# Daily Archives: January 8, 2021

## Why do tubes have a tendency to buckle when bent?

Why do tubes have a tendency to buckle when bent? Experiment with a straight soda straw, and describe your observations. Recall that, in bending of any section, one-half of the cross section is under tensile stresses and the other half under compressive stresses. Also,

compressing a column tends to buckle it, depending on its slenderness. Bending of a tube

subjects it to the same state of stress, and since most tubes have a rather small thickness compared to their diameter, there is a tendency for the compression side of the tube to buckle.

Thus, the higher the diameter-to-thickness ratio, the greater the tendency to buckle during

bending.

## In deep drawing of a cylindrical cup, is it always necessary that there to be tensile circumferential stresses on the element in the cup wall, a shown in Fig. 7.50b? Explain.

In deep drawing of a cylindrical cup, is it always necessary that there to be tensile circumferential stresses on the element in the cup wall, a shown in Fig. 7.50b? Explain.

The reason why there may be tensile hoop stresses in the already formed cup in Fig. 7.50b

on p. 388 is due to the fact that the cup can be tight on the punch during drawing. That is why

they often have to be stripped from the punch with a stripper ring, as shown in Fig. 7.49a on

p. 387. There are situations, however, whereby, depending on material and process parameters,

the cup is sufficiently loose on the punch so that there are no tensile hoop stresses developed.

## explain why and how these variables influence the force.

Make a list of the independent variables that influence the punch force in deep drawing of a cylindrical cup, and explain why and how these variables influence the force.

The independent variables are listed at the beginning of Section 7.6.2. The student should be

able to explain why each variable influences the punch force, based upon a careful reading of the

materials presented. The following are sample answers, but should not be considered the only acceptable ones.

(a) The blank diameter affects the force because the larger the diameter, the

greater the circumference, and therefore the greater the volume of material to be deformed.

(b) The clearance, c, between the punch and die directly affects the force; the smaller

the clearance the greater the thickness reduction and….

## Are square grid patterns, as shown in Fig. 7.65, useful? Explain.

Comment on the role of the size of the circles placed on the surfaces of sheet metals in determining their formability. Are square grid patterns, as shown in Fig. 7.65, useful? Explain. We note in Fig. 7.65 on p. 400 that, obviously, the smaller the inscribed circles, the more accurately we can determine the magnitude and location of strains on the surface of the sheet

being formed. These are important considerations. Note in the figure, for example, how

large the circles are as compared with the size of the crack that has developed. As for square

grid patters, their distortion will not give a clear and obvious indication of the major and minor

strains. Although they can be determined from geometric relationships, it is tedious work to….

## What are the reasons for developing forminglimit diagrams?

What are the reasons for developing forminglimit diagrams? Do you have any specific criticisms of such diagrams? Explain. The reasons for developing the FLD diagrams

are self-evident by reviewing Section 7.7.1. Criticisms pertain to the fact that:

(a) the specimens are still somewhat idealized,

(b) frictional conditions are not necessarily representative of actual operations, and

(c) the effects of bending and unbending during actual forming operations, the presence

of beads, die surface conditions, etc., are not fully taken into account.

## Explain the reasoning behind Eq. (7.20) for normal anisotropy, and Eq. (7.21) for planar

1.Explain the reasoning behind Eq. (7.20) for normal anisotropy, and Eq. (7.21) for planar

anisotropy, respectively. Equation (7.20) on p. 391 represents an average

R value by virtue of the fact that all directions (at 45circ intervals) are taken into account.

2. Describe why earing occurs. How would you avoid it? Would ears serve any useful purposes?

Explain. Earing, described in Section 7.6.1 on p. 394, is due to the planar anisotropy of the sheet metal. Consider a round blank and a round die cavity; if there is planar anisotropy, then the blank will have less resistance to deformation in some directions compared to others, and will thin more in directions of greater resistance, thus developing ears.

## estimate the direction in which the blank was cut.

It was stated in Section 7.7.1 that the thicker the sheet metal, the higher is its curve in the

forming-limit diagram. Explain why. In forming-limit diagrams, increasing thickness

tends to raise the curves. This is because the material is capable of greater elongations since

there is more material to contribute to length.

2. Inspect the earing shown in Fig. 7.57, and estimate the direction in which the blank was cut.

The rolled sheet is stronger in the direction of rolling. Consequently, that direction resists

flow into the die cavity during deep drawing and the ear is at its highest position. In Fig. 7.57

on p. 394, the directions are at about ±45_ on the photograph.

## Explain what would happen if this limit is exceeded

It is known that the strength of metals depends on their grain size. Would you then expect

strength to influence the R value of sheet metals? Explain. It seen from the Hall-Petch Eq. (3.8) on p. 92 that the smaller the grain size, the higher the yield strength of the metal. Since grain size also influences the R values, we should expect that there is a relationship between strength and R

values.

2.Equation (7.23) gives a general rule for dimensional relationships for successful drawing without a blankholder. Explain what would happen if this limit is exceeded. If this limit is exceeded, the blank will begin to wrinkle and we will produce a cup that has wrinkled walls.

## Explain why the three broken lines (simple tension, plane strain, and equal biaxial stretching) in Fig. 7.63a have those particular slopes.

Explain why the three broken lines (simple tension, plane strain, and equal biaxial stretching) in Fig. 7.63a have those particular slopes. Recall that the major and minor strains shown in Fig. 7.63 on p. 399 are both in the plane of the sheet. Thus, the simple tension curve has a negative slope of 2:1, reflecting the Poisson’s ratio effect in plastic deformation. In other words, the minor strain is one-half the major strain in simple tension, but is opposite in sign. The

plane-strain line is vertical because the minor strain is zero in plane-strain stretching. The

equal (balanced) biaxial curve has to have a 45_ slope because the tensile strains are equal

to each other. The curve at the farthest left is for pure shear because, in….

## Comment on how these methods could improve drawability.

It has been suggested that deep drawability can be increased by (a) heating the flange and/or (b) chilling the punch by some suitable means. Comment on how these methods could improve drawability. Refering to Fig. 7.50, we note that:

(a) heating the flange will lower the strength of the flange and it will take less energy

to deform element A in the figure, thus it will require less punch force. This will reduce

the tendency for cup failure and thus improve deep drawability. (b) chilling the punch will increase the strength of the cup wall, hence the tendency for cup failure by the longitudinal tensile stress on element B will be less, and

deep drawability will be improved.