1、Designation: E 1561 93 (Reapproved 2003)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 (e) 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, parti
3、cularly 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 an
5、alysis. 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:E6 Terminology Relat
6、ing to Methods of Mechanical Test-ing2E 837 Test Method for Determining Residual Stresses bythe Hole-Drilling Strain-Gage Method23. 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-strai
7、n 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 fro
8、m the a axis and the c axis islocated 120 counterclockwise from the a axis.3.2.3 ea, eb,ecthe 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 repre
9、sent 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 anddirect (membrane) stresses, the separ
10、ate bending and mem-brane stresses can be obtained as shown in 4.4.1This practice is under the jurisdiction of ASTM Committee E28 on MechanicalTesting and is the direct responsibility of Subcommittee E28.01 on Calibration ofMechanical Testing Machines and Apparatus.Current edition approved June 10,
11、2003. Published January 2004. Originallyapproved in 1993. Last previous edition approved in 1998 as E156193(1998).2Annual Book of ASTM Standards, Vol 03.01.FIG. 1 0 45 90 RosetteFIG. 2 0 60 120 Rosette1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959
12、, United States.3.2.4 e8a, e8b, e8creduced membrane strain components(4.4).3.2.5 e9a, e9b,e9creduced bending strain components (4.4).3.2.6 e1the calculated maximum (more tensile or lesscompressive) principal strain.3.2.7 e2the calculated minimum (less tensile or morecompressive) principal strain.3.2
13、.8 gMthe calculated maximum shear strain.3.2.9 u1the angle from the reference line to the directionof e1. This angle is less than or equal to 180 in magnitude.3.2.10 C, Rvalues used in the calculations. C is thelocation, along the e-axis, of the center of the Mohrs circle forstrain and R is the radi
14、us of that circle.4. Procedure4.1 Fig. 3 shows a typical Mohrs circle of strain for a0 45 90 rosette. The calculations when ea, eb, ec, aregiven are:C 5ea1ec2(1)R 5 =ea2 C!21 eb2 C!2(2)e15 C 1 R (3)e25 C 2 RgM5 2Rtan 2u15 2 eb2 C! / ea2ec(4)4.1.1 If ebC, then the e1-axis is counterclockwise from the
15、reference line.4.2 Fig. 7 shows a typical Mohrs circle of strain for a0 60 120 rosette. The calculations when ea, eb, ec, aregiven are:C 5ea1eb1ec3(5)R 5 =2/3ea2 C!21 eb2 C!21 ec2 C!2# (6)e15 C 1 R (7)e25 C 2 RgM5 2Rtan 2u15eb2ec!=3ea2 C!(8)4.2.1 If ec eb0, then the e1-axis is clockwise from therefe
16、rence 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 calculated angle refers to thedirection of the maximum principal strain e1rather than theminimum principal strain e2. Fig. 10
17、 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 the numerator and denominatorof the right-hand sides of (Eq 4) and (Eq 8). When bothnumerator and denominator are positiv
18、e, 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 within the range0 # u1# 45 counterclockwise of the reference line.FIG. 3 Typical Mohrs Circle of Strain for a 0 45 90R
19、osetteFIG. 4 Differential Element on the Undeformed SurfaceFIG. 5 Deformed Shape of Differential ElementFIG. 6 Planes of Maximum Shear StrainE 1561 93 (2003)24.3.2 Several computer languages have arctangent functionsthat directly place the angle 2u1in its correct orientation inaccordance with the sc
20、heme illustrated in Fig. 10. Whenworking in Fortran or C, the two-argument arctangent func-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 isotr
21、opic materials. It can, however,be important for anisotropic materials, such as composites.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 i
22、s initially as shown in Fig. 4. Itsdeformed shape, corresponding to the assumed strains, isshown 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
23、in the surface at the intended site ofthe rosette, back-to-back rosette installations are commonlyemployed, 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.
24、5.2.1 Label as in Fig. 8, which follows the sign conventionof Fig. 1 and Fig. 2 as the observer 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 (
25、see Fig. 9).4.5.2.3 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 4.5.2.2, wherein the ob-server fixes the a legs of the rosettes on bot
26、h 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 the labeling in 4.5.2.1 to accomplishthe basic purpose of back-to-bac
27、k rosette installations. TheFIG. 7 Typical Mohrs Circle of Strain for a 0 60 120RosetteFIG. 8 Gage Labeling for Back-to-Back RosettesFIG. 9 Gage Labeling for Back-to-Back RosettesFIG. 10 Correct Placement of the Double Angle 2 u1E 1561 93 (2003)3following procedure is limited to test materials which
28、 arehomogeneous in the thickness direction, or are symmetricallyinhomogeneous with respect to the midpoint of the thickness,as in many laminated composite 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 leve
29、lsnormally encountered in the stress analysis of typical metal test objects.They start to become detectably inaccurate for strain levels greater thanabout 1 %. Rosette data reduction for large strains is beyond the scope ofthis guide.NOTE 2The Mohrs circle for strain is constructed in generally thes
30、ame manner as the Mohrs circle for stress. Normal strains, e, are plottedas abscissae-positive for elongation and negative for contraction. One-halfthe 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
31、 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 convention, 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 wire
32、d toautomatically cancel the bending components of strain withinthe Wheatstone bridge circuit, the following relationships canbe employed with the rosette 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
33、 through-the-thickness uniform strains, after removing thesuperimposed bending strains):e8a5 eA1eA1!/2 (9)e8b5 eB1eB1!/2 (10)e8c5 eC1eC1!/2 (11)4.6.2 For the bending components of strain, at both surfacesof the test object:e9a56eA2eA1!/2 (12)e9b56eB2eB1!/2 (13)e9c56eC2eC1!/2 (14)where:ea, eb, ec= re
34、duced membrane strain components inthe directions of the three rosette legs whenlabeled in accordance with Fig. 9.e9a, e9b, e9c= reduced bending strain components in thedirections of the three rosette legs whenlabeled in accordance with Fig. 9.4.6.3 The strain terms in (Eq 9) through (Eq 14) withcap
35、italized subscripts represent the measured strains (aftercustomary corrections) from the corresponding rosette legs asshown in Fig. 9.5. Report5.1 The rosette data analysis may be part of the report on atest program. Report the following information:5.1.1 Description of gages and measuring equipment
36、,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 circle for strain; rosette; shearstrain; strain; strain gages; tensile strainASTM International takes no position respecting the v
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38、ubject 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 are invited either for revision of this standard or for additional standardsand should be addressed to ASTM International Headq
39、uarters. Your comments will receive careful consideration at a meeting of theresponsible technical committee, which you may attend. If you feel that your comments have not received a fair hearing you shouldmake your views known to the ASTM Committee on Standards, at the address shown below.This stan
40、dard 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 (2003)4
