PSI - Issue 5

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

842

3

logarithm of highly stressed volume. In basic form proposed by Kuguel (1961), this model is expressed as:

v



AV





(1)

a

n

%

where:

A , v – parameters dependent on the material, V n % – highly stressed volume for n = 95, 90. For any relation V n % , Eq. (1) can be noted as follows:

v

   

   

V V

 

a

n

,1

%, 2



(2)

a

n

,2

%,1

where:

σ a ,1 , σ a ,2 – fatigue strength of specimen for volume V n %,1 , V n %,2 . Eq. (1), (2) apply to a specific limit below which no decrease to the fatigue strength of the material takes place. This value corresponds to the lower threshold volume and is usually adopted within the range 30 ÷ 60 mm 3 (Kloos et al. (1981)). The v coefficient is the inclination of the straight line described by Eq. (1) or (2). The value of v coefficient is defined differently, since it is dependent on material, size and shape. It is usually assumed at a level of 0.03 or 0.05 (Härkegård and Halleraker (2010)). Implementation of the size effect model is possible only provided that identical, homogenous microstructure and properties of the material are maintained. The highly stressed volume model does not take into account changes to the mechanical properties of the surface, impact of residual stresses, or surface porosity. The described approach was used for describing the experimental data for fatigue tests (Götz and Eulitz (2013)). The method was used in conjunction with the weakest link theory and the cracking mechanics for highly stressed surface. This is justified due to the fact of initiation of a fatigue crack on the specimen surface. The experimental tests were performed for austenitic acid-resistant steel 1.4301. This material is very frequently used in producing machinery used in the food industry. One example are vibratory machines whose operating loads are variable in time. Construction errors, as well as failure to take into account the actual strength values is often the reason of breakdowns of structural nodes. The selected test material is characterized by sensitivity of its strength and fatigue properties on changing the object dimensions. The differences in the obtained fatigue life are noticeable, which was confirmed experimentally on minispecimens. Similar examinations were also performed for other structural materials (aluminium alloy by Tomaszewski et al. (2014, 2017), steel by Tomaszewski et al. (2016)). Sensitivity of the material on the size effect is described with the use of cross-sectional area coefficient K . The K coefficient determines the relationship between strength (dependent on the type of tests: ultimate tensile strength, fatigue strength) of the standard specimen ( s index) and another one, of any sectional area ( o index). The determined experimental values of K coefficient are presented in Table 1. Steel 1.4301 features a significantly higher content of alloying elements than other materials. In statistical representation of the size effect this may translate into higher probability of the occurrence of potential places initiating a fatigue crack. A change in the chemical composition may be treated as a measure of the material structure homogeneity. Table 2 summarizes the chemical composition of steel 1.4301.The mechanical properties for two specimen sizes are summarized in Table 3. 3. Experimental tests 3.1. Material