Analysis of Variable Amplitude Fatigue Data of the P355NL1
Steel Using the Effective Strain Damage Model
Pereira, Hlder F.S.G. UCVE, IDMEC Plo FEUP
Campus da FEUP
Rua Dr. Roberto Frias, 404
4200-465 Porto, Portugal
Tel.: +351 22 508 1491; Fax: +351 22 508 1532
E-mail address: [email protected]
De Jesus, Ablio M.P. Engineering Department Mechanical Engineering
University of Trs-os-Montes and Alto Douro
Quinta de Prados, 5001-801 Vila Real, Portugal
Tel.: +351 259 350 306; Fax: +351 259 350 356
E-mail address: [email protected]
DuQuesnay, David L. Department of Mechanical Engineering
Royal Military College of Canada
PO Box 17000 Station Forces
Kingston, Ontario, Canada
Tel.: +1 613 541 6000; Fax: +1 613 542 8612
E-mail address: [email protected]
Silva, Antnio L. L.
Engineering Department Mechanical Engineering
University of Trs-os-Montes and Alto Douro
Quinta de Prados, 5001-801 Vila Real, Portugal
Tel.: +351 259 350 356; Fax: +351 259 350 356
E-mail address: [email protected]
Abstract
This paper proposes an analysis of variable amplitude fatigue data obtained for the
P355NL1 steel, using a strain-based cumulative damage model. The fatigue data consist of
constant and variable amplitude block loading which was applied to both smooth and
notched specimens, previously published by the authors. The strain-based cumulative
damage model, which has been proposed by D. L. DuQuesnay, is based on the growth and
closure mechanisms of microcracks. It incorporates a parameter termed net effective strain
range, which is a function of the microcrack-closure behaviour and inherent ability to resist
fatigue damage. A simplified version of the model is considered which assumes crack closure
at the lowest level for the entire spectrum and does not account for varying crack opening
stresses. In general, the model produces conservative predictions within an accuracy range
of two on lives, for both smooth and notched geometries, demonstrating the robustness of
the model.
1 Introduction
Pressure vessel components invariably experience non-uniform loading histories during
their service life, motivating research on material and component performance under
variable amplitude loading, and the continual development of more reliable and accurate
fatigue damage models.
Important pressure vessels design codes (ex. EN13445 standard [1]) propose procedures
for fatigue analysis of variable amplitude loading that are supported by constant amplitude
fatigue data and a linear damage summation rule, as proposed by Palmgren and Miner [2].
This type of analysis neglects any load sequential effects that occur during the fatigue
loading history, which is an important limitation. In fact, the linear summation rule does not
consider the interaction effects between higher to lower stress levels or vice-versa. The linear
damage rule also neglects the damage induced by any stress below the fatigue endurance
limit.
Most of metallic materials and components exhibit more complex behaviours than
modelled by the linear damage rule. However, and despite the limitations of the fatigue linear
damage rule, the linear rule still is nowadays widely used for design purposes due to its
simplicity.
It has been verified that some metallic materials and components exhibit highly
nonlinear fatigue damage evolution with load dependency [3-5]. The last two characteristics
yield to nonlinear damage accumulation with load sequential effects. Thus, depending on
load history, the Palmgren-Miners rule can lead to inconsistent predictions, i.e. conservative
or non conservative predictions.
Several attempts have been done to propose more reliable fatigue damage rules. Manson
[6], Fatemi [7] and Schijve [8] present comprehensive reviews about these fatigue damage
models. However, the new propositions are often limited to very specific conditions (e.g.
certain loading sequences, materials).
This paper presents an evaluation of a strain-based cumulative damage model that has
been proposed to predict crack initiation under variable amplitude loading [9-11]. This model
proposes a net effective strain range () as a damage parameter which accounts for
microcrack closure behaviour (cl, cl) and inherent resistance to fatigue (i, i) of metals
and alloys. The effective strain damage model is based on fracture mechanics concepts and
the effect of crack closure on the growth behaviour of short fatigue cracks as described in
[10]. This model has been shown to successfully predict crack initiation behaviour for a wide
range of alloys, load histories and component geometries, thus displaying versatility and
accuracy not provided by other analytical models [9-11]. This model is applied together with
the linear damage summation rule. Nevertheless, the use of a crack-closure derived effective
strain range confers to the proposed approach the capacity to account for both mean-stress
effects in fatigue and for changes in damage accumulation rates following overloads in
spectrum loading applications. The last characteristic load dependency effects - is typical
on nonlinear damage accumulation models.
The strain-based cumulative damage model is applied to assess variable amplitude
experimental data, recently published for a pressure vessel steel the P355NL1 (EN 10028-
3) steel [3-5]. Smooth specimens, under variable amplitude strain-controlled loading, and
notched specimens under variable amplitude stress-controlled loading were investigated.
