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Effects of cyclic torsional prestraining and overstrain on fatigue life and damage behavior of brass alloy
Materials and Design 31 (2010) 3742–3747
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Effects of cyclic torsional prestraining and overstrain on fatigue life and damage behavior of brass alloy Ridha Mnif *, Riadh Elleuch, Foued Halouani Laboratoire des Systèmes Electro-mécaniques (LASEM), Ecole Nationale d’Ingénieurs de Sfax, (ENIS) BP 599-3018, Tunisia
a r t i c l e
i n f o
Article history: Received 20 December 2009 Accepted 9 March 2010 Available online 11 March 2010 Keywords: Brass Torsion Overstrain Prestraining Fatigue life Fracture surface
a b s t r a c t Many practical structural members and parts may be subjected to fluctuating plastic deformation by prestraining due to manufacturing and machining process (forming operation, straightening, etc.) and unintentional overstrains (misuse, accidents, under design, etc.). For this reason, the effect of the prestrain and periodic overstrains on fatigue life and damage behavior was being necessary considered for reasonable fatigue design. In this context, an experimental program was conducted to study the effects of overstrain and prestraining on fatigue life and damage behavior of brass alloy subjected to cyclic torsional loading. To establish baseline fatigue behavior, several virgin specimens were tested under fully-reversed strain control and constant amplitude fatigue torsional loading up to failure. The obtained experimental results showed that the fatigue life depends strongly on the strain amplitude and prestraining type (monotonic or cyclic). In addition, a beneficial effect in the fatigue life was observed for all tests with periodic overstrain. Cyclic fatigue fracture on a macroscopic scale revealed features reminiscent of locally ductile and brittle mechanisms. At the same time, microscopic analysis indicated a difference on fatigue fracture surface morphology between the conducted tests and those performed under constant amplitude loading. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction It is widely known that in the last decade’s copper alloys have been more and more used in the production industry, mainly in components of sanitary installations (valves, pipe couplings, etc.). The components are often subjected to cyclic stress due to internal pressure variation and unintentional overstrains. Therefore, fatigue property is essentially needed in the safe life design of components. In most studies on the mechanical properties, such as the creep behavior, the fracture mechanisms and the cyclic deformation behavior, of the material under investigation is used in a well-defined annealed condition. Only in rare cases, the effect arising from prestrain and periodic overstrain on the subsequent cyclic deformation behavior is taken into account, even though engineering materials often undergo a (thermo-)mechanical pretreatment such as swaging, rolling or forging. Therefore, the influence of a mechanical prehistory on the subsequent cyclic deformation behavior and cyclic life is of particular interest for technical applications of respective materials. Unfortunately, the effects resulting from prestraining depend on numerous parameters and influence the macroscopic mechanical properties and the microstructure in a very complex manner. * Corresponding author. Tel.: +216 74 274 088; fax: +216 74 275 595. E-mail addresses: [email protected] (R. Mnif), [email protected] (R. Elleuch), [email protected] (F. Halouani). 0261-3069/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.matdes.2010.03.015
The effect of quasi-static plastic prestrain on fatigue behavior has been studied for many years in great detail on numerous types of metallic materials. It appears that the most studied [1–6] material is steel and that effects of prestrain vary from no apparent fatigue benefit to either a significant benefit or detriment. For example, Uemura’s work [4] on mild steel concludes that the effect of prestraining in degrading fatigue life in the domain of low-cycle fatigue is evident, but there is no apparent depreciation in the domain of medium to high-cycle fatigue. For these investigations, specimens were tensile prestrained from 25% to 85% of the static fracture strain. On mild steel too, Gustavsson and Melander [5,6] concludes that contrary to prestrain below 5%, high degrees of prestraining (i.e. above 15%) have a positive effect on the fatigue resistance. The fatigue strength increases by up to about 50%. The effect of prestrain type (tensile or torsional prestrain) on the fatigue limit of carbon steel was also investigated [1]. The results obtained showed that the fatigue limit of the torsional-prestrained specimen was higher than that of the tensile-prestrained specimen and the degree of cyclic softening induced by fatigue loading in the torsional-prestrained specimen was lower than that in the tensile-prestrained specimen. At the same many studies [7–13] have been conducted on nonferrous alloys such as nickel alloys, the relative effects of monotonic prestrain on subsequent cyclic behavior were more harmful than the effects of precycling on subsequent monotonic behavior [7]. Concerning aluminium alloys, Wang’s [8] reported that the effect of plastic deformation (10% prestretching is used) showed a
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considerable effect on the fatigue life, depending on the stress level. A reduction of more than 20% in the fatigue strength has been observed near the fatigue limit whereas less or no reduction may be expected at higher stress levels (around 105cycles). The effect of dislocation substructures on fatigue crack propagation (FCP) behavior in copper and alpha brass was also studied [9]. Dislocation cells were formed by this prestraining in copper and 90/10 brass and when they formed the resistance to FCP at intermediate propagation rates (5 10–9–10–7 m/cycle) increased with increasing of prestrain. On the other hand the effects of periodic overstrain has been studied by several researchers through comparative fatigue testing [14,15]. It is well-known that one of the major characteristics of variable fatigue loads, especially overloads, is the accelerations and/or retardations of the fatigue crack due to the complex interaction of many factors such as the overload ratio, the timing of overloads, the stress ratio, the yield stress of the material, the thickness of the structure, and the stress history [16–18]. Many structural steels display distinct fatigue limits when tested under constant amplitude fatigue cycling conditions. These materials often display substantial reductions in long-life fatigue resistance when occasional, periodic overstrains are introduced between large numbers of constant amplitude fatigue cycles. These periodic overstrains can lead to dramatic reductions in the originally perceived fatigue limit for the material [15,19]. However overstrains may purposely be applied to produce some beneficial effects on the fatigue resistance of the components because of sufficient magnitude can result in a transient reduction in the rate of fatigue crack growth at the baseline level. It has been also well established that this reduction is closely related to the residual compressive stress field induced in the vicinity of crack tips [20–22]. This paper presents and discusses the influence of prestraining and periodic overstrains on cyclic strain amplitude-controlled fatigue response, fatigue life and fracture characteristics of brass alloy. The high-cycle fatigue properties and final fracture characteristics of the alloy are discussed in terms of the specific roles played by the concurrent and synergistic influences of magnitude of prestraining type (monotonic or cyclic), periodic overstrain and macroscopic aspects of fracture.
3L
r¼
pffiffiffi 3:3 3M 2pa3
3.1. Monotonic prestraining (MPS) fatigue tests
ð1Þ
ð2Þ
Table 1 Mechanical properties of brass alloy measured under monotonic torsion.
