Buckling of residually stressed cylindrical tubes under compression

TL;DR

This paper investigates how residual stresses influence the buckling stability of cylindrical tubes under compression, revealing that residual stress can alter buckling modes and stability thresholds depending on tube geometry.

Contribution

It provides an exact bifurcation condition for buckling considering residual stresses, highlighting their impact on mode transitions and stability in cylindrical tubes.

Findings

Residual stress affects buckling behavior in thick-walled tubes.

Residual stress can delay or accelerate buckling depending on its characteristics.

Mode transitions depend on tube slenderness and residual stress distribution.

Abstract

We evaluate the loss of stability of axially compressed slender and thick-walled tubes subject to a residual stress distribution. The nonlinear theory of elasticity, when used to analyze the underlying deformation, shows that the residual stress induces preferred directions in the reference configuration. The incremental theory, given in Stroh form, is used to derive an exact bifurcation condition. The critical stretch and the associated critical buckling mode are identified for axisymmetric and asymmetric increments in the deformation. Mode transitions are illustrated as the tube slenderness varies. For slender tubes, Euler buckling is energetically favorable, and the effect of residual stress is negligible. However, for short and thick-walled tubes where barreling mode is dominant, the residual stress significantly affects the buckling behavior and may eliminate barreling instability. We show that, depending on its magnitude and direction, residual stress can either accelerate or delay instability. Phase diagrams for various modes are obtained and provide insight into pattern selection across different tube geometries.