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ASTM D790-2010

ASTM D790-2010
ASTM D790-2010

Designation:D790–10

Standard Test Methods for

Flexural Properties of Unreinforced and Reinforced Plastics and Electrical Insulating Materials1

This standard is issued under the?xed designation D790;the number immediately following the designation indicates the year of original adoption or,in the case of revision,the year of last revision.A number in parentheses indicates the year of last reapproval.A superscript epsilon(′)indicates an editorial change since the last revision or reapproval.

This standard has been approved for use by agencies of the Department of Defense.

1.Scope*

1.1These test methods cover the determination of?exural properties of unreinforced and reinforced plastics,including high-modulus composites and electrical insulating materials in the form of rectangular bars molded directly or cut from sheets, plates,or molded shapes.These test methods are generally applicable to both rigid and semirigid materials.However,?exural strength cannot be determined for those materials that do not break or that do not fail in the outer surface of the test specimen within the5.0%strain limit of these test methods. These test methods utilize a three-point loading system applied to a simply supported beam.A four-point loading system method can be found in Test Method D627

2.

1.1.1Procedure A,designed principally for materials that break at comparatively small de?ections.

1.1.2Procedure B,designed particularly for those materials that undergo large de?ections during testing.

1.1.3Procedure A shall be used for measurement of?exural properties,particularly?exural modulus,unless the material speci?cation states otherwise.Procedure B may be used for measurement of?exural strength only.Tangent modulus data obtained by Procedure A tends to exhibit lower standard deviations than comparable data obtained by means of Proce-dure B.

1.2Comparative tests may be run in accordance with either procedure,provided that the procedure is found satisfactory for the material being tested.

1.3The values stated in SI units are to be regarded as the standard.The values provided in parentheses are for informa-tion only.

1.4This standard does not purport to address all of the safety concerns,if any,associated with its use.It is the responsibility 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.

N OTE1—These test methods are not technically equivalent to ISO178.

2.Referenced Documents

2.1ASTM Standards:2

D618Practice for Conditioning Plastics for Testing

D638Test Method for Tensile Properties of Plastics

D883Terminology Relating to Plastics

D4000Classi?cation System for Specifying Plastic Materi-als

D4101Speci?cation for Polypropylene Injection and Extru-sion Materials

D5947Test Methods for Physical Dimensions of Solid Plastics Specimens

D6272Test Method for Flexural Properties of Unreinforced and Reinforced Plastics and Electrical Insulating Materials by Four-Point Bending

E4Practices for Force Veri?cation of Testing Machines

E691Practice for Conducting an Interlaboratory Study to Determine the Precision of a Test Method

2.2ISO Standard:3

ISO178Plastics—Determination of Flexural Properties

3.Terminology

3.1De?nitions—De?nitions of terms applying to these test methods appear in Terminology D883and Annex A1of Test Method D638.

4.Summary of Test Method

4.1A bar of rectangular cross section rests on two supports and is loaded by means of a loading nose midway between the supports.A support span-to-depth ratio of16:1shall be used unless there is reason to suspect that a larger span-to-depth

1These test methods are under the jurisdiction of ASTM Committee D20on Plastics and are the direct responsibility of Subcommittee D20.10on Mechanical Properties.

Current edition approved April1,2010.Published April2010.Originally approved https://www.wendangku.net/doc/b618902678.html,st previous edition approved in2007as D790–07′1.DOI: 10.1520/D0790-10.

2For referenced ASTM standards,visit the ASTM website,https://www.wendangku.net/doc/b618902678.html,,or contact ASTM Customer Service at service@https://www.wendangku.net/doc/b618902678.html,.For Annual Book of ASTM Standards volume information,refer to the standard’s Document Summary page on the ASTM website.

3Available from American National Standards Institute(ANSI),25W.43rd St., 4th Floor,New York,NY10036,https://www.wendangku.net/doc/b618902678.html,.

*A Summary of Changes section appears at the end of this standard. Copyright?ASTM International,100Barr Harbor Drive,PO Box C700,West Conshohocken,PA19428-2959,United States. --`,`,`````,`,,```,,,,,,`,``-`-`,,`,,`,`,,`---

ratio may be required,as may be the case for certain laminated materials (see Section 7and Note 7for guidance).

4.2The specimen is de?ected until rupture occurs in the outer surface of the test specimen or until a maximum strain (see 12.7)of

5.0%is reached,whichever occurs ?rst.

4.3Procedure A employs a strain rate of 0.01mm/mm/min (0.01in./in./min)and is the preferred procedure for this test method,while Procedure B employs a strain rate of 0.10mm/mm/min (0.10in./in./min).

5.Signi?cance and Use

5.1Flexural properties as determined by these test methods are especially useful for quality control and speci?cation purposes.

5.2Materials that do not fail by the maximum strain allowed under these test methods (3-point bend)may be more suited to a 4-point bend test.The basic difference between the two test methods is in the location of the maximum bending moment and maximum axial ?ber stresses.The maximum axial ?ber stresses occur on a line under the loading nose in 3-point bending and over the area between the loading noses in 4-point bending.

