Damage mechanisms and life prediction in high temperature fatigue of a unidirectional SiC–Ti composite

International Journal of Fatigue 24 (2002) 369–379 www.elsevier.com/locate/ijfatigue

Damage mechanisms and life prediction in high temperature fatigue of a unidirectional SiC–Ti composite N. Legrand a

a,1,*

, L. Remy a, L. Molliex b, B. Dambrine

b

Centre des Mate´riaux, Ecole des Mines de Paris, UMR CNRS 7633, 91003 Evry, France b SNECMA direction technique, 77000 Moissy-Cramayel, France

Abstract Isothermal fatigue tests are performed in the longitudinal direction at 450°C on a unidirectional SiC/Ti composite. Three major damage mechanisms are identified: the matrix cyclic softening which overloads fibers leading to their progressive rupture; the interfacial degradation of these broken fibers and their oxidation by the environment. Damage kinetics are estimated using microscopic observations and acoustic emission. Finally, a micromechanical model is used in order to understand the respective influence of these damage mechanisms. It is shown that, at a sufficient load level, fatigue fracture of the composite strongly depends on the interfacial degradation kinetics and that fiber oxidation by the environment generates more progressive damage and considerably reduces the composite fatigue life compared to loading under vacuum.  2002 Published by Elsevier Science Ltd. Keywords: Metal matrix composites; High temperature fatigue; Acoustic emission; Damage accumulation; Environmental effects; Fatigue modeling; Micromechanics

1. Introduction Titanium based metal matrix composites (MMC) reinforced by unidirectionnal continuous SiC fibers are attractive for use in aircraft-engine components, such as compressor discs, because of their higher specific strength and stiffness at medium temperature with respect to monolithic materials such as superalloys. Due to centrifugal forces, stress state in a rotating MMC compressor disc is mainly biaxial. Cyclic stresses are maximum in the hoop direction along the fiber axis, whereas in the transverse direction at 90° of the loading axis, radial stresses are much lower but could be a fatigue design limitation because of the poor capability of the composite in that direction. Thus a better understanding about the fatigue behavior of these materials along both orientations mentioned above is necessary for future industrial developments. Concerning the longitudinal orientation, a large amount of previous work has concentrated on modeling. These analyses are mainly * Corresponding author. Tel.: +33-3-8770-4261; fax: +33-3-87704127. E-mail address: [email protected] (N. Legrand). 1 Present address: Irsid (Usinor group), French Iron and Steel Research Institute, BP 30320 57283 Maizie`res-Les-Metz, France. 0142-1123/02/$ - see front matter  2002 Published by Elsevier Science Ltd. PII: S 0 1 4 2 - 1 1 2 3 ( 0 1 ) 0 0 0 9 2 - 5

phenomenological and use macroscopic experiments [1– 3]. The main goal is to develop low cost and reliable fatigue life prediction methodologies. Moreover, these authors can extrapolate fatigue life prediction to a wide number of loading types (low cycle fatigue, thermomechanical fatigue In Phase and Out of Phase). Nevertheless, some of these approaches do not take into account physical aspects of the composite material: approaches based on linear or non linear fatigue damage accumulation [1,2] take into consideration only damage associated with fiber and/or matrix. Damage processes at the interface are ignored (since these approaches are phenomenological), whereas the work investigated in this paper demonstrates that it plays a key role in the composite fatigue fracture. In contrast to these phenomenological approaches mentioned above, some researchers [4–8] have analyzed in detail the physical nature of the fatigue damage mechanisms of a SCS6/Ti15-3 composite at room temperature. These authors study nucleation and growth of short fatigue cracks. Guo et al. [8] demonstrate in the SCS6/Ti15-3 composite that matrix cracks nucleate near a fiber failure and once nucleated, short matrix crack growth rate becomes greater than that of monolithic matrix. Moreover, they also investigated experimentally the interfacial degradation in fatigue of SCS6/Ti15-3

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Nomenclature sm, em Mechanical matrix stress, mechanical matrix strain along fiber axis smzzth, emzzth Thermal residual matrix stress and strain along fiber axis sc, ec Mechanical composite stress, mechanical composite strain (loading path) Composite stress amplitude ⌬sc ec(N) Maximum composite strain measured in a fatigue cycle N: mechanical ratchetting sf(N) Maximum stress experienced by fibers in a fatigue cycle N sfmax(N) Maximum stress imposed to a fiber close to a broken fiber sfzzth Thermal residual axial fiber stress Scale parameter sL sR(i,j,k) Fracture stress of a fiber link indexed by i, j, k mw, srf(L) Fiber Weibull modulus and fiber mean fracture stress for a gage length L Pr Pr(i,j,k) Fiber fracture probability, fracture probability of a link indexed by (i,j,k) ⌫ Gamma function D Fiber diameter Fiber elastic modulus (=400 GPa), fiber volume fraction Ef Vf dLcrit/dN Interfacial degradation kinetics of a broken fiber Load transfer coefficient from a broken fiber to its neighbours Kf Lsd(N) Load transfer length for a broken fiber at cycle N Lcrit(N) Unloaded length along a broken fiber at cycle N Interfacial shear stress ti m Friction coefficient at the fiber matrix interface N Fatigue cycle NR(i,j,k) Number of cycles to failure for the link (i,j,k) Number of cycles to composite failure Nf ⌬N Fatigue cycle increment used in simulations (=100) Number of fiber failures in a same cycle increment ⌬N nr Maximum number of fiber failures accepted in a same cycle increment ⌬N nmax T Test temperature (°C)

smooth samples still at room temperature, by fatigue tests followed by push out tests: the dominant mechanisms in this degradation are wear asperities at the interface and relaxation of radial residual thermal stresses in the matrix. The present work extends these physical approaches to high temperature fatigue degradation, where environmental effects may add to pure fatigue damage mechanims and significantly interact with them. Moreover, in contrast to the above phenomenological approaches which predict only the composite fatigue rupture, our work attempts to predict both rupture and damage kinetics in fatigue regimes where fiber failures are the most important damage, and matrix crack growth is of minor importance.

2. Material and experimental procedure The material is a titanium alloy Ti6Al–4V with an equiaxed microstructure reinforced by long SCS6 Textron fibers 0.140 mm in diameter. This metal matrix composite is processed by the foil fiber foil route with a fiber volume fraction of 33%. Fatigue tests are perfor-

med in the longitudinal direction at 450°C in stress control with a 340 MPa/s stress rate. The specimen geometry is shown in Fig. 1 and the mechanical axial strain is measured with a MTS extensometer. For some of the fatigue tests, an acoustic emission sensor able to work at high temperature is used to record on line fiber fracture. This acoustic equipment, manufactured by Physical Acoustic Corporation, is composed by a Locan AT 2.8900 model. After matrix chemical etching (with 15% HF, 15% HNO3, H2O), SEM (scanning electron microscopy) is used to observe the interfacial degradation. SCS6 fiber properties, extracted from pristine and fatigued specimens, are evaluated using tensile tests on monofilaments with a 25 mm gage length. Using an unimodal Weibull distribution function (Eq. (1)), these tensile tests give an evaluation of the Weibull modulus mw (which defines the scatter of fracture strength).

冋冉 冊册

Pr⫽1⫺exp ⫺

sapp s0

mw

(1)

where Pr is the fracture probability of a fiber loaded at

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Fig. 2. Experimental fatigue loops of the SCS6/Ti6-4 composite and Ti6-4 matrix, deduced with the law of mixture. Fatigue test: ⌬sc=1300 MPa, T=450°C, Nf=7196 cycle.

N, the matrix loading path (sm,em) is deduced from the experimental composite loading path (sc,ec) with the law of mixture, using the following relationship: Fig. 1.

