Diffusion Creep
Diffusion creep is a type of creep deformation in materials that occurs at high temperatures and low stresses. It is driven by the movement of atoms through the crystal lattice, leading to the gradual flow and deformation of the material. This process is important in understanding the behavior of materials in high-temperature environments, such as in the aerospace and power generation industries.
8 Key excerpts on "Diffusion Creep"
eBook - ePub- Louisette Priester, Louisette Priester(Authors)
- 2013(Publication Date)
- Wiley-ISTE(Publisher)
...TLD creep is an extension to the nanograins of the classical Diffusion Creep, which takes into account the short diffusion circuits along the triple junctions (called here triple lines) and the very large boundary areas in nanocyrstallized materials. In this model, the creep rate varies as δ 2 /d 4 and this type of creep only applies to grain sizes d lower than 4δ. GBP creep considers grain boundaries as a separate phase with a specific creep rate. The deformation rate is proportional to D GB /d 2 but is independent of the thickness of the grain boundary δ, in contrast to the Coble creep. For nanograined materials, there is a very limited amount of reliable experimental creep data, because of the difficulties in developing bulk materials with stable microstructures. Therefore, the parameters of the developed models are hardly accessible experimentally. We can draw a parallel between the behavior in creep and the behavior in sintering, which is a classical manufacturing process of dense materials with controlled microstructures. For rates of densification under load, we again find the same dependences in grain size as those of the creep rates. Similarly, for very small grain sizes, a controlling interface reaction mechanism in series with a diffusion mechanism can explain much lower densification rates than those resulting from diffusion mechanisms. The considerations developed in this chapter show how the diffusion mechanisms are fundamental in high temperature plastic deformation. However, creep laws for microstructured materials cannot be extrapolated to nanograined materials. The high temperature dynamics of the grain boundaries are the predominant phenomenon to understand and control. From the creep point of view, nanograined materials have not satisfied the hopes they have raised. 4.6. Bibliography [ART 83] A RTZ E., A SHBY M.F., V ERRALL R.A., Acta Metallurgica, 31, p. 1977-1989, 1983. [ASH 69] A SHBY M.F., Scripta Metallurgica, 3, p...
eBook - ePubPractical Guide to the Packaging of Electronics
Thermal and Mechanical Design and Analysis, Third Edition
- Ali Jamnia(Author)
- 2016(Publication Date)
- CRC Press(Publisher)
...Appendix F: Creep When a material is subjected to external loads, the internal structure (i.e., grain lattice, crystals, or molecules, in the case of many plastics) has to move in order to be aligned in a formation that would withstand the external loads. This new alignment may be called a state of stress, considering that there would be a tendency for the material to revert back to its natural state once the loads are removed. If enough energy (generally in the form of heat) is provided, this internal structure tends to accept the new formation as a natural state, and thus the state of stress is either lessened or relieved altogether. This phenomenon is called creep and is defined by Lau (1993) as a mathematical model to represent the behavior of rate-sensitive elastoplastic materials at elevated temperatures. Clearly, this behavior depends on the material’s properties and temperature levels, along with residence time at those levels and applied loads. In and of itself, creep may not be considered a failure mechanism; however, it may lead to catastrophic failures. If creep is allowed to continue, deformations are enlarged and, eventually, strains become so large that the structure loses its load-carrying capacity and fails either in a buckling mode or a stress rupture. Nearly all materials exhibit creep near their melting points. Although this proximity to the melting point varies from material to material, in general, once temperature value surpasses 50% of the melting point, creep and strain rates associated with creep become important factors that may not be ignored. In electronics packaging, solders and plastics are particularly at risk because of their relatively low melting temperatures and operating temperatures that may exceed the 50% threshold (Pecht 1991; Lau 1993; Lau et al. 1998). Stages of Creep The process of creep development is not uniform or constant. Figure F.1 depicts a typical creep curve with the three stages of creep identified...
