Fatigue p355nl1

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


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


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


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.

[%]

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1

t

[%]

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1

t

[%]

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

2.1

t

[%]

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

t

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

0

1

2

3

4

5

6

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


L+nH L-H sequence

=0.5/1%

100

1000

10000

100 1000 10000



L+nH

H-L sequence

=1.5/0.75%

1000

10000

1000 10000

L-H sequence

=0.75/1.5%



L+nH

1000

10000

1000 10000Predicted Life, nL+nH


L+nH

H-L-H() sequence

=1/0.5%

1000

10000

1000 10000

L-H-L() sequence

=0.5/1%


Experim

ental Life, n

L+nH

1000

10000

1000 10000


L+nH


H-L-H() sequence

=1.5/0.75%

1000

10000

1000 10000

L-H-L() sequence

=0.75/1.5%


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%


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



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


L-H sequence (R=0)

=280/400 MPa


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


L+nH



1E+4

1E+5

1E+4 1E+5

L-H sequence (R=0)

=280/330 MPa


L+nH



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


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


L+nH



1E+3

1E+4

1E+5

1E+3 1E+4 1E+5



L+nH

H-L sequence (R=0.3)

=400/350 MPa


1E+3

1E+4

1E+5

1E+3 1E+4 1E+5

L-H sequence (R=0.3)

=350/400 MPa


Experimental L

ife, n

L+nH


5E+3

5E+4

5E+5

5E+3 5E+4 5E+5



L+nH

H-L-H() sequence (R=0.0)

=330/280 MPa


5E+3

5E+4

5E+5

5E+3 5E+4 5E+5



L+nH L-H-L() sequence (R=0.0)

=280/330 MPa


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



1E+3

1E+4

1E+5

1E+3 1E+4 1E+5

L-H-L() sequence (R=0.3)

=350/400 MPa



L+nH


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


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


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


Experimental Life, cycles DuQuesnay

et al.

Figure 15 - Fatigue life predictions for notched specimens under variable amplitude block loading.

Documents

Fatigue p355nl1