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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.

研究目标可概括如下：1.研究一种石墨烯单层的构型模型，该单层附着在PMMA衬底上，并被一层薄薄的PMMA覆盖。对于这种构型，将从最初的二维偏微分方程组推导出控制常微分方程组的简单系统。可能的界面内聚分层将在纯模式II行为的假设下沿界面进行研究。2.使用描述界面行为的梯形(或双线性)定律，剪滞模型将与用于确定粘结脱粘长度的简单准则一起应用。在确定弹性粘结长度后，必须确定滑移界面长度，最后确定粘结界面长度。常微分方程组(弹性区、滑移区和粘聚区)的三个相应的解将在适当的连续性条件下相互匹配。研究石墨烯长度对粘结界面脱粘的影响。计算方法所提出的研究将在具有零/有限界面厚度的石墨烯/聚合物结构的一维线性模型的框架内进行。该结构是由拉伸应变加载的。选择修正剪力滞法作为分析工具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。虽然该方法已经在这一领域得到了认可，但它的进一步发展和推广将伴随着界面的本构梯形(或双线性)定律，描述其内聚行为。因此，首先通过推导修正的剪力滞常微分方程组，然后通过制定适当的边界条件和连续性条件来执行分析建模，所述边界条件和连续性条件与拉伸应变下石墨烯单层与宿主聚合物衬底之间的重叠的弹性、滑移和内聚区的解相匹配。这些问题的申请者迄今积累的经验是克服上述计算问题的保证。