WO2022037305A1 - 一种陶瓷基复合材料铺层预制体优化设计方法 - Google Patents

一种陶瓷基复合材料铺层预制体优化设计方法 Download PDF

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WO2022037305A1
WO2022037305A1 PCT/CN2021/105170 CN2021105170W WO2022037305A1 WO 2022037305 A1 WO2022037305 A1 WO 2022037305A1 CN 2021105170 W CN2021105170 W CN 2021105170W WO 2022037305 A1 WO2022037305 A1 WO 2022037305A1
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stress
composite material
ceramic matrix
finite element
fiber
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PCT/CN2021/105170
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French (fr)
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高希光
刘晨阳
宋迎东
张盛
董洪年
于国强
董成乾
尤超
张禄
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南京航空航天大学
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Priority to US17/603,281 priority Critical patent/US20220309213A1/en
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/10—Numerical modelling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2113/00—Details relating to the application field
    • G06F2113/26—Composites
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

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  • the invention belongs to the field of ceramic matrix composite material design, in particular to an optimization design method for a ceramic matrix composite material layup preform.
  • Ceramic matrix composite material is a kind of advanced composite material which is made of ceramic as matrix and compounded with various fibers. Its density is only 1/3 to 1/4 of that of superalloy. material of choice. However, the ceramic matrix composite is a typical heterogeneous anisotropic multiphase material, and its preform structure has a great influence on the macroscopic mechanical properties. If the prefab structure is designed unreasonably, it will not only fail to give full play to the optimal performance of the material, but also fail to meet the most basic design requirements.
  • the present invention provides an optimization design method for a prefabricated layer of a ceramic matrix composite material, so as to realize the optimization of the mesoscopic structure of the layer and the optimization of the fiber volume fraction of the layer and the direction of the fibers in the layer, Take full advantage of material properties.
  • the present invention adopts the following technical solutions:
  • a ceramic matrix composite material layup prefab optimization design method comprising the following steps:
  • Step 1 Based on the strength analysis results of the macroscopic model of the ceramic matrix composite member, a preliminary design scheme for the prefabricated structure of the laminate is established;
  • Step 2 perform finite element strength analysis on the prefabricated layer structure in step 1, and obtain the corresponding first principal stress, normal stress and shear stress of each finite element element;
  • Step 3 Calculate the angle between the first principal stress of each finite element element and the reference Cartesian coordinate system according to the stress result obtained in Step 2;
  • Step 4 Using the included angle information of each finite element element obtained in step 3, change the element coordinate system of each finite element element, so that the material principal direction of each finite element element is consistent with the first principal stress direction;
  • Step 5 Calculate the material parameter data of each finite element element using the composite material mixing law
  • Step 6 According to the material parameter data of each finite element element obtained in step 5, the strength analysis of the layered prefabricated body structure in step 1 is performed again, and if the strength requirements are not met, return to step 1 to redesign the layered prefabricated body structure;
  • Step 7 According to the transverse strength calculation formula of the composite material mixing law, combined with the strength analysis results obtained in Step 6, select the appropriate meso-structure type for each layup.
  • the finite element strength analysis is performed on the macroscopic model of the ceramic matrix composite material, the unit position information of the stress distribution boundary region is extracted, and the information is imported into the macroscopic model and reflected.
  • the material components carry out the preliminary design of the prefabricated structure.
  • the corresponding first principal stress ⁇ 1 , normal stress ⁇ x and ⁇ y , shear stress ⁇ yx , ⁇ zx and ⁇ zy , ⁇ x and ⁇ y respectively represent X Normal stress in the direction of axis and Y axis
  • ⁇ yx represents the shear stress in the direction perpendicular to the Y axis and parallel to the X axis
  • ⁇ zx represents the shear stress in the direction perpendicular to the Z axis and parallel to the X axis
  • ⁇ zy represents the direction perpendicular to the Z axis and parallel to the axis
  • X, Y, and Z are the three coordinate axes of the reference rectangular coordinate system, respectively.
  • step 3 the following one-point stress state formula is used to obtain the angle between the first principal stress direction of each finite element element and the three-coordinate axis of the reference rectangular coordinate system:
  • l 1 , m 1 and n 1 are the angles between the first principal stress and the X, Y, and Z axes of the reference coordinate system, respectively.
