# ASTM E855-08 (Reapproved 2013)

Designation: E855 − 08 (Reapproved 2013)Standard Test Methods forBend Testing of Metallic Flat Materials for SpringApplications Involving Static Loading1This standard is issued under the fixed designation E855; 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.1. Scope1.1 This standard describes three test methods2for deter-mining the modulus of elasticity in bending and the bendingstrength of metallic strips or sheets intended for the use in flatsprings:1.1.1 Test Method A—a cantilever beam,1.1.2 Test Method B—a three-point loaded beam (that is, abeam resting on two supports and centrally loaded), and1.1.3 Test Method C—a four-point loaded beam (that is, abeam resting on two supports and loaded at two points equallyspaced from each support).1.2 The values stated in inch-pound units are to be regardedas standard. The values given in parentheses are mathematicalconversions to SI units that are provided for information onlyand are not considered standard.1.3 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.2. Referenced Documents2.1 The following documents of the issue in effect on dateof use of these test methods form a part of these test methodsto the extent referenced herein:2.2 ASTM Standards:3E4 Practices for Force Verification of Testing MachinesE6 Terminology Relating to Methods of Mechanical TestingE111 Test Method for Young’s Modulus, Tangent Modulus,and Chord ModulusE177 Practice for Use of the Terms Precision and Bias inASTM Test MethodsE691 Practice for Conducting an Interlaboratory Study toDetermine the Precision of a Test Method3. Terminology3.1 Definitions of Terms Specific to This Standard:3.1.1 In addition to the terms in Terminology E6, thefollowing descriptions of terms apply in connection with thesetest methods for determining bend properties:3.1.2 bend properties—those properties of a material thatare associated with elastic and inelastic behavior when abending force is applied, or that involve the relationshipbetween bending stress and strain.3.1.3 bending stress at outer fiber (FL−2)—the nominalstress in the outer fibers of a beam resulting from application ofa bending load.3.1.4 elastic limit in bending (FL−2)—the greatest bendingstress that a material is capable of sustaining without perma-nent strain remaining after complete release of the bendingmoment.3.1.5 modulus of elasticity in bending (FL−2)—the ratio ofbending stress to corresponding strain below the elastic limit inbending.3.1.6 span length (L)—the distance between supports.3.1.7 uniform bending moment (FL)—a bending momentthat produces a uniform strain at the outer fibers throughout thegage length of the specimen.3.1.8 bending proof strength (FL−2)—the nominal stress inthe outer fibers of a beam that results in a specific permanentstrain in the outer fibers upon unloading.3.1.9 cyclic bending yield strength (FL−2)—the maximumnominal stress in uniform cyclic bending resulting from a givenplastic deformation in the outer fibers of a beam.3.1.10 offset yield strength in bending (FL−2)—the nominalstress in the outer fibers of a beam in bending at which aspecified limiting deviation from proportionality of bendingstress to bending strain is exhibited. The deviation is expressedin terms of strain.1These test methods are under the jurisdiction of ASTM Committee E28 onMechanical Testing and are the direct responsibility of Subcommittee E28.02 onDuctility and Formability.Current edition approved April 1, 2013. Published April 2013. Originallyapproved in 1981. Last previous edition approved in 2008 as E855 – 08. DOI:10.1520/E0855-08R13.2Method D, which appeared in the last previous edition, was dropped because ofthe unavailability of commercial testing equipment.3For 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.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States14. Significance and Use4.1 Measurements of bending strength and modulus ofelasticity in bending should be made for materials whoseprincipal stressing mode is bending. For many materials, thetensile and compressive moduli are somewhat different. Sincethe bending modulus is a combination of the tensile andcompressive moduli, it is often different from each of them.4.2 Precise measurements of the modulus of elasticity inbending and bending strength require due regard for numerousvariables that may affect their determination. These include (1)characteristics such as specimen orientation with respect to therolling direction, grain size, residual stresses, previous strainhistory, dimensions and specimen preparation, orientation ofdeformed grains relative to the direction of the normal stress;and (2) test conditions, such as tem-perature, temperature variations, condition of the test equip-ment and