1、Designation: D 4476 09Standard Test Method forFlexural Properties of Fiber Reinforced Pultruded PlasticRods1This standard is issued under the fixed designation D 4476; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of las
2、t revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope*1.1 This test method covers the determination of the flexuralproperties of fiber-reinforced pultruded plastic rods. The spec
3、i-men is a rod with a semicircular cross section, molded or cutfrom lengths of pultruded rods (see Fig. 1). This test method isdesigned for rods with a diameter of12 in. or greater.NOTE 1There is no known ISO equivalent for this test method.1.2 The values stated in either SI units or inch-pound unit
4、sare to be regarded separately as standard. The values stated ineach system may not be exact equivalents; therefore, eachsystem shall be used independently of the other. Combiningvalues from the two systems may result in nonconformancewith the standard.1.3 This standard does not purport to address a
5、ll of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2D 618 Practice for
6、Conditioning Plastics for TestingD 883 Terminology Relating to PlasticsD 3918 Terminology Relating to Reinforced Plastic Pul-truded ProductsE4 Practices for Force Verification of Testing MachinesE 691 Practice for Conducting an Interlaboratory Study toDetermine the Precision of a Test Method3. Termi
7、nology3.1 For definitions of terms used in this test method, seeTerminology D 883 or Definitions D 3918.4. Summary of Test Method4.1 A rod of semicircular construction is tested in flexure asa simple beam. The specimen rests on two supports and isloaded by means of a loading nose midway between thes
8、upports (see Fig. 3).1This test method is under the jurisdiction ofASTM Committee D20 on Plasticsand is the direct responsibility of Subcommittee D20.18 on Reinforced Thermoset-ting Plastics.Current edition approved Sept. 1, 2009. Published September 2009. Originallyapproved in 1985. Last previous e
9、dition approved in 2003 as D 4476 - 03.2For 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 Cross Section o
10、f Test SpecimenFIG. 2 Arbor Dimensions1*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.4.2 The specimen is deflected until rupture occurs in theouter fibers, or until t
11、he maximum fiber strain of 5 % isreached, whichever occurs first.5. Significance and Use5.1 Flexural properties determined by this test method areespecially useful for quality control and specification purposes.5.2 The maximum axial fiber stresses occur on a line underthe loading nose. The use of th
12、e semicircular cross sectioneliminates premature compression shear that has been noted inthree-point flexure tests on full-round rods.5.3 Flexural properties may vary with specimen depth,temperature, atmospheric conditions, and differences in rate ofstraining.5.4 Before proceeding with this test met
13、hod, referenceshould be made to the specification of the material being tested.Any test specimen preparation, conditioning, dimensions, ortesting parameters, or combination thereof, covered in thematerials specification shall take precedence over those men-tioned in this test method. If there are no
14、 material specifica-tions, then the default conditions apply.6. Apparatus6.1 Testing MachineA properly calibrated testing ma-chine that can be operated at constant rates of crosshead motionover the range indicated, and in which the error in theload-measuring system shall not exceed 61 % of the maxi-
15、mum load expected to be measured. It shall be equipped witha deflection-measuring device. The stiffness of the testingmachine shall be such that the total elastic deformation of thesystem does not exceed 1 % of the total deflection of the testspecimen during test, or appropriate corrections shall be
16、 made.The load-indicating mechanism shall be essentially free ofinertial lag at the crosshead rate used. The accuracy of thetesting machine shall be verified in accordance with PracticesE4.6.2 Loading Nose and SupportsThe loading nose shallhave cylindrical surfaces. In order to avoid excessive inden
17、ta-tion or failure due to stress concentration directly under theloading nose, the radius of the nose shall be at least 6.4 mm (14in.) for all specimens. Larger-radius noses are recommended ifsignificant indentation or compressive failure occurs. Thecurvature of the loading nose in contact with the
18、specimen shallbe sufficiently large to prevent contact of the specimen with thesides of the nose. The supports shall consist of anvils to supportthe round section of the segment (see Fig. 2).6.3 MicrometersSuitable micrometers for measuring thediameter of the test specimen to an incremental discrimi
