Numerical simulation of residual stress relaxation around a cold‐expanded fastener hole under longitudinal cyclic loading using different kinematic hardening models

Abstract

A B S T R A C T Cold expansion of fastener holes creates compressive residual stresses around the hole.This well-known technique improves fatigue life by reducing tensile stress around the holes. However, cyclic loading causes these compressive residual stresses to relax, thus reducing their beneficial effect. Estimation of the fatigue life without considering the residual stress relaxation might lead to inaccurate results. In this research, numerical studies were carried out using 2D finite element (FE) models to determine the initial tangential and radial residual stress distributions generated by cold expansion and their relaxation under cyclic loading. To predict the stress relaxation, four nonlinear kinematic hardening models were applied in simulation of stress/strain path. The results obtained from the FE analysis were compared with available experimental results. A good agreement between the numerical and experimental results was observed.Keywords cold expansion; fastener hole; finite element simulation; residual stress relaxation. N O M E N C L A T U R Eā = current centre of the yield surface in the deviatoric stress spacē a 4 = threshold term C i = nonlinear kinematic hardening model parameter E = elastic modulus H = plastic modulus m = nonlinear kinematic hardening model parameter M = number of segments required for multilinear representation of the uniaxial stress-strain R = stress ratio s¯= deviatoric stress tensor S u = tensile strength ᾱ = current centre of the yield surface in total stress space δ = multiaxial parameter in the kinematic hardening rule ε p = plastic strain tensor γ i = nonlinear kinematic hardening model parameters ν = Poisson's ratio σ = stress tensor σ y = yield stress σ 0 = size of the yield surface

Experimental assessment of the redistribution of 3-D residual stresses during early fatigue at split-sleeve cold expanded reamed A/C fastener holes

“…Recent numerical studies, has underlined the importance of the use of real stress redistributions in predictions. It is obvious that residual stress varies during crack growth [73,74]. The numerical solutions using different kinematic hardening rules for open holes [74] have been reported to be in agreement with the available experimental results of the previous work [8].…”

“…How these stresses can withstand external loads is still a question. The majority of research so far suggests that fatigue life modeling and predictions for critical airframes containing cold expanded holes rely on precise determination of initial and current distributions of the residual stresses during cyclic loading [3,8,39,43,66,[68][69][70][71][72]74]. The stability of the initial distribution is of prime importance.…”

“…This is because of the complex nature of the expansion process. Due to extensive material constraint, plain-strain condition dominates at the mid-section and plane-stress condition is effective on each plate surface [40,74]. Thus, split-sleeve cold expanded holes are weak at inlet sides where cracking often starts at high service loads.…”

“…Extensive literature so far covers so many results of several reports particularly on the relaxation of residual stresses at cold expanded holes, where always the decay in stress has been attributed to micro-plasticity or sometimes cracking about the hole [8,66,72,74]. From the point of micro-plasticity, cyclic hardening and softening in precipitation-hardened aluminum alloys is mostly promoted by a mechanism in which the precipitate geometry and distribution as well as dislocation-particle interactions can be altered by cyclic straining.…”

“…While the constraint is maximized at mid-section (plain-strain), the sliding mandrel minimizes the material constraint at the vicinity of the inlet corner [74]. The state of stress at the inlet side is therefore the plane-stress condition.…”