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Strengthening Mechanisms the Mechanical Properties of a Material Are Controlled by the Microstructure

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Strengthening Mechanisms the Mechanical Properties of a Material Are Controlled by the Microstructure Strengthening Mechanisms The mechanical properties of a material are controlled by the microstructure. Tensile strength is controlled by the work‐hardening rate. The work‐hardening rate controls the amount of uniform deformation (elongation). The higher the elongation, the tougher the material and the greater deformability. The ability of a metal to plastically deform depends on the ability of dislocations to move. Reducing or inhibiting mobility of dislocations enhances mechanical strength. Four main ways of controlling the strength: (a) Solid Solution Hardening; (b) Grain Boundaries; (c) Precipitation hardening and (d) Work Hardening (Dislocation Hardening) Strengthening in crystals results from the restriction of dislocation motion. We can restrict dislocation motion by altering, promoting, or adding: Bond type: Choice of basic material Dislocation‐ dislocation interactions: Work hardening Grain boundaries : Hall‐Petch relationship Solute atoms: Solid solution hardening Precipitates or dispersed particles : Precipitation hardening or dispersion hardening Phase changes: Transformation hardening or toughening. How can we do to increase strength? • GENERAL One simple method is to place obstacles in the path of dislocations that will either slow them down or stop them completely until the stress is high enough to move them further. This works for crystals! In non‐crystalline materials we do different things. • SPECIFIC Dislocations distort the crystal lattice. Various obstacles also distort the crystal lattice. Stress/strain fields from both will interact with each other, which reduces v (the dislocation velocity). This in effect increases the stress required to cause the material to “flow” (i.e., it increases the flow stress) and thus the “strength” of the material. General model for strengthening (1) REFERENCE: L.M. Brown and R.K. Ham, in Strengthening Mechanisms in Crystals, edited by A. Kelly and R.B. Nicholson, Wiley, New York, 1971, pp. 9‐70. Consider a slip plane that contains a random array of obstacles. We don’t care what the obstacles are at this point. As the dislocations are being anchor by the Gb ⎛φ ⎞ τ ≅ Cos⎜ c ⎟ obstacles, extra “work” is required to move the L' ⎝ 2 ⎠ dislocation through the array of obstacles. This results in a higher stress to cause “flow”. Gb τ Max = SOLID SOLUTION STRENGTHENING L •Impurity atoms that go into solid solution impose lattice strains on surrounding host atoms •Lattice strain field interactions between dislocations and impurity atoms result in restriction of dislocation movement •This is one of the most powerful reasons to make alloys, which have higher strength than pure metals. •Example: 24k gold is too soft. If we put in 16% silver and 9% copper, we get an alloy that looks just like pure gold, but is much more strong and durable. We call this 18k gold. (18/24 = 75% gold) There are two types of solid solutions: Substitutional Solid Solution: Solute and solvent atoms are roughly of the same size and the solute atoms will replace the solvent atoms in its position in the crystal structure. Interstitial Solids Solution: The solute atoms are smaller than the solvent atoms and they will occupy interstitial positions in the solvent lattice. Substitutional Ni/Cu Interstitial C/Fe The factors that control the tendency for the formation of substitutional solid solutions are given by the Hume‐Rothery Rules. Factors for high solubility in Substitutional alloys (Hume‐Rothery Solubility Rules) •Similar atomic size (to within 15%) •Similar crystal structure •Similar electronegativity (otherwise a compound is formed) •Similar valence Composition can be expressed in weight percent, useful when making the solution, and in atomic percent, useful when trying to understand the material at the atomic level. Example Ni is completely miscible in Cu (all rules apply) Zn is partially miscible in Cu (different valence, different crystal structure) Ni ‐ Cu binary isomorphous Limited solubility alloy (eutectic) alloys Ni Cu Pb Cu crystal structure FCC FCC FCC FCC atomic radius 0.125 0.128 0.175 0.128 2.4% 36.7% electronegativities 1.8 1.8 1.6 1.8 valence 2 +2 + 2+, 4+ 2 + Solubility Cu in Ni 100% Solubility Cu in Pb 0.1% Solid Solution: homogeneous maintain crystal structure contain randomly dispersed impurities (substitutional or interstitial) Second Phase: as solute atoms are added, new compounds / structures are formed, or solute forms local precipitates Why it works?? Small atoms like to live here. (they reduce lattice strain caused by the dislocation). Big atoms (or interstitials) like to live here (there is more space.) Atoms of either type diffuse to