PSI - Issue 39

Yuri Petrov et al. / Procedia Structural Integrity 39 (2022) 552–559 Yuri Petrov/ Structural Integrity Procedia 00 (2019) 000 – 000

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4

| =0, <0 = 0 | =0, <0 = ( ) |

(5).

<0 = | <0 = 0

If the step load ( ) = ∙ ( ) ( ( ) − Heaviside step function) is considered, the stress intensity factor is given by formula ( ) = ∙ ∙ √ , = 4√2⁄ √ 1 √1 − 2 , = 1 1 ⁄ (6). If arbitrary load ( ) is applied to the crack faces, the expression for the corresponding SIF dependence ( ) is calculated using convolution: ( ) = ∫ ( ) ⋅ ′( − ) 0 (7). This way formula (7) can be used to evaluate the ( ) function for a rectangular pulse (with amplitude and pulse duration ) load ( ) = ( ( ) − ( − )) : ( ) = ∙ ∙ (√ − √ − ) (8). Firstly, a case when fracture takes place before the loading pulse ends ( ∗ ≤ ) is considered. If (8) is substituted to the fracture criterion (2), dependence of the load pulse amplitude on the fracture time ∗ : = 2 3 ∙ (( ∗ ) 3⁄2 − ( ∗ − ) 3⁄2 ) (9). Figure 1 shows dependence of a normalized stress intensity factor ( ) ⁄ on a normalized time ∗ ⁄ . For the considered ∗ ≤ case time moments ∗ (fracture time) and ∗ − are marked with squares. For this case the SIF value increases till the fracture moment and exceeds the static ultimate value : ( ∗ ) = 2 3 ∙ ∙ 1⁄2 (( ∗ ) 3⁄2 − ( ∗ − ) 3⁄2 ) > (10). Now if fracture is supposed to take place after the load pulse ends ( ∗ > ), which means that the fracture delay occurs. The SIF values for ≤ equal those calculated in the previous case, however for > the ( ) values decrease (shown using a dotted line in figure 1). The corresponding ∗ and ∗ − values are marked with rhombus symbols. Thus, in this case the fracture delay (equaling ∗ − ) is present and the SIF value drops below after reaching the maximum. For each loading pulse amplitude there exists minimal pulse duration leading to fracture and crack initiation. For any pulse with amplitude and duration < fracture will not take place and thus this case can be regarded as a threshold case. For the considered situation the fracture time ∗ can be evaluated from expression max ∫ ( ) − = (11).