adherence to the recommended test procedure.5. Fundamental Assumptions5.1 The test section of the specimen is subjected to uniformbending moment (applies to Test Method C only).5.2 The neutral axis is located at the centerline of thethickness of the test specimen.5.3 Transverse cross sections of the beam remain plane andnormal to the longitudinal fibers of the beam during bending.5.4 The effect of shear stresses is negligible.TEST METHOD A—CANTILEVER BEAM TEST6. Scope6.1 This test method covers the determination of the modu-lus of elasticity in bending and the offset yield strength inbending of flat metallic strips or sheets for spring applications.The test procedure involves measurements of the appliedmoment and the corresponding angle of deflection of acantilever beam. The thickness range covered is 0.015 to 0.130in. (0.38 to 3.30 mm). This test method is not applicable fornonlinear elastic materials.7. Summary of Test Method7.1 The test specimen is loaded as a simple cantilever beam,and the bending moment is measured at predetermined incre-ments of angular deflection. When the maximum desireddeflection is reached, the bending moment is removed and thepermanent set angle resulting from the bend is recorded. Alltesting is performed under conditions of plane strain (that is,ratio of specimen width/thickness 10). The bending momentand deflection data obtained are normalized with regard tospecimen geometry. These normalized terms are then plotted toproduce a stress-strain curve for cantilever bending that issimilar to a stress-strain curve for tension or compression. Themodulus of elasticity in bending and the offset yield strength inbending are determined from the bending stress-strain curveusing a procedure similar to that used for tensile stress-straincurves.8. Significance and Use8.1 This test method may be used for obtaining values ofoffset yield strength in bending and modulus of elasticity inbending. These values are useful to spring designers todetermine spring constants and permissible maximum deflec-tion of flat springs. It should be recognized that the offset yieldstrength in bending as determined by this test method is notnecessarily equal to either the yield strength in tension, thecyclic yield strength in bending, or to bending proof strengthsdetermined by other methods.8.2 The test method can also serve the following purposes:8.2.1 For research and development to study the effects ofmetallurgical variables, such as composition, heat treatment,fabrication operations and alloy development.8.2.2 For information or specification purposes, to provide amanufacturing quality control where suitable correlations havebeen established with service behavior.8.3 Due to necessary approximations in this test methodregarding the specimen’s deflection, D, and span, L,itisrecommended that a deflection angle of 30° not be exceeded.These approximations are explained in Appendix X1.8.4 Rate of loading is controlled only to the extent that therate of angular change of the rotating jaw is fixed at 58 to66°/min. Actual rate of stressing will depend on the specimenwidth and thickness and the weight of the pendulum.9. Apparatus9.1 The cantilever bend test apparatus4shown in Fig. 1consists of the following components:9.1.1 Specimen Holder, A vise, V, to which an angulardeflection indicator, I1, is attached. The specimen holder isrotated about point O.9.1.2 Pendulum Weighing System, composed of a set ofdetachable weights, an angular deflection scale with a momentpointer indicator, I2, a loading pin that transmits the bendingforce of the pendulum system to the free end of the cantileverspecimen, and a weight to counter-balance the loading pin. The4The Olsen Stiffness Tester meets the requirements of this test method.(Test Method A)FIG. 1 Cantilever Bend Test ApparatusE855 − 08 (2013)2pendulum weighing system pivots about point O. For apendulum system (Fig. 2) having no internal moments, the totalbending moment, M, is:M 5 wdsinθ (1)where:M = bending moment at angle θ, lbf·in (N·m),w = total load applied by pendulum system, lbf (N),d = length of the pendulum arm, in (m), andθ = angle through which the pendulum system rotates, rad.9.1.3 Angular Deflection Scale, A, is graduated in degrees ofarc and indicates the angle through which the rotating vise hasbeen turned relative to the pendulum system. This is thedifference between the angle through which the vise has beenturned and the angle through which the load pendulum hasbeen deflected, and is designated as angle φ. The loading pinhas a diameter of 0.25 in. (6.35 mm), and the distance betweenthe clamping point (that is, center of rotation of the pendulumsystem) and the center of the loading pin is 2.0 in. (50.8 mm).The reason for specifying the pin diameter