FREE ELECTRONIC LIBRARY - Dissertations, online materials

Pages:     | 1 |   ...   | 15 | 16 || 18 | 19 |


-- [ Page 17 ] --

corresponds to the most intense part of the ring which normally occurs in the middle along the horizontal direction of the image. A summary of the macrostress values for each of the stress tensor components (see Section 3.7) is given in Table 6.2. The macrostress values are calculated using the Young’s modulus values, Em, determined from the nanoindentation measurements reported in Chapter 5 (Table 5.1). Given the magnitude of the planar stress components,  11 and  22, and the relatively low shear stress component,  12, it may be concluded that these samples are in a state of biaxial stress, i.e., in-plane. Due to the limited penetration of X-rays, macrostresses measured using XRD normally belong to this stress state [He (2009)].

Macrostresses determined using diffraction methods have two main types of error associated with them: statistical error, which arises from the random arrival of X-ray photons at the detector, causing some variability in the intensity at any 2 position, and instrumental error, which can be a result of specimen alignment, effect of beam optics, etc.

–  –  –

[Noyan and Cohen (1987)]. More important are the practical sources of error. Prevey (1986) classifies these practical sources of error as follows: 1. instrumental and positioning errors, 2.

effect of sample geometry and microstructure (typically grain size), and 3. X-ray elastic constants.

The instrumental error is normally a result of the high precision required to determine the diffraction line position. Thus, extremely precise positioning of the diffraction apparatus or the sample to accuracies of approximately 0.025 mm is critical but often difficult. Instrumental and positioning issues can result in errors in internal stress measurement of approximately ±14 MPa for high diffraction angle techniques [Prevey (1986)]. The current study made use of a high diffraction angle technique, i.e., the (311) diffraction line, in order to minimize instrumental and positioning errors on the final results.

When put in to context, a ±14 MPa error may affect more those samples which have relatively low macrostress values, for example, samples no. 1-6 with grain sizes greater than 20 nm (Table 6.2). In this case, 14 MPa could represent a significant portion of the actual macrostress value. However, samples with high macrostresses, e.g., samples no. 7-9 would not be greatly influenced by this error since 14 MPa is rather small when compared to the experimental values (Table 6.2).

Effects of sample geometry, including roughness, pitting, or curvature of the surface within the irradiated area, can result in systematic error similar to sample positioning. All samples were generally free of roughness or pitting; however, some of the foils (e.g., samples no. 1, 8, and 9) were not without some degree of curvature. In order to minimize the effect

–  –  –

of the curvature, the samples were affixed to the holder as firmly and as flat as possible.

However, there was no guarantee that the curvature was completely eliminated. This factor is likely to have played a role in the noticeable differences between respective planar stress component values for samples no. 1, 8 and 9. Large grain sizes can reduce the number of crystals contributing to the diffraction line resulting in asymmetry and random error in peak location and macrostress measurement. In the current study, all samples had a relatively small grain sizes and thus, such an effect is minimized. Rather, the relatively small grain sizes provided for a good statistical sampling and fairly accurate macrostress measurement.

When analyzing the macrostress in materials that are elastically anisotropic, the use of macroscopic elastic constants is essential for obtaining true values. In this case, the bulk elastic constants should be replaced with X-ray elastic constants that depend on the lattice plane (hkl) where the measurement is performed. Included in the plane specific X-ray elastic constant calculation is a value called the radiocrystallographic anisotropy factor ( ARX ). This value typically ranges between 1 and the single crystal anisotropy factor [Lu (1996)]. For Ni-based (fcc) materials, a value of 1.52 was used [He (2009)]. In the case of the current samples, the anisotropy of the materials was analyzed earlier and shown to increase with the addition of Fe (see Chapter 5). Unfortunately, the absence of elastic constant values for each of the materials containing Fe did not allow for the use of an accurate value for ARX.

6.3.2. Effect of Grain Size on Macrostress In order to investigate a possible dependency of macrostresses on grain size, the three stress components from Table 6.2 are plotted in Fig. 6.5 (shear stress component,  12 ) and

–  –  –

Fig. 6.6 (planar stress components,  11 and  22 ) as a function of grain size. The shear stress component,  12, tends to have a relatively low value over the entire grain size range. The planar components,  11 and  22, remain relatively low down to about 20 nm. However, below 20 nm, there is a sharp increase in the compressive macrostress. The results of ElSherik et al. (2005), who used the sin 2  method are also plotted in Fig. 6.6. Their values, which were also determined in the as-deposited state, were compressive and fit well with the data points from the current study. The observed trend for the planar components,  11 and  22, with grain size suggests the presence of an inherent dependency on grain size, especially when it is sufficiently lower than 20 nm.

–  –  –

This dependency on grain size is not consistent with studies of measured macrostresses using XRD techniques on materials produced by other synthesis methods. For example, Sanders et al. (1995) measured the macrostress in nanocrystalline Pd prepared by inert gas condensation and warm compaction using the sin2ψ method and found the macrostress in the as-deposited state to be compressive and in the range of -20 to -40 MPa.

The corresponding grain size range was approximately 3 to 26 nm. It should be noted that the nanocrystalline Pd was produced by a method which is known to produce materials with considerable amounts of porosity [e.g., Nieman et al. (1991)]. The presence of porosity was also the root cause of large reductions in the Young’s modulus values [Krstic et al. (1993), Zugic et al. (1997), Sanders et al. (1997)]. The relatively low macrostress values reported by Sanders et al. (1995) may also be related to the presence of porosity. Although the current

–  –  –

materials were not analyzed for porosity, it is well known that the electrodeposition technique produces materials with relatively low porosity when compared to materials produced by the inert gas condensation technique [Haasz et al. (1995), Van Petegem et al.

