ASTM E1561-93(2009)

Standard Practice for Analysis of Strain Gage Rosette Data

ABSTRACT
This practice defines a reference axis for each of the two principal types of rosette configurations and the equations used for three-element strain gage rosette data analysis. The primary uses of this analysis procedure are to determine the directions and magnitudes of the principal surface strains, and to determine residual stresses. This is important for consistency in reporting results and for avoiding ambiguity in data analysis, especially when computers are used. There are several possible sets of equations, but the set presented herein is perhaps the most common.
SCOPE
1.1 The two primary uses of three-element strain gage rosettes are (a) to determine the directions and magnitudes of the principal surface strains and (b) to determine residual stresses. Residual stresses are treated in a separate ASTM standard, Test Method E 837. This practice defines a reference axis for each of the two principal types of rosette configurations used and presents equations for data analysis. This is important for consistency in reporting results and for avoiding ambiguity in data analysis—especially when computers are used. There are several possible sets of equations, but the set presented here is perhaps the most common.

General Information

• Status: Historical
• Publication Date: 31-Aug-2009
• ICS: 77.040.99 - Other methods of testing of metals
• Technical Committee: E28 - Mechanical Testing
• Drafting Committee: E28.01 - Calibration of Mechanical Testing Machines and Apparatus

Relations

• Replaces: ASTM E1561-93(2003) - Standard Practice for Analysis of Strain Gage Rosette Data
• Effective Date: 01-Sep-2009
• Referred By: ASTM E998-19 - Standard Test Method for Structural Performance of Architectural Glass Products Under the Influence of Uniform Static Loads
• Effective Date: 01-Sep-2009

Standards Content (Sample)

NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
Designation: E1561 − 93(Reapproved 2009)
Standard Practice for
Analysis of Strain Gage Rosette Data
This standard is issued under the fixed designation E1561; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
INTRODUCTION
There can be considerable confusion in interpreting and reporting the results of calculations
involving strain gage rosettes, particularly when data are exchanged between different laboratories.
Thus, it is necessary that users adopt a common convention for identifying the positions of the gages
and for analyzing the data.
1. Scope For the 0° – 60° – 120° rosette (Fig. 2) the axis of the b gage is
located 60° counterclockwise from the a axis and the c axis is
1.1 The two primary uses of three-element strain gage
located 120° counterclockwise from the a axis.
rosettes are (a) to determine the directions and magnitudes of
3.2.3 ε , ε ,ε —the strains measured by gages a, b, and c,
the principal surface strains and (b) to determine residual
a b c
respectively, positive in tension and negative in compression.
stresses. Residual stresses are treated in a separate ASTM
After corrections for thermal effects and transverse sensitivity
standard, Test Method E837. This practice defines a reference
axis for each of the two principal types of rosette configura- have been made, the measured strains represent the surface
strains at the site of the rosette. It is assumed here that the
tions used and presents equations for data analysis. This is
important for consistency in reporting results and for avoiding elasticmodulusandthicknessofthetestspecimenaresuchthat
ambiguity in data analysis—especially when computers are mechanical reinforcement by the rosette are negligible. For test
used. There are several possible sets of equations, but the set objects subjected to unknown combinations of bending and
presented here is perhaps the most common. direct (membrane) stresses, the separate bending and mem-
brane stresses can be obtained as shown in 4.4.
2. Referenced Documents
3.2.4 ε' , ε' , ε' —reduced membrane strain components
a b c
2.1 ASTM Standards:
(4.4).
E6 Terminology Relating to Methods of Mechanical Testing
3.2.5 ε" ,ε" ,ε" —reducedbendingstraincomponents(4.4).
a b c
E837 Test Method for Determining Residual Stresses by the
3.2.6 ε —the calculated maximum (more tensile or less
Hole-Drilling Strain-Gage Method
compressive) principal strain.
3. Terminology 3.2.7 ε —the calculated minimum (less tensile or more
compressive) principal strain.
3.1 The terms in Terminology E6 apply.
3.2.8 γ —the calculated maximum shear strain.
M
3.2 Additional terms and notation are as follows:
3.2.9 θ —the angle from the reference line to the direction
3.2.1 reference line—the axis of the a gage.
of ε . This angle is less than or equal to 180° in magnitude.
3.2.2 a, b, c—the three-strain gages making up the rosette.
3.2.10 C, R—values used in the calculations. C is the
For the 0° – 45° – 90° rosette (Fig. 1) the axis of the b gage is
location, along the ε-axis, of the center of the Mohr’s circle for
located 45° counterclockwise from the a (reference line) axis
strain and R is the radius of that circle.
and the c gage is located 90° counterclockwise from the a axis.
4. Procedure
This practice is under the jurisdiction ofASTM Committee E28 on Mechanical
Testing and is the direct responsibility of Subcommittee E28.01 on Calibration of
4.1 Fig. 3 shows a typical Mohr’s circle of strain for a
Mechanical Testing Machines and Apparatus.
0° – 45° – 90° rosette. The calculations when ε , ε , ε , are
a b c
Current edition approved Sept. 1, 2009. Published September 2009. Originally
given are:
approvedin1993.Lastpreviouseditionapprovedin2003asE1561–93(2003).DOI:
10.1520/E1561-93R09.
ε 1ε
a c
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
C 5 (1)
contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM 2
Standards volume information, refer to the standard’s Document Summary page on
2 2
the ASTM website. R 5 = ε 2 C 1 ε 2 C (2)
~ ! ~ !
a b
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E1561 − 93 (2009)
FIG. 4 Differential Element on the Undeformed Surface
FIG. 1 0° – 45° – 90° Rosette
FIG. 5 Deformed Shape of Differential Element
FIG. 2 0° – 60° – 120° Rosette
FIG. 6 Planes of Maximum Shear Strain
4.1.2 If ε >C, then the ε -axis is counterclockwise from
b 1
the reference line.
4.2 Fig. 7 shows a typical Mohr’s circle of strain for a
FIG. 3 Typical Mohr’s Circle of Strain for a 0° – 45° – 90° Ro-
sette
ε 5 C1R (3)
ε 5 C 2 R
γ 5 2R
M
tan 2θ 5 2 ~ε 2 C!/ε 2 ε (4)
1 b a c
4.1.1 If ε b 1 FIG. 7 Typical Mohr’s Circle of Strain for a 0° – 60° – 120° Ro-
reference line. sette
E1561 − 93 (2009)
0° – 60° – 120° rosette. The calculations when ε , ε , ε , are
a b c
given are:
ε 1ε 1ε
a b c
C 5 (5)
2 2 2
R 5 =2/3@~ε 2 C! 1~ε 2 C! 1~ε 2 C! # (6)
a b c
ε 5 C1R (7)
ε 5 C 2 R
γ 5 2R
M
~ε 2 ε !
b c
tan 2θ 5 (8)
=
3~ε 2 C!
a
4.2.1 If ε − ε < 0, then the ε -axis is counterclockwise
c b 1
from the reference line.
4.2.2 If ε − ε = 0, then θ = 0°.
c b 1
4.2.3 If ε − ε > 0, then the ε -axis is clockwise from the
c b 1
reference line (see Note 1).
4.3 Identification of the Maximum Principal Strain Direc-
FIG. 9 Gage Labeling for Back-to-Back Rosettes
tion:
4.3.1 Care must be taken when determining the angle θ
using (Eq 4)or(Eq 8) so that the calculated angle refers to the
direction of the maximum principal strain ε rather than the
minimum principal strain ε . Fig. 10 shows how the double
angle 2θ can be placed in its correct orientation relative to the
reference line shown in Fig. 1 and Fig. 2. The terms “numera-
tor”and“denominator”refertothenumeratoranddenominator
of the right-hand sides of (Eq 4) and (Eq 8). When both
numerator and denominator are positive, as shown in Fig. 10,
FIG. 10 Correct Placement of the Double Angle 2 θ
the double angle 2θ lies within the range 0° ≤ 2θ ≤ 90°
1 1
counterclockwise of the reference line. Therefore, in this
particularcase,thecorrespondingangleθ lieswithintherange
0°≤θ ≤ 45° counterclockwise of the reference line. ac
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