The material studied was a brass alloy with the following chemical composition in weight percent: 58.5% Cu, 2.8% Pb, 0.25% Sn, 0.11% Ni, 0.21% Fe, and 0.01% Al and the balance Zn. The material was received in the form of extruded bar (120 mm U 6 mm) from which fatigue specimens (cylinder of 6 mm in diameter and 32 mm in length) were machined. After machining, the useful surface of the specimen was polished mechanically to a 3 lm finish. Fatigue tests were conducted on a torsional materials test system (Deltalab EM 400) [23]. A triangular wave signal was used for total strain control under strain ratio Re = 1(Re = emin/emax). During testing, the torque (T) and twist angle (h) values were continually recorded and the von Mises effective stress (r) and effective strain (e) were calculated using Eq. (1) and (2) [24].
ha
3. Tests results and discussions
Fig. 2 shows the typical cyclic hardening curves of brass alloy, recorded for the virgin and monotonic prestrained (MPS) specimens under two mechanical strains (1.4%, 4.2%). The curves are obtained by plotting cyclic resolved equivalent stress against the number of cycles (N). A similar level stress response to cyclic loading was identified between the virgin and monotonic prestrained specimens. Hence, the cyclic behavior can be attributed to the relaxation phenomenon leading to a continuous decrease of stress for primary dozen cycles. Furthermore, it should be mentioned that prestraining specimen presents a pronounced linearly decrease of mean stress with the number of cycle. However for the virgin material, we note a quasi stability of mean stress. At applied constant effective strain amplitude of 1.4%, it was found in the present work that the effect of 1.4% monotonic prestrain increases the fatigue life slightly 10% as compared with the as-received material. However, at 4.2% monotonic prestrain, a reduction of the fatigue life was noticed. The reduction of fatigue life could be attributed a deformation and damage mechanisms. In fact, monotonic prestraining can induce microscopic slips steps on the surface of the specimen and these slip steps can also serve as microcrack initiation sites during the subsequent fatigue loading. It has been shown in earlier studies that the significance of predeformation depends strongly on the dislocation slip behavior [25–27]. For materials exhibiting planar slip, even small degrees of prestraining lead to an increase of the resulting stress amplitudes, a reduction of cyclic life and a shift of the cyclic stress–strain curve to higher stress values [25]. For materials showing wavy slip, the influence of a predeformation is more complex. The predominant effect depends on the degree of prestraining and the loading parameters applied during subsequent cycling [26]. For example, copper behaves as if it were history-independent only if the plastic strain amplitude is sufficiently high [27]. However, in most cases the various changes in the mechanical behavior due to predefor-
2. Material and fatigue testing procedure
e ¼ pffiffiffi
performed using a servoelectronic testing machine (this machine was also used for fatigue tests).The mechanical properties of brass alloy measured under monotonic torsion are given in Table 1. In order to get a better understand of the effects of cyclic torsional overstrain and prestraining on fatigue life and damage behavior of brass alloy, three types of loading histories were conducted under strain control and at constant strain rate e_ = 5.6 103 s1 (Fig 1): (i) monotonic torsional prestraining (MPS) followed by strain controlled cycling loading to failure with variation strain amplitude De = 2%. The prestrains used were 1.4% and 2.4% in monotonic torsion, (ii) cyclic torsional prestraining (CPS) at strain amplitude ±4.2% followed by cycling at constant amplitude with variation amplitude strain De = 2%, (iii) periodic cyclic overstrain (POS) under strain amplitude 4.2% divided by smaller constant amplitude cycles (g) in the range of ±0.35– ±2.1% strain. The prestraining and overstrain effects were investigated by cycling hardening/softening curves and fatigue life curves developed during cyclic torsional loading. Quantitative fatigue damage was also assessed by microscopic observations of surface fracture.
The present study focuses on total strain controlled fatigue. To control the total strain, it is necessary to have information about the range of material plasticity. Monotonic torsion tests were
Yield stress, r0.2% (MPa)
Ultimate stress strength, Rm (MPa)
Shear modulus, G (GPa)
227
480
36
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a
Monotonic prestrained
ε
c
b
Cyclice prestarined
ε
Overstrain
ε Small amplitude ( η)
4,2%
2,2%
N
0
N
0
N
0
- 4,2%
Fig. 1. Illustration of loading histories: (a) monotonic prestraining (MPS); (b) cyclic prestraining (CPS); (c) periodic cyclic overstrain (POS).
Monotonic prestraining (1.4%)
Virgin specimen
300 200 100 0 -100 -200 -300 -400 0
5000
10000
15000
Virgin specimen
Cyclic prestraining (4.2%)
400
Effective stress (MPa)
Effective stress (MPa)
Monotonic prestraining (4.2%)
20000
500 400 300 200 100 0 -100 -200 -300 -400 -500
Number of cycles
0
5000
10000
15000
20000
Number of cycles Fig. 2. Cyclic hardening–softening of virgin specimen and monotonic prestrained (MPS) specimen curve (De = 2%, e_ = 5.6 103 s1).
Fig. 3. Cyclic hardening–softening of virgin specimen and cyclic prestrained (CPS) specimen curves (De = 2%, e_ = 5.6 103 s1).
mation can be explained on the basis of the corresponding microstructural alterations.
η = 1000
3.2. Cyclic prestraining (CPS) fatigue tests Fig. 3 shows the typical cyclic hardening curves of brass alloy, recorded for the as-received and cyclic prestrained (CPS) specimens under mechanical strain 4.2%. At the same equivalent strain amplitude 1%, the maximum stress level recording to the CPS specimen is more important than that of virgin specimen by a factor of 1.7. In terms of life, contrary to what is observed in monotonic prestrained specimens under mechanical strain 2.4%, the experimental results shows that the fatigue life of cyclic torsionalprestrained specimen was higher than that virgin specimen. The result means that the effect of the prestrain type on the fatigue life is related to the cyclic softening and the cyclic softening depends on the relationship between prestrain type and mean stress effect. The cyclic hardening behavior results for CPS can be attributed to the generation and interaction between dislocations leading to a continuous decrease in plastic strain. The difference of fatigue life therefore has to reflect the effect of cyclic prestraining on grain boundary which modifies the structure and the evolution of dislocation [26,27]. 3.3. Periodic overstrain (POS) fatigue tests Fig. 4 illustrates the effect of periodic overstrain (POS) amplitude ±4.2% on the fatigue life of brass alloy during cyclic torsional for different amplitudes. We note that the overload applied during the test increased slightly the fatigue life of brass alloy for all tests. Similar fatigue endurance, compared with constant amplitude tests was obtained. The beneficial effect on the fatigue resistance fatigue life can be attributed to a transient retardation in the rate
Effective strain (%)
4.5
η = 4000
4
η = 6000
3.5 Constant amplitude
3 2.5
Cyclic periodic overstrain
2 1.5 1
Constant amplitude strain
0.5 0 1.0E+02
1.0E+03
1.0E+04
1.0E+05
1.0E+06
Number of cycles (Nr) Fig. 4. Effect of periodic cyclic overstrain (POS) on fatigue life.
