The bending stiffness of carbon/epoxy and glass/epoxy cross-ply laminates with intralaminar cracks in the surface 90° plies and local delaminations were studied experimentally using 4-point bending tests. The bending stiffness is defined as the slope of the relation between the applied bending moment and the corresponding midplane curvature. To measure the midplane curvature of laminates with different damage states, the digital image correlation system was used. The reduction in the bending stiffness with increasing density of transverse cracks and delamination length was also analyzed using a 3-D FEM model. The analysis and optical microscopy observations showed that, in the initial stage of damage evolution, local delaminations were small, but with increasing load, the delaminations grew rapidly from the tips of existing and newly created cracks, enhancing the bending stiffness degradation. As an alternative to the 3-D FEM modelling of the test, analytical approaches in conjunction with the classical laminate theory were suggested. The analytical approach was based on the concept of the “effective stiffness of damaged ply,” where the initial stiffness of the damaged ply was replaced by the effective stiffness depending on the damage state. In the present work, two routines were used to determinate the effective stiffness of the damaged ply: a) back-calculation from the difference in the stiffnesses of damaged and undamaged laminates employing the FEM model of the representative volume element; b) simple analytical fitting functions. It is shown that the analytical approach suggested is accurate and convenient for predicting the degradation of bending stiffness of a laminate with an evolving microdamage.

使用四点弯曲试验，通过实验研究了碳/环氧树脂和玻璃/环氧树脂交叉层压板的弯曲刚度，这些层压板在90°层表面具有层状裂缝和局部分层。弯曲刚度定义为施加的弯矩与相应的中平面曲率之间的关系的斜率。为了测量具有不同损伤状态的层压板的中平面曲率，使用了数字图像相关系统。还使用3-D FEM模型分析了弯曲刚度随横向裂纹密度和分层长度的增加而降低的情况。分析和光学显微镜观察表明，在损伤演化的初期，局部分层很小，但随着载荷的增加，分层从现有和新产生的裂纹的尖端迅速增长，加剧了弯曲刚度的降低。作为测试的3-D FEM建模的替代方法，提出了结合经典层压理论的分析方法。该分析方法基于“受损帘布层的有效刚度”的概念，其中，取决于损坏状态，将受损帘布层的初始刚度替换为有效刚度。在本工作中，使用两个例程来确定损坏的层板的有效刚度：a）使用代表体积元素的FEM模型从损坏和未损坏的层压板的刚度差中反算；b）简单的分析拟合功能。