CN105930579B - Residual Stiffness prediction technique after a kind of oxidation of control of two-dimensional braided ceramic matric composite - Google Patents
Residual Stiffness prediction technique after a kind of oxidation of control of two-dimensional braided ceramic matric composite Download PDFInfo
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- 238000007254 oxidation reaction Methods 0.000 title claims abstract description 72
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Abstract
Description
技术领域technical field
本发明涉及一种二维编织陶瓷基复合材料氧化后剩余刚度预测方法。The invention relates to a method for predicting the residual stiffness of a two-dimensional braided ceramic matrix composite material after oxidation.
背景技术Background technique
二维编织陶瓷基复合材料具有高比强、高比模、耐高温、耐腐蚀和低密度等优良性能，在空天飞行器高温防护系统具有广泛的需求。材料在其使用过程中，由于受到高温环境因素的影响，会逐渐产生氧化损伤，导致材料力学性能下降，进而严重影响工程构件的使用寿命与安全。刚度指材料在受力时抵抗弹性变形的能力，研究二维平纹编织陶瓷基复合材料氧化后剩余刚度对其应用有着重要意义。Two-dimensional braided ceramic matrix composites have excellent properties such as high specific strength, high specific modulus, high temperature resistance, corrosion resistance and low density, and have a wide demand in high temperature protection systems for aerospace vehicles. During the use of materials, due to the influence of high-temperature environmental factors, oxidative damage will gradually occur, resulting in a decrease in the mechanical properties of the material, which will seriously affect the service life and safety of engineering components. Stiffness refers to the ability of a material to resist elastic deformation when it is stressed. It is of great significance to study the residual stiffness of two-dimensional plain weave ceramic matrix composites after oxidation.
由于单向陶瓷基复合材料存在非纤维方向力学性能弱等缺点，其应用范围受到了限制。二维编织结构陶瓷基复合材料的出现，克服了单向复合材料的缺点，同时在厚度方向上纤维束整体化更高，增加了材料层间剪切强度，减少了分层现象，并提高了复合材料抗冲击性能和弯曲疲劳性能，因此大大扩展了陶瓷基复合材料的应用范围。Due to the disadvantages of unidirectional ceramic matrix composites such as weak mechanical properties in non-fiber directions, their application range is limited. The emergence of two-dimensional braided ceramic matrix composites overcomes the shortcomings of unidirectional composite materials, and at the same time, the fiber bundles are more integrated in the thickness direction, which increases the shear strength between layers of materials, reduces delamination, and improves The impact resistance and bending fatigue performance of composite materials have greatly expanded the application range of ceramic matrix composites.
然而由于二维编织陶瓷基复合材料是一种新型结构材料，国内外还没有高效的方法预测其氧化后的剩余刚度，也未见公开的发明专利。杨成鹏(杨成鹏,矫桂琼,王波,等.2D-C/SiC复合材料的氧化损伤及刚度模型[J].复合材料学报,2009,26(3):175-181.)采用实验的方法测试了2D C/SiC复合材料在700℃环境下的剩余刚度，并基于细观结构的变化建立了计算公式，计算值与实验值较为吻合。但通过实验的方式要消耗大量的实验资金，其提出的计算模型也只能计算离散的特定温度下的剩余刚度。However, since the two-dimensional braided ceramic matrix composite is a new type of structural material, there is no efficient method at home and abroad to predict its residual stiffness after oxidation, and there is no published invention patent. Yang Chengpeng (Yang Chengpeng, Jiao Guiqiong, Wang Bo, et al. Oxidation damage and stiffness model of 2D-C/SiC composites [J]. Journal of Composite Materials, 2009,26(3):175-181.) used experimental methods to test The residual stiffness of 2D C/SiC composites at 700 °C was calculated, and a calculation formula was established based on the changes in the mesostructure. The calculated values were in good agreement with the experimental values. However, the experimental method consumes a lot of experimental funds, and the proposed calculation model can only calculate the residual stiffness at discrete specific temperatures.