Constant and variable amplitude blocks were considered in the study.
2 The Net Effective Strain Range Model
The net effective strain range model has been developed on the basis of the fatigue
behaviour of small cracks observed quantitatively under both constant amplitude and
overload spectrum loading conditions [9-11]. Such observations have led to the evolution of
a model whose two basic criteria for the infliction of damage upon a cyclically loaded material
by microcracks are: (i) to inflict damage, a crack must be open; and (ii) once open, damage
is imparted by a crack only if cycling is sufficient to overcome a capacity for resisting fatigue
damage intrinsic to the material. In order to model these two phenomena, the effective
strain range (eff) and the intrinsic fatigue limit (i) were proposed to define together
the net effective strain range () as a damage parameter for both constant amplitude and
spectrum fatigue analyses.
The effective strain range (eff) is the strain range over which intrinsic flaws (small
surface and sub-surface cracks) remain open. This parameter has been shown to adequately
account for both mean stress effects in fatigue and for changes in damage accumulation
rates following overloads [12]. An opening stress (op) dependent on cyclic yield stress (y)
and the maximum (max) and minimum (min) stresses corresponding to the largest rainflow
cycle in a spectrum, is defined to support the effective strain range definition according to:
min
2
maxmax 1
=
y
op (1)
where and are material constants to be experimentally determined. Although experience
has shown crack closure stresses lower than crack opening stresses, as illustrated in Fig. 1,
the evaluation of the crack closure is a difficult task since no accurate procedure for its
evaluation is available. An unconservative assumption is to assume the closure stress equal
to the opening stress. According to Fig. 1, if the closure stress is assumed equal to the
opening stress, then cycle A is closed and cycle B is partially closed, their damaging effects
being omitted or partially omitted from the final damage computation. The maximum stress
can be lower, equal or higher than the yield stress, resulting in tensile or compressive
stresses. For high-cycle fatigue the maximum stress is only slightly higher than the yield
stress.
To provide a conservative estimate of the crack closure behaviour, this paper uses a
strain-based closure criterion which assumes a closure strain (cl) equal to the opening strain
(op). This assumption can be supported by experimental data [13,14]. Therefore, according
to Fig. 1, cycles A and B are assumed open and thus their damaging effects accounted into
the fatigue damage. Since the magnitudes of crack opening stresses occur in a region of
linear elastic behaviour, the corresponding op can be determined from op by a simple
Hookes law calculation, using the minimum stress and strain in the spectrum:
E
op
op
min
min
+= (2)
The effective strain range is the difference between the maximum strain in a cycle and
the larger (higher absolute value) of either the crack opening strain, or the minimum strain
in the cycle as expressed in the following equations:
=
opopeff
opeff
minmax
minminmax
,
, (3)
It is assumed that opening strain is constant throughout the variable amplitude spectrum
at a value defined by equations (1) and (2) relative to the largest rainflow cycle in the
spectrum.
Experimental evidence has shown that after a large overload, subsequent smaller cycles
may inflict damage if the overload promotes the crack opening under those smaller stress
cycles. However this damaging effect gradually decreases with the reduction in the small
cycles range, until a lower limit referred as intrinsic fatigue limit, i. While microcracks
remain open throughout small cycles with magnitudes below i, their failure to impart
damage implies that intrinsic fatigue limit represents an inherent resistance of a material to
fatigue damage. It is worth noting that i is independent of mean stress. As previously
stated, mean stress effects are accounted for by the effective strain range [9-11].
Finally, subtracting the intrinsic fatigue limit from the effective strain range results the
net effective strain range:
ieff =*
(4)
The net effective strain range can be considered a damage parameter that accounts
conveniently for changes in damage accumulation rate that occurs at different mean stresses
under constant amplitude loading, and the increase in damage accumulation rate that occurs
for cycles following overloads, under variable amplitude loading. The net effective strain
range can be related to the number of cycles to failure using the following power relation:
( )BfAE =
* (5)
where A and B are materials constants to be determined using constant and/or overload
fatigue data. It is interesting to note that this relation is a two-power terms relation which
the second term corresponds to the intrinsic strain limit appearing in the effective net strain
range definition, Eq. (4), leading to an horizontal asymptote (unit exponent in the second
power term).
The model described in this section, as proposed by DuQ uesnay, has been applied
together the linear damage accumulation rule. Although using the linear damage rule, the
assessment procedures under analysis present an important advantage over the classical S-
N approaches, which is the strain-based damage parameter sensitive to the interaction
between load cycles. This characteristic is usually not predicted by the classical S-N
approaches.
3 Experimental Details
The P355NL1 steel, supplied in the form of 314020005.1 mm3 plates, is analyzed in
this study. This steel is intended for pressure vessel applications and is a normalized fine
grain low alloy carbon steel. The chemical composition and mechanical properties of the
material are given in Tables 1 and 2, respectively.
