Issue 41

V.M. Machado et alii, Frattura ed Integrità Strutturale, 41 (2017) 236-244; DOI: 10.3221/IGF-ESIS.41.32 241 P applied on the cracked piece, then for a Ramberg-Osgood material with strain-hardening coefficient H and exponent h , it can be shown [4] that the crack driving force J is given in a clearer engineering notation by:                    1 h h 1 h 2 el pl I pc Y J J J K E P P S w a H a w h ( ) ( , ) h (4) where K I (P) is the SIF applied on the cracked piece (as if it remained LE), P pc is the plastic collapse load, S Y is the yielding strength, w is the cracked piece width, w  a is its residual ligament, and h is a non-dimensional function that depends on the cracked piece geometry and on the strain-hardening exponent h . Although not as easy to find as K I values, h- values may be found in tables for some simple geometries. However, this is not a major barrier in practice, since they can nowadays be calculated in most finite element (FE) codes for more complex components. To model the short crack behavior, like its LE analog K th (a) , the size-dependent crack propagation threshold J th (a) must include the a 0 effect:   th th 0 J a J 1 a a ( ) ( ) (5) Hence, like in the LE case, EP cracks grow whenever their driving force J is higher than their size-dependent threshold J th (a), a material property that can be properly measured, and stop otherwise. Cracks that depart from a notch tip can be much affected by its stress gradient when their size is small or similar to the notch tip radius  , so they can start and then stop after growing for a while, becoming thus non-propagating. Figure 4 e.g. shows this behavior for a crack that departs from a notch with   1mm and stops at a size a  1.8mm , when its J become smaller than its threshold J th (a) , becoming non-propagating. If P remains fixed, notice that this cracked component would then tolerate cracks with size 1.8 < a < 9mm . Figure 4 : EP crack that starts at a notch tip and then stops after growing for 1.8mm. E XPERIMENTAL EAC RESULTS urves K I (a)  a and J I (a)  a are calculated for notched DC(T) specimens by finite element analyses made using a suitable 2D Abaqus/CAE FE model, considering EP conditions near the notch tip as needed. These curves, which quantify the crack driving force, can be compared with the K EACth (a)  a and J EACth (a)  a curves, which quantify the material resistance to EAC conditions, including short crack effects. Such visual comparisons are very helpful in practice, since they can map the whole cracking problem. This technique is then used to make predictions about the short crack behavior that can be experimentally verified. To do so, notched DC(T)s of AISI 4140 steel (whose crack initiation and long crack growth EAC thresholds in a solution of H 2 S, S EAC  332MPa and K EACth  34.2MPa  m , have been previously measured by ASTM F1624 and ISO 7539 standards, and by NACE procedures [18-19]) are tested under EAC conditions as follows. First, two DC(T)s with a useful width w  60mm and a notch of length b  15mm and tip radius  2mm are EAC tested in the H 2 S solution under two load levels, P  6750N and P  8250N , which induce LE conditions around the notch tip. C