CN109884105B - Method for determining carbon interface consumption volume of ceramic matrix composite material in oxidation environment - Google Patents
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- 239000000463 material Substances 0.000 title claims abstract description 106
- OKTJSMMVPCPJKN-UHFFFAOYSA-N Carbon Chemical compound [C] OKTJSMMVPCPJKN-UHFFFAOYSA-N 0.000 title claims abstract description 104
- 229910052799 carbon Inorganic materials 0.000 title claims abstract description 104
- 238000007254 oxidation reaction Methods 0.000 title claims abstract description 51
- 230000003647 oxidation Effects 0.000 title claims abstract description 39
- 238000000034 method Methods 0.000 title claims abstract description 27
- 239000011153 ceramic matrix composite Substances 0.000 title claims abstract description 17
- 239000000835 fiber Substances 0.000 claims abstract description 156
- 239000011159 matrix material Substances 0.000 claims abstract description 53
- 238000012163 sequencing technique Methods 0.000 claims abstract description 8
- QVGXLLKOCUKJST-UHFFFAOYSA-N atomic oxygen Chemical compound [O] QVGXLLKOCUKJST-UHFFFAOYSA-N 0.000 claims description 7
- 229910052760 oxygen Inorganic materials 0.000 claims description 7
- 239000001301 oxygen Substances 0.000 claims description 7
- 230000008569 process Effects 0.000 claims description 7
- 239000007789 gas Substances 0.000 claims description 6
- 230000004913 activation Effects 0.000 claims description 4
- 238000004364 calculation method Methods 0.000 claims description 4
- 230000001590 oxidative effect Effects 0.000 claims description 4
- 230000035484 reaction time Effects 0.000 claims description 4
- 229910010271 silicon carbide Inorganic materials 0.000 description 27
- HBMJWWWQQXIZIP-UHFFFAOYSA-N silicon carbide Chemical compound [Si+]#[C-] HBMJWWWQQXIZIP-UHFFFAOYSA-N 0.000 description 26
- 239000000758 substrate Substances 0.000 description 9
- 239000011184 SiC–SiC matrix composite Substances 0.000 description 8
- 230000008859 change Effects 0.000 description 6
- 238000012360 testing method Methods 0.000 description 5
- 239000002131 composite material Substances 0.000 description 4
- 239000011204 carbon fibre-reinforced silicon carbide Substances 0.000 description 3
- 238000013461 design Methods 0.000 description 2
- 238000002474 experimental method Methods 0.000 description 2
- 238000004088 simulation Methods 0.000 description 2
- 238000012935 Averaging Methods 0.000 description 1
- MYMOFIZGZYHOMD-UHFFFAOYSA-N Dioxygen Chemical compound O=O MYMOFIZGZYHOMD-UHFFFAOYSA-N 0.000 description 1
- 230000009471 action Effects 0.000 description 1
- 239000000919 ceramic Substances 0.000 description 1
- 150000001875 compounds Chemical class 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 238000011156 evaluation Methods 0.000 description 1
- 238000001914 filtration Methods 0.000 description 1
- 230000007246 mechanism Effects 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 229910003465 moissanite Inorganic materials 0.000 description 1
- 230000002093 peripheral effect Effects 0.000 description 1
- 238000005498 polishing Methods 0.000 description 1
- 238000002360 preparation method Methods 0.000 description 1
- 239000002296 pyrolytic carbon Substances 0.000 description 1
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Abstract
The invention discloses a method for determining the consumption volume of a carbon interface in an oxidation environment of a ceramic matrix composite, which comprises the following steps: counting the total number of fibers on the cross section of the material, measuring the average thickness of an interface and the average diameter of the fibers, obtaining the number of cracks of a matrix, the distance between the cracks of the matrix and the distance between two end surfaces of the material and adjacent cracks, and sequencing the cracks from small to large; dividing the fibers on the cross section into independent fibers, single-point contact fibers, two-point contact fibers and multi-point contact fibers, and counting the number of the fibers of corresponding types; calculating the area of the carbon interface at the outer side of each type of fiber and the mass fraction of carbon contained in the material; calculating the interface consumption length of the material at different oxidation moments; comparing 1/2 of the interface consumption length and the crack spacing of the matrix, 1/2 of the distance between two end faces of the material and the adjacent cracks to obtain the total length of the carbon interface consumption, and finally calculating to obtain the interface consumption volume. The invention can accurately give the carbon interface consumption volume and the distribution condition thereof after the material is oxidized for a certain time.
