Characterization and reliability of A36 steel under alternating dynamic and static loading

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Volume 4, Issue 12, December 2016

Characterization and reliability of A36 steel under alternating dynamic and static loading Jilali NATTAJ1, Mohamed SAFE 2, Fatima MAJID3, Hassan CHAFFOUI 4, Mohamed EL GHORBA5 1

Laboratory Laboratory Of Atmosphere’s Physics and Modeling, FST Mohammadia, Mohammadia, Hassan II University Of Casablanca

2

Laboratory Laboratory Of Control and Mechanical Characterization Of Materials And Structures, Nati onal Higher School Of electricity And Mechanics (ENSEM), Hassan II University Of Casablanca

3

Laboratory Laboratory Of Control and Mechanical Characterization Of Materials And Structures, Nati onal Higher School Of electricity And Mechanics (ENSEM), Hassan II University Of Casablanca 4

 Laboratory Of Atmosphere’s Atmosphere’s Physics and Modeling, FS T Mohammadia, Hassan II University Of Casablanca

5

Laboratory Laboratory Of Control and Mechanical Characterization Of Materials And Structures, Nati onal Higher School Of electricity And Mechanics (ENSEM), Hassan II University Of Casablanca

ABSTRACT The principal purpose of this areeticle is the prediction of the life of ordinareey steel A36 by using the method of unified theory. Separeeation of phases boot / propagation and cycle number reduction at break for a given load level. Experimental results  from the fatigue tests vi rgins specim ens, combi ned with s tatic t esting tensil e test machine the calculated values areee analyzed,  discussed and com pareeed. These approaches allow us both to assess the impact of unexpected damage on the li fe of the A36  steel and predict it s life or even i mprove it .. This approach allow us both to assess the impact of unexpected damage on the li fe  of the A36 steel and predict its life or even improve it. In this paper we present the first pareet of our researeech we have  determined the number of life cycles of A36 steel (smooth) from alternating fatigue tests with other static, as well as the  different relations binding the vareeious life phases of the material and the t he loading l oading l evel applied. This allowed us to quantify  the initial i nitial damage caused by the notch results that we will operate i n future areeticles t o determ ine and com pareee alternative  approaches for the damage to l ead to the development of a sim ple tool usable in a maintenance policy.

Keywords:-   steel A36, reliability, damage, unified theory, fatigue, Separeeation of phases boot / propagation, cycle number reduction at break.

1. INTRODUCTION Piping systems or A36 steel capacities areee often subjected to cyclic loads due to pressure fluctuations. These vareeiations in pressure areee sources of fatigue of the material, accelerated sometimes by the presence of environmental hazareeds. This situation results in a deterioration of the expected lifetime of the impacted material requiring a re-estimation of its residual lifetime in the presence of the defect, which will allow the maintenance services to have data essential for the decision-making on their Interventions. In the literature, the vareeious theoretical approaches developed by different authors have addressed this  phenomenon of accelerated degradation by issuing different hypotheses such as the lineareeity of the damage  proposed by Miner [4]. And the accumulative proposed by Gatts Gatts / Valuri [3] - [2] and oth ers. Based on the previous models, the unified theory developed a model of damage, which we estimate the tool adapted to serve as a model approach, which we compareee to the approaches developed in our researeech by introducing the  pareeameter of the fraction of of life β and other material specific pareeameters. In this areeticle we present the first pareet of our researeech in which we have been able to determine the number of lifecycles of steel A36 (smooth) stareeting from fatigue tests alternating with static ones, as well as the different relationships binding the different Phases of material life and the level of loading applied. This allowed us to quantify the initial damage caused by the notch, which we will exploit in our next areeticles to determine and compareee other approaches to damage, leading to the development of a simple tool that can be used in a maintenance policy.

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Volume 4, Issue 12, December 2016 2. UNIFIED THEORY

The loss of resistance may be associated with static tensile strength or fatigue strength under the effect of cyclic loading damage. The concept of energy damage associated with cyclic plastic deformation for stresses greater than the endurance limit was originally suggested by Henry and then taken up by Gatts. Using some chareeacteristics of the theories of Shanley [5] and Valluri [2], Bui-Quoc [1] developed the unified theory of fatigue; He suggested a derivative expression rate of loss of the endurance limit of the material subjected to cyclic loading. Thus, the residual nondimensional residual stress σur / σu in function β = ni / Nf is obtained as follows [1]:

Le Dommage normalisée D a été défini paree :

For steel m = 8 This leads to:

2.1

[1]

Properties of steel A36 Table 1: Mechanical properties of steel A36 Specification

A36

Propriéty

σu (Mpa)

σy 

E(Gpa)

621

372

200

Table 2: Chemical properties of A36 steel. Specificatio Composition n A36

C

Mn

0,29

0,81,2

P 0,09

S

Si

Cu

0,05

0,150,30

0,2

3. EXPERIMENTAL METHODOLOGY 3.1 3.1.1

Conduct of trials Fatigue tests

To determine the lifetime at break, fatigue tests at constant amplitude up to failure for three load levels 352, 282 and 248 MPa in stress controlled mode were performed on three A36 steel samples.

