3. Application of Schmid's law How to determine the active S.S. for all the equivalent SS (2 Determine the active S.S. by Reflection Rule Orientation cell for cubic crystals Given: BCC Crystal having 110]slip system Determine: active slip system in response to tensile loading along
3. Application of Schmid’s law ① How to determine the active S.S. for all the equivalent S.S. ② Determine the active S.S. by Reflection Rule. • Orientation cell for cubic crystals. • Given: BCC Crystal having {110}slip system. Determine : active slip system in response to tensile loading along
Solution a. draw a orientation cell b. Label the loading direction in the cell c. Determine the active S.S. by reflection rule
Solution: a. Draw a orientation cell. b. Label the loading direction in the cell. c. Determine the active S.S. by reflection rule
4. Determine the active slip systems by Schmidt's law (1 Draw a standard projection 00 110 11 o111 010 011 o11 010 111 101 line 110 110 -y line 100 e
4. Determine the active slip systems by Schmidt's law ① Draw a standard projection x=z line x=y line y=z line
Label the loading direction in standard projection Mi Irror rule Umax=(cos ncoso)
② Label the loading direction in standard projection. ③ Mirror rule max max = (cos cos)
given u v w, determine active slip system 100 110 110 case1 along [4211 010 011 011 010 FCC, orientation triangle [l110100 11 slip system is (11 1)[1011 110 110 100 100 case2 according to the mirror-refraction oIo o1 ou1r along [215 10 orientation triangle: [101]-[111]-[001 11 011 01 rule the active slip system is 111 (111[o11 101 110 110 100
case1. along FCC, orientation triangle : slip system is [421] [111][110][100] (11 1)[101] case2. along orientation triangle: according to the mirror-refraction rule the active slip system is [215] (111)[011] given [u v w], determine active slip system [101]−[111]−[001]
5. Determine the active slip systems by Reflection Rule
5. Determine the active slip systems by Reflection Rule
Example Given: BCC crystal having 110]111>slip system Determine active slip system in response to tensile loading along [123] Solve 100 Draw a standard projection 110 110 io① (2 Label the loading direction in standard projection OIo 01101o Determine the active SS by 11 下 111 Reflection Rule 101 110 110 100
Example: Given: BCC crystal having {110} slip system Determine active slip system in response to tensile loading along . [123] Solve: ① Draw a standard projection. ② Label the loading direction in standard projection. ③ Determine the active S.S by Reflection Rule
a) F locate inside the orientation triangle(Fi), single slip (111)[011 b) F locate at the edge of the orientation triangle(F2), doubl ( duplex)sip.(11)01]+(11)101 F locate at the corner of the orientation triangle, multiple p. 001 011 111 When the axis of load is in the edge or corner of the orientation triangle, muli-slip occurs
④ a) locate inside the orientation triangle ( ), single slip. b) locate at the edge of the orientation triangle ( ), double (duplex) slip. c) locate at the corner of the orientation triangle, multiple slip. F F1 F F2 When the axis of load is in the edge or corner of the orientation triangle, muli-slip occurs. (111)[011] (111)[011]+ (111)[101] F 001 111 101 111011 F1 F2 F3
6. A tensile force is applied on a BCC cylindrical bar with across section of 25mm2 The initial axis is 421. The crss is 0. 4MPa. The slip plane is 110y Determine: ① initial SS ③ duplex s.S 4 the shear strain y and the indices of the axis at the moment when duplex starts 5 stable position
6. A tensile force is applied on a BCC cylindrical bar with across section of 25mm2 . The initial axis is . The CRSS is 0.4MPa . The slip plane is . [421] {110} Determine: ① initial S.S. ② P ③ duplex S.S. ④ the shear strain and the indices of the axis at the moment when duplex starts ⑤ stable position
Solution Draw a standard projection 100 Determine orientation triangle 110 110 [1]-[110]-[1001 011 011 010 010 11 101 mirror refraction rule 110 110 (101)111 100 ②P<a<z
Solution: Draw a standard projection Determine orientation triangle: [111]−[110]−[100] ① initial S.S. mirror refraction rule ② (101)[11 1] P c ， F3