16 2.Fundamental Mechanical Properties of Materials F Necking FIGURE 2.6.Necking of a test sample that was stressed in a tensile machine. where y is the shear strain Aa/a tan a =a and G is the shear modulus. The modulus of elasticity is a parameter that reveals how "stiff" a material is,that is,it expresses the resistance of a material to elastic bending or elastic elongation.Specifically,a material hav- ing a large modulus and,therefore,a large slope in the stress-strain diagram deforms very little upon application of even a high stress.This material is said to have a high stiffness.(For average values,see Table 2.1.)This is always important if one re- quires close tolerances,such as for bearings,to prevent friction. Stress-strain diagrams vary appreciably for different materials and conditions.As an example,brittle materials,such as glass, stone,or ceramics have no separate yield strength,tensile strength, or breaking strength.In other words,they possess essentially no plastic (ductile)region and,thus,break already before the yield strength is reached [Figure 2.7(a)].Brittle materials (e.g.,glass) are said to have a very low fracture toughness.As a consequence, tools (hammers,screwdrivers,etc.)should not be manufactured from brittle materials because they may break or cause injuries. Ductile materials (e.g.,many metals)on the other hand,with- stand a large amount of permanent deformation (strain)before they break,as seen in Figure 2.7(a).(Ductility is measured by the amount of permanent elongation or reduction in area,given in percent,that a material has withstood at the moment of fracture.) Many materials essentially display no well-defined yield strength in the stress-strain diagram;that is,the transition be- tween the elastic and plastic regions cannot be readily determined [Figure 2.7(b)].One therefore defines an offset yield strength at which a certain amount of permanent deformation(for example,where  is the shear strain a/a
tan 
 and G is the shear modulus. The modulus of elasticity is a parameter that reveals how “stiff” a material is, that is, it expresses the resistance of a material to elastic bending or elastic elongation. Specifically, a material hav￾ing a large modulus and, therefore, a large slope in the stress–strain diagram deforms very little upon application of even a high stress. This material is said to have a high stiffness. (For average values, see Table 2.1.) This is always important if one re￾quires close tolerances, such as for bearings, to prevent friction. Stress–strain diagrams vary appreciably for different materials and conditions. As an example, brittle materials, such as glass, stone, or ceramics have no separate yield strength, tensile strength, or breaking strength. In other words, they possess essentially no plastic (ductile) region and, thus, break already before the yield strength is reached [Figure 2.7(a)]. Brittle materials (e.g., glass) are said to have a very low fracture toughness. As a consequence, tools (hammers, screwdrivers, etc.) should not be manufactured from brittle materials because they may break or cause injuries. Ductile materials (e.g., many metals) on the other hand, with￾stand a large amount of permanent deformation (strain) before they break, as seen in Figure 2.7(a). (Ductility is measured by the amount of permanent elongation or reduction in area, given in percent, that a material has withstood at the moment of fracture.) Many materials essentially display no well-defined yield strength in the stress–strain diagram; that is, the transition be￾tween the elastic and plastic regions cannot be readily determined [Figure 2.7(b)]. One therefore defines an offset yield strength at which a certain amount of permanent deformation (for example, 16 2 • Fundamental Mechanical Properties of Materials Necking F F FIGURE 2.6. Necking of a test sample that was stressed in a tensile machine