5.3Flexural properties may vary with specimen depth,temperature,atmospheric conditions,and the difference in rate of straining as speci?ed in Procedures A and B (see also Note 7).

5.4Before proceeding with these test methods,reference should be made to the ASTM speci?cation of the material being tested.Any test specimen preparation,conditioning,dimensions,or testing parameters,or combination thereof,covered in the ASTM material speci?cation shall take prece-dence over those mentioned in these test methods.Table 1in Classi?cation System D4000lists the ASTM material speci?-cations that currently exist for plastics.

6.Apparatus

6.1Testing Machine —A properly calibrated testing ma-chine that can be operated at constant rates of crosshead motion over the range indicated,and in which the error in the load measuring system shall not exceed 61%of the maximum load expected to be measured.It shall be equipped with a de?ection measuring device.The stiffness of the testing machine shall be

such that the total elastic deformation of the system does not exceed 1%of the total de?ection of the test specimen during testing,or appropriate corrections shall be made.The load indicating mechanism shall be essentially free from inertial lag at the crosshead rate used.The accuracy of the testing machine shall be veri?ed in accordance with Practices E4.

6.2Loading Noses and Supports —The loading nose and supports shall have cylindrical surfaces.The default radii of the loading nose and supports shall be 5.060.1mm (0.19760.004in.)unless otherwise speci?ed in an ASTM material speci?cation or as agreed upon between the interested parties.When the use of an ASTM material speci?cation,or an agreed upon modi?cation,results in a change to the radii of the loading nose and supports,the results shall be clearly identi?ed as being obtained from a modi?ed version of this test method and shall include the speci?cation (when available)from which the modi?cation was speci?ed,for example,Test Method D790in accordance with Speci?cation D4101.

6.2.1Other Radii for Loading Noses and Supports —When other than default loading noses and supports are used,in order to avoid excessive indentation,or failure due to stress concen-tration directly under the loading nose,they must comply with the following requirements:they shall have a minimum radius of 3.2mm (1?8in.)for all specimens.For specimens 3.2mm or greater in depth,the radius of the supports may be up to 1.6times the specimen depth.They shall be this large if signi?cant indentation or compressive failure occurs.The arc of the loading nose in contact with the specimen shall be sufficiently large to prevent contact of the specimen with the sides of the nose.The maximum radius of the loading nose shall be no more than four times the specimen depth.

6.3Micrometers —Suitable micrometers for measuring the width and thickness of the test specimen to an incremental discrimination of at least 0.025mm (0.001in.)should be used.All width and thickness measurements of rigid and semirigid plastics may be measured with a hand micrometer with ratchet.A suitable instrument for measuring the thickness of nonrigid test specimens shall have:a contact measuring pressure of 2562.5kPa (3.660.36psi),a movable circular contact foot 6.3560.025mm (0.25060.001in.)in diameter and a lower ?xed anvil large enough to extend beyond the contact foot in all directions and being parallel to the contact foot within 0.005mm (0.002in.)over the entire foot area.Flatness of foot and anvil shall conform to the portion of the Calibration section of Test Methods D594

7.7.Test Specimens

7.1The specimens may be cut from sheets,plates,or molded shapes,or may be molded to the desired ?nished dimensions.The actual dimensions used in Section 4.2,Cal-culation,shall be measured in accordance with Test Methods D5947.

N OTE 2—Any necessary polishing of specimens shall be done only in the lengthwise direction of the specimen.

7.2Sheet Materials (Except Laminated Thermosetting Ma-terials and Certain Materials Used for Electrical Insulation,Including Vulcanized Fiber and Glass Bonded Mica):

TABLE 1Flexural Strength

Material Mean,103

psi

Values Expressed in Units of %

of 103psi V r A V R B r C R D ABS

9.99 1.59 6.05 4.4417.2DAP thermoset 14.3 6.58 6.5818.618.6Cast acrylic 16.3 1.6711.3 4.7332.0GR polyester

19.5 1.43 2.14 4.05 6.08GR polycarbonate 21.0 5.16 6.0514.617.1SMC

26.0

4.76

7.19

13.5

20.4

A

V r =within-laboratory coefficient of variation for the indicated material.It is obtained by ?rst pooling the within-laboratory standard deviations of the test results from all of the participating laboratories:Sr =[[(s 1)2+(s 2)2...+(s n )2]/n]1/2then V r =(S r divided by the overall average for the material)3100.B

V r =between-laboratory reproducibility,expressed as the coefficient of varia-tion:S R ={S r 2+S L 2}1/2where S L is the standard deviation of laboratory means.Then:V R =(S R divided by the overall average for the material)3100.C

r =within-laboratory critical interval between two test results =2.83V r .D

R =between-laboratory critical interval between two test results =2.83V R

.

