FIBER/MATRIX DEBONDING CRITERIONS IN SIC/TI COMPOSITE. NUMERICAL AND EXPERIMENTAL ANALYSIS

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1 FIBER/MATRIX DEBONDING CRITERIONS IN SIC/TI COMPOSITE. NUMERICAL AND EXPERIMENTAL ANALYSIS A. Thionnet 1, J. Renard 1 1 Eole Nationale Supérieure des Mines de Paris - Centre des Matériaux P. M. Fourt BP Evry Cedex - Frane Université de Bourgogne BP Dijon Cedex Fane KEYWORDS : metal matrix omposite, debonding, modelling INTRODUCTION As SiC/Ti metal matrix omposite have good mehanial properties, they have been hosen these last years for aeronautial appliations. In order to inrease their utilization, it beomes neessary to detet and analyze the propagation of the various types of damages whih our when the omposite struture is loaded. The linear elasti behaviour of these materials is orretly simulated by homogenization models. However, the dissipative phenomenon as well as the indued non-linearities are still badly understood. The properties and the behaviour of these omposite materials depend, not only on the intrinsi onstituent properties but also on the interfae between the fiber and the matrix. This study analyzes the influene of the debonding between the two onstituents. Our approah is arried out both experimentally and numerially. For eah of these two investigations, we first analyze the phenomenon at the mirosopi sale (where we distinguish the onstituents of the heterogeneous material) and then its influene on the mesosopique sale (where we do not distinguish anymore the onstituents of the material now beome homogeneous). Experimentally, the use of fine analysis tehnis (optial mirosopy, spetrometry...) enables to observe the debonding phenomenon at its mirosopi sale. Then, experiments allow to quantify the influene of the phenomenon at the mesosopi sale. Numerially, the mirosopi phenomenon is analyzed using a finite element alulation with a mesh having the sale of the fiber and the matrix where the debonding is realized by penalties. A homogenization proess helps to reah the mesosopi sale and evaluate the influene of the degradation on the behaviour of the equivalent homogeneous material. Finally, the numerial and the experimental response of a omposite sample submitted to a transversal tration loading is ompared at the marosopi sale (the sale of the struture). This approah is realised in the both ases with or without taking into aount the uring residual stresses.

2 The originality of the present study is to show the feasibility to get some mesosopi quantities [1] from mirosopi information and observations. One appliation is the determination of a mesosopi debonding riterion built up from its loal equivalent. DESCRIPTION OF THE MATERIAL The studied omposite material is made by hot ompation (950 C) of 1 SiC long fibers' layers in a titanium metal matrix. The matrix is a "super-α titanium alloy. The Silion arbide fibers, the diameter of whih is about 100 µm (Fig. 1), are surrounded by a arbon deposit of approximately µm of thikness (Fig. ). The fiber / matrix debonding arises from the rupture of this zone (Fig. 3). The mirostruture of the omposite is approximately periodi with a fiber volume fration of about 0.3, a arbon deposit of 0.01 and a volume fration of matrix of about The differene between the oeffiients of thermal expansion of the reinforement and the matrix gives the appearane of a residual stress field. These residual stresses an be damageable for the material, as they affet the bonding between the fiber and the matrix. A solution is to introdue an interphase suffiiently smooth between the fiber and the matrix that absorbs gaps of displaement. This is the reason why the fiber presents on its periphery a protetive arbon deposit whih play this role. The proposed study analyzes the rupture of this interphase leading to the debonding between the fiber and the matrix (Fig. 3). Fig. 1 - Mirostruture of the Si-Ti omposite Fig. - Interphase

3 Fig. 3 - Situation of the debonding phenomenon during a torsion test on a T90 speimen EXPERIMENTAL ANALYSIS At the mirosopi level, we observe where and when debonding appears in the representative ell of the material. At the marosopi level, we reord the loading-unloading urve during a test on a sample representative of the elementary volume of the material and the evolution of the number of debondings for different loadings. The used speimen (Fig. 4), alled T90, are trilaminar (a SiC-Ti layer between two titanium layers) and suh that Si fibers are loated at 90 from the axis of the speimen. (X, Y, Z) is the artesian frame of the speimen where the X axis is parallel to its length. After polishing the lateral faes and inreasing the load, the debondings are observed and ounted on a hosen zone of one lateral fae (Fig. 4). The same proedure is repeated at eah load inrease. By this way we follow the surfaial evolution of the debonding. Fig. 4 - Tested speimen ( : observed area) Choie of the Applied Loading on to the Speimen To observe the debondings, the speimen was loaded with a torque along the X axis. The used mahine allows to apply a linear time-dependant torque. Thus we obtain the evolution of the torque C versus the angle Ω. This devie has a mobile jaw whih avoid some parasite stress during the torsional loading. The main motivation for the hoie of the torsional loading is that the indued state of stress is simple. Indeed, we have simulated the torsion of the T90 speimen by the finite element method using a pseudo-tridimensionnal element. The analysis of the numerial simulation on the lateral side of the speimen shows that only omponant σ xy and σ xz are non zero. But, if we look more attentively, we observe that in fat only σ xz is not signifiantly null in the Si- Ti ply. Thus, if we note (x 1, x, x 3 ) the loal orthotropi frame of the SiC-Ti material where the x 1 axis is parallel to the fibers (Fig. 4), the mesosopi state of stress in the omposite ply of the T90 speimen is the following : σ = σ 3 0 σ 3 0. Superfiial Evolution of the Debonding Phenomenon After loading the T90 speimen we observe the zone of the lateral side. We plot their density D S versus the applied torque (Fig. 6) and we reord the marosopi response of the speimen

