Determination of Calibration Factors of the Hole Drilling Method for Orthotropic Composites using an Exact Solution

Abstract

The hole drilling method has been used for measurement of the residual stresses in various materials. The released strains measured by the hole drilling method are converted to residual stresses using calibration factors. There is a standard for the hole drilling method for isotropic materials. Also for orthotropic materials, there are various methods for converting the released strains to residual stresses. In these methods the numbers of calibration factors vary from two to nine (a three by three matrix). In this article, calibration factors of the orthotropic plates are determined based on an exact solution method. For this purpose, assuming a plane stress condition, stresses and strains around the area under a rosette strain gage mounted to an orthotropic plate are calculated. A hole in the center of the rosette strain gage changes the distribution of the stresses and strains. Using the closed form solution proposed in this research the released strains and the calibration factors are calculated, and the residual stresses are found. Also, calibration factors for any orthotropic material with any level of orthotropy are calculated. These factors are independent of the loading and depend on the material properties of orthotropic materials and the ratio of the rosette diameter to the hole diameter. The material properties and the ratio of the rosette diameter to the hole diameter are considered in the equations, therefore there is no need for presenting the results in tabular form or any interpolations. The results for an orthotropic unidirectional ply made of carbon/epoxy are presented. Also, the calibration factors for three different unidirectional composites are calculated. The results obtained from the proposed closed form solution are compared with the simulated hole drilling method. A good agreement between the results shows the reliability of the closed form solution presented in this study.

Keywords

exact solution residual stresses orthotropic materials calibration factors hole drilling method.

Get full access to this article

View all access options for this article.

References

Determining Residual Stresses by the Hole-Drilling Strain-Gage Method , ASTM Standard E837, American Society for Testing and Materials , 2004.

Schajer, G.S. (1988). Measurement of Non-Uniform Residual Stresses Using the Hole-Drilling Method. Part I. Stress Calculation Procedures, Journal of Engineering Materials and Technology, Transactions of the ASME, 110: 344—349.

Schajer, G.S. (1988). Measurement of Non-Uniform Residual Stresses Using the Hole-Drilling Method. Part II. Practical Application of the Integral Method, Journal of Engineering Materials and Technology, Transactions of the ASME, 110: 338—343.

Petrucci, G. and Zuccarello, B. (1998). A New Calculation Procedure for Non-uniform Residual Stress Analysis by the Hole-drilling Method, Strain Analysis , 33(1): 27—37.

Bateman, M.G. , Millera, O.H. , Palmera , T.J. , Breena, C.E.P. and Kingston , E.J. (2005). Measurement of Residual Stress in Thick Section Composite Laminates Using the Deep-hole Method, International Journal of Mechanical Sciences, 47: 1718—1739.

Prasad, C.B. , Prabhakaran, R. and Thompkins, S. (1987). Determination of Calibration Constants for the Hole-Drilling Residual Stress Measurement Technique Applied to Orthotropic Composites, Composite Structures, Part I: Theoretical Considerations , 8(2): 105—118.

Schajer, G.S. and Yang, L. (1994). Residual-Stress Measurement in Orthotropic Materials Using the Hole-Drilling Method, Experimental Mechanics, 34: 324—333.

Sicot, O. , Gong. X.L. , Cherouat, A. and Lu, J. (2004). Determination of Residual Stress in Composite Laminates Using the Incremental Hole-Drilling Method, Composite Materials, 37: 831—843.

Sicot, O. , Gong. X.L. , Cherouat A. and Lu, J. (2004). Influence of Experimental Parameters on Determination of Residual Stress Using the Incremental Hole-Drilling Method, Composite Science and Technology, 64: 171—180.

10.

Shokrieh, M.M. and Kamali, S.M. (2005). Theoretical and Experimental Studies on residual Stresses in Laminated Polymer Composites, Journal of Composite Materials, 39(24): 2213—2225.

11.

Shokrieh, M.M. and Ghasemi, A.R. (2007). Simulation of Central Hole Drilling Process for Measurement of Residual Stresses in Isotropic, Orthotropic and Laminated Composites Plates, Journal of Composite Materials , 41(4): 435—452.

12.

Savin, G.N. (1961). Stress Concentration around Holes (International Series of Monographs in Aeronautics and Astronautics. Division 1: Solid and Structural Mechanics), Pergamon Press, Oxford.

13.

Matlab , The Language of Technical Computing, Version 7.

14.

Tsai, S.W. and Hahn, H.T. (1980). Introduction to Composite Materials .

15.

Schajer, G.S. (1993). Use of Displacement Data to Calculate Strain Gauge Response in Non-Uniform Strain Fields, Strain, 29(1): 9—13.

16.

Aoh, J.N. and Wei, C.S. (2003). On the Improvement of Calibration Coefficients for Hole-Drilling Integral Method, Part II. Experimental Validation of Calibration Coefficients, Journal of Engineering Materials and Technology, Transactions of the ASME, 125(2): 107—115.

17.

Hwang, B.W. , Shu, C.M. and Kim, S.H. (2003). Finite Element Analysis of Calibration Factors for the Modified Incremental Strain Method , Journal of Strain Analysis for Engineering Design, 38(1): 45—51.

18.

ANSYS Help System , Analysis Guide and Theory Reference, Ver. 9.