今日更新:Composite Structures 4 篇,Composites Part A: Applied Science and Manufacturing 4 篇,Composites Part B: Engineering 1 篇
Efficient derivation of a nonlinear cohesive bridging law for numerical delamination simulations under static and fatigue loading
G. Hacker, G. Just, S. Scheffler, I. Koch, M. Gude, R. Rolfes
doi:10.1016/j.compstruct.2025.119585
静态和疲劳载荷下数值分层模拟非线性黏结桥接规律的有效推导
Delamination is a frequent and critical type of damage that occurs in composite structures under static and fatigue loading. This work presents a novel method to derive a nonlinear traction-separation law (TSL) for a cohesive zone model (CZM) used for delamination simulations is presented. By solving an ordinary differential equation (ODE) resulting from the energy balance of the cohesive zone, a nonlinear TSL is directly derived from R-curves that were determined experimentally in standard quasi-static double cantilever beam (DCB) tests. A superimposed conventional bilinear TSL is required to match the initial energy release rate of the R-curves. This bilinear TSL is intended to model brittle fracture while the nonlinear part models the R-curve effects mainly caused by fiber bridging. In order to consider R-curve effects under fatigue loading conditions as well, an established fatigue CZM is embedded into both parts of the TSL using the same set of four required input parameters. The fatigue parameters are determined inversely by means of cyclic DCB tests. It is demonstrated that the numerical model is able to reproduce the force–displacement curves of the conducted quasi-static DCB tests with a higher accuracy, if the TSL is derived by the new method instead of the preexisting and commonly used J-integral approach. Furthermore, the model is able to reproduce experimental data from conducted cyclic DCB test with a limited number of input parameters which significantly decreases the effort of inverse parameter identification.
分层是复合材料结构在静载荷和疲劳载荷作用下发生的一种常见且关键的损伤类型。本文提出了一种新的方法来推导用于分层模拟的内聚带模型(CZM)的非线性牵引-分离律(TSL)。通过求解由内聚区能量平衡引起的常微分方程(ODE),直接从标准准静态双悬臂梁(DCB)试验中得到的r曲线推导出非线性TSL。需要一个叠加的传统双线性TSL来匹配r曲线的初始能量释放率。双线性TSL用于模拟脆性断裂,非线性部分模拟主要由纤维桥接引起的r曲线效应。为了考虑疲劳载荷条件下的r曲线效应,将一个已建立的疲劳CZM嵌入到TSL的两个部分,使用相同的4个所需输入参数。通过循环DCB试验反求疲劳参数。结果表明,如果采用新方法代替现有常用的j积分法推导TSL,则该数值模型能够以更高的精度再现所进行的准静态DCB试验的力-位移曲线。此外,该模型能够在有限输入参数的情况下再现循环DCB试验的实验数据,大大减少了参数逆辨识的工作量。
Simple ana lytical modeling of residual flexural properties of hybrid PEEK thermoplastic composite laminate under kerosene flame exposure
Lanhui Lin, Benoit Vieille, Christophe Bouvet, Tanguy Davin
doi:10.1016/j.compstruct.2025.119648
煤油火焰下混杂PEEK热塑性复合材料层合板残余弯曲性能的简单解析建模
The present work aims to propose a simple two-layer ana lytical model to determine the residual bending properties of hybrid carbon/glass fibers reinforced PEEK (CG/PEEK) laminates under localized kerosene flame exposure (1100 °C and 116 kW/m2 by a burner bench). It is intended to better understand the relationship between thermally-induced damages and the residual bending properties and also to predict the changes of the flexural properties as a function of flame exposure time. On the one hand, the influence of porosity induced by isothermal heating conditions (temperature ranging from the melting one to the point of resin decomposition) on post-heat flexural properties is examined, which allows the effects of different phase transitions of the PEEK matrix to be dissociated. The residual flexural strength and stiffness of thermally degraded laminates decrease rapidly with the increasing amount of porosity as function of exposure temperature and heating time (400 – 450 – 500 – 525 – 550℃ for 300 – 600 – 900 s). These isothermal tests allow master curves to be formulated that show the correlations between porosity ratio and residual flexural properties. These master curves, combined with through-thickness observations, are expected to provide a comprehensive interpretation of the post-fire flexural behavior of different layers. On the other hand, by means of a two-layer (char layer and decomposition layer) model considering different distances from the flame, it is possible to determine the residual bending properties of post-fire CG/PEEK laminates as a function of the flame exposure times. The proposed ana lytical model shows a good agreement with the experimental results (obtained in the preliminary study), and the important role of the char layer and its residual properties under long-time flame exposures are highlighted
