Issue 43

L.C.H. Ricardo, Frattura ed Integrità Strutturale, 43 (2018) 57-78; DOI: 10.3221/IGF-ESIS.43.04 62 where σ = Applied stress (MPa) σ ys = Yield strength (MPa) a = Crack length (m)                       1 1 2 I ys K a (2.16) Furthermore, the plastic zone size for plane conditions can easily be determined by combining eqs. (2.4) and (2.12). Thus,                       2 2 1 2 2 I ys ys K a r (2.17) In plane strain condition, yielding is suppressed by the triaxial state of stress and the plastic zone size is smaller than that for plane stress as predicted by the α parameter in eq. (2.17). The same reasoning can be used for mode III. Thus, the plastic zone becomes [12].            2 1 2 III ys K r (2.18) Dugdale’s approximation Dugdale [17] proposed a strip yield model for the plastic zone under plane stress conditions. Consider Fig. 3 which shows the plastic zones in the form of narrow strips extending a distance r each, and carrying the yield stress σ ys The phenomenon of crack closure is caused by internal stresses since they tend to close the crack in the region where a < x < c . Furthermore, assume that stress singularities disappear when the following equality is true K σ = - K I , where K σ is the applied stress intensity factor and K I is due to yielding ahead of the crack tip [6]. Hence, the stress intensity factors due to wedge internal forces are defined by       a r A a P a x K dx a x a (2.19)       a r B a P a x K dx a x a (2.20) According to the principle of superposition, the total stress intensity factor is K I = K A + K B so that                a r I a P a x a x K dx a x a x a (2.21)    2 cos I a x K P ar a (2.22) The plastic zone correction can be accomplished by replacing the crack length a for the virtual crack length ( a+r ), and P for σ ys Thus, the stress intensity factor are: