Strength of Material can be increased by hindering dislocation , which is responsible for plastic deformation. Dislocation: A displacement of part of a crystal lattice structure. " dislocations are present due to the accidents of imperfect growth" Different ways to hinder dislocation motion/Strengthening mechanisms : In single-phase materials Grain size reduction Solid solution strengthening Strain hardening In multi-phase materials Precipitation strengthening Dispersion strengthening Martensite strengthening
Ordinarily ductility is sacrificed when an alloy is strengthened. The relationship between dislocation motion and mechanical behavior of metals is significance to the understanding of strengthening mechanisms. The ability of a metal to plastically deform depends on the ability of dislocations to move. Virtually all strengthening techniques rely on this simple principle: Restricting or Hindering dislocation motion renders a material harder and stronger.
Strengthening by Grain size reduction Grain boundaries are barriers to slip. • Barrier "strength" increases with Increasing angle of misorientation. • Smaller grain size: more barriers to slip It is based on the fact that dislocations will experience hindrances while trying to move from a grain into the next because of abrupt change in orientation of planes . Adapted from Fig. 7.14, Callister 7e. (Fig. 7.14 is from A Textbook of Materials Technology , by Van Vlack , Pearson Education, Inc., Upper Saddle River, NJ.) Yield strength is related to grain size (diameter, d) as Hall- Petch relation :
Strengthening by Grain size reduction ( Contd …) Grain Size Reduction Techniques: Increase Rate of solidification from the liquid phase. Perform Plastic deformation followed by an appropriate heat treatment . Notes: Grain size reduction also improves toughness of many alloys . Small-angle grain boundaries are not effective in interfering with the slip process because of the small crystallographic misalignment across the boundary . Boundaries between two different phases are also impediments to movements of dislocations.
Solid solution strengthening Impurity atoms distort the lattice & generate stress. Stress can produce a barrier to dislocation motion. Impure foreign atoms in a single phase material produces lattice strains which can anchor the dislocations. Effectiveness of this strengthening depends on two factors–size difference and volume fraction of solute. Solute atoms interact with dislocations in many ways: elastic interaction modulus interaction stacking-fault interaction electrical interaction short-range order interaction long-range order interaction Elastic, modulus, and long-range order interactions are of long-range i.e. they are relatively insensitive to temperature and continue to act about 0.6 Tm.
Adapted from Fig. 7.4, Callister 7e. Stress Concentration at Dislocations
S mall impurities tend to concentrate at dislocations on the “Compressive stress side” R educe mobility of dislocation increase strength Strengthening by Alloying Adapted from Fig. 7.17, Callister 7e.
Large impurities concentrate at dislocations on “Tensile Stress” side – pinning dislocation Adapted from Fig. 7.18, Callister 7e.
e.g. : Solid Solution Strengthening in Copper Tensile strength & yield strength increase with wt% Ni Empirical relation: Alloying increases YS and TS.
Strain hardening Phenomenon where ductile metals become stronger and harder when they are deformed plastically is called strain hardening or work hardening. Increasing temperature lowers the rate of strain hardening. Hence materials are strain hardened at low temperatures, thus also called cold working. During plastic deformation, dislocation density increases. And thus their interaction with each other resulting in increase in yield stress. Dislocation density ( ρ) and shear stress ( τ) are related as follows:
During strain hardening, in addition to mechanical properties, physical properties also changes: A small decrease in density An appreciable decrease in electrical conductivity Small increase in thermal coefficient of expansion Increased chemical reactivity (decrease in corrosion resistance). Deleterious effects of cold work can be removed by heating the material to suitable temperatures– Annealing . It restores the original properties into material. It consists of three stages– recovery, recrystallization and grain growth. In industry, alternate cycles of strain hardening and annealing are used to deform most metals to a very great extent. Strain hardening ( contd …)
Impact of Cold Work As cold work is increased ……. Yield strength ( YS) increases. Tensile strength (TS) increases . Ductility (%EL or %AR) decreases . For Low-Carbon Steel, Adapted from Fig. 7.20, Callister 7e.
D o =15.2mm Cold Work D d =12.2mm Copper Cold W ork Analysis What is the tensile strength and ductility after cold working?
% Cold Work 100 300 500 700 Cu 20 40 60 yield strength (MPa) % Cold Work tensile strength (MPa) 200 Cu 400 600 800 20 40 60 340MPa TS = 340MPa ductility (%EL) % Cold Work 20 40 60 20 40 60 Cu 7% % EL = 7% YS = 300 MPa Adapted from Fig. 7.19, Callister 7e. (Fig. 7.19 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.) Cold W ork Analysis What is the tensile strength and ductility after cold working?
tensile strength (MPa) ductility (%EL) tensile strength ductility Recovery Recrystallization Grain Growth 600 300 400 500 60 50 40 30 20 annealing temperature (ºC) 200 100 300 400 500 600 700 1 hour treatment at T anneal ... decreases TS and increases % EL . Effects of cold work are reversed! Effect of Heating After % CW Adapted from Fig. 7.22, Callister 7e. (Fig. 7.22 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.) • 3 Annealing stages to discuss...