当前，如何准确的预测二维编织陶瓷基复合材料氧化后的剩余刚度是本技术领域重要而难以解决的问题。At present, how to accurately predict the residual stiffness of two-dimensional braided ceramic matrix composites after oxidation is an important and difficult problem in this technical field.
发明内容Contents of the invention
发明目的：针对上述现有技术，提出一种能有效预测二维编织陶瓷基复合材料氧化后剩余刚度预测方法。Purpose of the invention: Aiming at the above-mentioned prior art, a method for effectively predicting the remaining stiffness of two-dimensional braided ceramic matrix composites after oxidation is proposed.
技术方案：一种二维编织陶瓷基复合材料氧化后剩余刚度预测方法，包括如下步骤：Technical solution: A method for predicting the residual stiffness of a two-dimensional braided ceramic matrix composite after oxidation, including the following steps:
(1)，基于质量损失率理论和纤维退化规律假设，建立氧化动力学模型；(1), based on the theory of mass loss rate and the assumption of fiber degradation law, an oxidation kinetic model is established;
(2)，基于氧化动力学模型，采用有限元软件，建立氧化后的微观尺度的单胞模型；(2), based on the oxidation kinetic model, using finite element software to establish a micro-scale unit cell model after oxidation;
(3)，施加微观尺度的单胞模型的周期性边界条件；(3), applying the periodic boundary conditions of the micro-scale unit cell model;
(4)，计算该单胞模型6个方向的弹性参数；(4), calculate the elastic parameter of 6 directions of this unit cell model;
(5)，采用有限元软件，建立二维编织陶瓷基复合材料单胞模型；(5), using finite element software to establish a two-dimensional braided ceramic matrix composite unit cell model;
(6)，将计算得到的氧化后微观尺度的单胞模型6个方向的弹性参数作为纱线的基本属性，带入二维编织陶瓷基复合材料单胞模型；(6), the calculated elastic parameters of the oxidized micro-scale unit cell model in 6 directions are used as the basic properties of the yarn, and brought into the two-dimensional braided ceramic matrix composite material unit cell model;
(7)，施加所述二维编织陶瓷基复合材料单胞模型的周期性边界条件；(7), applying the periodic boundary condition of the two-dimensional braided ceramic matrix composite material unit cell model;
(8)，计算得到二维编织陶瓷基复合材料轴向的剩余弹性模量。(8), calculate the axial residual elastic modulus of the two-dimensional braided ceramic matrix composite.
作为本发明的优选方案，所述步骤(1)中，所述质量损失率理论分为两个温度区间：As a preferred version of the present invention, in the step (1), the mass loss rate is theoretically divided into two temperature intervals:
1)当温度在400℃～700℃区间时，公式如下：1) When the temperature is between 400°C and 700°C, the formula is as follows:
其中，λr是复合材料的质量损失率，W是复合材料的质量，ΔW是材料的质量变化量，K0是与氧化速率相关的常数，是氧气的体积分数，P是大气气压，Mc是碳纤维的摩尔质量，R是气体常数，T是环境温度，Er是氧化反应活化能，t是氧化时间，Seff是碳的有效反应面积；其中，Seff＝μW，μ是碳的反应有效系数；where λr is the mass loss rate of the composite, W is the mass of the composite, ΔW is the mass change of the material, K0 is a constant related to the oxidation rate, is the volume fraction of oxygen, P is the atmospheric pressure, Mc is the molar mass of carbon fiber, R is the gas constant, T is the ambient temperature, Er is the activation energy of oxidation reaction, t is the oxidation time, S eff is the effective reaction area of carbon ; Wherein, S eff =μ W, μ is the reaction effective coefficient of carbon;
2)当温度在700℃～900℃区间时，公式如下：2) When the temperature is in the range of 700°C to 900°C, the formula is as follows:
其中，Nc是碳的摩尔密度，λ是与初始状态有关的常数，Tc是基体开裂温度，Lc是涂层厚度；where Nc is the molar density of carbon, λ is a constant related to the initial state, Tc is the substrate cracking temperature, and Lc is the coating thickness;
所述纤维退化规律假设：假设纤维以圆形的规律在高温下进行退化，公式如下：The assumption of the fiber degradation law: assume that the fiber degrades at high temperature in a circular manner, the formula is as follows:
其中，δ是纤维的氧化长度，ρf和ρc分别表示纤维和复合材料的密度，L是复合材料的长度，H是复合材料的高度，n是碳的物质的量，Nf是单位面积内纤维的数量；where, δ is the oxidation length of the fiber, ρf and ρc represent the densities of the fiber and the composite material, respectively, L is the length of the composite material, H is the height of the composite material, n is the amount of carbon substance, and Nf is the unit area the number of inner fibers;
将所述复合材料的质量损失率λr带入所述纤维的氧化长度δ的计算公式(3)，得到：The mass loss rate λ r of the composite material is brought into the calculation formula (3) of the oxidation length δ of the fiber to obtain:
1)当温度在400℃～700℃区间时：1) When the temperature is between 400°C and 700°C:
2)当温度在700℃～900℃区间时：2) When the temperature is between 700°C and 900°C:
由此可得氧化后纤维的剩余半径为：It can be obtained that the remaining radius of the fiber after oxidation is:
1)当温度在400℃～700℃区间时，公式如下：1) When the temperature is between 400°C and 700°C, the formula is as follows:
2)当温度在700℃～900℃区间时，公式如下：2) When the temperature is in the range of 700°C to 900°C, the formula is as follows:
其中，rf是纤维氧化后的剩余半径，rf0是纤维未氧化时的初始半径。where rf is the remaining radius of the fiber after oxidation, and rf0 is the initial radius of the fiber when it is not oxidized.
作为本发明的优选方案，所述步骤(2)中，假设氧化为均匀贯穿式氧化，氧化后纤维各处半径相等。As a preferred solution of the present invention, in the step (2), assuming that the oxidation is a uniform through-type oxidation, the radii of the fibers after oxidation are equal.
作为本发明的优选方案，所述步骤(3)中，所施加的边界条件满足位移的连续性和在模型相反两个平面应力分布的一致性。As a preferred solution of the present invention, in the step (3), the applied boundary conditions satisfy the continuity of the displacement and the consistency of the stress distribution of the two opposite planes in the model.
作为本发明的优选方案，所述步骤(4)中，所述6个方向的弹性参数包括x、y、z三个方向的弹性模量Ex、Ey、Ez，xy、xz、yz三个方向的剪切模量Gxy、Gxz、Gyz，以及泊松比vxy、vxz、vyz。As a preferred solution of the present invention, in the step (4), the elastic parameters in the six directions include the elastic modulus E x , E y , E z in the three directions of x, y, and z , xy, xz, yz Shear modulus G xy , G xz , G yz in three directions, and Poisson's ratio v xy , v xz , v yz .
作为本发明的优选方案，所述步骤(7)中，施加周期性边界条件为：As a preferred version of the present invention, in the step (7), the periodic boundary condition is imposed as follows:
其中，Z+和Z-分别表示垂直于Z轴的两个相反的边界表面，为在Z+边界表面上的位移，为在Z-边界表面上的位移，xi Z+为Z+表面上节点的位移量，xi Z-为Z-表面上节点的位移量，为在边界表面上位移的周期性部分，θi为周期性结构的平均应变张量。where Z+ and Z- represent two opposite boundary surfaces perpendicular to the Z axis, respectively, is the displacement on the Z+ boundary surface, is the displacement on the Z-boundary surface, x i Z+ is the displacement of the nodes on the Z+ surface, x i Z- is the displacement of the nodes on the Z- surface, is the periodic part of the displacement on the boundary surface, and θi is the average strain tensor of the periodic structure.