Description
Technical Field
The invention relates to a method for determining the consumption volume of a carbon interface in an oxidation environment of a ceramic matrix composite, in particular to a method for determining the consumption volume of a carbon interface in an oxidation environment of a unidirectional silicon carbide fiber toughened silicon carbide ceramic matrix composite.
Background
The silicon carbide fiber toughened silicon carbide ceramic matrix composite (SiC/SiC) has excellent performances of high temperature resistance, low density, high specific strength, high specific modulus and the like, so that the silicon carbide fiber toughened silicon carbide ceramic matrix composite becomes one of novel high-temperature structural materials which cannot be replaced in the aerospace field, is widely applied to aerospace engine hot end components, aerospace round-trip heat protection systems, high-speed brakes, gas turbine hot end components, high-temperature gas filtration, heat exchangers and the like, has high working environment temperature and commonly has an oxidizing medium such as oxygen. The component materials comprise silicon carbide fibers, carbon interfaces and silicon carbide matrixes, and because the thermal expansion coefficients of the matrixes, the fibers and the interfaces are not matched, a plurality of micro-cracks exist on the prepared matrixes, and the micro-cracks can become flow channels of an oxidation medium, so that the oxidation medium enters the composite material to oxidize and corrode the carbon interfaces. The oxidation consumption of the carbon interface enables the SiC fiber and the matrix to be in direct contact, the mutual friction resistance is increased, meanwhile, the internal stress concentration of the material is caused, and the brittle fracture of the material is easily caused under the action of load.
The consumption volume and distribution of the carbon interface in the unidirectional SiC/SiC material can be rapidly and effectively calculated, an important theoretical basis can be provided for strength and service life evaluation in the service process of the material, and necessary technical support is provided for reliability design of the material. At present, the following two techniques are mainly used for determining the consumed volume and distribution of the internal carbon interface of the unidirectional SiC/SiC material:
the document "Oxidation Mechanisms and Kinetics of 1D-SiC/C/SiC composite materials: I, An Experimental application. journal of the American Ceramic Society,1994,77(2): 459-66" discloses a method for measuring the volume consumed by the interface of a unidirectional SiC/C/SiC material in An oxidizing environment by experimentally measuring the volume consumed by the interface by resistance testing of the material after Oxidation for different times based on the difference in the electrical conductivity of pyrolytic carbon and SiC fibers and the matrix. However, this method is not in accordance with the actual method because only the oxidation of the interface at the cross section perpendicular to the fiber direction is considered, and the influence of the existence of matrix microcracks on the oxidation of the interface is not considered. On the other hand, the preparation and test processes of the material have great loss in time, manpower and material resources, so that the application of the experimental method in material design is limited.
Patent CN103093063B, "a method for detecting damage to a unidirectional silicon carbide fiber toughened silicon carbide ceramic matrix composite in an oxidation environment," selects a representative volume element containing one crack and one fiber based on an average crack spacing hypothesis, and calculates the carbon interface consumption length at the crack of the matrix by applying an oxidation kinetics equation, but the method does not consider the influence of the nonuniformity of the initial material microcrack distribution on the interface oxidation consumption, nor the influence of the mutual contact of a plurality of fibers on the interface oxidation consumption, so that the distribution of the interface consumption volume in the unidirectional SiC/SiC material cannot be accurately predicted.
Therefore, it is necessary to provide a simple and effective method capable of accurately predicting the distribution of the interface consumption volume in the unidirectional SiC/SiC material.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the method for determining the carbon interface consumption volume in the oxidation environment of the ceramic matrix composite is provided, and the problem that the interface consumption volume distribution of the unidirectional SiC/SiC composite in the oxidation environment cannot be accurately predicted in the prior art is solved.