fatigue growth at the baseline level. This retardation is closely related to the residual stress field induced in the vicinity of the crack tip [27,28] and to be closely related to the elastic–plastic behavior of the material [29–31]. Many researchers [15,32] have found that damage calculations made on variable amplitude load histories using constant amplitude strain-life curves could be very non-conservative. This inaccuracy arises because overload cycles in variable amplitude load histories can reduce crack closure and allow small cycles, whose amplitudes are below the constant amplitude fatigue limit, to cause significant damage. To account for this small cycle damage, Topper and Lam [33] propose developing an effective strain-life curve by applying periodic overloads at certain maximum intervals, so that all the applied small cycle strain ranges, most
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importantly those below the constant amplitude fatigue limit, are fully effective. At specimen failure, an equivalent fatigue life for the small cycles can then be obtained using linear damage rule LDR: m X ni no ns 1 g ¼ þ ¼ no ð þ Þ ¼ 1 N N N N N o s o s i i¼1
ð3Þ
where ni is the number of cycles at amplitude i, Ni is the expected constant amplitude life at amplitude i, ‘o’ indicates overload cycle, ‘s’ indicates smaller cycle, and g is the number of smaller cycles between overload cycles. The equivalent fatigue life (Neq) in terms of number of small cycles is calculated using a linear damage accumulation should be
no 1 Neq ¼ ns = 1 ¼ 1 1 No ns gN o
ð4Þ
where No is taken from the constant amplitude strain-life curve. Using this equivalent small cycle life and plotting the overload tests on the basis of the amplitude of the small cycles gives the equivalent strain-life curve (Fig. 5) of Fig. 4 3.4. Macrofractography Under constant amplitude test, torsional cyclic loading induces a typical fracture in the specimen as shown in Fig. 6. Both transgranular and intergranular cracks were seen on the fatigued brass. Intergranular cracking dominated the fracture process. This can be correlated with the high intergranular stresses, which would be ε
4.5
η= 1000
η N
4
Effective strain (%)
expected to result from planar slip. For previous work [23], SEM assessment of crack profiles indicated that: (i) near the fracture surface, secondary microcracks developed and interfered with principal crack propagation; (ii) tortuosity and crack branching is common and has been previously detected for planar slip material and (iii) crack propagated parallel to the loading axial direction. Observation of fracture surface showed that it is characterized by irregular and rough surface relief created by the formation of pores or voids. The void growth dominates the failure process until the deformation localizes, and the large voids coalesce by reduction of the intervoid ligament. In addition we note that the convergence of cracks to center region, which grow inward and slowly propagate on the shallow of surface in directions of maximum shear stress leading to serrated fracture surface. The center region is obtained by rupturing the specimen after testing. As compared to fatigue tests at constant amplitude, the incorporation of main stress by monotonic prestraining induces a pronounced modification of process damage. The follow-up tests showed that the failure began with the propagation a primary crack in the in the longitudinal shear plan (i.e. parallel to the loading axial direction). After that the fatigue crack deviated from its original plane to an angle of approximately 45° (i.e. maximum principal stress plane) developed into macrocracks leading to fatigue failure in Fig. 7. The change of fracture path occurs at a distance of approximately 800 lm from the crack initial area. It should be mentioned that the new feature on the fracture surface under MPS condition are firstly the temper colors produced by oxidation reaction and secondly the fractured asperities transferred
η= 4000 η= 6000
3.5
Constant amplitude
3
ε= ±2,1% , η= 1000
2.5 ε= ±1,4% , η= 1000
2
ε= ±0,35% , η= 6000
1.5
1.2
1
1
0.5
0.8
0 1.0E+02
ε= ±0,7% , η= 4000
0.6
1.0E+03
1.0E+04
1.0E+05
Equivalent Number of cycles (Neq)
0.4 0.2 0 1.0E+04
Fig. 5. Equivalent strain-life curve.
Fig. 6. Fatigue fracture surfaces of specimen tested under constant amplitude strain e = ±1.4.
1.0E+05
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(1) Primary crack (parallel to the loading axial direction
(2) Deviation of crack with an angle of approximately 45°
2mm Fig. 7. Typical fracture fatigue under monotonic prestraining (MPS) condition (e = ±0.7%, e_ = 5.6 103 s1).
from the mating surface, characteristic of a ductile torsional overload failure. A similar fracture was observed in the case of cyclic prestraining (CPS) condition. Under MPS condition, the fracture surface features were characteristic of bending fatigue (BF), a distinct area of bending torsion fatigue (BTF), and a region between the BF and BTF, overloading (OL) (Fig. 8a). The fracture surface area exhibiting BF features ranged from less than 25% of the total fracture surface area. The overloaded region marked by OL shows ductile dimples (Fig. 8b). The BTF area was considerably larger than the BF and OL areas, and therefore, it was possible to identify striations. Multiple cracks were generated in the BTF case, which had independent paths and directions and affected the CBTF crack growth patterns. Cleavage type features were observed at the beginning of the BTF area. A
fractograph of a transition region between BTF and OL, which shows voids together with striations, is shown in Fig. 8. Some of the fracture features observed in this investigation, for example, cleavage, kink band formation and block striations were also reported by other workers [34] in the case of Ti–6Al–4V crack growth studies, Inconel 718, GH36, low carbon steels and high strength steels under uniaxial loading condition. Under periodic cyclic overstrain (POS), the appearance of a fatigue fracture surface is extremely dependent on the amplitude strain. The microscopic analyses underline two types of fracture surface. At low small cycles amplitude such as e = ±0.7%, fracture surface was characterized by a similar fractography observed in the case of MPS condition (Fig. 9a). However, for high small cycle amplitudes, such as e = ±2.1%, fracture surface revealed a similar
BTF
OL
(a)
BF 1 mm
(b)
100µm
Fig. 8. Typical SEM images of fracture surface obtained for monotonic prestrained (MPS) specimen e = 1.4% (De = 2%, e_ = 5.6 103 s1) characterized by (a) bending torsion fatigue area, overloaded (OL) region and bending fatigue (BF) region, (b) ductile dimples crated by formation and growth of voids.
Fig. 9. Typical fracture fatigue under periodic cyclic prestraining (POS) condition: (a) e = ± 0.7%, g = 6000, e_ = 5.6 103 s1 and (b) e = ±2.1%, g = 1000, e_ = 5.6 103 s1.
R. Mnif et al. / Materials and Design 31 (2010) 3742–3747
topography observed in the case of constant strain amplitudes test (Fig. 9b). The transition for fracture process was attributed to the competition effect between the magnitudes of cyclic overstrains amplitude and cyclic small amplitude in damage mechanism. It has been shown in earlier studies that the significance of prestrain depends on the degree of overstrain and the loading parameters applied during subsequent cycling. For example, copper behaves as if it were history-independent only if the plastic strain amplitude is sufficiently high [35]. However, in most cases the various changes in the mechanical behavior due to overstrain can be explained on the basis of the corresponding microstructural alterations. These points out that micro structural analysis are important to understand and assess the dependence on (thermo) mechanical prehistory.
4. Conclusions The objective of the present paper was to study the effects of prestraining and periodic overstrains and on fatigue life and damage behavior of brass alloy during cyclic torsional. Three types of loading histories were conducted under strain control and at constant strain rate e_ = 5.6 103 s1: (i) monotonic torsional prestraining (MPS) followed by strain controlled cycling loading to failure, (ii) cyclic torsional prestraining (CPS) followed by cycling at constant amplitude with variation amplitude, (iii) periodic cyclic overstrain (POS) divided by smaller constant amplitude cycles (g). Microscopic observations of surface fracture were also made to get a better understanding of the fatigue damage process. The following conclusions can be drawn from the current study. – Under MPS condition, the fatigue life is extremely dependent on the amplitude prestraining. The effect may be attributed to a competition between strain hardening and formation of several slip bands that may occur at the surface of the material, which constitute the origin of cracks formations. However for all tests under CPS and POS, compared with constant amplitude tests, a beneficial effect on fatigue life and similar fatigue endurance was noted – A similar level stress response to cyclic loading was identified between the virgin and monotonic prestrained specimens. For CPS condition, the level stress obtained is more important than that of virgin specimen. – Torsional cyclic loading induces the fracture of specimen by formation and coalescence of voids and a serrated factory roof. Under prestraining condition, the fracture surface features were characteristic of bending fatigue (BF), a distinct area of bending torsion fatigue (BTF), and a region between the BF and BTF, overloading (OL). However for POS condition, the fracture topography depends strongly on the strain amplitude of small cycles. The effect of overstrain is more marked that the difference between the magnitude of overstrain amplitude and small amplitude cycles is important.