  • V f is the fiber volume fraction
  • ⁇ 1 is the first principal stress
  • ⁇ f is the maximum stress borne by the reinforcing fibers
  • ⁇ m is the maximum stress borne by the matrix
  • E 1 , E 2 , and E 3 are the elastic moduli of the composite material in the three directions of 1, 2, and 3, the 1 direction is the fiber reinforcement direction, and the 2nd and 3 directions are the two directions perpendicular to the fiber reinforcement direction, E f is the elastic modulus of the reinforcing fiber, and E m is the elastic modulus of the matrix;
  • v 12 , v 13 , and v 23 are the three-direction Poisson’s ratios of the composite material
  • v 12 represents the compressive (tensile) strain in two directions caused by unit tensile (compressive) strain in one direction
  • v 13 represents the compressive (tensile) strain in one direction.
  • v 23 represents the compressive (tensile) strain in 3 directions caused by unit tensile (compressive) strain in 2 directions
  • v f is the Poisson’s ratio of reinforcing fibers
  • vm is the matrix Poisson’s ratio
  • G 12 , G 13 , and G 23 are the three-direction shear modulus of the composite material, representing the ratio of shear stress to shear strain in the 1-2 direction, the 1-3 direction, and the 2-3 direction, respectively, and G f is the reinforcement Fiber shear modulus, G m is the matrix shear modulus, G f23 is the shear modulus of the reinforcing fiber in the 2-3 direction;
  • ⁇ 2 ⁇ m [1-2(V f / ⁇ ) 1/2 ]
  • ⁇ 2 is the transverse strength and ⁇ m is the matrix strength.
  • the types of mesostructures include unidirectional reinforced structure, plain weave structure and three-dimensional weave structure.
  • the layered prefab structure of the present invention is designed based on the actual stress of the ceramic matrix composite component, and the design scheme can effectively improve the bearing capacity of the component;
  • the present invention optimizes different mesostructures, optimizes the fiber volume fraction and fiber direction according to the stress conditions of different parts of the ceramic matrix composite material, and can give full play to the performance of the ceramic matrix composite material. ;
  • the optimization method provided by the present invention is suitable for the optimization design of various ceramic matrix composite components.
  • Fig. 1 is the flow chart of the optimized design scheme of the prefabricated layer
  • Fig. 2 is the position distribution diagram of the stress boundary element in the turbine rotor blade airfoil
  • FIG. 3 is a schematic diagram of a design scheme of a prefabricated body of a turbine rotor blade blade body layup.
  • the optimization design method of the prefabricated layer includes the following steps:
  • Step 1 Establish a preliminary design scheme based on the strength analysis results of the macroscopic model of the ceramic matrix composite member.
  • the finite element strength analysis is carried out on the macroscopic model of the ceramic matrix composite component, the unit position information of the stress distribution boundary area is extracted, and the information is reflected in the component model, and the preliminary design of the prefabricated structure of the component is carried out.
  • Step 2 Extract the stress results after the finite element analysis. Perform finite element strength analysis on the prefabricated model of the component layer designed in step 1, and obtain the corresponding first principal stress ⁇ 1 , normal stress ⁇ x and ⁇ y , shear stress ⁇ yx , ⁇ zx and ⁇ corresponding to each finite element element zy .
  • Step 3 Obtain the angle between the first principal stress of each finite element element and the reference coordinate system.
  • the one-point stress state formula (where l 1 , m 1 and n 1 are the angles between the first principal stress and the X, Y, and Z axes of the reference coordinate system, respectively)
  • the first principal stress direction of each finite element element and the reference rectangular coordinate system are obtained.
  • Step 4 In the finite element software, the main direction of the material changes with the element coordinate system. Using the angle information of each finite element element obtained in step 3, the element coordinate system of each finite element element is changed, so that the principal direction of the material of each element is consistent with the first principal stress direction.
  • Step 5 The bearing strength of the composite material considered by this method refers to the maximum stress that the fiber and the matrix can bear when bearing simultaneously.
