清华大学：《材料科学基础》课程教学资源（PPT课件讲稿）Chapter 3 Application of Schmid's law

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