Chapter 2

MATERIALS AND PROCESSES

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F I G U R E 2 - 3

A Tensile Test Specimen of Mild, Ductile Steel Before and After Fracture the ductile steel curve shown, the stress appears to fall off to a smaller value at the fracture point f. The drop in apparent stress before the fracture point (from u to f in Figure 2-2 a) is an artifact caused by the “necking-down” or reduction in area of the ductile specimen. The reduction of cross-sectional area is nonuniform along the length of the specimen as can be seen in Figure 2-3.

Because the stress is calculated using the original area Ao in equation 2.1 a, it un-derstates the true value of stress after point u. It is difficult to accurately monitor the dynamic change in cross-sectional area during the test, so these errors are accepted. The strengths of different materials can still be compared on this basis. When based on the uncorrected area Ao this is called the engineering stress-strain curve, as shown in Figure 2-2.

The stress at fracture is actually larger than shown. Figure 2-2 also shows the true stress-strain curve that would result if the change in area were accounted for. The engineering stress-strain data from Figure 2-2 are typically used in practice. The most commonly used strength values for static loading are the yield strength Sy and the ultimate tensile strength Sut. The material stiffness is defined by Young’s modulus, E.

In comparing the properties of different materials, it is quite useful to express those properties normalized to the material’s density. Since light weight is nearly always a goal in design, we seek the lightest material that has sufficient strength and stiffness to withstand the applied loads. The specific strength of a material is defined as the strength divided by the density. Unless otherwise specified, strength in this case is assumed to mean ultimate tensile strength, though any strength criterion can be so normalized. The strength-to-weight ratio (SWR) is another way to express the specific strength. Specific stiffness is the Young’s modulus divided by material density.

 

Ductility and Brittleness

The tendency for a material to deform significantly before fracturing is a measure of its ductility. The absence of significant deformation before fracture is called brittleness.

DUCTILITY The stress-strain curve in Figure 2-2 a is of a ductile material, mild steel.

Take a common paper clip made of mild-steel wire. Straighten it out with your fingers.

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MACHINE DESIGN -

An Integrated Approach

 

 

 

Stress 

 

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Sut

f

Sy

y

 

offset line

 

E

 

 

 

F I G U R E 2 - 5

 

 

 

Strain 

A Tensile Test Specimen of Brittle Cast Iron Before and After Fracture 0.002

 

F I G U R E 2 - 4

Bend it into some new shape. You are yielding this ductile steel wire but not fractur-Stress-Strain Curve of a

Brittle Material

ing it. You are operating between point y and point f on the stress-strain curve of Figure 2-2 a. The presence of a significant plastic region on the stress-strain curve is evidence of ductility.

Figure 2-3 shows a test specimen of ductile steel after fracture. The distortion called necking-down can clearly be seen at the break. The fracture surface appears torn and is laced with hills and valleys, also indicating a ductile failure. The ductility of a material is measured by its percent elongation to fracture, or percent reduction in area at fracture. Materials with more than 5% elongation at fracture are considered ductile.

BRITTLENESS Figure 2-4 shows a stress-strain curve for a brittle material. Note the lack of a clearly defined yield point and the absence of any plastic range before fracture. Repeat your paper-clip experiment, this time using a wooden toothpick or matchstick. Any attempt to bend it results in fracture. Wood is a brittle material.

Brittle materials do not exhibit a clear yield point, so the yield strength has to be defined at the intersection of the stress-strain curve and an offset line, drawn parallel to the elastic curve and offset some small percentage such as 0.2% along the strain axis.

Some brittle materials like cast iron do not have a linear elastic region, and the offset line is taken at the average slope of the region. Figure 2-5 shows a cast iron test specimen after fracture. The break shows no evidence of necking and has the finer surface contours typical of a brittle fracture.

The same metals can be either ductile or brittle depending on the way they are manufactured, worked, and heat treated. Metals that are wrought (meaning drawn or pressed into shape in a solid form while either hot or cold) can be more ductile than metals that are cast by pouring molten metal into a mold or form. There are many exceptions to this broad statement, however. The cold working of metal (discussed below) tends to reduce its ductility and increase its brittleness. Heat treatment (discussed below) also has a marked effect on the ductility of steels. Thus it is difficult to generalize about the relative ductility or brittleness of various materials. A careful look at all the mechanical properties of a given material will tell the story.

 

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