# ASTM D790-17

Designation: D790 − 17Standard Test Methods forFlexural Properties of Unreinforced and Reinforced Plasticsand Electrical Insulating Materials1This standard is issued under the fixed designation D790; 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.This standard has been approved for use by agencies of the U.S. Department of Defense.1. Scope*1.1 These test methods are used to determine the flexuralproperties of unreinforced and reinforced plastics, includinghigh modulus composites and electrical insulating materialsutilizing a three-point loading system to apply a load to asimply supported beam (specimen). The method is generallyapplicable to both rigid and semi-rigid materials, but flexuralstrength cannot be determined for those materials that do notbreak or yield in the outer surface of the test specimen withinthe 5.0 % strain limit.1.2 Test specimens of rectangular cross section are injectionmolded or, cut from molded or extruded sheets or plates, or cutfrom molded or extruded shapes. Specimens must be solid anduniformly rectangular. The specimen rests on two supports andis loaded by means of a loading nose midway between thesupports.1.3 Measure deflection in one of two ways; using crossheadposition or a deflectometer. Please note that studies have shownthat deflection data obtained with a deflectometer will differfrom data obtained using crosshead position. The method ofdeflection measurement shall be reported.NOTE 1—Requirements for quality control in production environmentsare usually met by measuring deflection using crosshead position.However, more accurate measurement may be obtained by using andeflection indicator such as a deflectometer.NOTE 2—Materials that do not rupture by the maximum strain allowedunder this test method may be more suited to a 4-point bend test. The basicdifference between the two test methods is in the location of the maximumbending moment and maximum axial fiber stresses. The maximum axialfiber stresses occur on a line under the loading nose in 3-point bending andover the area between the loading noses in 4-point bending. A four-pointloading system method can be found in Test Method D6272.1.4 The values stated in SI units are to be regarded as thestandard. The values provided in parentheses are for informa-tion only.1.5 The text of this standard references notes and footnotesthat provide explanatory material. These notes and footnotes(excluding those in tables and figures) shall not be consideredas requirements of the standard.1.6 This standard does not purport to address all 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.NOTE 3—This standard and ISO 178 address the same subject matter,but differ in technical content.1.7 This international standard was developed in accor-dance with internationally recognized principles on standard-ization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recom-mendations issued by the World Trade Organization TechnicalBarriers to Trade (TBT) Committee.2. Referenced Documents2.1 ASTM Standards:2D618 Practice for Conditioning Plastics for TestingD638 Test Method for Tensile Properties of PlasticsD883 Terminology Relating to PlasticsD4000 Classification System for Specifying Plastic Materi-alsD4101 Specification for Polypropylene Injection and Extru-sion MaterialsD5947 Test Methods for Physical Dimensions of SolidPlastics SpecimensD6272 Test Method for Flexural Properties of Unreinforcedand Reinforced Plastics and Electrical Insulating Materi-als by Four-Point BendingE4 Practices for Force Verification of Testing MachinesE83 Practice for Verification and Classification of Exten-someter Systems1These test methods are under the jurisdiction of ASTM Committee D20 onPlastics and are the direct responsibility of Subcommittee D20.10 on MechanicalProperties.Current edition approved July 1, 2017. Published July 2017. Originally approvedin 1970. Last previous edition approved in 2015 as D790 – 15ɛ2. DOI: 10.1520/D0790-17.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at service@astm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.