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56 Batch Processing

is prevented by constraints, as in a thermocouple or in a purposes the cyclic life of materials is expressed as a func-
pressure transducer. When the stresses are caused by sud- tion of the total strain range. There is a total strain range,
den changes in conditions, the process is referred to as ∼0.006, below which materials failure does not happen
thermal or pressure shock. Stresses caused under shock regardless of the number of stress–strain cycles applied.
conditions are greater than those due to slow temperature It corresponds to a high-cycle fatigue limit where the life
or pressure changes because of the steeper changes that are of the material reaches 1 million cycles.
generated and the larger rates of application of the stresses.
Many materials are affected by the rate at which the load is SEE ALSO THE FOLLOWING ARTICLES
applied. Some of them are embrittled and unable to with-
stand a shock stress that they can absorb when it is slowly
CHEMICAL PROCESS DESIGN • FRACTURE AND FA-
applied. In dealing with these stresses, it is important to
TIGUE • PHARMACEUTICALS • REACTORS IN PROCESS
account for plastic flow effects that occur when the yield
ENGINEERING • STOCHASTIC PROCESSES
point is exceeded and also how the flow may change dur-
ing progressive thermal or pressure cycling of the material.
Computational techniques are being developed to account BIBLIOGRAPHY
for inelastic effects such as creep and plastic flow, which
include cyclic effects in the computational procedure and American Institute of Chemical Engineers, Center for Chemical Process
in the interpretation of material behavior. Safety, New York.
Fatigue is a manifestation of a cumulative process lead- Barona, N., and Bacher, S. (1983). “Fundamentals of Batch Processing,”
ing to progressive fracture under cyclic loading. It starts Am. Inst. Chem. Eng., New York.
Chai, C.-P., and Valderrama, J. O. (1982). Chem. Eng. Sci. 37 (3), 494.
at cracks of the surface of the material, which propagate
Creed, M. J., Fausky, H. K. et al. “An easy inexpensive approach to the
inward. It is due to slip concentrated in isolated slip bands DIERS procedure,” Chem. Eng. Prog. 86 (3), 45.
inside the grains. It has a statistical behavior in the sense Knopf, F. C., Okos, M. R., and Reklaitis, G. V. (1982). Ind. Eng. Chem.
that a population of similar specimens break at widely dif- Process Des. Dev. 21, 79.
ferent numbers of cycles following a normal distribution. Mauderli, A., and Rippin, D. W. T. (1979). Comput. Chem. Eng. 3, 199.
Reiner, F., and Musier, H. (1990). “Batch process management,” Chem.
Cyclic loading restrains the life of the materials. Plastic
Eng. Prog. 86 (6), 66.
strain appears to determine the low-cycle range (<10,000 Renard, M. D. (1979). Comput. Chem. Eng. 3, 9.
cycles) of a material. The total strain, elastic plus plastic, Silver, L. H., Bacher, S., and Hacik, J. (1982). In “Computer Aided
is the factor determining the long-cycle range. Alterna- Process Plant Design” (M. E. Leesley, ed.), p. 720, Gulf Publishing,
tively, materials life can be regarded as being governed by Houston, TX.
Sinha, N. K., and Kuszta, B. (1983). “Modeling and Identification of
stress ranges; this is the total stress to which the material is
Dynamic Systems,” Van Nostrand–Reinhold, Princeton, NJ.
subjected during the cyclic load. However, the stress range Tahamatsu, T., Hashimito, I., and Hasebe, S. (1982). Ind. Eng. Chem.
is not as well known as the strain range, and for practical Process Des. Dev. 21, 431.