Influence of minimum element size to determine crack closure stress by the finite element method

Numerical simulation of plasticity induced crack closure: Identification and discussion of parameters

“…This decreasing influence can be explained by a lever effect: the rotation imposed by a remote plastic wedge produces a small vertical movement near the crack tip. This lever effect explains the lower stabilization period required for plane strain conditions [23,36]. In fact, crack opening is larger at interior positions of the crack front, therefore the effect of the remote plastic wake is lower.…”

“…Classical mesh refinement studies have been developed, however the literature disagrees about the existence of the typical convergence of results with mesh refinement. Gonzalez and Zapatero [36] considered up to 140 linear elements within the monotonous plastic zone and found near stable closure values. Parks et al [38] considered a pure kinematic hardening model and obtained a minimum stable value of U for L 1 /r p,c % 0.77-0.91, the size of the cyclic plastic zone being r p,c .…”

“…In situations with very small element sizes and where long propagation is required for stabilization, it is interesting to perform extrapolation of crack closure values in order to perform a limited number of crack propagations and save numerical simulation time. González-Herrera and Zapatero [36] and Jiang et al [35], respectively, proposed the following extrapolation models:…”

“…Solanki et al [28] indicated that a crack growing under cyclic loading with R = 0 had a reversed plastic zone about 1/10 the size of the forward plastic zone (while for a stationary crack this is about 1/4 the size). Therefore, if L 1 is too large, the occurrence Number of load cycles between crack increments (P2) [35] Number of crack increments necessary for stabilisation (Da = RDa i P r p,m ) [21,28,35,37] Closure definition Last contact or inversion of stresses at crack tip [22,44] Crack opening or crack closure [36,45] of reversed plasticity will not be modelled. The increase in DK, produced by the increase in crack length or Dr, and the use of higher order elements may be accomplished by an increase in L 1 .…”

Finite element simulation of plasticity induced crack closure with different material constitutive models

“…A brief review concerning material modelling in the numerical simulation of crack closure reveals that most of the published works considers the metallic materials stress-strain response modelled as elastic-perfectly plastic [9][10][11][12][13][14][15][16][17][18][19][20][21][22] or bi-linear [5,9,12,20,[23][24][25][26][27][28][29][30][31]. Some of the published works employed material constitutive relationships that ignore kinematic hardening [10,[32][33][34].…”