Slope-Controlled Polynomial Strength Criteria for UD Plies
摘要
Known strength criteria were examined to identify the extreme cases of limit surface. Assuming convexity, these cases lead to pairs of triangles, two quadrilaterals, or two hexagons containing four normal strengths X+ , X- , Y+ , Y- on the axes σx and σy in σx - σy plane. The real limit surface is expected to lie between these idealizations. Based on the selected cases, a geometric method of introducing strength criteria for a unidirectional (UD) ply under planar stress conditions was proposed. The linear combination of two polygons of each pair leads to the polynomial criteria of third, fourth or sixth order, which necessarily contain four basic strengths. The slope of the tangents to the basic strengths is specified with controls. Even power dependence with the normalized in-plane shear strength τxy is provided. The parameters of the criteria have a direct geometric interpretation and act as slope controls. An adjustment parameter allows for design choices ranging from conservative to progressive. These parameters are constrained to ensure a plausible limit surface, particularly when material behaviour at biaxial stress states is not known. The approach discussed includes known strength criteria and several criteria for isotropic materials. Established criteria such as Tsai-Wu, Puck, and Cuntze can be easily approximated and valuated with them. This approach gives a fresh look at the criteria and makes them easier to apply. The method proposed is a rational and robust tool that provides a reliable assessment of failure under biaxial stress conditions. The method is also well suited for education.