2.Fundamental Mechanical Properties of Materials 19 tuates about a fixed stress level.Thus,the yield strength in these cases is defined as the average stress that is associated with the lower yield point.Upon further stressing,the material eventually hardens,which requires the familiar increase in load if additional deformation is desired.The deformation at the lower yield point starts at locations of stress concentrations and manifests itself as discrete bands of deformed material,called Ltiders bands,which may cause visible striations on the surface.The deformation oc- curs at the front of these spreading bands until the end of the lower yield point is reached. A few polymeric materials,such as nylon,initially display a linear and,subsequently,a nonlinear (viscoelastic)region in the stress-strain diagram [Figure 2.7(d)].Moreover,beyond the yield strength,a bathtub-shaped curve is obtained,as depicted in Fig- ure2.7(d). Stress-strain curves may vary for different temperatures [Fig- ure 2.7(e)].For example,the yield strength,as well as the tensile strength,and to a lesser degree also the elastic modulus,are of- ten smaller at elevated temperatures.In other words,a metal can be deformed permanently at high temperatures with less effort than at room temperature.This property is exploited by indus- trial rolling mills or by a blacksmith when he shapes red-hot metal items on his anvil.The process is called hot working. On the other hand,if metals,alloys,or some polymeric mate- rials are cold worked,that is,plastically deformed at ambient tem- peratures,eventually they become less ductile and thus harder and even brittle.This is depicted in Figure 2.8(a),in which a ma- terial is assumed to have been stressed beyond the yield strength. Upon releasing the stress,the material has been permanently de- formed to a certain degree.Restressing the same material [Fig- ure 2.8(b)]leads to a higher or and to less ductility.The plastic deformation steps can be repeated several times until eventually oy=or=oB.At this point the workpiece is brittle,similar to a ceramic.Any further attempt of deformation would lead to im- mediate breakage.The material is now work hardened(or strain hardened)to its limit.A coppersmith utilizes cold working(ham- mering)for shaping utensils from copper sheet metal.The strain hardened workpiece can gain renewed ductility,however,by heating it above the recrystallization temperature (which is ap- proximately 0.4 times the absolute melting temperature).For copper,the recrystallization temperature is about 200C. The degree of strengthening acquired through cold working is given by the strain hardening rate,which is proportional to the slope of the plastic region in a true stress-true strain curve.This needs some further explanation.The engineering stress and thetuates about a fixed stress level. Thus, the yield strength in these cases is defined as the average stress that is associated with the lower yield point. Upon further stressing, the material eventually hardens, which requires the familiar increase in load if additional deformation is desired. The deformation at the lower yield point starts at locations of stress concentrations and manifests itself as discrete bands of deformed material, called Lüders bands, which may cause visible striations on the surface. The deformation oc￾curs at the front of these spreading bands until the end of the lower yield point is reached. A few polymeric materials, such as nylon, initially display a linear and, subsequently, a nonlinear (viscoelastic) region in the stress–strain diagram [Figure 2.7(d)]. Moreover, beyond the yield strength, a bathtub-shaped curve is obtained, as depicted in Fig￾ure 2.7(d). Stress–strain curves may vary for different temperatures [Fig￾ure 2.7(e)]. For example, the yield strength, as well as the tensile strength, and to a lesser degree also the elastic modulus, are of￾ten smaller at elevated temperatures. In other words, a metal can be deformed permanently at high temperatures with less effort than at room temperature. This property is exploited by indus￾trial rolling mills or by a blacksmith when he shapes red-hot metal items on his anvil. The process is called hot working. On the other hand, if metals, alloys, or some polymeric mate￾rials are cold worked, that is, plastically deformed at ambient tem￾peratures, eventually they become less ductile and thus harder and even brittle. This is depicted in Figure 2.8(a), in which a ma￾terial is assumed to have been stressed beyond the yield strength. Upon releasing the stress, the material has been permanently de￾formed to a certain degree. Restressing the same material [Fig￾ure 2.8(b)] leads to a higher T and to less ductility. The plastic deformation steps can be repeated several times until eventually y
T
B. At this point the workpiece is brittle, similar to a ceramic. Any further attempt of deformation would lead to im￾mediate breakage. The material is now work hardened (or strain hardened) to its limit. A coppersmith utilizes cold working (ham￾mering) for shaping utensils from copper sheet metal. The strain hardened workpiece can gain renewed ductility, however, by heating it above the recrystallization temperature (which is ap￾proximately 0.4 times the absolute melting temperature). For copper, the recrystallization temperature is about 200°C. The degree of strengthening acquired through cold working is given by the strain hardening rate, which is proportional to the slope of the plastic region in a true stress–true strain curve. This needs some further explanation. The engineering stress and the 2 • Fundamental Mechanical Properties of Materials 19