本工作旨在提出一个简单的两层分析模型,以确定混合碳/玻璃纤维增强PEEK (CG/PEEK)层压板在局部煤油火焰暴露(1100 °C和116 kW/m2燃烧器台)下的残余弯曲性能。旨在更好地理解热致损伤与残余弯曲性能之间的关系,并预测弯曲性能随火焰暴露时间的变化。一方面,研究了等温加热条件(从熔点到树脂分解点的温度范围)引起的孔隙率对热后弯曲性能的影响,从而可以解离PEEK基体不同相变的影响。随着暴露温度和加热时间(400 ~ 450 ~ 500 ~ 525 ~ 550℃,300 ~ 600 ~ 900 s)的增加,热降解层压板的残余抗弯强度和刚度迅速降低。这些等温测试允许制定主曲线,显示孔隙率和残余弯曲性能之间的相关性。这些主曲线与贯穿厚度观测相结合,有望提供不同层的火灾后弯曲行为的综合解释。另一方面,通过考虑到与火焰的不同距离的两层(炭层和分解层)模型,可以确定火灾后CG/PEEK层压板的残余弯曲性能作为火焰暴露时间的函数。所提出的分析模型与实验结果(初步研究结果)吻合良好,并突出了焦炭层及其在长时间火焰照射下的残余性能的重要作用
Neural network-assisted design optimization with adaptive sampling for tow-steered composite structures
Bangde Liu, Xin Liu
doi:10.1016/j.compstruct.2025.119588
带自适应采样的神经网络辅助双舵复合结构设计优化
Tow-steered composites offer significant potential for enhancing weight reduction and performance in aerospace structures. However, optimizing realistic tow-steered composite designs using finite element (FE)-based methods is often computationally prohibitive due to the expansive design space. Neural network (NN) models have emerged as a cost-effective alternative to FE-based optimization approaches. However, advanced NN models typically require substantial training data to achieve high accuracy, and the generation of this data through FE ana lysis of tow-steered composite structures remains computationally intensive. To address this challenge, this study introduces an adaptive sampling method that effectively reduces the required training data while enhancing the accuracy of NN-based design optimization. The proposed method is demonstrated on two tow-steered composite structures with different numbers of design variables, showcasing its ability to achieve improved optimization accuracy and reduced costs. The proposed method can be applied to other NN-based optimization problems, mitigating computational demands associated with generating training data.
牵引复合材料在提高航空结构的减重和性能方面具有巨大的潜力。然而,由于设计空间的扩大,使用基于有限元(FE)的方法优化现实的牵引复合材料设计通常在计算上是令人望而却步的。神经网络(NN)模型已成为基于fe的优化方法的一种经济有效的替代方法。然而,先进的神经网络模型通常需要大量的训练数据才能达到高精度,并且通过对牵引复合结构的有限元分析生成这些数据仍然需要大量的计算。为了解决这一挑战,本研究引入了一种自适应采样方法,该方法有效地减少了所需的训练数据,同时提高了基于神经网络的设计优化的准确性。在两个具有不同设计变量数量的双舵复合结构上进行了验证,证明了该方法能够提高优化精度并降低优化成本。该方法可以应用于其他基于神经网络的优化问题,减少与生成训练数据相关的计算需求。
Numerical simulation of three-point bending deformation for 3D woven preforms based on the virtual yarn modeling strategy
Geyi You, Junbo Xie, Jiawei Chen, Wei Jiao, Li Chen
doi:10.1016/j.compstruct.2025.119652
基于虚拟纱线建模策略的三维机织预制件三点弯曲变形数值模拟
SiC fiber reinforced ceramic matrix composites are widely used in the aerospace field for their good mechanical properties at high temperature. Deformation of the fiber preforms is however inevitable in the manufacturing process of complex-shaped composite components. The bending behavior plays a crucial role in determining of the preform geometries. This paper proposes a novel modeling strategy to generate yarn structures and simulate bending deformation of SiC fiber 3D woven preforms. Low bending stiffness of the yarn is decoupled from high tension stiffness through the shell/truss hybrid meshes, and the bending stiffness is calibrated by cantilever bending test of SiC fiber yarns. The bending deformation and load–deflection response of SiC fiber 3D woven preform is well predicted using this modeling method. Microstructure deformations including the variations of weft yarn arrangement, and warp yarn path are quantitatively ana lyzed by Euclidean distance-based metric an alysis. The simulation results are verified by three-point bending test of the preform specimen and the Micro-CT scanning of the deformed preform sample. This work provides a yarn-level modeling method which can be widely applied on other textile preforms. The virtual yarn modeling strategy is more efficient than the fiber-level approaches, thus has advantage on simulations of large-sized preforms.
