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MECHANICAL PROPERTIES OF MATERIALS NOTES

Large elastic deformations are observed in elastomers (e.g., natural rubber,

silicones), for which the relationship between elastic strain and stress is nonlinear.

In elastomers, the large elastic strain is related to the coiling and uncoiling of

spring-like molecules. In dealing with such materials, we use the slope of the

tangent at any given value of stress or strain as a varying quantity that replaces

the Young’s modulus [Figure 6-1(c)]. We define the shear modulus (G) as the

slope of the linear part of the shear stress-shear strain curve.

Permanent or plastic deformation in a material is known as plastic strain. In

this case, when the stress is removed, the material does not go back to its original

shape. A dent in a car is plastic deformation! Note that the word “plastic” here

does not refer to strain in a plastic (polymeric) material, but rather to permanent

strain in any material. The rate at which strain develops in a material is defined as

the strain rate. You will learn later in this chapter that the rate at which a material

is deformed is important from a mechanical properties perspective. Many

materials considered to be ductile behave as brittle solids when the strain rates

are high. Silly Putty® (a silicone polymer) is an example of such a material. When

the strain rates are low, Silly Putty® can show significant ductility. When stretched

rapidly (at high strain rates), we do not allow the untangling and extension of the

large polymer molecules and, hence, the material snaps. When materials are

subjected to high strain rates, we refer to this type of loading as impact loading.

A viscous material is one in which the strain develops over a period of time

and the material does not return to its original shape after the stress is removed.

The development of strain takes time and is not in phase with the applied stress.

Also, the material will remain deformed when the applied stress is removed (i.e.,

the strain will be plastic). A viscoelastic (or anelastic) material can be thought of

as a material with a response between that of a viscous material and an elastic

material. The term “anelastic” is typically used for metals, while the term

“viscoelastic” is usually associated with polymeric materials. Many plastics (solids

and molten) are viscoelastic. A common example of a viscoelastic material is Silly

Putty®.

In a viscoelastic material, the development of a permanent strain is

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MECHANICAL PROPERTIES OF MATERIALS NOTES

 Large elastic deformations are observed in elastomers (e.g., natural rubber, silicones), for which the relationship between elastic strain and stress is nonlinear. In elastomers, the large elastic strain is related to the coiling and uncoiling of spring-like molecules. In dealing with such materials, we use the slope of the tangent at any given value of stress or strain as a varying quantity that replaces the Young’s modulus [Figure 6-1(c)]. We define the shear modulus (G) as the slope of the linear part of the shear stress-shear strain curve.  Permanent or plastic deformation in a material is known as plastic strain. In this case, when the stress is removed, the material does not go back to its original shape. A dent in a car is plastic deformation! Note that the word “plastic” here does not refer to strain in a plastic (polymeric) material, but rather to permanent strain in any material. The rate at which strain develops in a material is defined as the strain rate. You will learn later in this chapter that the rate at which a material is deformed is important from a mechanical properties perspective. Many materials considered to be ductile behave as brittle solids when the strain rates are high. Silly Putty® (a silicone polymer) is an example of such a material. When the strain rates are low, Silly Putty® can show significant ductility. When stretched rapidly (at high strain rates), we do not allow the untangling and extension of the large polymer molecules and, hence, the material snaps. When materials are subjected to high strain rates, we refer to this type of loading as impact loading.  A viscous material is one in which the strain develops over a period of time and the material does not return to its original shape after the stress is removed. The development of strain takes time and is not in phase with the applied stress. Also, the material will remain deformed when the applied stress is removed (i.e., the strain will be plastic). A viscoelastic (or anelastic) material can be thought of as a material with a response between that of a viscous material and an elastic material. The term “anelastic” is typically used for metals, while the term “viscoelastic” is usually associated with polymeric materials. Many plastics (solids and molten) are viscoelastic. A common example of a viscoelastic material is Silly Putty®.  In a viscoelastic material, the development of a permanent strain is