eBook - ePub- Michael E. Kassner(Author)
- 2015(Publication Date)
- Butterworth-Heinemann(Publisher)
...Chapter 3 Diffusional Creep M.-T. Perez-Prado, and M.E. Kassner Abstract Non-dislocation-based diffusional creep at high temperatures (T ≈ T m) and very low stresses in fine-grained materials was qualitatively suggested 50 years ago by Nabarro. This was rigorously (quantitatively) proposed and described by Herring. Mass transport of vacancies through the grains from one grain boundary to another was described. Excess vacancies are created at grain boundaries perpendicular to the tensile axis with a uniaxial tensile stress. The theory, however, is controversial. Keywords Diffusional creep; Stress; Tensile stress Non-dislocation-based diffusional creep at high temperatures (T ≈ T m) and very low stresses in fine-grained materials was qualitatively suggested 50 years ago by Nabarro [237]. This was rigorously (quantitatively) proposed and described by Herring [51]. Mass transport of vacancies through the grains from one grain boundary to another was described. Excess vacancies are created at grain boundaries perpendicular to the tensile axis with a uniaxial tensile stress. The concentration may be calculated using [23] c = c v [ exp (σ b 3 k T) − 1 ] (106) where c v is the equilibrium concentration of vacancies. Usually (σb 3 / kT) >> 1, and therefore Eqn (106) can be approximated by c = [ c v (σ b 3 k T) ] (107) These excess vacancies diffuse from the grain boundaries lying normal to the tensile direction towards those parallel to it, as illustrated in Figure 51. Grain boundaries act as perfect sources and sinks for vacancies. Thus, grains would elongate without dislocation slip or climb. The excess concentration of vacancies per unit volume is, then, c v σ / kT. If the linear dimension of a grain is g, the concentration gradient is c v σ / kTg. The steady-state flux of excess vacancies can be expressed as D v c v σ / kTg, where g is the grain size. The resulting strain rate is given by, Figure 51 Nabarro-Herring model of diffusional flow...
eBook - ePub- Fujio Abe, Torsten-Ulf Kern, R Viswanathan(Authors)
- 2008(Publication Date)
- Woodhead Publishing(Publisher)
...7 Diffusion behaviour of creep-resistant steels H. Oikawa; Y. Iijima Tohoku University, Japan 7.1 Introduction In the early 1950s, Sherby and coworkers (e.g., Sherby et al., 1954) analysed creep data and diffusion data of several metals and claimed that the temperature dependence of both phenomena is similar to each other. This finding first gave us a sound physical base for discussing creep mechanisms. In those days, however, creep data were very limited and diffusion data were also a few and their values were scattered over a wide range. Therefore, they had to base their discussion on average values of these limited data. Today, the view is well established (Sherby and Burke, 1967 ; Mukherjee, et al., 1969) that the temperature dependence of creep at high temperature is close to that of diffusion in pure metals (see Fig. 7.1). A similar correlation has also been found in solid solution alloys (Monma et al., 1964). 7.1 Correlation between the activation energies of high-temperature creep, Q c, and of lattice self-diffusion, Q D, in pure metals. Diffusion is one of most fundamental processes governing creep deformation. In this chapter diffusion behaviour in metals and alloys will be outlined and then the role of diffusion in creep deformation will be discussed. Finally, some fundamental diffusion data which are deemed to be useful in discussing creep of steels will be cited. 7.2 Diffusion and creep 7.2.1 Activation energies It is worthwhile noting that there is an essential difference in the physical meaning of temperature dependence of creep and of diffusion, although the temperature dependences of these two phenomena are close to each other under some conditions. Diffusion in simple metals can be recognized as a thermally activated process, where the activation energy is the sum of the formation energy and the migration energy of vacancies...
eBook - ePubAdditive and Traditionally Manufactured Components
A Comparative Analysis of Mechanical Properties
- Joshua Pelleg(Author)
- 2020(Publication Date)
- Elsevier(Publisher)
...The rate of deformation is a function of exposure time, temperature, and applied load and depends on material properties. Creep is the tendency of a solid material to move slowly under the influence of mechanical stress but still below the yield strength and deform permanently. Creep is more severe in materials that are subjected to heat for long periods and generally increase as their temperature increase until a critical failure (dimensional and shape changes, which makes a component useless) is reached near the melting point. Therefore, creep is of concern to engineers when designing components to operate under high stress or high temperatures. However, creep may occur at relatively moderate temperatures in many cases. Even some ceramics with low-temperature ductility may creep ~ 0.5 T m. An important consideration is the choice of the type of material, namely, single or polycrystalline material. In order to eliminate grain boundary sliding in the material while exposed to some elevated temperature single crystal is the obvious choice. However, for many reasons such as other mechanical properties or cost factor consideration, polycrystalline materials are used despite their limitations for high-temperature applications. Grain size is a factor. A compromise must be made between small grain size, which enhances most of the mechanical properties, and large grained material, which is preferred for long-time exposure (creep) at high temperature. Ti6Al4V alloy also known as Ti64 is the most commonly used titanium alloy. It exhibits good mechanical and physical properties and due to its lightweight it is used in aerospace applications. These unique properties are strongly affected by chemical composition, microstructure, deformation, and heat-treatment history. The most commonly used titanium alloy is the two-phase (α + β) alloy. Significant research was devoted to improving the microstructure and attaining appropriate mechanical properties...