The invention adopts the following technical scheme for solving the technical problems:
a method for determining the consumption volume of a carbon interface in an oxidation environment of a ceramic matrix composite comprises the following steps:
step 3, dividing the fibers on the cross section of the material into independent fibers, single-point contact fibers, two-point contact fibers and multi-point contact fibers according to whether the fibers on the cross section of the material are in mutual contact and the number of contact points, and counting the number of the fibers of the corresponding type;
step 4, calculating the area of the carbon interface at the outer side of each type of fiber based on the average thickness of the carbon interface, the average diameter of the fiber and the number of contact points between the fibers, and further calculating the mass fraction of carbon contained in the material;
step 5, obtaining the number a of matrix cracks on the outer surface of the material, measuring the distance between adjacent matrix cracks and the distance between two cross sections of the material in the fiber direction and the adjacent matrix cracks, wherein the distances are a +1, sequencing the distances from small to large, and taking the minimum distance as the 1 st distance and the maximum distance as the a +1 st distance;
step 6, calculating the consumption length r of the carbon interface of the material at different oxidation moments based on the oxidation kinetic equationc；
Step 7, consuming the carbon interface for a length rcCompare with 1/2 for the distance found in step 5: when r isc<The total consumed carbon interface length is l at the minimum distance/2c_c＝(2a+2)rc(ii) a When r iscTotal carbon interface consumption length l is larger than or equal to maximum distance/2c_cThe sum of all the distances obtained in the step 5; when r iscBetween 1/2 at a certain distance, i.e.
x＝1,…,a，lc_cEqual to the sum of the 1 st to the x-th distances plus (2a +2-2x) rc；
And 8, calculating to obtain the carbon interface consumption volume and the distribution rule thereof in the material oxidation process based on the total area of the carbon interface on the cross section of the material and the total carbon interface consumption length.
As a preferable embodiment of the present invention, the average thickness of the carbon interface in step 2 is calculated by the following formula:
wherein e is the average thickness of the carbon interface, n is the total number of fibers, eiThe thickness of the carbon interface around the i-th fiber in 1/100 representing the total number of randomly selected fibers.
As a preferable scheme of the invention, the average diameter of the fibers in the step 2 is calculated by the following formula:
wherein d isfIs the average diameter of the fibers, n is the total number of fibers, dfiThe diameter of the ith fiber in 1/100 representing the total number of randomly selected fibers.
As a preferable embodiment of the present invention, the area of the carbon interface outside the fiber in step 4 is calculated by the following formula:
wherein S iscjJ is 0,1, …, q, q is the number of the maximum contact points between the fibers, r is the area of the carbon interface outside the fiber with j contact points between the fibersfIs the average fiber radius and e is the average thickness of the carbon interface.
As a preferable embodiment of the present invention, the carbon interface consumption length r in step 6cThe calculation formula is as follows:
wherein k is0Is the oxidation reaction rate constant of the carbon interface, EaIs the oxidation reaction activation energy of the carbon interface, R is the general gas constant, T is the ambient temperature,
is the partial pressure of oxygen in the environment, McIs the molar mass of the carbon interface, pcTo the density of the carbon interface, t is the oxidation reaction time.
Compared with the prior art, the invention adopting the technical scheme has the following technical effects:
1. the invention considers the influence of the actual distribution of the fiber in the unidirectional SiC/SiC composite material on the content of the carbon interface, simultaneously considers the oxidation of the carbon interface when oxygen enters from two end surfaces of the material vertical to the fiber and the oxidation of the internal interface of the material when oxygen enters from a crack of a matrix, and can accurately give the consumed volume and the distribution condition of the carbon interface after the material is oxidized for a certain time.
2. The whole calculation process is simple and efficient, and the defects of high cost and long time consumption of an experimental method are overcome.
Drawings
FIG. 1 is a schematic diagram of a geometric model of a multi-matrix crack-containing unidirectional SiC/SiC composite material according to an embodiment of the present invention.
Fig. 2 is a schematic view of a fiber contact type of a material section.
FIG. 3 is a schematic of the area of a single point contact fiber interface.
FIG. 4 is a flow chart of the calculation of the interface consumption length around an individual fiber.
