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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Most of the published studies have been performed with the limit of 10 4 -10 6 cycles. It is worth mentioning at this point that composite materials are usually tested up to this cycle number limit, even though even within these limits, significant damage is often not easily noticeable. However, the stiffness of the material changes, the element heats up, the resonance frequency also changes, and microcracks may appear in the material, especially at the interphase between the fibers and the matrix, imperceptible to the unarmed eye. There are publications in which the fatigue life of up to 10 9 cycles is analyzed by Michel, Kieselbach and Martens (2006), but it is a rare solution, and the range of cycles considered in the present paper usually gives sufficient information about the material. In the analyzed test results, the presented fatigue characteristics at different angles are close to parallelism, which made it possible to determine the constants occurring in formulas (1) - (4) for a constant number of cycles, N = 10 5 . Based on the test results, there were determined maximum normal stress in the direction along the main axis X, in the transverse direction Y, and the shear strength in this plane S. The X value was the tensile strength of the specimens cut at the angle = 0°, the Y value is the tensile strength of the specime n’s angle = 90°, The S value is the strength value at = 45°, divided by 2.2. The value of 2.2 provided the best agreement of the calculations with the experiment of Philippidis and Vassilopoulos (2002a, 2002b). As a result, we obtained values:  X = 89.55 MPa,  Y = 40.47 MPa,  S = 57.60/2.2 = 26.18 MPa, and then, on this basis, the coefficients appearing in the proposed formulas (3) and (4) for the value of equivalent stresses were determined:  X/Y = 2.21,  X/S = 3.42. 4. Application of the multi-axial fatigue criterion in the critical plane for composites Due to the fact that criteria proposed for composite materials are nonlinear due to the components of the stress state, they cannot be applied to experimental or non-proportional loads in phase. Therefore, it is proposed to apply a linear relationship for the components of the stress state in the form of the following expression for the equivalent normal stress in the critical plane defined by this stress by Grzelak, Łagoda and Macha (1991) and Łagoda, Kurek and Głowacka (2020) as ( ) = 1 2 ( ) + 2 2 ( ) + 2 6 (2 ) , (10) where is the angle where the function (3) obtained maximum value. As a result, the obtained amplitudes of equivalent stresses were compared with the experimental fatigue life. It has been shown that the newly proposed criterion for reduced stress, can be successfully applied to composite materials. In the course of further considerations, a modification of formula (10) to its final form was proposed ( ) = 1 2 ( ) + 2 2 ( ) + 4 6 (2 ) (11) by adding a reduction factor of 0.5 to the last component. This approach has no physical explanation, but it did affect satisfactory results. It is a common practice to enter correction factors, especially for empirical formulas. For individual cut out angles θ, the maximum of the function (11) was determined due to the angle of the location of the critical plane α. Thus, the location of this plane is determined, which, as for steel, is not identified as a damage plane, but is only a calculation plane. The experience so far in fatigue testing of metals has shown that the transition to defining fatigue in the critical plane produces good results. Currently, this approach dominates in solving multi axial fatigue problems for such materials. The orientation of such a plane is considered not in the macro but in the meso scale. More precisely, it is a certain neighborhood of the critical point where the maximum stress occurs. As a result, the orientation of such a position must be found. The critical plane in the case of a plane stress state is defined by the angle α , for which the maximum stress amplitude value expressed by formula (11) is achieved. Table 2 compares the calculated orientations of the critical planes depending on the specimen’s cut out angle.