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**Significance and Use**

5.1 Flexural properties as determined by this test method are especially useful for quality control and specification purposes. They include:

5.1.1 Flexural Stress (σ_{f})—When a homogeneous elastic material is tested in flexure 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. Flexural stress is calculated for any point on the load-deflection curve using equation (Eq 3) in Section 12 (see Notes 5 and 6).

Note 5: Eq 3 applies 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 Eq 3 is used to calculate stress for materials that are not true Hookean materials. The equation is valid for obtaining comparison data and for specification purposes, but only up to a maximum fiber strain of 5 % in the outer surface of the test specimen for specimens tested by the procedures described herein.

Note 6: When testing highly orthotropic laminates, the maximum 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 Eq 3 is 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.

5.1.2 Flexural Stress for Beams Tested at Large Support Spans (σ_{f})—If support span-to-depth ratios greater than 16 to 1 are used such that deflections in excess of 10 % of the support span occur, the stress in the outer surface of the specimen for a simple beam is reasonably approximated using equation (Eq 4) in 12.3 (see Note 7).

Note 7: When large support span-to-depth ratios are used, significant end forces are developed at the support noses which will affect the moment in a simple supported beam. Eq 4 includes additional terms that are an approximate correction factor for the influence of these end forces in large support span-to-depth ratio beams where relatively large deflections exist.

5.1.3 Flexural Strength (σ_{fM})—Maximum flexural stress sustained by the test specimen (see Note 6) during a bending test. It is calculated according to Eq 3 or Eq 4. Some materials that do not break at strains of up to 5 % give a load deflection 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 flexural strength is calculated for these materials by letting P (in Eq 3 or Eq 4) equal this point, Y.

**FIG. 1 Typical Curves of Flexural Stress (σ _{f}) Versus Flexural Strain (ε_{f})**

Note 1: Curve a: Specimen that breaks before yielding.

Curve b: Specimen that yields and then breaks before the 5 % strain limit.

Curve c: Specimen that neither yields nor breaks before the 5 % strain limit.

5.1.4 Flexural 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.

Note 8: Flexural Offset Yield Strength may differ from flexural strength defined in 5.1.3. Both methods of calculation are described in the annex to Test Method D638.

5.1.5 Flexural Stress at Break (σ_{fB})—Flexural stress at break of the test specimen during a bending test. It is calculated according to Eq 3 or Eq 4. Some materials give a load deflection curve that shows a break point, B, without a yield point (Fig. 1, Curve a) in which case σ_{fB} = σ_{fM}. Other materials give a yield deflection curve with both a yield and a break point, B (Fig. 1, Curve b). The flexural stress at break is calculated 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 outer surface of a test specimen at a given strain is calculated in accordance with Eq 3 or Eq 4 by letting P equal the load read from the load-deflection curve at the deflection corresponding to the desired strain (for highly orthotropic laminates, see Note 6).

5.1.7 Flexural Strain, ɛ_{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. Flexural strain is 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 modulus 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-deflection curve and using Eq 6 in 12.5.1 (for highly anisotropic composites, see Note 9).

Note 9: Shear deflections can seriously reduce the apparent modulus of highly anisotropic composites when they are tested at low span-to-depth ratios.4 For this reason, a span-to-depth ratio of 60 to 1 is recommended for flexural 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 fibers of the beam along its lower face. Since the flexural 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.

5.1.8.2 Secant 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 pre-specified stress or strain in accordance with the appropriate material specification or by customer contract. It is calculated in accordance with Eq 6 by letting m equal the slope of the secant to the load-deflection curve. The chosen stress or strain point used for the determination of the secant shall be reported.

5.1.8.3 Chord Modulus (E_{f})—The chord modulus is calculated from two discrete points on the load deflection curve. The selected points are to be chosen at two pre-specified stress or strain points in accordance with the appropriate material specification 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 Eq 7 in 12.5.2.

5.2 Experience has shown that flexural properties vary with specimen depth, temperature, atmospheric conditions, and strain rate as specified in Procedures A and B.

5.3 Before proceeding with these test methods, refer to the ASTM specification of the material being tested. Any test specimen preparation, conditioning, dimensions, or testing parameters, or combination thereof, covered in the ASTM material specification shall take precedence over those mentioned in these test methods. Table 1 in Classification System D4000 lists the ASTM material specifications that currently exist for plastics.

**1. Scope**

1.1 These test methods are used to determine the flexural properties of unreinforced and reinforced plastics, including high modulus composites and electrical insulating materials utilizing a three-point loading system to apply a load to a simply supported beam (specimen). The method is generally applicable to both rigid and semi-rigid materials, but flexural strength cannot be determined for those materials that do not break or yield in the outer surface of the test specimen within the 5.0 % strain limit.

1.2 Test specimens of rectangular cross section are injection molded or, cut from molded or extruded sheets or plates, or cut from molded or extruded shapes. Specimens must be solid and uniformly rectangular. The specimen rests on two supports and is loaded by means of a loading nose midway between the supports.

1.3 Measure deflection in one of two ways; using crosshead position or a deflectometer. Please note that studies have shown that deflection data obtained with a deflectometer will differ from data obtained using crosshead position. The method of deflection measurement shall be reported.

Note 1: Requirements for quality control in production environments are usually met by measuring deflection using crosshead position. However, more accurate measurement may be obtained by using an deflection indicator such as a deflectometer.

Note 2: Materials that do not rupture by the maximum strain allowed under this test method 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 fiber stresses. The maximum axial fiber 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. A four-point loading system method can be found in Test Method D6272.

1.4 The values stated in SI units are to be regarded as the standard. The values provided in parentheses are for information only.

1.5 The text of this standard references notes and footnotes that provide explanatory material. These notes and footnotes (excluding those in tables and figures) shall not be considered as requirements of the standard.

1.6 *This 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 appropriate safety and health practices and determine the applicability 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 accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.*

**2. Referenced Documents** *(purchase separately)* The documents listed below are referenced within the subject standard but are not provided as part of the standard.

**ASTM Standards**

D618 Practice for Conditioning Plastics for Testing

D638 Test Method for Tensile Properties of Plastics

D883 Terminology Relating to Plastics

D4000 Classification System for Specifying Plastic Materials

D4101 Specification for Polypropylene Injection and Extrusion Materials

D5947 Test Methods for Physical Dimensions of Solid Plastics Specimens

D6272 Test Method for Flexural Properties of Unreinforced and Reinforced Plastics and Electrical Insulating Materials by Four-Point Bending

E4 Practices for Force Verification of Testing Machines

E83 Practice for Verification and Classification of Extensometer Systems

E691 Practice for Conducting an Interlaboratory Study to Determine the Precision of a Test Method

E2309 Practices for Verification of Displacement Measuring Systems and Devices Used in Material Testing Machines

**ICS Code**

ICS Number Code 29.035.20 (Plastic and rubber insulating materials)

**UNSPSC Code**

UNSPSC Code 13100000(Rubber and elastomers); 39121721(Electrical insulators)

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**DOI:** 10.1520/D0790-17

**Citation Format**

ASTM D790-17, Standard Test Methods for Flexural Properties of Unreinforced and Reinforced Plastics and Electrical Insulating Materials, ASTM International, West Conshohocken, PA, 2017, www.astm.org

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