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7.2.1Materials1.6mm(1?16in.)or Greater in Thickness—For?atwise tests,the depth of the specimen shall be the thickness of the material.For edgewise tests,the width of the specimen shall be the thickness of the sheet,and the depth shall not exceed the width(see Notes3and4).For all tests,the support span shall be16(tolerance61)times the depth of the beam.Specimen width shall not exceed one fourth of the support span for specimens greater than3.2mm(1?8in.)in depth.Specimens3.2mm or less in depth shall be12.7mm(1?2 in.)in width.The specimen shall be long enough to allow for overhanging on each end of at least10%of the support span, but in no case less than6.4mm(1?4in.)on each end.Overhang shall be sufficient to prevent the specimen from slipping through the supports.

N OTE3—Whenever possible,the original surface of the sheet shall be unaltered.However,where testing machine limitations make it impossible to follow the above criterion on the unaltered sheet,one or both surfaces shall be machined to provide the desired dimensions,and the location of the specimens with reference to the total depth shall be noted.The value obtained on specimens with machined surfaces may differ from those obtained on specimens with original surfaces.Consequently,any speci?-cations for?exural properties on thicker sheets must state whether the original surfaces are to be retained or not.When only one surface was machined,it must be stated whether the machined surface was on the tension or compression side of the beam.

N OTE4—Edgewise tests are not applicable for sheets that are so thin that specimens meeting these requirements cannot be cut.If specimen depth exceeds the width,buckling may occur.

7.2.2Materials Less than1.6mm(1?16in.)in Thickness—The specimen shall be50.8mm(2in.)long by12.7mm(1?2in.) wide,tested?atwise on a25.4-mm(1-in.)support span.

N OTE5—Use of the formulas for simple beams cited in these test methods for calculating results presumes that beam width is small in comparison with the support span.Therefore,the formulas do not apply rigorously to these dimensions.

N OTE6—Where machine sensitivity is such that specimens of these dimensions cannot be measured,wider specimens or shorter support spans,or both,may be used,provided the support span-to-depth ratio is at least14to1.All dimensions must be stated in the report(see also Note5).

7.3Laminated Thermosetting Materials and Sheet and Plate Materials Used for Electrical Insulation,Including Vulcanized Fiber and Glass-Bonded Mica—For paper-base and fabric-base grades over25.4mm(1in.)in nominal thickness,the specimens shall be machined on both surfaces to a depth of25.4mm.For glass-base and nylon-base grades, specimens over12.7mm(1?2in.)in nominal depth shall be machined on both surfaces to a depth of12.7mm.The support span-to-depth ratio shall be chosen such that failures occur in the outer?bers of the specimens,due only to the bending moment(see Note7).Therefore,a ratio larger than16:1may be necessary(32:1or40:1are recommended).When laminated materials exhibit low compressive strength perpendicular to the laminations,they shall be loaded with a large radius loading nose(up to four times the specimen depth to prevent premature damage to the outer?bers.

7.4Molding Materials(Thermoplastics and Thermosets)—The recommended specimen for molding materials is127by 12.7by3.2mm(5by1?2by1?8in.)tested?atwise on a support span,resulting in a support span-to-depth ratio of16(tolerance 61).Thicker specimens should be avoided if they exhibit signi?cant shrink marks or bubbles when molded.

7.5High-Strength Reinforced Composites,Including Highly Orthotropic Laminates—The span-to-depth ratio shall be cho-sen such that failure occurs in the outer?bers of the specimens and is due only to the bending moment(see Note7).A span-to-depth ratio larger than16:1may be necessary(32:1or 40:1are recommended).For some highly anisotropic compos-ites,shear deformation can signi?cantly in?uence modulus measurements,even at span-to-depth ratios as high as40:1. Hence,for these materials,an increase in the span-to-depth ratio to60:1is recommended to eliminate shear effects when modulus data are required,it should also be noted that the ?exural modulus of highly anisotropic laminates is a strong function of ply-stacking sequence and will not necessarily correlate with tensile modulus,which is not stacking-sequence dependent.

N OTE7—As a general rule,support span-to-depth ratios of16:1are satisfactory when the ratio of the tensile strength to shear strength is less than8to1,but the support span-to-depth ratio must be increased for composite laminates having relatively low shear strength in the plane of the laminate and relatively high tensile strength parallel to the support span.

8.Number of Test Specimens

8.1Test at least?ve specimens for each sample in the case of isotropic materials or molded specimens.

8.2For each sample of anisotropic material in sheet form, test at least?ve specimens for each of the following conditions. Recommended conditions are?atwise and edgewise tests on specimens cut in lengthwise and crosswise directions of the sheet.For the purposes of this test,“lengthwise”designates the principal axis of anisotropy and shall be interpreted to mean the direction of the sheet known to be stronger in?exure.“Cross-wise”indicates the sheet direction known to be the weaker in ?exure and shall be at90°to the lengthwise direction.

9.Conditioning

9.1Conditioning—Condition the test specimens in accor-dance with Procedure A of Practice D618unless otherwise speci?ed by contract or the relevant ASTM material speci?ca-tion.Conditioning time is speci?ed as a minimum.Tempera-ture and humidity tolerances shall be in accordance with Section7of Practice D618unless speci?ed differently by contract or material speci?cation.

9.2Test Conditions—Conduct the tests at the same tempera-ture and humidity used for conditioning with tolerances in accordance with Section7of Practice D618unless otherwise speci?ed by contract or the relevant ASTM material speci?ca-tion.