19、nationof at least 0.025 mm (0.001 in.) shall be used.7. Test Specimen7.1 The test specimen shall consist of a pultruded rod cutinto two parts so that the cross section of each part is smallerthan a half-round section (see Fig. 1).7.2 The specimen length shall be 16 to 24 times its thicknessor depth,
20、 plus at least 20 % of the support span to allow aminimum of 10 % overhang at the supports (see Fig. 3).NOTE 2As a general rule, support span-to-depth ratios of 16 to 1 aresatisfactory when the ratio of the tensile strength to shear strength is lessthan 20 to 1, but the support span-to-depth ratio s
21、hould be increased forcomposite laminates having relatively low shear strength in the plane ofthe laminate and relatively high tensile strength parallel to the supportspan.7.3 Number of SpecimensThe number of test specimens isoptional. However, a minimum of five specimens is required toobtain a sati
22、sfactory average and standard deviation.8. Conditioning8.1 ConditioningCondition the test specimen at 23 6 2C(73.4 6 3.6F) and 50 6 10 % relative humidity for not lessthan 40 h prior to test in accordance with Procedure A ofPractice D 618, for those tests where conditioning is required.FIG. 3 Schema
23、tic of Flexural TestD4476092In cases of disagreement, the tolerances shall be 61C(61.8F) and 65 % relative humidity. These conditions arerecommended for research and development trials, but notnecessarily for quality control. However, temperature controlto 22.2 6 5.6C (72 6 10F) is recommended for q
24、ualitycontrol.8.2 Test ConditionsConduct tests in the standard labora-tory atmosphere of 23 6 2C (73.4 6 3.6F) and 50 6 10 %relative humidity, unless otherwise specified in the test methodor in other specifications. In cases of disagreement, thetolerances shall be 61C (61.8F) and 65 % relative humid
25、-ity.8.3 Preconditioning in other environments to simulatespecified conditions and durations is permissible.8.4 Testing in other environmental conditions is permis-sible.9. Procedure9.1 Use an untested specimen for each measurement. Mea-sure the diameter before cutting and depth of the specimen toth
26、e nearest 0.025 mm (0.001 in.) at the center of the supportspan.9.2 Determine the support span to be used as described inSection 6 and set the support span to within 1 % of thedetermined value.9.3 Machine crosshead rate shall be 3 mm/min (0.1 in./min)for samples where D/2 is 0.25 to 0.375 in. and 6
27、mm/min (0.2in./min) for samples where D/2 is 0.375 to 0.5 in. The test timeshould be monitored and the loading rate adjusted. If the testtime is less than 20 s, the loading rate should be reduced. If thetest time is greater than 200 s, the loading rate should beincreased.10. Retests10.1 Values for p
28、roperties at rupture shall not be calculatedfor any specimen that breaks at some obvious, fortuitous flaw,unless such flaws constitute a variable being studied. Retestsshall be made for any specimen on which values are notcalculated.11. Calculation11.1 Maximum Fiber StressWhen a beam of homoge-neous
29、, elastic material is tested in flexure as a simple beamsupported at two end points and loaded at the midpoint, themaximum fiber stress in the outer fibers occurs at midspan.This stress may be calculated for any point on the load-deflection curve by the following equation (Notes 2 and 3):S 5P L C4I(
30、1)where:S = stress in the outer fibers at midspan, N/m2(psi),P = load at a given point on the load-deflection curve, N(lbf),L = support span, m (in.),I = moment of inertia, m4(in.4),=R4F182G 2 H! S1 12A3BG 2 H/2D289A42G 2 H!GC = distance from centroid to extremities, m (in.),=R S1 24A36G 2 3HD,R = D
31、/2 m (in.),A =g 2 2g! , where g =TR,B =1g,G = arc sine A, rad,H =2A B,g = T/R relative thickness of specimen, m (in.),T = thickness of specimen, m (in.), andD = original diameter of specimen, m (in.).NOTE 3Eq 1 applies directly to materials for which the stress islinearly proportional to strain up t
32、o the point of rupture and for which thestrains are small. Since this is not always the case, a slight error will beintroduced in the use of this equation. The equation will, however, be validfor comparison data and specification values up to the maximum fiberstrain of 5 % for specimens tested by th
33、e procedure herein described.NOTE 4The preceding calculation is not valid if the specimen isslipping excessively between the supports.11.2 Modulus of Elasticity:11.2.1 Tangent Modulus of ElasticityThe tangent modulusof elasticity, often called the “modulus of elasticity,” is theratio, within the ela
34、stic limit, of stress to corresponding strain,and shall be expressed in newtons per square metre (pounds-force per square inch). It is calculated by drawing a tangent tothe steepest initial straight-line portion of the load-deflectioncurve and using Eq 2 as follows:Eb5P L348 I Y(2)where:Eb= modulus
