In Part 1, Mohr's circle of stress was used to illustrate how multiaxial tensile stresses can reduce or even eliminate shear stresses that are essential for ductility. Now, we will consider the effect of compressional loading in one direction while tensile loading occurs in a second.

Figure 1 shows a cube with biaxial loading. In the horizontal direction, a tensile load is applied, resulting in a stress s₁. In the vertical direction, a compressional load is applied, resulting in a negative stress s₂. No stress is applied in the third direction, so s₃ is zero. For this example, we will assume that s₂ = - s₁/₂. Three circles can be drawn: s₁ - s₂, s₁ - s₃, and s₂ - s₃. The vertical dimension represents the shear stresses that result.

For the conditions shown, s₁ is well below the so-called yield strength, but as can be seen from Mohr's circle for s₁ - s₂, the shear stress t_1-2 is approaching the critical value.

In Figure 2, the tensile and compressional loading both are increased, and significant ductile behavior will occur on shear plane t_1-2. Notice that s₁ only now is approaching the so-called yield strength, yet significant ductile behavior has already occurred.

In Figure 3, the loads are increased again, to the point at which the tensile strength is reached. Yielding has occurred along two sets of shear planes, because t_1-3 and t_1-2 both have exceeded the critical shear values. The size of Mohr's circle (s₁ -s₂) demonstrates how effectively compressional loading encourages yielding when tensile loads are also present.

Steel mills have utilized this phenomenon for years when rolling plate (see Figure 4). When compressional loads are applied to reduce the thickness of steel, the steel is simultaneously pulled. The biaxial loading of compression (through the rolls) and tension (pulling the steel) reduces the amount of force required to reduce the thickness of the steel. Simply put, yielding occurs at a lower level of force.

Occasionally, we can take advantage of this same behavior in the design and fabrication of welded connections. Consider, for example, a splice of a heavy rolled, wide flange section. Figure 5 shows the bottom flange of such a splice. Weld access holes have been provided to enable the weld to be made across the full width of the flange. These holes are, typically, manually flame cut, with the possibility of gouges being present on the as-cut surface, particularly in the curved portions of the hole.

Sometimes, when the groove weld is made for the splice, cracking of the steel will occur, initiating at a gouge in the flame cut weld access hole. The driving force behind the cracking is weld shrinkage, which is made worse by the stress concentration associated with the gouge. Such cracks occur with limited deformation of the steel before fracture.

Residual stresses in welds and base metal result from the volumetric shrinkage that must occur as welds cool. Consider the longitudinal shrinkage of the weld as shown in Figure 5: It creates a residual tensile stress in the weld and the adjoining base metal. Moving away from the weld, the residual tensile stresses decrease to zero, eventually becoming residual compressive stresses. The weld also shrinks transversely, creating a residual tensile stress in the base metal.

A splice with a relatively small weld access hole is shown in Figure 5. Consider a small cube of material near the point where the weld access hole meets the flange. It is located in a region of residual tensile stress in one direction (due to the longitudinal shrinkage of the weld), as well as residual tensile stress in another direction (resulting from the transverse shrinkage). With biaxial tensile stresses present, ductility will be inhibited because of the reduction in shear stresses. Should there be a gouge at this location that was caused by flame cutting, cracking may occur due to the residual stresses from welding. Limited or no ductility will be seen.

A larger weld access hole is shown in Figure 6. While the transverse shrinkage will continue to create tensile stresses, the access hole has been sized so that the curved portion is at a location of zero longitudinal residual stress. Should a gouge be present in this larger access hole surface, more ductility would be expected – and cracking possibly avoided – because only uniaxial stresses are present.

In Figure 7, an even larger weld access hole is shown, one that terminates in an area of residual compression. The resultant stress field is similar to that depicted in Figure 2 where shear stresses are encouraged because of the presence of the compressional residualstresses. The enhanced ductility that results will encourage localized yielding, reducing cracking tendencies even ifgouges are present. This is one of the reasons for the minimumweld access hole dimensions that are required in some codes.

In the final segment of this series, we will examine factors that inhibit ductility.

Omer W. Blodgett, Sc.D., P.E., senior design consultant with The Lincoln Electric Co., struck his first arc on his grandfather's welder at the age of ten. He is the author of Design of Welded Structures and Design of Weldments, and an internationally recognized expert in the field of weld design. In 1999, Blodgett was named one of the "Top 125 People of the Past 125 Years" by Engineering News Record. Blodgett may be reached at (216) 383-2225.