206 Modern Physical Metallurgy and Materials Engineering observations on virgin crystals of aluminium and cop- per, but not with those made on certain alloys, or pure metal crystals given special treatments(e. g. quenched Lattice from a high temperature or irradiated with neutron Results from the latter show that the crystal continues to slip on the primary system after the orientation has direction reached the symmetry line, causing the orientation to overshoot this line, i.e. to continue moving toward Lattice [101, in the direction of primary slip. A otation mount of this additional primary slip the conjugate system suddenly operates, and further slip shootin that slip on the conjugate system must intersect that on the primary system, and to do this is presumably more difficult than tofit a new slip plane in the relatively undeformed region between those planes on which slip cess Is direction more difficult in materials which have a low stacking fault energy(e. g. a-brass) 7.3.6 Relation between work-hardening and Figure 7.12 (a)and (b) show the slip process in an slip constrained single crystal;(c) illustrates the plastic ending in a crystal gripped at its ends. The curves of Figure 7, I show that following the yield phenomenon a continual rise in stress is required to continue deformation. i.e. the flow stress of a deformed metal increases with the amount of strain. This resis raca tance of the metal to further plastic fiow as the defor mation proceeds is known as work-hardening. The legree of work-hardening varies for metals of different rystal structure, and is low in hexagonal metal crys- als such as zinc or cadmium, which usually slip on one family of planes only. The cubic crystals harden rapidly on working but even in this case when sl icted to one e specimen A, Figure 7, 14) the coefficient of harden may plane efined as slope of the plastic portion of the stress-strain curve, is small. Thus this type of harden- ing, like overshoot, must be associated with the inte Figure 7.13 Stereographic representation of (a)slip systens action which results from slip on intersecting familie in fcc crystals and(b) overshooting of the primary slip of planes. This interaction will be dealt with more fully moving along the zone, shown broken in Figure 7. 13a, towards [101], i.e. A decreasing and increasing Specr As slip occurs on the one system, the primary sys em, the slip plane rotates away from its position of maximum resolved shear stress until the orientation of the crystal reaches the [001]-[11 1] symmetry line Beyond this point, slip should occur equally on both he primary system and a second system(the system)(11 1)[011], since these two syster single slip equal components of shear stress. Subsequer the process of multiple or duplex slip the I rotate so as to keep equal stresses on the two active sys ems, and the tensile axis moves along the symmetry gure 7.14 Stress-stl ilium deformed line towards [1 12]. This behaviour agrees with early by single and multiple slip (after Liicke and Lange, 1950)206 Modern Physical Metallurgy and Materials Engineering plane.~ (a) ,Slip direction Lattice ,Lattice rotation "- Slip q direction (b) (c) Figure 7.12 (a) and (b) show the slip process in an unconstrained single crystal; (c) illustrates the plastic bending in a crystal gripped at its ends. c,. ,..,~, 1~01] IUQ llt I~III"~ t,v,J Crdl(.ll 1114,111"~ ,o+,, I11 ~r...r__. ~ ,.~I~111 Cross l~,llnl II Pr,mlry pllne (a) I0.1 Figure 7.13 Stereographic representation of (a) slip systems in fcc crystals and (b) overshooting of the primary slip system. observations on virgin crystals of aluminium and cop￾per, but not with those made on certain alloys, or pure metal crystals given special treatments (e.g. quenched from a high temperature or irradiated with neutrons). Results from the latter show that the crystal continues to slip on the primary system after the orientation has reached the symmetry line, causing the orientation to overshoot this line, i.e. to continue moving towards [1 0 1 ], in the direction of primary slip. After a certain amount of this additional primary slip the conjugate system suddenly operates, and further slip concen￾trates itself on this system, followed by overshooting in the opposite direction. This behaviour, shown in Figure 7.13b, is understandable when it is remembered that slip on the conjugate system must intersect that on the primary system, and to do this is presumably more difficult than to 'fit' a new slip plane in the relatively undeformed region between those planes on which slip has already taken place. This intersection process is more difficult in materials which have a low stacking fault energy (e.g. c~-brass). 7.3.6 Relation between work-hardening and slip The curves of Figure 7.1 show that following the yield phenomenon a continual rise in stress is required to continue deformation, i.e. the flow stress of a deformed metal increases with the amount of strain. This resis￾tance of the metal to further plastic flow as the defor￾mation proceeds is known as work-hardening. The degree of work-hardening varies for metals of different crystal structure, and is low in hexagonal metal crys￾tals such as zinc or cadmium, which usually slip on one family of planes only. The cubic crystals harden rapidly on working but even in this case when slip is restricted to one slip system (see the curve for specimen A, Figure 7.14) the coefficient of harden￾ing, defined as the slope of the plastic portion of the stress-strain curve, is small. Thus this type of harden￾ing, like overshoot, must be associated with the inter￾action which results from slip on intersecting families of planes. This interaction will be dealt with more fully in Section 7.6.2. moving along the zone, shown broken in Figure 7.13a, towards [ 1 0 1], i.e. ~ decreasing and 4> increasing. As slip occurs on the one system, the primary sys￾tem, the slip plane rotates away from its position of maximum resolved shear stress until the orientation of the crystal reaches the [0 0 1] - [ 1 1 1] symmetry line. Beyond this point, slip should occur equally on both the primary system and a second system (the conjugate system) (1 1 1) [0 1 1 ], since these two systems receive equal components of shear stress. Subsequently, during the process of multiple or duplex slip the lattice will rotate so as to keep equal stresses on the two active sys￾tems, and the tensile axis moves along the symmetry line towards [1 1 2]. This behaviour agrees with early '%~o~ I /;p~c,m+oB. [111] ~100[ st,p)llb""~ ' (s,ngte Soe;me; A, I I o I ~) 3 z. 5 6 G! Dde -----,,- % Figure 7.14 Stress-strain curves for aluminium deformed by single and multiple slip (after Liicke and Lange, 1950)