A two-dimensional finite element method is used to develop stress intensity factor solutions for continuous surface flaws in structures subjected to an arbitrary loading. The arbitrary loading produces a stress profile σ acting perpendicularly to a given section S of the structure. The stress profile is represented by a third degree polynomial σ=A0+A1x+A2x2+A3x3
Stress intensity factor solutions are developed for continuous surface flaws introduced in particular sections S in the structure considered. Solutions are developed for a surface flaw in a flat plate, for both circumferential and longitudinal flaws inside a cylindrical vessel, and for circumferential flaws at several locations inside a reactor vessel nozzle.
The superposition principle is used, and the crack surface is subjected successively to uniform (σ = A0), linear (σ = A1x), quadratic (σ = A2x2), and cubic (σ = A3x3) stress profiles. The corresponding stress intensity factors (KI(0), KI(1), KI(2), KI(3)) are then derived for various crack depths using the calculated stress profile in the region of the crack tip. The total stress intensity factor corresponding to the cracked structure subjected to the arbitrary stress profile is expressed as the sum of the partial stress intensity factors for each type of loading. KI=KI(0)+KI(1)+KI(2)+KI(3)=πa[K0F1+2aπA1F2+a22A2F3+4a23πA3F4] where, a is the crack depth and F1, F2, F3, and F4 are the magnification factors relative to the geometry considered. The results are presented in terms of magnification factors versus fractional distance through the wall (a/t) and reveal the strong influence of the geometry of the structure and of the crack orientation.
The stress intensity factor solutions obtained using this method are compared to solutions obtained using other methods, when available. In the case of the plate geometry, the solution obtained for the linear loading (σ = A0 + A1x) is shown to agree well with the boundary collocation solution reported by Brown and Srawley. The stress intensity factor solutions for the circumferential and longitudinal cracks in the cylindrical vessel compare well with solutions obtained by Labbeins et al using the weight functions method proposed by Bueckner, and are also in good agreement with the solution for uniform loading (σ = A0) obtained using the line spring method proposed by Rice.
A method is described for obtaining lower bound KIc values, using compact specimens. The specimens are tested at temperatures for which valid KIc values cannot be obtained according to recommended specimen size requirements (ASTM Test for Plain-Strain Fracture Toughness of Metallic Materials (E 399-72)). This concept has been proposed by Witt and is called the “Equivalent Energy Method.” The procedure can be summarized as follows: 1. Select any point of the linear portion of the load-deflection curve (Point B). Measure the area under the load-deflection curve up to maximum load and divide this area by the area up to Point B. Call the ratio of areas b. 2. Using the load at Point B as PB calculate KBd as follows: KBd=b2PBbd(2bd)1/2ƒ(aw) If the specimen meets the ASTM E 399-72 size requirements, KBd, as calculated above, represents the fracture toughness KIc. Experimental verifications of the Equivalent Energy Concept are also presented. The results show that lower bound fracture toughness values can be obtained with compact specimens, utilizing the method as proposed by Witt. At a given temperature, the lower bound values obtained increase with increasing specimen thickness.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.