1、Designation: E 1561 93 (Reapproved 2009)Standard Practice forAnalysis of Strain Gage Rosette Data1This standard is issued under the fixed designation E 1561; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision
2、. 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, partic
3、ularly 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
4、magnitudes ofthe principal surface strains and (b) to determine residualstresses. Residual stresses are treated in a separate ASTMstandard, Test Method E 837. This practice defines a referenceaxis for each of the two principal types of rosette configura-tions used and presents equations for data ana
5、lysis. 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 Relat
6、ing to Methods of Mechanical Test-ingE 837 Test Method for Determining Residual Stresses bythe Hole-Drilling Strain-Gage Method3. Terminology3.1 The terms in Terminology E6apply.3.2 Additional terms and notation are as follows:3.2.1 reference linethe axis of the a gage.3.2.2 a, b, cthe three-strain
7、gages making up the rosette.For the 0 45 90 rosette (Fig. 1) the axis of the b gage islocated 45 counterclockwise from the a (reference line) axisand 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 islocated 60 counterclockwise from
8、the a axis and the c axis islocated 120 counterclockwise from the a axis.3.2.3 a, b,cthe strains measured by gages a, b, and c,respectively, positive in tension and negative in compression.After corrections for thermal effects and transverse sensitivityhave been made, the measured strains represent
9、the surfacestrains at the site of the rosette. It is assumed here that theelastic modulus and thickness of the test specimen are such thatmechanical reinforcement by the rosette are negligible. For testobjects subjected to unknown combinations of bending and1This practice is under the jurisdiction o
10、f ASTM Committee E28 on MechanicalTesting and is the direct responsibility of Subcommittee E28.01 on Calibration ofMechanical Testing Machines and Apparatus.Current edition approved Sept. 1, 2009. Published September 2009. Originallyapproved in 1993. Last previous edition approved in 2003 as E156193
11、(2003).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.FIG. 1 0 45 90 RosetteFIG. 2 0 60 120 Rosette1Copyrigh
12、t ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.direct (membrane) stresses, the separate bending and mem-brane stresses can be obtained as shown in 4.4.3.2.4 8a, 8b, 8creduced membrane strain components(4.4).3.2.5 9a, 9b,9creduced bending str
13、ain components(4.4).3.2.6 1the calculated maximum (more tensile or lesscompressive) principal strain.3.2.7 2the calculated minimum (less tensile or morecompressive) principal strain.3.2.8 gMthe calculated maximum shear strain.3.2.9 u1the angle from the reference line to the directionof 1. This angle
14、 is less than or equal to 180 in magnitude.3.2.10 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.4. Procedure4.1 Fig. 3 shows a typical Mohrs circle of strain for a0 45 90 rosette. The calculation
15、s when a, b, c, aregiven are:C 5a1c2(1)R 5 =a2 C!21 b2 C!2(2)15 C 1 R (3)25 C 2 RgM5 2Rtan 2u15 2 b2 C! / a2c(4)4.1.1 If bC, then the 1-axis is counterclockwise from thereference 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
16、:FIG. 3 Typical Mohrs Circle of Strain for a 0 45 90RosetteFIG. 4 Differential Element on the Undeformed SurfaceFIG. 5 Deformed Shape of Differential ElementFIG. 6 Planes of Maximum Shear StrainFIG. 7 Typical Mohrs Circle of Strain for a 0 60 120RosetteE 1561 93 (2009)2C 5a1b1c3(5)R 5 =2/3a2 C!21 b2
17、 C!21 c2 C!2# (6)15 C 1 R (7)25 C 2 RgM5 2Rtan 2u15b2c!=3a2 C!(8)4.2.1 If c b0, 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 u1using (Eq 4) or (Eq 8) so that the calc
18、ulated angle refers to thedirection of the maximum principal strain 1rather than theminimum principal strain 2. Fig. 10 shows how the doubleangle 2u1can be placed in its correct orientation relative to thereference line shown in Fig. 1 and Fig. 2. The terms “numera-tor” and “denominator” refer to th
19、e numerator and denominatorof the right-hand sides of (Eq 4) and (Eq 8). When bothnumerator and denominator are positive, as shown in Fig. 10,the double angle 2u1lies within the range 0 # 2u1# 90counterclockwise of the reference line. Therefore, in thisparticular case, the corresponding angle u1lies
20、 within the range0 # u1# 45 counterclockwise of the reference line.4.3.2 Several computer languages have arctangent functionsthat directly place the angle 2u1in its correct orientation inaccordance with the scheme illustrated in Fig. 10. Whenworking in Fortran or C, the two-argument arctangent func-
21、tions ATAN2 or atan2 can be used for evaluating (Eq 4) and(Eq 8).4.4 Interpretation of Maximum Shear StrainOrdinarilythe sense of the maximum shear strain is not significant whenanalyzing the behavior of isotropic materials. It can, however,be important for anisotropic materials, such as composites.