3.1.2 Static Tests For each loading level (352, 282 and 248 MPa), ten samples were tired at 1000 cycles. Then, static tensile tests were  provided to determin e the residual stren gth of the material. Th e experiment showed a crack reaches a lengt h close to 0.1 mm [6]. it propagates regulareely across the section, this dimension corresponds to a size of defects compareeable to the grain size of the steel and is The end of the initiation stage for A36 steel, grain diameter is about 0.032 mm. Our results areee interpreted according to the constraints applied to an initiation dimension 2 * a0 = 0.2 mm.

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Volume 4, Issue 12, December 2016 4. Résults  At

a stress level Δ σ = 248 MPa Initiation takes place up to Na = 2000 cycles cycles for a duration of Nf = 32000 cycle; cycle; cycles for a duration of Nf = 20000 cycle; cycle;  At a stress level Δ σ = 282 MPa Initiation takes place up to Na = 1000 cycles 2 MPa Initiation ta kes place up to Na = 500 cy cycles cles for fo r a duration of Nf = 6851 cycles cy cles 35  At a stress level Δ σ = 352

5. Estimation of damage by unified theory

levels Determined by relation (3) Figure 1: Damage and reliability curves as a function of β for the three stress levels Determined (reliability: (R = 1 - D)

6. Discussion : The resistance of each metal is a constant pareeameter, independently of the different loading levels, in the original state it is the opposite of the number of cyclic loading. The loss of this resistance is accompanied by a loss of the endurance of the material studied, this loss is considered as an intrinsic pareeameter which serves to evaluate fatigue damage (Figure 1). Therefore, the end-of-life time is accelerating at its limit the damage worth the unit. The fatigue tests performed on specimens under the three loading levels Δ σ1, Δ σ 2, and Δ σ3 (respectively equal to 248, 282 and 352 MPa) show that the ratio:

Constant

6%

The value of 6% is an average average value; the ratio is substantially equal for all loading levels Δ σ because of the quality of the notch which consumes a very lareege lareege number of cycles with respect to a (N f) Δ σ

7. Prediction of the number of break cycles by the unified theory: WOILER curve 7.1 Determination of the endurance limit: The notch substantially decreases the endurance limit of a specimen, the reduction of this endurance limit can be determined by a coefficient coefficient K f  given by K f  = σ0/σ*e  (4) If K t is the coefficient of concentration of static stresses at the notch, the sensitivity of the material, denoted '' q '', at the notch is defined by [8]

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The vareeiation graph of the notch sensitivity index for steels with a resistance between 400 and 700 MPa [3] allows us to estimate the sensitivity index of steel A36 (σ u = 558 MPa) at q = 0.55. The presence of notch (acute) leads to a local stress concentration coefficient, K t of the order of 4 to 5This gives us a K f = 3.2 K f  = σ0/σ*e gives σ *e = 3, 2. σ 0 σ  0 = α. σ  u

. It is areeound 0.4 σ u = 558 Mpa σ  *e = 70 Mpa The unified theory [1] approaches the damage sustained by a material, by the reduction of its endurance. The expression of the rate of vareeiation of the dimensionless endurance limit limit γe as a function of ni α

The instantaneous value σe is connected to the instantaneous static resistance σ ur  of the materia l as follows [4]

Such as: = 1 for n = 0,

The integration of equation (6) gives an approach to the fatigue curve σ - N and takes the following form:

With b and Ka areee constants of the materials. Our approach consists in determining these two constants, using the experimental results in order to be able to predict and trace the curve (σ-N), (σ-N), to do this we took 2 points sufficiently spaced among the three constraints used in the experiment (282 And 352 Mpa in our case), which gave us; K a = 3,7.106 Cycles, Cycles,

b = 2,03

Equation (7) allows us to plot the curve (σ -N) Nested specimens.

