P. Mogilersky, 4. Zanguil Materials Science and Engineering 4354(2003)58-66 2. Kineties of oxidation mode i during the oxidation of the reinforcement. For example, for the oxidation of Sic to amorphous silica, k a 2. 19 Consider a composite containing non-oxide reinforce- Disregarding the volume change associated with the ment particles in an oxide matrix, oxidizing in mode I, possible reaction between the matrix and the product of Fig. la. During oxidation, an oxide film with the the reinforcement oxidation, complete oxidation of the permeability Ps grows on each reinforcement particle, reinforcement within the layer Az will increment the resulting in the formation on the composite surface of thickness of the oxidized layer by an oxidized layer(consisting of the matrix, the product of the reinforcement oxidation, and, possibly, the =△[l+f(k-1) product of a reaction between them) with effective which along with Eq(2)gives thickness 4△ of unoxidized material adiacent to the△,=△M(=△ oxidation front(currently located at depth z beneath the 1+f(k-1) rface), Fig. la. At this stage, no assumptions regard where ing the thickness of this layer is made other than that the this layer and that it is thick enough to contain a 51+f-0 statistically representative number of reinforcement particles. Since the oxidation proceeds in mode I,we is the volume fraction of the product of reinforcement can assume at the same time that this layer is thin oxidation in the oxidized layer enough such that the variation of oxygen partial On the other hand, AVs can be expressed through the pressure within it is negligible hickness, h, of the oxide on completely oxidized Such a layer contains a total volume of the reinforce- particles: ment(per unit area of the composite surface): △=B△Sh △V=△zf where f is the volume fraction of the reinforcement where S. and v. are the average surface area and phase. After complete oxidation it will transform into a volume of the reinforcement particles, and B is a form volume AVs of the oxidation product, given by factor that depends on the particle shape(see Appendi △V=kAzf Let us now choose the value az such that the total surface area of the reinforcement particles contained in here k is the coefficient of the volumetric change this layer is equal to the area of the sample surface(or in other words, such that the layer will have a unit surface I For clarity, in the following treatment the term'oxide film'is used area of the reinforcement particles per unit area of the mposite surface during its oxidation. While the former is generally P JS, =/urface) to describe the oxide growing on individual particles of reinforcement during their oxidation inside the matrix. The term oxidized layer is A used to describe the completely oxidized material growing on the single phase(e.g. silica in case of Sic reinforcement), the latter may ontain a number of phases including the original matrix, the product This will reduce Eq(6)to of reinforcement oxidation, and/or possible products of the reaction △V=Bh Oxide. h Coating 8°8 0:自:0::合 合:Q Fig. I. Growth of the oxidized layer during oxidation mode I of CMCs(a)and oxidation of a fat substrate under an oxide coating(b)2. Kinetics of oxidation mode I Consider a composite containing non-oxide reinforce￾ment particles in an oxide matrix, oxidizing in mode I, Fig. 1a. During oxidation, an oxide film with the permeability Ps grows on each reinforcement particle, resulting in the formation on the composite surface of an oxidized layer (consisting of the matrix, the product of the reinforcement oxidation, and, possibly, the product of a reaction between them) with effective oxygen permeability Po. 1 Consider now a layer of the thickness Dz of unoxidized material adjacent to the oxidation front (currently located at depth z beneath the surface), Fig. 1a. At this stage, no assumptions regard￾ing the thickness of this layer is made other than that the process of actual oxidation takes place entirely within this layer and that it is thick enough to contain a statistically representative number of reinforcement particles. Since the oxidation proceeds in mode I, we can assume at the same time that this layer is thin enough such that the variation of oxygen partial pressure within it is negligible. Such a layer contains a total volume of the reinforce￾ment (per unit area of the composite surface): DV Dzf (1) where f is the volume fraction of the reinforcement phase. After complete oxidation it will transform into a volume DVs of the oxidation product, given by: DVskDzf (2) where k is the coefficient of the volumetric change during the oxidation of the reinforcement. For example, for the oxidation of SiC to amorphous silica, k :/2.19. Disregarding the volume change associated with the possible reaction between the matrix and the product of the reinforcement oxidation, complete oxidation of the reinforcement within the layer Dz will increment the thickness of the oxidized layer by DzoDz[1f (k1)] (3) which along with Eq. (2) gives: DVs Dzokf 1 f (k  1) Dzofs (4) where fs kf 1 f (k  1) (5) is the volume fraction of the product of reinforcement oxidation in the oxidized layer. On the other hand, DVs can be expressed through the thickness, h, of the oxide on completely oxidized particles: DVsbDzf S¯ rh V¯ r (6) where S¯ r and V¯ r are the average surface area and volume of the reinforcement particles, and b is a form factor that depends on the particle shape (see Appendix A). Let us now choose the value Dz such that the total surface area of the reinforcement particles contained in this layer is equal to the area of the sample surface (or in other words, such that the layer will have a unit surface area of the reinforcement particles per unit area of the composite’s surface): Dz V¯ r f S¯ r1 (7) This will reduce Eq. (6) to DVsbh (8) Fig. 1. Growth of the oxidized layer during oxidation mode I of CMCs (a) and oxidation of a flat substrate under an oxide coating (b). 1 For clarity, in the following treatment the term ‘oxide film’ is used to describe the oxide growing on individual particles of reinforcement during their oxidation inside the matrix. The term ‘oxidized layer’ is used to describe the completely oxidized material growing on the composite surface during its oxidation. While the former is generally single phase (e.g. silica in case of SiC reinforcement), the latter may contain a number of phases including the original matrix, the product of reinforcement oxidation, and/or possible products of the reaction between the two. P. Mogilevsky, A. Zangvil / Materials Science and Engineering A354 (2003) 58
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