22、Mohrs circle for strain can be used for interpretation of thesense of the shear strain. Fig. 3 shows a typical circle for a04590 rosette. A differential element along and perpen-dicular to the reference line is initially as shown in Fig. 4. Itsdeformed shape, corresponding to the assumed strains, is
23、shown in Fig. 5. The planes of maximum shear strain are at 45to the u1direction as in Fig. 6 (see Note 2).4.5 Back-to-Back Rosettes:4.5.1 When the loading of a member or structure mayintroduce bending strains in the surface at the intended site ofthe rosette, back-to-back rosette installations are c
24、ommonlyemployed, as shown in Fig. 8 and Fig. 9, to permit separatedetermination of the bending and membrane strains.4.5.2 When rosettes are used on both sides of thin materials,the labeling alternatives are:4.5.2.1 Label as in Fig. 8, which follows the sign conventionof Fig. 1 and Fig. 2 as the obse
25、rver faces each of the rosettes.4.5.2.2 Label, for example, the gage on face 1 in thecounterclockwise direction and the gage on face 2 in theclockwise direction, both as seen by an observer facing therosette (see Fig. 9).FIG. 8 Gage Labeling for Back-to-Back RosettesFIG. 9 Gage Labeling for Back-to-
26、Back RosettesFIG. 10 Correct Placement of the Double Angle 2 u1E 1561 93 (2009)34.5.2.3 Labeling (4.5.2.1) requires no sign change in thedata reduction equations or in the interpretation of the angles.Results are still interpreted as the observer faces the rosette.4.5.2.4 Labeling as described in 4.
27、5.2.2, wherein the ob-server fixes the a legs of the rosettes on both sides of the plateor skin to coincide in direction, is particularly convenient forthe separation of bending and membrane strains. It also reducesthe likelihood of a wiring or computational error which mayoccur in converting from t
28、he labeling in 4.5.2.1 to accomplishthe basic purpose of back-to-back rosette installations. Thefollowing procedure is limited to test materials which arehomogeneous in the thickness direction, or are symmetricallyinhomogeneous with respect to the midpoint of the thickness,as in many laminated compo
29、site materials.NOTE 1The equations in 4.1 and 4.2 are derived from infinitesimal(linear) strain theory. They are very accurate for the low strain levelsnormally encountered in the stress analysis of typical metal test objects.They start to become detectably inaccurate for strain levels greater thana
30、bout 1 %. Rosette data reduction for large strains is beyond the scope ofthis guide.NOTE 2The Mohrs circle for strain is constructed in generally thesame manner as the Mohrs circle for stress. Normal strains, , are plottedas abscissae-positive for elongation and negative for contraction. One-halfthe
31、 shear strains, g/2, are plotted as ordinates. If the shear strains onopposite sides of an element of area appear to form a clockwise couple,then g/2 is plotted on the upper half of the axis. Similarly shear strainswhich appear to form a counterclockwise couple plot on the lower half.With this conve
32、ntion, angular directions on the circle are the same asangular directions on the specimen. See Fig. 3.4.6 In those cases where the gages are not wired toautomatically cancel the bending components of strain withinthe Wheatstone bridge circuit, the following relationships canbe employed with the rose
33、tte labeling in Fig. 9 to separatelydetermine the membrane and bending strain components.4.6.1 For the membrane components of the strain (that is,the through-the-thickness uniform strains, after removing thesuperimposed bending strains):8a5 A1A1!/2 (9)8b5 B1B1!/2 (10)8c5 C1C1!/2 (11)4.6.2 For the be
34、nding components of strain, at both surfacesof the test object:9a56A2A1!/2 (12)9b56B2B1!/2 (13)9c56C2C1!/2 (14)where:a, b, c= reduced membrane strain components inthe directions of the three rosette legs whenlabeled in accordance with Fig. 9.9a, 9b, 9c= reduced bending strain components in thedirect
35、ions of the three rosette legs whenlabeled in accordance with Fig. 9.4.6.3 The strain terms in (Eq 9) through (Eq 14) withcapitalized subscripts represent the measured strains (aftercustomary corrections) from the corresponding rosette legs asshown in Fig. 9.5. Report5.1 The rosette data analysis ma
36、y be part of the report on atest program. Report the following information:5.1.1 Description of gages and measuring equipment,5.1.2 Location and orientation of strain gage rosette,5.1.3 Measured strains (corrected), and5.1.4 Calculation of principal strains.6. Keywords6.1 bending strain; Mohrs circl
37、e for strain; rosette; shearstrain; strain; strain gages; tensile strainASTM International takes no position respecting the validity of any patent rights asserted in connection with any item mentionedin this standard. Users of this standard are expressly advised that determination of the validity of
38、 any such patent rights, and the riskof infringement of such rights, are entirely their own responsibility.This standard is subject to revision at any time by the responsible technical committee and must be reviewed every five years andif not revised, either reapproved or withdrawn. Your comments ar
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40、eived a fair hearing you shouldmake your views known to the ASTM Committee on Standards, at the address shown below.This standard is copyrighted by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959,United States. Individual reprints (single or multiple copies) of this standard may be obtained by contacting ASTM at the aboveaddress or at 610-832-9585 (phone), 610-832-9555 (fax), or serviceastm.org (e-mail); or through the ASTM website(www.astm.org).E 1561 93 (2009)4
