Mode Mixity for Circular Hollow Section $X$ Joints With Weld Toe Cracks

This paper describes the mode mixity of stress-intensity factors for surface cracks at weld toes located at the saddle point in circular hollow section $X$ joints. The remote loading applies a uniform tensile stress at the end of the brace along its axis. The three-dimensional finite element models employ mesh tieing between a topologically continuous, global mesh and a separate, local crack-front mesh. Analyses of a simple plate model that approximates key features of toe cracks at the brace-chord intersection verify the negligible effects of the recommended mesh-tieing scheme on stress intensity factors. The linear-elastic analyses compute the mixed-mode stress intensity factors along the crack front using an interaction-integral approach. The mixed-mode stress intensity factors indicate that the crack front experiences predominantly mode I loading, with $KIII→0$ near the deepest point on the front $(ϕ=π∕2)$⁠. The total crack driving force, described by the $J$ integral, reaches a maximum value at the deepest point of the crack for the crack aspect ratio $a∕c=0.25$ considered here. The mode-mixity angle, $ψ=tan−1(KII∕KI)$⁠, at $ϕ=π∕2$ is compared for a range of practical X-joint configurations and crack-depth ratios. The present study demonstrates that the mode-mixity angle $ψ$ increases with increasing brace-to-chord diameter ratio $(β)$ and decreasing chord radius to wall thickness ratio $(γ)$⁠. Values of the nondimensional stress intensity factors (⁠$FI=KI∕σ¯brπa$ and $FII=KII∕σ¯brπa$⁠), however, show an opposite trend, with higher crack driving forces for small $β$ and large $γ$ ratios. The variations in the brace-to-chord wall thickness ratio $(τ)$ and the crack depth ratio $(a∕t0)$ do not generate significant effects on the mode mixity.