  • the volume of each finite element unit can be obtained by using the composite material mixing law Fraction (fiber volume fraction). The effect of volume fraction on other material parameters can also be derived from the composite mixing law.
  • V f is the fiber volume fraction
  • ⁇ 1 is the first principal stress
  • ⁇ f is the maximum stress borne by the reinforcing fibers
  • ⁇ m is the maximum stress borne by the matrix
  • E 1 , E 2 , and E 3 are the elastic moduli of the composite material in the three directions of 1, 2, and 3, the 1 direction is the fiber reinforcement direction, and the 2nd and 3 directions are the two directions perpendicular to the fiber reinforcement direction, E f is the elastic modulus of the reinforcing fiber, and E m is the elastic modulus of the matrix.
  • v 12 , v 13 , and v 23 are the three-direction Poisson’s ratio of the composite material, v f is the Poisson’s ratio of the reinforcing fiber, and v m is the matrix Poisson’s ratio;
  • G 12 , G 13 , and G 23 are the three-direction shear modulus of the composite material, G f is the shear modulus of the reinforcing fiber, G m is the matrix shear modulus, and G f23 is the 2-3 direction of the reinforcing fiber. shear modulus;
  • ⁇ 2 ⁇ m [1-2(V f / ⁇ ) 1/2 ]
  • ⁇ 2 is the transverse strength
  • ⁇ m is the matrix strength
  • the transverse strength is perpendicular to the reinforcement direction.
  • Step 6 According to the new material parameter data of each finite element element obtained in step 5, the strength analysis of the prefabricated structure of the ceramic matrix composite material in step 1 is carried out again. Layer prefab structures are designed.
  • Step 7 Determine the final optimized design scheme.
  • the mesostructure of composite materials includes unidirectional reinforced structure, plain weave structure and three-dimensional weave structure.
  • the unidirectional reinforcement structure has only one reinforcement direction, and the strength is weak in the other two directions;
  • the plain weave structure has two reinforcement directions, and the strength along the thickness direction is weak;
  • the three-dimensional weave structure has excellent mechanical properties in three directions.
  • the transverse strength calculation formula of the composite material mixing law analyze the calculation results obtained in step 6, and select the appropriate mesostructure type (unidirectional reinforcement, plain weave and three-dimensional weave) for each layup to meet the strength requirements. So far, the macroscopic appearance of each layup of the component prefab, the optimized mesostructure type of each layup, the optimized layup fiber volume fraction and the fiber direction (first principal stress direction) in the layup are given.
  • the layered prefab structure is made of SiC fiber cloth.
  • the turbine rotor blade first uses the finite element analysis software to analyze the strength of the ceramic-based turbine rotor blade macro model, extract the coordinates of the stress boundary points, and import these points into the blade.
  • the macro model and reflected in the component model, as shown in Figure 2.
  • the airfoil can be divided into three parts: the middle leaf, the leaf basin and the leaf back.
  • the layering scheme of each part is refined, and finally the airfoil structure is obtained.
  • the layered prefab structure of the airfoil part is composed of 14 SiC fiber cloths of different shapes stacked.
  • the angle between the first principal stress direction of each finite element element and the three-coordinate axis of the reference rectangular coordinate system is obtained.
  • the elastic moduli in three directions are defined when defining the material parameters of the silicon carbide fiber, and the one with the largest moduli is the main direction of the material.
  • the main direction of the material in each finite element element changes with the change of the direction of the coordinate axis of the element coordinate system.
  • the main direction of the material of the element can be changed by changing the direction of the coordinate axis of the element coordinate system, and the element coordinate system can be established by establishing a local coordinate system. to change.
  • the local coordinate system is established by rotating the X, Y, and Z axes of the reference coordinate system in turn. Therefore, it is necessary to know the three angles between the main direction of each element and the overall coordinate system. Based on this method, the optimization of fiber orientation is realized.
  • step 7 the optimization of the mesoscopic structure of each layup is completed, and the optimized design scheme of the final airfoil layup prefabricated body structure is obtained.
