A New Rosette Design for More Reliable Hole-drilling Residual Stress Measurements by G. S. Schajer and M. Tootoonian ABSTRACT--A new six-element strain gage rosette is pre- sented that can greatly improve residual stress measurement accuracy when using the hole-drilling method. The proposed rosette consists of three pairs of sector-shaped radial and cir- cumferential gages connected as half-bridges. This rosette design increases effective strain sensitivity by a factor of 2.3 compared with a standard ASTM rectangular rosette, and can identify stresses at one-third greater depths from the mea- surement surface. Experimental measurements confirm the- oretical strain response calculations within 3-4 percent. Apart from a small increase in time to complete the electrical con- nections, the practical use of the proposed rosette is identical to that of a conventional three-element rosette. Introduction The hole-drilling method 1-4 is a popular technique for measuring residual stresses near the surface of a specimen. The experimental procedure is simple, economical and effec- tive. It involves drilling a small hole and using a strain gage rosette, such as that shown in Fig. 1, to measure the result- ing strain changes in the surrounding material. These strain changes can be quite large at the hole edge, but they diminish rapidly with distance from the hole. Because the strain gages must lie some distance from the hole, they measure only a fraction of the maximum strain change, typically about one- third. As a result, the sensitivity of the hole-drilling method is modest, with typical measured strains in the range 100- 3001x~. Thus, careful experimental technique is essential to ensure that any strain measurement errors are minimized and are small compared with the measured strains. In the most common application, 1 the residual stresses are assumed to be uniform with depth from the specimen surface. The hole-drilling method can also evaluate residual stresses that vary with depth from the specimen surface. 5-1~ In this case, an incremental technique is used in which re- lieved strains are measured during a series of small hole depth increments. However, such nonuniform stress mea- surements are much more sensitive to measurement errors than uniform stress evaluations. 5'7'1~ This error sensitiv- ity occurs because the strains are measured at the specimen surface, whereas the desired nonuniform stresses are deep in the interior. St. Venant's principle indicates that the surface strain response rapidly becomes insensitive to the effects of G. S. Schajer is Professor, and M. Tootoonian is a Graduate Student, Depart- ment of Mechanical Engineering, University of British Columbia, Vancouver, British Columbia, Canada V6TIZ4. Original manuscript submitted: November 30, 1995. Final manuscript received: January 24, 1997. interior stresses at increasing distances from the measurement surface. These considerations indicate that two main objectives are involved when seeking to enhance the stress evaluation ac- curacy of the hole-drilling method. The first objective is to increase the overall sensitivity of the strain measurements. The second objective is to increase the strain sensitivity to interior stresses. Unfortunately, to a large extent, these two objectives are mutually exclusive. In most cases, a change that advances one of them impairs the other. For example, reducing the length of each strain gage of the rosette in Fig. 1 increases the proportion of the gage area that is close to the hole edge. This change increases strain sensitivity. However, it also concentrates the strain sensitivity on the stresses close to the specimen surface, and thus diminishes the ability to identify interior stresses. Such concentration on the surface stresses can be undesirable even in the uniform stress case because the surface stresses may not be representative of the interior. This study is aimed toward designing a modified hole- drilling rosette that increases both overall strain sensitivity and interior stress sensitivity. Three rosette design variables are examined: strain gage direction, strain gage size and rosette layout. The resulting rosette design proposed here involves changes in all three design variables. Theoretical calculations and experimental measurements confirm that the new rosette has an overall strain sensitivity more than dou- ble that of the traditional ASTM rectangular design shown in Fig. 1. The new rosette can also identify stresses at one-third greater depths from the specimen surface. Uniform Stress Hole Drilling The simplest measurement type occurs when the residual stresses are uniform with depth from the surface. In this case, the strain measured by a typical gage in the strain gage rosette shown in Fig. 1 is (1 + ( = --(frmax + O'min ) 2E a (1) q- ~-~ (Oma x -- O'min) COS2if, where E = measured strain Crmax,Crmi n = principal stresses 13= angle to maximum principal stress direction E = Young's modulus v = Poisson's ratio a,/~ = calibration constants Experimental Mechanics 9 299