Specimen geometry.

sm⫽

sapp stress, and so is the scale parameter taking into account the volume of loaded material. To obtain mw, the N measured fracture stresses are classified in an increasing order from i=1 to N. Then, a fracture probability is attributed to every fracture stress with the following Weibull estimator [9]: (i−0.5) Pri⫽ N

(2)

Finally, the different couples (srfi, Pri) are reported in a diagram

冉 冉 冊冊

ln ln

1 ⫺ln(srfi). 1−Pri

The slope of the curve, determined by a linear regression, is the Weibull modulus of the distribution mw and srf(25) its mean fracture stress. 3. Experimental results

(sc−Ef·ec·Vf) ⫹smzzth (1−Vf)

em⫽ec⫹emzzth

(3) (4)

emzzth and smzzth are respectively the thermal residual strain and stress in matrix due to the difference of thermal expansion coefficient between matrix and fiber, evaluated by modeling [10–13]. Ef, Vf are the fiber Young’s modulus and fiber volume fraction, equal to 400 GPa and 33%, respectively. The hysteresis observed on matrix fatigue loops in the composite (Fig. 2) on every cycle shows significant plastic strain in matrix, which creates a strong mean stress drop. Finally, this figure shows that matrix loading in the composite is neither in stress control nor in strain control, it is a mixture of both types of loading, whereas the composite material is loaded in stress control. In addition to these observations, mechanical ratchetting of the composite, significant at the beginning of cycling, is also noticed and is certainly due to the mean stress drop of the matrix mentioned above. This mechanical ratchetting ec(N) is then used to evaluate sf(N), the increase of the maximum stress exerted on fibers during cycling through the following equation: sf(N)⫽ec(N)·Ef⫺sfzzth

(5)

3.1. (Stress–strain) behavior The cyclic behavior of the composite loaded in the longitudinal direction is shown in Fig. 2 for a 1300 MPa stress amplitude (around 90% of the tensile strength). The first loading path is characterized by a matrix plasticity. This plasticity is moreover confirmed by the experimental loading path of the matrix (sm,em) in the composite, presented in the same figure. During a cycle

With Eq. (5), the evolution of the maximum axial fiber stress during cycling may be estimated at different composite stress levels as illustrated in Fig. 3. 3.2. Acoustic emission in fatigue Using the acoustic emission equipment, four fatigue tests were performed on the composite at a 1100 MPa

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Fig. 3. Axial fiber stress evolution as a function of fatigue cycles for different composite stress levels. Evolution deduced from the experimental mechanical ratchetting of the composite ec(N) and Eq. (5). Mechanism 1.

stress amplitude, with two of them interrupted before final fracture (at about 90% of the total life); and one test was performed at 1200 MPa stress amplitude. Results of the tests performed until final fracture are presented in Fig. 4. They show that acoustic signals are recorded at the beginning and at the end of cycling. This gives evidence that the material is damaged mostly at the beginning and at the end of fatigue life since damage is proportional to acoustic emission signals. 3.3. Microstructural fatigue damage The observation of fracture surfaces at high stress levels revealed a matrix rupture almost exclusively ductile at 1100 or 1200 MPa stress amplitude. This fracture mode is typically a rupture in tension and thus is due to final fracture. That is the reason why, at high stress levels, fatigue fracture of the composite is almost exclusively due to fiber fractures, and matrix damage is much less influential. In contrast, for lower stress levels (below 1100 MPa), matrix crack nucleation and propagation were often observed in fatigue, sometimes on large areas of the fracture surface; consequently in that regime matrix cracking is greatly responsible for final fracture of the composite. After the interrupted tests mentioned above (performed at a high stress level: 1100 MPa), fatigue specimens were chemically etched to remove matrix. Then, fibers already broken in the samples were observed in a SEM microscope (Fig. 5): these observations clearly show that the interface close to a broken fiber is strongly damaged over an important length (several millimeters), whereas fibers in the neighbourhood are intact. Strong wear effects were observed in

