PSI - Issue 5

Tomasz Tomaszewski et al. / Procedia Structural Integrity 5 (2017) 840–847 Tomasz Tomaszewski et al. / StructuralIntegrity Procedia 00 (2017) 000 – 000

841

2

size effect is defined as the statistical approach. Statistical defects of the material (points, such as small pores; linear, such as dislocations; surface-type, such as grain boundaries) are distributed in the given volume, irrespectively of the element size. Increasing the specimen cross-section causes an increase to the randomly distributed defects. This leads to the higher probability of initiating a crack in larger specimens. Taking into account the gradient of stress in the size effect is described as geometric approach (Kloos et al. (1981)). This applies to the conditions of tests in which non-linear distribution of load occurs, e.g. concentration of stresses (notched specimen), or bending, torsion load. This paper analyzes bending loads. Schematic presentation of the loading of specimens of various sizes with bending moment is presented on Fig. 1. At given length a 0 , the stress gradient in a small specimen ( σ 1 ) will be smaller than in the standard specimen ( σ 2 ). The relation is true provided that identical distribution of stress is assumed, i.e. fixed value of nominal stress ( σ n ), theoretical stress concentration factor ( α k ) (Makkonen (2003)).

Fig 1. Impact stress gradient in the range of size effect for smooth specimen ( α k = const) and bending load.

The purpose of this paper is to verify the impact of stress gradient in reference to the size effect for a small specimen (referred to as a minispecimen). The tests cover analysis of fatigue strength in respect of high-cycle fatigue. The results were analyzed using a selected analytical model taking into account the adopted test conditions. A number of tests was performed for the purpose of searching for materials vulnerable to the size effect, the origin of which will result from statically distributed defects in the material. Detailed conditions of performing these tests are described in the Tomaszewski et al. (2014, 2016, 1017) papers. The tests were usually performed in axial load conditions. The assessment of structural material properties based on evaluations employing small specimens has been developed for many years. This is evident in the existence of the Small Specimen Test Techniques conference. The discussed problems concern, among others, testing materials used in the nuclear industry by Nogami et al. (2013). Miniaturization of test specimens is necessary for many reasons. This results from the impossibility of manufacturing a standard specimen due to the limited size of the structural element (e.g. from thin-walled blades of gas turbines by Peter et al. (2011), from thin-walled heater pipes by Olbricht et al. (2013)).Another reason of performing tests on small size specimens is the limited quantity of test material collected from an object that is new or already in use. 2. Highly stressed volume model The idea of describing the impact of stress gradient and specimen size on the fatigue properties of materials was realized with the use of the volume method. It was proposed by Kuguel (1961), and then employed by Sonsino and Fischer (2005). This model is based on highly stressed volume V n % . The parameter is defined as the material volume subjected to at least n % of maximum stress ( σ n % = n % σ max ). This particular area of the specimen is characterized by increased probability of initiation of a fatigue crack. The percent of the total volume assumes a value of 95% by Kuguel (1961) or 90% by Sonsino and Fischer (2005).This method determines the correlation of fatigue strength and volume V n % . It is described in the form of linear dependence of a logarithm of local stress amplitude and