SURFACE PLASTIC DEFORMATION (SPD)

As we have seen previously, useful EPD may be done only if the working load is of constant direction relative to the part. At that, the direction of the load vector relative to other objects, such as the housing, the ground, and the like, should not be considered. For example, a radial force applied to a shaft from gear teeth is of constant direction relative to the housing, but the shaft is rotating, so the vector of the bending moment rotates with reference to the shaft. As this takes place, each point of the shaft is loaded alternately in tension and in compression, and the EPD by bending in any direction can’t help but make the shaft crooked. In this case, it is useful to induce residual compressive stresses in the surface layer of the part — throughout or in the high-stressed portion of it.

Just a minute! A careful reader might say. If there is a residual compressive stress in the surface layer and the working stress changes cyclically from tension to compression, the stresses will alternately subtract and add. So the maximum tension stress will be less but the maximum com-pressive stress will be greater than without any residual stresses.

Yes, that is what is going to happen. But, what should be taken into account here is that the strength of steels is identical in compression and in tension, but only under a constant load. Under cyclic load, when materials fail by fatigue, it is not so.

Investigators made fatigue tests of T-shaped beams (Figure 3.14) bent by pulsating moment M.

The direction of the bending moment was chosen so as to have the compressive stresses greater than the tension stresses. The needed relation between these stresses was achieved by controlling the width of flange W. (The wider the flange, the lower is the position of the neutral axis and the FIGURE 3.13 Torsional deformation of a round beam that yields according to Figure 3.9b.

S_y

less the tension stress as compared to the compressive stress.) The fatigue cracks that appeared were mostly on the tensioned side. On the compressed side, cracks were obtained only when the compressive stress was about twice the magnitude of the tensile stress. Consequently, the fatigue strength of steels may be increased by decreasing the tensile stresses, even at the cost of an increase of the compressive stresses. But if the total compressive stress exceeds the yield point of the material, the residual stress decreases. The mechanism of residual stress loss is discussed in the following text.

The two methods most commonly used for SPD are burnishing (with balls or rollers) and shot peening. When burnishing, the surface layer is rolled out like dough on a table. To let the dough expand freely, the cook powders the table with flour. But in our case, the “table” (the layers underneath the plastically deformed layer) is bonded with the “dough” and resists its expansion.

The interaction between them creates some balanced system of internal stresses: compressive in the surface layer and tension underneath it (Figure 3.15). In addition to the compressive residual stress, the plastically deformed layer is somewhat stronger (see Figure 3.9). These two factors enable increase in the load capacity of the parts.

FIGURE 3.14 Bending stresses in a T-beam.

FIGURE 3.15 Residual stress distribution after shot peening or cold rolling.

M M

0 0

Compressive stress

Tensile stress W

Compressive stress Tensile stress

The burnishing roller should be pressed against the surface by a force that depends on the strength of the material, the diameters of the part and the roller, and the desired thickness of the deformed layer. The larger the diameter of the part, the thicker (as a rule) the plastically deformed layer should be (millimeters or even centimeters) to achieve a considerable increase in strength.

The shape of the roller also depends on the shape of the burnished surface. Usually, the working surface of the roller is shaped to a circular form (Figure 3.16a and Figure 3.16b), sometimes with a cylindrical portion (Figure 3.16c). To burnish a fillet, the radius of the roller profile should be less than the fillet radius. Figure 3.16d shows a special profile roller for burnishing fillets²: when the tool rotates with the shaft, the changing profile of the roller surface causes the contact points to alternately sweep from the center of the fillet to the sides, and back to the center. In this way, the contact spots of the fillet with the roller cover the entire surface of the fillet.

The same goal (creation of plastically deformed layer with residual compressive stress) is achieved by shot peening. A stream of hard spherical shots strikes the surface of the part at high velocity. Each shot dents the surface and produces a small plastic deformation. Thousands of shots create a plastically deformed layer. Its thickness doesn’t exceed 0.4 – 0.5 mm. After shot peening, the surface has a specific “pock-marked” appearance. The geometry of the shot-peened surfaces changes slightly, requiring those surfaces that have to be exact and smooth (such as shaft necks for bearings) to have subsequent fine machining, usually grinding. This process may be harmful because heating is inevitable while grinding and may relax the residual compressive stress and even change it to tension stress. The result of the machining can’t be controlled by nondestructive methods, and this reduces the reliability of this process.

Shot peening is successfully used for parts of complicated shape that can’t be burnished and don’t have to have an exact surface, such as springs, engine connecting rods, etc.

Burnishing allows creating a much thicker plastically deformed layer than shot peening, and, in case subsequent grinding is needed, the local overheating is much less dangerous. Besides, the surface after burnishing is very smooth, so that for some surfaces (for example, threads) SPD via burnishing may eliminate the need for further processing. And what is more, small and midsized threads are usually formed by rolling, without any cutting tools.

Finally, let’s discuss the issue of the possible loss of residual stress.

Figure 3.17a shows a very simplified stress distribution in the initial state: the part is unloaded, and in the shot-peened layer, there is a residual compressive stress σr that equals approximately 0.5 Sy (Sy is the yield point). Under this layer, there are tension stresses of relatively small magnitude. Dashed line 1 represents the stress pattern caused by bending the part with moment M.

The sum of the two patterns shown in Figure 3.17b represents the stress distribution in the loaded part. In the lower portion of the part, the compressive residual stress σr subtracts from the tension bending stress σb, and this results in a sharp decrease of the stress in this layer. In the upper portion FIGURE 3.16 Shapes of typical rollers for burnishing shafts.

(a) (b) (c) (d)

of the part, the compressive residual stress σr and the compressive bending stress σb are additive, and their sum exceeds S_y. But in the material, the yield stress can’t be exceeded at this magnitude of strain, and part of this sum (marked 2) is cut off. After the part is unloaded, the residual stress in the upper portion becomes less by exactly the cut off piece 2 (Figure 3.17c). In the lower portion, the residual stress remains the same until the part is bent in the opposite direction (Figure 3.17d).

Then, the residual stress will be lost in the lower portion as well.

If the sum σr + σb doesn’t exceed the yield stress, the residual compressive stress in the plastically deformed layer remains unchanged.

REFERENCES

1. Verhovsky, A.V., Broken cross-section hypothesis and its application to calculation of bars of com-plicated shape, Transactions of Tomsk Polytechnic Institute on the Name of S. M. Kirov, Vol. 61/1, Tomsk, 1947 (in Russian).

2. Almen, J.O. and Black, P.H., Residual Stresses and Fatigue in Metals, McGraw-Hill, New York, San Francisco, Toronto, London.

3. Peterson, R. E., Stress Concentration Factors, John Wiley & Sons, New York, London, Sydney, Toronto, 1974.

FIGURE 3.17 Loss of residual stress due to reversed bending.

M

σr

σr + σb

σb

1

S_y

2

(a) (b)

(c) (d)

M Residual tensile

stress

Part II