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Strain-Gradient Hardening

Strain-Gradient Hardening. Dr. Richard Chung Dept. of Chemical and Materials Engineering San Jose State University. Strain Gradients.

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Strain-Gradient Hardening

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  1. Strain-Gradient Hardening Dr. Richard Chung Dept. of Chemical and Materials Engineering San Jose State University

  2. Strain Gradients • When material is deformed, the plastic strain gradients are created and kept within it. These will work-harden the material (more than if such gradients are not exist). • Strengths of the material will be increased due to geometrical dislocations. • The thinner the thickness (or diameter), the higher the stress developed. • The density of geometrical dislocations (G) indicates that strain gradients must exist over distances on the order of micrometers in order to significantly increase flow stress.  is the constant of order unit

  3. STRENGTHENING STRATEGYCOLD WORK (%CW) • Room temperature deformation. • Common forming operations change the cross sectional area: -Forging -Rolling Adapted from Fig. 11.7, Callister 6e. -Drawing -Extrusion

  4. DISLOCATIONS DURING COLD WORK • Ti alloy after cold working: • Dislocations entangle with one another during cold work. • Dislocation motion becomes more difficult. Adapted from Fig. 4.6, Callister 7e. (Fig. 4.6 is courtesy of M.R. Plichta, Michigan Technological University.) 17

  5. RESULT OF COLD WORK • Dislocation density (d) goes up: Carefully prepared sample: d ~ 103 mm/mm3 Heavily deformed sample: d ~ 1010 mm/mm3 • Ways of measuring dislocation density: 40mm Micrograph adapted as courtesy of W.G. Johnson, General Electric Co.) OR • Yield stress increases as rd increases: 18

  6. DISLOCATION-DISLOCATION TRAPPING • Dislocation generate stress. • This traps other dislocations. 20

  7. IMPACT OF COLD WORK • Yield strength (s ) increases. • Tensile strength (TS) increases. • Ductility (%EL or %AR) decreases. y Adapted from Fig. 7.18, Callister 6e. (Fig. 7.18 is from Metals Handbook: Properties and Selection: Iron and Steels, Vol. 1, 9th ed., B. Bardes (Ed.), American Society for Metals, 1978, p. 221.) 21

  8. COLD WORK ANALYSIS • What is the tensile strength & ductility after cold working? Adapted from Fig. 7.16, Callister 7e. (Fig. 7.16 is adapted from Metals Handbook: Properties and Selection: Iron and Steels, Vol. 1, 9th ed., B. Bardes (Ed.), American Society for Metals, 1978, p. 226; and Metals Handbook: Properties and Selection: Nonferrous Alloys and Pure Metals, Vol. 2, 9th ed., H. Baker (Managing Ed.), American Society for Metals, 1979, p. 276 and 327.) 22

  9. Stress-Strain Behavior vs. Temperature • Results for polycrystalline iron: • sy and TS decrease with increasing test temperature. • %EL increases with increasing test temperature. • Why? Vacancies help dislocations past obstacles. 23

  10. EFFECT OF HEATING AFTER %CW • 1 hour treatment at Tanneal... decreases TS and increases %EL. • Effects of cold work are reversed! • 3 Annealing stages to discuss... Adapted from Fig. 7.20, Callister 7e. (Fig. 7.20 is adapted from G. Sachs and K.R. van Horn, Practical Metallurgy, Applied Metallurgy, and the Industrial Processing of Ferrous and Nonferrous Metals and Alloys, American Society for Metals, 1940, p. 139.) 24

  11. RECOVERY Annihilation reduces dislocation density. • Scenario 1 • Scenario 2 25

  12. RECRYSTALLIZATION • New crystals are formed that: --have a small disl. density --are small --consume cold-worked crystals. 0.6 mm 0.6 mm Adapted from Fig. 7.21 (a),(b), Callister 7e. (Fig. 7.21 (a),(b) are courtesy of J.E. Burke, General Electric Company.) 33% cold worked brass New crystals nucleate after 3 sec. at 580C. 26

  13. FURTHER RECRYSTALLIZATION • All cold-worked crystals are consumed. 0.6 mm 0.6 mm Adapted from Fig. 7.21 (c),(d), Callister 7e. (Fig. 7.21 (c),(d) are courtesy of J.E. Burke, General Electric Company.) After 8 seconds After 4 seconds 27

  14. GRAIN GROWTH • At longer times, larger grains consume smaller ones. • Why? Grain boundary area (and therefore energy) is reduced. 0.6 mm 0.6 mm Adapted from Fig. 7.21 (d),(e), Callister 7e. (Fig. 7.21 (d),(e) are courtesy of J.E. Burke, General Electric Company.) After 8 s, 580C After 15 min, 580C coefficient dependent on material and T. • Empirical Relation: exponent typ. ~ 2 elapsed time grain diameter at time t. 28

  15. SUMMARY • Dislocations are observed primarily in metals and alloys. • Here, strength is increased by making dislocation motion difficult. • Particular ways to increase strength are to: --decrease grain size --solid solution strengthening --precipitate strengthening --cold work • Heating (annealing) can reduce dislocation density and increase grain size. 29

  16. Summary (cont’d) • Grain boundaries and certain large and/or incoherent particles are nondeformable. (dislocations can’t pass through them) • Deformation in materials generate the plastic strain gradients in the materials. • Material size due to presence of strain gradients may or may not be a factor depending on the type of mechanical loading. • Cell size is closely associated with the drawing strain. In general, the larger the strain, the smaller the cell size.

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