Importance of n-value in sheet-metal forming. ... It is also a mechanical property that not only determines how a material strengthens, but how well it forms in a.
SHRI GURU GOBIND SINGHJI INSTITUTE OF ENGG & TECHNOLOGY DEPARTMENT OF PRODUCTION ENGINEERING SUBJECT: MECHANICAL WORKING OF METALS
EXPERIMENT NO: 5
AIM: DETERMINE STRAIN-HARDENING EXPONENT, n-value. AIM: Determine Strain-hardening exponent, n-value OBJECTIVES: The strain hardening exponent, also known asstrain hardening index, denoted byn, is a materials constant whichis used in calculations for stress-strain behavior in work hardening. After performing this experiment, the students will be able to:
Understand the strain hardening exponent, n-value.
Determine the strain hardening exponent, n-value.
Importance of n-value in sheet-metal forming.
THEORY: 1) STRAIN HARDENING EXPONENT (n-value): Strain hardening coefficient „n‟ is a coefficient, which gives a quantitative measurement of the strainhardening characteristic of a material. It can be defined as: n = d ln Ϭt / d ln ε Where, Ϭt = true stress ε = true strain Strain hardening is represented by the exponent “n” in the flow stress equation, which approximates the relation between true stress and true strain during plastic deformation of a metal. The constant n plays a crucial role in sheet metal forming, Strain hardening is a means of strengthening a metal prior to its delivery to the customer. The temper of an alloy is partially determined by the amount of strain hardening it undergoes at the production mill. However, strain hardening behavior is not limited to the mill, but occurs any time that the metal is permanently deformed. It is also a mechanical property that not only determines how a material strengthens, but how well it forms in a stamping die. This property can be seen in a material‟s true stress-strain curve. The strain hardening exponent (n) determines how the metal behaves when it is being formed. Materials that have higher n values have better formability than those with low n values. As metals work harden, their remaining capacity for work hardening decreases. This means that high strength tempers of a given material typically would have lower n values than lower strength tempers of the same alloy.It is the measure of increase in hardness and strength caused by plastic deformation
FIG.1. TRUE STRESS-STRAIN CURVE ON LINEAR SCALE
FIG.2. TRUE STRESS-STRAIN CURVE ON LOGARTHMIC SCALE The majority of the stress-strain curve falls onto two straight lines, as shown in the chart on Figure 1. The first line, shown in blue, represents the elastic portion of the stress-strain curve, where Hooke‟s law holds and the elastic modulus is constant (i.e., σ =E ε). The second line represents the plastic region of the curve where strain hardening occurs. Here, the stress-strain relationship can be summed up by a power law (i.e. σ=K εn). On the logarithmic scales, this exponential function is mapped onto a straight line (log σ = log K + n log ε), whose slope is equal to the strain hardening exponent (n), and whose intercept with a true strain value of 1 is the strength coefficient (K). Often, the strain hardening exponent is referred to by its symbol, and is simply called the “n-value”. In the case shown in Figure 1, linear regression of the curve in Figure 1, one finds that, n = 0.0713, Log10 K = 5.1577, Therefore, K = 143780.5.
The equation describing the plastic portion of the curve is thus σ =143780.5ε0.0713 psi. The green line in the plot on figure 1 shows that the power function is a good approximation of the plastic portion of the curve, if one ignores the section in the elastic region.
2) DETERMINING STRAIN HARDENING EXPONENT: Strain hardening coefficient „n‟ is determined by the dependence of the flow stress on the level of strain. The strain-hardening exponent, n, is a primary metal property that can be determined by a simple tension test or from the measurementof strain in a special specimen. When metal alloys are cold worked, their yield strength increases. The n-value is the amount of strengthening for each increment of straining. The higher the n-value, the steeper the stress-strain curve in the uniform elongation region of the tensile test.
FIG.3. EFFECT OF n-VALUE ON STRESS-STRAIN CURVE Excessive stretching of sheet-metal leads to local necking and tearing of the stamping. The n-value is the one property of sheet-metal that helps the most in evaluating its relative stretchability.
