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# 8.5 Residual Stress

Unhomogenous heating causes local thermal expansion of metals. This is reflected in residual stress after cooling. Residual stress is a tensile stress in the center of a weld. Tensile stress in a weld is compensated by compressive stress in base metal. Weld metal is squeezed as it cools. During welding, edges move relative to each other, mostly perpendicular to the welding direction. Residual stress results in shrinkage of the structure. The choice of welding sequence affects the distortion of the welded structure. If a welder uses opposite directions, the distortion is smaller. If a weld is below the neutral axis the shape is concave up. If a weld is over the neutral axis the shape is concave down. The angle b is small for small weld depths. The angle is not too large if the weld depth is equal to the thickness of the plate. A similar effect can be observed in a tee-joint. For thin plates the displacement caused by residual stress is rather large, it decreases as thickness increases. Residual stress is at a maximum for a rigid structure with a large number of welds and with closed loops. The structures are shown in order of increasing rigidity. The residual stress decreases as annealing temperature increases. There are annealing procedures that can reduce residual stress to zero.

## 8.6 Strength

Strength of a welded joint depends on weld geometry and strength of materials. The minimum cross section of a weld is considered in strength calculations. Throat a is at a minimum. Throat is the distance from the root to the surface of a fillet weld. The throat of a fillet is a measure of the weld size. Critical force P for a lap joint using a 45 degree filet weld depends on allowable shear stress for the weld material tallowable. Bending stress is small if moment of inertia of the weld cross-section is large. The moment depends on the cross sectional area and it's distance from the neutral axis shown in the figure. The second example is three times stronger than the first. The tensile strength of a butt-joint is higher for the case with low stress concentration. Build-up welds are often produced to increase wear resistance, not tensile strength. Spot resistance welding. The nugget is stronger under shear than in tension. Strength of nugget increases with thickness. Contrary to uniform low-carbon steel plate, it's weld joint can have a brittle fracture mechanism: smaller critical stress at low temperature. Usually the temperature of brittle-ductile transition is below zero, ranging from -100oC to -40oC. Annealing increases the ductility of materials and prevents brittle fracture. Crack resistance characteristic - the critical value of stress intensity factor depends on test temperature. Usually the brittle fracture for base metal, weld and heat-affected zone are similar, lower limits are equivalent. The characteristic of ductile fracture (upper limit) is usually smaller in the welded zone. Presence of oxygen in weld material affects the embrittlement of the material. High oxygen content corresponds to embrittlement (relatively high transition temperature).

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