PSI - Issue 1

Paulo Chambel et al. / Procedia Structural Integrity 1 (2016) 134–141 Author name / StructuralIntegrity Procedia 00 (2016) 000 – 000

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4

of body forces, as well as thermal induced stresses and traction stresses applied in the faces of the crack, as mentioned by Brocks et al. (2002) and Hellån (1985). In this case, J-integral value is assumed to have always the same value for all paths that enclose a hole or a crack, it is identical to the energy release rate for a plane crack extension (Budiansky and Rice 1973), and the two-dimensional J-integral along the closed contour  is given by Eq. (3) (Rigby and Aliabadi 1998).

 

  

  

J

   x Wdy T u

ds

(3)



 

where  is a closed contour – path of the integral – surrounding the crack tip, W represents the strain energy density or loading work per unit volume, T is the traction vector on ds , which includes the Cartesian components of stress tensor and is defined to the outward normal along  ( j ij i T n   ), u is the displacement vector at ds and ds is the increment of the contour path. The stress-intensity factor, K, and the J-integral are two approaches for evaluating the stress field at the vicinity of a crack tip and for a linear elastic material the stress intensity factors can be related to the J-integral, in combined modes, using Eq. (4) and Eq. (5) for plane-strain and plane stress conditions, respectively (Brocks at al. 2002) (Rigby and Aliabadi 1998).

1 2 

1     E

(4)



2 2 

   

  

   

2

J J I J II J     

K I K II

III K

III

E

1 2 2 K I K II III E J J I J II J     

(5)

1     E



   

  

   

2

III K

Crack propagation will occur when the strain energy release rate criterion is met, that is when the stress intensity factor at the crack tip reaches a critical value (Hutchinson 1983). In addition, variables such as the crack length, or the specimen thickness, are also important to define the extent of yielding at the crack tip, but also to influence cracking due to mixed mode. In fact, crack growth within a finite thickness is never restricted to mode I but instead is a mixture of modes I and III (Hellån 1985). Therefore, mode I or mode III could be dominant and if mode II loading is also included, the crack motion could occur out of its original tangent plane not corresponding to the assumption of a codirectional growth (Hellån 1985). J-Integral values can be obtained either through numerical methods (FEM) or by experimental tests and opening Mode I is the most studied crack propagation mode, while modes II and III are not so extensively studied. Hence, this work aims to study all opening modes from a numerical point of view and to study opening-mode III from an

experimental point of view. 2. Material and methods 2.1. Numerical simulations

A tridimensional standard compact specimen C(T) was designed and modeled in ANSYS Mechanical (Figure 3a), according to ASTM E647 (2000) and ASTM E1820 (2001), in order to calculate stress-intensity factors, K I, II, III , and J-integral values, J I,II,III , at the crack tip under plane-strain state. In addition, a second model of a compact specimen C(T) was designed and modeled in ANSYS Mechanical (Figure 3b), in order to simulate a crack under plane-stress state. The overall dimensions of the plane-stress compact specimen C(T) also followed ASTM standards ASTM E647 (2000) and ASTM E1820 (2001) , with the exception of the specimen’s thi ckness, which was not equal to 0.5W, but defined equal to 2.5 mm, which was the thickness of the specimens to be tested. The finite element meshes of the uncracked C(T) specimens were firstly composed by several regular solid elements (SOLID186) (Figure 3a,b), which were placed along its width (W) and thickness (B), in order to obtain J I,II,III results at the free surfaces and in the nodes distributed along the specimen thickness. Using the commercial software Zencrack, a 3D crack-block, named s03_t23x1, using collapsed nodes and midside nodes dislocated to ¼ of