FIG.4. STANDARD TENSILE-TEST SPECIMEN
TABLE 1. STANDARD TENSILE-TEST SPECIMEN’S DIMENSIONS The n-value can be obtained by conducting a simple tensile test in which the specimen is stretched until it fractures, as in figure 4. The procedure for the test is as follows: 1. Measure and record the original thickness of the reduced section of the specimen to at least 0.0005 in. and the width of reduced section to at least 0.001 in. 2. Grip the specimen in the testing machine in a manner to ensure axial alignment of the specimen and attach the extensometer. 3. The speed of testing shall be such that the loads and strains are accurately measured. 4. The test speed, defined in terms of rate of separation of heads during tests, free running crosshead speed, or rate of straining shall be between 0.05 and 0.50 in./in. of the length of the reduced section per minute. The speed setting shall not be changed during the strain interval over which „n‟ is to be measured. 5. If the yield point, yield point elongation, yield strength, or any other combination of these is to be determined also, the rate of stress application or crosshead separation during the portion of the test shall be within a particular range. After exceeding the strain necessary for this information, adjust the crosshead speed to within the range specified prior to the next step. 6. Record the load and corresponding displacement for at least five approximately equally spaced levels of strain encompassing the range of interest specified in the product specification. Usually the greatest of these strains is at or slightly prior to the strain at which the maximum load occurs, and usually the lower bound of these strains is the yield strain or the end of yield-point extension. 7. If multiple n-values are to be determined, use at least five stress and strain values for the calculation of n in each interval of strain. 8. Determine the strain hardening exponent from the logarithmic form of the power curve representation of the true stress-strain curve within the plastic range, ln Ϭ = ln K + n ln ε
9. Calculate the values of true stress and true strain as following, True stress, Ϭ = S (1 + e) True strain, ε = ln (1 + e) Where, „S‟ and „e‟ are engineering stress and engineering strain respectively. 10. Obtain the logarithms of the true stress – true strain pairs. From these paired sets of (ln Ϭ, ln ε), calculate, via linear regression analysis of ln Ϭ vs. ln ε, the slope „n‟ and standard error of the slope.
FIG.5. MAGNITUDES OF ELONGATION AT ONSET OF NECKING VARYING WITH
n-value
FIG.6. DATA FROM TENSILE-TEST REPRESENTED IN, (a) ENGINEERING STRESS-STRAIN CURVE (b) TRUE STRESS-STRAIN CURVE
3) IMPORTANCE OF STRAIN HARDENING EXPONENT (n-value): The n-value plays a crucial role in sheet metal forming. The larger the n-value, the flow-stress increases rapidly with strain, which results in the distribution of strain uniformly throughout the sheet and even in low strain areas. Due to this uniform distribution, forming limit or formability increases. Thus, more material can elongate before necking. Thus, as the n-value increases, the material's resistance to necking increases, and the material can be stretched farther before necking starts. The effect of the n-value in deep drawing is ambiguous. In cup drawing, for example, higher n-values may reduce wrinkling, i.e. a high n-value results in higher strain hardening in the cup wall, so the material does notfracture easily when the blank holder force is increased. On the other hand, with increased strain hardening, the drawing force and the stress in the cup wall also increase, which may lead to fracture. The effect of the n value on deformation in a tensile test was investigated with the finite element method(FEM) simulation using the FEM softwareDEFORM2D. Standard tensile testing procedure andspecimen dimensions were used as prescribed inAmerican Society for Testing and Materials (ASTM)E8.It is well-known that increasing the n value alsoincreases the formability of the material. The purposeof this investigation was to illustrate this phenomenonby using FEM simulation. The specimen geometrywas provided by a mesh, which is similar to circle grids on sheet metal.The gauge lengths for n values of 0.2, 0.4, and 0.6were measured after deformation. The initial gauge length was 50 millimeters beforedeformation; for the n values of 0.2, 0.4, and 0.6,stretched lengths of 64 mm, 74 mm, and 94 mm wereobtained, respectively, at the onset of necking, as shown in figure 2b, 2c and 2d.
FIG.7. FRACTURE PREDICTED BY FEM SIMULATION
Fracture also can be predicted by FEM simulation using the appropriate fracture criterion. Figure 6 shows the fractured specimens for each n-value. It is also quite obvious that materials with higher n values elongate more before fracture takes place.
CONCLUSION: In this way, we have studied the strain-hardening exponent, i.e. n-value.
REVIEW QUESTIONS: 1. What is the strain-hardening exponent? 2. How the n-value is determined? 3. What is the role of n-value in sheet-metal forming? 4. What is the effect of n-value in deep drawing? 5. What is the effect of n-value in fracture of material? 6. How the n-value assist in determining stretchability in sheet-metal?
