Characterization of uniaxial fatigue behavior of precipitate strengthened Cu-NiSi alloy ( SICLANIC ® )

Fatigue tests were conducted on cylindrical bars specimens to understand the fatigue behavior of SICLANIC. Although it displays good resistance in monotonic tension, this material weakens and shows a softening in repeated solicitation. This has been verified through a SEM observation, the Cu-Ni-Si alloy presents transgranular failure by cleavage. The MansonCoffin diagram exhibited the plastic deformation accommodation. The plastic deformation becomes periodic and decreases progressively as the cycle number increases. The approximations of Manson Coffin give fatigue parameters values which are in good agreement with the experience.


INTRODUCTION
t present, increasing demand for copper and copper alloys leads to the all-time high price of copper.Copper is widely used in electrical, electronic and thermal applications.Particularly, in an application where the high conductivity of copper is required, one should choose a copper alloy with higher percentage of copper, while there is a compromise required with the mechanical properties of the alloy.Hence, recent developments of copper alloys mainly focus on this issue and adapt to various strengthening mechanisms, such as precipitation hardening.Precipitates hardened copper alloys contain additive elements in small quantities that improves the mechanical characteristics by forming precipitates, without greatly altering their electrical conductivity [1].The mechanical strength of these alloys is improved by precipitation of the secondary phase particles during the quenching and tempering heat treatment processes [2][3][4].Thus, A the precipitation hardened copper alloys offer cost saving and they are suitable for many industrial applications under various mechanical loading conditions.Cu-Ni-Si alloys strengthened by precipitation hardening are used in very wide range of electrical and electromagnetic applications.However, the cyclic circulation of alternating current induces fatigue failure during the high frequency electromagnetic applications [5].Fatigue behavior of Cu-Ni-Si alloys has been investigated in few articles [6][7][8][9].In [6], authors investigated the microstructure of the material at different heat treatment states and its influence on the low cycle fatigue (LCF) and high cycle fatigue (HCF).They have noticed a softening effect of the copper alloy under LCF [6].Goto et al. [8] studied the role of the Ni2Si curing compound in fatigue crack initiation and propagation mechanism and identified a localized fatigue behavior.Zhao et al. [9] agree that the curing compound in Cu-Ni-Si is coherent with the matrix.Consequently, the main mechanism of crossing the secondary phase (Ni 2 Si) by a sliding dislocation is shearing.Besides, the alloys studied are of a different chemical composition than that of proposed in this work.This work is proposed to determine the fatigue characteristics for a Cu-Ni-Si alloy known by its trade name of SICLANIC ® .The SICLANIC ® is also strengthened by the precipitation of the Ni 2 Si phase [10].This alloy was mainly studied from a microstructure based investigation [11,12]; while there exist few other studies with the focus on the mechanical aspects [13,14].However, fatigue properties of this alloy has never been reported before in the literature.Fatigue test results are often represented by probabilistic Wöhler curve using statistical method and this curve has been developed due to the dispersions of tests results.In recent years, Castillo and Fernández-Canteli worked on the statistical analysis of the S-N and E-N fatigue curves [15], and they extended the probabilistic model to the strain damage evaluation to estimate fatigue life prediction in many applications [16,17].In this study, the probabilistic model of ASTM E 739 [18] is applied to estimate Wöhler curves.

MATERIAL AND EXPERIMENTAL PROCEDURES
ICLANIC ® alloy used in this study has the chemical composition with 96.9 % of copper, 2.5 % nickel and 0.6 % silicon in weight percent.The material has been received in bars of 14 mm × 14 mm× 60 mm dimension.To optimize high cycle fatigue tests, we chose classical specimen shape with circular section according to the ASTM E466-07 standard (Fig. 1) at MOROCCO CETIM.The fatigue tests were carried out on an MTS biaxial hydraulic machine model 17 with imposed stress at a temperature of 20 °C.During the tests, the temperature was controlled using a thermocouple (Fig. 2).Solicitations were loaded in uniaxial cyclical mode, with a sinusoidal waveform, according to repeated tensile loads.
And the ratio of extreme stresses (maximum and minimum), also called load ratio and defined by: where, σ min and σ max are respectively the minimum and maximum stresses to which the specimen is subjected.The tests are conducted with zero-based loading at stress ratio R= 0 (Fig. 3), this implies the following equations:

RESULTS AND ANALYSIS
atigue tests of studied material should be preceded by mechanical analysis of his answers to simple solicitation through tensile tests.Starting fatigue tests requires the definition of the first value of the maximum imposed stress.

