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基于晶体微观有限元方法的多相复合涂层高温摩擦应力场模拟*

  • 黄啸1

    机 构：

    1. 中国矿业大学（北京）机电与信息工程学院 北京 100083

    ×
  • ， 翟傲霜1

    机 构：

    1. 中国矿业大学（北京）机电与信息工程学院 北京 100083

    ×
  • ， 张凤娇1

    机 构：

    1. 中国矿业大学（北京）机电与信息工程学院 北京 100083

    ×
  • ， 王俊煜1

    机 构：

    1. 中国矿业大学（北京）机电与信息工程学院 北京 100083

    ×
  • ， 邵天敏2

    机 构：

    2. 清华大学摩擦学国家重点实验室 北京 100084

    ×

1. 中国矿业大学（北京）机电与信息工程学院 北京 100083；
2. 清华大学摩擦学国家重点实验室 北京 100084；

Simulation of High Temperature Friction Stress Field of Multiphase Composite Coating Based on Crystal Microscopic Finite Element Method

  • HUANG Xiao1

    Affiliation：

    1. School of Mechanical Electronic & Information Engineering, China University of Mining & Technology, Beijing 100083 , China

    ×
  • ， ZHAI Aoshuang1

    Affiliation：

    1. School of Mechanical Electronic & Information Engineering, China University of Mining & Technology, Beijing 100083 , China

    ×
  • ， ZHANG Fengjiao1

    Affiliation：

    1. School of Mechanical Electronic & Information Engineering, China University of Mining & Technology, Beijing 100083 , China

    ×
  • ， WANG Junyu1

    Affiliation：

    1. School of Mechanical Electronic & Information Engineering, China University of Mining & Technology, Beijing 100083 , China

    ×
  • ， SHAO Tianmin2

    Affiliation：

    2. State Key Laboratory of Tribology, Tsinghua University, Beijing 100084 , China

    ×

1. School of Mechanical Electronic & Information Engineering, China University of Mining & Technology, Beijing 100083 , China；
2. State Key Laboratory of Tribology, Tsinghua University, Beijing 100084 , China；

作者简介:

黄啸,男,1988年出生,博士,讲师。主要研究方向为表面工程与应力模拟。E-mail:hx@cumtb.edu.cn;

翟傲霜,女,1994年出生,硕士。主要研究方向为表面工程与应力模拟。E-mail:aoshuangzz@qq.com;

邵天敏(通信作者),男,1963年出生,博士,教授,博士研究生导师。主要研究方向为摩擦学与表面工程。E-mail:shaotm@tsinghua.edu.cn

中图分类号:TG335;O242

DOI:10.11933/j.issn.1007−9289.20211106002

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目录contents

    摘要

    对高温摩擦磨损工况下多相复合涂层的热-力耦合应力场的模拟研究尚不充分。基于 Voronoi 多边形建立 NiCr-Cr3C2-CaF2 / BaF2多相复合涂层的晶体微观有限元模型，模拟复合涂层中各相的占比、分布形态和热-力学参数，求解得到热-力耦合工况下的 von Mises 应力和第一主应力分布。结果表明：在高温摩擦工况下，多相复合涂层的应力显著高于均匀涂层，尤其是在硬质相尖端附近易产生局部高应力区域，改善相的形态将锐角钝化能够有效缓解局部高应力现象；热-力耦合应力场与黏结相和硬质相的弹性模量密切相关，通过调节各相模量能够有效调控复合涂层的 Mises 应力和拉应力值。基于微观有限元方法的热-力耦合应力场模拟可为高温摩擦磨损工况下多相复合涂层的优化设计提供理论依据。

    Abstract

    Thermal sprayed NiCr-Cr3C2-CaF2 / BaF2 composite coatings can be used as high-temperature wear-resistant material for aeroengine brush seal runway. High temperature friction and wear produces a coupling stress field formed by the superposition of thermal stress and friction stress. At the same time, the morphology and properties of each phase in the composite coating will have a significant impact on the coupling stress field. The thermal-mechanical coupling stress field simulation study of multiphase composite coatings under high temperature friction and wear conditions is still insufficient. The coupling stress distribution is simulated by finite element method to predict the potential failure mode of the coating and provide a basis for the design of brush sealing coating. Based on Voronoi polygon, the crystal micro finite element model of NiCr-Cr3C2-CaF2/BaF2 multiphase composite coating is established. The proportion, distribution morphology and thermal-mechanical parameters of each phase in the composite coating is simulated, and the von Mises stress and the first principal stress distribution under thermal-mechanical coupled conditions is obtained. The results show that the stress of the composite coating is significantly higher than that of the uniform coating, especially at the tip of the hard phase. Improving the morphology of the phase and passivating the acute angle can effectively alleviate the local intense stress. At the same time, the thermal-mechanical coupling stress field is closely related to the elastic modulus of bonded phase and hard phase. Mises stress and tensile stress of composite coating can be effectively controlled by adjusting the modulus of each phase. The thermal-mechanical coupling stress field simulation based on the microscopic finite element method provides a theoretical basis for the optimal design of multiphase composite coatings under high temperature friction and wear conditions.

