numero25

F. V. Antunes et alii, Frattura ed Integrità Strutturale, 25 (2013) 54-60 ; DOI: 10.3221/IGF-ESIS.25.09 56 Gauss point, the monotonic plastic deformation increases and reversed plastic deformation starts. The plastic deformation has he highest magnitude when the Gauss point is immediately ahead of crack tip (position n in Fig. 2c). The comparison of Fig. 2a and 2b indicates that plastic deformation level is significantly higher for a mesh with 8  m elements (M8) compared with a mesh with 32  m elements (M32). In fact, the reduction of mesh size approaches the Gauss tip to crack flank, which increases the stress concentration factor. Additionally, more load cycles are applied when the crack approaches the Gauss point. Other Gauss points have similar behavior; however the levels of monotonic and reversed plastic deformation, and therefore the residual plastic deformation, vary. -4 -3 -2 -1 0 1 2 3 4 5 0.00 0.01 0.02  yy yy / ys -4 -3 -2 -1 0 1 2 3 4 5 0.00 0.01 0.02  yy yy / ys GP 1 5 n Figure 2 : Influence of finite element mesh on stress-strain curves. a) Mesh M32. b) Mesh M8. c) Position of the Gauss point. (a=10mm; W=30 mm;  max =47.5 MPa;  min =0.8 MPa). The location of the Gauss point relatively to the initial crack tip position has a major influence on residual plastic deformation. Fig. 3 presents the equivalent plastic strain along crack flank, which remains after crack propagation. A peak is evident at the beginning of crack propagation (a 0 =5 mm), which is followed by a progressive decrease until a stabilization is reached. The material hardening model influences the plastic deformation level, but not the global trend. The kinematic hardening model gives higher plastic deformation levels, which is linked to the occurrence of reversed plastic deformation during unloading. Fig. 4 shows the effect of stress state and mesh refinement. A peak still is observed at the beginning of crack propagation, but the deformation increases with crack propagation for the plane strain state which wasn’t expected. The use of finite elements with 8  m at the crack tip (mesh M8) instead of 16  m elements (mesh M16) increases the plastic deformation level. This could be expected since the decrease of element size approaches the Gauss points to the crack tip and additionally more load cycles are applied because the crack increments are smaller. Therefore the monotonic and reversed plastic deformation levels, and consequently the maximum stress and plastic deformation, are higher for mesh M8 compared to the mesh M16. Fig. 5b presents normalized stress-strain curves (  yy -  yy ), registered as the crack propagates under plane stress conditions, for Gauss points (GP) in different elements ahead of the initial crack tip (E1, E2, E8 in Fig. 5a). The crack is initially at position C0 indicated, and propagates ahead of element 8 (E8). The non-linear behaviour of the  yy -  yy curves at the first loading indicates the occurrence of yielding in all the elements analysed, i.e., that the initial monotonous plastic deformation extends ahead of element 8. However, the plastic deformation level is significantly higher for element E1, because it is closer to the crack tip. When the crack is extended one element, element E2 is immediately ahead of crack tip but the deformation does not reach the level obtained previously for element E1, which is due to the previous hardening.