FIG. 5 is a schematic view showing the volume distribution of consumed carbon interface in each case, wherein (a) is
(b) Is composed of
(c) Is composed of
(d) Is composed of
(e) Is composed of
FIG. 6 is a comparison curve of the unidirectional SiC/SiC material without considering the matrix crack model prediction result and the multi-matrix crack distribution simulation result and the test result.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
The invention discloses a method for determining the consumption volume of an oxidation environment interface of a unidirectional SiC/SiC composite material, which comprises the following steps:
(1) polishing two sections of a unidirectional SiC/SiC composite material sample in a fiber direction until the two sections are smooth, measuring the size of the material in each direction, calculating the volume of the material, and measuring the mass of the material by adopting a high-precision mass sensor;
the unidirectional SiC/SiC composite material sample is of a cuboid structure and has a long and a wideHigh is l, w, h, the volume V of the materialcomp＝l*w*h。
(2) Placing the polished material into a Scanning Electron Microscope (SEM), shooting the cross section of the material, counting the total number of fibers, and measuring the average value of the interface thickness and the average diameter of the fibers;
the total number n of the fibers is obtained by counting the fiber circular section in the material section;
the average interface thickness e is obtained by randomly selecting 1/100 of the total number n of the fibers, measuring the thickness of the interface layer around the fibers and then averaging the thicknesses, namely:
in the formula, eiThe thickness of the interface layer around the ith fiber is shown.
Average diameter d of fiberfThe diameter of these fibers was also measured by randomly choosing 1/100 for the total number of fibers n, and then taking the average, i.e.:
in the formula (d)fiThe diameter of the ith fiber is shown.
The number a of microcracks of the matrix on the outer surface of the material is obtained by shooting the statistics of the surface of the cuboid test piece, and the interval l between the cracks of the matrixcThe distance d between the two end faces of the material and the adjacent matrix crackcAll measured by SEM with a ruler.
(3) Dividing the fibers on the cross section of the material into independent fibers, single-point contact fibers, two-point contact fibers and multi-point contact fibers according to whether the fibers are in mutual contact in the SEM picture of the cross section of the material and the number of contact points, and counting the number of the fibers of corresponding types;
counting the number q of the maximum contact points between the fibers by SEM pictures of the material section, and determining the number v of the fibers without contact points with other fibers0There are 1Number v of fibers at contact point (single point contact fibers)1Number v of fibers having 2 points of contact with other fibers (two-point contact fibers)2Number v of fibers having q contact points with other fibers (two-point contact fibers)qThen, there are:
n＝v0+v1+v2+...+vq(3)
(4) calculating the area of the carbon interface outside each fiber based on the average thickness of the interface and the number of contact points between the fibers, and further calculating the mass fraction of carbon contained in the material;
area S of carbon interface on outer surface of independent fiberc0Comprises the following steps:
Sc0＝π[(rf+e)2-rf 2](4)
in the formula, rfDenotes the average fiber radius.
Area S of carbon interface on outer surface of fiber having j contact points with other fiberscjComprises the following steps:
the total interfacial area S on the cross section of the materialcComprises the following steps:
Sc＝v0Sc0+v1Sc1+...+vjScj+...+vqScq(6)
in the formula, ScqThe carbon interfacial area of the outer surface of the fiber where there are q contact points with other fibers.
Mass fraction omega of carbon interfacecCan be expressed as:
in the formula, ρcDenotes the density of the carbon interface, pcompDenotes the density, V, of the compositefRepresenting the volume content of the fibres, which can be measured by measuring the content of fibres in a SEM photograph of a cross-section of the materialArea SfCalculating:
(5) obtaining the number of microcracks of the matrix on the outer surface of the material and the distance between the microcracks, further measuring the distance between two end surfaces of the material and the cracks adjacent to the matrix, and sequencing the distance between the cracks of the matrix and the distance between the two end surfaces of the material and the cracks adjacent to the matrix from small to large;
the number of the matrix cracks is a, and the matrix crack spacing is lcThe distance d between the two end faces of the material and the adjacent matrix crackcThen, there are:
lc1+lc2+...+lca-1+dc1+dca＝l (9)
in the formula Ic1Denotes the spacing between the first and second matrix cracks, lca-1Denotes the distance between the a-1 st and the a-th substrate cracks from left to right, dc1Indicating the distance between the left end face of the material and the first crack of the substrate, dcaThe distance between the a-th substrate crack and the right end face of the material is shown.