 similar to that in a viscous material. Unlike a viscous material, when the applied stress is removed, part of the strain in a viscoelastic material will recover over a period of time. Recovery of strain refers to a change in shape of a material after the stress causing deformation is removed. A qualitative description of development of strain as a function of time in relation to an applied force in elastic, viscous, and viscoelastic materials is shown in Figure 6-2. In viscoelastic materials held under constant strain, if we wait, the level of stress decreases over a period of time. This is known as stress relaxation. Recovery of strain and stress relaxation are different terms and should not be confused. A common example of stress relaxation is provided by the nylon strings in a tennis racket. We know that the level of stress, or the “tension,” as the tennis players call it, decreases with time.

Engineering Stress and Strain: 0:Before the test begins Properties Obtained from the Tensile Test:  Yield Strength: As we apply stress to a material, the material initially exhibits elastic deformation. The strain that develops is completely recovered when the applied stress is removed. As we continue to increase the applied stress, the material eventually “yields” to the applied stress and exhibits both elastic and plastic deformation. The critical stress value needed to initiate plastic deformation is defined as the elastic limit of the material. In metallic materials, this is usually the stress required for dislocation motion, or slip, to be initiated. In polymeric materials, this stress will correspond to disentanglement of polymer molecule chains or sliding of chains past each other. The proportional limit is defined as the level of stress above which the relationship between stress and strain is not linear. In most materials, the elastic limit and proportional limit are quite close; however, neither the elastic limit nor the proportional limit values can

be determined precisely. Measured values depend on the sensitivity of the equipment used. We, therefore, define them at an offset strain value (typically, but not always, 0.002 or 0.2%). We then draw a line parallel to the linear portion of the engineering stress strain curve starting at this offset value of strain. The stress value corresponding to the intersection of this line and the engineering stress strain curve is defined as the offset yield strength, also often stated as the yield strength.  When we design parts for load-bearing applications, we prefer little or no plastic deformation. As a result, we must select a material such that the design stress is considerably lower than the yield strength at the temperature at which the material will be used. We can also make the component cross-section larger so that the applied force produces a stress that is well below the yield strength. On the other hand, when we want to shape materials into components (e.g., take a sheet of steel and form a car chassis), we need to apply stresses that are well above the yield strength.  Tensile Strength: The stress obtained at the highest applied force is the tensile strength (SUTS), which is the maximum stress on the engineering stress strain curve. This value is also commonly known as the ultimate tensile strength. In many ductile materials, deformation does not remain uniform. At some point, one region deforms more than others and a large local decrease in the cross- sectional area occurs (Figure 6-7). This locally deformed region is called a “neck.” This phenomenon is known as necking. Because the cross-sectional area becomes smaller at this point, a lower force is required to continue its deformation, and

 For many metals in the elastic region, the Poisson’s ratio is typically about 0.3 (Table 6-3). During a tensile test, the ratio increases beyond yielding to about 0.5, since during plastic  Tensile Toughness: The energy absorbed by a material prior to fracture is known as tensile toughness and is sometimes measured as the area under the true stress strain curve (also known as the work of fracture). We will define true stress and true strain in Section 6-5. Since it is simpler to measure engineering

stress strain, engineers often equate tensile toughness to the area under the engineering stress strain curve.

a result, glass processing (e.g., fiber drawing or bottle manufacturing) is performed at high temperatures.

 Strain gage or Extensometer - A device used for measuring change in length (strain).  From an atomic perspective, plastic deformation corresponds to the breaking of bonds with original atom neighbors and then reforming bonds with new neighbors.  After removal of the stress, the large number of atoms that have relocated, do not return to original position.  Yield strength is a measure of resistance to plastic deformation.  Localized deformation of a ductile material during a tensile test produces a necked region.  Permanent deformation for metals is accomplished by means of a process called slip, which involves the motion of dislocations.  Most structures are designed to ensure that only elastic deformation results when stress is applied.

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MECHANICAL PROPERTIES OF MATERIALS NOTES