  • 0 前言

  • 航空发动机封严技术是提高发动机推力、降低油耗的重要保障，常见的航发封严技术有篦齿密封、刷式密封、指尖密封等。其中刷式密封是接触式密封的典型代表，具有泄漏量低、结构简单的特点，密封部件主要由刷丝、背板、前板、跑道等部分构成。刷式密封工作时刷丝在气压作用下与密封跑道滑动接触，长期摩擦将会引起跑道磨损，同时高温环境可能加速材料磨损。利用热喷涂技术制备耐高温、耐磨损涂层可以有效提升刷式密封跑道的磨损寿命[1-2]。在众多热喷涂材料中，NiCr-Cr3C2 是一种金属陶瓷复合材料，常用于制备高温耐磨涂层，使用温度可达900℃，具有良好的高温力学和耐磨性能，在航发刷式密封涂层中有潜在的应用前景[3-5]。 NiCr-Cr3C2涂层主要含硬质相Cr3C2和黏结相NiCr，为了降低摩擦还可添加少量Ag和CaF2/BaF2 共晶体作为润滑相[6]，在本文中用化学式NiCr-Cr3C2-CaF2/BaF2 代表由三种不同成分和结构材料组成的多相复合涂层。

  • 刷式密封跑道耐磨涂层在服役过程中由于摩擦作用会产生接触应力，同时还要承受高温所引发的热应力，上述热-力耦合应力场将显著强于常温时的摩擦应力场，从而加速涂层塑性变形和裂纹萌生、扩展，导致涂层失效[7-8]。已有文献报道采用有限元方法模拟涂层服役时的热-力耦合应力场分布特点，为涂层优化设计提供了理论依据[9-11]。但已有研究所针对涂层多为均匀涂层，所建立模型为均匀材料有限元模型，未考虑微观结构对热-力耦合应力场的作用机理和作用规律。近年来微观有限元方法在复合材料中得到了较为广泛的应用，微观有限元在常规有限元基础上构建多组分复合材料模型，用于研究复合材料各组分占比、形态、性能对服役性能的影响[12-13]。本文采用微观有限元方法，建立了NiCr-Cr3C2-CaF2/BaF2 复合涂层的晶体塑性有限元模型，模拟了热喷涂片状组织的晶体学特征，研究了相的形态和性能参数对热-力耦合应力场的作用规律，可为高温磨损环境下航发刷封涂层的优化设计提供依据。

  • 1 模拟方法

  • 1.1 微观有限元模型的建立

  • 近年来Voronoi多边形常用于晶体中晶粒大小和形态分布的建模[14-15]。Voronoi多边形内有唯一控制点，多边形内任一点与控制点距离最近，而与相邻多边形内控制点的距离较远。本文使用Neper插件建立了基于Voronoi多边形的复合涂层微观结构模型[16]。例如，图1a所示为NiCr-Cr3C2-CaF2/BaF2 热喷涂多相复合涂层的SEM图，如图1b所示为复合涂层模型，模型尺寸为200 μm×100 μm，共包括400个多边形，代表了400个热喷涂粉末颗粒，颗粒尺寸符合对数正态分布，平均尺寸为10 μm，尺寸分布方差为0.25 μm。由于热喷涂的冲击力可将熔融状态粉末撞击成扁平状，因此模型中热喷涂颗粒的长-短轴比设定为4∶1。使用Abaqus导入上述涂层模型并划分网格，对不同的颗粒赋予材料特性，根据试验工艺NiCr、Cr3C2、CaF2/BaF2三种颗粒的体积分数分别为40%、50%、10%，所得到有限元模型如图2所示，其中红色为黏结相NiCr，白色为硬质相Cr3C2，绿色为润滑相CaF2/BaF2。计算所用三种材料的常温力学性能和热膨胀系数如表1所示[17-21]。高温环境下材料的弹性模量通常会降低、热膨胀系数会升高，依据文献报道，本文采用温度每升高100℃， NiCr合金弹性模量下降2.4%、热膨胀系数增加2%的变化趋势作为NiCr黏结相的计算参数[18, 22]；而Cr3C2、 CaF2/BaF2陶瓷材料采用随温度每升高100℃弹性模量下降2%、热膨胀系数增大1%作为硬质相和润滑相的计算参数[23-24]。在建模时NiCr视为弹塑性材料，其屈服极限为960MPa[25]，将上述文献中的名义应力-应变曲线转化为真实应力-应变曲线作为NiCr合金塑性变形之后的后继屈服行为模拟参数，而将Cr3C2、 CaF2/BaF2 视为弹性材料。由于复合涂层有较多的尖角结构，网格划分采用三节点三角形单元。