Annihilation reduces dislocation density. Recovery • Scenario 1 Results from diffusion • Scenario 2 4. opposite dislocations meet and annihilate Dislocations annihilate and form a perfect atomic plane. extra half-plane of atoms extra half-plane of atoms atoms diffuse to regions of tension 2 . grey atoms leave by vacancy diffusion allowing disl. to “climb” t R 1. dislocation blocked; can’t move to the right Obstacle dislocation 3 . “Climbed” disl. can now move on new slip plane
• New grains are formed that: -- have a low dislocation density -- are small -- consume cold-worked grains. 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 580 C. 0.6 mm 0.6 mm Recrystallization
• All cold-worked grains are consumed. Adapted from Fig. 7.21 (c),(d), Callister 7e. (Fig. 7.21 (c),(d) are courtesy of J.E. Burke, General Electric Company.) After 4 seconds After 8 seconds 0.6 mm 0.6 mm Further Recrystallization
Recrystallization Temperature, T R T R = recrystallization temperature = point of highest rate of property change T R 0.3-0.6 T m (K) Due to diffusion annealing time T R = f( t ) shorter annealing time => higher T R Higher % CW => lower T R – strain hardening Pure metals lower T R due to dislocation movements Easier to move in pure metals => lower T R
• At longer times, larger grains consume smaller ones. • Why? Grain boundary area (and therefore energy) is reduced. After 8 s, 580 º C After 15 min, 580 º C 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.) Grain Growth • Empirical Relation: coefficient dependent on m aterial & Temp . grain dia. At time t. elapsed time exponent typ. ~ 2 This is: Ostwald Ripening
T R Adapted from Fig. 7.22, Callister 7e. º º T R = recrystallization temperature
Precipitation & Dispersion hardening Foreign particles can also obstructs movement of dislocations i.e. increases the strength of the material. Foreign particles can be introduced in two ways– precipitation and mixing – and –consolidation technique. Precipitation hardening is also called age hardening because strength increases with time. Requisite for precipitation hardening is that second phase must be soluble at an elevated temperature but precipitates upon quenching and aging at a lower temperature. e .g.: Al-alloys, Cu-Be alloys, Mg-Al alloys, Cu-Sn alloys If aging occurs at room temperature – Natural aging If material need to be heated during aging – Artificial aging .
In dispersion hardening, fine second particles are mixed with matrix powder, consolidated, and pressed in powder metallurgy techniques. For dispersion hardening, second phase need to have very low solubility at all temperatures . e.g.: oxides, carbides, nitrides, borides, etc. Dislocation moving through matrix embedded with foreign particles can either cut through the particles or bend around and by pass them. Cutting of particles is easier for small particles which can be considered as segregated solute atoms. Effective strengthening is achieved in the bending process, when the particles are submicroscopic in size. Precipitation & Dispersion hardening (contd..)
Adapted from Fig. 11.22, Callister . Schematic temperature-versus-time plot showing both solution and precipitation heat treatments for precipitation hardening. Adapted from Fig. 11.23, Callister . Schematic diagram showing strength and hardness as a function of the logarithm of aging time at constant temperature during the precipitation heat treatment .
Martensite strengthening This strengthening method is based on formation of martensitic phase from the retained high temperature phase at temperatures lower then the equilibrium invariant transformation temperature. Martensite forms as a result of shearing of lattices. Martensite plate lets assumes characteristic lenticular shape that minimizes the elastic distortion in the matrix. These platelets divide and subdivide the grains of the parent phase. Always touching but never crossing one another. Martensite platelets grow at very high speeds (1/3 rd of sound speed) i.e. activation energy for grow this less. Thus volume fraction of martensite exist is controlled by its nucleation rate.
Martensite strengthening ( contd …) Martensite platelets attain their shape by two successive shear displacements- first displacement is a homogeneous shear through out the plate which occurs parallel to a specific plane in the parent phase known as the habit plane, second displacement, the lesser of the two, can take place by one of two mechanisms: slip as in Fe-C martensite or twinning as in Fe-Ni Martensite . Martensite formation occurs in many systems. e.g.: Fe-C, Fe-Ni, Fe-Ni-C, Cu-Zn, Au-Cd, and even in pure metals like Li, Zr and Co. However, only the alloys based on Fe and C show a pronounced strengthening effect . High strength of Martensite is attributed to its characteristic twin structure and to high dislocation density. In Fe-C system, carbon atoms are also involved in strengthening .