  • the layers 1-4 adopt the plain weave structure
  • the layers 5-8 adopt the unidirectional reinforcement structure
  • the layers 1-6 adopt the unidirectional reinforcement structure
  • the inner fiber volume fractions were 10.4%, 10.0%, 8.5%, 8.1%, 5.0% and 6.8%, respectively, and the inner fiber volume fractions of layers 7-14 were all 5.0%.

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Abstract

一种陶瓷基复合材料铺层预制体优化设计方法，综合考虑了构件强度要求、几何外形及铺层预制体特性，基于相应力学公式对组成预制体的各铺层纤维体积分数、铺层内纤维方向进行了优化，进而优选出了各铺层细观结构，实现了充分发挥材料性能的目的，适用于多种陶瓷基复合材料构件的优化设计。

Description

一种陶瓷基复合材料铺层预制体优化设计方法
本申请要求于2020年08月20日提交中国专利局、申请号为CN202010846564.2、发明名称为“一种陶瓷基复合材料铺层预制体优化设计方法”的中国专利申请的优先权，其全部内容通过引用结合在本申请中。
技术领域
本发明属于陶瓷基复合材料设计领域，具体涉及一种陶瓷基复合材料铺层预制体优化设计方法。
背景技术
陶瓷基复合材料是以陶瓷作为基体并与多种纤维复合而成的一类先进复合材料，其密度仅为高温合金的1/3～1/4，是应用于高推重比航空发动机热端部件的首选材料。然而，陶瓷基复合材料是一种典型的非均质各向异性多相材料，其预制体结构对宏观力学性能的影响很大。若预制体结构设计得不合理，不仅无法发挥材料的最优性能，甚至不能满足最基本的设计要求。
现有技术只是对构件宏观外形进行了适应陶瓷基复合材料特性的修改，仅考虑了如何利用增强纤维成型为所需要的宏观结构，而并未对预制体结构进行优化。如中国专利CN201711371076.5《一种陶瓷基复合材料涡轮转子叶片》，该发明虽然考虑了很多宏观的封严结构，但并没有叶身核心预制体结构的详细设计方案；又如中国专利CN201810612357.3《一种陶瓷基涡轮转子叶片预制体的设计方法》，该方法虽然给出了一种涡轮转子叶片的铺层预制体设计方案，但该方案并未给出各铺层的纤维体积分数以及铺层内纤维方向，未能充分发挥纤维性能。
因此，如何在最初的设计过程中对陶瓷基复合材料铺层预制体结构进行优化，充分发挥陶瓷基复合材料性能，是本技术领域一项重要且难以解决的关键技术。
发明内容
本发明针对现有技术中的不足，提供一种陶瓷基复合材料铺层预制体优化设计方法，以实现对铺层细观结构的优选以及铺层纤维体积分数、铺层内纤维方向的优化，充分发挥材料性能。
为实现上述目的，本发明采用以下技术方案：
一种陶瓷基复合材料铺层预制体优化设计方法，包括如下步骤：
步骤1：基于陶瓷基复合材料构件宏观模型的强度分析结果，建立铺层预制体结构的初步设计方案；
步骤2：对步骤1的铺层预制体结构进行有限元强度分析，得到各个有限元单元相应的第一主应力、正应力和切应力；
步骤3：根据步骤2得到的应力结果，计算各个有限元单元第一主应力与基准直角坐标系的夹角；
步骤4：利用步骤3中得到的各个有限元单元的夹角信息，改变各个有限元单元的单元坐标系，使得各个有限元单元的材料主方向与第一主应力方向一致；
步骤5：利用复合材料混合定律计算各个有限元单元的材料参数数据；
步骤6：根据步骤5得到的各个有限元单元的材料参数数据，对步骤1的铺层预制体结构再次进行强度分析，若不满足强度要求则返回步骤1重新对铺层预制体结构进行设计；
步骤7：根据复合材料混合定律的横向强度计算公式，结合步骤6得到的强度分析结果，选择各铺层适宜的细观结构类型。