4 giving the value of the applied torque aording to the angle (Fig. 5). The main onlusion is that the debondings however important seems not affet the global behaviour. Indeed, although we observe a lot of debondings on the speimen faes, nothing proves that they propagate all along the fibers, far in the width of the speimen. To evaluate their penetration, finite element alulations with a homogenization method have been used. NUMERICAL ANALYSIS OF THE DEBONDING INFLUENCE ON THE BEHAVIOUR The homogenization method used suppose periodi properties of the studied omposite. Calulations are realized by finite elements method on the representative elementary ell of the material. Calulated harateristis of the homogenized behaviour alulated of our virgin material are relatively in good agreement with the values found experimentally by Robertson [] on a lose material. Conerning the influene of the debonding on the behaviour of the material, the study is realized using two different ways. First, by simulating really the debonding by splitting the nodes of the mesh between the two primary layers, i.e. on a irle of 1 µm superior to the fiber. This approah indues loally a penetration of the onstituents if we do not manage the ontat in the ase of the shear loadings. Seond, we simulate the debonding by weakening a small part of arbon interphase (we have divided by 100 the initial harateristis of the arbon, in a zone of thikness 1.00 mm) situated around the fiber. Results obtained by this method do not give signifiant differene when ompared to the first approah. We suppose a omplete debonding what has for onsequene to overestimate the stiffness losses. C ( N. m )) D S Test Simulation Ω ( rad / m ) C ( N.. m ) ) Fig. 5 - Marosopi response torque/angle for the T90 speimen in torsion Fig. 6 - Superfiial debonding / torque urve

5 Fig. 7 - Damaged elements artography in the SiC-Ti layer of the straight setion of the T90 speimen in torsion NUMERICAL ANALYSIS OF THE VOLUMIC CHARACTER OF THE DEBONDINGS Experimentally, we get the value of the torque C 0 for whih appear the first debondings on the T90 speimen. The finite element alulation gives the ritial debonding stress tensor σ 0. To estimate the penetration of these debondings into the material, we realized the simulation of the torsional test by the following steps : we load until the torque C0 and we look in whih elements a debonding ritial state of stress has been reahed. The damaged behaviour of these elements is alulated during the homogenization step. The torque is then inreased, and so on. The artography of damaged elements indiates the depth of penetration of the debonding (Fig. 7) and we give the torque/angle simulated urve (Fig. 5). Numerially, we observe a derease of the speimen torsion modulus of approximately 5% while the experimental urve shows no derease. This an be explained beause dereases of material modulus have been overestimated and beause the alulation by finite element method is realized with plane strain elements. ANALYSIS WITHOUT CONSIDERATION OF THE RESIDUAL STRESSES Identifiation of the Mirosopi Debonding Criterion By applying the mesosopi state of stress σ 0 on the representative ell of the material, the proedure of loalization assoiated with the homogenization gives the mirosopi state of stress in all point of this ell. We an therefore aess to the normal and tangential strength between the two primary layers, loated lose the debonding. In besides, a mirography of the

