Load Shedding Due to Growing Crack

The crack growth solver can redistribute a load during crack growth. Figure 1 shows a typical example of load shedding/redistribution due to a growing crack. In the case of a single crack in a lug, the cracked section W2 becomes less rigid than the un-cracked section W1, and part of the applied load is transferred to section W1. This situation would not happen in the case of two symmetric cracks because both sections have to hold the same amount of load equal to the half of the load applied to the lug.
Figure 1. Schematic Illustration of the Load Shedding Effect in an Attachment Lug


It has been shown using finite element analysis that this effect is relatively small, as long as crack stays quarter-elliptical, but becomes significant when the crack breaks through the entire thickness of the lug.
Figure 2. The Load Shedding/Redistribution Effect On the Stress Distribution in the Cracked Ligament


Introduction of the load shedding parameter, L S c / W MathType@MTEF@5@5@+= feaahGart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGmbGaam4ua8aadaqadaqaa8qacaWGJbGaai4laiaadEfaa8aa caGLOaGaayzkaaaaaa@3BEE@ , enables the estimation of the amount of load taken by the cracked section ‘W2’ and the estimation of the actual load. Once the shedding parameter LS is estimated, the shedding parameter could be used to reduce stress at the crack (Figure 2).
Figure 3.


Where,
c MathType@MTEF@5@5@+= feaahGart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGJbaaaa@36FF@
Crack length
Out of test data, the load shedding parameter was fitted into the following expression 5:
Figure 4.


A, B, and q are required inputs. In this particular example, A = 0.45 MathType@MTEF@5@5@+= feaahGart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqaiabg2 da9iaaicdacaGGUaGaaGinaiaaiwdaaaa@3AAC@ , B = 0.238 MathType@MTEF@5@5@+= feaahGart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOqaiabg2 da9iaaicdacaGGUaGaaGOmaiaaiodacaaI4aaaaa@3B6B@ and q = 0.65 MathType@MTEF@5@5@+= feaahGart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyCaiabg2 da9iaaicdacaGGUaGaaGOnaiaaiwdaaaa@3ADE@ were taken.

In actual crack growth calculation, the shedding parameter is used to reduce stress intensity factor:
Figure 5.


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