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Questions and Answers
What is the primary role of cold work in thermodynamically driven changes?
At what temperature range does creep deformation typically begin for metals?
Which mechanism dominates dislocation creep in the temperature range of $0.3 - 0.5 Tm$?
What happens to the creep strain rate as temperature increases and stress is held constant?
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In which type of creep does atomic movement occur around grain boundaries at low stress levels?
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What does the diffusion coefficient (D) signify in the context of diffusion?
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Which factor has an exponential dependence on temperature (T) in the diffusion equation?
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In the equation $D = D_{0} \exp(\frac{-Q_{d}}{RT})$, which variable represents the gas constant?
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Which of the following statements about the diffusion coefficient for interstitial and substitutional diffusion is correct?
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What is the formula used to plot the natural logarithm of the diffusion coefficient against the inverse of temperature?
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Study Notes
Diffusion and Temperature
- Diffusion coefficient (D) has an exponential dependence on temperature (T)
- D is plotted on a log scale
- Interstitial diffusion is much faster than substitutional diffusion
- Diffusion can be described by the following equation:
- D = Do exp(-Qd / RT)
- D is the diffusion coefficient (m2/s)
- Do is the pre-exponential factor (m2/s)
- Qd is the activation energy (J/mol or eV/atom)
- R is the gas constant (8.314 J/mol-K)
- T is the absolute temperature (K)
Diffusion
- Diffusion is a process of mass transport by atomic motion
- Diffusion can be measured to determine the rate of mass transport
- Recovery is a process that occurs after cold work
- Recovery is driven by thermodynamically stored energy and atomic mobility
Summary
- Thermodynamically driven changes require a driving force and system mobility
- Cold work provides the stored energy
- Self- or vacancy diffusion provide the mobility
- Recovery and recrystallization occur with increasing temperature
- Grain boundary area provides a driving force for grain growth at high temperatures
Creep Observation
- Creep is time-dependent deformation at a constant stress, often at elevated temperatures
- Creep is observed in metals at temperatures above 0.3 to 0.4Tm and in ceramics at temperatures above 0.4 to 0.5Tm, where Tm is the melting temperature
- Creep deformation demonstrates three stages: damage initiation, damage accumulation, and steady state
Creep Rate
- Creep strain rate increases with increasing stress
- The relationship between creep strain rate and stress follows a power law:
- ε̇ = Bσⁿ
- ε̇ is the creep strain rate
- B is a material constant
- σ is the stress
- n is a stress sensitivity exponent
- The value of n can change with stress, and this transition is temperature and grain size dependent
- Creep strain rate increases exponentially with increasing temperature
- The relationship between creep strain rate and temperature follows the Arrhenius equation:
- ε̇ = C exp(-Q / RT)
- ε̇ is the creep strain rate
- C is a material constant
- Q is the activation energy for creep
- R is the gas constant
- T is the absolute temperature (K)
Combined Temperature and Stress Dependence
- The creep strain rate equation combines temperature and stress dependence:
- ε̇ = Aσⁿ exp(-Q / RT)
- ε̇ is the creep strain rate
- A is a material constant
- σ is the stress
- n is a stress sensitivity exponent
- Q is the activation energy for creep
- R is the gas constant
- T is the absolute temperature (K)
- The values of A, n, and Q are material dependent and can vary with stress and temperature
Summary of Creep Mechanisms
- There are different creep mechanisms that dominate at different temperatures and stresses
-
Medium Temperature
- Low stress: Diffusion creep, dominated by grain boundary diffusion
- Medium stress: Dislocation creep, dominated by core diffusion
- High stress: Power law breakdown, dominated by dislocation glide
-
High Temperature
- Low stress: Diffusion creep dominated by bulk diffusion
- Medium stress: Dislocation creep dominated by bulk diffusion
- High stress: Power law breakdown, dominated by dislocation glide
Mechanism I: Dislocation Creep
- Dislocation creep (or power law creep) occurs when dislocation climb is very easy
- Dislocation climb occurs by diffusion of vacancies
- Dislocation climb is dominant, so there is no dependence on the slip plane
- Core diffusion dominates at temperatures between 0.3 – 0.5Tm
- Bulk diffusion dominates at temperatures above 0.5Tm
Mechanism II: Diffusion Creep
- Diffusion creep occurs at low stresses, where dislocation movement is not feasible
- Atoms diffuse around grains, providing stress relief
- There is no dislocation involvement
- At low temperatures, atoms diffuse along grain boundaries (Coble creep)
Phase Diagrams - Continued
- Phase diagrams are graphical representations of the relationships between phases and their compositions under equilibrium conditions
- Phase diagrams are used to predict the phases present in a material at a given temperature and composition
- Tie lines are horizontal lines drawn through the two-phase region of a phase diagram
- The lever rule is used to determine the relative amounts of each phase present at equilibrium
Microstructure from Solidification
- Microstructure is the distribution of phases in a material observed through a microscope
- Microstructure is influenced by solidification conditions
- Equilibrium solidification occurs when the system is allowed to solidify slowly, resulting in a homogeneous structure
- Non-equilibrium solidification occurs when the system is cooled rapidly, resulting in a heterogeneous microstructure with micro-segregation
- Micro-segregation is the variation in composition within a phase due to rapid cooling rates
Eutectic Phase Diagram
- A eutectic phase diagram is a binary phase diagram that has a eutectic point
- The eutectic point is the point at which a liquid phase transforms directly into two solid phases
- There are two solid phases present at room temperature
- The lever rule is used to determine the relative amounts of each phase at equilibrium
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Description
This quiz explores the relationship between diffusion and temperature, focusing on key concepts such as the diffusion coefficient, interstitial versus substitutional diffusion, and the mathematical formulations governing these processes. Understanding these principles is essential for studying mass transport and thermodynamic changes in materials science.