Monotonic tensile behavior
Tensile tests have been carried out to characterize the monotonic properties of the material.Tests were conducted until the failure on a Zwick Roell machine under displacement mode.An additional test where an extensometer was used to the gauge length was performed to measure accurately the Young modulus.Monotonic tensile properties values are summarized in Tab. 1.  Furthermore, the remarkable tensile strength of 615 MPa enhanced by the presence of silicon, the SICLANIC ® has an elongation at fracture of higher than 10%.This ductility is mainly due to the high temperature of the solution treatmentquench phase during the hardening treatment.
The progressive passage, in the stress-strain curve, from linear elasticity to plastic deformation requires the definition of the conventional yield strength YS 0.2% which is of the order of 498 MPa.From this stress value, we realize a low permanent elongation which can be measured accurately.Mechanical behavior ceases to be elastic to become plastic.

S-N curve
SICLANIC ® fatigue results show significant dispersion.This dispersion is now considered as one of physical fatigue aspects [19].Indeed, for the same material, and the same load level, the lifetime may be different.

Iso-probabilistic S-N curve
As it is, the fatigue curve gives a tendency on the material behavior, but it is of limited use: we know that for a given stress level, half the specimens break for cycle number less than N(σ),the other half breaks for cycle number more than N(σ).For given stress level, the ratio between maximum and minimum value of failure cycle can exceed 10.In a probabilistic concept, Wöhler curve represents the border separating the area where failure is less likely (left of the curve) to the area where failure is most likely (right part of the curve).The fatigue life is generally described by the statistical longevity curve called iso-probabilistic Wöhler curve or median curve (N50, that to say 50% of survival specimens) [20].For the SICLANIC ® , fatigue curve median is illustrated in Fig. 4.

Probabilistic S-N curve
The confidence interval method using the probability of Student's law is also frequent to characterize fatigue behavior.It does not estimate directly the number of cycle to failure, but the estimations have percentage chance to containing the Nf .Thus, it is interesting to work in confidence interval of 80% that will give proper framing 80 times out of 100 on average, which meaning, if we could repeat the same tests a large number of times, affirming each time than Nf is in this interval, we would be wrong 20 times out of 100 on average.Fig. 5 shows SICLANIC ® probabilistic Wöhler curve corresponding at 80% of survival, such a curve is sometimes called "curve design".The two probability methods appear in good agreement; they give very close values of the endurance limit.The estimated value of SICLANIC ® endurance limit is 250 MPa.

Fractography
Fatigue fracture surfaces of SICLANIC ® are often irregular; the majority of them are planar and perpendicular to the stress axis.Fig. 6 shows the fracture surface specimen which failed in 5×10 5 cycles.A fatigue fracture surface consists of three regions associated with crack initiation, crack growth, and final overload.The darker region (ZA zone) presents the initial fatigue and slow crack growth in one or a few load cycles (Fig. 7).Surface crack initiation is located in the same area for all specimen tests.For certain specimens, we notice the existence of two crack initiation sites, one next to the other.Beach marks (macroscale) and striations (microscale) in surface indicate fatigue loading.Failure by cleavage proves that we are at the brittle failure case, which is common for long-life fatigue.Cleavage occurs by direct separation along crystallographic planes, and the failure is transgranular.

