The FA B R ICATO R | An FMA Publication

w w w. t h e f a b r i c a t o r. c o m | June 2006

By Richard Gedney

Sheet metal forming operationsvary from simple to difficult; atone end of the spectrum is bend-ing; in the middle is stretching;

and at the other end is deep drawingof complex parts. Regardless of theforming operation, the sheet materi-a l ’s mechanical properties greatlyinfluence its formability, which is ameasure of the amount of deforma-tion a material can withstand beforeexcessive thinning or fracture occurs.Determining how much a materialcan deform is necessary for designing areproducible forming operation.Testing the incoming sheet material isalso essential because material proper-ties may vary from coil to coil andaffect the part quality and scrap rate.

Plastic Strain Ratio

The plastic strain ratio, r, is considereda direct measure of sheet metal’sdrawability and is useful for evaluatingmaterials intended for forming shapesby deep drawing (see lead photo). Ther value is the ratio of the true strain in

the width direction to the true strainin the thickness direction when asheet material is pulled in uniaxialtension beyond its elastic limit (seeFigure 1). Determining the plasticstrain ratio is governed by ASTME517 Standard Test Method forPlastic Strain Ratio r for Sheet Metal.The plastic strain ratio is calculated asshown in Equation 1.

r = ew/et

W h e r e :True width strain ew = ln(wf/wo)True thickness strain et = ln(tf/to)wf = Final widthwo = Original widthtf = Final thicknessto = Original thicknessEquation 1 shows that the r value

is dependent on the ratio of width andthickness changes as the sample ispulled in tension. The word p l a s t i c i nthe phrase plastic strain ratio i m p l i e sthat you have exceeded the speci-m e n ’s elastic limit and that only thestrain that induces plastic flow is con-sidered in the calculation. Because it isdifficult to measure thickness changesa c c u r a t e l y, it is assumed the volume ofthe specimen remains constant and

Drawing metal successfullyrelies, in part, on understandingprecisely how the metal reacts totensile forces. When subjected totensile forces, a flat section of sheetmaterial becomes thinner becauseof dimensional changes in its widthand thickness. The ratio of thechanges in width and thicknessmake up the plastic strain ratio.(Photo courtesy of ITW Drawform) .

FIGURE 1 In this typical test specimen used for measuring the plastic strainratio, r., the “45” denotes 45 degrees, which is the angle relative to the rolled direc-tion from which the specimen was cut. The gauge marks are 2 inches apart from eachother before the test. They are required only for manual calculation of the r value.

Measuring the plastic strain ratio of sheet metalsA us eful tool for evalu ating materi al

Reprinted with permission from the June 2006 issue of The FA B R I C AT O R®, copyright 2006 by FMA Communications Inc., Rockford, Illinois, w w w. t h e f a b r i c a t o r. c o m.

FIGURE 3 Stress, plotted on the Y axis, is the force divided by the original cross-sectional area of the specimen; strain, plotted on the X axis, is how the metal deformsunder the applied stress. A small amount of stress induces elastic deformation (the

region from O to A). As the phrase e l a s-tic deformation implies, the deformationis not permanent; removing the stressallows the material to return to its origi-nal shape. Between points A and F, thematerial undergoes plastic deformation.The material actually flows, and whenthe stress is removed, the material mayspring back but will not return to its orig-inal shape. F is the point of fracture.

The FA B R ICATO R | An FMA Publication

June 2006 | w w w. t h e f a b r i c a t o r. c o m

the thickness strain is expressed as et =l n ( Lowo/ Lfwf). After substituting et

into Equation 1 and inverting it toeliminate negative values, the plasticstrain ratio is given by Equation 2.

r = ln(wo/ wf) / l n ( Lfwf/ Lowo)Where:

Lf = Final lengthLo = Original length

Equation 2 enables you to calculatethe plastic strain ratio either manuallywith a set of calipers or automaticallywith the use of two extensometers—one to measure the change in axialgauge length and the other to measurethe change in width (see Figure 2). Ifyou use the manual approach, it isnecessary to measure with calipers thespecimen width and the distancebetween gauge marks before testing.You pull the specimen to a strain lessthan maximum force (point D inFigure 3), unload it, and measure thefinal width and gauge length.

If you use the automatic method ,you can pull the specimen until it frac-tures (see Figure 4). This enables youto determine the ultimate strength,yield strength, and elongation in thesame pull, which saves time andm o n e y. To calculate the plastic strainsusing the automatic method, you mustcalculate and subtract the elasticstrains from the measured strains.