有益效果：本发明提供的二维编织陶瓷基复合材料氧化后剩余刚度预测方法，基于质量损失率模型和纤维退化规律假设，提出了考虑纤维氧化的动力学模型。基于氧化动力学模型，采用有限元法建立了考虑纤维氧化的微观尺度模型和二维编织陶瓷基复合材料单胞尺度模型，预测了材料的剩余刚度。本发明提出的预测模型充分考虑了纤维随氧化时间、温度的退化规律，因此能够精确的预测出二维编织陶瓷基复合材料氧化后的剩余刚度且节约了大量的实验成本。Beneficial effects: The method for predicting residual stiffness of two-dimensional braided ceramic matrix composites after oxidation provided by the present invention proposes a kinetic model considering fiber oxidation based on the mass loss rate model and the assumption of fiber degradation law. Based on the oxidation kinetics model, a microscale model considering fiber oxidation and a two-dimensional woven ceramic matrix composite unit cell scale model were established by using the finite element method, and the residual stiffness of the material was predicted. The prediction model proposed by the invention fully considers the degradation law of fibers with oxidation time and temperature, so it can accurately predict the residual stiffness of the two-dimensional braided ceramic matrix composite material after oxidation and save a lot of experimental costs.
附图说明Description of drawings
图1是裂纹尖端附近碳纤维氧化扫描电镜图；Figure 1 is a scanning electron microscope image of carbon fiber oxidation near the crack tip;
图2是陶瓷基复合材料二维平面模型；Fig. 2 is a two-dimensional plane model of a ceramic matrix composite;
图3是单向陶瓷基复合材料氧化示意图；Fig. 3 is a schematic diagram of unidirectional ceramic matrix composite material oxidation;
图4是氧化后的微观模型；Fig. 4 is the microscopic model after oxidation;
图5是在氧化后微观模型边界条件示意图；Fig. 5 is a schematic diagram of the boundary conditions of the microscopic model after oxidation;
图6是二维平纹编织陶瓷基复合材料单胞模型；Fig. 6 is a two-dimensional plain weave ceramic matrix composite unit cell model;
图7是二维平纹编织陶瓷基复合材料单胞模型边界条件示意图；Fig. 7 is a schematic diagram of boundary conditions of a two-dimensional plain weave ceramic matrix composite material unit cell model;
图8是该预测模型的具体流程图；Fig. 8 is the concrete flowchart of this predictive model;
图9是空气环境下700℃时二维平纹编织C/SiC复合材料轴向的剩余弹性模量预测值与的实验值的对比曲线；Figure 9 is a comparison curve between the predicted value and the experimental value of the axial residual elastic modulus of the two-dimensional plain weave C/SiC composite material at 700 °C in the air environment;
图10是空气环境下800℃时二维平纹编织C/SiC复合材料轴向的剩余弹性模量预测值与的实验值的对比曲线；Figure 10 is a comparison curve between the predicted value and the experimental value of the axial residual elastic modulus of the two-dimensional plain weave woven C/SiC composite material at 800 °C in the air environment;
图11是空气环境下850℃时二维平纹编织C/SiC复合材料轴向的剩余弹性模量预测值与的实验值的对比曲线；Figure 11 is a comparison curve between the predicted value and the experimental value of the residual elastic modulus in the axial direction of the two-dimensional plain weave C/SiC composite material at 850 °C in the air environment;
图12是空气环境下900℃时二维平纹编织C/SiC复合材料轴向的剩余弹性模量预测值与的实验值的对比曲线。Figure 12 is a comparison curve between the predicted value and the experimental value of the axial residual elastic modulus of the two-dimensional plain weave C/SiC composite material at 900 °C in the air environment.
具体实施方式Detailed ways
下面结合附图对本发明做更进一步的解释。The present invention will be further explained below in conjunction with the accompanying drawings.
本实施例以二维平纹编织C/SiC复合材料为例，对700℃～900℃区间范围内材料氧化后的剩余刚度进行预测，其中材料性能参数如表1所示。In this example, the two-dimensional plain weave C/SiC composite material is taken as an example to predict the residual stiffness of the material after oxidation in the range of 700°C to 900°C. The material performance parameters are shown in Table 1.
