Measuring The Ductility Of Metals

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Measuring the Ductility of MetalsBy Richard GedneyADMET, Inc.Ductility is defined as the ability of a material to deform plastically before fracturing. Its measurement is of interest tothose conducting metal forming processes; to designers of machines and structures; and to those responsible forassessing the quality of a material that it is being produced.Measures of DuctilityTwo measures of ductility are Elongation and Reduction of Area. The conventional means by which we obtain thesemeasures is by pulling a specimen in tension until fracture. ASTM E8 Standard Test Methods for Tension Testing ofMetallic Materials governs the determination of Elongation and Reduction of Area for metals. Elongation is defined asthe increase in the gage length of a test piece subjected to tensile forces divided by the original gage length. Elongationis expressed as a percentage of the original gage length and is given by:𝑷𝒆𝒓𝒄𝒆𝒏𝒕 𝑬𝒍𝒐𝒏𝒈𝒂𝒕𝒊𝒐𝒏 𝑳𝑳𝟎 𝟏𝟎𝟎Eq. 1Where: 𝑳𝟎 is the original gage length. 𝑳 is the change in length of the original gage length.Measured after the specimen fractures and the specimen isfitted together (see Figure 2).The original gage length, 𝐿0 , as specified in ASTM E8 is usually 1.0 in, 2.0 in, 4.0 in or 8.0 inches and is dependent on thesize of the specimen. A punch is often used to apply the gage marks to each specimen (see Figure 1). The change ingage length, L, is determined by carefully fitting the ends of the fractured specimen together and measuring thedistance between the gage marks (see Figure 2). In reporting the Elongation, ASTM E8 requires both the original gagelength and percentage increase. If any portion of the fracture occurs on or outside a gage mark, the Elongation andReduction of Area may not be representative of the material.Figure 1 - Flat ASTM E8 dogbone sample with 2 inch gage marks (Lo) applied with a punch.ADMET, Inc. 51 Morgan Dr. Norwood, MA (781) 769-0850support@admet.com, sales@admet.com, www.admet.com1

Reduction of Area is also expressed as a percentage and is given by:𝑷𝒆𝒓𝒄𝒆𝒏𝒕 𝑹𝒆𝒅𝒖𝒄𝒕𝒊𝒐𝒏 𝒐𝒇 𝑨𝒓𝒆𝒂 𝑨𝟎 𝑨𝒇𝑨𝟎 𝟏𝟎𝟎Eq. 2Where: 𝑨𝟎 is the original crossectional area.𝑨𝒇 is the crossectional area after fracture and corresponds tothe narrowest part of the neck which occurs at the point offracture (see Figure 2).Figure 2 - Tensile specimen pulled to fracture. Depicts region where necking occurred.Test Parameters that Affect DuctilityElongation results are affected by changes in gage length, specimen geometry and speed of testing or strain rate. Inaddition, heat dissipation caused by devices that contact the specimen such as grips and extensometers, become afactor when specimens are not tested at ambient temperatures.Gage LengthAs a rule, the larger the gage length, the smaller the measured Elongation for a given material. When a specimen ispulled in tension to fracture a region of local deformation occurs and is called the neck (see Figure 2). The onset ofnecking occurs as the force begins to drop after the maximum force has been reached on the stress strain curve (seeFigure 3). Up to the point at which the maximum force occurs (Point D, dP 0), the strain is uniform along the gagelength; meaning that the strain is independent of gage length. However, once necking starts, the gage length becomesvery important. When the gage length is short, the necking region occupies a much larger portion of the gage length.Conversely, for longer gage lengths, the necking occupies a smaller portion of the gage length.ADMET, Inc. 51 Morgan Dr. Norwood, MA (781) 769-0850support@admet.com, sales@admet.com, www.admet.com2

