Dadej Konrad, Valvo Paolo Sebastiano, Bieniaś Jarosław
Faculty of Mechanical Engineering, Lublin University of Technology, Nadbystrzycka 36, 20-618 Lublin, Poland.
Department of Civil and Industrial Engineering, University of Pisa, Largo Lucio Lazzarino, I-56122 Pisa, Italy.
Materials (Basel). 2020 Jul 8;13(14):3046. doi: 10.3390/ma13143046.
This paper focuses on the effects of transverse shear and root rotations in both symmetric and asymmetrical end-notched flexure (AENF) interlaminar fracture toughness tests. A theoretical model is developed, whereas the test specimen is subdivided into four regions joined by a rigid interface. The differential equations for the deflection and rotations of each region are solved within both the Euler-Bernoulli simple beam theory (SBT) and the more refined Timoshenko beam theory (TBT). A concise analytical equation is derived for the AENF deflection profile, compliance, and transverse shearing forces as a function of the specimen geometry, stacking sequence, delamination length, and fixture span. Modeling results are compared with numerical finite element analyses, obtaining a very good agreement. Performed analyses suggest that even in the case of symmetrical and unidirectional laminates considered as pure mode II fracture, a complex compression/tension and bending moment state is present, as well as a slight contribution of anti-planar shear at the vicinity of the crack tip.
本文重点研究了横向剪切和根部旋转在对称和非对称端部切口弯曲（AENF）层间断裂韧性试验中的影响。建立了一个理论模型，将试样细分为由刚性界面连接的四个区域。在欧拉-伯努利简单梁理论（SBT）和更精确的铁木辛柯梁理论（TBT）中求解每个区域的挠度和旋转的微分方程。推导出了一个简洁的解析方程，用于描述AENF挠度分布、柔度和横向剪切力与试样几何形状、铺层顺序、分层长度和夹具跨度的函数关系。将建模结果与数值有限元分析进行了比较，结果吻合得很好。进行的分析表明，即使在被视为纯II型断裂的对称和单向层压板的情况下，也存在复杂的压缩/拉伸和弯矩状态，以及裂纹尖端附近反平面剪切的轻微贡献。