*A Summary of Changes section appears at the end of this standardCopyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United StatesThis international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.1E691 Practice for Conducting an Interlaboratory Study toDetermine the Precision of a Test MethodE2309 Practices for Verification of Displacement MeasuringSystems and Devices Used in Material Testing Machines2.2 ISO Standard:3ISO 178 Plastics—Determination of Flexural Properties3. Terminology3.1 Definitions—Definitions of terms applying to these testmethods appear in Terminology D883 and Annex A2 of TestMethod D638.4. Summary of Test Method4.1 Atest specimen of rectangular cross section rests on twosupports in a flat-wise position and is loaded by means of aloading nose located midway between the supports. Unlesstesting certain laminated materials (see 7 for guidance), asupport span-to-depth (of specimen) ratio 16:1 shall be used.The specimen is deflected until rupture occurs in the outersurface of the test specimen or until a maximum strain (see5.1.6) of 5.0 % is reached, whichever occurs first.4.2 Procedure A is designed principally for materials thatbreak at comparatively small deflections and it shall be used formeasurement of flexural properties, particularly flexuralmodulus, unless the material specification states otherwise.Procedure A employs a strain rate of 0.01 mm/mm/min (0.01in./in./min) and is the preferred procedure for this test method.4.3 Procedure B is designed principally for those materialsthat do not break or yield in the outer surface of the testspecimen within the 5.0 % strain limit when Procedure Aconditions are used. Procedure B employs a strain rate of 0.10mm/mm/min (0.10 in./in./min).4.4 Type I tests utilize crosshead position for deflectionmeasurement.4.5 Type II tests utilize an instrument (deflectometer) fordeflection measurement.4.6 The procedure used and test type shall be reportedNOTE 4—Comparative tests may be run in accordance with eitherprocedure, provided that the procedure is found satisfactory for thematerial being tested. Tangent modulus data obtained by Procedure Atends to exhibit lower standard deviations than comparable resultsobtained by means of Procedure B.5. Significance and Use5.1 Flexural properties as determined by this test method areespecially useful for quality control and specification purposes.They include:5.1.1 Flexural Stress (σf)—When a homogeneous elasticmaterial is tested in flexure as a simple beam supported at twopoints and loaded at the midpoint, the maximum stress in theouter surface of the test specimen occurs at the midpoint.Flexural stress is calculated for any point on the load-deflectioncurve using equation (Eq 3) in Section 12 (see Notes 5 and 6).NOTE 5—Eq 3 applies strictly to materials for which stress is linearlyproportional to strain up to the point of rupture and for which the strainsare small. Since this is not always the case, a slight error will beintroduced if Eq 3 is used to calculate stress for materials that are not trueHookean materials. The equation is valid for obtaining comparison dataand for specification purposes, but only up to a maximum fiber strain of5 % in the outer surface of the test specimen for specimens tested by theprocedures described herein.NOTE 6—When testing highly orthotropic laminates, the maximumstress may not always occur in the outer surface of the test specimen.4Laminated beam theory must be applied to determine the maximumtensile stress at failure. If Eq 3 is used to calculate stress, it will yield anapparent strength based on homogeneous beam theory. This apparentstrength is highly dependent on the ply-stacking sequence of highlyorthotropic laminates.5.1.2 Flexural Stress for Beams Tested at Large SupportSpans (σf)—If support span-to-depth ratios greater than 16 to 1are used such that deflections in excess of 10 % of the supportspan occur, the stress in the outer surface of the specimen fora simple beam is reasonably approximated using equation (Eq4)in12.3 (see Note 7).NOTE 7—When large support span-to-depth ratios are used, significantend forces are developed at the support noses which will affect themoment in a simple supported beam. Eq 4 includes additional terms thatare an approximate correction factor for the influence of these end forcesin large support span-to-depth ratio beams where relatively large deflec-tions exist.5.1.3 Flexural Strength (σfM)—Maximum flexural stresssustained by the test specimen (see Note 6) during a bendingtest. It is calculated according to Eq 3 or Eq 4. Some materialsthat do not break at strains of up to 5 % give a load deflectioncurve that shows a point at which the load does not increasewith an increase in strain, that is, a yield point (Fig. 1, Curveb), Y. The flexural strength is calculated for these materials byletting P (in Eq 3 or Eq 4) equal this point, Y.5.1.4 Flexural Offset Yield Strength—Offset yield strength isthe stress at which the stress-strain curve deviates by a givenstrain (offset) from the tangent to the initial straight line portionof the stress-strain curve. The value of the offset must be givenwhenever this property is calculated.NOTE 8—Flexural Offset Yield Strength may differ from flexuralstrength defined in 5.1.3. Both methods of calculation are described