ASTM E1561-20

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 E837. 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.  
1.2 The equations in 4.2 and 4.3 of this practice are derived from infinitesimal (linear) strain theory. They are very accurate for the low strain levels normally encountered in the stress analysis of typical metal test objects. They become detectably inaccurate for strain levels greater than about 1 %. Rosette data reduction for larger strains is beyond the scope of this practice.  
1.3 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

General Information

• Status: Published
• Publication Date: 31-Aug-2020
• 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

Standards Content (Sample)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: E1561 − 20
Standard Practice for
1
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* 2. Referenced Documents
2
1.1 The two primary uses of three-element strain gage 2.1 ASTM Standards:
rosettes are (a) to determine the directions and magnitudes of E6 Terminology Relating to Methods of Mechanical Testing
the principal surface strains and (b) to determine residual E837 Test Method for Determining Residual Stresses by the
stresses. Residual stresses are treated in a separate ASTM Hole-Drilling Strain-Gage Method
standard, Test Method E837. This practice defines a reference
3. Terminology
axis for each of the two principal types of rosette configura-
tions used and presents equations for data analysis. This is
3.1 ThetermsinTerminologyE6apply.Thesetermsinclude
important for consistency in reporting results and for avoiding
modulus of elasticity and residual stress.
ambiguity in data analysis—especially when computers are
3.2 Definitions of Terms Specific to This Standard:
used. There are several possible sets of equations, but the set
3.2.1 reference line—the axis of the a gage.
presented here is perhaps the most common.
3.3 Symbols:
1.2 The equations in 4.2 and 4.3 of this practice are derived
3.3.1 a, b, c—the three-strain gages making up the rosette.
from infinitesimal (linear) strain theory.They are very accurate
3.3.1.1 Discussion—For the 0° – 45° – 90° rosette (Fig. 1)
for the low strain levels normally encountered in the stress
the axis of the b gage is located 45° counterclockwise from the
analysis of typical metal test objects. They become detectably
a (reference line) axis and the c gage is located 90° counter-
inaccurate for strain levels greater than about 1 %. Rosette data
clockwise from the a axis. For the 0° – 60° – 120° rosette (Fig.
reduction for larger strains is beyond the scope of this practice.
2) the axis of the b gage is located 60° counterclockwise from
1.3 This international standard was developed in accor-
thea axis and thec axis is located 120° counterclockwise from
dance with internationally recognized principles on standard-
the a axis.
ization established in the Decision on Principles for the
3.3.2 ε , ε , ε —the strains measured by gages a, b, and c,
a b c
Development of International Standards, Guides and Recom-
respectively, positive in tension and negative in compression.
mendations issued by the World Trade Organization Technical
3.3.2.1 Discussion—After corrections for thermal output
Barriers to Trade (TBT) Committee.
and transverse sensitivity have been made, the measured
strains represent the surface strains at the site of the rosette. It
1
This practice is under the jurisdiction ofASTM Committee E28 on Mechanical
Testing and is the direct responsibility of Subcommittee E28.01 on Calibration of
2
Mechanical Testing Machines and Apparatus. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Current edition approved Sept. 1, 2020. Published October 2020. Originally contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
approvedin1993.Lastpreviouseditionapprovedin2014asE1561–93(2014).DOI: Standards volume information, refer to the standard’s Document Summary page on
10.1520/E1561-20. the ASTM website.
*A Summary of Changes section appears at the end of this standard
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
1

---------------------- Page: 1 ----------------------
E1561 − 20
axis. Similarly plot shear strains that appear to form a coun-
terclockwise couple on the lower half. With this convention,
angular directions on the circle are the same as angular
directions on the specimen. See Fig. 3.
4.2 Fig. 3 shows a typical Mohr’s circle of strain for a
0° – 45° – 90° rosette. The calculations when ε , ε , ε , are
a b c
given are:
ε 1ε
a c
C 5 (1)
2
2 2
R 5 = ε 2 C 1 ε 2 C (2)
~ ! ~ !
a b
FIG. 1 0° – 45° – 90° Rosette
γ 5 2R (3)
M
ε 5 C1R
1
ε 5 C 2 R
2
ε 2 C
~ !
b
...

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: E1561 − 93 (Reapproved 2014) E1561 − 20
Standard Practice for
1
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 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 E837.
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.
1.2 The equations in 4.2 and 4.3 of this practice are derived from infinitesimal (linear) strain theory. They are very accurate for
the low strain levels normally encountered in the stress analysis of typical metal test objects. They become detectably inaccurate
for strain levels greater than about 1 %. Rosette data reduction for larger strains is beyond the scope of this practice.
1.3 This international standard was developed in accordance with internationally recognized principles on standardization
established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
2. Referenced Documents
2
2.1 ASTM Standards:
E6 Terminology Relating to Methods of Mechanical Testing
E837 Test Method for Determining Residual Stresses by the Hole-Drilling Strain-Gage Method
3. Terminology
3.1 The terms in Terminology E6 apply. These terms include modulus of elasticity and residual stress.
3.2 Definitions of Terms Specific to This Standard:
1
This practice is under the jurisdiction of ASTM Committee E28 on Mechanical Testing and is the direct responsibility of Subcommittee E28.01 on Calibration of
Mechanical Testing Machines and Apparatus.
Current edition approved April 15, 2014Sept. 1, 2020. Published August 2014October 2020. Originally approved in 1993. Last previous edition approved in 20092014
as E1561–93(2009).E1561–93(2014). DOI: 10.1520/E1561-93R14.10.1520/E1561-20.
2
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
*A Summary of Changes section appears at the end of this standard
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
1

---------------------- Page: 1 ----------------------
E1561 − 20
3.2.1 reference line—the axis of the a gage.
3.3 Symbols:
3.3.1 a, b, c—the three-strain gages making up the rosette.
3.3.1.1 Discussion—
For the 0° – 45° – 90° rosette (Fig. 1) the axis of the b gage is located 45° counterclockwise from the a (reference line) axis and
the c gage is located 90° counterclockwise from the a axis. 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 located 120° counterclockwise from the a axis.
3.3.2 ε , ε , ε —the strains measured by gages a,b, and c, respectively, positive in tension and negative in compression.
a b c
3.3.2.1 Discussion—
After corrections for thermal effectsoutput and transverse sensitivity have been made, the measured strains represent the surface
strains at the site of the rosette. It is assumed here that the elastic modulus of elasticity and thickness of the test specimen are such
that mechanical reinforcement by the rosette areis negligible. For test objects subjected to unknown combinations of bending and
direct (membrane) stres
...