Thermal Expansion

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"Stresses (compressive, tensile, or shear) due to unequal temperature distribution and non-uniform temperature gradients, cause more failures in high-temperature equipment than all other influences combined amounting to approximately 90% of the total number of cases. It is destructive chiefly because the engineer does not include in his design proper allowance for or provision against temperature inequalities or because the operator imposes temperature differentials which cause localized dimensional changes with accompanying stresses greater than the elastic strength of the alloy at the given temperature."

- F. A. Fahrenwald. Some Principals Underlying the Successful Use of Metals at High Temperatures, Proceedings of ASTM, 1924 V. 24



Little has changed over the last 90 years. The vast majority of failures reported to Rolled Alloys, involving breaking or deformation in service, are due to restraint of thermal expansion. For successful design and installation of high temperature equipment it is critical to take thermal expansion into account, and to be able to calculate the amount of expansion to be expected. Below is a simple table for calculating total expansion, in inches per foot of length, for a given temperature.


Thermal Expansion
Total Thermal Expansion, inches/foot
Temp, °F  Carbon Steel  446  304 309 310 RA 253 MA RA330 RA333 601 600 RA 602 CA
70-200 0.0139 0.00874 0.0145 0.0137 0.0131 0.0141 0.0129 0.0109 0.0119 0.0115 0.0103
70-400 0.0376 0.0225 0.0372 0.0356 0.0348 0.0370 0.0341 - 0.0317 0.0305 0.0297
70-600 0.0623 - 0.0604 0.0591 0.0569 0.0610 0.0566 - 0.0516 0.0502 0.0496
70-800 0.0885 0.0526 0.0876 - 0.0806 0.0859 0.0797 - 0.0727 0.0710 0.0710
70-1000 0.0904 0.0681 0.115 0.108 0.106 0.111 0.104 0.0960 0.0949 0.0937 0.0915
70-1200 0.113 0.0854 0.144 - 0.133 0.137 - 0.122 0.120 0.117 0.115
70-1400 - 0.102 0.174 - 0.160 0.164 - 0.148 0.147 0.142 0.144
70-1600 - 0.123 - 0.185 0.186 0.193 0.180 0.173 0.175 0.167 0.174
70-1800 - 0.152 - - 0.214 0.224 0.208 0.201 0.204 0.193 0.201
70-2000 - - - - 0.245 - - - 0.236 - 0.227

To convert these numbers to the metric system, multiply by 83.33 to get millimeters of expansion for every meter of length, for the stated temperature, which is in Fahrenheit


For an example of how to use this table, consider a 20 foot long muffle made of RA330, operating at 1800°F. Read 0.208 inch/ft from the chart above, multiply by 20 feet for a total expansion of 4.16 inches

The more general way to calculate thermal expansion is to use the mean coefficients of thermal expansion, such as those given on the next page.

To use the table on page 2, multiply the length of the part in inches, times the difference between room temperature and operating temperature, times the expansion coefficient. Note that these coefficients are all multiplied by 10-6, which is the same as dividing by one million.

For example, consider that 20 foot long muffle made of RA330, operating at 1800°F:

20 feet X 12 inches/foot X (1800-70°F) X 10.0x10-6 = 240 inches X 1730°F X 10x10-6 = 4.152 inches.


Mean Coefficient of Thermal Expansion
ALLOY Temperature, °F
200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000
304, 316* 8.9 9.2 9.5 9.7 9.8 10.0 10.1 10.2 10.3 10.4 10.6 10.7 10.8 10.8 - - - - -
2205 7.2 7.3 7.5 7.7 - - - - - - - - - - - - - - -
321 9.3 - 9.4 - 9.5 - 10.0 - 10.3 10.5 10.6 - 10.9 - 11.1 - 11.4 - -
309 8.8 8.9 9.0 9.2 9.3 9.4 - - 9.7 - - - - 10.0 10.1 - - - -
310 8.4 8.6 8.8 - 8.95 - 9.2 - 9.5 - 9.8 - 10.05 - 10.15 - 10.3 - 10.6
Carbon Steel* 6.7 6.9 7.1 7.3 7.4 7.6 7.8 7.9 8.1 8.2 8.3 8.4 - - - - - - -
RA 253 MA® 9.06 - 9.34 - 9.59 - 9.81 - 9.97 - 10.14 - 10.3 - 10.5 - 10.8 - -
410 5.5 - - - - - - - - - 6.5 - - - - - - - -
RA330® 8.3 8.4 8.6 8.7 8.9 9.0 - 9.2 9.3 9.4 9.6 - - 9.7 9.8 9.9 10.0 - -
HR-120™ 7.95 - 8.29 - 8.56 - 8.80 - 8.98 - 9.24 - 9.52 - 9.72 - 9.84 - -
353 MA® 8.48 - 8.68 - 8.88 - 9.07 - 9.27 - 9.46 - 9.66 - 9.86 - 10.05 - -
800H/AT 7.9 - 8.8 - 9.0 - 9.2 - 9.4 - 9.6 - 9.9 - 10.2 - - - -
446 5.6 - 5.7 5.8 - 5.9 6.0 - 6.1 - 6.3 - 6.4 - 6.7 6.9 7.3 - -
600 7.4 - 7.7 - 7.9 - 8.1 - 8.4 - 8.6 - 8.9 - 9.1 - 9.3 - -
601 7.6 - 8.01 - 8.11 - 8.3 - 8.5 - 8.87 - 9.19 - 9.51 - 9.82 - 10.18
RA 602 CA® 6.6 - 7.5 - 7.8 - 8.1 - 8.2 - 8.5 - 9.0 - 9.5 - 9.7 - 9.8
RA333® 7.0 - - 8.0 - - - - 8.6 - 9.0 - 9.3 9.3 9.4 9.5 9.7 - -
HH - - - - - - - - 9.5 - 9.7 - 9.9 - 10.2 - 10.5 - 10.7
HK - - - - - - - - 9.4 - 9.6 - 9.8 - 10.0 - 10.2 - 10.4
HT 7.9 - 8.14 - 8.37 - 8.61 - 8.85 - 9.09 - 9.33 - 9.56 - 9.8 - 10.04
HP - - - - - - - - 9.2 - 9.5 - 9.8 - 10.0 - 10.3 - 10.6
825 7.8 - 8.3 - 8.5 - 8.7 - 8.8 - 9.1 - 9.5 - 9.7 - - - -
20Cb-3® 8.2 8.3 8.4 - 8.65 - - 8.9 8.95 - 9.15 - 9.3 9.4 9.5 - - - -
AL-6XN® 7.9 8.3 8.37 8.42 8.6 8.7 8.8 8.85 8.96 - 9.3 - - - - - - - -
Ti Gr 2 4.8 - - - 5.1 - - - 5.4 - 5.6 - - - - - - - -
NOTE: All coefficients are reported as inch/inch °F x 10-6, room temp to indicated temp. Multiply by 1.8 for metric units.
*ASME Section II Part D Table TE-1