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The Science and Engineering of

Materials, 4

th

ed

Chapter 11 – Dispersion Strengthening by Phase

Transformations and Heat Treatment

Objectives of Chapter 11

• Discuss dispersion strengthening by studying a variety

of solid-state transformation processes including

precipitation or age hardening and the eutectoid

reaction.

• Examine how nonequilibrium phase

transformations—in particular, the martensitic

reaction—can provide strengthening.

Chapter Outline (Continued)

 11.7 Requirements for Age Hardening

 11.8 Use of Age-Hardenable Alloys at

High Temperatures

 11.9 The Eutectoid Reaction

 11.10 Controlling the Eutectoid

Reaction

 11.11 The Martensitic Reaction and

Tempering

 11.12 The Shape-Memory Alloys

(SMAs)

 Strain energy - The energy required to permit a

precipitate to fit into the surrounding matrix during

nucleation and growth of the precipitate.

 Avrami relationship - Describes the fraction of a

transformation that occurs as a function of time. This

describes most solid-state transformations that involve

diffusion, thus martensitic transformations are not

described.

Section 11.

Nucleation and Growth in

Solid-State Reactions

©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.

Figure 11.2 The effect of temperature on recrystallization of cold-worked copper.

©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license. Figure 11.3 (a) The effect of temperature on the rate of a phase transformation is the product of the growth rate and nucleation rate contributions, giving a maximum transformation rate at a critical temperature. (b) Consequently, there is a minimum time (t (^) min) required for the transformation, given by the “ C -curve”.

©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning

is a trademark used herein under license.™

Figure 11. Arrhenius plot of transformation rate versus reciprocal temperature for recrystallization of copper (for Example 11.1.

Example 11.1 SOLUTION

From Figure 11.2, the times required for 50%

transformation at several different temperatures can be

calculated:

The rate of transformation is an Arrhenius equation, so

a plot of ln (rate) versus 1/ T (Figure 11.4 and

Equation 11-4) allows us to calculate the constants in

the equation. Taking natural log of both sides of

Equation 11-4:

ln(Growth rate) = ln A – ( Q / RT )

 Widmanstätten structure - The precipitation of a second

phase from the matrix when there is a fixed

crystallographic relationship between the precipitate and

matrix crystal structures.

 Interfacial energy - The energy associated with the

boundary between two phases.

 Dihedral angle - The angle that defines the shape of a

precipitate particle in the matrix.

 Coherent precipitate - A precipitate whose crystal

structure and atomic arrangement have a continuous

relationship with the matrix from which the precipitate is

formed.

Section 11.

Alloys Strengthened by

Exceeding the Solubility Limit

©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license. Figure 11.5 The aluminum-copper phase diagram and the microstructures that may develop curing cooling of an Al-4% Cu alloy.

©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.

Figure 11.7 The effect of surface energy and the dihedral angle on the shape of a precipitate.

©2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license. Figure 11.8 (a) A noncoherent precipitate has no relationship with the crystal structure of the surrounding matrix. (b) A coherent precipitate forms so that there is a definite relationship between the precipitate’s and the matrix’s crystal structure.

Section 11.

Applications of Age-Hardened

Alloys

Figure 11.9 (a) A stress-strain curve showing the increase in strength of a bake- hardenable steel as a result of strain hardening and precipitation hardening. ( Source: U.S. Steel Corporation, Pittsburgh, PA .)

Figure 11.9 (b) A graph showing the increase in the yield strength of a bake hardenable steel ( Source: Bethlehem Steel, PA .) (c) A TEM micrograph of a steel containing niobium (Nb) and manganese (Mn). The niobium react with carbon (C) and forms NbC precipitates that lead to strengthening. ( Courtesy of Dr. A.J. Deardo, Dr. I. Garcia, Dr. M. Hua, University of Pittsburgh .)