Figure 3 - Stress-Strain CurveSpecimen DimensionsThe cross sectional area of a specimen also has a significant effect on Elongation measurements. The slimness ratio, K,defined as the gage length divided by the square root of the crossectional area is given below.𝑺𝒍𝒊𝒎𝒏𝒆𝒔𝒔 𝑹𝒂𝒕𝒊𝒐 𝑳𝟎 𝑨𝟎Eq.3Where: 𝑳𝟎 is the original gage length.𝑨𝟎 is the original crossectional area of specimen.Experiments have shown that as the slimness ratio decreases the measured Elongation increases. A graphical depictionof the relationship between slimness ratio and Elongation is given below (Figure 4). Holding the slimness ratio, K,constant will minimize the effect of changes in specimen dimensions on Elongation.Reduction of Area is normally measured only on round test specimens because the shape of the reduced section in theneck remains essentially circular throughout the test. With rectangular test pieces, the corners prevent uniform flowfrom occurring, and consequently the shape in the neck is no longer rectangular. In general, as Reduction of Areaincreases the minimum allowable bend radius for a sheet material decreases.ADMET, Inc. 51 Morgan Dr. Norwood, MA (781) 769-0850support@admet.com, sales@admet.com, www.admet.com3

Figure 4 - Relationship between Slimness Ratio, K and ElongationTesting Speed/Strain RateGenerally, higher strain rates have an adverse effect on the ductility of materials. Meaning, Elongation values decreaseas the strain rate increases. Metals that are brittle are more sensitive to strain rate. Also, the strain rate sensitivity ofmetals is quite low at room temperature but increases with increasing temperature.Are Elongation and Reduction of Area Related?The occurrence of necking in a tension test makes it impossible to convert an Elongation measurement to a Reductionof Area measurement. While they usually vary in the same way as a function of test temperature or alloy content forexample, it is not always the case. Elongation and Reduction of Area measure different types of material behavior.Provided the gage length is not too short, Elongation is chiefly influenced by uniform Elongation and thus is dependenton the strain-hardening capacity of the material. Reduction of Area is more a measure of the deformation required toproduce fracture and its chief contribution results from the necking process. Because of the complicated stress state ina neck, values of Reduction of Area are dependent on specimen geometry and deformation behavior, and they shouldnot be taken as true material properties. However, Reduction of Area is the most structure sensitive ductilityparameter, and as such it is useful in detecting quality changes in a material.Test Methods and SpecificationsMaterial properties that have a direct or indirect influence on formability and product quality are, Ultimate TensileStrength, Yield Strength, Young’s Modulus, Ductility, Strain Hardening Exponent and the Plastic Strain Ratio. All ofthese parameters can be determined by cutting a test specimen from the blank and performing a tensile test. Below isa list of ASTM test specifications that govern the determination of these parameters.ASTM E8/E8MStandard Test Methods for Tension Testing of Metallic Materials governs the determination of Ultimate TensileStrength, Yield Strength plus Elongation and Reduction of Area which are measures of ductility.ADMET, Inc. 51 Morgan Dr. Norwood, MA (781) 769-0850support@admet.com, sales@admet.com, www.admet.com4

ASTM E111Standard Test Method for Young’s Modulus, Tangent Modulus, and Chord Modulus is used for determining Young’sModulus.ASTM E646Standard Test Method for Tensile Strain-Hardening Exponents (n-values) of Metallic Sheet Materials is used fordetermining the Strain Hardening Exponent.ASTM E517Standard Test Method for Plastic Strain Ratio r for Sheet Metal governs the determination of r. Of all the mechanicalproperties determined by a tensile test, ASTM E517 is the most difficult and requires close attention to detail.Copies of the ASTM test methods mentioned in this article may be obtained from ASTM, the American Society forTesting and Materials (www.astm.org).ADMET, Inc. 51 Morgan Dr. Norwood, MA (781) 769-0850support@admet.com, sales@admet.com, www.admet.com5

measures is by pulling a specimen in tension until fracture. ASTM E8 Standard Test Methods for Tension Testing of Metallic Materials governs the determination of Elongation and Reduction of Area for metals. Elongation is defined as the increase in the gage length of a test piece subjected to tensile forces divided by the original gage length.

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