PSI - Issue 19

Ho Sung Kim / Procedia Structural Integrity 19 (2019) 472–481 Author name / Structural Integrity Procedia 00 (2019) 000–000 The constant fatigue life (CFL) diagram on the plane of mean stress ( ���� ) versus alternating stress ( � ) (Fig. 1) is useful not only for providing information of fatigue lives in relation with stress ratios but also for predicting S-N curves at various stress ratios. It consists of ordinate for σ a , abscissa for σ mean , radial lines emanating from the origin for constant stress ratios, and CFL lines. The CFL lines may be decomposed into two sets. One of the sets which hereafter will be referred to as the first cycle CFL lines can be theoretically identified using the quasi-static ultimate compressive ( �� ) and tensile ( �� ) strengths. The other set of CFL lines (which hereafter will be referred to as fatigue CFL lines) depends on the experimental fatigue behaviour (Fig. 2a). In the case of fibre reinforced composites, yield strength ( � ) and ultimate strength ( � ) are approximately equal unlike the monolithic ductile materials. However, � may be preferably used for monolithic ductile materials as suggested by Soderberg (1930) depending on the definition of failure. 2.2.1 The first cycle CFL lines The first cycle CFL lines are a locus of failure points within the first load cycle (about 0.5 cycle between 0.25 to 0.75 cycles). It can be intuitively found from the schematic load cycling at different stress ratios as shown in Fig. 1. The dot in each load cycle in Fig. 1 represents a failure point corresponding to either �� or �� . For example, the failure point at R =0.5 is found to be ��� = �� and N f =0.5cycle. Thus, the first cycle CFL lines consists of two straight lines forming an isosceles right triangle for approximately linear relationships between σ a and σ mean for each half of the triangle for the whole range of stress ratios. The location of the isosceles triangle apex is found to be � = � �� �|� �� | � (5) and ���� = � �� �|� �� | � . (6) Accordingly, the location of σ mean for the triangle apex depends on the static strengths. If �� > | �� | , then ���� = ( �� − | �� |)/2 > 0 as shown Fig. 1; and if �� < | �� | , then ���� = ( �� − | �� |)/2 < 0. Thus, the stress ratio of the radial line passing through the apex ( � or χ ) is found to be � = χ = � ���� �� � � ���� �� � = �|� �� | � �� (7) and its slope ( � ) is also found to be � = � �� �|� �� | � �� �|� �� | . (8) The critical stress ratio (χ) as seen indicates a location for the transition of the first cycle CFL line slope dictated by the static strengths. The first cycle CFL line on the right side of R = χ is due to the mean loading ���� > ( �� − | �� |)/2 generating the failure in tension mode, while that of left side of the radial line at R = χ is due to the mean loading ���� < ( �� − | �� |)/2 , generating the failure in compression mode. The intercept value on � -axis of the first cycle CFL line is found to be | �� | if �� > | �� | (Fig. 1) or | �� | if �� < | �� | . Thus, the first cycle CFL lines is theoretically determined once the static strengths are given. If a set of experimental results would not conform to the theoretical description here, the experiment may be judged to be erroneously conducted (Vassilopoulos, 2010). 2.2.2 Fatigue CFL lines Unlike the first cycle CFL lines, we do not know how CFL lines look like until the experimental fatigue data sets at different stress ratios are available. We do know, however, that the two distinctive types of static loading for the 475 4