This paper analyses data from fatigue tests of smooth and polished specimens, extracted
in the longitudinal (lamination) direction of the steel plate [3,4,15]. The geometry of these
specimens, defined according to the ASTM E606-92 standard, is illustrated in Fig. 2. In
addition, fatigue data from double notched rectangular specimens, extracted in the
longitudinal/lamination direction of the steel plates are analyzed [5,15]. The geometry of
theses specimens is illustrated in Fig. 3. This geometry has an elastic stress concentration
factor, Kt, equal to 2.17.
All fatigue tests were conducted in an INSTRON 8801 servo-hydraulic machine, rated to
100 kN. The fatigue tests of the smooth specimens were conducted under strain-controlled
conditions with null strain ratio; the tests of the notched details were performed under
remote uniaxial stress-controlled conditions.
The following test data were analyzed for the smooth specimens [3,4,15]:
Constant amplitude tests.
Two constant amplitude blocks applied in high-low (H-L) and low-high (L-H)
sequences, as illustrated in Fig. 4. The following pairs of strain ranges were combined
according to the two investigated sequences: 0.5/1.0% and 0.75/1.5%.
Multiple alternated constant amplitude blocks applied in H-L-H-L (...) and L-H-L-H (...)
sequences (see Fig. 5) for the strain range combinations of 0.5/1.0% and 0.75/1.5%.
Variable amplitude blocks applied in H-L (...), L-H (...), L-H-L (...) and random
sequences as illustrated in Fig. 6. Blocks illustrated in Fig. 6 were obtained for a
maximum strain of 2.1%. Also, similar blocks with a maximum strain of 1.05% were
tested. These blocks are composed of individual cycles extracted from truncated
Gaussian distributions as illustrated in Fig. 7.
For the notched specimens the following fatigue data was assessed [4, 15]:
Constant amplitude test data under the stress ratios R=0.0, R=0.15 and R=0.3.
Two constant amplitude blocks applied in the H-L and L-H sequences, similar to Fig. 4,
but under remote stress control. There are data available for R=0.0 for the stress
ranges combinations of 280/230 MPa and 280/400 MPa. Also there are data available
for R=0.15 and stress range combinations of 330/400 MPa and for R=0.3 and
350/400MPa stress range combinations.
Multiple alternated constant amplitude blocks applied in the H-L-H-L (...) and L-H-L-H
(...) sequences (similar to Fig. 5) for R=0.0 and the stress range combinations of
330/280 MPa and 350/400 MPa.
Variable amplitude blocks applied in H-L (...), L-H (...), L-H-L (...) and random
sequences as illustrated in Fig. 8. Blocks from Figs. 8a) to 8d) are composed by single
cycles with R=0, extracted from a Gaussian distribution of stress ranges with an
average of 220 MPa and standard deviation of 124.1 MPa. This Gaussian distribution
was truncated at a minimum stress range of 20 MPa and a maximum stress range of
420 MPa. Blocks from Figs. 8e) to 8h) were composed by single cycles with R=0.3
extracted from a Gaussian distribution of maximum stresses with average value of 220
MPa and standard deviation of 124.1 MPa, truncated at 20 and 420 MPa. Finally, Figs.
8i) and 8j) illustrate random blocks generated using sequences of pseudo cycles with
R=0, R=0.3 and R=0.5. For these latter spectra, the application of a cycle counting
technique, such as the rainflow technique, will result in distinct cycles from those
pseudo cycles.
4 Results and Discussion
In order to evaluate the net effective strain, the opening stress, op, and the intrinsic
fatigue limit, i, must be evaluated for the P355NL1 steel. The opening stress can be
evaluated using equation (1). Since specific tests for measuring the opening and closure
stresses of short fatigue cracks on smooth specimens were not performed, resulting the
constants and , values available in literature for a comparable steel the SAE1045 steel
were adopted: =0.75 and =0.0 [17]. The SAE1045 steel grade (ultimate tensile
strength=745MPa, 0.2% monotonic yield stress=466MPa; 0.2% cyclic yield stress=405MPa;
%weight: 0.46 C, 0.17 Si, 0.081 Mn [17]) shows higher strength properties than the
P355NL1 steel, which may be attributed to the higher carbon content. However, the P355NL1
steel presents some alloy elements that attenuate the differences between the carbon
contents. It is worthwhile to note that data available in literature about short cracks
opening/closure behaviour is very limited, and the proposed solution may affect the accuracy
of the predictions. Nevertheless, the quality of the predictions is satisfactory, as discussed
hereafter.
