1、Designation: E1561 93 (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.
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, particul
3、arly 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 ma
4、gnitudes 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 analys
5、is. 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
6、 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 thr
7、ee-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 loc
8、ated 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
9、 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 bendin
10、g and direct (membrane) stresses, theseparate bending and membrane stresses can be obtained asshown in 4.4.3.3.3 a,b, creduced membrane strain components (4.4).3.3.4 a“, b“, c“reduced bending strain components (4.4).3.3.5 1the calculated maximum (more tensile or lesscompressive) principal strain.3.3
11、.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
12、 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 of ASTM Committee E28 on MechanicalTesting and is the direct responsibility of Subcommittee E28.01 on Calibration ofMechanical Testing Machines and A
13、pparatus.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.o
14、rg. 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 States14. Procedure4.1 Fig. 3 shows a typical Mohrs circle of strain for
15、 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 2 b2 C!/a2 c(4)4.1.1 If bC, 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 calculation
16、s 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 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 determini
17、ng 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.
18、The terms “numera-tor” and “denominator” refer to the numerator and denominatorof the right-hand sides of (Eq 10) and (Eq 14). When bothnumerator and denominator are positive, as shown in Fig. 10,the double angle 21lies within the range 0 21 90counterclockwise of the reference line. Therefore, in th
19、isparticular case, the corresponding angle 1lies within the range0 1 45 counterclockwise of the reference line.4.3.2 Several computer languages have arctangent functionsthat directly place the angle 21in its correct orientation inFIG. 1 0 45 90 RosetteFIG. 2 0 60 120 RosetteFIG. 3 Typical Mohrs Circ
20、le of Strain for a 0 45 90 Ro-sette FIG. 4 Differential Element on the Undeformed SurfaceE1561 93 (2014)2accordance with the scheme illustrated in Fig. 10. Whenworking in Fortran or C, the two-argument arctangent func-tions ATAN2 or atan2 can be used for evaluating (Eq 10) and(Eq 14).4.4 Interpretat
21、ion of Maximum Shear StrainOrdinarily thesense 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.Mohrs circle for strain can be used for interpretation of thesense of the shear
22、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, isshown in Fig. 5. The planes of maximum shear strain are at 45to the 1direction a
23、s in Fig. 6 (see Note 2).4.5 Back-to-Back Rosettes:FIG. 5 Deformed Shape of Differential ElementFIG. 6 Planes of Maximum Shear StrainFIG. 7 Typical Mohrs Circle of Strain for a 0 60 120 Ro-setteFIG. 8 Gage Labeling for Back-to-Back RosettesFIG. 9 Gage Labeling for Back-to-Back RosettesFIG. 10 Correc
24、t Placement of the Double Angle 2 1E1561 93 (2014)34.5.1 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 commonlyemployed, as shown in Fig. 8 and Fig. 9, to permit separatedetermination o
25、f 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 observer faces each of the rosettes.4.5.2.2 Label, for example, the gage on face 1 in
26、 thecounterclockwise direction and the gage on face 2 in theclockwise direction, both as seen by an observer facing therosette (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 ob
27、server 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 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 wirin
28、g or computational error which mayoccur in converting from the 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
29、 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 levelsnormally encountered in the stress analysis of typical metal test objects.They start to
30、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 thesame manner as the Mohrs circle for stress. Normal strains, , are plottedas abscissae-posit
31、ive for elongation and negative for contraction. One-halfthe shear strains, /2, are plotted as ordinates. If the shear strains onopposite sides of an element of area appear to form a clockwise couple,then /2 is plotted on the upper half of the axis. Similarly shear strainswhich appear to form a coun
32、terclockwise 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 wired toautomatically cancel the bending components of strain withinthe Wheatstone bridge circuit
33、, 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 through-the-thickness uniform strains, after removing thesuperimposed bending strains):a5 A1
34、A1!/2 (9)b5 B1B1!/2 (10)c5 C1C1!/2 (11)4.6.2 For the bending components of strain, at both surfacesof the test object:a“56A2 A1!/2 (12)b“56B2 B1!/2 (13)c“56C2 C1!/2 (14)where:a, b, c= reduced membrane strain components in the di-rections of the three rosette legs when labeled inaccordance with Fig.
35、9.a“, b“, c“= reduced bending strain components in the direc-tions of the three rosette legs when labeled inaccordance with Fig. 9.4.6.3 The strain terms in (Eq 15) through (Eq 20) withcapitalized subscripts represent the measured strains (aftercustomary corrections) from the corresponding rosette l
36、egs 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,5.1.2 Location and orientation of strain gage rosette,5.1.3 Measured strains (corrected), and5.1.4 Calculation
37、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 validity of any patent rights asserted in connection with any item mentionedin this standard. Users of this stand
38、ard are expressly advised that determination of the validity of 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 andi
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40、ich 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 standard is copyrighted by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959,
41、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). Permission rights to photocopy the standard may also be secured from the Copyright Clearance Center, 222Rosewood Drive, Danvers, MA 01923, Tel: (978) 646-2600; http:/ 93 (2014)4