eBook - ePub- R. E. Smallman, A.H.W. Ngan(Authors)
- 2013(Publication Date)
- Butterworth-Heinemann(Publisher)
...Chapter 7 Diffusion Diffusion is an important process by which point defects and solute atoms can migrate inside solid materials at elevated temperatures. Diffusion is governed by Fick’s two laws, the first relating diffusional speed to concentration gradient as driving force and the second on conservation of mass. Mathematical solution to Fick’s laws depends on configurations, such as thin film versus surface. Microscopically, diffusion involves atomic jumps and is governed by activation energies of vacancy formation and migration. Diffusion is important in industrial processes, such as carburization, and material behaviour, such as creep. Enhanced diffusion may take place along short-circuit paths, including dislocation cores and grain boundaries. Keywords Diffusion; Fick’s laws; steady-state diffusion; non-steady-state diffusion; error function; carburization; thin-film diffusion; surface diffusion; short-circuited diffusion 7.1 Introduction Everyone has some experience with diffusion from an early age. Brewing tea, mixing colours and washing a bleeding cut in water sees the spreading of ‘colour’ molecules by random exchanges with water molecules. They move from regions where they are concentrated to dilute regions. This movement down a concentration gradient is the basis of diffusion. Such diffusion behaviour is not unique to liquids but occurs in solids as well by thermally activated movement of solute atoms in the solvent lattice. 7.2 Diffusion laws A knowledge of diffusion theory is essential in understanding many areas of physical metallurgy, particularly at elevated temperatures. A few examples include such commercially important processes as annealing, heat treatment, the age hardening of alloys, sintering, surface hardening, oxidation and creep...
eBook - ePubEngineering Physics of High-Temperature Materials
Metals, Ice, Rocks, and Ceramics
- Nirmal K. Sinha, Shoma Sinha(Authors)
- 2022(Publication Date)
- Wiley(Publisher)
...However, many of the established concepts have been questioned in recent years as demands for extending the life expectancy of structures at increasingly higher operating temperatures are on the rise, for example in the power‐generation industry and in aerospace applications. Examination of the microstructure‐based physical phenomena governing early periods of creep deformation (primary or transient stage) and the kinetics of creep damage eventually controlling failures has given new insights and direction that requires open discussion. A brief survey of the phenomenological aspects of creep, fracture, and failure properties is presented in this chapter. First, the presentation focuses on the traditional experimental and analytical approaches. It then shifts attention to technically sophisticated, but simple, experimental approaches in light of “hindsight 20/20” introduced in Section 1.8.1 in Chapter 1. The base method utilizes the simple process of stopping the test, unloading completely, and examining the strain recovery, if any. 6.2 Steady‐State Creep Constitutive equations can help correlate macroscopic high‐temperature deformation and failure behaviors of engineered metals, alloys, and other materials, in terms of the operating micromechanisms, and clarify the role of microstructural variables. They are developed on the basis of a “steady state,” originally developed for creep of pure metals under constant load (CL) (not necessarily constant stress), and extended to nonmetallic polycrystals. The concept of steady state is supposed to represent a state of structural stability and a balanced mechanical response between the hardening and softening effects within the structure on application of an external force. Hypothetically, this is viewed to occur during the stage called “secondary creep.” The tug‐of‐war between the two opposing effects is assumed to occur during the transient stage (called primary creep) after the application of the stress...
eBook - ePubPhenomenological Creep Models of Composites and Nanomaterials
Deterministic and Probabilistic Approach
- Leo Razdolsky(Author)
- 2019(Publication Date)
- CRC Press(Publisher)
...2 Creep Laws for Composite Materials 2.1 Introduction Modern classical methods of investigation in mechanics of deformable rigid bodies are based on three hierarchical levels: mechanics of microinhomogeneous media, phenomenological models of a continuous medium and boundary-value problems that are seemingly little related to each other. Within the continuum mechanics, the traditional way of constructing a phenomenological model begins with a specially organized creep test of the material. The results are analyzed and the material model is constructed, which is then applied to the solution of the corresponding boundary-value problem. For non-stationary external loads, the boundary value problem must be solved taking into account the loading history, which in the case of a high temperature effect on the structure means the analytical dependence of the temperature on time. Undoubtedly, this approach has both advantages and disadvantages. On the one hand, the laws of inelastic deformation in phenomenological theories are formulated for an arbitrary body and can be described as the creep theory of materials of a very diverse nature (metals, polymers, concrete, soils and so on). On the other hand, with the concretization of these general laws for one or another type of materials and environmental loading conditions, it actually describes the phenomenon, but does not explains any specific data of it. Also there is a need for a defining macro-experiment results wherein experiments are carried out in the rigid limits of temperature-force loading and of limit state condition that is used as well as the problem of extrapolation of calculated results for a particular phenomenological theory beyond the boundaries of this framework. Therefore, in order to more adequately reflect the processes of the inelastic creep deformation along with phenomenological theories in parallel, theories based on micro-inhomogeneity development of irreversible deformations are needed...