(6) Calculating the interface consumption length of the material at different oxidation moments based on an oxidation kinetic equation;
length of interface consumption rcComprises the following steps:
in the formula, k0Is the oxidation reaction rate constant of the carbon interface, EaIs the activation energy of the oxidation reaction at the carbon interface, R is the universal gas constant, T is the ambient temperature,
is the partial pressure of oxygen in the environment, McIs the molar mass of the carbon interface and t is the oxidation reaction time.
(7) Comparing 1/2 of the calculated interface consumption length and the distance between the matrix cracks and 1/2 of the distance between two end faces of the material and the adjacent matrix cracks, and sequencing the two end faces from small to large; if the interface consumed length is greater than or equal to 1/2 of the matrix crack spacing, the interface consumed length is equal to 1/2 of the matrix crack spacing and does not change with the increase of time; if the interface wear length is less than 1/2 for the matrix crack spacing, the interface wear length is equal to the calculated value and increases with time; similarly, if the calculated interface wear length is greater than or equal to 1/2 of the distance between the two end surfaces of the material and the adjacent substrate crack, the interface wear length is equal to 1/2 of the distance between the two end surfaces of the material and the adjacent substrate crack and does not change any more with time; if the calculated interface consumption length is less than 1/2 of the distance between the two end surfaces of the material and the adjacent matrix crack, the interface consumption length is equal to the calculated value and increases along with the increase of time;
(8) calculating to obtain the interface consumption volume and the distribution rule thereof in the material oxidation process based on the interface cross-sectional area and the consumption length;
volume consumed at interface VCCan be expressed as:
VC＝nlc_cSc(11)
in the formula Ic_cThe total length of carbon interface consumption around an individual fiber.
The following is to take the unidirectional SiC/C/SiC composite material in pure oxygen environment of 700 ℃ and 100KPa as an example, and calculate the consumption volume and distribution condition of the carbon interface at different oxidation moments.
(1) Grinding two sections of a unidirectional SiC/SiC composite material sample in the fiber direction to be smooth, measuring the dimension of the material in each direction to be respectively 13mm, 3mm and 3mm, and calculating the volume V of the material as shown in figure 1comp＝l*w*h＝117mm3Measuring the mass m of the material by using a high-precision mass sensorcomp0.29835 g;
(2) placing the polished material into a Scanning Electron Microscope (SEM), shooting the cross section of the material, counting the total number of fibers to be n-24570, randomly selecting 245 fibers, and measuring the average thickness of the peripheral interfaceThe value e is 0.1 μm and the mean fiber diameter df＝14μm；
(3) In the present embodiment, the fiber volume content VfCan be expressed as:
in the present embodiment, the density ρ of the materialcompCan be expressed as:
(3) dividing the fibers on the cross section of the material into independent fibers, single-point contact fibers, two-point contact fibers and multi-point contact fibers according to whether the fibers are in mutual contact and the number of contact points in the SEM photograph of the cross section of the material, wherein the number of the independent fibers is 3292, the number of the single-point contact fibers is 7567, the number of the two-point contact fibers is 5848, the number of the three-point contact fibers is 3882, the number of the four-point contact fibers is 2359, the number of the five-point contact fibers is 1278, and the number of the six-point contact fibers is;
(4) calculating the area of the carbon interface outside each fiber based on the average thickness of the interface and the number of contact points between the fibers, and further calculating the mass fraction of carbon contained in the material;
in the present embodiment, the area S of the carbon interface on the outer surface of the independent fiberc0Comprises the following steps:
Sc0＝π[(rf+e)2-rf 2]＝4.4274μm2(14)
thus, the area S of the carbon interface on the outer surface of all the individual fibersc_indComprises the following steps:
Sc_ind＝3292×4.4274＝14575.0008um2(15)
in the present embodiment, the area S of the carbon interface on the outer surface of the single-point contact fiberc1Comprises the following steps:
in the formula (I), the compound is shown in the specification,
as shown in fig. 3, therefore, Sc1＝4.3090μm2Area S of carbon interface on outer surface of all single-point contact fibersc_1Comprises the following steps:
Sc_1＝7567×4.3090＝32606.203μm2(17)
likewise, the area S of the carbon interface between the two points contacting the outer surface of the fiberc2Comprises the following steps:
thus, Sc2＝4.1906μm2All two points contact the area S of the carbon interface on the outer surface of the fiberc_2Comprises the following steps:
Sc_2＝5848×4.1906＝24506.6288μm2(19)
similarly, the area S of the carbon interface on the outer surface of the fiber in three-point contactc3＝4.0722μm2All two points contact the area S of the carbon interface on the outer surface of the fiberc_3Comprises the following steps:
Sc_3＝3882×4.0722＝15808.2804μm2(20)
similarly, the area S where four points contact the carbon interface on the outer surface of the fiberc4＝3.9538μm2All four points contact the area S of the carbon interface on the outer surface of the fiberc_4Comprises the following steps:
Sc_4＝2359×3.9538＝9327.0142μm2(21)
likewise, the area S of the carbon interface at the outer surface of the five-point contact fiberc5＝3.8354μm2All five points contact the area S of the carbon interface on the outer surface of the fiberc_5Comprises the following steps:
Sc_5＝1278×3.8354＝4901.6412μm2(22)
likewise, six point contact the area S of the fiber outer surface carbon interfacec6＝3.717μm2All five points contact the area S of the carbon interface on the outer surface of the fiberc_6Comprises the following steps:
Sc_6＝344×3.717＝1278.648μm2(23)
thus, the total area S of the carbon interfacecCan be expressed as:
Sc＝Sc_ind+Sc_1+Sc_2+...+Sc_6＝0.103mm2(24)
in the present embodiment, the mass fraction ω of carboncCan be expressed as:
(5) obtaining the initial number of microcracks of the matrix on the outer surface of the material as a to 3, sequencing the matrix cracks from left to right, wherein the interval between the matrix cracks is lc1＝7mm,lc23mm and further measuring the distance d between the two end faces of the material and the adjacent matrix crackc1＝2mm,dc31mm, as shown in fig. 1, sequencing the crack spacing of the matrix and the distance between two end faces of the material and the adjacent matrix crack from small to large;
in this embodiment, the spacing between 3 matrix cracks and the distance between two end faces of the material and the adjacent matrix crack are ordered as:
dc3＜dc1＜lc2＜lc1(26)
(6) calculating the interface consumption length of the material at different oxidation moments based on an oxidation kinetic equation;
in the present embodiment, k0Is the oxidation reaction rate constant, k, of the carbon interface0＝1070，EaIs the activation energy of oxidation reaction at the carbon interface, Ea123000J/mol, R is the universal gas constant, R is 8.3145J/mol, K is ambient temperature, T is 973.15K,
is the partial pressure of oxygen in the environment,
Mcis the molar mass of the carbon interface, Mc12g/mol, t is the oxidation reaction time, the interfacial consumption length rcComprises the following steps:
(7) comparing 1/2 of the calculated interface consumption length and the distance between the matrix cracks and 1/2 of the distance between two end faces of the material and the adjacent matrix cracks, and sequencing the two end faces from small to large; if the interface consumed length is greater than or equal to 1/2 of the matrix crack spacing, the interface consumed length is equal to 1/2 of the matrix crack spacing and does not change with the increase of time; if the interface wear length is less than 1/2 for the matrix crack spacing, the interface wear length is equal to the calculated value and increases with time; similarly, if the calculated interface wear length is greater than or equal to 1/2 of the distance between the two end surfaces of the material and the adjacent substrate crack, the interface wear length is equal to 1/2 of the distance between the two end surfaces of the material and the adjacent substrate crack and does not change any more with time; if the calculated interface consumption length is less than 1/2 of the distance between the two end surfaces of the material and the adjacent matrix crack, the interface consumption length is equal to the calculated value and increases along with the increase of time;
in the present embodiment, the interface consumption length r is set tocCrack spacing from substratecThe distance d between two end faces of the material and the adjacent matrix crackcThe total length of the carbon interface consumption around the individual fibers is represented as l in FIG. 4c_c。
(8) And calculating to obtain the interface consumption volume and the distribution rule thereof in the material oxidation process based on the interface cross-sectional area and the consumption length.
In the present embodiment, the interface consumption length r is determined according to the difference in timecCrack spacing from substratecThe distance d between two end faces of the material and the adjacent matrix crackcThe distribution of the consumed volume of the interface around the single fiber can be determined by the size relationship between the fibers, and is illustrated by the example of the independent fiber (see (A) in FIG. 5a) The formulae (a), (b), (c), (d) and (e).
