ASTM_E_1561_-_93_2014.pdf

Designation:E156193(Reapproved 2014)Standard Practice forAnalysis of Strain Gage Rosette Data1This standard is issued under the fixed designation E1561;the number immediately following the designation indicates the year oforiginal adoption or,in the case of revision,the year of last revision.A number in parentheses indicates the year of last reapproval.Asuperscript epsilon()indicates an editorial change since the last revision or reapproval.INTRODUCTIONThere can be considerable confusion in interpreting and reporting the results of calculationsinvolving 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 gagesand for analyzing the data.1.Scope1.1 The two primary uses of three-element strain gagerosettes are(a)to determine the directions and magnitudes ofthe principal surface strains and(b)to determine residualstresses.Residual stresses are treated in a separate ASTMstandard,Test Method E837.This practice defines a referenceaxis for each of the two principal types of rosette configura-tions used and presents equations for data analysis.This isimportant for consistency in reporting results and for avoidingambiguity in data analysisespecially when computers areused.There are several possible sets of equations,but the setpresented here is perhaps the most common.2.Referenced Documents2.1 ASTM Standards:2E6 Terminology Relating to Methods of Mechanical TestingE837 Test Method for Determining Residual Stresses by theHole-Drilling Strain-Gage Method3.Terminology3.1 The terms in Terminology E6 apply.3.2 Definitions of Terms Specific to This Standard:3.2.1 reference linethe axis of the a gage.3.3 Symbols:3.3.1 a,b,cthe three-strain gages making up the rosette.3.3.1.1 DiscussionFor the 0 45 90 rosette(Fig.1)the axis of the b gage is located 45 counterclockwise from thea(reference line)axis and the c gage is located 90 counter-clockwise from the a axis.For the 0 60 120 rosette(Fig.2)the axis of the b gage is located 60 counterclockwise fromthe a axis and the c axis is located 120 counterclockwise fromthe a axis.3.3.2 a,b,cthe strains measured by gages a,b,and c,respectively,positive in tension and negative in compression.3.3.2.1 DiscussionAfter corrections for thermal effectsand transverse sensitivity have been made,the measuredstrains represent the surface strains at the site of the rosette.Itis assumed here that the elastic modulus and thickness of thetest specimen are such that mechanical reinforcement by therosette are negligible.For test objects subjected to unknowncombinations of bending and direct(membrane)stresses,theseparate bending and membrane stresses can be obtained asshown in 4.4.3.3.3a,b,creduced membrane strain components(4.4).3.3.4a,b,creduced bending strain components(4.4).3.3.5 1the calculated maximum(more tensile or lesscompressive)principal strain.3.3.6 2the calculated minimum(less tensile or morecompressive)principal strain.3.3.7 Mthe calculated maximum shear strain.3.3.8 1the angle from the reference line to the directionof 1.3.3.8.1 DiscussionThis angle is less than or equal to 180in magnitude.3.3.9 C,Rvalues used in the calculations.C is thelocation,along the-axis,of the center of the Mohrs circle forstrain and R is the radius of that circle.1This practice is under the jurisdiction ofASTM Committee E28 on MechanicalTesting and is the direct responsibility of Subcommittee E28.01 on Calibration ofMechanical Testing Machines and Apparatus.Current edition approved April 15,2014.Published August 2014.Originallyapproved in 1993.Last previous edition approved in 2009 as E156193(2009).DOI:10.1520/E1561-93R14.2For referenced ASTM standards,visit the ASTM website,www.astm.org,orcontact ASTM Customer Service at serviceastm.org.For Annual Book of ASTMStandards volume information,refer to the standards Document Summary page onthe ASTM website.Copyright ASTM International,100 Barr Harbor Drive,PO Box C700,West Conshohocken,PA 19428-2959.United States1 4.Procedure4.1 Fig.3 shows a typical Mohrs circle of strain for a0 45 90 rosette.The calculations when a,b,c,aregiven are:C 5a1c2(1)R 5=a2 C!21b2 C!2(2)15 C1R(3)25 C 2 RM5 2Rtan 215 2b2 C!/a2 c(4)4.1.1 If b C,then the 1-axis is counterclockwise fromthe reference line.4.2 Fig.7 shows a typical Mohrs circle of strain for a0 60 120 rosette.The calculations when a,b,c,aregiven are:C 5a1b1c3(5)R 5=2/3a2 C!21b2 C!21c2 C!2#(6)15 C1R(7)25 C 2 RM5 2Rtan 215b2 c!=3a2 C!(8)4.2.1 If c b 0,then the 1-axis is clockwise from thereference line(see Note 1).4.3 Identification of the Maximum Principal Strain Direc-tion:4.3.1 Care must be taken when determining the angle 1using(Eq 10)or(Eq 14)so that the calculated angle refers tothe direction of the maximum principal strain 1rather than theminimum principal strain 2.Fig.10 shows how the doubleangle 21can be placed in its correct orientation relative to thereference line shown in Fig.1 and Fig.2.The