In this paper, fiber waviness, as one of the most frequently occurring defects in fiber reinforced composites, is numerically investigated with regard to the formation of residual stresses in fiber metal laminates. Furthermore, the prediction of the residual stress state in the thickness direction by means of the simulated hole drilling method is studied. To this regard, a global-local finite element analysis based on the submodel technique is presented. The submodel technique essentially consists of two governing steps: In the first step, a global model is first utilized to calculate and analyze the residual stress distribution and deformation in the intrinsically joined hybrid structure. Effective cure-dependent thermo–elastic properties predicted by a numerical homogenization procedure were used to simulate the curing-process and analyze the residual stresses state. However, the dimension of the intrinsically manufactured hybrid plate is large compared to the diameter of the drilled hole (2 mm), so that a local model is necessary, which provides only a geometric partial portion of the global model. The local model takes the global stress state into account and is subsequently used to simulate the incremental hole drilling method with a refined mesh discretization. The production-related fiber waviness is modeled by an element-wise orientation approximating a sinus function. In order to validate the global-local modeling approach, a comparison between numerical results and experimental data from literature is presented. The comparison between global residual stress state (global model) and the simulated hole drilling method (local model) is used to assess the applicability and reliability of the hole drilling method in case of fiber waviness. It is found that an in-plane fiber waviness leads to a rather low variance of residual stresses over thickness. In case of an out-of-plane fiber waviness, oscillating residual stress fields occur over the entire thickness along the fiber direction. Moreover, the current limits of the incremental hole drilling method could be pointed out by the presented investigations. It is seen that the simulated results of the incremental hole drilling method are sensitive to waviness, even if the amplitude-wavelength-ratio is small. Without further adjustment of the calibration coefficients the oscillating stress and strain fields lead, in particular fiber waviness in thickness direction, to unreliable predictions. For the experimental application it can be concluded that the specimens have to be carefully examined with regard to fiber waviness.

中文翻译：

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纤维波纹度对残余应力状态的影响及其在纤维金属层压板中的钻孔方法预测：整体-局部有限元分析

在本文中，对纤维波纹度作为纤维增强复合材料中最常见的缺陷之一，就纤维金属层压板中残余应力的形成进行了数值研究。此外，研究了通过模拟钻孔方法预测厚度方向残余应力状态的方法。为此，提出了基于子模型技术的局部局部有限元分析方法。子模型技术本质上包括两个控制步骤：在第一步中，首先使用全局模型来计算和分析固有结合的混合结构中的残余应力分布和变形。通过数值均化程序预测的与固化有关的有效热弹性性质可用于模拟固化过程并分析残余应力状态。但是，与钻孔的直径（2毫米）相比，固有制造的混合板的尺寸较大，因此需要局部模型，该局部模型仅提供整体模型的几何部分。局部模型考虑了整体应力状态，随后用于模拟细化网格离散化的增量钻孔方法。与生产相关的纤维波纹度是通过近似于窦函数的元素取向来建模的。为了验证全局局部建模方法，提出了数值结果和来自文献的实验数据之间的比较。通过比较整体残余应力状态（整体模型）和模拟钻孔方法（局部模型）来评估纤维波纹情况下钻孔方法的适用性和可靠性。发现平面内的纤维波纹度导致厚度上残余应力的变化相当小。在平面外的波纹度的情况下，沿纤维方向在整个厚度上都会发生振荡残余应力场。而且，目前的研究可以指出增量钻孔方法的当前局限性。可以看出，即使振幅-波长比很小，增量钻孔方法的模拟结果对波度也很敏感。在不进一步调整校准系数的情况下，会产生振荡应力和应变场，特别是在厚度方向上的纤维波纹度，这是不可靠的预测。对于实验应用，可以得出结论，必须仔细检查样品的纤维波纹度。