Acknowledgement The authors are grateful to SOPAL Society (Tunisia). Special thanks to his manager for all valuable help with specimen preparation. References [1] Kang Minwoo, Aono Yuuta, Noguchi Hiroshi. Effect of prestrain type on the rotating bending fatigue limit of carbon steel. J Solid Mech Mater Eng 2008;2:82–94.
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[2] Le Quochung, Kang Hong Tae, Kridli Ghassan, Khosrovaneh AK, Yan Benda. Effect of prestrain paths on mechanical behavior of dual phase sheet steel. Int J Fatigue 2009;31:607–15. [3] Degtyarev VA. The effect of plastic prestrain on mechanical characteristics of grade 45 steel and D16T alloy under static and cyclic loading. Strength Mater 2005;37(4). [4] Uemura T. A fatigue life estimation of specimens excessively prestrained in tension. Fatigue Fract Eng Mater Struct 1998;21:151–8. [5] Gustavsson A, Melander A. Fatigue of a highly prestrained dual phase sheet steel. Fatigue Fract Eng Mater Struct 1995;18(2):201–10. [6] Gustavsson A, Melander A. Variable-amplitude fatigue of a dual-phase sheet subjected to prestrain. Fatigue 1994;16:503–9. [7] Harvey DP, Bonenberger RJ, Wolla JM. Effects of sequential cyclic and monotonic loadings on damage accumulation in nickel 270. Int J Fatigue 1998;20:291–300. [8] Wang G. Effect of local plastic stretch on total fatigue life evaluation. In: Proceedings of the 15th European conference of fracture, 2004. [9] Ishii Hitoshi, Yukawa Kazuhiko. The role of dislocation substructures in fatigue crack propagation in copper and alpha brass. Metall Mater Trans A 1979;10. [10] Schoeler K, Christ H-J. Influence of prestraining on cyclic deformation behaviour and microstructure of a single-phase Ni-base superalloy. Int J Fatigue 2001;23:767–75. [11] Lanning David B, Nicholas Theodore, Haritos George K. Effect of plastic prestrain on high cycle fatigue of Ti–6Al–4V. Mech Mater 2002;34:127–34. [12] Froustey Catherine, Lataillade Jean Luc. Influence of large pre-straining of aluminium alloys on their residual fatigue resistance. Int J Fatigue 2008;30:908–16. [13] Jia WP, Fernandes JV. Mechanical behaviour and the evolution of the dislocation structure of copper polycrystal deformed under fatigue_/tension and tension_/fatigue sequential strain paths. Mater Sci Eng 2003;A348:133–44. [14] Whittaker MT, Evans WJ. Effect of prestrain on the fatigue properties of Ti834. Int J Fatigue 2009;31:1751–7. [15] Bonnen JJF, Topper TH. The effect of bending overloads on torsional fatigue in normalized 1045 steel. Int J Fatigue 1999;21:23–33. [16] Daneshpour S, Koçak M, Langlade S, Horstmann M. Effect of overload on fatigue crack retardation of aerospace Al-alloy laser welds using crack-tip plasticity analysis. Int J Fatigue 2009;31:1603–12. [17] Moo Lee J, Ho Cho B. Experimental observation and modeling of the retardation of fatigue crack propagation under the combination of mixed-mode single overload and constant amplitude loads. Int J Fatigue 2009:848–1857. [18] Weidner A, Tirschler W, Blochwitz C. Overstraining effects on the crackopening displacement of microstructurally short cracks. Mater Sci Eng A 2005;390:414–22. [19] Jurcevic R, DuQuesnay D, Topper T, Pompetzki M. Fatigue damage accumulation in 2024-T351 aluminium subjected to periodic reversed overloads. Int J Fatigue 1990;12:259–66. [20] Borrego LP, Ferreira JM, Pinho da Cruz JM, Costa JM. Evaluation of overload effects on fatigue crack growth and closure. Eng Fract Mech 2003;70:1379–97. [21] Byrne J, Hall RF, Powell BE. Influence of LCF overloads on combined HCF/LCF crack growth. Int J Fatigue 2003;25:827–34. [22] Romeiro F, de Freitas M, da Fonte M. Fatigue crack growth with overloads/ underloads: interaction effects and surface roughness. Int J Fatigue 2009;31:1889–94. [23] Mnif R, Kchaou M, Elleuch R, Halouani F. Cyclic behaviour and damage analysis of brass alloy under cyclic torsional loading. J Fail Anal Prevent 2007;7:450–5. [24] Correa ECS, Aguilar MTP, Silva EMP, Cetlin PR. The effect of sequential tensile and cyclic torsion straining on work hardening of steel and brass. J Mater Process Technol 2003;142:282–8. [25] Hoffmann G, Ottinger O, Christ H-J. The influence of mechanical prehistory on the cyclic stress–strain response and microstructure of single-phase metallic materials. LCF3. In: Rie K-T, editor. Proceedings of low cycle fatigue and elastoplastic behaviour congress. London: Elsevier; 1993. p. 106–11. [26] Christ H-J, Hoffmann G, Ottinger O. History effects in metals during constant and variable amplitude testing. I: wavy dislocation glide behaviour. Mater Sci Eng 1995;A201:1–12. [27] Feltner CE, Laird C. Cyclic stress–strain response of F.C.C. metals and alloys – phenomenological experiments. Acta Metall 1967;15:1621–32. [28] Lee EU, Glinka G, Vasudevanc AK, Iyyerd N, Phana ND. Fatigue of 7075-T651 aluminum alloy under constant and variable amplitude loadings. Int J Fatigue 2009;31:1858–64. [29] Skorupa M. Load interaction effects during fatigue crack growth under variable amplitude loading – a literature review part II: qualitative interpretation. Fatigue Fract Eng Mater Struct 1999;22(10):905–26. [30] Pommi er S. Cyclic plasticity and variable amplitude fatigue. Int J Fatigue 2003;25(9–11):983–97. [31] Pommier S, DeFreitas M. Effect on fatigue crack growth of interactions between overloads. Fatigue Fract Eng Mater Struct 2002;25:709. [32] NE Dowling. Estimation and correlation of fatigue lives for random loading. Int J Fatigue 1988:179–85. [33] TH Topper, TS Lam. Effective strain-fatigue life data for variable amplitude fatigue. Int J Fatigue 1997:137–43. [34] Goswami Tarun. Conjoint bending torsion fatigue-fractography. Mater Des 2002;23:385–90. [35] Feltner CE, Laird C. Cyclic stress–strain response of F.C.C. metals and alloys phenomenological experiments. Acta Metall 1967;15:1621–32.