SiC纤维增强陶瓷基复合材料以其良好的高温力学性能在航空航天领域得到了广泛的应用。然而,在复杂形状复合材料构件的制造过程中,纤维预成形件的变形是不可避免的。弯曲性能对预成形几何形状的确定起着至关重要的作用。本文提出了一种新的模拟SiC纤维三维机织预制件纱线结构和弯曲变形的建模方法。通过壳/桁架混合网格将纱线的低弯曲刚度与高拉伸刚度解耦,并通过SiC纤维纱线的悬臂弯曲试验对其弯曲刚度进行标定。利用该建模方法可以很好地预测SiC纤维三维编织预制件的弯曲变形和载荷-挠度响应。采用基于欧几里得距离的度量分析方法,定量分析了织物的微结构变形,包括纬纱排列和经纱路径的变化。通过预成形试样的三点弯曲试验和变形后预成形试样的Micro-CT扫描验证了模拟结果。本工作提供了一种纱线级的建模方法,可广泛应用于其他纺织预制品的建模。虚拟纱线建模策略比纤维级建模方法更有效,因此在大型预成型的仿真中具有优势。
Impact of curing profiles on the Thermo-Mechanical properties of an underfill in Board-Level microelectronic Packaging: Effect on reliability
Zbyněk Plachý, Jonáš Uřičář, Denis Froš, Anna Pražanová, Karel Dušek, Attila Géczy
doi:10.1016/j.compositesa.2025.109298
固化轮廓对板级微电子封装中底填料热机械性能的影响:对可靠性的影响
The paper investigates the effect of isothermal curing profiles, based on detailed kinetic an alysis, on the mechanical, thermomechanical, and microstructural properties of an epoxy composite microelectronic packaging underfill material for enhanced electronics reliability. Five isothermal profiles were developed based on detailed Kamal-Sourour kinetic modelling to achieve near-complete curing. Subsequent characterisation included DSC, tensile tests, DMA, microhardness measurements, and SEM-EDS ana lysis. The results revealed a complex dependence of properties on the curing profile. The 170 °C profile provided the optimal ultimate tensile strength (UTS≈71.5 MPa) and Young’s modulus (5.53 GPa), which correlated with the most homogeneous polymer network as determined by the narrowest glass transition width. Conversely, T g values exhibited a strong inverse relationship with UTS and Young’s modulus, qualified by strong negative Spearman correlations (−1.0 to −0.9). The 150 °C profile resulted in the highest toughness. The microstructural ana lysis confirmed SiO2 filler sedimentation at 110 °C, while profiles at 150–170 °C showed the most uniform filler distribution. The thermal degradation of the material was observed at the 190 °C profile. The study demonstrates that the specific temperature–time profile, not just the achieved degree of cure, critically dictates the underfill’s microstructure and final properties. Identification of the optimal process window, approximately 150–170 °C for this material, is essential for achieving desired performance while minimising defects, a fundamental aspect of reliability in electronic applications. Furthermore, this defined processing window provides the flexibility to adapt curing profiles to the thermal constraints of a component or assembly, helping to mitigate thermomechanical stress during manufacturing.