Cyclical behavior law
The comparison between the cyclic behavior curve and monotonic behavior curve reveals a softening during the cyclic loading (Fig. 8).The conventional yield strength falling of 19% in the cyclic tensile.Hardening or softening phenomena depend on the materials and their heat treatments.So, the evolution of fatigue mechanical characteristics depends on the initial state of the solid solution [21].Softening is generally observed for steels whose structures are naturally work hardened by quenching and tempering, this softening corresponds to a decrease of the yield strength which can reach 30%.Similarly, SICLANIC ® structural hardening by heat treatment of quenching and tempering leads to a stable phase represents a cyclical softening.The softening of SICLANIC ® is similar to the others Cu-Ni-Si alloys behavior in low cycle fatigue, such behavior is usually attributed to the formation of intense bands of slip in which the precipitation hardening effect has been reduced [2].
In structural analysis, design of parts is based on yield strength YS, however, for SICLANIC ® , which has a cyclic softening in fatigue solicitation (YS'0.2< YS 0. 2), even a cycle level of σa < YS 0.2, could result a deformation higher than εmax and placing the piece out of service.
The following equation describes the cyclic behavior:  Prediction of softening or hardening phenomena According to Smith, Hirschberg and Manson [22], softening occurs when UTS / YS 0.2 < 1.2, while hardening appears for UTS / YS 0.2 ˃ 1.4.In the case where the ratio is between 1.2 and 1.4, one or the other of the softening and hardening phenomena can be observed.As a result of the examination of various materials, Morrow [23] finds that if the value of n is higher than 0.1, hardening or stability occurs; however, if n is less than 0.1 the softening happens during the material is cycling.In Tab. 3, we have compiled the predictions of SICLANIC ® cyclical behavior, the predictions are in agreement with experience, however, the criteria used consider the characteristics determined outside the deformation domain (<2%) such as UTS and n.
A new definition of the hardening criteria is introduced by Lieurade [24], taking the ratio σ 1 / YS 0.2 , of which parameters correspond to the experience, since they are located in plastic deformation field.It has been shown in the case of steels that if σ 1 / YS 0. 2 is less than 1.3 there is softening, while if σ1 / YS 0.2 is higher than 1.5 there is hardening.The ratio Δσ1 / σ1 defines the hardening rate.

Plastic strain energy
Many researchers have used the cyclic plastic strain energy as damage criterion in low cycle fatigue.The dissipation of the mechanical energy is initially caused by the cyclic plastic strain connected, at microscopic level, to the dislocation movement and then, by the stress which relates to these dislocations resistance of displacement.
If we consider ΔW the mechanical energy per cycle as design parameter, the law of simple damage consists in supposing that there will be a failure when the total energy Wf has reached a critical value.
Halford [25] proposed a relation for measurement of the area under the hysteresis loop (Fig. 9), provided that the stress and the plastic strain are measured from the tip of the loop.In the majority of cases, the difference between the energy measured directly from the hysteresis curve by a planimeter and that calculated by Eq. ( 7) is less than 10%.
where n' is the cyclic hardening coefficient.The total energy to failure W f is defined by the Eq. ( 8): Fig. 10 shows a significant decrease in mechanical energy ΔW per cycle when the number of cycles increases.Practically this energy does not vary during a test since Δε and Δσ evolve inversely.The experimental points are placed around a curve corresponding to the following relation: On the other hand, there is an increase in the total energy to failure Wf when the number of cycles increases (Fig. 11).Fatigue resistance Basquin and Manson-Coffin defined experimentally laws characterizing low cycle fatigue life, between strain variations ∆ε and the fatigue life.
-Manson-Coffin relation: -Basquin relation: SICLANIC ® cyclic tests were conducted at imposed stress, achievement of fatigue resistance curves ε -N cannot be direct.We used prediction formulas.These formulas have been proposed in principle to limit the number of tests and to avoid even realize one fatigue test.The resistance relations fatigues are predicted by two methods, whose coordinates come from monotonic characteristic of the alloy.a) Four correlation point method This method developed by Manson and Halford [25], allows the plot of elastic and plastic lines by knowing some monotonic characteristics.b) Universal slopes method A second estimation method for resistance curves is proposed [27].Manson, after many tests on various materials, made the followings hypotheses: elastic and plastic lines have respectively mean slopes of -0.12 and -0.6.The points corresponding to the total strain variations ∆εt are placed on an asymptotic curve to the elastic and plastic lines.For low cycle fatigue, plastic strain predominates.The curve representing the plastic strain variation is placed above that of elastic strain up to a certain number of cycles (Fig. 12).SICLANIC ® damage behavior, at low number of cycles, is accommodated by plastic cyclic strain.In approximating of the yield stress, plasticizing will be located at certain points of the alloy structure.The plastic strain curve presents an important slope; this reflects the high gradient of this parameter.This gradient is a sign of cracks priming.Approximation methods appear in agreement at the strain values.However, this agreement is not verified for the number of cycles in transition point P Tr .The universal slopes method seems most pertinent.The elastic line expressing SICLANIC ® resistance is located in the same order as the monotonic characteristics UTS and YS0.2%.For the plastic line, the capacity of plastic cyclical strain is dependent on the ductility; it operates to the same effect as this last.In terms of total strain, the SICLANIC ® resistance is closely linked to materiel ductility at low cycle (predominance of ∆ε p -N relation), and the yield strength and ultimate tensile strength at high cycle (predominance of ∆ε el -N).Moreover, many researchers have linked coefficients b and c to the cyclic hardening coefficient n ' , Tab. 5 shows some formulas results.Morrow has proposed the following relation: Tomkins [28] proposes on his side:

CONCLUSIONS
echanical characterization of SICLANIC ® proves that it is an alloy with high tensile characteristics.However, in cyclical loading, material shows moderate fatigue resistance.Results for fatigue analysis summarized as follows: 1.The mechanical properties (yield strength, hardening coefficient) of the SICLANIC ® are considerably modified by the application of high stress cycles, even in small numbers.The SICLANIC ® is softened under the fatigue loading.Hardening coefficient calculation with analytical models also predicts SICLANIC ® softening phenomena.2. If certain cycles reach stress levels close to or even more than YS 0.2 , we can meet a softening behavior, so a lowering of The YS 0.2 up to YS'0.2.High stress levels can cause harmful and permanent deformations to the proper functioning of the part.3. The fractography analysis of the SICLANIC ® specimens exhibits a transgranular failure during a cyclic solicitation.
Fractures arise at the grain boundaries, and flat surfaces in the crystalline material confirms the cleavage failure.Stress variation between the stress levels of the monotonic and cyclic tensile curves for 1% of plastic deformation ∆ε el elastic strain variation ∆εp plastic strain variation ∆εt total strain variation ∆W mechanical strain energy

Figure 1 :Figure 2 :
Figure 1: Fatigue specimen (a) schematic illustration showing the specimen geometry and (b) image of the actual fatigue specimen.

Figure 6 :
Figure 6: Fracture surface of the specimen.

Figure 7 :
Figure 7: Fatigue failure initiation site on cleavage planes of global dimension highlighted in the white box have approximately 426 µm ×284 µm.

Figure 8 :
Figure 8: Comparison between monotonic and cyclic tensile curves for SICLANIC ® .It is the law of cyclic consolidation or cyclic hardening law, where ′ and n' are respectively the coefficient and the exponent of cyclic hardening.In Tab. 2, the monotonic and cyclic mechanical characteristics of SICLANIC ® are compared.The extent of variation of the hardening coefficient is due to the cyclic deformation.It goes from a relatively low value (0.034) to a higher value of 0.136.

Figure 10 :
Figure 10: Evolution of mechanical energy per cycle in terms of fatigue lifetime.

Figure 11 :
Figure 11: Variation of the total energy to failure as function of fatigue lifetime.

Figure 12 :
Figure 12: Resistance fatigue curves for SICLANIC ® predicted using (a) four correlation point method and (b) a universal slopes method.

Table 5 :
Comparison of the SICLANIC ® fatigue exponent by different formulas.The values of b and c suggested by Manson-Coffin are close to those obtained by using Morrow and Tomkins relations.These numerical expressions based on the coefficient of hardening ′ calculated experimentally are in good agreement with the Manson-Coffin approximations.

Table 2 :
monotonic and cyclic mechanical characteristics of SICLANIC ®

Table 4 :
Low cycle fatigue characteristics for the SICLANIC ® .