13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- Case I is the extensively studied loading configuration—uniform tension, i.e. ( ) 1= s x (5) Case II is a combined tension and bending load that decreases linearly from unity to zero, ( ) 1 =− + s x x t (6) This was selected as a representative of the linear stress variation. Case III represents a stress variation existing on the wall of a cylindrical vessel subjected to a uniform internal pressure, which can be expressed as ( ) ( ) − + − = 2 o 2 o 2 i 2 o 2 i 1 R x R R R pR s x (7) where iR and oR are the inner and outer radii of the vessel, respectively; p is the internal pressure. In the simulation, the ratio of i oR R is chosen to be 2 and p to be 1 MPa. The location where x=0 corresponds to the external wall of the vessel, thus the modelled crack is similar to an external surface crack in a cylinder. Case IV is a typical stress distribution existing in cruciform fillet welded joints [7], as shown in Fig. 5. Verreman et al. [7] proposed the following equations to describe the stress variation occurring at the weld toe ( ) i i i t x t x s x = ∑ = − 4 0 λ α 0.5 0≤ ≤ x t (8) ( ) i i i t t x t t x s x − − = ∑ = − 4 0 λ α 1 0.5≤ ≤ x t (9) The above equations were obtained by fitting them to the two dimensional elastic element results. For the particular cruciform fillet joint shown in Fig. 4, the following parameters have been used: α=0, 0λ=0.414, 1λ=0.815, 2λ=-1.71, 3λ=4.16, 4λ=-3.7. High stress concentration can be found at the weld toe, which is the reason why the crack initiation is often induced there. This crack problem has been received a great deal of attention due to its importance in engineering practice. a l l t t CRACK AT WELD TOE l/t = 0.5 θ = 45 Figure 4. Cruciform fillet welded joint Case V is used by the author to demonstrate the ability of the numerical technique to simulate the fatigue crack growth in a complex stress field containing compression. It is well known that compressive stresses are often generated on purpose to resist fatigue cracking as well as its subsequent growth. The shot peening is usually considered beneficial to delaying or even avoiding
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