PSI - Issue 13

Yinghao Dong et al. / Procedia Structural Integrity 13 (2018) 1714–1719 Yinghao Dong, Xiaofan He, Yuhai Li / Structural Integrity Procedia 00 (2018) 000–000

1715

2

Nomenclature

a c

crack depth

half the crack length elasticity modulus

E

h

plate height

K I K n

mode I stress intensity factor

normalized mode I stress intensity factor the maximum relative crack depth

l t

plate thickness

W

plate width

remote uniform tensile stress parametric angle of the ellipse

σ

θ

have been employed to develop K I solutions for a surface cracked plate, including the approximate analytic method, experimental methods, the alternating method, the finite element method (FEM) and the curve fitting method. For a surface cracked finite plate subjected to remote uniform tension, Newman (1979) assessed various K I solu tions by correlating the fracture data on surface cracked tension specimens of epoxy with the estimated K I values at failure. It was indicated that the K I evaluated by Raju and Newman (1977) with the three-dimensional finite element method yielded the best accuracy while the solution given by Newman and Raju (1981, 1983) (hereafter referred to as Newman-Raju solution) was the most accurate solution in closed form. Hosseini and Mahmoud (1985) further verified Newman-Raju solution by comparing the K I evaluated by Newman-Raju solution with photoelastic K I measurements. Because of the closed form, satisfactory accuracy and the ability to estimate the K I at an arbitrary point on the crack front, Newman-Raju solution has been widely employed in analyzing surface crack-related problems. However, the application of Newman-Raju solution is restricted by the ratio of crack length along the surface direction (hereafter referred to as crack length, denoted as 2 c ) to the plate width (i.e. W ): Newman-Raju solution applies when 2 c / W is less than 0.5. Additionally, we found that Newman-Raju solution tends to overestimate the K I at the depth point, and the accuracy of Newman-Raju solution at the depth point is inferior to that at the surface point. We feel that Newman-Raju solution needs to be improved in terms of accuracy and application ranges. In this paper, we adopted the curve fitting method to develop a K I expression for a surface cracked finite plate subjected to remote uniform tension. First, by using the domain integral method provided by Abaqus, we obtained highly accurate numerical K I solutions for a number of surface crack configurations covering a wide range of t / W , c / a and a / t ( a is the crack depth and t is the plate thickness, Fig. 1). Second, the numerical K I solutions were fitted by assumed functions, with a closed K I expression obtained. Finally, a detailed analysis was conducted on the accuracy of the K I expression. Compared with Newman-Raju solution, the accuracy is improved and the application range is enlarged in terms of 2 c / W , making the proposed K I expression promising for engineering applications. The domain integral method provide by the finite element (FE) software, Abaqus, is characterized by robustness and high accuracy Syste`mes (2015). The core of the domain integral method involves the calculation of J -integral and the interaction integral. Three modes of SIFs, K I , K II and K III , can be extracted from the J -integral with the aid of interaction integrals Syste`mes (2015). Because of the symmetry about y − z plane, we built a half model of the surface cracked plate with the ratio of height to width (i.e. h / W ) of 3.0, as shown in Fig. 2. With respect to the FE model, a ring of quadratic wedge elements (C3D15) was used to define the crack front, for which the mid-side nodes on the sides connected to the crack front were moved to the 1 / 4 point nearest the crack front to create 1 / √ r singularity of the stress / strain field at the crack front. The remainder of the contour integral region was defined by five rings of quadratic hexahedral elements (C3D20) providing five paths for J -integral calculations (Fig. 2 (a)). In the other parts, quadratic tetrahedron elements (C3D10) or quadratic hexahedral elements (C3D20) 2. Finite element analysis