PSI - Issue 13

Andrzej Kurek et al. / Procedia Structural Integrity 13 (2018) 2210–2215 Kurek Andrzejet al. / Structural Integrity Procedia 00 (2018) 000 – 000

2211

2

, = , + , = ′ (2 ) 0 + ′ (2 ) 0

(1)

where: γ a,t – total shear strain amplitude expressed as the sum of the amplitudes of elastic shear strain γ a,e and plastic shear strain γ a,p , 2 N f – the number of loading recurrences (reversals), G – the shear modulus,  ' f , b 0 – fatigue life coefficient and exponent for shear strain, γ' f , c 0 – coefficient and exponent of fatigue plastic shear strain. The original MCB characteristic has been developed for tension-compression while analysing the strain, stress and the number of cycles until destruction. Model (1) is used only in the case, when it is possible to determine separately both elastic γ a,e and plastic γ a,p component of total strain γ a,t proved by Marcisz et al. (2012) and Niesłony and Kurek (2012) . Due to the character of the test carried on the newly designed strain-controlled machine and the lack of Ramberg-Osgood stress-strain curve (2) for shear loading, it was impossible to use the most commonly used MCB model. This relation is defined by the Ramberg and Osgood (1943): , = , + , = + ( ′ ) 1 0′ , (2) where:  a – shear stress amplitude, H' – cyclic strength coefficient, 0 ′ – cyclic strengthening exponent for shear strain. Another issue has been shown in the study by Radhakrishnan (1992), where it is pointed out that the sense of plastic strain amplitude in the expression (1) depends on fatigue life, and thus c is not a constant value. Moreover, various authors proposed other empirical model making total strain amplitude dependent on the number of cycles. Among these models there is the Langer (1962) proposal, which is used in numerous studies and promoted e.g. by Manson (1965 and 1979) and Chopra (1999): = − ( , − ) , (3) where: A, B, C – constants to select special form of the characteristic for a given material. Another characteristic is proposed by Kandil (2000) and Gorash and Chen (2013), in the following form: , = − ( ) + 2 ( ) , (4) where: A, B, C – constants to select special form of the characteristic for a given material. Since in case of bending it is not possible to separate elastic and plastic component, then characteristic (1) cannot be used but it is possible to use characteristics (7) or (8), or other empirical form of a strain characteristic. For example, this may be a combination of characteristics (7) and (8) in the following form: ( , − ) = − ( ) + 2 ( ) , ( 5) where: A, B, C, D - constants to select special form of the characteristic for a given material. An extensive review of fatigue characteristics can be found e.g. in the study Niesłony et al. (2012) . The new form, which is proposed there, requires 4 material constants to be determined, same as for the popular characteristic MCB (1). 2. Experiment Our studies were performed on the newly constructed machine, more details in Kulesa et al. (2016b), as shown on Fig. 1, where Δf – total deflection, l – arm of the lever and F – force, where moment = ∙ . The idea behind this machine is that using the screw on the eccentric we can set the deflection of machine arm acting on the specimen, that deflection is set as constant and controlled by the linear displacement sensor. The strain amplitude on specimen is correlated with the arm displacement. The machine was calibrated using specimen with strain gauges,