10.Procedure

10.1Procedure A:

10.1.1Use an untested specimen for each measurement. Measure the width and depth of the specimen to the nearest 0.03mm(0.001in.)at the center of the support span.For specimens less than2.54mm(0.100in.)in depth,measure the depth to the nearest0.003mm(0.0005in.).These measure-ments shall be made in accordance with Test Methods D5947

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10.1.2Determine the support span to be used as described in Section7and set the support span to within1%of the determined value.

10.1.3For?exural?xtures that have continuously adjust-able spans,measure the span accurately to the nearest0.1mm (0.004in.)for spans less than63mm(2.5in.)and to the nearest 0.3mm(0.012in.)for spans greater than or equal to63mm (2.5in.).Use the actual measured span for all calculations.For ?exural?xtures that have?xed machined span positions,verify the span distance the same as for adjustable spans at each machined position.This distance becomes the span for that position and is used for calculations applicable to all subse-quent tests conducted at that position.See Annex A2for information on the determination of and setting of the span.

10.1.4Calculate the rate of crosshead motion as follows and set the machine for the rate of crosshead motion as calculated by Eq1:

R5ZL2/6d(1) where:

R=rate of crosshead motion,mm(in.)/min,

L=support span,mm(in.),

d=depth of beam,mm(in.),and

Z=rate of straining of the outer?ber,mm/mm/min(in./ in./min).Z shall be equal to0.01.

In no case shall the actual crosshead rate differ from that calculated using Eq1,by more than610%.

10.1.5Align the loading nose and supports so that the axes of the cylindrical surfaces are parallel and the loading nose is midway between the supports.The parallelism of the apparatus may be checked by means of a plate with parallel grooves into which the loading nose and supports will?t when properly aligned(see A2.3).Center the specimen on the supports,with the long axis of the specimen perpendicular to the loading nose and supports.

10.1.6Apply the load to the specimen at the speci?ed crosshead rate,and take simultaneous load-de?ection data. Measure de?ection either by a gage under the specimen in contact with it at the center of the support span,the gage being mounted stationary relative to the specimen supports,or by measurement of the motion of the loading nose relative to the supports.Load-de?ection curves may be plotted to determine the?exural strength,chord or secant modulus or the tangent modulus of elasticity,and the total work as measured by the area under the load-de?ection curve.Perform the necessary toe compensation(see Annex A1)to correct for seating and indentation of the specimen and de?ections in the machine.

10.1.7Terminate the test when the maximum strain in the outer surface of the test specimen has reached0.05mm/mm (in./in.)or at break if break occurs prior to reaching the maximum strain(Notes8and9).The de?ection at which this strain will occur may be calculated by letting r equal0.05 mm/mm(in./in.)in Eq2:

D5rL2/6d(2) where:

D=midspan de?ection,mm(in.),

r=strain,mm/mm(in./in.),

L=support span,mm(in.),and

d=depth of beam,mm(in.).

N OTE8—For some materials that do not yield or break within the5% strain limit when tested by Procedure A,the increased strain rate allowed by Procedure B(see10.2)may induce the specimen to yield or break,or both,within the required5%strain limit.

N OTE9—Beyond5%strain,this test method is not applicable.Some other mechanical property might be more relevant to characterize mate-rials that neither yield nor break by either Procedure A or Procedure B within the5%strain limit(for example,Test Method D638may be considered).

10.2Procedure B:

10.2.1Use an untested specimen for each measurement.

10.2.2Test conditions shall be identical to those described in10.1,except that the rate of straining of the outer surface of the test specimen shall be0.10mm/mm(in./in.)/min.

10.2.3If no break has occurred in the specimen by the time the maximum strain in the outer surface of the test specimen has reached0.05mm/mm(in./in.),discontinue the test(see Note9).

11.Retests

11.1Values for properties at rupture shall not be calculated for any specimen that breaks at some obvious,fortuitous?aw, unless such?aws constitute a variable being studied.Retests shall be made for any specimen on which values are not calculated.

12.Calculation

12.1Toe compensation shall be made in accordance with Annex A1unless it can be shown that the toe region of the curve is not due to the take-up of slack,seating of the specimen,or other artifact,but rather is an authentic material response.

12.2Flexural Stress(s f)—When a homogeneous elastic material is tested in?exure as a simple beam supported at two points and loaded at the midpoint,the maximum stress in the outer surface of the test specimen occurs at the midpoint.This stress may be calculated for any point on the load-de?ection curve by means of the following equation(see Notes10-12):

s f53PL/2bd2(3) where:

s=stress in the outer?bers at midpoint,MPa(psi),

P=load at a given point on the load-de?ection curve,N (lbf),

L=support span,mm(in.),

b=width of beam tested,mm(in.),and

d=depth of beam tested,mm(in.).

N OTE10—Eq3applies strictly to materials for which stress is linearly proportional to strain up to the point of rupture and for which the strains are small.Since this is not always the case,a slight error will be introduced if Eq3is used to calculate stress for materials that are not true Hookean materials.The equation is valid for obtaining comparison data and for speci?cation purposes,but only up to a maximum?ber strain of 5%in the outer surface of the test specimen for specimens tested by the procedures described herein.

