5.9. FURTHER READING 113
ere are then seven independent coefficients to be determined from the finite element analysis.
is contrasts with the isotropic case, where there are only two independent coefficients. For the
isotropic case, Equation (5.1) appears in matrix form as
2
4
A C B 0 A B
A 2B A
A B 0 A C B
3
5
2
4
x
xy
y
3
5
D
2
4
"
1
"
2
"
3
3
5
: (5.28)
Because of their greater complexity, residual stress measurements in orthotropic materials
are generally limited to the basic case where the stress is uniform through the hole depth.
5.9 FURTHER READING
General References
• Mathar J (1934). Determination of Initial Stresses by Measuring the Deformation Around
Drilled Holes. Transactions ASME, 56(4):249–254.
• ASTM (2013). Determining Residual Stresses by the Hole-drilling Strain-gage Method.
Standard Test Method E837-13, American Society for Testing and Materials, West Con-
shohocken, PA.
• Grant PV, Lord JD, Whitehead PS (2002). e Measurement of Residual Stresses by the
Incremental Hole Drilling Technique. Measurement Good Practice Guide, No. 53, National
Physical Laboratory, Teddington, UK.
• Vishay Measurements Group, Inc. (1993). Measurement of Residual Stresses by the Hole-
Drilling Strain-Gage Method. Tech Note TN-503-6, Vishay Measurements Group, Inc.,
Raleigh, NC. 16pp.
• Schajer GS and Whitehead P (2013). Hole-Drilling and Ring Core Methods. Chapter 2
in Practical Residual Stress Measurement Methods, G. Schajer, (Ed.), Wiley, Chichester, UK.
• Ajovalasit A, Scafidi M, Zuccarello B, Beghini M, Bertini L, Santus C, Valentini E, Ben-
incasa A, Bertelli L (2010). e Hole-Drilling Strain Gauge Method for the Measure-
ment of Uniform or Non-uniform Residual Stresses, AIAS Residual Stress Working Group,
TR01:2010, Florence, Italy, 70pp.
• Oettel R (2000). e Determination of Uncertainties in Residual Stress Measurement
(using the Hole Drilling Technique). Code of Practice 15, Issue 1, EU Project SMT4-
CT97-2165.
• Rendler NJ, Vigness I (1966). Hole-Drilling Strain-gage Method of Measuring Residual
Stresses. Experimental Mechanics, 6(12):577–586.
114 5. STRESS COMPUTATIONS
Calibration Method
• Beaney EM (1976). Accurate Measurement of Residual Stress on Any Steel Using the
Center Hole Method. Strain 12(3):99–106.
• Schajer GS (1981). Application of Finite Element Calculations to Residual Stress Mea-
surements. Journal of Engineering Materials and Technology, 103(2):157–163.
• Nau A, von Mirbach D, Scholtes B (2013). Improved Calibration Coefficients for the
Hole-Drilling Method Considering the Influence of the Poisson Ratio. Experimental Me-
chanics, 53(8):1371–1381.
• Boiten RG, ten Cate W (1952). A Routine Method for the Measurement of Residual
Stresses in Plates. Applied Scientific Research A3(5):317–343.
• Bueckner H (1958). e Propagation of Cracks and the Energy of Elastic Deformation.
Transactions ASME, 80:1225–1230.
• Baldi A (2017). Far-Field Boundary Conditions for Calculation of Hole-Drilling Residual
Stress Calibration Coefficients. Experimental Mechanics, 57(4):659–664.
• Blödorn R, Bonomo LA, Viotti MR, Schroeter RB, Albertazzi A (2017). Calibration
Coefficients Determination rough FEM Simulations for the Hole-Drilling Method
Considering the Real Hole Geometry. Experimental Techniques, 41(1):37–44.
Strain Gauge Modeling
• Schajer GS (1993). Use of Displacement Data to Calculate Strain Gauge Response in
Non-uniform Strain Fields, Strain, 29(1):9–13.
Incremental Stress Computation
• Bijak-Zochowski M (1978). A Semidestructive Method of Measuring Residual Stresses.
VDI-Berichte, 313:469–476.
• Niku-Lari A, Lu J, Flavenot JF (1985). Measurement of Residual-stress Distribution by
the Incremental Hole-Drilling Method, Experimental Mechanics, 25(2):175–185.
• Schajer GS (1988). Measurement of Non-uniform Residual Stresses Using the Hole-
Drilling Method. Journal of Engineering Materials and Technology, 110(4) Part I:338–343,
Part II:344–349.
• Zuccarello B (1999). Optimal Calculation Steps for the Evaluation of Residual Stress by
the Incremental Hole Drilling Method. Experimental Mechanics, 39(2):117–124.
5.9. FURTHER READING 115
• Schajer GS (2007). Hole-Drilling Residual Stress Profiling with Automated Smoothing.
Journal of Engineering Materials and Technology, 129(3):440–445.
• Schajer GS, Rickert TJ (2011). Incremental Computation Technique for Residual Stress
Calculations Using the Integral Method. Experimental Mechanics, 51(7):1217–1222.
• Schajer GS, Winiarski B, Withers PJ (2013). Hole-Drilling Residual Stress Measurement
with Artifact Correction Using Full-field DIC. Experimental Mechanics, 53(2):255–265.