E rrors in Determining

the Plastic Strain Ratio

If you were to perform an error analy-sis on Equation 2, you would find thatthe r value is much more sensitive toerrors in width measurement thanerrors in length measurement. R val-ues that are off by more than 40 per-cent are not unheard of. Furthermore,the reported values are always greater

than the true value. The two primarysources of errors in width strain meas-urement are caused by:

• Edge curling (the specimen’sedges curl along the length of thespecimen as it is pulled).

• Concentrated stresses (the sharp,knifelike edges on the extensometercreate highly concentrated stressesthat result in increased localized strain-ing at the point of measurement). B o t hsources of error result in greater widthstrains and higher r values.

After each test you need to inspectthe specimen to determine if it is flat.Errors in the r value persist unless youcompensate for the curling. Errorsassociated with sharp knife edges areeasily eliminated by installing knifeedges with rounded or flat surfaces atthe point of contact.

Other Points to Consider

For many materials, the r valueremains constant over the range ofplastic strains up to the maximumforce applied to the specimen. Forsome sheet materials, however, the rvalue varies with the applied axialstrain. For such materials, you shouldreport the as-tested strain level.

Because rolled sheet metals devel-op planar anisotropy (characteristicsthat are directional), sample orienta-tion can be significant to the measure-ment of the plastic strain ratio.Therefore, you must cut test speci-mens 0 degrees, 45 degrees, and 90degrees respective to the rolling direc-tion, and you must report the cutdirection with each result.

Richard Gedney ispresident ofADMET Inc.,51 Morgan Drive,

Norwood, MA 02062, 781-769-0850, fax781-769-0884, www.admet.com.

FIGURE 4 A specimen pulled to fracture typically exhibits necking, or thinning.The width and thickness of the specimen decreases noticeably near the point of fracture.

TEST METHODS AND SPECIFICATIONS Material properties that have a direct or indirect influence on the forma-bility and product quality are the ultimate tensile strength, yield strength,Yo u n g ’s modulus, ductility, strain-hardening exponent, and the plasticstrain ratio. You can determine all of these parameters by cutting a testspecimen from the blank and performing a tensile test. The followingASTM specifications govern these parameters:

• ASTM E8/E8M Standard Test Methods for Tension Testing ofMetallic Materials governs the determination of ultimate tensile strength,yield strength, elongation, and reduction of area. These are measures of duc-t i l i t y.

• ASTM E111 Standard Test Method for Yo u n g ’s Modulus, Ta n g e n tModulus, and Chord Modulus is used for determining Yo u n g ’s mod u l u s .

• ASTM E646 Standard Test Method for Tensile Strain-HardeningExponents (n-values) of Metallic Sheet Materials is for determining thestrain-hardening exponent.

• ASTM E517 Standard Test Method for Plastic Strain Ratio r forSheet Metal determines the plastic strain ratio. Of all the mechanicalproperties determined by a tensile test, the plastic strain ratio is the mostdifficult and requires close attention to detail.

ASTM Intl., 100 Barr Harbor Drive, West Conshohocken, PA 19428, 610-832-9585, fax 610-832-9555, www. a s t m . o r g

FIGURE 2 This axial and averaging transverse extensometer attached to a flatmetal test specimen is a typical arrangement for determining the plastic strain ratio.(Photo courtesy of Epsilon Technology Inc.)

Want more information?• I n t e rested in learning more about metals? See “The stru c t u re of metal” a t

w w w. t h e f a b r i c a t o r. c o m / M e t a l l u rg y / M e t a l l u rg y _ A rt i c l e . c f m ? I D = 5 6 8.

• Need to know how steels are classified? See “Carbon content, steel classi-

fications, and alloy steels” at w w w. t h e f a b r i c a t o r. c o m / M e t a l l u rg y / M e t a l l u rg y _

A rt i c l e . c f m ? I D = 6 8 5.

• If you need a quick re f e rence for metallurgical terms, see Principal Metals’

online glossary at w w w. p r i n c i p a l m e t a l s . c o m / g l o s s a ry / l i s t . h t m.

Reprinted with permission from the June 2006 issue of The FA B R I C AT O R®, copyright 2006 by FMA Communications Inc., Rockford, Illinois, w w w. t h e f a b r i c a t o r. c o m.