PSI - Issue 41

Karolina Głowacka et al. / Procedia Structural Integrity 41 (2022) 232 – 240 Głowacka K., Łagoda T./ Structural Integrity Procedia 00 ( 2019) 000 – 000

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result, equations for equivalent stresses. This applies to both statics and fatigue. When it comes to isotropic materials, with particular emphasis on metallic materials, engineers are generally able to select and apply appropriate criterion that considers the complex state of stress. However, when it comes to composite materials, it is not that simple.

Nomenclature N number of cycles dispersion X

normal strength in the direction along the main axis normal strength in the direction transverse to the main axis

Y S

shear strength in the XY plane position of critical plane

α

θ angle of cutting specimens stress amplitude maximum stress

The problem of reducing complex stress state to the equivalent uniaxial stress in composite materials is already encountered in statics. This is because such materials have different properties depending on the constituent materials. First of all, the type of matrix and reinforcement used is important, as well as the percentage of reinforcement. The properties of the material depend on the manufacturing technique and, in addition, the properties of the material can be improved by appropriate preparation of the fibers. In addition, it is very important to arrange the fibers in the composite. Composite materials, especially those in which the reinforcement is in the form of continuous fibers, are characterized by anisotropic properties, which further complicates the analysis of their properties. A separate problem is the problem of fatigue of such materials. With few exceptions, fatigue tests are performed in a uniaxial stress state. On the other hand, the complex state of stress is realized in the case of three- or four-point bending or by cutting the test specimens at different angles in relation to the direction of the reinforcement fibers. One of the first works in this field is the work from Chamis and Sinclair (1976), when the tensile strength of the glass / epoxy composite was analyzed in the unidirectional reinforcement of speci mens cut at an angle of 10° in relation to the directivity of the composite. In the same year, Rotem (1997) made an attempt to assess the fatigue life of a composite laminate with reinforcement arranged in different directions. In another study by Awerbuch and Hahn (1981), both the static and fatigue strength of graphite / epoxy unidirectional composite of specimens cut out at different angles (0°, 10°, 20°, 30°, 45°, 60°, 90°) were analyzed in relation to the directionality of the fibers. In this case, due to the proportionality of loads, the proposed criterisa for statics are used. Such a possibility exists due to the fact that the course of stresses is proportional. In practical terms, such loads may not be proportional. Then the statics criteria cannot be applied in the case of operational (random) or disproportionate loads. Then the linear criteria should be applied due to the complex state of stress, as well as for metal materials. The aim of this study is to propose a new criterion that will be linear with respect to the stress state components. Its verification will be presented on the basis of the results of available fatigue test results under proportional loads in order to verify whether it can be proposed in complex operating disproportionate stress states. 2. Criteria for multi-axial fatigue used in composites The multi-axis criteria used for composites are mainly those that were proposed in their original form for statics and, after modification, used with varying degrees of success in the analysis of fatigue processes. As a rule, they are written in the form of a limit curve. In the following, only some of them will be presented together with the conversion to an expression into an equivalent value. Structures made of composite materials are usually designed as thin-walled structures, therefore it is sufficient from a constructional point of view to analyze the stress in a plane stress state. In addition, considering the plane stress state noticeably simplifies the form of the equation, and omitting the component in the third direction does not significantly affect the results. Accordingly, the stress criteria will be presented confined to planar stress. In the following parts of the paper we will stick to the notation used for composites, i.e. Voigt's