Fig. 4. Experimental acoustic emission curve in fatigue for two different composite stress levels on SCS6/Ti6-4: cumulated energy as a function of fatigue cycles. Fatigue test at 450°C. (a) ⌬sc=1200 MPa, Nf=4430 cycles. (b) ⌬sc=1100 MPa, Nf=9866 cycles.

this damaged zone which suggests that this damage is due to fatigue. Moreover, it was observed that this damaged length varied from one broken fiber to another in the specimen, from several tens of microns to five millimeters for a test interrupted at about 10,000 fatigue cycles [11]: this observation proves that the interface close to a fiber fracture is progressively degraded in fatigue and that the earlier the fiber was broken in cycling, the longer its degraded interface is. These interface degradation kinetics are approximately constant (as confirmed below) and were estimated at about 0.5 µm/cycle/half fiber (=5 mm in 10,000 cycles for half a fiber) or 1 µm/cycle/fiber: it is supposed in this estimation that the longest degraded interfaces (5 mm for

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Fig. 5. Interfacial degradation near a broken fiber in the SCS6/Ti64 composite loaded in fatigue. Fatigue test: ⌬sc=1100 MPa, T=450°C, interrupted at 11,194 cycles, first ply of the specimen. Mechanism 2.

half a fiber), oberved in the specimen, correspond to the fibers broken during the first fatigue cycle, which is confirmed by further modeling. Details of the estimation of these degradation kinetics may be found in [11]. In addition to interfacial degradation, striations similar to fatigue striations were observed in the damaged zones close to fibers already broken (Fig. 6): their constant spacing supports the constant interfacial damage kinetics assumed above [11]. Results concerning fiber properties extracted from specimens are reported in Fig. 7. These curves show that tensile strength of fibers extracted from the virgin material may be modeled by the following equation:

冉 冊

ln(25) 1 ⫺ ·ln(L) ln[srf(L)]⫽ln[srf(25 mm)]⫹ mw mw

(6)

which gives a Weibull modulus about 11 and a 4500 MPa mean fracture stress (for a 25 mm gage length). Secondly, results from Fig. 7(a) and (b) also show that fiber properties inside the composite may be degraded drastically during fatigue loading in air. This evolution seems not to be homogeneous in the specimen since the queue of the fatigued distribution is strongly damaged (weak population) whereas its upper part is undamaged (strong population). This degradation is probably due to environment. This hypothesis is supported by the two following features: firstly, fatigue life in air is about three times lower than the one under vacuum as observed with one fatigue test at 1000 MPa stress amplitude ( Vf=30%) at 450°C and as shown by [11] on a SM1140+/Ti6242 composite. Secondly, it was observed that the carbon interface of fibers close to the fatigued

Fig. 6. A broken fiber extracted from fatigue sample SCS6/Ti6-4 before final rupture. (a) Tilted view of the broken fiber and its degraded interface: presence of striations. (b) High magnification of striations observed on the fiber. Fatigue test: ⌬sc=1100 MPa, T=450°C, interrupted at 11,194 cycles.

specimen sides has partly disappeared due to the influence of the environment [11].

4. Discussion and modeling 4.1. Micromechanisms responsible for fatigue damage According to the above experimental data, three major damage mechanisms seem influential in the composite fatigue fracture. 4.1.1. Mechanism 1: a global and progressive overloading of fibers The load transfer from matrix to fibers is responsible for the progressive fiber overloading (Fig. 3). This trans-

