %] C
Si
0.15
0.30
Mn 0.50
Mechanical properties [MPa, %]
P
S
Cr
Ni
Cu
Fe
σS
σB
ψ
0.013
0.013
0.19
0.05
0.14
Bal.
283
449
60
Fig. 1
(a)
(b)
(c)
Fig. 2
4x10
-2
Plastic strain range ∆εp
∆εpNf0.40= 0.33 1*
10-2
f=0.1Hz 3
4 1
3
Smooth specimen No surface layer removal Surface layer removal Partially notched specimen No surface layer removal Surface layer removal Numbers associated to symbols are number of removal Arrows show the non-broken specimens * Larger crack initiated from outside partial notch
10-3 103
104
Number of cycles to failure Nf
4x10 4
Fig. 3
Stress range ∆σ, MPa
750
600 Arrows show the cycles where the cracked surface layer was removed
450
300 0
Partially notched specimen ∆εp=0.0111, ∆εt=0.0139 ∆εp=0.0132, ∆εt=0.0161
5000
10000
Number of cycles N (a)
(b)
15000
Fig. 4
Crack length l, mm
3
2
Holed specimen Partially notched specimen d/2=h=0.05mm ∆εp= 0.0090 ∆εp= 0.0132 ∆εp= 0.0132 d=h=0.2mm ∆εp= 0.0132
Approximated curve of shifting the original data of
1
0 0
0.2
0.4
0.6
0.8
1
Relative number of cycles, N/Nf (a)
Crack length l, mm
Partially notched specimen ∆εp= 0.0090 ∆εp= 0.0132
100
Approximated curve of shifting the original data of
10-1 Holed specimen d/2=h=0.05mm ∆εp= 0.0132 d=h=0.2mm ∆εp= 0.0132
10-2 0
0.2
0.4
0.6
0.8
Relative number of cycles, N/Nf (b)
1
Fig. 5
(a1)
(a2)
(b1)
(b2)
(c1)
(c2)
Fig. 6
550 Nonfatigued specimen
∆εp=0.0132
Stress σ, MPa
450
300 Fatigued specimen Partially notched specimen l=1.7mm (Fatigue cycle N/Nf=2.17, Surface layer was removed 4 times at every 1/2Nf cycles) l=0.8mm (Fatigue cycle N/Nf=0.67, Ordinary fatigue test, No surface removal) Holed specimen, d=h=0.2mm l=0.4mm (Fatigue cycle N/Nf=0.16) l=1.4mm (Fatigue cycle N/Nf=0.42)
150
0
0
1
2
3
4
Elongation δ, mm
5
6
7
Fig. 7
Fig. 8
l=0.4mm
1 0.3mm
0.8mm
∆εp=0.0132 ∆σ=597MPa
0mm
Fracture ductility ε f
3 0.75
1.21mm
A C
0.5
B 4
1*
1.4mm
1.7mm
1.7mm
1.9mm Initial ductility
Smooth specimen Surface layer removal Holed specimen d/2=h=0.05mm d=h=0.2mm
notched specimen 0.25 Partially No surface layer removal Surface layer removal (Numbers associated to symbols are number of removal)
0 0
0.5
1
1.5
2
2.5
Relative number of cycles N/Nf
(a)
l=0.12mm
l=0.46mm
l=0.0mm
1.5
Fracture ductility ε f
B
l=0.125mm
l=0.5mm
1 l=0.85mm
l=0.92mm
C
Initial ductility Plain specimen, Cracked ∆εp=0.0104, ∆σ=471MPa 0.5 ∆εp=0.0254, ∆σ=541MPa Holed specimen, Cracked ∆εp=0.0254, ∆σ=541MPa Plain specimen, Crack removed ∆εp=0.0254, ∆σ=541MPa ∆εp=0.0104, ∆σ=471MPa
0 0
l=0.8mm
l=1.6mm
0.2
0.4
0.6
0.8
Relative number of cycles N/Nf
(b)
l=1.58mm
A
l=1.6mm
1
Fig. 9 1
Fracture ductility ε f
∆εp=0.0132 ∆σ=597MPa
0.75 3 A, B and C
4 1*
0.5
Initial ductility Smooth specimen Partially notched specimen Surface layer 0.25 No surface layer removal removal Surface layer removal Holed specimen (Numbers associated to symbols d/2=h=0.05mm are number of removal) d=h=0.2mm
0 0
0.5
1
1.5
2
Crack length l, mm
(a)
Fracture ductility ε f
1.5
C
1
A Initial ductility Plain specimen, Cracked ∆εp=0.0104, ∆σ=471MPa ∆εp=0.0254, ∆σ=541MPa Holed specimen, Cracked ∆εp=0.0254, ∆σ=541MPa
0.5
0
0
0.5
1 Crack length l, mm
(b)
1.5
2
Fig. 10
Top view (a1)
Top view (a2)
Top view
Top view
View from inclined direction (b1)
View from inclined direction (b2)
Top view
Top view
View from inclined direction (c1)
View from inclined direction (c2)
Fig. 11
View from inclined direction
Top view (a)
View from inclined direction
Top view (b)
View from inclined direction
Top view (c)
View from inclined direction
Top view (d)
Appendix A1
(a)
(a)
(b)
JIJF 3596
Captions of Table and Figures
Table 1. Chemical composition and mechanical properties of material (σS; Yield stress [MPa], σB; Ultimate tensile strength [MPa], ψ; Reduction of area [%])
Fig. 1 Geometry and dimensions of the specimen and notches (in mm): (a) Specimen, (b) Partial notch, (c) Hole
Fig. 2 Relationship between plastic strain range ∆εp and the number of cycles to failure Nf
Fig. 3 Examples of variations in the stress range and observation of cracks: (a) Variations in the stress range. The
arrows show the cycles where the cracked surface layer was removed, (b) Surface conditions just before the third
time surface removal
Fig. 4 Crack growth curves (∆εp=0.0132, Nf=4510 and ∆εp=0.009, Nf=13990): (a) l vs. N/Nf, (b) ln l vs. N/Nf Fig.5 Observation of crack growth: (a) Partially notched specimen (∆εp=0.009), (a1) N=6300, l=0.2mm, (a2) N=10100, l=1.01mm; (b) Holed specimen (d= h= 0.2 mm, ∆εp=0.0132), (b1) N=1000, l=0.48mm, (b2) N=1900, l=1.4mm; (c) Holed specimen (d/2=h=0.05mm, ∆εp =0.0132), (c1) N=3100, l=0.38mm,
(c2) N=4080, l=1.9mm
Fig. 6 Results of tensile tests (l denotes the length of main surface crack when tensile test was started)
Fig. 7 Crack deformation and extension during tensile test of fatigued specimen with l=1.6mm after fatigue test
with ∆εp=0.01 Fig. 8 Relationship between fracture strain εf and relative number of cycles N/Nf . The numbers associated with the
data points denote the crack length l at the moment of tensile test. Nf is the fatigue life of partially notched
specimens: (a) 0.15% carbon steel (The meaning of the mark * is explained in Fig. 2), (b) 70/30 brass
Fig. 9 Variations in fracture ductility εf as a function of the length of surface crack l: (a) 0.15% carbon steel
(* see Fig. 2), (b) 70/30 brass
Fig. 10 Morphologies of fracture surface after tensile tests in the case of 70/30 brass (∆εp = 0.0254): (a) Cup and
cone type fracture; (a1) Nonfatigued specimen, (a2) l = 0.1 mm , (b) Smooth specimen; broken by shear mode;
(b1) l = 0.8 mm, (b2) l = 1.6 mm; (c) Holed specimen (d = 0.2mm), (c1) l = 0.86 mm, (c2) l = 1.6 mm
Fig. 11 Morphologies of fracture surface after tensile tests in the case of 0.15% carbon steel (∆εp = 0.0132):
(a) Specimen after surface removal with l=0mm, (b) Partially notched specimen with l=1.21mm, (c) Partially
notched specimen with l=1.7mm, (d) Holed specimen (d = 0.2mm) with l=1.4mm
Fig. A1 Examples of crack initiation site: (a) Crack initiation mostly at ferrite grain boundaries, (b) The site of
crack initiation from an exceptionally large defect which was contained in the specimen from the begining (This
specimen corresponds to the data with symbol * in Fig. 2.)
Highlights 1. The main damage which affects fatigue life is initiation and growth of cracks. 2. The fatigue life was extended by removing small cracks. 3. There is a critical length of fatigue crack which causes the loss of ductility. 4. The loss of fracture ductility is related to the fracture types in tensile tests.