  • 图1 复合涂层组织结构与Voronoi多边形模型

  • Fig.1 Microstructure of composite coating and Voronoi polygon model

  • 图2 复合涂层有限元模型 （红色：NiCr；白色：Cr3C2；绿色：CaF2/BaF2）

  • Fig.2 Finite element model of composite coating (red: NiCr; white: Cr3C2; green: CaF2/BaF2)

  • 表1 三种材料的常温力学性能和热膨胀系数

  • Table1 Mechanical properties and coefficient of thermal expansion of three materials

  • 1.2 高温摩擦的有限元模拟

  • 航发刷封跑道涂层服役温度可达800℃，由于复合涂层中各相材料之间的热膨胀系数差异，高温条件下涂层将产生内应力；与此同时刷丝在涂层表面的摩擦将产生接触应力，二者叠加为热-力耦合应力场。本文预设室温20℃时涂层的内应力为零，温度变化过程为涂层材料整体变化，即升温时涂层各部分温度同时上升，热应力由各相的热膨胀系数差异产生。所施加的接触载荷形式为上表面中心处的均布面载荷，载荷分布宽度为100 μm，以模拟刷丝的接触形式。施加的法向载荷为300MPa，切向载荷在0～180MPa，以模拟摩擦因数在0～0.6的变化。模型所采用边界条件为左右边界无横向位移，下边界无纵向位移，上表面为自由表面，在采用上述边界条件的情况下，施加接触力和温度场后，应力计算结果在边界附近未产生异常的应力集中或应力奇异的现象。热-力耦合模拟过程分两步完成，第一步为温度场的整体上升所导致的热应力，第二步为施加接触和摩擦力从而在热应力基础上产生耦合应力场。

  • 2 结果与讨论

  • 2.1 多相复合涂层接触应力场特点

  • 由于热-力耦合应力场是热应力和接触应力的叠加，为了揭示耦合应力场的特点和规律，本节仅施加接触载荷而未施加温度场，并对比研究均匀涂层与多相复合涂层的接触应力场特点。根据复合材料等效弹性模量Halpain-Tsai模型[26]，计算得到多相复合涂层的等效弹性模量约为268GPa，并假设均匀涂层的塑性力学行为与NiCr相一致。如图3a、 3b所示为等效均匀材料在300MPa载荷下，摩擦因数为0.2时（摩擦力方向从左向右）的von Mises应力和第一主应力分布。从图3a可以看出，在法向和切向载荷的共同作用下，接触区域右侧即摩擦前端的Mises应力强于摩擦后端，并且Mises应力峰值位置位于外表面，约为216.3MPa。从图3b可知最大拉应力位于接触区域后端的涂层表面，应力峰值约为107.9MPa。

  • 图3 均匀涂层摩擦应力分布

  • Fig.3 Friction stress distribution in uniform coating

  • 如图4a、4b所示为多相复合涂层在300MPa法向载荷、摩擦因数0.2作用下的Mises应力及第一主应力分布。复合涂层中Mises应力峰值约为500MPa，最大拉应力峰值约为277MPa，相比于均匀涂层增加了131%和157%。多相复合涂层中的应力分布不均匀，对照图4a中的应力分布与图2的相分布可知，Mises应力峰值位于接触区前端硬质相Cr3C2 颗粒的尖端，其中硬质相与润滑相交接处的尖端附近Mises应力强度显著增大，故推断在接触载荷作用下硬质相的尖端发生了局部区域应力增大现象。如图4b所示，拉应力主要位于接触区的后端表面，对照图2的相分布图可知，应力峰值位于Cr3C2 颗粒的尖端，这表明在多相复合涂层中主应力同样存在局部区域应力增大现象。在上述摩擦载荷作用下涂层未发生塑性变形。