The yield stress considered in equation (1) was the value listed in Table 2. The constant
amplitude strain-life data derived for the P355NL1 steel under zero strain ratio is plotted in
Fig. 9, using the effective strain concept, resulting in a closure free strain-life curve. Figure 9
also includes the total strain versus life data. It is important to note that full mean stress
relaxation was assumed resulting a fully-reversible stress (R=-1). The analysis of the closure
free strain-life curve shows an endurance limit which corresponds to the intrinsic fatigue
limit, i [10]. The strain data is represented in the form of elastic or pseudo elastic stresses,
through the multiplication of strains by the Young modulus. The resulting intrinsic fatigue
limit (Ei) is approximately equal to 300 MPa. In this paper, the closure free fatigue data
was derived from constant amplitude fatigue data using the closure strain definition.
However, the preferable way to derive that closure free data is through periodic overloading
testing [10].
In Fig. 10 the constant amplitude strain life data is plotted using the net effective strain
life as damage parameter. The experimental data is well correlated using the power relation
proposed in equation (5), resulting the constants A=50 GPa and B=-0.5.
In this section, results of fatigue life predictions for both smooth and notched specimens
under the variable amplitude loading histories described above are presented and discussed.
Predictions are made using the computer code developed by Lynn and DuQuesnay [11]
which implements the strain-based cumulative damage model described in this paper. For
the variable amplitude blocks, op is calculated as the lowest value (largest cycle) in the
spectrum and is used to calculate Eeff for all cycles in the spectrum. Hence, the order of the
cycles is not important for variable amplitude loading the same life prediction results. For
H-L sequences, the high stress levels are assumed to set the op for the entire test. No crack
closure build up was modelled. For L-H sequences, the op for the L cycles was used for the L
cycles, then the op for the remaining H cycles was used for the H cycles. For H-L-H-L and L-
H-L-H sequences, because they are repetitive, the op of the H cycles was used for the entire
cycle sequence. For the random spectrum loading tests, op was taken as the value for the
largest cycle. In the notched specimen tests this meant an R=0 (or very near 0) cycle with
nominal =420MPa. The max and min, max and min in the notch root were calculated for the
notched specimens using Neubers rule [18] with Kt=2.17, K'=777 MPa, n'=0.1065 and
E=205 GPa. No relaxation of stresses was modelled. Masings hypothesis [18] was used with
the above K', n' and E values. It has been recognized that the Neubers rule may
overestimate the strains, leading to conservative fatigue predictions. However, the
assessment of the predicted strains is not an easy task and was not performed in this
investigation.
Figure 11 shows the life predictions for the smooth specimens under constant amplitude
block loading. Figure 12 illustrates the life predictions for the smooth specimens under
variable amplitude block loading. It can be verified that, in general, predictions fall within a
range between half/twice the experimental life which confirms the capability of the model to
predict fatigue damage under variable amplitude loading. Just few cases fall outside this
band, but on the conservative side. Authors believe that the accuracy of the predictions
would be improved if the closure stress formula was assessed for the P355NL1 steel, and in
particular its constants were evaluated for the low cycle fatigue domain. Also, the simplified
assumption of a stationary closure stress may be responsible for some inaccuracy on
predictions.
Figure 13 shows the experimental S-N curves of the notched detail and the predicted
ones, using the strain-based fatigue damage model discussed in this paper, which is based
on data from smooth specimens. In general the model captures the general trend of the S-N
curves.
Figure 14 illustrates the predictions for the notched specimens under constant amplitude
block loading and Fig. 15 plots the predictions for variable amplitude block loading. The same
trend of predictions made for the smooth specimens is verified, i.e., predictions fall within
the half/twice experimental lives. Only three predictions are outside this range on the unsafe
region, which were obtained for the variable amplitude block loading.
This paper also includes fatigue predictions for the notched specimens according to the
EN 13445 procedures [1]. The rules proposed for unwelded material were applied. Strain-life
data from smooth specimens was the basis for the current EN procedures for unwelded
material. This data was transformed into pseudo elastic stresses through a multiplication by
the Young modulus of the material. Safety coefficients of 1.5 on stresses and 10 on fatigue
lives were applied to the original average experimental S-N curves to derive the actual
design curves included in the EN procedures. In the analysis carried out in this paper, the
reservoir cycle counting method was used together with the linear damage summation rule,
as suggested in the standard. Fully elastic stress analysis was adopted with plasticity
corrections applied whenever required. A surface roughness equivalent to a machined
surface was adopted. Two alternative analyses are presented: with and without the safety
margins referred in the standard.