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geneously every fiber of the composite and creates progressive fiber breaks. Its kinetics depend on the composite load level and may be estimated by Eq. (5). 4.1.2. Mechanism 2: a local and progressive interfacial degradation of broken fibers These broken fibers are locally unloaded on a critical length Lcrit and their nearest neighbours are overloaded on the same length. These breaks are then followed by a progressive degradation of their interface due to the cyclic shear stress (in phase with the macroscopic loading) which exists near the broken fiber. Consequently, the sustained lengths of fibers near the break move to follow the degraded interfacial of the broken fiber; and this motion (with kinetics (dLcrit)/(dN)=1 µm/cycle/fiber) is able to fracture new fibers as illustrated in Fig. 8(b). The discontinuous acoustic emission evolution (Fig. 4) may be partly explained by this phenomenon. 4.1.3. Mechanism 3: fatigue oxidation of fibers Added to these two damage mechanisms in pure fatigue, a fatigue–environmental effect was observed which degrades fiber fracture properties (Fig. 7(a)). The degradation kinetics of this phenomenon may be quantified by the strong Weibull modulus decrease from 11 to 3.3 (Fig. 7(b)). 4.2. Micromechanical statistical modeling in fatigue

Fig. 7. Properties of SCS6 fibers extracted from the first ply of the SCS6/Ti6-4 composite. Population size: 39 pristine and 49 fatigued fibers. Mechanism 3. Fatigue test: ⌬sc=1100 MPa, T=450°C, interrupted at 9525 fatigue cycles. (a) Weibull diagram of pristine and fatigued fibers. (b) Weibull diagrams for the two populations of fatigued fibers: Undamaged fatigued fibers (strong population) and damaged fatigued fibers (weak population).

fer is due to matrix cyclic softening (coming from matrix cyclic plasticity) or more exactly to its mean stress drop: the part of the mechanical loading sustained by matrix during cycling is less and less important; nevertheless, the composite mean stress being constant (because fatigue tests are performed in stress control), fiber stress must increase to compensate for this matrix mean stress drop. A macroscopic consequence of this phenomenon is the mechanical ratchetting of the composite observed in fatigue. This global mechanism overloads homo-

4.2.1. Interest of a micromechanical modeling The three micromechanisms involved in the composite fatigue fracture have shown (as it is commonly observed in heterogeneous materials) that damage accumulation is not homogeneous in the composite though the macroscopic mechanical loading is homogeneous (in contrast to monolithic metals). Indeed, close to a broken fiber, the interface is strongly degraded whereas far enough from this break, it is unchanged. Therfore, this confirms that volume element methodologies widely used for metals cannot be applied to MMCs to predict fatigue life. However, a micromechanical analysis is able to take into consideration this heterogeneous damage. Such a model is exposed in the next section. 4.2.2. Modeling principles Next, simulations are made extending a statistical micromechanical modeling called SIRCUD (Simulation of the Resistance of a Composite UniDirectional) which was initially developed by Molliex [12] to predict tensile strength of MMCs. This model has been modified to take into consideration the degradation due to fatigue loading. It is able to take into account first fiber breaks (failures of the weakest links), which is the statistical aspect of the material, and the following stress redistribution as

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Fig. 8. (a) Scheme of the stress transfer around a broken fiber: transverse plane. The stress transfer is modeled by a simple geometrical effect: Only the closest fibers are affected by a fiber break. (b) Scheme of the axial stress profiles along a broken fiber and its nearest neighbour for an interfacial frictional sliding (longitudinal plane): Movement of the transfer lengths during cycling by interfacial degradation of the broken fiber.

illustrated in Fig. 8. New ruptures are then made possible by the global and progressive load transfer from matrix to fibers (mechanim 1: Fig. 3); to a motion of the overloaded lengths due to the interfacial degradation (mechanism 2) and to environment (mechanim 3). For the sake of computer simplicity, our modeling simulates a growth of the stress transfer lengths from a fiber break to its neighbours due to the interfacial degradation (mechanim 2) though, according to our observations, these lengths move with the interfacial degradation without growing as shown in Fig. 8(b). The simulated composite material in fatigue is composed by X×Y fibers, each of them composed of Z links with 100 µm length: a 3-D meshing (x,y,z) is thus computed.

