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.