In the embodiment, the consumption volume change rule of the carbon interface is represented by the mass loss rate of the material, a change curve of the mass loss rate of the unidirectional SiC/SiC composite material along with time is shown in FIG. 6, and the simulation result of the prediction model considering the multi-matrix crack distribution provided by the invention can be seen to be well matched with the test result by comparing the matrix crack model which is not considered with the multi-matrix crack model which is considered.
The above embodiments are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modifications made on the basis of the technical scheme according to the technical idea of the present invention fall within the protection scope of the present invention.
Claims (5)
1. A method for determining the consumption volume of a carbon interface in an oxidation environment of a ceramic matrix composite is characterized by comprising the following steps:
step 1, obtaining the volume and the mass of the ceramic matrix composite material, and calculating to obtain the density of the material;
step 2, counting the total number of fibers according to the cross section of the material in the fiber direction, and calculating the average thickness of a carbon interface and the average diameter of the fibers;
step 3, dividing the fibers on the cross section of the material into independent fibers, single-point contact fibers, two-point contact fibers and multi-point contact fibers according to whether the fibers on the cross section of the material are in mutual contact and the number of contact points, and counting the number of the fibers of the corresponding type;
step 4, calculating the area of the carbon interface at the outer side of each type of fiber based on the average thickness of the carbon interface, the average diameter of the fiber and the number of contact points between the fibers, and further calculating the mass fraction of carbon contained in the material;
step 5, obtaining the number a of matrix cracks on the outer surface of the material, measuring the distance between adjacent matrix cracks and the distance between two cross sections of the material in the fiber direction and the adjacent matrix cracks, wherein the distances are a +1, sequencing the distances from small to large, and taking the minimum distance as the 1 st distance and the maximum distance as the a +1 st distance;
step 6, calculating the consumption length r of the carbon interface of the material at different oxidation moments based on the oxidation kinetic equationc；
Step 7, consuming the carbon interface for a length rcCompare with 1/2 for the distance found in step 5: when r isc<The total consumed carbon interface length is l at the minimum distance/2c_c＝(2a+2)rc(ii) a When r iscTotal carbon interface consumption length l is larger than or equal to maximum distance/2c_cThe sum of all the distances obtained in the step 5; when r iscBetween 1/2 at a certain distance, i.e.
x＝1,…,a，lc_cEqual to the sum of the 1 st to the x-th distances plus (2a +2-2x) rc；
And 8, calculating to obtain the carbon interface consumption volume and the distribution rule thereof in the material oxidation process based on the total area of the carbon interface on the cross section of the material and the total carbon interface consumption length.
2. The method for determining the consumed volume of the carbon interface in the oxidation environment of the ceramic matrix composite according to claim 1, wherein the average thickness of the carbon interface in the step 2 is calculated by the following formula:
wherein e is the average thickness of the carbon interface, n is the total number of fibers, eiThe thickness of the carbon interface around the i-th fiber in 1/100 representing the total number of randomly selected fibers.
3. The method for determining the carbon interfacial consumption volume in an oxidizing environment of a ceramic matrix composite according to claim 1, wherein the average fiber diameter in step 2 is calculated by the formula:
wherein d isfIs the average diameter of the fibers, n is the total number of fibers, dfiThe diameter of the ith fiber in 1/100 representing the total number of randomly selected fibers.
4. The method for determining the consumed volume of the carbon interface in the oxidation environment of the ceramic matrix composite according to claim 1, wherein the area of the carbon interface at the outer side of the fiber in the step 4 is calculated by the following formula:
wherein S iscjJ is 0,1, …, q, q is the number of the maximum contact points between the fibers, r is the area of the carbon interface outside the fiber with j contact points between the fibersfIs the average fiber radius and e is the average thickness of the carbon interface.
5. The method for determining the carbon interface consumption volume in an oxidizing environment of a ceramic matrix composite according to claim 1, wherein the carbon interface consumption length r in step 6cThe calculation formula is as follows:
wherein k is0Is the oxidation reaction rate constant of the carbon interface, EaIs the oxidation reaction activation energy of the carbon interface, R is the general gas constant, T is the ambient temperature,
is the partial pressure of oxygen in the environment, McIs the molar mass of the carbon interface, pcTo the density of the carbon interface, t is the oxidation reaction time.
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