in theannex to Test Method D638.5.1.5 Flexural Stress at Break (σfB)—Flexural stress at breakof the test specimen during a bending test. It is calculatedaccording to Eq 3 or Eq 4. Some materials give a loaddeflection curve that shows a break point, B, without a yieldpoint (Fig. 1, Curve a) in which case σfB= σfM. Other materialsgive a yield deflection curve with both a yield and a breakpoint, B (Fig. 1, Curve b). The flexural stress at break iscalculated for these materials by letting P (in Eq 3 or Eq 4)equal this point, B.5.1.6 Stress at a Given Strain—The stress in the outersurface of a test specimen at a given strain is calculated inaccordance with Eq 3 or Eq 4 by letting P equal the load read3Available from American National Standards Institute (ANSI), 25 W. 43rd St.,4th Floor, New York, NY 10036, http://www.ansi.org.4For a discussion of these effects, see Zweben, C., Smith, W. S., and Wardle, M.W., “Test Methods for Fiber Tensile Strength, Composite Flexural Modulus andProperties of Fabric-Reinforced Laminates,” Composite Materials: Testing andDesign (Fifth Conference), ASTM STP 674, 1979, pp. 228–262.D790 − 172from the load-deflection curve at the deflection correspondingto the desired strain (for highly orthotropic laminates, see Note6).5.1.7 Flexural Strain, ɛf—Nominal fractional change in thelength of an element of the outer surface of the test specimenat midspan, where the maximum strain occurs. Flexural strainis calculated for any deflection using Eq 5 in 12.4.5.1.8 Modulus of Elasticity:5.1.8.1 Tangent Modulus of Elasticity—The tangent modu-lus of elasticity, often called the “modulus of elasticity,” is theratio, within the elastic limit, of stress to corresponding strain.It is calculated by drawing a tangent to the steepest initialstraight-line portion of the load-deflection curve and using Eq6 in 12.5.1 (for highly anisotropic composites, see Note 9).NOTE 9—Shear deflections can seriously reduce the apparent modulusof highly anisotropic composites when they are tested at low span-to-depth ratios.4For this reason, a span-to-depth ratio of 60 to 1 isrecommended for flexural modulus determinations on these composites.Flexural strength should be determined on a separate set of replicatespecimens at a lower span-to-depth ratio that induces tensile failure in theouter fibers of the beam along its lower face. Since the flexural modulusof highly anisotropic laminates is a critical function of ply-stackingsequence, it will not necessarily correlate with tensile modulus, which isnot stacking-sequence dependent.5.1.8.2 Secant Modulus—The secant modulus is the ratio ofstress to corresponding strain at any selected point on thestress-strain curve, that is, the slope of the straight line thatjoins the origin and a selected point on the actual stress-straincurve. It shall be expressed in megapascals (pounds per squareinch). The selected point is chosen at a pre-specified stress orstrain in accordance with the appropriate material specificationor by customer contract. It is calculated in accordance with Eq6 by letting m equal the slope of the secant to the load-deflection curve. The chosen stress or strain point used for thedetermination of the secant shall be reported.5.1.8.3 Chord Modulus (Ef)—The chord modulus is calcu-lated from two discrete points on the load deflection curve. Theselected points are to be chosen at two pre-specified stress orstrain points in accordance with the appropriate materialspecification or by customer contract. The chosen stress orstrain points used for the determination of the chord modulusshall be reported. Calculate the chord modulus, Efusing Eq 7in 12.5.2.5.2 Experience has shown that flexural properties vary withspecimen depth, temperature, atmospheric conditions, andstrain rate as specified in Procedures A and B.5.3 Before proceeding with these test methods, refer to theASTM specification of the material being tested. Any testspecimen preparation, conditioning, dimensions, or testingparameters, or combination thereof, covered in the ASTMmaterial specification shall take precedence over those men-tioned in these test methods. Table 1 in Classification SystemD4000 lists the ASTM material specifications that currentlyexist for plastics.6. Apparatus6.1 Testing Machine—A testing machine capable of beingoperated at constant rates of crosshead motion over the rangeindicated and comprised of the following:6.1.1 Load Frame—The stiffness of the testing machineshall be such that the total elastic deformation of the systemdoes not exceed 1 % of the total deflection of the test specimenduring testing, or appropriate corrections shall be made.6.1.1.1 Fixed Member—A fixed or essentially stationarymembe