N OTE11—When testing highly orthotropic laminates,the

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stress may not always occur in the outer surface of the test specimen.4 Laminated beam theory must be applied to determine the maximum tensile stress at failure.If Eq3is used to calculate stress,it will yield an apparent strength based on homogeneous beam theory.This apparent strength is highly dependent on the ply-stacking sequence of highly orthotropic laminates.

N OTE12—The preceding calculation is not valid if the specimen slips excessively between the supports.

12.3Flexural Stress for Beams Tested at Large Support Spans(s f)—If support span-to-depth ratios greater than16to 1are used such that de?ections in excess of10%of the support span occur,the stress in the outer surface of the specimen for a simple beam can be reasonably approximated with the following equation(see Note13):

s f5~3PL/2bd2!@116~D/L!224~d/L!~D/L!#(4) where:

s f,P,L,b,and d are the same as for Eq3,and

D=de?ection of the centerline of the specimen at the middle of the support span,mm(in.).

N OTE13—When large support span-to-depth ratios are used,signi?cant end forces are developed at the support noses which will affect the moment in a simple supported beam.Eq4includes additional terms that are an approximate correction factor for the in?uence of these end forces in large support span-to-depth ratio beams where relatively large de?ec-tions exist.

12.4Flexural Strength(s fM)—Maximum?exural stress sustained by the test specimen(see Note11)during a bending test.It is calculated according to Eq3or Eq4.Some materials that do not break at strains of up to5%may give a load

de?ection curve that shows a point at which the load does not increase with an increase in strain,that is,a yield point(Fig.1, Curve B),Y.The?exural strength may be calculated for these materials by letting P(in Eq3or Eq4)equal this point,Y.

12.5Flexural Offset Yield Strength—Offset yield strength is the stress at which the stress-strain curve deviates by a given strain(offset)from the tangent to the initial straight line portion of the stress-strain curve.The value of the offset must be given whenever this property is calculated.

N OTE14—This value may differ from?exural strength de?ned in12.4. Both methods of calculation are described in the annex to Test Method D638.

12.6Flexural Stress at Break(s fB)—Flexural stress at break of the test specimen during a bending test.It is calculated according to Eq3or Eq4.Some materials may give a load de?ection curve that shows a break point,B,without a yield point(Fig.1,Curve a)in which case s fB=s fM.Other materials may give a yield de?ection curve with both a yield and a break point,B(Fig.1,Curve b).The?exural stress at break may be calculated for these materials by letting P(in Eq 3or Eq4)equal this point,B.

12.7Stress at a Given Strain—The stress in the outer surface of a test specimen at a given strain may be calculated in accordance with Eq3or Eq4by letting P equal the load read from the load-de?ection curve at the de?ection corresponding to the desired strain(for highly orthotropic laminates,see Note

11).

12.8Flexural Strain,′f—Nominal fractional change in the length of an element of the outer surface of the test specimen at midspan,where the maximum strain occurs.It may be calculated for any de?ection using Eq5:

′f56Dd/L2(5)

where:

′f=strain in the outer surface,mm/mm(in./in.),

D=maximum de?ection of the center of the beam,mm (in.),

L=support span,mm(in.),and

d=depth,mm(in.).

12.9Modulus of Elasticity:

12.9.1Tangent Modulus of Elasticity—The tangent modu-lus of elasticity,often called the“modulus of elasticity,”is the ratio,within the elastic limit,of stress to corresponding strain. It is calculated by drawing a tangent to the steepest initial straight-line portion of the load-de?ection curve and using Eq 6(for highly anisotropic composites,see Note15).

E B5L3m/4bd3(6)

where:

E B=modulus of elasticity in bending,MPa(psi),

L=support span,mm(in.),

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 and Properties of Fabric-Reinforced Laminates,“Composite Materials:Testing and Design(Fifth Conference),ASTM STP674,1979,pp.228–262.

N OTE—Curve a:Specimen that breaks before yielding.

Curve b:Specimen that yields and then breaks before the5%strain limit.

Curve c:Specimen that neither yields nor breaks before the5%strain limit.

FIG.1Typical Curves of Flexural Stress(?

f

)Versus Flexural

Strain(′

f

)--` , ` , ` ` ` ` ` , ` , , ` ` ` , , , , , , ` , ` ` -` -` , , ` , , ` , ` , , ` ---

b =width of beam tested,mm (in.),d =depth of beam tested,mm (in.),and

m

=slope of the tangent to the initial straight-line portion of the load-de?ection curve,N/mm (lbf/in.)of de?ec-tion.

N OTE 15—Shear de?ections can seriously reduce the apparent modulus

of highly anisotropic composites when they are tested at low span-to-depth ratios.4For this reason,a span-to-depth ratio of 60to 1is recommended for ?exural modulus determinations on these composites.Flexural strength should be determined on a separate set of replicate specimens at a lower span-to-depth ratio that induces tensile failure in the outer ?bers of the beam along its lower face.Since the ?exural modulus of highly anisotropic laminates is a critical function of ply-stacking sequence,it will not necessarily correlate with tensile modulus,which is not stacking-sequence dependent.

