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

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1 Characterization and reliability of A36 steel under alternating dynamic and static loading Jilali NATTAJ 1, Mohamed SAFE 2, Fatima MAJID 3, Hassan CHAFFOUI 4, Mohamed EL GHORBA 5 1 Laboratory Of Atmosphere s Physics and Modeling, FST Mohammadia, Hassan II University Of Casablanca 2 Laboratory Of Control and Mechanical Characterization Of Materials And Structures, National Higher School Of electricity And Mechanics (ENSEM), Hassan II University Of Casablanca 3 Laboratory Of Control and Mechanical Characterization Of Materials And Structures, National Higher School Of electricity And Mechanics (ENSEM), Hassan II University Of Casablanca 4 Laboratory Of Atmosphere s Physics and Modeling, FST Mohammadia, Hassan II University Of Casablanca 5 Laboratory Of Control and Mechanical Characterization Of Materials And Structures, National 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 virgins specimens, combined with static testing tensile test machine the calculated values areee analyzed, discussed and compareeed. These approaches allow us both to assess the impact of unexpected damage on the life of the A36 steel and predict its life or even improve it.. This approach allow us both to assess the impact of unexpected damage on the life 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 loading level applied. This allowed us to quantify the initial damage caused by the notch results that we will operate in future areeticles to determine and compareee alternative approaches for the damage to lead to the development of a simple 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 / Valuri [3] - [2] and others. 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 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. Volume 4, Issue 12, December 2016 Page 1

2 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 [1] This leads to: 2.1 Properties of steel A36 Table 1: Mechanical properties of steel A36 Specification Propriéty A36 σ u (Mpa) σ y E(Gpa) Table 2: Chemical properties of A36 steel. Specificatio Composition n A36 C Mn P S Si Cu 0,8-0,15-0,29 0,09 0,05 0,2 1,2 0,30 3. EXPERIMENTAL METHODOLOGY 3.1 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 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 determine the residual strength of the material. The experiment showed a crack reaches a length 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 mm. Our results areee interpreted according to the constraints applied to an initiation dimension 2 * a 0 = 0.2 mm. Volume 4, Issue 12, December 2016 Page 2

3 4. Résults At a stress level Δ σ = 248 MPa Initiation takes place up to Na = 2000 cycles for a duration of Nf = cycle; At a stress level Δ σ = 282 MPa Initiation takes place up to Na = 1000 cycles for a duration of Nf = cycle; At a stress level Δ σ = 352 MPa Initiation takes place up to Na = 500 cycles for a duration of Nf = 6851 cycles 5. Estimation of damage by unified theory Figure 1: Damage and reliability curves as a function of β for the three stress levels Determined by relation (3) (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 σ 1, Δ σ 2, and Δ σ 3 (respectively equal to 248, 282 and 352 MPa) show that the ratio: Constant 6% The value of 6% is an 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 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 K f given by K f = σ 0 /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] Volume 4, Issue 12, December 2016 Page 3

4 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 = 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 = σ 0 /σ* e gives σ* e = 3, 2. σ 0 σ 0 = α. σ u α. 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 γe as a function of n i The instantaneous value σ e is connected to the instantaneous static resistance σ ur of the material 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), 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, 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 Volume 4, Issue 12, December 2016 Page 4

5 The curve (σ -N) shows well the three zones of the Wohler curve (Olygocyclic below 10 3, the pareet with a lareege number of cycles beyond 10 3 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) in Figure 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 Δσ aree applied and the number of corresponding failure cycles N' f: [7] Hypothesis: This relationship is valid for Δ σ aree = C+ D.log.N f (8) 10² < N f < 10 6 N f = 10² pour Δ σ aree σ u N f = 10 6 approached to10 7 for Δ σ aree σ 0 These two limits conditions give us: C = 692 Mpa et D = -67 Mpa (8) Becomes: Δσ aree = log N f (9) N f = 10 (10,33 0,015 Δ σ aree) (10) For Δ σ aree [σ 0 = 224 Mpa, σ u = 558 Mpa], (9) Allows us to plot the curve(σ a, N f ), Figure N 4. Volume 4, Issue 12, December 2016 Page 5