表1Table 1
如图8所示，本方法具体步骤如下：As shown in Figure 8, the specific steps of this method are as follows:
(1)，基于质量损失率理论和纤维退化规律假设，建立氧化动力学模型。其中，质量损失率理论分为两个温度区间：(1), based on the theory of mass loss rate and the assumption of fiber degradation law, an oxidation kinetic model is established. Among them, the mass loss rate theory is divided into two temperature ranges:
1)当温度在400℃～700℃区间时，复合材料的质量损失率公式如下：1) When the temperature is in the range of 400 °C to 700 °C, the formula for the mass loss rate of the composite material is as follows:
其中，λr是复合材料的质量损失率；W是复合材料的质量；ΔW是复合材料的质量损失率的质量变化量；K0是与氧化速率相关的常数；是氧气的体积分数，在这里取20.95％；P是大气气压，在这里取101.325KPa；Mc是碳纤维的摩尔质量，在这里取12×103kg/mol；R是气体常数，在这里取8.3145J/(mol·K)；T是环境温度；Er是氧化反应活化能；t是氧化时间；Seff是碳的有效反应面积，Seff与试样的质量有关，表示为Seff＝μW，μ是碳的反应有效系数，μ取决于试样的微裂纹面积和孔隙横截面积以及试样密度，可通过实验测得。Wherein, λr is the mass loss rate of the composite material; W is the quality of the composite material; ΔW is the mass change of the mass loss rate of the composite material ; K0 is a constant related to the oxidation rate; is the volume fraction of oxygen, here 20.95%; P is the atmospheric pressure, here is 101.325KPa; M c is the molar mass of carbon fiber, here is 12×10 3 kg/mol; R is the gas constant, here is 8.3145J/(mol K); T is the ambient temperature; E r is the activation energy of oxidation reaction; t is the oxidation time; S eff is the effective reaction area of carbon, S eff is related to the quality of the sample, expressed as S eff = μW, μ is the effective coefficient of carbon reaction, μ depends on the micro-crack area and pore cross-sectional area of the sample and the sample density, which can be measured through experiments.
2)当温度在700℃～900℃区间时，复合材料的质量损失率公式如下：2) When the temperature is in the range of 700°C to 900°C, the formula for the mass loss rate of the composite material is as follows:
其中，Nc是碳的摩尔密度；λ是与初始状态有关的常数；Tc是基体开裂温度，在这里取1030℃；Lc是涂层厚度。Among them, N c is the molar density of carbon; λ is a constant related to the initial state; T c is the cracking temperature of the substrate, which is taken as 1030 °C here; L c is the thickness of the coating.
纤维退化规律假设：根据图1所示的扫描电镜照片和图2所示的陶瓷基复合材料二维平面模型，假设纤维以圆形的规律在高温下进行退化，如图3所示，纤维的氧化长度即为图中BD段的长度；r0即OD的距离，指的是拟合的氧化区域的圆心O到纤维未氧化时表面的距离；r'即为OC的距离，指的是拟合的氧化区域的半径；α即为r0和r'之间的夹角。纤维退化规律公式如下：Assumption of fiber degradation law: According to the scanning electron microscope photos shown in Figure 1 and the two-dimensional planar model of ceramic matrix composites shown in Figure 2, it is assumed that the fibers degrade in a circular pattern at high temperatures, as shown in Figure 3, the fiber The oxidation length is the length of the BD segment in the figure; r 0 is the distance of OD, which refers to the distance from the center O of the fitted oxidation region to the surface of the fiber when it is not oxidized; r' is the distance of OC, which refers to the distance from the fitting The combined radius of the oxidation region; α is the angle between r 0 and r'. The formula of fiber degradation law is as follows:
其中，δ是纤维的氧化长度；ρf和ρc分别表示纤维和复合材料的密度；L是复合材料的长度，H是复合材料的高度，如图2所示；n是碳的物质的量；Nf是单位面积内纤维的数量。Among them, δ is the oxidation length of the fiber; ρf and ρc respectively represent the density of the fiber and the composite; L is the length of the composite, H is the height of the composite, as shown in Figure 2; n is the amount of carbon ; N f is the number of fibers per unit area.
