By OMER W. BLODGETT, ScD., P.E.

Whenever an arc weld is made, the hot weld metal as well as the surrounding hot base metal must shrink as the metal cools. This shrinkage causes distortion in relatively flexible, limber members. When members are more restrained and rigid, the shrinkage strains must be accommodated by the base metal yielding. However, sometimes the base metal cracks instead, often in a brittle-like manner with no signs of deformation prior to fracture. Often, designers and fabricators assume that the steel has insufficient ductility, and that a materials problem exists.

For many years, engineering schools taught that the yield point is the primary indicator of ductility. A typical stress-strain curve as obtained from simple tensile specimens seems to reinforce this idea. While such curves and test specimens are useful, they fail to supply a complete understanding of material behavior.

In order for a material to exhibit ductility, four conditions are necessary:

• The loading must result in a shear stress.
• The shear stress must exceed a critical value.
• The shear stress must result in movement in a favorable direction.
• There must be a sufficient volume of material to result in substantial movement.

In this article, we'll examine the first two.

During WWII, I uncovered a gem of a book by Max Gensamer. Titled "Strength of Material Under Combined Stresses," it contains this quotation: "This is an important concept and needs to be emphasized: no shear stress, no plastic deformation or flow." Gensamer says that in the absence of shear stresses, ductility is impossible.

Mohr's circle of stress provides helpful insight into the concept of shear stresses. Consider a simple uniaxial tensile specimen as shown in Figure 1, and the corresponding Mohr's circle of stress.

The horizontal axis represents the tensile stress while the vertical axis denotes shear. The applied load results in a tensile stress s₁, which is plotted on the grid. Since no load is applied in the other two orthogonal directions, s₂ and s₃ are shown on the grid as zero. Three circles are then drawn: s₁ - s₂, s₁- s₃, and s₂- s₃. Only one circle actually appears in Figure 1, although three are actually present. The circles representing s₁ - s₂ and s₁ - s₃ are on top of each other while s₂ - s₃ is represented as a point on the plot.

The applied tensile load that results in s₁ also generates two shear stresses, t_1-2 and t_1-3. Theoretically, a third shear stress exists, t_2-3, but it has a value of zero because there is no vertical dimension associated with the point plot of the stress field s₂ - s₃.

Increasing the load on the tensile specimen generates the conditions of Figure 2. The increased tensile load results in increased shear stresses that now exceed the critical value, which is called the critical shear strength. Notice that this occurs at what is commonly called the yield strength of the material. Once these shear stresses exceed the critical shear strength, movement along the slip planes oriented at a 45-degree angle to the applied load will occur. Two shear stresses, t_1-2 and t_1-3, have a sufficient magnitude of shear, and thus two sets of slip planes are involved. Because the magnitude of shear stress t_2-3 is zero, it will not cause any movement.

When the specimen is loaded even further as shown in Figure 3, ductility continues to be exhibited until the applied load causes the critical tensile strength to be exceeded. At this point, fracture occurs, but only after significant plastic deformation has taken place. If ductility relieves the force that caused this movement (as is the case with weld metal shrinkage), the stresses will be reduced.

Figure 4 illustrates a different loading scheme. Rather than a single, uniaxial force, three forces in three directions are applied. For our purposes, stresses s₂ and s₃ will be assumed to be one half of s₁. Mohr's circle looks very different in this situation. Once again, while only one circle is visible, three actually exist: s₁-s₂,s ₁-s₃ (which are on top of each other), and s₂-s₃, which has a radius of zero. Notice that the shear stresses (the vertical dimension) are reduced as compared to those shown in Figure 1, even though the magnitude of s₁ is the same in both cases.

In Figure 5, the loading has increased to the level where yielding was experienced as shown in Figure 2. However, the stresses in the other two directions (s₂ and s₃), and the corresponding reduction in shear stress has resulted in a condition in which the critical shear strength has not been exceeded, and thus no ductility (yielding) is observed, despite the fact that s₁ is beyond what was called the yield strength in Figure 2.

When the loading is further increased, the critical tensile strength is exceeded as shown in Figure 6, yet no ductility is observed since the resulting shear stresses are still below the critical values. Again, notice that the so-called yield strength has been exceeded, yet no yielding has occurred. Any further loading would cause fracture, but with no sign of ductility.

Thus, we return to the words of Gensamer, which I have condensed to "No Shear, No Ductility". In the absence of shear stresses, no ductility can be experienced.

With this background in place, we'll return to the topic of ductility again, in part two, to examine factors that encourage ductility, and in part three, to consider factors that discourage 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.