Determination of the Most Appropriate Mesh Size for a 2‐d Finite Element Analysis of Fatigue Crack Closure Behaviour

Abstract

A two-dimensional elastic-plastic finite element analysis is performed for plane stress conditions with 4-node isoparametric elements to examine closure behaviour of fatigue cracks, giving special attention to the determination of the most appropriate mesh sizes. It is found that a smaller mesh size does not always give more accurate simulation results in the fatigue crack closure analysis, unlike a conventional structural analysis. A unique, most-appropriate mesh size exists for a given loading condition that will provide numerical results which agree well with experimental data. The most appropriate mesh size can be determined approximately in terms of the theoretical reversed plastic zone sue. In particular, the ratio of the most appropriate mesh size to the theoretical reversed plastic zone size is nearly constant for a given stress ratio in the so-called crack-length-fixed method proposed in this study. By using the concept of the most appropriate mesh size, the finite element analysis can predict fatigue crack closure behaviour very well.Keywords-Fatigue crack closure; Finite element method; Most-appropriate mesh size, Crack-lengthfixed method. NOMENCLATURE a, a, = half crack length and initial crack length da/dN = crack growth rate E = Young's modulus H' = linear strain hardening parameter (du/ds) K , , , K-= maximum and minimum stress intensity factors due to applied loading KO, = opening stress intensity factor R = stress ratio (= K-IK,,) U = crack opening ratio [=(K,, -Kop)/(Kpu. -K-)] Aa, Aa* = mesh size and most appropriate mesh sue u,,,, u,, = opening and closing stress urnax, u-=maximum and minimum applied stress ur = yield stress v = Poisson's ratio up, Aup = theoretical monotonic and reversed plastic zone sizes

A short summary on finite element modelling of fatigue crack closure

“…Ref. [61] suggested from their FE study on the CCT geometry with Q4 elements that, a unique, most-appropriate mesh size exists for a given loading condition that will give good numerical results with close accord with the experimental results. The value of the most-appropriate mesh size was found to be nearly constant, ranging from 0.77 to 0.91 times the reversed plastic zone size (r c ); however, in terms of the monotonic plastic zone size it was seen to decrease with increasing K max , for the ranges of R (0-0.3) considered, suggesting that r c may relate better for estimating appropriate mesh size.…”

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

“…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 .…”

“…So, it is important to define the minimum crack extension needed to stabilize the opening level. It is usually sufficient to increase the crack ahead of the monotonic plastic zone resulting from the first load cycle [38,43,48].…”

“…So, it is important to define the minimum crack extension needed to stabilize the opening level, that is equal to the sum of the partial crack increments, i.e., Da stb ¼ P ðDaÞ i , with i varying from 1 to the number of increments necessary for stabilisation. Parks et al [38] suggested that to achieve closure stabilised values, the crack must propagate ahead of the monotonic plastic zone resulting from the first load cycle (r p ). Wu and Ellyin [48] found that under plane stress conditions the opening level reaches a stable value when the crack tip propagates over half of the initial plastic zone.…”

“…The second load cycle slightly deforms the fracture surface, reducing the closure level. Therefore at least two load cycles between each crack increment must be applied [20,30,38].…”