工程科学学报，第39卷，第9期：1396-1402,2017年9月 Chinese Journal of Engineering,Vol.39,No.9:1396-1402,September 2017 D0l:10.13374/j.issn2095-9389.2017.09.013;htp:/journals.usth.edu.cn 干/湿状态下HFRP搭接接头的剪切蠕变试验及分数 阶导数流变模型 王小萌，周储伟区 南京航空航天大学机械结构力学及控制国家重点实验室，南京210016 ☒通信作者，E-mail:zcw@nuaa.cdu.cm 摘要搭接是纤维增强复合材料(FP)的重要连接方式，长期性能是该技术实际工程应用的关键.对不同恒定应力和湿 度状态下混杂FRP(HFRP)双搭接接头的剪切蠕变性能进行了试验研究.试验观测到了明显的蠕变变形，测定了蠕变与恒定 应力及湿度的关系.进一步采用分数阶导数流变模型对试件的蠕变进行模拟.根据模型所包含的Mittag--Leffler函数的性质 采用了改进的Pl优化算法，并确定了合理的初值，结合试验曲线拟合得到模型各参数值.根据搭接接头蠕变的特点，在 经典分数阶流变模型中引入了表征应力水平对搭接接头非线性蠕变特性影响的函数，提出了一种改进的分数阶蠕变柔量计 算公式.研究结果表明，该流变模型能够采用简单的表达形式和较少的参数对试件的非线性蠕变行为进行拟合，在30%~ 70%恒定应力范围内准确模拟了双剪搭接接头的蠕变曲线. 关键词HFRP;搭接接头；剪切蠕变；分数阶导数流变模型 分类号TB332.1 Experiment and fractional derivative rheological modeling of the shear creep of HFRP overlap joints under dry and moist environments WANG Xiao-meng,ZHOU Chu-wei State Key Laboratory of Mechanics and Control of Mechanical Structures,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China Corresponding author,E-mail:zcw@nuaa.edu.cn ABSTRACT The long-term performance of overlap adhesion,one of the major joint technologies of FRP,is key to its practical engi- neering application.Experiments on the creep behaviors of the double lap joint of a hybrid FRP (HFRP)were conducted.Obvious creeps were observed and measured under various environments reflecting different levels of shear stress and humidity.Then,a frac- tional derivative rheological model was proposed to characterize the creep deformation of the overlap joints.By applying the Mittag- Leffler function to the proposed model,an improved Powell optimization algorithm with an initial-value calculation method was utilized to determine the values of the fitting parameters on the basis of the experimental data obtained.By introducing stress influence func- tions to the conventional fractional calculus,a modified formula of fractional creep compliance was considered to reflect the influence of stress level on the creep property of the overlap joint.Results indicate that the model is capable of predicting the creep behavior of o- verlap joints up to a sustained stress level of 30%-70%of the shear strength with relative simple mathematical expressions and only a few fitting parameters. KEY WORDS HFRP;overlap joint;shear creep;fractional derivative rheological model 收稿日期：2017-01-17 基金项目：国家白然科学基金资助项目(11272147,10772078)：航空科学基金资助项目(2013Z52074):机械结构力学及控制国家重点实验室 基金资助项目(0214G02):国家重点实验室开放基金资助项目(ZD130011353,ZD150021556):江苏省研究生培养创新工程资助项目(KYLX- 0220):江苏省高校优势学科建设工程项目工程科学学报,第 39 卷,第 9 期:1396鄄鄄1402,2017 年 9 月 Chinese Journal of Engineering, Vol. 39, No. 9: 1396鄄鄄1402, September 2017 DOI: 10. 13374 / j. issn2095鄄鄄9389. 2017. 09. 013; http: / / journals. ustb. edu. cn 干 / 湿状态下 HFRP 搭接接头的剪切蠕变试验及分数 阶导数流变模型 王小萌, 周储伟苣 南京航空航天大学机械结构力学及控制国家重点实验室, 南京 210016 苣通信作者, E鄄mail: zcw@ nuaa. edu. cn 收稿日期: 2017鄄鄄01鄄鄄17 基金项目: 国家自然科学基金资助项目(11272147, 10772078);航空科学基金资助项目(2013ZF52074);机械结构力学及控制国家重点实验室 基金资助项目(0214G02);国家重点实验室开放基金资助项目(IZD130011353, IZD150021556);江苏省研究生培养创新工程资助项目(KYLX_ 0220);江苏省高校优势学科建设工程项目 摘 要 搭接是纤维增强复合材料(FRP)的重要连接方式,长期性能是该技术实际工程应用的关键. 对不同恒定应力和湿 度状态下混杂 FRP(HFRP)双搭接接头的剪切蠕变性能进行了试验研究. 试验观测到了明显的蠕变变形,测定了蠕变与恒定 应力及湿度的关系. 进一步采用分数阶导数流变模型对试件的蠕变进行模拟. 根据模型所包含的 Mittag鄄鄄 Leffler 函数的性质 采用了改进的 Powell 优化算法,并确定了合理的初值,结合试验曲线拟合得到模型各参数值. 根据搭接接头蠕变的特点,在 经典分数阶流变模型中引入了表征应力水平对搭接接头非线性蠕变特性影响的函数,提出了一种改进的分数阶蠕变柔量计 算公式. 研究结果表明,该流变模型能够采用简单的表达形式和较少的参数对试件的非线性蠕变行为进行拟合,在 30% ~ 70% 恒定应力范围内准确模拟了双剪搭接接头的蠕变曲线. 关键词 HFRP; 搭接接头; 剪切蠕变; 分数阶导数流变模型 分类号 TB332郾 1 Experiment and fractional derivative rheological modeling of the shear creep of HFRP overlap joints under dry and moist environments WANG Xiao鄄meng, ZHOU Chu鄄wei 苣 State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China 苣Corresponding author, E鄄mail:zcw@ nuaa. edu. cn ABSTRACT The long鄄term performance of overlap adhesion, one of the major joint technologies of FRP, is key to its practical engi鄄 neering application. Experiments on the creep behaviors of the double lap joint of a hybrid FRP (HFRP) were conducted. Obvious creeps were observed and measured under various environments reflecting different levels of shear stress and humidity. Then, a frac鄄 tional derivative rheological model was proposed to characterize the creep deformation of the overlap joints. By applying the Mittag鄄鄄 Leffler function to the proposed model, an improved Powell optimization algorithm with an initial鄄value calculation method was utilized to determine the values of the fitting parameters on the basis of the experimental data obtained. By introducing stress influence func鄄 tions to the conventional fractional calculus, a modified formula of fractional creep compliance was considered to reflect the influence of stress level on the creep property of the overlap joint. Results indicate that the model is capable of predicting the creep behavior of o鄄 verlap joints up to a sustained stress level of 30% 鄄鄄70% of the shear strength with relative simple mathematical expressions and only a few fitting parameters. KEY WORDS HFRP; overlap joint; shear creep; fractional derivative rheological model