本文在详细的动力学分析的基础上,研究了等温固化轮廓对环氧复合微电子封装底填料力学、热力学和微观结构性能的影响,以提高电子可靠性。基于详细的kamal - sour动力学模型,开发了5条等温曲线,以实现近乎完全的固化。随后的表征包括DSC,拉伸测试,DMA,显微硬度测量和SEM-EDS分析。结果显示,性能的复杂依赖于固化轮廓。170°C的轮廓提供了最佳的极限拉伸强度(UTS≈71.5 MPa)和杨氏模量(5.53 GPa),这与最窄的玻璃化转变宽度决定的最均匀的聚合物网络相关。相反,T g值与UTS和杨氏模量表现出强烈的反比关系,具有强烈的负Spearman相关性(- 1.0至- 0.9)。150°C的轮廓产生了最高的韧性。显微结构分析证实了SiO2填料在110℃时的沉降,而在150 ~ 170℃时的剖面显示填料分布最均匀。在190℃剖面下观察到材料的热降解。研究表明,特定的温度-时间曲线,而不仅仅是达到的固化程度,对下填体的微观结构和最终性能有着关键的影响。确定该材料的最佳工艺窗口(约150-170°C)对于实现所需性能,同时最大限度地减少缺陷至关重要,这是电子应用可靠性的基本方面。此外,这种定义的加工窗口提供了灵活性,使固化轮廓适应组件或组件的热约束,有助于减轻制造过程中的热机械应力。
Improved fiber–matrix bonding of continuous aramid fiber reinforced acrylonitrile-styrene-acrylate polymer using in-situ impregnation material extrusion additive manufacturing technique
Nishant Jain, Mathias Czasny, Johannes Schmidt, Sara Alves Santos, David Schmiedjell, Sabine Hild, Aleksander Gurlo
doi:10.1016/j.compositesa.2025.109299
利用原位浸渍材料挤压增材制造技术改进了连续芳纶纤维增强丙烯腈-苯乙烯-丙烯酸酯聚合物的纤维-基体粘合
This study compares the fiber–matrix bonding of acrylonitrile-styrene-acrylate (ASA) terpolymer reinforced with standard-finish (A1) and adhesion-activated finish (A2) aramid fibers (Twaron®) manufactured using an in-situ additive manufacturing (AM) material extrusion technique. A2 fibers showed a slightly higher total surface energy (γs ∼ 49.45 mN/m) compared to A1 fibers (γs ∼ 44.20 mN/m) indicating potentially higher interfacial interaction of A2 fibers with polymer matrix. For single-line manufactured composites, the fiber–matrix bonding performance of the A2-ASA composite improved significantly on increasing the processing temperature from 240 °C to 300 °C resulting in an increase in ultimate tensile strength (UTS) from 694 MPa to 870 MPa. In contrast, A1-ASA composites showed a reduction in UTS from 674 MPa to 544 MPa over the same temperature. Improved mechanical performance of the composite reinforced with A2 fibers was also observed in the multi-layer manufactured composite, where UTS reached 450 MPa and a Young’s modulus of 33 GPa, compared to 426 MPa and 15 GPa for the standard finish fibers. The flexural properties confirm the observed improvements in the mechanical properties of A2-ASA composite. The observation derived from the experimental results indicates that the properties of the fiber surface are crucial for enhancing the fiber–matrix bonding, particularly during the manufacturing process of continuous fiber-reinforced composites utilising material extrusion AM techniques. This ASA-aramid composite can be further exploited as a high-performance composite with improved weatherability for outdoor applications.