A fracture probability Pr(i,j,k) is randomly attributed to each link indexed (i,j,k) in the 3-D meshing. Fracture stresses sR(i,j,k) are calculated using the experimental fiber properties srf(L=25 mm), mw and the Weibull theory (Eq. (7)) (sL is a scale factor):

冋 冉 冊册 冋册 冉 冊

sR(i,j,k)⫽sL· ln sL⫽

1 1−Pr(i,j,k)

srf(25 mm) L · L0 1 ⌫ 1+ mw

−1 mw

1 mw

(7) (8)

where L is fiber link size, equal to 100 µm. This value was chosen by Molliex [12] sufficiently small to get, by

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isolating the weakest link among n links, the theoretical strength of a fiber with a n∗/Ll length (Ll is the length of the link). L0 is gage length for experimental tensile tests on fibers, equal to 25 mm, and ⌫ is the gamma function. The interface is modeled with the interfacial shear stress ti, which determines for a fractured fiber the length Lsd (and consequently the number of links) over which a fiber is unloaded: Lsd(N)⫽

sf(N)·D 2·ti

(9)

where D is fiber diameter, and sf(N) is maximum axial stress applied to the fibers far from any broken fiber, as a function of fatigue cycles and composite stress level (Fig. 3), simulated by a cycle increment ⌬N equal to 100. The interfacial shear stress is a function of radial thermal residual stresses srr present at the interface: ti⫽m·srr

(10)

where srr is the radial thermal stress at the interface, evaluated by an analytical calculation [10–13], and m is the interfacial friction coefficient, equal to 0.5 according to [12]. After a fiber break, its neighbours are overloaded on the same length Lsd by the quantity Kf·sf(N) defined by Eq. (11), where Kf depends on the number of fibers already broken in the neigbourhood of the break (Fig. 8(a)). sf max(N)⫽Kf·sf(N)

Algorithm of the SIRCUD program.

(11)

The local interface degradation dLcrit/dN, evaluated to 1 µm/cycle for a 1100 MPa stress amplitude, is used to calculate the length Lcrit(N) over which a broken fiber is unloaded and over which its neighbours are overloaded. For a link indexed (i,j,k), broken at a cycle NR(i,j,k), this length grows as a function of the number of cycles N as: dLcrit Lcrit(N)⫽Lsd(N)⫹[N⫺NR(i,j,k)]· dN

Fig. 9.

(12)

It is supposed that these interfacial degradation kinetics are not dependent on the stress level. The modeling is able to predict the number of cycles to composite failure Nf for a predetermined stress level: this fatigue fracture is reached when there is a catastrophic enchainment of fiber ruptures in a same cycle increment. It indicates also the moment and location of fiber fractures in the composite. The general synoptic illustrating the different steps of this computer program is presented in Fig. 9. 4.2.3. Simulation results Using this modeling, we can quantify the respective influence of mechanisms 1 and 2 by performing calcu-

lations with both mechanisms simulated separately on the one hand and simultaneously on the other hand (mechanism 3, environment, is ignored at first). Firstly, by separating these two mechanisms, a simulation was carried out by accounting only for the local interfacial degradation, without taking into account the matrix cyclic softening (Fig. 10). It means that the maximum fiber stress remains constant at every fatigue cycle. This simulation shows that, at this load level (1300 MPa), the local interfacial degradation, following the rupture of the weakest links during the first cycle, leads to new breaks and to the final composite fracture. Secondly, a simulation was carried out by applying damage mechanisms 1 and 2 together. It was compared with the experimental damage kinetics (Fig. 11). The modeling demonstrates that an increase of the interfacial degradation kinetics dLcrit/dN by a factor of 4 decreases the fatigue life by the same factor. The interfacial degradation kinetics seems to play a key role in the fatigue fracture of the material. However, the model tends to overestimate the composite fatigue life even for important interfacial degradation kinetics (4 µm/cycle), which is anyway unrealistic compared with the one measured (1 µm/cycle). This overestimation of the predictions suggests that fatigue damage of the composite

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Fig. 10.

