Shear lag analysis by a cohesive bilinear model for the interface stress transfer in a graphene monolayer nanocomposite

通过内聚双线性模型对石墨烯单层纳米复合材料中的界面应力传递进行剪切滞后分析

基本信息

批准号：
406297755
负责人：
Professor Dr.-Ing. Wilfried Becker
金额：
--
依托单位：
Fachgebiet Strukturmechanik
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2018
资助国家：
德国
起止时间：
2017-12-31 至 2018-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/406297755?language=en
关键词：
Shear lag analysis cohesive bilinear

项目摘要

The research objectives can be summarized as follows:1. Study of a configuration model of a graphene monolayer attached to a PMMA substrate and covered by an additional thin PMMA top layer. For this configuration a simple system of governing ordinary differential equations will be derived from the originally two-dimensional system of partial differential equations. The possible interface cohesive delamination will be studied under the assumption of pure mode II behaviour along the interface. 2. Using a trapezoidal (or bilinear) law describing the interface behaviour, the shear lag model will be applied together with a simple criterion serving for finding the cohesive debond length. After determining the elastic bond length the slipping interface length has to be determined and finally the cohesive one. The three respective solutions of the system of ordinary differential equations (for elastic, slipping and cohesive zones) will be matched to each other with appropriate continuity conditions. The effect of the length of the graphene on the cohesive interface debonding will be also studied.Computational methodology The proposed research will be done in the frame of a one-dimensional linear model for the graphene/polymer structure with a zero/finite thickness of the interface. The structure is loaded by a tensile strain. The choice of the modified shear lag method as an analytical tool is based on its well-known advantages for different problems in lightweight structures and composite materials. Although the method is already approved in this field, its further development and extension will go along with a constitutive trapezoidal (or bilinear) law for the interface, describing its cohesive behaviour. Thus, the analytical modelling is performed first by the derivation of the modified shear lag system of ordinary differential equations and second by the formulation of suitable boundary and continuity conditions matching the solutions for elastic, slipping and cohesive zones for the overlap between the graphene monolayer and hosting polymer substrate under tensile strain. The hitherto accumulated experience by the applicants for these kinds of problems is a guarantee for overcoming the computational problems discussed above.

研究目标可以总结如下：1。对附着在PMMA底物上的石墨烯单层配置模型的研究，并被其他薄PMMA顶层覆盖。对于这种配置，一个简单的管理普通微分方程的系统将从最初的二维偏微分方程系统中得出。可能会在沿界面的纯模式II行为的假设下研究可能的介绍分层。 2。使用描述界面行为的梯形（或双线性）定律，将剪切滞后模型与简单的标准一起应用，用于查找凝聚力的剥离长度。确定弹性键长后，必须确定滑动界面长度，最后是凝聚力。普通微分方程系统（用于弹性，滑动和凝聚区）系统的三个解决方案将在适当的连续性条件下相互匹配。还将研究石墨烯对脱粘的长度对粘合界面脱根的影响。结构由拉伸应变加载。修改后的剪切滞后方法作为一种分析工具的选择是基于其对轻质结构和复合材料中不同问题的众所周知的优势。尽管该方法已经在该领域获得了批准，但其进一步的发展和扩展将与界面的构成性梯形（或双线）定律一起进行，描述其凝聚力的行为。因此，首先，通过对普通微分方程的修改剪切滞后系统的推导进行分析建模，其次是通过适当的边界和连续性条件的制定，与弹性，滑动和粘性区域的溶液相匹配，以使石墨烯单层和托管聚合物在累积的聚合物底物之间重叠。迄今为止，申请人在这些问题上积累了经验，可以保证克服上面讨论的计算问题。