Figures 14 and 15 also illustrate the data from the predictions carried out using the EN
13445 standard. The analysis of the results reveals that predictions based on the EN 13445
procedures, including the safety coefficients are always conservative, with only one
exception for the random spectra data. Some predictions based on the standard fall within
the accuracy band for variable amplitude blocks (Fig. 15). Results from Fig. 14 shows that
the standard is excessively conservative, since all data falls outside the two times accuracy
band. If the safety factors are removed from the standard procedures, the predictions are
generally unsafe. Some predictions made for constant amplitude block data fall within the
accuracy band. For the variable amplitude blocks the predictions become excessively unsafe.
The comparison of performances between the net effective strain-based model and the
EN 13445 procedures highlights the satisfactory performance of the net effective strain-
based model.
5 Concluding Remarks
This paper presents an analysis of recently published variable amplitude fatigue data of a
pressure vessel steel the P355NL1 steel. Both smooth and notched geometries were
analyzed. A strain-based fatigue damage model, based on a concept of a net effective
strain which takes into account micro-crack closure effects and inherent ability of these
cracks to resist to fatigue damage, was applied to assess the available experimental data
using the linear damage accumulation rule. The model produced very reasonable predictions
within a 2 times accuracy band. On only few cases predictions fall outside this accuracy
band.
As already demonstrated in previous studies [9-11,17], this paper illustrates that the
cumulative damage summation model, based on the growth and closure mechanisms of
micro-cracks, successfully predicts crack initiation behaviour for a wide range of loading
histories, thus displaying versatility and accuracy not provided by other analytical models,
such as those included in design codes of practice.
It must be noted that predictions resulted from a simplified version of the model which
assumed crack closure conservatively at the lowest predicted level for the spectrum and did
not account for varying crack opening stresses. Also, the crack closure stress was not derived
experimentally for the P355NL1 steel. Parameter values from a similar steel were adopted. If
these issues would be addressed, more accurate predictions will likely occur.
Nomenclature
A = coefficient of equation (5);
= exponent of equation (5);
b = Fatigue strength exponent;
c = Fatigue ductility exponent;
E = Youngs modulus;
K = cyclic hardening coefficient;
Kt = elastic stress concentration factor;
Nf = number of cycles to failure;
n' = cyclic hardening exponent;
R = stress or strain ratios;
= coefficient of equation (1);
= coefficient of equation (1);
= net effective strain range;
eff = effective strain range;
i = intrinsic fatigue limit (strain);
i = intrinsic fatigue limit (stress);
cl = microcrack closure strain;
f = fatigue ductility coefficient;
max = maximum strain;
min = minimum strain;
op = microcrack opening strain;
= Poissons coefficient;
cl = microcrack closure stress;
f = fatigue strength coefficient;
max = maximum stress;
min = minimum stress;
op = microcrack opening stress;
UTS = ultimate tensile strength;
y = cyclic yield stress;
0.2 = monotonic yield strength.
References
[1] European Committee for Standardization - CEN, 2002, EN 13445: Unfired Pressure
Vessels, European Standard, Brussels.
[2] Miner, M.A., 1945, Cumulative Damage in Fatigue, Journal of Applied Mechanics, 67,
pp. A159-A169.
[3] Pereira, H.F.G.S., De Jesus, A.M.P., Fernandes, A.A. and Ribeiro, A.S, 2008, Analysis of
Fatigue Damage under Block Loading in a Low Carbon Steel, Strain, 44, pp. 429-439
[4] Pereira, H.F.G.S., De Jesus, A.M.P., Fernandes, A.A. and Ribeiro, A.S, 2009, Cyclic and
Fatigue Behavior of the P355NL1 Steel under Block Loading, Journal of Pressure Vessel
Technology, 131 (2), pp. 021210(1)-021210(9).
[5] Pereira, H.F.G.S., De Jesus, A.M.P., Ribeiro, A.S. and Fernandes, A.A., 2008, Fatigue
Damage Behavior of a Structural Component Made of P355NL1 Steel under Block Loading,
Journal of Pressure Vessel Technology, 131 (2), pp. 021407(1)-021407(9).
[6] Manson, S. S., Halford, G. R., 1986, Re-examination of cumulative fatigue damage
analysis - an engineering perspective, Engineering Fracture Mechanics, 25, pp. 538-571.
[7] Fatemi A., Yang L., 1998, Cumulative fatigue damage and life prediction theories: a
survey of the state of the art for homogeneous materials, International Journal of Fatigue,
20(1), pp. 9-34.
[8] Schijve, J., 2003, Fatigue of structures and materials in the 20th century and the state of
the art, Materials Science, 39(3), pp. 307-333.
[9] DuQuesnay, D.L., MacDougall, C., Dabayeh, A. and Topper, T.H., 1995, Notch fatigue
behaviour as influenced by periodic overloads, International Journal of Fatigue, 17(2), pp.
91-99.