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Effects of cyclic torsional prestraining and overstrain on fatigue life and damage behavior of brass alloy Ridha Mnif *, Riadh Elleuch, Foued Halouani Laboratoire des Systèmes Electro-mécaniques (LASEM), Ecole Nationale d’Ingénieurs de Sfax, (ENIS) BP 599-3018, Tunisia
a r t i c l e
i n f o
Article history: Received 20 December 2009 Accepted 9 March 2010 Available online 11 March 2010 Keywords: Brass Torsion Overstrain Prestraining Fatigue life Fracture surface
a b s t r a c t Many practical structural members and parts may be subjected to fluctuating plastic deformation by prestraining due to manufacturing and machining process (forming operation, straightening, etc.) and unintentional overstrains (misuse, accidents, under design, etc.). For this reason, the effect of the prestrain and periodic overstrains on fatigue life and damage behavior was being necessary considered for reasonable fatigue design. In this context, an experimental program was conducted to study the effects of overstrain and prestraining on fatigue life and damage behavior of brass alloy subjected to cyclic torsional loading. To establish baseline fatigue behavior, several virgin specimens were tested under fully-reversed strain control and constant amplitude fatigue torsional loading up to failure. The obtained experimental results showed that the fatigue life depends strongly on the strain amplitude and prestraining type (monotonic or cyclic). In addition, a beneficial effect in the fatigue life was observed for all tests with periodic overstrain. Cyclic fatigue fracture on a macroscopic scale revealed features reminiscent of locally ductile and brittle mechanisms. At the same time, microscopic analysis indicated a difference on fatigue fracture surface morphology between the conducted tests and those performed under constant amplitude loading. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction It is widely known that in the last decade’s copper alloys have been more and more used in the production industry, mainly in components of sanitary installations (valves, pipe couplings, etc.). The components are often subjected to cyclic stress due to internal pressure variation and unintentional overstrains. Therefore, fatigue property is essentially needed in the safe life design of components. In most studies on the mechanical properties, such as the creep behavior, the fracture mechanisms and the cyclic deformation behavior, of the material under investigation is used in a well-defined annealed condition. Only in rare cases, the effect arising from prestrain and periodic overstrain on the subsequent cyclic deformation behavior is taken into account, even though engineering materials often undergo a (thermo-)mechanical pretreatment such as swaging, rolling or forging. Therefore, the influence of a mechanical prehistory on the subsequent cyclic deformation behavior and cyclic life is of particular interest for technical applications of respective materials. Unfortunately, the effects resulting from prestraining depend on numerous parameters and influence the macroscopic mechanical properties and the microstructure in a very complex manner. * Corresponding author. Tel.: +216 74 274 088; fax: +216 74 275 595. E-mail addresses: [email protected] (R. Mnif), [email protected] (R. Elleuch), [email protected] (F. Halouani). 0261-3069/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.matdes.2010.03.015
The effect of quasi-static plastic prestrain on fatigue behavior has been studied for many years in great detail on numerous types of metallic materials. It appears that the most studied [1–6] material is steel and that effects of prestrain vary from no apparent fatigue benefit to either a significant benefit or detriment. For example, Uemura’s work [4] on mild steel concludes that the effect of prestraining in degrading fatigue life in the domain of low-cycle fatigue is evident, but there is no apparent depreciation in the domain of medium to high-cycle fatigue. For these investigations, specimens were tensile prestrained from 25% to 85% of the static fracture strain. On mild steel too, Gustavsson and Melander [5,6] concludes that contrary to prestrain below 5%, high degrees of prestraining (i.e. above 15%) have a positive effect on the fatigue resistance. The fatigue strength increases by up to about 50%. The effect of prestrain type (tensile or torsional prestrain) on the fatigue limit of carbon steel was also investigated [1]. The results obtained showed that the fatigue limit of the torsional-prestrained specimen was higher than that of the tensile-prestrained specimen and the degree of cyclic softening induced by fatigue loading in the torsional-prestrained specimen was lower than that in the tensile-prestrained specimen. At the same many studies [7–13] have been conducted on nonferrous alloys such as nickel alloys, the relative effects of monotonic prestrain on subsequent cyclic behavior were more harmful than the effects of precycling on subsequent monotonic behavior [7]. Concerning aluminium alloys, Wang’s [8] reported that the effect of plastic deformation (10% prestretching is used) showed a
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considerable effect on the fatigue life, depending on the stress level. A reduction of more than 20% in the fatigue strength has been observed near the fatigue limit whereas less or no reduction may be expected at higher stress levels (around 105cycles). The effect of dislocation substructures on fatigue crack propagation (FCP) behavior in copper and alpha brass was also studied [9]. Dislocation cells were formed by this prestraining in copper and 90/10 brass and when they formed the resistance to FCP at intermediate propagation rates (5 10–9–10–7 m/cycle) increased with increasing of prestrain. On the other hand the effects of periodic overstrain has been studied by several researchers through comparative fatigue testing [14,15]. It is well-known that one of the major characteristics of variable fatigue loads, especially overloads, is the accelerations and/or retardations of the fatigue crack due to the complex interaction of many factors such as the overload ratio, the timing of overloads, the stress ratio, the yield stress of the material, the thickness of the structure, and the stress history [16–18]. Many structural steels display distinct fatigue limits when tested under constant amplitude fatigue cycling conditions. These materials often display substantial reductions in long-life fatigue resistance when occasional, periodic overstrains are introduced between large numbers of constant amplitude fatigue cycles. These periodic overstrains can lead to dramatic reductions in the originally perceived fatigue limit for the material [15,19]. However overstrains may purposely be applied to produce some beneficial effects on the fatigue resistance of the components because of sufficient magnitude can result in a transient reduction in the rate of fatigue crack growth at the baseline level. It has been also well established that this reduction is closely related to the residual compressive stress field induced in the vicinity of crack tips [20–22]. This paper presents and discusses the influence of prestraining and periodic overstrains on cyclic strain amplitude-controlled fatigue response, fatigue life and fracture characteristics of brass alloy. The high-cycle fatigue properties and final fracture characteristics of the alloy are discussed in terms of the specific roles played by the concurrent and synergistic influences of magnitude of prestraining type (monotonic or cyclic), periodic overstrain and macroscopic aspects of fracture.
3L
r¼
pffiffiffi 3:3 3M 2pa3
3.1. Monotonic prestraining (MPS) fatigue tests
ð1Þ
ð2Þ
Table 1 Mechanical properties of brass alloy measured under monotonic torsion.