12.9.2Secant Modulus —The secant modulus is the ratio of stress to corresponding strain at any selected point on the stress-strain curve,that is,the slope of the straight line that joins the origin and a selected point on the actual stress-strain curve.It shall be expressed in megapascals (pounds per square inch).The selected point is chosen at a prespeci?ed stress or strain in accordance with the appropriate material speci?cation or by customer contract.It is calculated in accordance with Eq 6by letting m equal the slope of the secant to the load-de?ection curve.The chosen stress or strain point used for the determination of the secant shall be reported.

12.9.3Chord Modulus (E f )—The chord modulus may be calculated from two discrete points on the load de?ection curve.The selected points are to be chosen at two prespeci?ed stress or strain points in accordance with the appropriate material speci?cation or by customer contract.The chosen stress or strain points used for the determination of the chord modulus shall be reported.Calculate the chord modulus,E f using the following equation:

E f 5~s f 22s f 1!/~′f 22′f 1!

(7)

where:

s f 2and s f 1are the ?exural stresses,calculated from Eq 3or Eq 4and measured at the prede?ned points on the load de?ection curve,and ′f 2and

′f 1are the ?exural strain values,calculated from Eq 5and measured at the predetermined points on the load de?ection curve.

12.10Arithmetic Mean —For each series of tests,the arithmetic mean of all values obtained shall be calculated to three signi?cant ?gures and reported as the “average value”for the particular property in question.

12.11Standard Deviation —The standard deviation (esti-mated)shall be calculated as follows and be reported to two signi?cant ?gures:

s 5=~(X 2nX

ˉ!/~n 21!(8)

where:

s =estimated standard deviation,X =value of single observation,n =number of observations,and

X

ˉ=arithmetic mean of the set of observations.13.Report

13.1Report the following information:

13.1.1Complete identi?cation of the material tested,includ-ing type,source,manufacturer’s code number,form,principal dimensions,and previous history (for laminated materials,ply-stacking sequence shall be reported),

13.1.2Direction of cutting and loading specimens,when appropriate,

13.1.3Conditioning procedure,

13.1.4Depth and width of specimen,13.1.5Procedure used (A or B),13.1.6Support span length,

13.1.7Support span-to-depth ratio if different than 16:1,13.1.8Radius of supports and loading noses,if different than 5mm.When support and/or loading nose radii other than 5mm are used,the results shall be identi?ed as being generated by a modi?ed version of this test method and the referring speci?cation referenced as to the geometry used.13.1.9Rate of crosshead motion,

13.1.10Flexural strain at any given stress,average value and standard deviation,

13.1.11If a specimen is rejected,reason(s)for rejection,13.1.12Tangent,secant,or chord modulus in bending,average value,standard deviation,and the strain level(s)used if secant or chord modulus,

13.1.13Flexural strength (if desired),average value,and standard deviation,

13.1.14Stress at any given strain up to and including 5%(if desired),with strain used,average value,and standard devia-tion,

13.1.15Flexural stress at break (if desired),average value,and standard deviation,

13.1.16Type of behavior,whether yielding or rupture,or both,or other observations,occurring within the 5%strain limit,and

13.1.17Date of speci?c version of test used.

14.Precision and Bias

14.1Tables 1and 2are based on a round-robin test conducted in 1984,in accordance with Practice E691,involv-ing six materials tested by six laboratories using Procedure A.For each material,all the specimens were prepared at one

TABLE 2Flexural Modulus

Material Mean,103

psi

Values Expressed in units of %

of 103psi V r A V R B r C R D ABS

338 4.797.6913.621.8DAP thermoset 485 2.897.188.1520.4Cast acrylic 81013.716.138.845.4GR polyester

816 3.49 4.209.9111.9GR polycarbonate 1790 5.52 5.5215.615.6SMC

1950

10.9

13.8

30.8

39.1

A

V r =within-laboratory coefficient of variation for the indicated material.It is obtained by ?rst pooling the within-laboratory standard deviations of the test results from all of the participating laboratories:Sr =[[(s 1)2+(s 2)2...+(s n )2]/n ]1/2then V r =(S r divided by the overall average for the material)3100.B

V r =between-laboratory reproducibility,expressed as the coefficient of varia-tion:S R ={S r 2+S L 2}1/2where S L is the standard deviation of laboratory means.Then:V R =(S R divided by the overall average for the material)3100.C

r =within-laboratory critical interval between two test results =2.83V r .D

R =between-laboratory critical interval between two test results =2.83V R

.

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source.Each “test result”was the average of ?ve individual determinations.Each laboratory obtained two test results for each material.

N OTE 16—Caution:The following explanations of r and R (14.2-14.2.3)are intended only to present a meaningful way of considering the approximate precision of these test methods.The data given in Tables 2and 3should not be applied rigorously to the acceptance or rejection of materials,as those data are speci?c to the round robin and may not be representative of other lots,conditions,materials,or https://www.wendangku.net/doc/b618902678.html,ers of these test methods should apply the principles outlined in Practice E691to generate data speci?c to their laboratory and materials,or between speci?c laboratories.The principles of 14.2-14.2.3would then be valid for such data.