为优化上述技术方案，采取的具体措施还包括：
进一步地，所述步骤1中，对陶瓷基复合材料构件宏观模型进行有限元强度分析，提取应力分布边界区域的单元位置信息，将该信息导入宏观模型中并进行体现，据此对陶瓷基复合材料构件进行铺层预制体结构的初步设计。
进一步地，所述步骤2中，得到各个有限元单元相应的第一主应力σ 1，正应力σ x和σ y，切应力τ yx、τ zx和τ zy，σ x、σ y分别表示X轴和Y轴方向的正应力，τ yx表示方向垂直于Y轴平行于X轴的切应力，τ zx表示方向 垂直于Z轴平行于X轴的切应力，τ zy表示方向垂直于Z轴平行于Y轴的切应力，X、Y、Z分别为基准直角坐标系的三个坐标轴。
进一步地，所述步骤3中，利用如下的一点应力状态公式得到各个有限元单元第一主应力方向与基准直角坐标系三坐标轴夹角：
l 1(σ x-σ 1)+m 1τ yx+n 1τ zx＝0
l 1τ xy+m 1(σ y-σ 1)+n 1τ zy＝0
Figure PCTCN2021105170-appb-000001
Figure PCTCN2021105170-appb-000002
Figure PCTCN2021105170-appb-000003
式中，l 1、m 1和n 1分别为第一主应力与基准坐标系X、Y、Z轴夹角。
进一步地，所述步骤5中，在已知第一主应力、纤维强度和基体强度的前提下，利用如下的复合材料混合定律得到各个有限元单元的材料参数数据：
纤维体积分数：
Figure PCTCN2021105170-appb-000004
式中，V f为纤维体积分数，σ 1为第一主应力，σ f为增强纤维承载的最大应力，σ m为基体承载的最大应力；
弹性模量：
E 1＝E fV f+E m(1-V f)
Figure PCTCN2021105170-appb-000005
式中，E 1、E 2、E 3为复合材料在1、2、3三方向弹性模量，1方向为纤维增强方向，2、3方向为垂直于纤维增强方向的两个方向，E f为增强纤维弹性模量，E m为基体弹性模量；
泊松比：
v 12＝v 13＝v fV f+v m(1-V f)
Figure PCTCN2021105170-appb-000006
式中，v 12、v 13、v 23为复合材料三方向泊松比，v 12表示1方向的单位拉(压)应变所引起的2方向的压(拉)应变，v 13表示1方向的单位拉(压)应变所引起的3方向的压(拉)应变，v 23表示2方向的单位拉(压)应变所引起的3方向的压(拉)应变，v f为增强纤维泊松比，v m为基体泊松比；
剪切模量：
Figure PCTCN2021105170-appb-000007
Figure PCTCN2021105170-appb-000008
式中，G 12、G 13、G 23为复合材料三方向剪切模量，分别表示1-2方向、1-3方向、2-3方向的切应力与切应变之比，G f为增强纤维剪切模量，G m为基体剪切模量，G f23为增强纤维2-3方向的剪切模量；
横向强度：
σ 2＝σ m[1-2(V f/π) 1/2]
式中，σ 2为横向强度，σ m为基体强度。
进一步地，所述步骤7中，细观结构类型包括单向增强结构、平纹编织结构和三维编织结构。
本发明的有益效果是：
1、本发明的铺层预制体结构是基于陶瓷基复合材料构件实际受力情况进行设计的，该设计方案能有效提高构件承载能力；
2、与现有技术相比，本发明针对陶瓷基复合材料构件不同部位的受力情况优选了不同的细观结构、优化了纤维体积分数和纤维方向，更能充分发挥陶瓷基复合材料的性能；
3、本发明提供的优化方法适用于多种陶瓷基复合材料构件的优化设计。
附图说明
图1是铺层预制体优化设计方案流程图；
图2是应力边界单元在涡轮转子叶片叶身部位的位置分布图；
图3是涡轮转子叶片叶身铺层预制体设计方案示意图。
具体实施方式
现在结合附图对本发明作进一步详细的说明。
如图1所示的铺层预制体优化设计方法，具体包括如下步骤：
