Dugdale plastic zone size and CTOD equations for the compact specimen

Abstract

The Dugdale model concept [i] has been used with center crack tension specimens in several fracture analyses [2] and in the development of simple crack closure models [3] for cracked metallic materials. Currently, the compact specimen is the most widely used specimen for fracture toughness and fatigue crack growth rate testing.To use the Dugdale model with the compact specimen (see Figure l(a)), equations for stress intensity factor K and crack surface displacement V must be obtained for the two loading cases shown in Figure l(b)--a pair of pin loads P and a uniform stress o^ acting on a segment p of the crack surunit thickness.) face.(P is load per oThe pin-loaded case was previously analyzed [4] to obtain stress intensity factors and crack surface displacements.Srawley [5] fitted the results from [4] with a power series to obtain an equation for K. The boundary collocation method [4] is used herein to analyze the case for uniform stress.Both stress intensity factors and crack surface displacements, under plane stress conditions (~ = 0.3), were calculated.The Dugdale model for the compact specimen requires that the "finiteness" condition of Dugdale be satisfied.This condition states that the K at the tip of the plastic zone (at d = a + p) is zero. From this condition, the plastic zone size (p) was calculated for various a/w and P/wo 0 ) ratios.An equation was then fitted to these results and was p/a = (~w/8a)(PF/WOo)2F 0 where (l) F = (2 + ~)(0.886 + 4.64a -13.32~ 2 + 14.72a 3 -5.6a 4)/(I -a)~2(2) F 0 = i + fl(P/WOo) + f2(P/WOo)2fl = -2.687(1 -~) + 0.167/~ 2 (4) Int Journ of Fracture 24 (1984)

Notch Fatigue Crack Initiation and Propagation Life under Constant Amplitude Loading through Residual Stress Field

“…f present the contribution of crack closure and the parameters C, n, p, q were determined experimentally and ∆K th is the crack propagation threshold value of the stress-intensity factor range. For constant amplitude loading, the function f determined by Newman [28] can be written as (Eq. 7).…”