[10] DuQuesnay, D.L., 2002, Applications of Overload Data to Fatigue Analysis and Testing,
in Application of Automation Technology in Fatigue and Fracture Testing and Analysis: Fourth
Volume, ASTM STP 1411, A.A. Braun., P.C. McKeighan, A. M. Nicolson, and R.D. Lohr, Eds.,
American Society for Testing and Materials, West Conshohocken, PA, pp. 165-180.
[11] Lynn, A.K., DuQuesnay, D.L., 2002, Computer simulation of variable amplitude fatigue
crack initiation behaviour using a new strain-based cumulative damage model, International
Journal of Fatigue, 24, pp. 977-986.
[12] DuQuesnay, D.L., Topper, T.H. Yu, M.T. and Pompetzki, M.A., 1992, The effective stress
range as a mean stress parameter, International Journal of Fatigue, 14(1), pp. 45-50.
[13] Vormwald, M., 1991, The Consequences of Short Crack Closure on Fatigue Crack
Growth Under Variable Amplitude Loading, Fatigue and Fracture of Engineering Materials and
Structures, 14(2/3), pp. 205-225.
[14] Vormwald, M., Heuler, P., Krae, C., 1994, Spectrum Fatigue Life Assessment of Notched
Specimens Using a Fracture Mechanics Based Approach, ASTM STP 1231, pp. 221-240.
[15] Pereira, H.F.G.S., 2006, Fatigue Behaviour of Structural Components under Variable
Amplitude Loading, MSc Thesis, FEUP, Porto, Portugal (in Portuguese).
[16] De Jesus, A.M.P., Ribeiro, A.S. and Fernandes, A.A., 2006, Low Cycle Fatigue and Cyclic
Elastoplastic Behaviour of the P355NL1 steel, Journal of Pressure Vessel Technology, 128(3),
pp. 298-304.
[17] Lam, T.S., Topper, T.H. and Conle, F.A., 1998, Derivation of crack closure and crack
growth rate data from effective-strain fatigue lifedata for fracture mechanics fatigue life
predictions, International Journal of Fatigue, 20(10), pp. 703710.
[18] Dowling, N.E., 1999, Mechanical Behaviour of Materials, 2nd ed., Prentice Hall.
Table 1 Chemical composition of the P355NL1 steel (% weight).
Table 2 Mechanical properties of the P355NL1 steel [16].
Figure 1 Crack opening versus crack closure stresses [11].
Figure 2 Geometry of the smooth specimens (dimensions in mm).
Figure 3 Geometry of the notched specimens (dimensions in mm).
Figure 4 Two constant amplitude blocks applied to the smooth specimens.
Figure 5 Multiple alternated constant amplitude blocks applied to the smooth specimens.
Figure 6 Variable amplitude blocks applied to the smooth specimens (max=2.1%, R=0).
Figure 7 Strain range distributions for the variable amplitude blocks applied to the smooth
specimens: a) maximum strain of 1.05%, average strain range of 0.55% and standard
deviation of 0.31%; b) maximum strain of 2.1%, average strain range of 1.1% and standard
deviation of 0.62%.
Figure 8 Variable amplitude blocks applied to the notched specimens (remote stress
control).
Figure 9 Effective strain range versus cycles data.
Figure 10 Net effective strain range versus cycles data.
Figure 11 Fatigue life predictions for smooth specimens under constant amplitude block
loading.
Figure 12 Fatigue life predictions for smooth specimens under variable amplitude block
loading.
Figure 13 Fatigue life predictions (S-N data) for notched specimens under constant
amplitude loading.
Figure 14 Fatigue life predictions for notched specimens under constant amplitude block
loading.
Figure 15 Fatigue life predictions for notched specimens under variable amplitude block
loading.
Table 1 Chemical composition of the P355NL1 steel (% weight).
C Si Mn P S Al Mo
0.133 0.35 1.38 0.014 0.0016 0.03 0.001
b i Ti V Cu Cr 0.025 0.148 0.016 0.002 0.137 0.025
Table 2 - Mechanical properties of the P355NL1 steel [16].
Ultimate tensile strength, UTS [MPa] 568
Monotonic yield strength, 0.2 [MPa] 418
Young modulus, E [GPa] 205.2
Poisson's coefficient, 0.275
Cyclic hardening coefficient, K' [MPa] 777
Cyclic hardening exponent, n' [-] 0.1068
Fatigue strength coefficient, 'f [MPa] 840.5
Fatigue strength exponent, b [-] -0.0808
Fatigue ductility coefficient, 'f [-] 0.3034
Fatigue ductility exponent, c [-] -0.6016
Figure 1 - Crack opening versus crack closure stresses [11].
Figure 2 Geometry of the specimens (dimensions in mm).
Figure 3 - Geometry of the notched specimens (dimensions in mm).
Figure 4 - Two constant amplitude blocks applied to the smooth specimens.