6 Figure N 4-Curve (σ, N f ) specimens without Notches 8.1 Compareeison between the two curves (σ, N f ) and (σ, N f ) (a) (b) (c) Figure N 5: Compareeison between the two curves (σ, N f) Blue, and (σ, N' f) Green 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 N in 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 N in corresponding to each loading level Δ σ. The fatigue tests careeried out on specimens under the three loading levels Δσ 1, Δσ 2 and Δσ 3 (respectively equal to 248, 282 and 352 Mpa) show that the ratio Volume 4, Issue 12, December 2016 Page 6

7 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 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 of N in, the number of total life cycles of a smooth material under Δ σ would be: N f = N in + N f So: N in = N f N f (11) In other words N in 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, from (10) we have N f = 10 (10, 33 0,015 Δσ aree) So for all Δσ σ 0 = K f. σ* 0 = 224 Mpa we have: N in = 10 (10, 33 0,015 Δ σ aree) Nf It is also known that Na + N p = N f (results of the tests on notched specimens). (11) gives N in = N f N a N P N in + N a +N P = 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 : Volume 4, Issue 12, December 2016 Page 7

8 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 Volume 4, Issue 12, December 2016 Page 8

9 9.3 Curve. 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 in Ln ( Figure N 8 Curve as a function of Δ σ aree Note: 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 σ 0. Initial Damage depends, in addition to notch quality, on the difference in loading level compareeed to the endurance of the material 10 Relationship between Δ σ and With N' a is the number of priming on smooth specimen. The relation of lineareeity between applied Δ σ and the ratio, [6] The more the exploitation of the results 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 The relation of lineareeity between applied Δ σ and the ratio,, [6] The more the exploitation of the results of the relation (10) and the boundareey conditions allow us to determine the constants of this linearee equation, We thus obtain: If Δ σ = σ u = 558 Mpa So 0 Volume 4, Issue 12, December 2016 Page 9

10 Relations (9) and (15) give: Figure N 9: Level of stress applied as a function of 16) will allow us to plot N'f as a function of Figure N 10: Number of breaking cycles as a function of Volume 4, Issue 12, December 2016 Page 10

11 11.Propagation rate in a smooth specimen: 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: N a N p From the above relationships, the curves N' a and 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. Volume 4, Issue 12, December 2016 Page 11

12 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 number (σ, N f ) relationship of 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 were able to determine the life fractions corresponding respectively to the phases of initiation and propagation of the crack in a smooth test piece 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 : σ 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 u : Ultimate constraint of the original material σ ur : Ultimate stress of the tired material, in static traction σ 0 : Endurance limit of the original material in controlled stress σ e : Instant endurance limit σ* 0 : Critical endurance limit γ = σ / σ 0, Stress pareeameter σ y : The elastic limit of the material; E: modulus of elasticity γ e = σ e /σ 0, γ* e = σ* e /σ 0, γ u = σ e /σ 0, References [1]. J.Dubuc, T. Bui-Quoc, A.Bazergui, A.Biron-«Unified Theory of cumulative Damage in metal fatigue» Rapport soumis à PVRC, Vol I et II, Ecole polytechnique, Avril 1969 [2]. S.R.Valluri, JL of aerosp. Eng. Vol 20, 1965, P 18-19, [3]. R, R.Gatts- Trans, ASME, JL of Bas.Eng. Vol 83, 1961, P [4]. M. Miner Trans ASME, JL of Appl. Mech, Vol , 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 BATHIAS & JEAN PAUL BAILON, Université de Compiègne. [7]. D.Dengel-Materiel pruf, Bd 13 Nr 5.P [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 positions in technical management of mareecchands ships. since 2001 Technical Director of a consulting firm specialized in the study and design of pressure equipments Since 2011 vacant teacher in Higher Institute of Mareeitime Studies Volume 4, Issue 12, December 2016 Page 12