步骤1：基于陶瓷基复合材料构件宏观模型的强度分析结果建立初步设计方案。对陶瓷基复合材料构件宏观模型进行有限元强度分析，提取应力分布边界区域的单元位置信息，将该信息体现在构件模型中，对构件进行铺层预制体结构的初步设计。
步骤2：提取有限元分析后的应力结果。对步骤1中设计好的构件铺层预制体模型进行有限元强度分析，得到各个有限元单元相应的第一主应力σ 1，正应力σ x和σ y，切应力τ yx、τ zx和τ zy。
步骤3：得到各个有限元单元第一主应力与基准坐标系夹角。利用一点应力状态公式(式中l 1、m 1和n 1分别为第一主应力与基准坐标系X、Y、Z轴夹角)得到各个有限元单元第一主应力方向与基准直角坐标系三坐标轴夹角：
l 1(σ x-σ 1)+m 1τ yx+n 1τ zx＝0
l 1τ xy+m 1(σ y-σ 1)+n 1τ zy＝0
Figure PCTCN2021105170-appb-000009
Figure PCTCN2021105170-appb-000010
Figure PCTCN2021105170-appb-000011
步骤4：在有限元软件中，材料主方向随单元坐标系发生改变。利用步骤3中得到的各个有限元单元的夹角信息，改变各个有限元单元的单元坐标系，使得各单元材料主方向与第一主应力方向一致。
步骤5：本方法所考虑的复合材料承载强度指纤维和基体同时承载时所能承受的最大应力。在已知第一主应力、纤维强度σ f(即增强纤维承载的最大应力)和基体强度σ m(即基体承载的最大应力)的前提下，利用复合材料混合定律可得到各个有限元单元体积分数(纤维体积分数)。体积分数对其他材料参数的影响亦可由复合材料混合定律得出。
纤维体积分数：
Figure PCTCN2021105170-appb-000012
式中，V f为纤维体积分数，σ 1为第一主应力，σ f为增强纤维承载的最大应力，σ m为基体承载的最大应力；
弹性模量：
E 1＝E fV f+E m(1-V f)
Figure PCTCN2021105170-appb-000013
式中，E 1、E 2、E 3为复合材料在1、2、3三方向弹性模量，1方向为纤维增强方向，2、3方向为垂直于纤维增强方向的两个方向，E f为增强纤维弹性模量，E m为基体弹性模量。
泊松比：
v 12＝v 13＝v fV f+v m(1-V f)
Figure PCTCN2021105170-appb-000014
式中，v 12、v 13、v 23为复合材料三方向泊松比，v f为增强纤维泊松比，v m为基体泊松比；
剪切模量：
Figure PCTCN2021105170-appb-000015
Figure PCTCN2021105170-appb-000016
式中，G 12、G 13、G 23为复合材料三方向剪切模量，G f为增强纤维剪切模量，G m为基体剪切模量，G f23为增强纤维2-3方向的剪切模量；
横向强度：
σ 2＝σ m[1-2(V f/π) 1/2]
式中，σ 2为横向强度，σ m为基体强度，横向强度垂直于增强方向。
步骤6：根据步骤5得到的各个有限元单元新的材料参数数据，对步骤1中的陶瓷基复合材料构件铺层预制体结构再次进行强度分析，若不满足强度要求则返回步骤1重新对铺层预制体结构进行设计。
步骤7：确定最终的优化设计方案。复合材料细观结构包括单向增强结构、平纹编织结构和三维编织结构。单向增强结构只有一个增强方向，另两个方向强度较弱；平纹编织结构则有两个增强方向，沿厚度方向强度较弱；三维编织结构在三个方向的力学性能都很优异。根据复合材料混合定律的横向强度计算公式，分析步骤6得到的计算结果，选择各铺层适宜的细观结构类型(单向增强、平纹编织及三维编织)以满足强度要求。至此，给出了构件预制体各铺层宏观外形、优选了各铺层细观结构类型、优化了铺层纤维体积分数以及铺层内纤维方向(第一主应力方向)。
接下来，以某型航空发动机涡轮转子叶片这一复杂构件为例对本方法进行阐述，重点展示其叶身部分的铺层预制体优化结果，具体包括如下内容：