  • 图4 复合涂层摩擦应力分布

  • Fig.4 Friction stress distribution of composite coatings

  • 如图5所示为摩擦因数在0～0.6变化时均匀涂层与复合涂层应力峰值的变化规律。可以看出随着摩擦因数增大，均匀涂层与复合涂层的应力峰值均增大，但复合涂层中的Mises应力和拉应力峰值增长斜率均高于均匀涂层。这表明多相复合涂层的应力对于外界载荷更加敏感，在涂层设计时有必要降低复合涂层中的应力值，防止局部应力增大现象的发生。摩擦因数在0～0.6变化时，复合涂层和均匀涂层均未发生塑性变形。

  • 2.2 多相复合涂层热应力场特点

  • 为了研究温度对复合涂层热应力的影响，在仅施加温度场的条件下，对比研究多相复合涂层与均匀涂层的热应力分布特点。根据等效介质理论[27]计算得到复合涂层等效热膨胀系数为11.3×10−6/℃，并假设均匀涂层热膨胀系数随温度每升高100℃ 而增大1%。由于均匀涂层热膨胀系数各处均匀一致，von Mises应力在涂层任意位置完全相同，其中200℃时von Mises应力为767.3MPa。同时在高温作用下均匀涂层各点发生等值膨胀，因此无拉应力产生，各点的第一主应力值均为0，上述结果如图6a、6b所示。

  • 图5 摩擦应力随摩擦因数变化趋势

  • Fig.5 Variation trend of friction stress with friction factor

  • 图6 均匀涂层中的热应力分布

  • Fig.6 Thermal stress distribution in homogeneous coatings

  • 多相复合涂层的热应力场与均匀涂层显著不同，如图7所示为200℃时多相复合涂层的Mises应力和第一主应力分布。从图中可知，多相复合涂层中的Mises应力峰值为1 994MPa，相比于均匀涂层增加了159.9%。对照图7a与图2的相分布可知， Mises热应力数值在润滑相中最低，在黏结相中其次，在硬质相中最高，尤其是在硬质相与润滑相交接处尖端附近应力显著增大，这是由于硬质相的热膨胀系数较小且弹性模量较大，与润滑相的性能差异显著，因此在硬质相尖端易产生应力增大区域。从图7b可知，最大拉应力约为946.3MPa，与Mises应力类似，拉应力主要分布在硬质相与润滑相的边界处，相比于Mises应力而言拉应力分布区域更广，在硬质相/润滑相边界附近广泛的区域存在拉应力影响区，而不局限于硬质相的尖端附近。

  • 图7 复合涂层热应力分布

  • Fig.7 Thermal stress distribution in composite coatings

  • 图8 所示为温度在200～800℃均匀涂层与复合涂层中应力变化趋势，随着温度的升高，复合涂层中的Mises应力和拉应力快速上升，表明复合涂层热应力对于温度较为敏感。根据图7中的应力分布可知复合涂层应力随温度快速上升的原因是，在硬质相附近产生了局部应力增大区域，由于Cr3C2 是脆性材料，难以发生塑性变形，进一步增大了应力值。在均匀NiCr涂层中，最大拉应力始终保持为0，这是因为均匀材料的热膨胀是均匀膨胀的，不会产生附加应力；均匀涂层中Mises应力随着温度升高几乎不变维持在1GPa以下，这是因为当Mises应力达到NiCr屈服强度后材料发生均匀塑性变形，可以有效缓解Mises应力的增长。

  • 图8 热应力随温度变化趋势

  • Fig.8 Variation trend of thermal stress with temperature

  • 2.3 多相复合涂层热-力耦合应力场规律及优化

  • 将摩擦力与温度场耦合施加于复合涂层，当法向应力为300MPa、摩擦因数0.2、温度为200℃时的Mises应力和第一主应力分布如图9所示。从图中可以看出，热-力耦合应力场与单纯的热应力场分布类似， Mises应力在硬质相/润滑相交接处尖端附近有局部应力增大区域，拉应力在硬质相/润滑相界面附近强度较高。接触应力对热-力耦合应力场的作用并不显著，施加接触应力后，Mises应力峰值上升约18%，这是由于温度和摩擦力产生的Mises强应力场位置重合，因此二者产生了叠加效应，导致热-力耦合状态下Mises应力峰值增大。施加摩擦力后，拉应力峰值相比于单一的温度场作用反而下降了约8%，这是由于摩擦力产生的拉应力主要位于接触区后端的小范围区域内，其余广大区域为压应力状态，而温度所引起的拉应力主要位于硬质相/黏结相界面处，因此上述两种外场引发的拉应力集中区域并不重合，反而是摩擦力所引发的压应力场缓解了部分热应力场。

