Issue34

Z. Marciniak et alii, Frattura ed Integrità Strutturale, 34 (2015) 1-10; DOI: 10.3221/IGF-ESIS.34.01 7 In Eq. (17), W(t), σ(t), ε(t) are continuous functions of time t, and ε i pl and ε i+1 pl are constant values in time t in the hysteresis loop with the number i, while  i pl is the plastic strain registered in the moment t i , when the stress  (t i ) is equal to zero, and remains constant to the moment t i+1 when the stress reaches zero again, i.e.  (t i+1 ) = 0. Then the new registered value of plastic strain  i+1 pl replaces the previous one  i pl . This procedure is repeated for each cycle of loading. Fig. 3 shows sample hysteresis loops and energy parameter course calculated on the basis of variable-amplitude history of stresses and strains. Energy parameter course calculation procedure for variable-amplitude loads: Step 1. In point 0, individual values of stresses, strains and energy parameter are: σ(t 0 ) = 0, ε(t 0 ) = 0, ε 0 pl = 0, W(t 0 ) = 0. Step 2. In point A, individual parameters have the following values: σ(t A ) = σ A , ε(t A ) = ε A , ε A pl = ε 0 pl =0, W(t A ) = 0.5·σ A ׀ ε A - ε 0 pl ׀ = 0.5·σ A ·ε A . Step 3. Then, going to point B we obtain: σ(t B ) = σ B =0, ε(t B ) = ε B = 0, ε B pl = ε B pl , W(t B ) = 0.5·σ B · ׀ ε B - ε B pl ׀ = 0. Step 4. Point C: σ(t C ) = σ C , ε(t C ) = ε C , ε C pl = ε B pl , W(t C ) = 0.5·σ C · ׀ ε C - ε B pl ׀ . Step 5. Point D: σ(t D ) = σ D =0, ε(t D ) = ε D =0, ε D pl = ε D pl , W(t D ) = 0.5·σ D · ׀ ε D - ε D pl ׀ = 0. Step 6. Point E: σ(t E ) = σ E , ε(t E ) = ε E , ε E pl = ε D pl , W(t E ) = 0.5·σ E · ׀ ε E - ε D ׀ pl , etc. Fig. 3d presents energy parameter course calculated based on above procedure . Figure 3 : Sample hysteresis loops a) , stress courses b) , strain courses c) , energy parameter courses d) . Fig. 4 shows energy fatigue characteristic for steel C45 according to the formula (17). The models and methods proposed above were used to assess fatigue life until crack initiation. Whereas, as regards development of fatigue cracks, Rozumek and Macha proposed an energy criterion based on parameter J for three crack modes [26]. This criterion was verified for mode I and mode III [27]. 2 2 2 1 I II III Ic IIc IIIc J J J J J J                         , (18) where J Ic , J IIc , J IIIc are critical values for modes I, II and III. The criterion (18) was successfully verified while tests of aluminium alloy and steels. Different bending (cracking mode I) to torsion (cracking mode III) ratio in steel 18G2A is shown in Fig. 5 [28]. It provides grounds to observe shift of experimental points towards increasing the value of parameter  J I , except of the