Sample Response

Figure 22 presents a finite-element-derived contour map of the S33 stress component, computed in Abaqus with nodal averaging at a 75% threshold, across six parametric cases (a)–(f) of a fillet-welded T-joint comprising a vertical web plate welded into a horizontal flange plate that incorporates four bolt holes for subsequent bolted assembly. Each panel pairs a full isometric view of the joint with a magnified two-dimensional cross-section through the weld root/toe region, allowing simultaneous assessment of the in-plane (along-bead) extent of the residual stress field and its through-thickness distribution. The reported stress ranges are quantitatively similar but not identical across the six cases: (a) +214.9/–119.6 MPa, (b) +198.5/–107.7 MPa, (c) +218.7/–95.8 MPa, (d) +214.6/–137.9 MPa, (e) +225.3/–117.3 MPa, and (f) +225.2/–98.6 MPa. The consistency of these ranges across all six parametric combinations confirms that the underlying physical mechanism — differential thermal shrinkage during weld cooling, producing a self-equilibrating field of tensile stress at the bead balanced by compressive stress in the surrounding material — is preserved regardless of the welding sequence or plate thickness investigated, with the two parameters modulating the magnitude and spatial character of the field rather than altering its fundamental nature.

Five of the six panels (a, b, c, e, f) display a common spatial signature: an elongated, lens-shaped zone of peak tensile stress running along the weld bead, symmetrically bounded by a halo of compressive stress that decays to near-zero in the surrounding base material. This elongation along the bead axis, rather than across it, is the characteristic fingerprint of a longitudinal-type residual stress component, consistent with the classical thermomechanical description of arc-welding residual stress fields in which tension develops parallel to the weld direction as the last-to-cool weld metal and adjacent heat-affected zone are restrained from full contraction by the surrounding base plate. Panel (d) departs markedly from this pattern, exhibiting two discrete tensile peaks separated by a visible stress minimum rather than a single continuous lobe, and it simultaneously records the most negative compressive value of the six cases. A bimodal, spatially discontinuous field of this type is the expected signature of an interrupted or segmented weld deposition sequence — for instance, a split or dual-start sequence — in contrast to the single continuous pass implied by the unimodal distribution observed in the other five cases, and represents the clearest sequence-dependent structural change captured in the figure.

A second and independent line of evidence emerges from the through-thickness colour banding within the web member in each cross-sectional inset. In panels (b) and (e), the web cross-section is rendered almost entirely in the tensile (red/orange) range from the weld root to the free edge, indicating a residual stress field that is essentially saturated through the full member thickness. In panels (a), (c), and (f), the web instead displays a graded sequence of colour bands transitioning from tensile at the root to compressive toward the free edge, indicating a pronounced through-thickness stress gradient. This distinction is mechanically consistent with a thickness effect: in thinner members, the thermally and plastically affected zone constitutes a larger proportion of the total cross-section, leaving comparatively little unaffected material to impose an elastic restraint gradient, whereas thicker members retain a larger volume of cooler, unaffected base material that sustains a steeper through-thickness stress gradient. The cross-sections in (b) and (e) are therefore interpreted as representing the thinner-plate condition, with (a), (c), and (f) representing the thicker-plate condition, a grouping that is physically motivated by the contour morphology itself rather than by external labelling.

These observations carry direct implications for the mechanical and fatigue performance of the joint. Tensile peaks of 199–225 MPa, located precisely at the weld toe — the canonical site of fatigue crack initiation in fillet-welded T-joints — represent a substantial fraction of the yield strength of conventional structural steel grades and will superimpose directly onto externally applied service stresses, raising the effective local mean stress and thereby reducing fatigue life relative to a hypothetical stress-free joint. The compressive troughs located away from the toe, most pronounced in panel (d) and least pronounced in panels (c) and (f), are not without engineering benefit: mid-panel compressive residual stress is known to improve local buckling resistance under in-service compressive loading, even though it does not mitigate the fatigue risk concentrated at the toe. This suggests that the combination yielding the most favourable fatigue performance (the most diffuse, lowest-magnitude toe stress) need not coincide with the combination yielding the most favourable buckling performance (the largest, most concentrated mid-panel compression), and that panel (d)'s atypical bimodal field may represent precisely this kind of trade-off rather than a uniformly inferior outcome.

Taken together, the six panels demonstrate that welding sequence and plate thickness act through two largely separable mechanisms: sequence governs the spatial continuity of the residual stress field along the weld bead, as evidenced by the qualitative discontinuity unique to panel (d), while thickness governs the through-thickness distribution and degree of saturation of that field, as evidenced by the contrast between the fully saturated web sections in (b) and (e) and the graded sections in (a), (c), and (f). Neither parameter substantially alters the peak tensile magnitude, which remains confined to a comparatively narrow band of 199–225 MPa across all six cases, indicating that the dominant lever for reducing weld-toe residual stress in this joint configuration is more likely to be the heat input or restraint condition than thickness or sequence alone. This dissociation between sequence/thickness effects on stress topology versus their comparatively limited effect on peak magnitude is the central, citable insight of the figure, and constitutes the most defensible basis for any design recommendation drawn from it regarding optimal welding sequence selection for fatigue-critical versus buckling-critical applications of this joint type.