(1)铺层预制体结构由SiC纤维布堆叠而成，涡轮转子叶片首先利用有限元分析软件对该陶瓷基涡轮转子叶片宏观模型进行强度分析，提取 应力边界点坐标，并将这些点导入叶片宏观模型中，并在构件模型中体现，如图2所示。综合叶身几何外形和导入的一系列应力边界点坐标，发现可将叶身分为叶中、叶盆和叶背三部分。随后，根据单层SiC纤维布的厚度，细化出各部分铺层方案，最终得到叶身结构。如图3所示，叶身部分的铺层预制体结构由14个不同形状的SiC纤维布堆叠而成。
(2)利用有限元分析软件对(1)中设计好的叶身铺层预制体结构进行强度分析，得到各个有限元单元相应的第一主应力σ 1，正应力σ x和σ y，切应力τ yx、τ zx和τ zy。
(3)利用步骤3中的一点内应力状态公式得到各个有限元单元第一主应力方向与基准直角坐标系三坐标轴夹角。在有限元分析软件中，在定义碳化硅纤维材料参数时定义了三个方向的弹性模量，其中模量最大的为材料主方向。各个有限元单元内的材料主方向随单元坐标系坐标轴方向的改变而改变，可以通过改变单元坐标系坐标轴方向的方式来改变该单元材料主方向，而单元坐标系可通过建立局部坐标系来改变。在有限元分析软件中，局部坐标系是通过对基准坐标系依次转动X、Y、Z轴建立的，因此需要知道各个单元的主方向与总体坐标系的三个夹角。基于此方法实现对纤维方向的优化。
(4)利用步骤5复合材料混合定律公式对(3)中纤维优化后的叶身铺层预制体结构进行最佳体积分数的确定以及相应材料参数的修改。
(5)对(4)中体积分数优化后的方案再次进行强度分析，满足强度要求进行下一步，不满足返回(1)。
(6)按照步骤7完成各铺层细观结构的优选，得到最终叶身铺层预制体结构优化设计方案。如图3所示，对叶身构件的铺层预制体初步设计方案优化后，1-4号铺层采用平纹编织结构，5-8号铺层采用单向增强结构；1-6号铺层内纤维体积分数分别为10.4％、10.0％、8.5％、8.1％、5.0％和6.8％，7-14号铺层内纤维体积分数均为5.0％。
以上仅是本发明的优选实施方式，本发明的保护范围并不仅局限于上述实施例，凡属于本发明思路下的技术方案均属于本发明的保护范围。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前提下的若干改进和润饰，应视为本发明的保护范围。

Claims (9)

  1. 一种陶瓷基复合材料铺层预制体优化设计方法，其特征在于，包括如下步骤：
    步骤1：基于陶瓷基复合材料构件宏观模型的强度分析结果，建立铺层预制体结构的初步设计方案；
    步骤2：对步骤1的铺层预制体结构进行有限元强度分析，得到各个有限元单元相应的第一主应力、正应力和切应力；
    步骤3：根据步骤2得到的应力结果，计算各个有限元单元第一主应力与基准直角坐标系的夹角；
    步骤4：利用步骤3中得到的各个有限元单元的夹角信息，改变各个有限元单元的单元坐标系，使得各个有限元单元的材料主方向与第一主应力方向一致；
    步骤5：利用复合材料混合定律计算各个有限元单元的材料参数数据；
    步骤6：根据步骤5得到的各个有限元单元的材料参数数据，对步骤1的铺层预制体结构再次进行强度分析，若不满足强度要求则返回步骤1重新对铺层预制体结构进行设计；
    步骤7：根据复合材料混合定律的横向强度计算公式，结合步骤6得到的强度分析结果，选择各铺层适宜的细观结构类型。
  2. 如权利要求1所述的一种陶瓷基复合材料铺层预制体优化设计方法，其特征在于：所述步骤1中，对陶瓷基复合材料构件宏观模型进行有限元强度分析，提取应力分布边界区域的单元位置信息，将该单元位置信息导入宏观模型中并进行体现，据此对陶瓷基复合材料构件进行铺层预制体结构的初步设计。
  3. 如权利要求1所述的一种陶瓷基复合材料铺层预制体优化设计方法，其特征在于：所述步骤2中，得到各个有限元单元相应的第一主应力σ 1，正应力σ x和σ y，切应力τ yx、τ zx和τ zy，σ x、σ y分别表示X轴和Y轴方向的正应力，τ yx表示方向垂直于Y轴平行于X轴的切应力，τ zx表示方向 垂直于Z轴平行于X轴的切应力，τ zy表示方向垂直于Z轴平行于Y轴的切应力，X、Y、Z分别为基准直角坐标系的三个坐标轴。