Figure 5 - Multiple alternated constant amplitude blocks applied to the smooth specimens.
[%]
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Figure 6 - Variable amplitude blocks applied to the smooth specimens (max=2.1%, R=0).
b) L-H block; 100 cycles
a) H-L block; 100 cycles
d) Random block; 100 cycles
c) L-H-L block; 200 cycles
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7
8
1.05
0.95
0.85
0.75
0.65
0.55
0.45
0.35
0.25
0.15
0.05
Gama de deformao, [%]
Freq, n de ciclos por bloco
Strain range
Absolute frequency/
No of cycles per strain range
a)
0
1
2
3
4
5
6
7
8
2.1
1.9
1.7
1.5
1.3
1.1
0.9
0.7
0.5
0.3
0.1
Gama de deformao, [%]
Freq, n de ciclos por bloco
Strain range
Absolute frequency/
No of cycles per strain range b)
Figure 7 - Strain range distributions for the variable amplitude blocks applied to the smooth
specimens: a) maximum strain of 1.05%, average strain range of 0.55% and standard deviation of 0.31%; b) maximum strain of 2.1%, average strain range of 1.1% and standard
deviation of 0.62%.
0
50
100
150
200
250
300
350
400
450
1 21 41 61 81 101 121 141 161 181 201
[MPa]
[MPa]
0
50
100
150
200
250
300
350
400
450
0 20 40 60 80 100 120 140 160 180 200
[MPa]
N
0
50
100
150
200
250
300
350
400
450
0 50 100 150 200 250 300 350 400
N
[MPa]
0
50
100
150
200
250
300
350
400
450
0 20 40 60 80 100 120 140 160 180 200
[MPa]
N
0
50
100
150
200
250
300
350
400
450
0 20 40 60 80 100 120 140 160 180 200
N
[MPa]
0
50
100
150
200
250
300
350
400
450
1 21 41 61 81 101 121 141 161 181 201
N
[MPa]
0
50
100
150
200
250
300
350
400
450
0 50 100 150 200 250 300 350 400
[MPa]
N
0
50
100
150
200
250
300
350
400
450
1 21 41 61 81 101 121 141 161 181 201
[MPa]
N
0
50
100
150
200
250
300
350
400
450
1 21 41 61 81 101 121 141 161 181 201
[MPa]
N
0
50
100
150
200
250
300
350
400
450
0 20 40 60 80 100 120 140 160 180 200
Figure 8 - Variable amplitude blocks applied to the notched specimens (remote stress
control).
a) H-L block; R=0; 100 cycles b) L-H block; R=0; 100 cycles
e) L-H block; R=0.3; 100 cycles
d) Random block; R=0; 100 cycles
f) H-L block; R=0.3; 100 cycles
g) L-H-L block; R=0.3; 200 cycles h) Random block; R=0.3; 100 cycles
i) Random block; R=0+R=0.3; 100 cycles j) Random block; R=0+R=0.3+R=0.5; 100 cycles
c) L-H-L block; R=0; 200 cycles
Figure 9 - Effective strain range versus cycles data.
Figure 10 - Net effective strain range versus cycles data.
1000
10000
1000 10000Predicted Life, nL+nH
Experimental Life, n
L+nH H-L sequence
=1/0.5%
1000
10000
100000
1000 10000 100000
Predicted Life, nL+nH
Experimental Life, n
L+nH L-H sequence
=0.5/1%
100
1000
10000
100 1000 10000
Predicted Life, nL+nH
Experimental Life, n
L+nH
H-L sequence
=1.5/0.75%
1000
10000
1000 10000
L-H sequence
=0.75/1.5%
Predicted Life, nL+nH
Experimental Life, n
L+nH
1000
10000
1000 10000Predicted Life, nL+nH
Experimental Life, n
L+nH
H-L-H() sequence
=1/0.5%
1000
10000
1000 10000
L-H-L() sequence
=0.5/1%
Predicted Life, nL+nH
Experim
ental Life, n
L+nH
1000
10000
1000 10000
Experimental Life, n
L+nH
Predicted Life, nL+nH
H-L-H() sequence
=1.5/0.75%
1000
10000
1000 10000
L-H-L() sequence
=0.75/1.5%
Predicted Life, nL+nH
Experimental L
ife, n
L+nH
Figure 11 - Fatigue life predictions for smooth specimens under constant amplitude block
loading.
1000
10000
1000 10000
H-L
L-H
L-H-L
RandomExperimental Life, cycles
Predicted Life, cycles
max=1.05%
100
1000
10000
100 1000 10000
H-L
L-H
L-H-L
RandomExperimental Life, cycles
max=2.1%
Predicted Life, cycles
Figure 12 - Fatigue life predictions for smooth specimens under variable amplitude block loading.