35、of elasticity in bending, N/m2(psi),P = load at a given point on the load-deflection curve, N(lbf),L = support span, m (in.),I = moment of inertia, m4(in.4),=R4F18G 2 H! S1 12A3BG 2 H/2D289A42G 2 H!GR = D/2, m (in.),A =g 2 2g! ,B =1g,G = arc sine A, rad,H =2A B,g = T/R relative thickness of specimen
36、, m (in.),T = thickness of specimen, m (in.), andD = original diameter, m (in.),11.3 Maximum StrainThe maximum strain in the outerfibers also occurs at midspan, and may be calculated asfollows:512 C YL2(3)where:D4476093 = maximum strain in outer fibers, m/m (in./in.),Y = maximum deflection at load c
37、hosen, m (in.),L = support span, m (in.)C = distance from centroid to extremities,=R S1 2 4A36G 2 3HD ,A =g 2 2g! ,g = T/R,G = arc sine A, rad,H =2A B,B =1gT = thickness of specimen, m (in.),R = D/2, andD = original diameter, m (in.).11.4 Arithmetic MeanFor each series of tests, the arith-metic mean
38、 of all values obtained shall be calculated to threesignificant figures and reported as the “average value” for theparticular property in question.11.5 Standard DeviationThe standard deviation (esti-mated) shall be calculated as follows and reported in twosignificant figures:S 5(X22 nX2n 1(4)where:s
39、 = estimated standard deviation,X = value of single observation,n = number of observations, andX= arithmetic mean of the set of observations.12. Report12.1 Report the following information:12.1.1 Complete identification of the material tested, includ-ing type, source, manufacturers code number, form
40、, principledimensions, and previous history,12.1.2 Method of cutting rods,12.1.3 Conditioning procedure,12.1.4 Depth and diameter of specimen,12.1.5 Support span length,12.1.6 Support span-to-depth ratio,12.1.7 Diameters of support and loading noses,12.1.8 Rate of crosshead motion,12.1.9 Flexural st
41、rength (if applicable), average value, andstandard deviation,12.1.10 Tangent modulus of elasticity in bending, averagevalue, and standard deviation,12.1.11 Stress at any given strain up to and including 5 % (ifdesired, with strain used, average value, and standard devia-tion), and12.1.12 Maximum str
42、ain in the outer fibers of the specimen(optional).13. Precision and Bias313.1 Tables 1 and 2 are based on a round robin conducted in1984, involving three materials tested by eleven laboratories.Each test result was based on five individual determinations.Each laboratory obtained two test results for
43、 each material.Tests were conducted at room temperature and 150F.NOTE 5The explanations of r and R (13.2-13.2.3) are intended only topresent a meaningful way of considering the approximate precision of thistest method. The data in Tables 1 and 2 should not be applied toacceptance or rejection of mat
44、erials, as these data apply only to thematerials tested in the round robin and are unlikely to be rigorouslyrepresentative of other lots, formulations, conditions, materials, or labo-ratories. Users of this test method should apply the principles outlined inPractice E 691 to generate data specific t
45、o their materials and laboratory(or between specific laboratories). The principles of 13.2-13.2.3 wouldthen be valid for such data.13.2 Concept of r and R in Tables 1 and 2If Srand SRhavebeen calculated from a large enough body of data, and for testresults that were averages from testing 5 specimens
46、 for eachtest result, then the following apply:13.2.1 RepeatabilityTwo test results obtained within onelaboratory shall be judged not equivalent if they differ by morethan the r value for that material. r is the interval representingthe critical difference between two test results for the samemateri
47、al, obtained by the same operator using the sameequipment on the same day in the same laboratory.13.2.2 ReproducibilityTwo test results obtained by differ-ent laboratories shall be judged not equivalent if they differ bymore than the R value for that material. R is the intervalrepresenting the criti
48、cal difference between two test results forthe same material, obtained by different operators using differ-ent equipment in different laboratories.13.2.3 Any judgement in accordance with 13.2.1 or 13.2.2would have an approximate 95 % (0.95) probability of beingcorrect.3Supporting data have been file
49、d at ASTM International Headquarters and maybe obtained by requesting Research Report RR: D20-1119.TABLE 1 Precision StatementFlexural Modulus,106, psiRoom TemperatureMaterialRodDiameterMean SrSRIrIRVinyl ester 0.85 in. 7.39 0.365 0.971 1.02 2.75Vinyl ester 1.00 in. 6.58 0.233 0.850 0.659 2.41Polyester 1.20 in. 6.38 0.359 0.832 1.02 2.35Flexural Strength,103, psiVinyl ester 0.85 in. 222 5.07 15.9 14.3 44.9Vinyl ester 1.00 in. 169 2.71 4.78 7.67 13.5Polyester 1.20 in. 175 3.44 4.05 9.74 11.5TABLE 2 Precision S