377

Fatigue fracture simulation of the SCS6/Ti6-4 composite due to damage mechanism 2: Interfacial degradation near broken fibers.

Fig. 11. The predicted and experimental damage kinetics of the SCS6/Ti6-4 composite. Two damage mechanims are considered: Overloading of fibers (mechanism 1) and interfacial degradation (mechanism 2). Simulation data: ⌬sc=1200 MPa, T=450°C and dLcrit/dN=1 or 4 µm/cycle.

material is not only due to fiber fracture followed by interfacial degradation. Other influences should probably be taken into account such as matrix cracking and environment. Matrix cracking is very complex to model and probably demands a specific study; it is beyond the scope of this work. Its influence is anyway certainly of second order for a 1200 MPa stress amplitude where matrix fatigue cracking is not significant, as mentioned previously. Environment degradation is also complex to model. However, of first order for high fatigue loadings, this degradation concerns fiber properties only (mechanism 3), according to our experimental data. Thus this environmental mechanism may be taken into account by a simulated drop of the Weibull modulus mw and of the mean fracture stress srf(25) of fiber as a function of fatigue cycles. According to measurements of fiber fracture properties (Fig. 7(b)), the Weibull modulus of fibers located close to the sample sides decreases from 11 (pristine fibers) to 3.3 after about 10,000 fatigue cycles. Thus a simulated drop of mw and srf(25) as a function of fatigue cycles was adjusted on the experimental fatigue life obtained at 1200 MPa: results of this adjustment are found in Fig. 12.

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Fig. 13. Predicted and experimental damage kinetics of SCS6/Ti6-4 composite as a function of fatigue cycles. Three damage mechanisms are considered: overloading of fibers (mechanism 1), interfacial degradation close to broken fibers (mechanism 2) and environmental degradation of fiber properties (mechanism 3). Simulation data: ⌬sc=1200 MPa, T=450°C, and dLcrit/dN=1 µm/cycle.

the experimental trends and demonstrates the ability of such an approach (semi-empirical, semi-physical) in future industrial developments for fatigue life predictions.

5. Conclusions

Fig. 12. SCS6 fiber damage kinetics used to simulate the progressive degradation of fiber properties due to environment (mechanism 3): Evolution of Weibull parameters (srf and mw) as a function of fatigue cycles N.

By introducing these fiber degradation kinetics (mechanism 3) superimposed on mechanisms 1 and 2 in the model, prediction of damage kinetics is in better accordance with the experimental result for a 1200 MPa stress amplitude, especially at the end of fatigue life, as shown in Fig. 13. Therefore, these investigations indicate that the heterogeneous and progressive degradation of fibers, due to environmental influence, generates very progressive damage in the composite, and considerably decreases its fatigue life compared to loading under vacuum. The main advantage of this model is its capability of predicting experimental damage kinetics measured by acoustic emission in a fatigue regime where there are fiber failures only. The results obtained are however more qualitative than quantitative: this is due to the difficulty in estimating more precisely the different damage kinetics at the different stress levels. The model gives

This work has attempted to understand the physical origin of high temperature longitudinal fatigue fracture of MMCs SCS6/Ti6-4. Three micromechanisms involved in the composite fatigue fracture were identified: the global load redistribution between fibers and matrix which tends to overload fibers during cycling; the interfacial degradation of the broken fibers and the environmental influence which affects the fiber fracture stresses located close to the sample side. The principles of micromechanical statistical modeling were presented. This modeling is able to confirm and quantify the influence of these different damage mechanisms on the composite fatigue fracture. It was demonstrated that at sufficient stress levels the local interfacial degradation close to the already broken fibers greatly influences the fatigue properties of the composite and that fiber degradation by the environment considerably reduces fatigue life in air.

Acknowledgements The authors would like to thank SNECMA Company (the French engine aircraft manufacturing company) for

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supporting this work and allowing publication of the results.

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