  4. 根据权利要求3所述的一种陶瓷基复合材料铺层预制体优化设计方法，其特征在于：所述步骤3中，所述夹角为各个有限元单元第一主应力方向与基准直角坐标系三坐标轴夹角。
  5. 如权利要求3或4所述的一种陶瓷基复合材料铺层预制体优化设计方法，其特征在于：所述步骤3中，利用如下的一点应力状态公式得到各个有限元单元第一主应力方向与基准直角坐标系三坐标轴夹角：
    l 1(σ x-σ 1)+m 1τ yx+n 1τ zx＝0
    l 1τ xy+m 1(σ y-σ 1)+n 1τ zy＝0
    Figure PCTCN2021105170-appb-100001
    Figure PCTCN2021105170-appb-100002
    Figure PCTCN2021105170-appb-100003
    式中，l 1、m 1和n 1分别为第一主应力与基准坐标系X、Y、Z轴夹角。
  6. 如权利要求1所述的一种陶瓷基复合材料铺层预制体优化设计方法，其特征在于：所述步骤5中，所述材料参数数据为纤维体积分数、弹性模量、泊松比、剪切模量和横向强度。
  7. 如权利要求1或6所述的一种陶瓷基复合材料铺层预制体优化设计方法，其特征在于：所述步骤5中，在已知第一主应力、纤维强度和基体强度的前提下，利用如下的复合材料混合定律得到各个有限元单元的材料参数数据：
    纤维体积分数：
    Figure PCTCN2021105170-appb-100004
    式中，V f为纤维体积分数，σ 1为第一主应力，σ f为增强纤维承载的最大应力，σ m为基体承载的最大应力；
    弹性模量：
    E 1＝E fV f+E m(1-V f)
    Figure PCTCN2021105170-appb-100005
    式中，E 1、E 2、E 3为复合材料在1、2、3三方向弹性模量，1方向为纤维增强方向，2、3方向为垂直于纤维增强方向的两个方向，E f为增强纤维弹性模量，E m为基体弹性模量；
    泊松比：
    v 12＝v 13＝v fV f+v m(1-V f)
    Figure PCTCN2021105170-appb-100006
    式中，v 12、v 13、v 23为复合材料三方向泊松比，v 12表示1方向的单位应变所引起的2方向的应变，v 13表示1方向的单位应变所引起的3方向的应变，v 23表示2方向的单位应变所引起的3方向的应变，v f为增强纤维泊松比，v m为基体泊松比；
    剪切模量：
    Figure PCTCN2021105170-appb-100007
    Figure PCTCN2021105170-appb-100008
    式中，G 12、G 13、G 23为复合材料三方向剪切模量，分别表示1-2方向、1-3方向、2-3方向的切应力与切应变之比，G f为增强纤维剪切模量，G m为基体剪切模量，G f23为增强纤维2-3方向的剪切模量；
    横向强度：
    σ 2＝σ m[1-2(V f/π) 1/2]
    式中，σ 2为横向强度，σ m为基体强度。
  8. 如权利要求1所述的一种陶瓷基复合材料铺层预制体优化设计方法，其特征在于：所述步骤7中，细观结构类型包括单向增强结构、平纹编织结构和三维编织结构。
  9. 一种发动机涡轮转子叶片，其特征在于，所述发动机涡轮转子叶片的叶身的铺层预制体结构由SiC纤维布堆叠而成，所述叶身分为叶中、叶盆和叶背三部分，根据单层SiC纤维布的厚度，细化出各部分铺层方案，得到叶身结构；所述叶身的铺层预制体结构由14个不同形状的SiC纤维布堆叠而成，其中，1-4号铺层采用平纹编织结构，5-8号铺层采用单向增强结构；1-6号铺层内纤维体积分数分别为10.4％、10.0％、8.5％、8.1％、5.0％和6.8％，7-14号铺层内纤维体积分数均为5.0％。
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