PSI - Issue 13

Tomasz Tomaszewski / Procedia Structural Integrity 13 (2018) 1756–1761 Author name / Structural Integrity Procedia 00 (2018) 000–000

1757

2

reduction is explained by the influence of factors related with the random distribution of defects in the material, its shape, type of load, and the impact of technological processes during the manufacturing of element (Carpinteri et al. (2009)). Kloos et al. (1981) defined the dependence of strength on the size of the object into several aspects: - Statistical size effect, the defects of the material are distributed statistically 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 specimen. - Technological size effect can be observed in objects with a complex production process (e.g. welded joints). A different degree of machining, e.g. surface layer thickness of rolled sheets or changes in stress in welded sheets with different thickness result in differences in strength properties. - Geometric size effect is applies to the conditions of tests in which non-linear distribution of load occurs, e.g. concentration of stress (notched specimen) or bending, torsion load. This paper analyses 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)). Bending load are characterized by irregular distribution of the stress level. This irregularity can be expressed by the derivation of the local stress σ max , determined as the relative stress gradient (Eichlseder (2002)): χ ' = 1 σ max ቀ d σ dx ቁ (1) χ ’ 2

M.

M.

a 0

χ ’ < 1

χ ’ 2

σ n

χ ’ 1

M.

M.

a 0

σ σ 1 2 <

σ

σ 1

σ 2

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

For a uniform stress distribution, the size effect is determined as a statistical distribution of defects in the material (Weibull (1949)). For load with gradient (bending, rotating), the size effect is defined based on the critical volume (Sonsino and Fisher (2005)). The method is commonly used for objects with different size, including notched specimens (Leitner et al. (2017), Rongqiao et al. (2017)) and in the bending load tests (Tomaszewski and Strzelecki (2016)). The analysis of the size effect is particularly significant in the case of a large-size object (Richard et al. (2013), Holka and Jarzyna (2016)). The purpose of the study was to verify the size effect model allowing for the loads with gradient and statistically distributed material defects. The analyses were carried out for materials susceptible to the size effect (acid-resistance steel 1.4301) within the range of small specimen size. The methodology and results of this tests has been described in the papers (Tomaszewski and Sempruch (2012, 2014)). Identification of strength properties of small specimens is recommended when the reference specimen cannot be sampled (Tomaszewski and Sempruch (2017)) or when the amount of material available for testing is limited (Zastempowski and Bochat (2015)). The test method can be applied to identification the fatigue properties of objects used in conditions that favour a high number of cycles, e.g. vibratory machines (Steyn (1995)) or objects subject to dynamic loading (Piątkowski (2010)).