Alternative Stress Calculation Methods
• Kelsey RA (1956). Measuring Non-uniform Residual Stresses by the Hole Drilling
Method. Proc. SESA, 14(1):181–194.
• Nickola WE (1986). Practical Subsurface Residual Stress Evaluation by the Hole Drilling
Method, Proc. SEM Spring Conference on Experimental Mechanics, New Orleans, pp. 47–
58.
• Schajer GS (1991). Strain Data Averaging for the Hole-Drilling Method. Experimental
Techniques, 15(2):25–28.
Error Analysis
• Vangi D (1994). Data Management for the Evaluation of Residual Stresses by the
Incremental Hole-Drilling Method. Journal of Engineering Materials and Technology,
116(4):561–566.
• Schajer GS, Altus E (1996). Stress Calculation Error Analysis for Incremental Hole
Drilling Residual Stress Measurements. Journal of Engineering Materials and Technology,
118(1):120–126.
• Scafidi M, Valentini E, Zuccarello B (2011). Error and Uncertainty Analysis of the Resid-
ual Stresses Computed by Using the Hole Drilling Method. Strain, 47(4):301–312.
• Casavola C, Pappalettera G, Pappalettere C, Tursi F (2013). Analysis of the Effects of
Strain Measurement Errors on Residual Stresses Measured by Incremental Hole-Drilling
Method. e Journal of Strain Analysis for Engineering Design, 48(5):313–320.
in Plate Specimen
• Schajer GS, Abraham C (2014). Residual Stress Measurements in Finite-thickness Ma-
terials by Hole-drilling. Experimental Mechanics, 54(9):1515–1522.
• Held E, Schuster S, Gibmeier J (2014). Incremental Hole-Drilling Method vs. in Com-
ponents: A Simple Correction Approach. Advanced Materials Research, 996:283–288.
116 5. STRESS COMPUTATIONS
• Schuster S, Steinzig M, Gibmeier J (2017). Incremental Hole Drilling for Residual Stress
Analysis of in Walled Components with Regard to Plasticity Effects. Experimental Me-
chanics, 11pp. https://doi.org/10.1007/s11340-017-0318-7
Hole Eccentricity Compensation
• Sandifer JP, Bowie GE (1978). Residual Stress by Blind-hole Method with Off-center
Hole. Experimental Mechanics, 18(5):173–179.
• Ajovalasit A (1979). Measurement of Residual Stresses by the Hole-Drilling Method:
Influence of Hole Eccentricity. e Journal of Strain Analysis for Engineering Design,
14(4):171–178.
• Beghini M, Bertini L, Mori LF (2010). Evaluating Non-uniform Residual Stress by the
Hole Drilling Method with Concentric and Eccentric Holes. Part I and Part II, Strain,
46(4):324–336 and 46(4):337–346.
• Nau A, Scholtes B (2012). Experimental and Numerical Strategies to Consider Hole Ec-
centricity for Residual Stress Measurement with the Hole Drilling Method. Materials
Testing, 54(5):296–303.
Material Plasticity Compensation
• Beghini M, Bertini L, Raffaelli P (1995). An account of Plasticity in the Hole-Drilling
Method of Residual Stress Measurement. e Journal of Strain Analysis for Engineering
Design, 30(3):227–233.
• Beghini M, Bertini L (1998). Recent Advances in the Hole Drilling Method for Residual
Stress Measurement. Journal of Materials Engineering and Performance, 7(2):163–172.
• Beghini M, Bertini L, Santus C (2010). A Procedure for Evaluating High Residual
Stresses by the Blind Hole Drilling Method Including the Effect of Plasticity. Journal
of Strain Analysis for Engineering Design, 45(4):301–318.
Orthotropic Materials
• Schajer GS, Yang L (1994). Residual-stress Measurement in Orthotropic Materials using
the Hole-Drilling Method. Experimental Mechanics, 34(4):324–333.
• Pagliaro P, Zuccarello B (2007). Residual Stress Analysis of Orthotropic Materials by the
rough-hole Drilling Method. Experimental Mechanics, 47(2):217–236.
5.9. FURTHER READING 117
• Prasad CB, Prabhakaran R, ompkins S (1987). Determination of Calibration Constants
for the Hole-Drilling Residual Stress Measurement Technique Applied to Orthotropic
Composites. Composite Structures, Part I: eoretical Considerations, 8(2):105–118; Part II:
Experimental Evaluations 8(3):165–172.
Residual Stress Computation Software
• Schajer GS. H-drill—Hole-Drilling Residual Stress Calculation Program. http://www.
schajer.org/index.htm
• SINT Technology. Restan MTS3000 Measurement System. http://www.residualst
ressmeasurement.com/the_hole-drilling_method.html
• Nobre JP, Dias AM, Domingos AJ, Morais R, Reis MJCS (2009). A Windows-
based Software Package to Evaluate Residual Stresses by the Incremental Hole-
Drilling Technique. Computer Applications in Engineering Education, 17(3):351–362.
https://www.researchgate.net/journal/1061-3773_Computer_Applications_
in_Engineering_Education
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