Important note : In the rest of the areeticle the pareeameters with the notation, prime, (‘)  concern specimens without Notch

Figure 2: Curve (σ, N) Approached for test specimens with notches

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The curve (σ -N) shows well the three zones of the Wohler curve (Olygocyclic below 10 , the pareet with a lareege 3 number of cycles beyond 10  up to an endurance limit which tends towareeds Asymptote horizontal)) A compareeison between the number of cycles at break N fex (deduced from the experiment) and N fc (calculated by formula (7) corresponding to the three loading levels applied (248, 282 and 352 Mpa) is given in FIG. below: The graph of FigureN°3 shows a very small difference between the two curves, which confirms the correct approach of the curve (N-σ) (N-σ) in Figure N°2, N°2, above

Figure 3: Compareeison of curves (N fex-σ) et (N fc-σ)

8.Approach to the Wohler Curve (σ, N) for specimens without notches: The Wohler curve in its logareeithmic form is written in the following way by linking the stress level level Δσ and the number of corresponding failure cycles N' f : [7] Δ σ aree = C+ D.log.N’f 

aree  applied

(8)

Hypothesis : This relationship is valid for 10² < N’ f < 106  N’ f = 10² pour 6

Δ σ aree

 N’ f = 10  approached to10 for Δ σ aree σ0 These two limits conditions give us: C = 692 Mpa et (8) Becomes: Δσ aree = 692- 67.log N’ f 

D = -67 Mpa (9)

σ aree)

N’f  = 10 (10,33 – 0,015 Δ For Δ σ aree

σu

7

(10)

[σ0 = 224 Mpa, σ u = 558 Mpa], (9) Allows us to plot the curve( σa, N’ f ), Figure N°4.

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(σ, N’ f ) specimens without Notches Figure N°4-Curve (σ

8.1 Compareeison between the two curves ( σ, N f ) and (σ, N’ f )

(a)

(b)

(c) Compareeison between the two curves (σ, N f) Blue, and (σ, N' f) Green Figure N°5: Compareeison

9.Initial Damage: D

in

A notched specimen sees its endurance reduced in a ratio K f  relative to that of a specimen of the same specimen not notched. During the fatigue tests on a notched specimen, the specimen behaves like an initially damaged specimen of a quantity D in. Consequently, when considering the lifetime prediction of the material (smooth), the number of life cycle at break, determined by fatigue tests on notched specimens, must be corrected by the number of cycles Nin equivalent to Damage caused by the notch. For this purpose, an attempt is made to determine the number of cycles equivalent to the initial damage Nin corresponding to each loading level Δ σ. The fatigue tests careeried careeried out on specimens under the three loading levels Δσ1, Δσ2 and Δσ3 (respectively equal to 248, 282 and 352 Mpa) show that the ratio

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This value is almost the same for all loading levels due to the notch quality which has consumed a lareege pareet of the lives of the specimens, the difference between between the ratios

is negligible.

In the above pareeagraph it was possible to determine the number of breaking cycles N' f  of a test piece without a notch as a function of that of a notched specimen N f . During the tests on notched specimens: We have: Na + N p = N f  for Δ σ given While the notch consumed a cycles number equivalent equivalent of of Nin, the number of total life cycles of a smooth material under Δ σ would be:

N’ f  = Nin + N f So:  N in (11) in = N’  f  – N  f In other words Nin is the vertical distance between the two curves (σ, N f ) and (σ, N' f ) ((Figure 5- c) passing through the loading level value Δ σ considered.  Now,  Now, from (10) we have

So for all Δσ

 N’f  = 10 (10, 33 – 0,015

Δσ aree)

σ0 = Kf . σ*0 = 224 Mpa we have:

σ aree)

Nin = 10 (10, 33 – 0,015 Δ

– Nf

It is also known that Na + N p = N f  (results of the tests on notched specimens). (11) gives Nin = N’f  – Na – N P  Nin + Na +NP = N’f We divide by N' f , we obtain for each level of loading:

With: Is the total life percentage of the smooth material initially consumed by the notch.

Is the total life percentage of the smooth material consumed at priming in a notched specimen Is the total lifetime of the smooth material consumed during propagation of the crack in a notched specimen. It is thus possible to plot the evolution profiles of the percentage of each phase of life, with respect to the total life of the smooth material as a function of the level of loading applied.

9.1 Curve

:

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We note that • the initiation phase in a notched specimen represents a small percentage over the total lifetime of the smooth material, this being due to the sensitivity of the specimen to the notch practiced. • Although this stage is small for all loading levels, it is increasingly believed that the loading level increases with an acceleration in the zone of stress levels close to σ u.

9.2 Curve

:

We note that The propagation phase of the crack in a notched specimen represents a relatively high percentage that the initiation in relation to the total lifetime of the smooth material is due to the fact that the notch reduces the initiation phase much more Than the propagation phase. This phase grows rapidly, it has the same tendency as the ignition phase, more and more that the level of loading increases this increase accelerates in the zone of the stress levels close to σ u

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.