将复合材料的质量损失率λr带入纤维的氧化长度δ的计算公式(3)，得到：Bringing the mass loss rate λ r of the composite material into the calculation formula (3) of the oxidation length δ of the fiber, we get:
1)当温度在400℃～700℃区间时：1) When the temperature is between 400°C and 700°C:
2)当温度在700℃～900℃区间时：2) When the temperature is between 700°C and 900°C:
若纤维未氧化时的初始半径为rf0，纤维氧化后的剩余半径为rf，根据关系rf＝rf0-δ可得氧化后纤维的剩余半径为：If the initial radius of the fiber is rf 0 when it is not oxidized, and the remaining radius of the fiber after oxidation is rf, according to the relationship rf=rf 0 -δ, the remaining radius of the oxidized fiber is:
1)当温度在400℃～700℃区间时，公式如下：1) When the temperature is between 400°C and 700°C, the formula is as follows:
2)当温度在700℃～900℃区间时，公式如下：2) When the temperature is in the range of 700°C to 900°C, the formula is as follows:
(2)，基于上述步骤(1)中的氧化动力学模型即式(6)和(7)，采用ANSYS软件，建立氧化后的微观尺度的单胞模型，如图4所示。其中假设氧化为均匀贯穿式氧化，氧化后纤维各处半径相等。(2) Based on the oxidation kinetic model in the above step (1), ie formulas (6) and (7), use ANSYS software to establish a micro-scale unit cell model after oxidation, as shown in FIG. 4 . It is assumed that the oxidation is uniform through-type oxidation, and the radii of the fibers after oxidation are equal.
(3)，施加微观尺度的单胞模型的周期性边界条件：所施加的边界条件满足位移的连续性和在微观尺度的单胞模型相反两个平面应力分布的一致性，如图5所示；所施加的周期性边界条件如表2所示。(3), applying the periodic boundary conditions of the micro-scale unit cell model: the imposed boundary conditions satisfy the continuity of the displacement and the consistency of the two plane stress distributions opposite to the micro-scale unit cell model, as shown in Figure 5 ; The periodic boundary conditions imposed are shown in Table 2.
表2Table 2
表中：S(x-,y,z)、S(x+,y,z)分别为x方向坐标最小和最大的两个平面，S(x,y-,z)、S(x,y+,z)分别为y方向坐标最小和最大的两个平面，S(x,y,z-)、S(x,y,z+)分别为z方向坐标最小和最大的两个平面。ux、uy、uz分别为x、y、z方向的位移约束，const表示平面内所有节点位移耦合。In the table: S(x - ,y,z), S(x + ,y,z) are the two planes with the smallest and largest coordinates in the x direction respectively, S(x,y - ,z), S(x,y + ,z) are the two planes with the smallest and largest coordinates in the y direction, respectively, and S(x,y,z - ), S(x,y,z + ) are the two planes with the smallest and largest coordinates in the z direction, respectively. u x , u y , and u z are the displacement constraints in the x, y, and z directions respectively, and const represents the displacement coupling of all nodes in the plane.
(4)，计算该单胞模型6个方向的弹性参数，6个方向的弹性参数包括x、y、z三个方向的弹性模量Ex、Ey、Ez，xy、xz、yz三个方向的剪切模量Gxy、Gxz、Gyz，以及泊松比vxy、vxz、vyz。(4), calculate the elastic parameters of the unit cell model in 6 directions, the elastic parameters in the 6 directions include the elastic modulus E x , E y , E z in the three directions of x, y, and z, and the three directions of xy, xz, and yz Shear moduli G xy , G xz , G yz in three directions, and Poisson's ratios v xy , v xz , v yz .
(5)，采用ANSYS软件，建立二维编织陶瓷基复合材料单胞模型，如图6所示；模型的尺寸参数如表3所示。(5) Using ANSYS software to establish a two-dimensional braided ceramic matrix composite unit cell model, as shown in Figure 6; the size parameters of the model are shown in Table 3.
表3table 3
其中，a为纱线宽度，b为同向纱线间间距，hf为纱线厚度，hb为基体层厚度。Among them, a is the yarn width, b is the spacing between yarns in the same direction, h f is the yarn thickness, and h b is the thickness of the base layer.