14.2Concept of “r”and “R”in Tables 1and 2—If S r and S R have been calculated from a large enough body of data,and for test results that were averages from testing ?ve specimens for each test result,then:

14.2.1Repeatability —Two test results obtained within one laboratory shall be judged not equivalent if they differ by more

than the r value for that material.r is the interval representing the critical difference between two test results for the same material,obtained by the same operator using the same equipment on the same day in the same laboratory.

14.2.2Reproducibility —Two test results obtained by dif-ferent laboratories shall be judged not equivalent if they differ by more than the R value for that material.R is the interval representing the critical difference between two test results for the same material,obtained by different operators using differ-ent equipment in different laboratories.

14.2.3The judgments in 14.2.1and 14.2.2will have an approximately 95%(0.95)probability of being correct.

14.3Bias —No statement may be made about the bias of these test methods,as there is no standard reference material or reference test method that is applicable.

15.Keywords

15.1?exural properties;plastics;stiffness;strength

ANNEXES

(Mandatory Information)A1.TOE COMPENSATION

A1.1In a typical stress-strain curve (see Fig.A1.1)there is a toe region,AC,that does not represent a property of the material.It is an artifact caused by a takeup of slack and

alignment or seating of the specimen.In order to obtain correct values of such parameters as modulus,strain,and offset yield point,this artifact must be compensated for to give the corrected zero point on the strain or extension axis.

A1.2In the case of a material exhibiting a region of Hookean (linear)behavior (see Fig.A1.1),a continuation of the linear (CD)region of the curve is constructed through the zero-stress axis.This intersection (B)is the corrected zero-strain point from which all extensions or strains must be measured,including the yield offset (BE),if applicable.The elastic modulus can be determined by dividing the stress at any point along the Line CD (or its extension)by the strain at the same point (measured from Point B,de?ned as zero-strain).A1.3In the case of a material that does not exhibit any linear region (see Fig.A1.2),the same kind of toe correction of the zero-strain point can be made by constructing a tangent to the maximum slope at the in?ection Point H 8.This is extended to intersect the strain axis at Point B 8,the corrected zero-strain https://www.wendangku.net/doc/b618902678.html,ing Point B 8as zero strain,the stress at any point (G 8)on the curve can be divided by the strain at that point to obtain a secant modulus (slope of Line B 8G 8).For those materials with no linear region,any attempt to use the tangent through the in?ection point as a basis for determination of an offset yield point may result in unacceptable

error.

N OTE —Some chart recorders plot the mirror image of this graph.

FIG.A1.1

Material with Hookean

Region

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A2.MEASURING AND SETTING SPAN

A2.1For ?exural ?xtures that have adjustable spans,it is important that the span between the supports is maintained constant or the actual measured span is used in the calculation of stress,modulus,and strain,and the loading nose or noses are positioned and aligned properly with respect to the supports.Some simple steps as follows can improve the repeatability of your results when using these adjustable span ?xtures.A2.2Measurement of Span:

A2.2.1This technique is needed to ensure that the correct span,not an estimated span,is used in the calculation of results.

A2.2.2Scribe a permanent line or mark at the exact center of the support where the specimen makes complete contact.The type of mark depends on whether the supports are ?xed or rotatable (see Figs.A2.1and A2.2).

A2.2.3Using a vernier caliper with pointed tips that is readable to at least 0.1mm (0.004in.),measure the distance between the supports,and use this measurement of span in the calculations.

A2.3Setting the Span and Alignment of Loading Nose(s)—To ensure a consistent day-to-day setup of the span and ensure the alignment and proper positioning of the loading nose,simple jigs should be manufactured for each of the standard setups used.An example of a jig found to be useful is shown in Fig.A2.3

.

N OTE —Some chart recorders plot the mirror image of this graph.

FIG.A1.2Material with No Hookean

Region

FIG.A2.1Markings on Fixed Specimen

Supports

FIG.A2.2Markings on Rotatable Specimen

Supports

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APPENDIX

(Nonmandatory Information)

X1.DEVELOPMENT OF A FLEXURAL MACHINE COMPLIANCE CORRECTION

X1.1Introduction

X1.1.1Universal Testing instrument drive systems always exhibit a certain level of compliance that is characterized by a variance between the reported crosshead displacement and the displacement actually imparted to the specimen.This variance is a function of load frame stiffness,drive system wind-up,load cell compliance and ?xture compliance.To accurately measure the ?exural modulus of a material,this compliance should be measured and empirically subtracted from test data.Flexural modulus results without the corrections are lower than if the correction is applied.The greater the stiffness of the material the more in?uence the system compliance has on results.X1.1.2It is not necessary to make the machine compliance correction when a de?ectometer/extensometer is used to mea-sure the actual de?ection occurring in the specimen as it is de?ected.