dislocations during high temperature processing, then exert forces on the dislocation later to keep them stuck. The Principle •Any inhomogeneity in a crystal lattice will create a strain field within a lattice. • Dislocations will interact with those strain fields. •The type of interaction will determine the degree of hardening or softening. •In general, solute atoms increase the strengths of crystals. However, under the right conditions they can decrease the strength. •The increase arises due to: –Short range ┴ ‐ solute interactions –Long range ┴ ‐ solute interactions • Dislocations will interact with solutes that lie on, above, and below slip planes. The most intense interactions will occur in close proximity to the slip plane. •Small impurity atoms exert tensile strains (see figure below) •Large impurity atoms exert compressive strains •Solute atoms tend to diffuse and segregate around dislocations to reduce overall strain energy –cancel some of the strain in the lattice due to the dislocations. Compressive Strains Imposed by Larger Substitutional Atoms Add nickel to copper, strength goes up, ductility goes down ‐ for the same reason: dislocation mobility is decreased. Note: trade‐off in properties The usual effect of solute addition is to raise the yield stress and the level of stress‐strain curve as a whole. Since solute atoms affect the entire stress‐strain curve, these atoms have more influence on the frictional resistance to the dislocation motion than on the static locking of the dislocations. According to their strengthening effect solute atoms fall into two broad categories: •Solute atoms that produce dilatational strains or spherical or symmetrical distortions, such as substitute atoms. Their relative contribution to the strengthening is low G/10. •Solute atoms that produce distortional (shear) strains or non‐ spherical or non‐symmetrical distortions, such as the interstitial atoms. Their relative contribution to the strengthening is high 3G. Elements in solid solution usually strengthen crystals. For substitutional solutions, the yield strength increases Δτ 4 = CGε 3 in proportion to their concentration of solutes. Δc Where c is the concentration of solute expressed as an δa atomic fraction, ε is the misfit parameter, C is a constant ε = a and G is the shear modulus. δc The effect of substitutional solutes is mainly attributable to interaction of the solutes with the dilatational stress field around edge dislocations. Substitutional solutes have letlit interaction with screw dislocations. Hence, substitutional and interstitial solutes are often consider to function as local elastic distortions within alloys. The interaction of the solutes with the dislocations depends on the character of the elastic strain field around the dislocation. The elastic strain fields of edge and screw dislocations are profoundly different. For a screw dislocation with a z‐axis For an edge dislocation with a z‐axis parallel to the dislocation line. parallel to the dislocation line. ⎡0 0 ε13 ⎤ ε⎡11 ε 12 0 ⎤ ε = ⎢0 0 ε ⎥ ε = ε⎢ ε 0 ⎥ ⎢ 23 ⎥ ⎢21 22 ⎥ ε⎣⎢31 ε 32 0 ⎦⎥ ⎣⎢0 0 ε33 ⎦⎥ The mutually exclusive character of the two strain fields provides that ideal screw dislocations should interact only with other defects that cause shear distortions along the dislocation core. Edge dislocations strain fields interact with defects that cause either volumetric strain components or shear strain components. Substitutional solutes produce primarily volumetric changes, while interstitial solutes (insertion of atoms into octahedral and tetrahedral positions) will produce either volumetric and distortional (shear) strains. Hence, interstitial atoms are anticipated as more efficient in strengthening. The graph below shows how different alloying additions affect the yield strength of a ferrite + pearlite structural steel. Strengthening due to different defects (Typical Values) The more potent strengtheners are the defects that produce non‐symmetrical strain fields (i.e., those with large shear components) The strengthening potency of interstitials is usually much greater Δτ than that of substitutional solutes. The solubility of interstitials is normally very small. The strengthening potency is expressed as: c Where c is the fraction of interstitial solute and Δτ = τ −τ ini The strengthening potency for interstitial solutes is at least an order of magnitude greater than that for substitutional strengthening. The magnitude of the misfit strain also plays a role f g Δa τ= τ +G ξ ε c ε = initial misfit a τinitial= shear yield strength of a pure material; ξ is a constant ; G is the shear modulus; εmisfit is the misfit strain; c is the solute .fraction The misfit strain exponent is f=3/2 and the concentration exponent g varies from 0.5 to 1. Solute interactions with dislocations. 1. Elastic interaction 2. Modulus interaction 3. Stacking fault interaction 4. Electrical (valence)
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