Method of Measuring n-value and r-value

1. SCOPE

This Standard specifies the method for measuring the n-value and r-value of cold rolled steel sheet, high-tension cold rolled steel sheet, and aluminum alloy cold rolled sheet.

Remarks: The units and numerical values expressed in this Standard are based on International System of Units [SI]. Coven-

tional units are noted in { } for informative reference. 2. TERMS AND DEFINITIONS

2.1 n-value (work hardening exponent) This is the value of the exponent n (C is constant) when the actual stress σa and the actual strain εa are approximated with the formula σa = Cεan.

2.2 r-value (Lankford value) This is a ratio of the cross direction strain to the thickness or axial direction strain (elongation).

2.3 Actual stress This is the value resulting from dividing the load by the parallel cross section of the test piece when some tension load is added to the test piece.

2.4 Actual strain This is the integral value of the axial direction strain changing every second divided by the length at every second when tensile load is added to the test piece.

3. TEST PIECE

3.1 Table 1 shows the direction for sampling the test piece.

Table 1 Test piece sampling direction Type Symbol Sampling direction (to rolling direction)

Cold rolled steel sheet (270 MPa class) SP120 0°

High-tension cold rolled steel sheet (340 MPa class or higher)

SP130 SP150 90°

5000 series NA150 0°

n-value

Aluminum alloy6000 series NA160 90°

r-value All types Three directions of 0°, 45°, and 90° Remark: The test piece sampling direction shall conform to JIS G 3135, JIS G 3141 and JIS H 4000.

3.2 In principle the test piece shall be the same as the JIS No. 5 test piece, but only when the test piece is

sampled from the actual part after forming, and JIS No. 13 test piece may be used (refer to Figure 1).

Normative References: See page 6.

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Figure 1 Test piece shape and dimension

Width (W) Distance between gauge marks (L)

Length of parallel part (P)

Radius of shoulder part (R)

Width of grip part (B)

n-value 50 No. 5

r-value 20, 25 Approx. 60 15 min. 30 min.

n-value 50 No. 13 B

r-value 20, 25 Approx. 60 20 to 30 20 min.

3.3 Any cross sections of test piece are uniform and the dimension variation of the parallel part (difference

between maximum value and minimum value) shall be 0.02 (mm) max., and the parallel part and the grip part shall be of a concentric circle.

3.4 The surface of the parallel part of the test piece shall be smooth with no cutting scratches, etc. 4. TEST EQUIPMENT 4.1 Tension tester

Tension tester shall be in accordance with JIS B 7721 (Tension testing machines).

4.2 Elongation measuring device Device shall be able to read a change of at least 0.01 (mm).

(Example) · Method for measuring elongation · Method for measuring distance between gauge marks

4.3 Width measuring device Device shall be able to measure the parallel part of the test piece and to read a change of at least 0.01 (mm).

(Example) · Method for measuring cross direction strain · Method for measuring distance between gauge marks

5. TEST METHOD

5.1 Test temperature The test temperature shall be within 5°C to 35°C and if necessary, make an entry of the temperature. However, for material that is sensitive to changes in temperature, the temperature shall be 20°C±2°C as a standard and shall conform to the instructions of the material Standard.

5.2 Method for measuring distance between gauge marks For measuring r-value, when measuring the elongation and width using a gauge line, make a mark with a marking stick, etc. in advance (refer to Figure 2). If the surface of the test piece is sensitive to surface scratches, make a mark on paint applied to the surface.

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Figure 2 Marking position and dimensions for measuring r value

(α) (α’)

Unit (mm) a b c

No. 5 5 10 No. 13 B

20, 25 2.5 5

Remarks (1): Gauge line A shall only be used when the local deformation of the parallel part is large.

(2): The distance between gauge lines shall be measured for the minimum value of the distance from (α) to (α’). 5.3 Loading method

5.3.1 Use a device appropriate for grasping the shape of the test piece. During the test, load shall be applied only to the axial direction of the test piece.

5.3.2 It is desirable that the load is applied at a uniform speed. For up to 1/2 of the load corresponding to the standard value of the tensile strength, the load may be applied at an appropriate speed, but after 1/2 of the load has been exceeded, the strain increase rate of the parallel part of the test piece shall be 20% to 80%/min. or less for steel sheet and 80%/min. or less for aluminum alloy.

5.4 Method for measuring n-value

5.4.1 A stress - strain diagram (refer to Figure 3) shall be drawn by recording the elongation continuously.

5.4.2 Obtain two or more points of nominal strain (ε) and nominal stress (σ) corresponding to the nominal strain from the stress - strain diagram obtained above. The guidelines of the ranges of measuring strain at this time are shown in Table 2. (Refer to Figure 3 and Table 2.) Although measurement is acceptable from 1% to the uniform elongation limit (Uel), it shall be clearly described when reporting. As the mini-mum value of the measurement strain range, yield strain is defined for material that does not indicate the yielding phenomenon, and the end point of the yield elongation is defined for material that indicates the yield phenomenon.