1E+02
1E+03
1E+02 1E+03 1E+04 1E+05 1E+06 1E+07
Kt=2.17, R=0
Observed
Predicted
Life, cycles to failure
Stress range, M
Pa
1E+02
1E+03
1E+02 1E+03 1E+04 1E+05 1E+06 1E+07
Kt=2.17, R=0.3
Observed
Predicted
Stress range, MPa
Life, cycles to failure
1E+02
1E+03
1E+02 1E+03 1E+04 1E+05 1E+06 1E+07
Kt=2.17, R=0.15
Observed
Predicted
Life, cycles to fa ilure
Stress range, M
Pa
Figure 13 - Fatigue life predictions (S-N data) for notched specimens under constant amplitude loading.
1E+3
1E+4
1E+5
1E+3 1E+4 1E+5
Predicted Life, nL+nH
Experimental Life, n
L+nH
H-L sequence (R=0)
=400/280 MPa
EN, with safetyEN, without safetyDuQuesnay et a l
1E+4
1E+5
1E+4 1E+5
Predicted Life, nL+nH
L-H sequence (R=0)
=280/400 MPa
Experimental Life, n
L+nH
EN, with safetyEN, without safetyDuQuesnay et al
1E+3
1E+4
1E+5
1E+3 1E+4 1E+5
H-L sequence (R=0)
=330/280 MPa
Experimental Life, n
L+nH
Predicted Life, nL+nH
EN, with safetyEN, without safetyDuQuesnay et a l
1E+4
1E+5
1E+4 1E+5
L-H sequence (R=0)
=280/330 MPa
Experimental Life, n
L+nH
Predicted Life, nL+nH
EN, with safetyEN, without safetyDuQuesnay et a l
1E+3
1E+4
1E+5
1E+3 1E+4 1E+5
H-L sequence (R=0.15)
=400/330 MPa
Experim
ental L
ife, n
L+nH
Predicted Life, nL+nH
EN, with safetyEN, without saf.DuQuesnay et al.
1E+3
1E+4
1E+5
1E+3 1E+4 1E+5
L-H sequence (R=0.15)
=330/400 MPa
Experimental Life, n
L+nH
Predicted Life, nL+nH
EN, with safetyEN, without saf.DuQuesnay et al.
1E+3
1E+4
1E+5
1E+3 1E+4 1E+5
Predicted Life, nL+nH
Experimental Life, n
L+nH
H-L sequence (R=0.3)
=400/350 MPa
EN, with safetyEN, without saf.DuQuesnay et al.
1E+3
1E+4
1E+5
1E+3 1E+4 1E+5
L-H sequence (R=0.3)
=350/400 MPa
Predicted Life, nL+nH
Experimental L
ife, n
L+nH
EN, with safetyEN, without saf.DuQuesnay et al.
5E+3
5E+4
5E+5
5E+3 5E+4 5E+5
Predicted Life, nL+nH
Experimental Life, n
L+nH
H-L-H() sequence (R=0.0)
=330/280 MPa
EN, with safetyEN, without safetyDuQuesnay et al
5E+3
5E+4
5E+5
5E+3 5E+4 5E+5
Predicted Life, nL+nH
Experimental Life, n
L+nH L-H-L() sequence (R=0.0)
=280/330 MPa
EN, with safetyEN, without safetyDuQuesnay et al
1E+3
1E+4
1E+5
1E+3 1E+4 1E+5
Experim
ental Life, n
L+nH H-L-H() sequence (R=0.3)
=400/350 MPa
Predicted Life, nL+nH
EN, with safetyEN, without safetyDuQuesnay et al
1E+3
1E+4
1E+5
1E+3 1E+4 1E+5
L-H-L() sequence (R=0.3)
=350/400 MPa
Predicted Life, nL+nH
Experimental Life, n
L+nH
EN, with safetyEN, without safetyDuQuesnay et al
Figure 14 - Fatigue life predictions for notched specimens under constant amplitude block loading.
1E+4
1E+5
1E+4 1E+5
H-L
L-H
L-H-LRamdom
EN, without safety
EN, with safety
Predicted Life, cycles
Experimental Life, cycles R=0DuQuesnay
et al.
1E+4
1E+5
1E+6
1E+4 1E+5 1E+6
H-L
L-H
L-H-L
Ramdom
EN, with safety
EN, without safety
R=0.3
Predicted Life, cycles
Experimental Life, cycles DuQuesnay
et al.
1E+4
1E+5
1E+6
1E+4 1E+5 1E+6
Ramdom (R=0+R=0.3)
Random (R=0+R=0.3+R=0.5)
EN, with safety
EN, without safety
Predicted Life, cycles
Experimental Life, cycles DuQuesnay
et al.
Figure 15 - Fatigue life predictions for notched specimens under variable amplitude block loading.