本研究比较了使用原位增材制造(AM)材料挤出技术制造的标准表面处理(A1)和粘合活化表面处理(A2)芳纶纤维(Twaron®)增强的丙烯腈-苯乙烯-丙烯酸酯(ASA)三元共聚物的纤维-基体粘合。与A1纤维(γs ~ 44.20 mN/m)相比,A2纤维显示出略高的总表面能(γs ~ 49.45 mN/m),表明A2纤维与聚合物基体的界面相互作用可能更高。对于单线制造的复合材料,当加工温度从240 °C增加到300 °C时,A2-ASA复合材料的纤维-基体结合性能得到显著改善,其极限抗拉强度(UTS)从694 MPa增加到870 MPa。相比之下,在相同温度下,A1-ASA复合材料的UTS从674 MPa降低到544 MPa。与标准整理纤维的426 MPa和15 GPa相比,A2纤维增强的多层复合材料的机械性能也得到了改善,其UTS达到450 MPa,杨氏模量为33 GPa。弯曲性能证实了观察到的A2-ASA复合材料力学性能的改善。实验结果表明,纤维表面的性能对增强纤维与基体的结合至关重要,特别是在利用材料挤压增材制造技术制造连续纤维增强复合材料的过程中。这种asa -芳纶复合材料可以进一步开发为高性能复合材料,改善室外应用的耐候性。
Surface modified UHMWPE fibers with functional interfacial layers: a strategy for enhanced composite interfacial and mechanical performance
Yan Wang, Xianhui Dong, Na Li, Yan Wang, Yinjun Chen, Junrong Yu, Zuming Hu, Meifang Zhu
doi:10.1016/j.compositesa.2025.109300
具有功能界面层的表面改性超高分子量聚乙烯纤维:增强复合界面和机械性能的策略
Ultra-high molecular weight polyethylene (UHMWPE) fiber is prized for the superior strength and modulus. Nevertheless, the s moothness of fiber surface and the absence of polar functional groups in polymer backbone result in poor interfacial adhesion with matrix of composites. This severely decreases the mechanical performance and impedes the practical applications of UHMWPE fiber-reinforced composites. To optimize the interfacial compatibility between UHMWPE fiber and matrix, a series of amphipathic polymer brush PVA-OCT oligomer and multi-armed molecule DiPE-OCT with various functional groups herein as interfacial modification agents were synthesized. These functional groups form tight interaction with UHMWPE fiber and matrix through the mechanical interlocking and hydrogen bonding interactions, respectively. After modification by interfacial modification agents, UHMWPE fiber-reinforced composites exhibited a significant enhancement in the interfacial bonding and mechanical properties. Notably, an enhancement of 158.1 % in interfacial shear strength (6.35 MPa) was achieved in modified UHMWPE fiber-reinforced epoxy composites compared to the control composite. Meanwhile, the flexural and tensile strengths of modified composites increased by 107.4 % and 53.3 %, respectively. Consequently, this study provides a facile and innovative method for the surface modification of UHMWPE fiber and remarkably reinforces UHMWPE fiber composites, actuating the industrial application of UHMWPE fiber composites.
超高分子量聚乙烯(UHMWPE)纤维因其优越的强度和模量而备受推崇。然而,纤维表面的光滑性和聚合物骨架中极性官能团的缺失导致其与复合材料基体的界面附着力较差。这严重降低了超高分子量聚乙烯纤维增强复合材料的力学性能,阻碍了其实际应用。为了优化UHMWPE纤维与基体的界面相容性,合成了一系列具有不同官能团的两亲聚合物刷式PVA-OCT低聚物和多臂分子DiPE-OCT作为界面改性剂。这些官能团分别通过机械联锁作用和氢键作用与超高分子量聚乙烯纤维和基体形成紧密的相互作用。界面改性剂对UHMWPE纤维增强复合材料进行改性后,其界面结合性能和力学性能均有显著提高。值得注意的是,改性UHMWPE纤维增强环氧复合材料的界面剪切强度(6.35 MPa)比对照复合材料提高了158.1 %。同时,改性复合材料的抗弯强度和抗拉强度分别提高了107.4 %和53.3% %。因此,本研究为超高分子量聚乙烯纤维的表面改性提供了一种简便、创新的方法,显著增强了超高分子量聚乙烯纤维复合材料的性能,推动了超高分子量聚乙烯纤维复合材料的工业化应用。
A damage tensor-based model for effective resistivity of CFRP θ1/θ2S laminates with matrix cracking
Keiji Ogi, Yuji Ozawa, Ryotaro Ozaki, K. Mizukami
doi:10.1016/j.compositesa.2025.109301
一种基于损伤张量的含基体开裂的 CFRP θ1/θ2S 层合板有效电阻率模型
This study presents a continuum damage mechanics (CDM)-inspired model for predicting the effective resistivity of θ1/θ2S CFRP laminates with matrix cracks in the θ2 plies. The laminate-level resistivity is evaluated using the electric-field lamination theory, and an explicit solution for the electric potential in a cracked 90° lamina is derived. This leads to ana lytical expressions for both the damage tensor and effective resistivity as functions of matrix crack density. The proposed model is validated against finite element ana lysis (FEA) and the existing closed-form solution (CFS). Across a wide range of conditions—including strong in-plane and through-thickness anisotropy—the CDM predictions show good agreement with FEA, and outperform the CFS particularly in highly anisotropic regimes. Applicability is demonstrated for both cross-ply and angle-ply laminates, as well as for laminates with three-dimensional anisotropy. Furthermore, a consistent relationship between resistivity change and stiffness degradation is shown, supporting the model’s relevance to electrical health monitoring (EHM) of CFRPs. These results offer a unified, physically grounded framework for evaluating damage-induced resistivity changes in electrically anisotropic composite laminates.