The material studied was a brass alloy with the following chemical composition in weight percent: 58.5% Cu, 2.8% Pb, 0.25% Sn, 0.11% Ni, 0.21% Fe, and 0.01% Al and the balance Zn. The material was received in the form of extruded bar (120 mm U 6 mm) from which fatigue specimens (cylinder of 6 mm in diameter and 32 mm in length) were machined. After machining, the useful surface of the specimen was polished mechanically to a 3 lm finish. Fatigue tests were conducted on a torsional materials test system (Deltalab EM 400) [23]. A triangular wave signal was used for total strain control under strain ratio Re = 1(Re = emin/emax). During testing, the torque (T) and twist angle (h) values were continually recorded and the von Mises effective stress (r) and effective strain (e) were calculated using Eq. (1) and (2) [24].
ha
3. Tests results and discussions
Fig. 2 shows the typical cyclic hardening curves of brass alloy, recorded for the virgin and monotonic prestrained (MPS) specimens under two mechanical strains (1.4%, 4.2%). The curves are obtained by plotting cyclic resolved equivalent stress against the number of cycles (N). A similar level stress response to cyclic loading was identified between the virgin and monotonic prestrained specimens. Hence, the cyclic behavior can be attributed to the relaxation phenomenon leading to a continuous decrease of stress for primary dozen cycles. Furthermore, it should be mentioned that prestraining specimen presents a pronounced linearly decrease of mean stress with the number of cycle. However for the virgin material, we note a quasi stability of mean stress. At applied constant effective strain amplitude of 1.4%, it was found in the present work that the effect of 1.4% monotonic prestrain increases the fatigue life slightly 10% as compared with the as-received material. However, at 4.2% monotonic prestrain, a reduction of the fatigue life was noticed. The reduction of fatigue life could be attributed a deformation and damage mechanisms. In fact, monotonic prestraining can induce microscopic slips steps on the surface of the specimen and these slip steps can also serve as microcrack initiation sites during the subsequent fatigue loading. It has been shown in earlier studies that the significance of predeformation depends strongly on the dislocation slip behavior [25–27]. For materials exhibiting planar slip, even small degrees of prestraining lead to an increase of the resulting stress amplitudes, a reduction of cyclic life and a shift of the cyclic stress–strain curve to higher stress values [25]. For materials showing wavy slip, the influence of a predeformation is more complex. The predominant effect depends on the degree of prestraining and the loading parameters applied during subsequent cycling [26]. For example, copper behaves as if it were history-independent only if the plastic strain amplitude is sufficiently high [27]. However, in most cases the various changes in the mechanical behavior due to predefor-
2. Material and fatigue testing procedure
e ¼ pffiffiffi
performed using a servoelectronic testing machine (this machine was also used for fatigue tests).The mechanical properties of brass alloy measured under monotonic torsion are given in Table 1. In order to get a better understand of the effects of cyclic torsional overstrain and prestraining on fatigue life and damage behavior of brass alloy, three types of loading histories were conducted under strain control and at constant strain rate e_ = 5.6 103 s1 (Fig 1): (i) monotonic torsional prestraining (MPS) followed by strain controlled cycling loading to failure with variation strain amplitude De = 2%. The prestrains used were 1.4% and 2.4% in monotonic torsion, (ii) cyclic torsional prestraining (CPS) at strain amplitude ±4.2% followed by cycling at constant amplitude with variation amplitude strain De = 2%, (iii) periodic cyclic overstrain (POS) under strain amplitude 4.2% divided by smaller constant amplitude cycles (g) in the range of ±0.35– ±2.1% strain. The prestraining and overstrain effects were investigated by cycling hardening/softening curves and fatigue life curves developed during cyclic torsional loading. Quantitative fatigue damage was also assessed by microscopic observations of surface fracture.
The present study focuses on total strain controlled fatigue. To control the total strain, it is necessary to have information about the range of material plasticity. Monotonic torsion tests were
Yield stress, r0.2% (MPa)
Ultimate stress strength, Rm (MPa)
Shear modulus, G (GPa)
227
480
36
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a
Monotonic prestrained
ε
c
b
Cyclice prestarined
ε
Overstrain
ε Small amplitude ( η)
4,2%
2,2%
N
0
N
0
N
0
- 4,2%
Fig. 1. Illustration of loading histories: (a) monotonic prestraining (MPS); (b) cyclic prestraining (CPS); (c) periodic cyclic overstrain (POS).
Monotonic prestraining (1.4%)
Virgin specimen
300 200 100 0 -100 -200 -300 -400 0
5000
10000
15000
Virgin specimen
Cyclic prestraining (4.2%)
400
Effective stress (MPa)
Effective stress (MPa)
Monotonic prestraining (4.2%)
20000
500 400 300 200 100 0 -100 -200 -300 -400 -500
Number of cycles
0
5000
10000
15000
20000
Number of cycles Fig. 2. Cyclic hardening–softening of virgin specimen and monotonic prestrained (MPS) specimen curve (De = 2%, e_ = 5.6 103 s1).
Fig. 3. Cyclic hardening–softening of virgin specimen and cyclic prestrained (CPS) specimen curves (De = 2%, e_ = 5.6 103 s1).
mation can be explained on the basis of the corresponding microstructural alterations.
η = 1000
3.2. Cyclic prestraining (CPS) fatigue tests Fig. 3 shows the typical cyclic hardening curves of brass alloy, recorded for the as-received and cyclic prestrained (CPS) specimens under mechanical strain 4.2%. At the same equivalent strain amplitude 1%, the maximum stress level recording to the CPS specimen is more important than that of virgin specimen by a factor of 1.7. In terms of life, contrary to what is observed in monotonic prestrained specimens under mechanical strain 2.4%, the experimental results shows that the fatigue life of cyclic torsionalprestrained specimen was higher than that virgin specimen. The result means that the effect of the prestrain type on the fatigue life is related to the cyclic softening and the cyclic softening depends on the relationship between prestrain type and mean stress effect. The cyclic hardening behavior results for CPS can be attributed to the generation and interaction between dislocations leading to a continuous decrease in plastic strain. The difference of fatigue life therefore has to reflect the effect of cyclic prestraining on grain boundary which modifies the structure and the evolution of dislocation [26,27]. 3.3. Periodic overstrain (POS) fatigue tests Fig. 4 illustrates the effect of periodic overstrain (POS) amplitude ±4.2% on the fatigue life of brass alloy during cyclic torsional for different amplitudes. We note that the overload applied during the test increased slightly the fatigue life of brass alloy for all tests. Similar fatigue endurance, compared with constant amplitude tests was obtained. The beneficial effect on the fatigue resistance fatigue life can be attributed to a transient retardation in the rate
Effective strain (%)
4.5
η = 4000
4
η = 6000
3.5 Constant amplitude
3 2.5
Cyclic periodic overstrain
2 1.5 1
Constant amplitude strain
0.5 0 1.0E+02
1.0E+03
1.0E+04
1.0E+05
1.0E+06
Number of cycles (Nr) Fig. 4. Effect of periodic cyclic overstrain (POS) on fatigue life.