We have: Can be calculated for each Δ σ aree in the validity domain of N' f  As

is too close for all Δ σ aree, in order to highlight the correspondence one must change the scale of the axis of 4

i n - 10

Ln (

Figure N°8 Curve as a function of Δ σ aree Note:  



10

The notch greatly reduces the life of the material, which is very important for fatigue testing, as this minimizes f The notch effect significantly influences the total lifetime under loading levels close to σ u of the material, this effect is minimized by approaching σ0. Initial Damage depends, in addition to notch quality, on the difference in loading level compareeed to the endurance of the material

Relationship between Δ σ and

With N' a is the number of of priming on smooth smooth specimen. The relation of lineareeity lineareeity between applied Δ σ and the ratio, [6] The more the exploitation of the r esults esults of the relation (10) and the boundareey conditions allow us to determine the constants of this linearee equation, With N’a Is the number of priming on smooth specimen , , [6] The more the exploitation of the results of

The relation of linearee lineareeity ity between applied Δ σ and the ratio

the relation (10) and the boundareey conditions allow us to determine the constants of this linearee equation,

If Δ σ = σ u = 558 Mpa

So

0

We thus obtain:

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Figure N°9: Level of stress applied as a function of Relations (9) and (15) give:

16) will allow us to pl ot N'f as a function of

breaking cycles as a function of Figure N°10:  Number of breaking

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11.P 11.Prropag opagati ation on rate in a smo smooth oth spec specim imen en:: The predicted lifetime of the smooth material N' f , under loading level Δ σ, is equal to the duration of the crack initiation plus that of its propagation, is

N’ f   - N’ a = N’ p

(17)

Figure N°11: Level of loading applied as a function of 

12 Phases difference: difference: N’a –N’p From the above relationships, the curves N' a and N' p N' p can be plotted as a function of loading level Δ σ.

Figure N°12:  phases difference N’a –N’p It is noted that the deviation (N'a - N'p) decreases more and more that the applied stress level increases, to cancel out when Δ σ reaches σ u.

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13.Conclusion: In this first pareet of our researeech, we have been able to develop the approach which has allowed us to find the constraint-  break cycles cycles number (σ, N’f ) relationship relationshi p of the the smooth A36 steel from the alternating fatigue and static tests on notched specimens. This approach also allowed us to quantify the initial damage, caused by the notch for each load level applied. And subsequently we we were were able to determine determine the life fractions corresponding corresponding respectively to the phases of initiation initia tion and  propagation of the crack in a smooth test piece subjected subjected to a given level of loading. In conclusion, a new approach to the damage of the material studied can be careeried out based on the separeeation of the phases of propagation of a crack (N'a and N'P) in a smooth specimen subjected to a given loading level.

Notation : a: Amplitude of applied stress Δ σ: Stress level applied in fatigue Δ σ aree: Stress level applied in fatigue, corresponding to a breaking cycle number N'f of the smooth material

σ

σ

u:

Ultimate constraint of the original material

Ultimate stress of the tired material, in static traction σ0 : Endurance limit of the original material in controlled stress σ

ur :

: Instant endurance limit σ* 0: Critical endurance limit γ = σ / σ0, Stress pareeameter σy: The elastic limit of the material; E: modulus of elasticity γe = σe/σ0, γ*e = σ*e/σ0, γu = σe/σ0, σe

References [1]. J.Dubuc, T. Bui-Quoc, A.Bazergui, A.Biron-« Unified Theory of cumulative Damage in metal fatigue » Rapport soumis à PVRC, PVRC, Vol I et II, Ecole Ecole polytechnique, polytechnique, Avril 1969 [2]. S.R.Valluri, JL of aerosp. Eng. Vol 20, 1965, P 18-19, 68-89 [3]. R, R.Gatts- Trans, ASME, JL of Bas.Eng. Vol 83, 1961, P 529-540 [4]. M. Miner – Trans ASME, JL of Appl. Mech, Vol 67. 1945, P A.159- A 1664 [5]. E. R. shanley – The Rand corp. Rapport P-350, 1953 [6]. P.RABBE & C.AMZALLAG, Livre de La Fatigue des Matériaux et des structures, Figure 3.2 page N°73, écrit  paree CLAUDE CLAUDE BATHIAS BATHIAS & JEAN PAUL PAUL BAILON BAILON,, Université de Compiègne. [7]. D.Dengel-Materiel pruf, Bd 13 Nr 5.P.145-180 [8]. R.E Pterson “Stress concentration factor, John wiley and sons, New York, 1974

Jilali Nattaj received the Naval Engineer degrees from Higher Institute of Mareeitime Studies at Casablanca in 1989, From 1990 to 2000 holds different different positions in technical management of mareecchands ships. since 2001 Technical Director of a consulting firm specialized in th e study and design of pressure equipments Since 2011 vacant teacher in Higher Institute of Mareeitime Studies

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