5.4.3 When there are 2 measuring points, find the n-value from formula (A).

5.4.4 In the case that there are three or more measuring points, calculate actual strain (εa) based on the nominal strain (ε) and nominal stress (σ) that are obtained in 5.4.2 above by using formula (B), calculate the actual stress (σa) by using formula (C), plot both values on the double logarithmic chart, draw a re-gression line by using the least squares method (E) and formula (D), and obtain the inclination (n value).

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Table 2. Guidelines of the measurement strain

range of the n-value

Uel Measurement strain range

20%<Uel 10 to 20 15%<Uel≤20% 5 to 15 10%<Uel≤15% 5 to 10

5%<Uel≤10% 4 to (Uel-1)

Figure 3 Stress - strain diagram

In the case of two measuring points, formula (A) for calculating the n-value (Refer to the explanation about derivation of this formula.)

ln {σ1(1 + ε1)/σ2(1 + ε2)} n =

ln {ln(1 + ε1)/ln(1 + ε2)}

Uniform elongation range Stress

Strain

In the case of three or more measuring points, formula (E) for calculating the n-value Formula (B) for calculating actual strain

εa = ln(1 + ε) Formula (C) for calculating actual stress

σa =σ(1 + ε) Regression coefficient formula (D)

σa =σa + n(ε - ε)

Formula (E) for calculating regression coefficient n-value

Σ(σa - σa) (εa - εa) n =

Σ(εa - εa)2

Figure 4 Actual stress - actual strain double

logarithmic chart

Actual strain

Actu

al s

tress

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5.5 Method for measuring r-value

5.5.1 Before providing strain for the test piece, measure width (W0) and the distance (L0) between the gauge marks. In the case of the measurement of width, measure at least three places including the positions of both gauge marks and the center of the marks, and the average of those is defined as the width (W0) of the test piece in principle.

5.5.2 The guidelines for the quantity of provided strain are shown in Table 3. However, the quantity of provided strain shall be the uniform elongation limit (Uel) or less of each material. The distance between the gauge marks of the test piece shape of No. 5 or No. 13B shall be 20 mm or 25 mm.

5.5.3 After providing strain for the test piece, measure the length between the gauge marks or the increase of the length, the width of the test piece or the decrease of the width. Measure them in the condition that the test force is eliminated.

5.5.4 Obtain the average width (W) of the parallel portion and axial direction length (L) of the deformed ten-sion test piece at the measurement positions and with the method similar to those before deformation, and calculate the r-value by using formula (F).

5.5.5 Use formula (G) to find the r -value. Table 3. Guidelines for the quantity

of provided strain of the r-value

Uel Quantity of provided strain

15%<Uel 15 10%<Uel≤15% 10

5%<Uel≤10% (Uel-1)

Formula (F) for calculating r-value

log (w0/w) r =

log (wL/w0L0)

Formula (G) for calculating r -value

r0° + 2r45° + r90° =r4

6. ROUNDING FIGURES

Round n-value and r-value measurement results to two decimal places.

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7. REPORT Include the following items in the report.

7.1 Notes concerning test pieces Name of material manufacturer, material name, type or symbols, and chemical composition. It is desirable to record such factors as the condition of the test piece surface, mechanical test results at room tem-perature, etc.

7.2 Shape, dimension, and sampling direction of test piece 7.3 Tester model 7.4 Tension speed

7.5 Accuracy of the strain measuring device used for measuring the n-value and r-value 7.6 Method for calculating n-value and r-value

Be sure to report the quantity of strain (ε1, ε2) at the two points used for measuring n-value.

7.7 n-value, r-value, and -value r 7.8 Other special conditions Normative References: JIS B 7721-1980 Tensile testing machines JIS G 3135-1986 Cold rolled high strength steel sheets with improved form-

ability for automobile structural uses JIS G 3141-1990 Cold-reduced carbon steel sheets and strips JIS H 4000-1988 Aluminum and aluminum alloy sheets and plates, strips and

coiled sheets JIS Z 2254-1996 Method of determining the plastic strain ratio for metallic

sheet and strip References: JIS Z 2201-1980 Test pieces for tensile test for metallic materials JIS Z 2241-1980 Method of tensile test for metallic materials NES M 2032-1998 High Tensile Strength Cold Rolled Carbon Steel Sheets and

Strips for Automobiles NES M 4064-1995 Cold Rolled Aluminum Alloy Sheets for Automobiles (for

Bodies)

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