本研究提出了一种受连续损伤力学(CDM)启发的模型,用于预测含 θ2 层间基体裂纹的 θ1/θ2S 碳纤维增强复合材料(CFRP)层合板的有效电阻率。采用电场叠层理论评估层合板级电阻率,并推导出含裂纹 90°层板中电位的显式解。由此得出损伤张量和有效电阻率随基体裂纹密度变化的解析表达式。所提出的模型通过有限元分析(FEA)和现有的闭式解(CFS)进行了验证。在包括强面内和层间各向异性在内的广泛条件下,CDM 预测结果与 FEA 结果吻合良好,并且在高度各向异性区域尤其优于 CFS。该模型适用于正交层合板、角向层合板以及具有三维各向异性的层合板。此外,还表明电阻率变化与刚度退化之间存在一致的关系,这支持了该模型在 CFRP 电学健康监测(EHM)中的相关性。这些结果为评估电各向异性复合层压板中由损伤引起的电阻率变化提供了一个统一且有物理依据的框架。
Constructing Robust C-N bonding Interphases of Carbon Fiber/Epoxy Composites via the Electrode-switching Electrochemical Surface Treatment of Carbon Fibers
Bing Zhang, Changyu Leng, Maoqun Hu, Xianglin Ma, Mengjiao Xu, Nannan Guo, Lili Ai, Qingtao Ma, Dengtai Yuan, Shishi Zhang, Qian Li, Dianzeng Jia, Luxiang Wang
doi:10.1016/j.composites b.2025.113029
通过碳纤维电极开关电化学表面处理构建碳纤维/环氧复合材料坚固的C-N键界面
The interphase formed between carbon fiber (CF) and polymer matrix is crucial to improve the mechanical properties of carbon fiber reinforced polymer (CFRP) composites. Various surface treatment methods have been developed for grafting functionalized molecules on the CF surface to form robust covalent bonding interphase. However, the state-of-the-art strategies demand long reaction time, complex operation and harsh reaction conditions, which cannot meet growing demands for large-scale actual production. Herein, an electrode-switching electrochemical surface treatment (ESET) method was proposed for the efficient and controllable grafting of ethylenediamine (EDA) molecules on the CF surface within merely 180 s. The obtained o-r-CF@EDA was successively used as the anode and cathode for grafting EDA molecules on the surface. It exhibited a high surface N content of 18.74 at.% (with a maximum of 32.04 at.%) and surface energy of 52.61 mN m-1. When combined with epoxy resin (EP) matrix, the average interfacial thickness of o-r-CF@EDA/EP composite reached 495.6 nm, resulting in an expected interlaminar shear strength (ILSS) of 126.5 MPa. Moreover, the reaction mechanis m of ESET method and covalent C-N bonds enhancing the interfacial interaction were discussed in-depth. This work presents promising strategy for grafting targeted molecules onto the CF surface and developing high-performance CFRP composites.
碳纤维与聚合物基体之间形成的界面相是提高碳纤维增强聚合物复合材料力学性能的关键。为了将功能化分子接枝到CF表面以形成牢固的共价键界面,已经开发了各种表面处理方法。然而,目前最先进的反应策略需要较长的反应时间、复杂的操作和苛刻的反应条件,无法满足日益增长的大规模实际生产的需求。本文提出了一种电极开关电化学表面处理(ESET)方法,可在180 s内将乙二胺(EDA)分子高效可控地接枝到CF表面。得到的o-r-CF@EDA依次作为阳极和阴极在表面接枝EDA分子。其表面氮含量高达18.74 at。%(最高为32.04)。%),表面能为52.61 mN -1。当与环氧树脂(EP)基体结合时,o-r-CF@EDA/EP复合材料的平均界面厚度达到495.6 nm,层间抗剪强度(ILSS)达到126.5 MPa。并对ESET法的反应机理和共价C-N键增强界面相互作用进行了深入探讨。这项工作为将目标分子接枝到CF表面和开发高性能CFRP复合材料提供了有前途的策略。