and pin location isexplained in Appendix X1.9.1.4 Moment Scale—This stationary scale measures theapplied moment as a function of the pendulum’s rotation θ.Afull scale reading of 100 corresponds to the pendulum’smaximum bending moment, Mm. This system shall be cali-brated such that the moment scale reading, f, is:f 5 100 wdsinθ/Mm(2)10. Test Specimens10.1 Rectangular test specimens shall be used. Specimenorientation relative to the rolling direction must be identified.Specimen curvature due to coil set is permitted if the ratio ofthe radius of curvature to thickness exceeds 500. However, thespecimen cannot be twisted or wavy. No attempt shall be madeto flatten or straighten specimens prior to testing. Care shall beexercised not to alter the microstructure during specimenpreparation. All burrs shall be removed before testing. Testingmachine capacity will determine the maximum allowablespecimen size.10.2 The recommended minimum specimen thickness is0.015 in. (0.38 mm). The thickness shall be measured at thefour corners and the center of the specimen. Specimens havingthickness variations in excess of 2 % of the average (of thesefive measured thicknesses) shall not be tested. The instrumentused to measure the thickness shall have a precision within 2 %of the average thickness.10.3 In Eq 3 in 11.1 it is shown that the value of themodulus of elasticity in bending varies as the third power ofthickness. Hence, thickness is by far the most critical measure-ment in the determination of the modulus.NOTE 1—For example, an error in the thickness measurement of60.0001 in. (0.0025 mm) for a specimen having the minimum recom-mended thickness of 0.015 in. (0.28 mm), the measurement is reproduc-ible to within 0.67 % and the error in modulus attributable to thereproducibility of the thickness measurement is 2 %. Further, if thethickness actually varies by 2 % over the gage section or by 0.0003 in.(0.0075 mm), the error in modulus attributable to actual thicknessvariation is 6 %, and the total error attributable to both measurement andactual variation is 8 %. Additional sources of uncertainty are the preci-sions of determining the span length, the specimen width, and the beamdeflection.10.4 The ratio of the specimen span to thickness shall begreater than 15; consequently, since the span is 2.0 in. (50.8mm), the specimen thickness cannot exceed 0.13 in. (3.30mm).10.5 The width to thickness ratio shall be greater than 10.The width shall be measured at both ends and the center of thespecimen. Specimens having width variations greater than0.5 % of the average width are not acceptable. The minimumspecimen width shall be 0.5 in. (12.7 mm). The specimen widthshall not extend beyond the vise or the loading pin.11. Procedure11.1 Place the machine on a level surface. Set the bendingspan to 2.0 in. (50.8 mm) and adjust the moment indicator tozero. For the best precision the maximum bending moment,Mm, should be chosen so that the moment scale reading isbetween 5 and 10 for an angular deflection of 3°. If this valueis not known, it can be estimated as follows:Mm5 25 Ebbh3φ/fL (3)where:Mm= pendulum’s maximum bending moment, in·lbf (N·m),Eb= modulus of elasticity in bending (can be approxi-mated by Young’s modulus) lbf/in.2(Pa),b = specimen width, in. (m),h = specimen thickness, in. (m),φ = angular deflection, rad (0.052 rad (3°) specified here),f = moment scale reading (select 7.5 in this case), andL = span, 2 in. (50.8 mm).11.2 Clamp the specimen firmly in the vise with its longedges approximately parallel to the face of the dial plate.(Test Method A)FIG. 2 Schematic of Pendulum SystemE855 − 08 (2013)311.3 Manually rotate the vise to bring the specimen againstthe loading pin. When contact is made, the angular deflectionindicator shall be set to indicate zero angle.11.4 Hold down the motor engaging lever and record themoment scale readings at increments of 2° angular deflection(φ) until the desired deflection, not exceeding 30°, is reached.The specimen then shall be unloaded. The permanent set angleresulting from the bend shall be read on the angular deflectionscale with the specimen contacting the loading pin at zero load.11.5 A minimum of six specimens shall be tested from eachsample. For specimens having an initial residual curvature, halfof the specimens shall be tested with the concave surfacefacing upwards and half with the convex surface facingupwards. All specimens shall be deflected to the same maxi-mum angle. The allowable maximum deflection angle is 30°.11.6 Replication required for evaluating material variabilitywithin either the same sample or among several suppliers shallbe covered in product specifications or upon agreement be-tween supplier and user.12. Calculation12.1 The bending moment-deflection data