fatigue growth at the baseline level. This retardation is closely related to the residual stress field induced in the vicinity of the crack tip [27,28] and to be closely related to the elastic–plastic behavior of the material [29–31]. Many researchers [15,32] have found that damage calculations made on variable amplitude load histories using constant amplitude strain-life curves could be very non-conservative. This inaccuracy arises because overload cycles in variable amplitude load histories can reduce crack closure and allow small cycles, whose amplitudes are below the constant amplitude fatigue limit, to cause significant damage. To account for this small cycle damage, Topper and Lam [33] propose developing an effective strain-life curve by applying periodic overloads at certain maximum intervals, so that all the applied small cycle strain ranges, most
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importantly those below the constant amplitude fatigue limit, are fully effective. At specimen failure, an equivalent fatigue life for the small cycles can then be obtained using linear damage rule LDR: m X ni no ns 1 g ¼ þ ¼ no ð þ Þ ¼ 1 N N N N N o s o s i i¼1
ð3Þ
where ni is the number of cycles at amplitude i, Ni is the expected constant amplitude life at amplitude i, ‘o’ indicates overload cycle, ‘s’ indicates smaller cycle, and g is the number of smaller cycles between overload cycles. The equivalent fatigue life (Neq) in terms of number of small cycles is calculated using a linear damage accumulation should be
no 1 Neq ¼ ns = 1 ¼ 1 1 No ns gN o
ð4Þ
where No is taken from the constant amplitude strain-life curve. Using this equivalent small cycle life and plotting the overload tests on the basis of the amplitude of the small cycles gives the equivalent strain-life curve (Fig. 5) of Fig. 4 3.4. Macrofractography Under constant amplitude test, torsional cyclic loading induces a typical fracture in the specimen as shown in Fig. 6. Both transgranular and intergranular cracks were seen on the fatigued brass. Intergranular cracking dominated the fracture process. This can be correlated with the high intergranular stresses, which would be ε
4.5
η= 1000
η N
4
Effective strain (%)
expected to result from planar slip. For previous work [23], SEM assessment of crack profiles indicated that: (i) near the fracture surface, secondary microcracks developed and interfered with principal crack propagation; (ii) tortuosity and crack branching is common and has been previously detected for planar slip material and (iii) crack propagated parallel to the loading axial direction. Observation of fracture surface showed that it is characterized by irregular and rough surface relief created by the formation of pores or voids. The void growth dominates the failure process until the deformation localizes, and the large voids coalesce by reduction of the intervoid ligament. In addition we note that the convergence of cracks to center region, which grow inward and slowly propagate on the shallow of surface in directions of maximum shear stress leading to serrated fracture surface. The center region is obtained by rupturing the specimen after testing. As compared to fatigue tests at constant amplitude, the incorporation of main stress by monotonic prestraining induces a pronounced modification of process damage. The follow-up tests showed that the failure began with the propagation a primary crack in the in the longitudinal shear plan (i.e. parallel to the loading axial direction). After that the fatigue crack deviated from its original plane to an angle of approximately 45° (i.e. maximum principal stress plane) developed into macrocracks leading to fatigue failure in Fig. 7. The change of fracture path occurs at a distance of approximately 800 lm from the crack initial area. It should be mentioned that the new feature on the fracture surface under MPS condition are firstly the temper colors produced by oxidation reaction and secondly the fractured asperities transferred
η= 4000 η= 6000
3.5
Constant amplitude
3
ε= ±2,1% , η= 1000
2.5 ε= ±1,4% , η= 1000
2
ε= ±0,35% , η= 6000
1.5
1.2
1
1
0.5
0.8
0 1.0E+02
ε= ±0,7% , η= 4000
0.6
1.0E+03
1.0E+04
1.0E+05
Equivalent Number of cycles (Neq)
0.4 0.2 0 1.0E+04
Fig. 5. Equivalent strain-life curve.
Fig. 6. Fatigue fracture surfaces of specimen tested under constant amplitude strain e = ±1.4.
1.0E+05
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(1) Primary crack (parallel to the loading axial direction
(2) Deviation of crack with an angle of approximately 45°
2mm Fig. 7. Typical fracture fatigue under monotonic prestraining (MPS) condition (e = ±0.7%, e_ = 5.6 103 s1).
from the mating surface, characteristic of a ductile torsional overload failure. A similar fracture was observed in the case of cyclic prestraining (CPS) condition. Under MPS condition, the fracture surface features were characteristic of bending fatigue (BF), a distinct area of bending torsion fatigue (BTF), and a region between the BF and BTF, overloading (OL) (Fig. 8a). The fracture surface area exhibiting BF features ranged from less than 25% of the total fracture surface area. The overloaded region marked by OL shows ductile dimples (Fig. 8b). The BTF area was considerably larger than the BF and OL areas, and therefore, it was possible to identify striations. Multiple cracks were generated in the BTF case, which had independent paths and directions and affected the CBTF crack growth patterns. Cleavage type features were observed at the beginning of the BTF area. A
fractograph of a transition region between BTF and OL, which shows voids together with striations, is shown in Fig. 8. Some of the fracture features observed in this investigation, for example, cleavage, kink band formation and block striations were also reported by other workers [34] in the case of Ti–6Al–4V crack growth studies, Inconel 718, GH36, low carbon steels and high strength steels under uniaxial loading condition. Under periodic cyclic overstrain (POS), the appearance of a fatigue fracture surface is extremely dependent on the amplitude strain. The microscopic analyses underline two types of fracture surface. At low small cycles amplitude such as e = ±0.7%, fracture surface was characterized by a similar fractography observed in the case of MPS condition (Fig. 9a). However, for high small cycle amplitudes, such as e = ±2.1%, fracture surface revealed a similar
BTF
OL
(a)
BF 1 mm
(b)
100µm
Fig. 8. Typical SEM images of fracture surface obtained for monotonic prestrained (MPS) specimen e = 1.4% (De = 2%, e_ = 5.6 103 s1) characterized by (a) bending torsion fatigue area, overloaded (OL) region and bending fatigue (BF) region, (b) ductile dimples crated by formation and growth of voids.
Fig. 9. Typical fracture fatigue under periodic cyclic prestraining (POS) condition: (a) e = ± 0.7%, g = 6000, e_ = 5.6 103 s1 and (b) e = ±2.1%, g = 1000, e_ = 5.6 103 s1.
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topography observed in the case of constant strain amplitudes test (Fig. 9b). The transition for fracture process was attributed to the competition effect between the magnitudes of cyclic overstrains amplitude and cyclic small amplitude in damage mechanism. It has been shown in earlier studies that the significance of prestrain depends on the degree of overstrain and the loading parameters applied during subsequent cycling. For example, copper behaves as if it were history-independent only if the plastic strain amplitude is sufficiently high [35]. However, in most cases the various changes in the mechanical behavior due to overstrain can be explained on the basis of the corresponding microstructural alterations. These points out that micro structural analysis are important to understand and assess the dependence on (thermo) mechanical prehistory.
4. Conclusions The objective of the present paper was to study the effects of prestraining and periodic overstrains and on fatigue life and damage behavior of brass alloy during cyclic torsional. Three types of loading histories were conducted under strain control and at constant strain rate e_ = 5.6 103 s1: (i) monotonic torsional prestraining (MPS) followed by strain controlled cycling loading to failure, (ii) cyclic torsional prestraining (CPS) followed by cycling at constant amplitude with variation amplitude, (iii) periodic cyclic overstrain (POS) divided by smaller constant amplitude cycles (g). Microscopic observations of surface fracture were also made to get a better understanding of the fatigue damage process. The following conclusions can be drawn from the current study. – Under MPS condition, the fatigue life is extremely dependent on the amplitude prestraining. The effect may be attributed to a competition between strain hardening and formation of several slip bands that may occur at the surface of the material, which constitute the origin of cracks formations. However for all tests under CPS and POS, compared with constant amplitude tests, a beneficial effect on fatigue life and similar fatigue endurance was noted – A similar level stress response to cyclic loading was identified between the virgin and monotonic prestrained specimens. For CPS condition, the level stress obtained is more important than that of virgin specimen. – Torsional cyclic loading induces the fracture of specimen by formation and coalescence of voids and a serrated factory roof. Under prestraining condition, the fracture surface features were characteristic of bending fatigue (BF), a distinct area of bending torsion fatigue (BTF), and a region between the BF and BTF, overloading (OL). However for POS condition, the fracture topography depends strongly on the strain amplitude of small cycles. The effect of overstrain is more marked that the difference between the magnitude of overstrain amplitude and small amplitude cycles is important.
