Elastic‐plastic Stress Analysis of Cold Expanded Fastener Holes

Abstract

A closed form solution technique first presented by Hsu and Fonnan for the radial expansion of a fastener hole is extended to include elastic-plastic unloading and therefore the creation of a reverse yielded zone. In addition, the dependence of interface pressure upon interference with an elastic insert is established. Numerous parametric studies are presented to demonstrate the effect of significant model variables and selected example calculations are compared with experimental results. NOMENCLATURE a = hole radius bl = radial distance to elastic-plastic boundary b, = radial distance to reverse yield boundary C = crack growth rate equation coefficient E =modulus of elasticity (plate) Ei = modulus of elasticity (insert) E, =secant modulus (plate) I, = applied expansion ratio 1, =interference ratio 1, = retained expansion ratio J2 = second invariant of the stress deviator tensor K,= crack growth rate equation coefficient n = strain hardening exponent (plate), crack growth rate equation exponent p = pressure r = radial coordinate in cylindrical coordinate system R = ratio of in-plane transverse plastic strain to through the thickness plastic strain, ratio cycle minimum to cycle maximum stress u = radial displacement B = Bauschinger parameter E = strain v = Poisson's ratio (plate) vi = Poisson's ratio (insert) 0 = tangential coordinate in cylindrical coordinate system u = stress ue = effective stress no = flow stress by = uniaxial yield strength

Finite-element simulation of residual stress induced by split-sleeve cold-expansion process of holes

“…Working on residual stress distribution, Guo (1993) achieved the exact solution for a cold-worked hole considering Ball's model (Ball, 1995) for a non-linear response of the unloading step. This analytical solution, such as all other analytical models (Nadai, 1943;Hsu and Forman, 1975;Rich and Impellizzeri, 1977), does not provide the stress differences through the thickness.…”

On the Measurement and Prediction of the Out-of-Plane Displacement Surrounding Cold-Expanded Holes

“…The literature presents several representative theories to evaluate the residual stress field, and these analytical models are perhaps an example of the historical development of plasticity theory [3][4][5][6][7]. However, these solutions are based on assumptions that neglect the through-thickness changes of residual stresses along the hole bore.…”

Plastic collapse mechanisms in thin disks subject to thermo-mechanical loading

“…An excellent review of previous works devoted to the problem of enlargement of a circular hole in thin plates has been given in [19]. The assumptions made regarding yield criterion, strain hardening and unloading have a significant effect on the predicted response and residual stress and strain fields [7]. Even though closed-form solutions involve more assumptions than numerical solutions, the former are necessary for studying qualitative effects and verifying numerical codes.…”

“…A significant amount of analytical and numerical research for various material models has been carried out in the area of stress and strain analysis of such structures (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] among many others). An excellent review of previous works devoted to the problem of enlargement of a circular hole in thin plates has been given in [19].…”