Numerical study of the effect of plastic wake on plasticity‐induced fatigue crack closure

Abstract

A B S T R A C T Fatigue crack closure is strongly influenced by the plastic wake developed because of the action of precedent cycles. It is related to the load sequence and is an additional difficulty for its determination. Finite-element method has been an alternative for the study of crack closure, commonly in constant-amplitude loading. However, such analyses are complex and computationally expensive, the length of the wake simulated being a critical parameter. In this paper, a comprehensive study of the effect of the plastic wake in fatigue crack closure is made. It is structured in two parts: one regarding the correct numerical modelling process and the other focussed on the influence of the wake under moderate variable-amplitude loading. After a brief description of the numerical methodology, results for different wake lengths are reported. The plastic wake is modelled with a new approach in which the final crack tip is fixed. Information regarding potential error is provided. Second, the load sequence effect is discussed. Crack closure is obtained for several load ratios, with wakes developed with different stress ratios. This permits the analysis of the influence of the load sequence over the crack-driving force compared with constant-amplitude loading.Keywords crack growth; fatigue crack closure; finite-element analysis; plastic wake. N O M E N C L A T U R Ea = crack length K I = stress intensity factor in mode I K max = maximum stress intensity factor K min = minimum stress intensity factor K ttop = crack opening, tip tensile criterion K ttcl = crack closure, tip tensile criterion K ncop = crack opening, node contact criterion K nccl = crack closure, node contact criterion K tt = crack closure/opening, tip tensile criterion K nc = crack closure/opening, node contact criterion

Finite element meshes for optimal modelling of plasticity induced crack closure

“…The opening values are low at the beginning and gradually increase, rising quickly at first and then more slowly as a stable value is reached. This is a well-known trend found by different authors [22,25,29,33,34]. The crack propagation required for stabilization, Da stab , is however dependent on load parameters.…”

“…7. The peak was observed for plane strain state by different authors [25,33,36,51,52], while others found a stable and fast increase without initial peak [22,23,53]. Lugo et al [38] showed that the peak is not only linked to the load level, but also to the T-stress.…”

“…Besides, a better accuracy at less expense is obtained if a fine mesh of linear elements is used rather than a comparable coarse mesh of quadratic elements. Gonzalez-Herrera and Zapatero [22] proposed a non-uniform mesh in the crack propagation region, in order to reduce the numerical effort. The element size reduces progressively up to final position of the crack tip, where the crack opening values are measured.…”

Analysis of the stress intensity factor along the thickness: The concept of pivot node on straight crack fronts

“…The parameters involved in the calculation of SIF are compared in this section between fracture and fatigue simulations …”

“…We also introduced a first three‐dimensional model with particular attention to aspects related to the study of the influence of thickness. Finally, an experimental validation was performed correlating the information obtained with the results of crack growth tests with constant amplitude loads . Since then, our objectives in numerical modelling have focused on the development of a complete three‐dimensional model of the problem.…”