Acknowledgement The authors are grateful to SOPAL Society (Tunisia). Special thanks to his manager for all valuable help with specimen preparation. References [1] Kang Minwoo, Aono Yuuta, Noguchi Hiroshi. Effect of prestrain type on the rotating bending fatigue limit of carbon steel. J Solid Mech Mater Eng 2008;2:82–94.
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[2] Le Quochung, Kang Hong Tae, Kridli Ghassan, Khosrovaneh AK, Yan Benda. Effect of prestrain paths on mechanical behavior of dual phase sheet steel. Int J Fatigue 2009;31:607–15. [3] Degtyarev VA. The effect of plastic prestrain on mechanical characteristics of grade 45 steel and D16T alloy under static and cyclic loading. Strength Mater 2005;37(4). [4] Uemura T. A fatigue life estimation of specimens excessively prestrained in tension. Fatigue Fract Eng Mater Struct 1998;21:151–8. [5] Gustavsson A, Melander A. Fatigue of a highly prestrained dual phase sheet steel. Fatigue Fract Eng Mater Struct 1995;18(2):201–10. [6] Gustavsson A, Melander A. Variable-amplitude fatigue of a dual-phase sheet subjected to prestrain. Fatigue 1994;16:503–9. [7] Harvey DP, Bonenberger RJ, Wolla JM. Effects of sequential cyclic and monotonic loadings on damage accumulation in nickel 270. Int J Fatigue 1998;20:291–300. [8] Wang G. Effect of local plastic stretch on total fatigue life evaluation. In: Proceedings of the 15th European conference of fracture, 2004. [9] Ishii Hitoshi, Yukawa Kazuhiko. The role of dislocation substructures in fatigue crack propagation in copper and alpha brass. Metall Mater Trans A 1979;10. [10] Schoeler K, Christ H-J. Influence of prestraining on cyclic deformation behaviour and microstructure of a single-phase Ni-base superalloy. Int J Fatigue 2001;23:767–75. [11] Lanning David B, Nicholas Theodore, Haritos George K. Effect of plastic prestrain on high cycle fatigue of Ti–6Al–4V. Mech Mater 2002;34:127–34. [12] Froustey Catherine, Lataillade Jean Luc. Influence of large pre-straining of aluminium alloys on their residual fatigue resistance. Int J Fatigue 2008;30:908–16. [13] Jia WP, Fernandes JV. Mechanical behaviour and the evolution of the dislocation structure of copper polycrystal deformed under fatigue_/tension and tension_/fatigue sequential strain paths. Mater Sci Eng 2003;A348:133–44. [14] Whittaker MT, Evans WJ. Effect of prestrain on the fatigue properties of Ti834. Int J Fatigue 2009;31:1751–7. [15] Bonnen JJF, Topper TH. The effect of bending overloads on torsional fatigue in normalized 1045 steel. Int J Fatigue 1999;21:23–33. [16] Daneshpour S, Koçak M, Langlade S, Horstmann M. Effect of overload on fatigue crack retardation of aerospace Al-alloy laser welds using crack-tip plasticity analysis. Int J Fatigue 2009;31:1603–12. [17] Moo Lee J, Ho Cho B. Experimental observation and modeling of the retardation of fatigue crack propagation under the combination of mixed-mode single overload and constant amplitude loads. Int J Fatigue 2009:848–1857. [18] Weidner A, Tirschler W, Blochwitz C. Overstraining effects on the crackopening displacement of microstructurally short cracks. Mater Sci Eng A 2005;390:414–22. [19] Jurcevic R, DuQuesnay D, Topper T, Pompetzki M. Fatigue damage accumulation in 2024-T351 aluminium subjected to periodic reversed overloads. Int J Fatigue 1990;12:259–66. [20] Borrego LP, Ferreira JM, Pinho da Cruz JM, Costa JM. Evaluation of overload effects on fatigue crack growth and closure. Eng Fract Mech 2003;70:1379–97. [21] Byrne J, Hall RF, Powell BE. Influence of LCF overloads on combined HCF/LCF crack growth. Int J Fatigue 2003;25:827–34. [22] Romeiro F, de Freitas M, da Fonte M. Fatigue crack growth with overloads/ underloads: interaction effects and surface roughness. Int J Fatigue 2009;31:1889–94. [23] Mnif R, Kchaou M, Elleuch R, Halouani F. Cyclic behaviour and damage analysis of brass alloy under cyclic torsional loading. J Fail Anal Prevent 2007;7:450–5. [24] Correa ECS, Aguilar MTP, Silva EMP, Cetlin PR. The effect of sequential tensile and cyclic torsion straining on work hardening of steel and brass. J Mater Process Technol 2003;142:282–8. [25] Hoffmann G, Ottinger O, Christ H-J. The influence of mechanical prehistory on the cyclic stress–strain response and microstructure of single-phase metallic materials. LCF3. In: Rie K-T, editor. Proceedings of low cycle fatigue and elastoplastic behaviour congress. London: Elsevier; 1993. p. 106–11. [26] Christ H-J, Hoffmann G, Ottinger O. History effects in metals during constant and variable amplitude testing. I: wavy dislocation glide behaviour. Mater Sci Eng 1995;A201:1–12. [27] Feltner CE, Laird C. Cyclic stress–strain response of F.C.C. metals and alloys – phenomenological experiments. Acta Metall 1967;15:1621–32. [28] Lee EU, Glinka G, Vasudevanc AK, Iyyerd N, Phana ND. Fatigue of 7075-T651 aluminum alloy under constant and variable amplitude loadings. Int J Fatigue 2009;31:1858–64. [29] Skorupa M. Load interaction effects during fatigue crack growth under variable amplitude loading – a literature review part II: qualitative interpretation. Fatigue Fract Eng Mater Struct 1999;22(10):905–26. [30] Pommi er S. Cyclic plasticity and variable amplitude fatigue. Int J Fatigue 2003;25(9–11):983–97. [31] Pommier S, DeFreitas M. Effect on fatigue crack growth of interactions between overloads. Fatigue Fract Eng Mater Struct 2002;25:709. [32] NE Dowling. Estimation and correlation of fatigue lives for random loading. Int J Fatigue 1988:179–85. [33] TH Topper, TS Lam. Effective strain-fatigue life data for variable amplitude fatigue. Int J Fatigue 1997:137–43. [34] Goswami Tarun. Conjoint bending torsion fatigue-fractography. Mater Des 2002;23:385–90. [35] Feltner CE, Laird C. Cyclic stress–strain response of F.C.C. metals and alloys phenomenological experiments. Acta Metall 1967;15:1621–32.