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Strengthening of Crystalline Materials. Dr. Richard Chung Department of Chemical and Materials Engineering San Jose State University. Learning Objectives. List and explain different strengthening mechanisms in a crystalline materials Discuss the methods to decrease the dislocation mobility
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Strengthening of Crystalline Materials Dr. Richard Chung Department of Chemical and Materials Engineering San Jose State University
Learning Objectives • List and explain different strengthening mechanisms in a crystalline materials • Discuss the methods to decrease the dislocation mobility • Identify various types of obstacles and discuss the interactions among them • Explain how dislocations will pass through strong or weak obstacles (obstacle spacing and angle) • Discuss the factors associated with the strengthening mechanisms – grain boundaries, grain size, plastic deformation, second phase, interstitial sites, etc.
Movement of A Dislocation t A B L L x t
The force acting on the dislocation per unit length is simply the product of two terms: shear stress and Burgers vector • The tension of the dislocation line (a change of strain energy) is defined as Gb2
Dislocation Positions Associated with A Frank-Read Source The following figures are selected from Barrett, Carig et al. The Principles of Engineering Materials, prentice-Hall, 1973, p.244.
Restricting the Motion of A Dislocation • The flow stress is increased when a dislocation encounters an array of obstacles.
c is a critical extrusion angle • c is smallwhen the obstacles are strong; c is big (180o)when the obstacles are weak
Work Hardening • Work hardening will increase the density of dislocation in a material • The flow stress is determined by the spacing between active slip planes and the overall dislocation density • The governing equation is expressed as: where is an empirical constant, o is the intrinsic strength of a material with low dislocation density
Resloved Shear Stress Dislocation Density Resloved Shear Stress
Cell Size Effect • Cell structure is developed due to the plastic strain created in a local area where different types of dislocation patterns emerge on multiple slip systems • The boundaries of a cell structure contains many dislocations. However, there are no dislocations discovered inside the cell. • The relationship between applied shear stress and the cell size are written as:
Boundary Strengthening • Boundaries are strong obstacles to dislocation motion • Microscopic yielding develops in a material due to dislocations piled up against the grain boundary in a grain • Macroscopic yielding develops when the dislocations are activated by the adjacent grains. • Hall-Petch equations: d is the grain diameter
Atomic size (Solute vs. Solvent) • Interaction between a moving dislocation and solute atoms depends on the local volume change. • If a smaller atom resides above a slip plane, a moving dislocation will encounter a negative dislocation interaction energy due to reduction in volume. Dislocation is attracted to the solute atom. • On the contrary, the dislocation would be repelled by the solute atom, if were placed below the slip plane.
Modulus Effect • Dislocation energy is proportional to shear modulus and to the Burgers vector surrounded Us1/2 Gb2 • The modulus effect does not depend on the position of the solute atoms • Dislocation energy will be reinforced or impaired depends on the modulus and size effects (hard or soft atoms) • A soft atom will strengthen a crystal more than a hard one
Particle Hardening • Three types of interphase boundaries: coherent (or ordered), fully disordered, intermediate type (partially ordered) • Several factors are involved: particle size, volume fraction, particle shape, the interfacial condition (bonding strength) between the particle and the matrix.
Interaction between Particles and Matrix • Coherency hardening will develop internal lattice strain due to different volume ratios (particle and matrix) • coh=(ap –am)/am • rf/b is the strengthening factor • When the particle parameter is greater than the matrix parameter, the particle is under compression.
Edge Dislocation Moving through An Ordered Particle Arrangement • Antiphase boundary Energy (APBE)
Summary • Effective obstacle spacing (L’) and the angle (c) between two bent lines • For weak obstacles, dislocations bend slightly before passing through them. • For strong obstacles, dislocations loop around them. • Dislocations can’t pass through grain boundaries and large incoherent particles. Strengthening effects are produced. • Strengthening effects in aggregates go by volume fractions.
