Numerical Example of Data-Reduction Procedures: Residual Stress Determination

Numerical Example of Data-Reduction Procedures ^*
A Micro-Measurements strain gage rosette, type CEA-062UL-120 , was applied to a cold-rolled steel bar. Elastic properties of the material are:

= 29.5 x 10 ⁶ psi, and

= 0.29. Using the RS-200 Milling Guide and the High-Speed Accessory, a 0.070-in diameter hole was drilled incrementally to a depth of 0.081 in. Since the gage circle diameter of the subject rosette is 0.202 in, the diameter ratio

= 0.347 for this example. The measured depths and strains for all increments are listed in Columns 1 and 3 of Table 1 .

The next step is to calculate the relieved strain parameters (

) and (

)** at each depth increment as shown in Columns 4-6 of Table 1 . For this purpose, the strain parameters at the "full-depth" hole are defined as the 100% relieved strain parameters.

Thus, at

= 0.4 (full depth):

Columns 4-6 of Table 1

To calculate the percent relieved strain parameters (or normalized parameters) at

= 0.050, for example:

Columns 4-6 of Table 1

These and all other normalized strain parameters are listed in Columns 4-6 of Table 1 . As recommended in ASTM E837 the normalized strains are plotted versus

(see below) for comparison with the uniform stress response. The experimental points, (

) in particular, fall well off the uniform stress response, and nonuniform stress is indicated.

Normalized relieved strains (from numerical example), compared to ASTM E837 uniform stress response.

Purely for demonstration purposes, the residual stress will first be calculated using only the maximum measured strains at the full-hole depth (0.081 in). The resulting stresses are those which would be inferred (erroneously) from the strain data by an experimenter who ignored the implications of Fig. 12, and assumed a uniform stress distribution.

Coefficients

and

for the full-depth hole can be read from Fig. 8a at the specified value of

= 0.347. Interpolating from the graph for the RE/UL rosettes:

= 0.147,

= 0.372

Substituting these values and the elastic properties of the steel into Eqs. ( 13 ):

Then, substituting 4

, 4

and the measured strains at

= 0.4 (from Column 3, Table 1 ) into Eqs. ( 11 ) yields:

= -33 deg from gage no. 1 to

, since

= +25 000 psi

= +12 000 psi

^* For simplicity and clarity in the presentation of this example, numerical values are given in U.S. customary units only. The procedure is, of course, unaffected by the units used.

^** Use

rather than

when the direction angle (

) is

(see ASTM E837).

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