X1.2Terminology

X1.2.1Compliance —The displacement difference between test machine drive system displacement values and actual specimen displacement

X1.2.2Compliance Correction —An analytical method of modifying test instrument displacement values to eliminate the amount of that measurement attributed to test instrument compliance.

X1.3Apparatus

X1.3.1Universal Testing machine X1.3.2Load cell

X1.3.3Flexure ?xture including loading nose and specimen supports

X1.3.4Computer Software to make corrections to the dis-placements

X1.3.5Steel bar,with smoothed surfaces and a calculated ?exural stiffness of more than 100times greater than the test material.The length should be at least 13mm greater than the support span.The width shall match the width of the test specimen and the thickness shall be that required to achieve or exceed the target stiffness.

X1.4Safety Precautions

X1.4.1The universal testing machine should stop the ma-chine crosshead movement when the load reaches 90%of load cell capacity,to prevent damage to the load cell.

X1.4.2The compliance curve determination should be made at a speed no higher than 2mm/min.Because the load builds up rapidly since the steel bar does not de?ect,it is quite easy to exceed the load cell capacity.X1.5Procedure

N OTE X1.1—A new compliance correction curve should be established each time there is a change made to the setup of the test machine,such as,load cell changed or reinstallation of the ?exure ?xture on the machine.If the test machine is dedicated to ?exural testing,and there are no changes to the setup,it is not necessary to re-calculate the compliance curve.N OTE X1.2—On those machines with computer software that automati-cally make this compliance correction;refer to the software manual to determine how this correction should be made.

X1.5.1The procedure to determine compliance follows:X1.5.1.1Con?gure the test system to match the actual test con?guration.

X1.5.1.2Place the steel bar in the test ?xture,duplicating the position of a specimen during actual testing.

X1.5.1.3Set the crosshead speed to 2mm/min.or less and start the crosshead moving in the test direction recording crosshead displacement and the corresponding load

values.

FIG.A2.3Fixture Used to Set Loading Nose and Support Spacing and

Alignment

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X1.5.1.4Increase load to a point exceeding the highest load expected during specimen testing.Stop the crosshead and return to the pre-test location.

X1.5.1.5The recorded load-de?ection curve,starting when the loading nose contacts the steel bar to the time that the highest load expected is de?ned as test system compliance. X1.5.2Procedure to apply compliance correction is as follows:

X1.5.2.1Run the?exural test method on the material at the crosshead required for the measurement.

X1.5.2.2It is preferable that computer software be used to make the displacement corrections,but if it is not available compliance corrections can be made manually in the following manner.Determine the range of displacement(D)on the load versus displacement curve for the material,over which the modulus is to be calculated.For Young’s Modulus that would steepest region of the curve below the proportional limit.For Secant and Chord Modulii that would be at speci?ed level of strain or speci?ed levels of strain,respectively.Draw two vertical lines up from the displacement axis for the two chosen displacements(D1,D2)to the load versus displacement curve for the material.In some cases one of these points maybe at zero displacement after the toe compensation correction is made.Draw two horizontal lines from these points on the load displacement curve to the Load(P)axis.Determine the loads (L1,L2).

X1.5.2.3Using the Compliance Correction load displace-ment curve for the steel bar,mark off L1and L2on the Load (P)axis.From these two points draw horizontal lines across till they contact the load versus displacement curve for the steel bar.From these two points on the load de?ection curve draw two vertical lines downwards to the displacement axis.These two points on the displacement axis determine the corrections (c1,c2)that need to be made to the displacements measure-ments for the test material.

X1.5.2.4Subtract the corrections(c1,c2)from the mea-sured displacements(D1,D2),so that a true measures of test specimen de?ection(D1-c1,D2-c2)are obtained.

X1.6Calculations

X1.6.1Calculation of Chord Modulus

X1.6.1.1Calculate the stresses(s f1,s f2)for load points L1 and L2from Fig.X1.1using the equation in12.23.

X1.6.1.2Calculate the strains(′f1,′f2)for displacements D1-c1and D2-c2from Fig.X1.3using the equation in12.8Eq. 5.

X1.6.1.3Calculate the?exural chord modulus in accor-dance with12.9.3Eq.7.

X1.6.2Calculation of Secant Modulus

X1.6.2.1Calculation of the Secant Modulus at any strain along the curve would be the same as conducting a chord modulus measurement,except that s f1=0,L1=0,and D1-c1 =0.

X1.6.3Calculation of Young’s Modulus

X1.6.3.1Determine the steepest slope“m”along the curve, below the proportional limit,using the selected loads L1and L2from Fig.X1.1and the displacements D1-c1and D2-c2 from Fig.X1.3.

X1.6.3.2Calculate the Young’s modulus in accordance with 12.9.1Eq.6

.

FIG.X1.1Example of Modulus Curve for a

Material FIG.X1.2Compliance Curve for Steel

Bar

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SUMMARY OF CHANGES

Committee D20has identi?ed the location of selected changes to this standard since the last issue (D790-07′1)that may impact the use of this standard.(April 1,2010)

(1)Revised Section 9.

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FIG.X1.3Example of the Material Curve Corrected for the

Compliance Corrected Displacement or

Strain

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