6 & & debonding phenomenon (Figs. 8-9) for the torque C0 allows to understand preeeding results and therefore, help to write a mirosopi debonding riterion. We all ω the area onstituted by the fiber and the part of the deposit of arbon that it is always interdependent and ω its frontier. By alling s the mirosopi stress tensor, we note s n = s T t s L x 1 s N n the stress vetor on ω, where the unit vetors n and t are respetively oriented with the normal to ω et with the tangent at ω in the plane of the ross setion. A loal debonding riterion an be written as : s T s T s L s L where s T et s L are the ritial tangential values and s N the ritial normal value of debonding. As first approximation, we an estimate s T VL and here the simulations give : s T VL MPa and s N MPa. However, in the literature, we find s L MPa [3]. Although onstituents and the proess of elaboration of the omposite are not rigorously idential, these values indiate an magnitude order. Thus, we observe that evaluated ritial values with the simulation are signifiatively lower than the experimental values. The main reason of this differene is that residual elaboration stress that put the fiber in ompression (binding) have not been taken in aount. It is the next objetive given to the ontinuation of this study. s N s N = 1 Fig 8 - Debonding mirography Fig. 9 - Debonding simulation Mesosopi Debonding Criterion If ε is the mesosopi strain tensor, we an write a debonding riterion at the sale of the homogeneous material as a quadrati form of its omponents : ε 11 ε 11 ε ε ε 33 ε 33 ε 3 ε 3 ε 13 ε 13 ε 1 ε 1 = 1 where ε 11, ε, ε 33, ε 3, ε 13 and ε 1 represent the different ritial debonding values. It is the finite element resolution of the six loalization problems of the homogenization that allow to determine these values in seeking for eah of them from what mesosopi deformation the debonding takes plae. This is obtain using the finite element similar to a spring (penalty) plaed to the plae of the possibly debonding, and whose behaviour of typial whole-ornothing is governed by the preeding mirosopi riterion.

7 Simulation of Transversal Tensile Tests The goal now is to simulate a transversal tests at room temperature on a SiC-Ti speimen (without titanium layers) alled S0 where the axis of the speimen are the same as the axis of SiC-Ti material defined in figure 3. The mesosopi debonding riterion is known. We an thus obtain the value of the stress tensor from whih the debonding starts. We found that the starting value of the debonding is very different between the experiment and the simulation (error : 00%). This is beause the manufaturing residual stresses have not been onsidered. We will see in the next setion wether the result for the transverse tensile test an be improved by onsidering the manufaturing residual stresses. ANALYSIS WITH CONSIDERATION OF THE RESIDUAL STRESSES Manufaturing Residual Stresses A quarter of the ell applying symmetri onditions on the axes and thus we obtain the manufaturing residual stresses [4]. Identifiation of a Mirosopi and a Mesosopi Debonding Criterion and Simulation of Transversal Tensile Tests Using the same mirosopi and mesosopi riterion equations and proeeding as in the ase without residual stresses, we determine first the harateristis of the loal debonding riterion (s T, s N ) and thus those of the mesosopi one (ε 11, ε = ε 33, ε 3, ε 13 = ε 1 ). Using the new identified ritial values in the mesosopi riterion, the simulated value agrees well with the experimental value (Fig. 10). Experimental test Simulation σ, GPa ε, % (1) : simulated debonding start, () : experimental debonding start (3) : simulated point giving the elasti slope of the ompletely damaged material Fig S0 speimen transverse tensile test at room temperature. Simulation with onsideration of the manufaturing residual stresses

8 CONCLUSION The debonding phenomenon between the fibre and the matrix was studied in a long fibre SiC- Ti metal-matrix omposite. The debonding between the two onstituents oured by the rupture in the arbon interphase. The analysis was both numerial and experimental and realized in a qualitative and quantitative ways. It shown the feasibility of the following methodology : to determine quantities at the sale of the homogeneous material from mirosopi informations and observations (i.e. at the sale of the onstituents of the material). An exemple is given for the determination of a mesosopi debonding riterion. This work is realized without and with onsideration of the manufaturing residual stresses. The onlusion is that they have a very signifiant role in the determination of the ritial debonding values. The use of numerial tehniques for the experimental analysis seems inreasingly neessary beause of the omplexity of the mirostrutures of the omposite materials and the omplexity of the phenomena involved. Although the alulation did not solved all problems, it has partly removed some ambiguities and has led to more finest understanding of the phenomena. ACKNOWLEDGEMENT : The authors wish to thank the SNECMA (Soiété Nationale d'etudes et de Constrution de Moteurs d'avions) for providing all the samples and the finanial support. Authors want also thank Mr. Y. FAVRY and Mr. J.C. TEISSEDRE for their assistane with the realization of tests. REFERENCES 1. Renard J., "Modelling of a Damaged Composite Speimen by a Miro-Maro numerial Simulation", Proeedings of the thirteen annual ASME-ETCE Composite Materials Symposium, P. 57-6, Yang C.J., Jeng S.M. Yang J.M., "Interfaial Properties Measurement for SiC Fiber reinfored Titanium Alloy Composites", Sripta Metallurgia and Materials, 4, p , Robertson J.G., "Manufature and properties of Sigma-Fibre reinfored Titanium", Agard Report n 796, (1994), pp Thionnet A., Renard J., "Miromehanial modelling of fibre/matrix interfae effets in transversely loaded SiC/Ti-6-4 metal-matrix omposites", Composites Sienes and Tehnology, 58, (1998), pp , 1998