(6)，将计算得到的氧化后微观尺度的单胞模型6个方向的弹性参数作为纱线的基本属性，带入二维编织陶瓷基复合材料单胞模型；(6), the calculated elastic parameters of the oxidized micro-scale unit cell model in 6 directions are used as the basic properties of the yarn, and brought into the two-dimensional braided ceramic matrix composite material unit cell model;
(7)，施加二维编织陶瓷基复合材料单胞模型的周期性边界条件，如图7所示，其表达式为：(7), apply the periodic boundary condition of the unit cell model of the two-dimensional braided ceramic matrix composite material, as shown in Figure 7, and its expression is:
其中，Z+和Z-分别表示垂直于Z轴的两个相反的边界表面，为在Z+边界表面上的位移，为在Z-边界表面上的位移，xi Z+为Z+表面上节点的位移量，xi Z-为Z-表面上节点的位移量，为在边界表面上位移的周期性部分，θi为周期性结构的平均应变张量。where Z+ and Z- represent two opposite boundary surfaces perpendicular to the Z axis, respectively, is the displacement on the Z+ boundary surface, is the displacement on the Z-boundary surface, x i Z+ is the displacement of the nodes on the Z+ surface, x i Z- is the displacement of the nodes on the Z- surface, is the periodic part of the displacement on the boundary surface, and θi is the average strain tensor of the periodic structure.
Z+和Z-两个边界面之间的相对位移量表示为：The relative displacement between Z+ and Z- two boundary surfaces is expressed as:
其中，表示Z+和Z-两个边界面上节点的位移改变量。in, Indicates the displacement change of nodes on the two boundary surfaces of Z+ and Z-.
(8)，根据公式EL为材料的轴向弹性模量，σm为单元轴向平均应力，εm为单元轴向平均应变，即可计算得到二维平纹编织C/SiC复合材料轴向的剩余弹性模量。(8), according to the formula E L is the axial elastic modulus of the material, σ m is the unit axial average stress, and ε m is the unit axial average strain, and the residual elastic modulus in the axial direction of the two-dimensional plain weave C/SiC composite can be calculated.
图9给出了700℃环境温度下二维平纹编织C/SiC复合材料轴向的剩余弹性模量预测值与的实验值的对比曲线。图10给出了800℃环境温度下二维平纹编织C/SiC复合材料轴向的剩余弹性模量预测值与的实验值的对比曲线。图11给出了850℃环境温度下二维平纹编织C/SiC复合材料轴向的剩余弹性模量预测值与的实验值的对比曲线。图12给出了900℃环境温度下二维平纹编织C/SiC复合材料轴向的剩余弹性模量预测值与的实验值的对比曲线。通过对比可见，本发明的方法能够有效预测二维编织陶瓷基复合材料氧化后的剩余刚度。Figure 9 shows the comparison curve of the predicted value and the experimental value of the residual elastic modulus in the axial direction of the two-dimensional plain weave C/SiC composite material at an ambient temperature of 700 °C. Figure 10 shows the comparison curve of the predicted value and the experimental value of the axial residual elastic modulus of the two-dimensional plain weave C/SiC composite material at an ambient temperature of 800 °C. Figure 11 shows the comparison curve between the predicted value and the experimental value of the residual elastic modulus in the axial direction of the two-dimensional plain weave C/SiC composite material at an ambient temperature of 850 °C. Figure 12 shows the comparison curve between the predicted value and the experimental value of the axial residual elastic modulus of the two-dimensional plain weave C/SiC composite material at an ambient temperature of 900 °C. It can be seen from the comparison that the method of the present invention can effectively predict the residual stiffness of the two-dimensional braided ceramic matrix composite after oxidation.
以上所述仅是本发明的优选实施方式，应当指出，对于本技术领域的普通技术人员来说，在不脱离本发明原理的前提下，还可以做出若干改进和润饰，这些改进和润饰也应视为本发明的保护范围。The above is only a preferred embodiment of the present invention, it should be pointed out that, for those of ordinary skill in the art, without departing from the principle of the present invention, some improvements and modifications can also be made, and these improvements and modifications can also be made. It should be regarded as the protection scope of the present invention.
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