  • 为了研究涂层各相性能对热-力耦合应力场的作用规律，本文分别调整硬质相和黏结相的弹性模量，并计算应力场的变化规律，计算结果如图10所示。当硬质相和黏结相弹性模量增大时，复合涂层的热-力耦合应力场增大，其中Mises应力对硬质相Cr3C2弹性模量显著更加敏感，在保持黏结相弹性模量不变的条件下，降低硬质相弹性模量可以有效降低Mises应力峰值，黏结相对Mises应力影响轻微。拉应力对硬质相和黏结相弹性模量敏感程度接近，降低硬质相和黏结相弹性模量对减小拉应力均有较为明显的效果。

  • 图9 热-力耦合工况下应力分布

  • Fig.9 Stress distribution under thermal-mechanical coupling condition

  • 图10 应力峰值随硬质相、黏结相弹性模量变化趋势

  • Fig.10 Variation of peak stress with the elastic modulus of hard phase and bonded phase

  • 从图8可以看出，复合涂层强应力区域位于硬质相的尖端位置，改变各相的形态有助于调节应力分布。如图10所示为各相形态钝化后的复合涂层模型，其硬质相、黏结相、润滑相配比与图2相同。施加热-力耦合载荷后，计算所得Mises应力与最大主应力如图11所示。从图11中可以看出，颗粒尖端钝化后应力得到有效缓解，其中Mises应力峰值降低了约38%，第一主应力峰值降低了约28%，由此可知颗粒形态会对复合涂层的应力场产生显著影响，将颗粒锐角钝化有利于缓解热-力耦合应力。

  • 图11 颗粒尖角钝化后的多相复合涂层模型

  • Fig.11 Multiphase composite coating model after particle sharp corner passivation

  • 图12 尖角钝化后复合涂层热-力耦合应力分布

  • Fig.12 Thermal-mechanical coupling stress distribution of composite coating after sharp corner passivation

  • 如图13所示为尖角颗粒和钝化后颗粒在热力耦合工况下的塑性变形结果，从图13a中可知，尖锐结构复合涂层中的最大塑性应变约为0.003 1，最大塑性应变位于NiCr与Cr3C2颗粒的两相交界处的微区，并且已发生塑性变形区域均位于上述两相交接处，再次证明尖角颗粒会导致强应力区域并引发塑性变形。从图13b中可知，钝化后复合涂层的最大塑性应变约为0.000 96，相比于尖锐结构降低了69%，最大塑性应变点同样位于NiCr与Cr3C2颗粒的两相交界处的微小区域内。

  • 图13 塑性变形分布图

  • Fig.13 The distribution of plastic zone

  • 3 结论

  • 采用微观有限元方法模拟了多相复合涂层热力耦合应力场，为高温摩擦磨损工况下复合涂层的设计提供了依据，模拟结果表明：

  • （1）复合涂层热-力耦合应力场可视为在热应力场的基础上叠加摩擦应力，其中热应力是主要应力来源。

  • （2）复合涂层热-力耦合应力场显著强于均匀涂层，这是由于von Mises应力和拉应力在硬质相尖端有局部高应力现象。

  • （3）热-力耦合工况下当摩擦力和温度恒定时，硬质相和黏结相弹性模量增大会增大Mises应力及拉应力。

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  • 基本信息

    中图分类号: TG335;O242
    DOI: 10.11933/j.issn.1007−9289.20211106002

    基金信息

    国家科技重大专项(2017-VII-0013-0110)；
    国家自然科学基金(51705533)；
    中央高校基本科研业务费(2021YQJD23)资助项目；
    Supported by National Science and Technology Major Project of China (2017-VII-0013-0110)；
    National Natural Science Foundation of China (51705533)；
    Fundamental Research Funds for the Central Universities (2021YQJD23).；

    引用信息

    稿件历史

    收稿日期: 2021-11-06

  • 参考文献

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