(2003), Zhou et al. (2009)]. Currently, it is not known what the effects of porosity is on macrostress, however, it is conceivable that long range stress fields in a material could diminish in the presence of sufficient porosity leading to a lower compressive macrostress value due to the presence of free internal surfaces in the grain boundary matrix. That is, stress relaxation may occur on the free internal surfaces associated with porosity in such materials. On the other hand, in fully dense materials, no internal surfaces for stress relaxation are available and therefore, stresses remain cumulative.

As shown in Fig. 6.6, when the grain size decreases below 20 nm, there is a sharp and distinct increase in the compressive macrostress values. Consequently, there is likely a relationship between the measured macrostresses and corresponding increasing intercrystal volume fraction or rather the number of interfaces in the solid. Such solid-solid interfaces are associated with stresses [Brooks (1952), Cahn and Larche (1982)]. According to Cahn and Larche (1982), an interface stress may be defined as: the reversible work per unit area to either elastically deform one phase relative to the other or both phases equally. In this case, phases may be interpreted as neighbouring grains which join to form the solid-solid interface, i.e., grain boundaries. This interpretation of grain boundaries is similar to that of Valiev et al.

(1986) who describe the “non-equilibrium” grain boundary. Such grain boundaries have long-range elastic fields since local elastic deformation is necessary for joining of the crystals.

This particular interpretation has been used to describe HR-TEM observations of localized

–  –  –

strains at grain boundaries [Wunderlich et al. (1990), Ping et al. (1995), Li et al. (2000), Valiev et al. (2000)] which are similar to the observations made in Chapter 4 (Section 4.4.2).

Considering the concepts of Cahn and Larche (1982), Cammarata and Eby (1991) developed a thermodynamic model which allows for the estimation of internal surface stresses via the determination of strain values. This model was initially used to determine strain values by detecting variations in lattice parameters for lamellar structures. Cammarata and Eby (1991) proposed an extension of the thermodynamic model’s application to very fine-grained metals and ceramics. That is, if the grains are considered to be spheres, the strain will depend on the grain size [Cammarata (1994), Cammarata (1997)],

–  –  –

where,  is the strain, K is the bulk modulus, f is the interface stress associated with grain boundaries, and d is the grain size.

The current nanocrystalline Ni and Ni-Fe alloys data may be analyzed using the relationship given by Eq. 6-1. The left side of the equation can be rearranged to include the bulk modulus, K. By substituting in the relationship between the bulk modulus, K, and the elastic modulus, E,

–  –  –

where,  is the Poisson ratio. If it is assumed that Hooke’s law applies, then the macrostress values  11 and  22 can be substituted and related to the grain size using the thermodynamic model of Cammarata and Eby (1991). By rearranging Eq. 6-3, the following expression is

–  –  –

Using the plot of the macrostress,  11 / 22, with the grain size, d, a curve can be fitted based on Eq. 6-4 and the coefficient,  4 f (1  2 ), can be determined and used to estimate a value for the interface stress associated with grain boundaries. In the calculation, the Poisson ratio,

–  –  –

nanocrystalline Ni and Ni-Fe alloys with the best fit curve based on Eq. 6-4. In general, the


–  –  –

Figure 6.7.

Plot of the planar components  11 and  22 for the nanocrystalline Ni samples as a function of grain size with the best fit (dashed) curve based on Eq. 6-4.

–  –  –

data fits well with the relationship. For illustrative purposes, the total intercrystal volume fraction based on Eq. 2-1 [Palumbo et al. (1990)] is also shown in Fig. 6.7 (solid line) to emphasize the significant increase in these defects (i.e., grain boundaries and triple junctions) with decreasing grain size.

The constant value from the best fit yields an interface stress value, f, of approximately 3.56 N/m. There are very few reports on experimental interface stress values.

For example, experimental values for surface stress of Ni have been reported to be 4.2 N/m and 2.1 N/m for the [001] and [110] directions, respectively [Lehwald et al. (1987)]. On the other hand, there are a number of calculations for surface stress values which for Ni have been reported to be 1.27 N/m and 0.43 N/m for the (100) and (111) surfaces, respectively.

The interface stress value determined for the nanocrystalline Ni and Ni-Fe alloys in the current study is in relatively good agreement with the interface stress value determined by Jiang et al. (2001) who calculated a value of 3.05 N/m for Ni. Jiang et al. (2001) obtained this value by developing thermodynamic equations that relate the interface excess free energy to the interface stress. As described in Chapter 2 (Section 2.1.4) the total enthalpy (stored energy), H, from a strained metal is approximately equal to the excess free energy, G (Eq. 2-5). The thermal analysis in Chapter 4 (Section 4.6) showed that the total enthalpy (stored energy) measured in the electrodeposited nanocrystalline Ni and Ni-Fe alloys are primarily due to intercrystal defects (i.e., grain boundaries and triple junctions). As the volume fraction of these intercrystal defects increases or the grain size decreases, the total enthalpy (stored energy) in these materials increases accordingly. If interface excess free

–  –  –

energy is related to the interface stress, then in a similar manner, an increase in intercrystal defects would cause an increase in the internal stress.

Weissmuller and Cahn (1997) also emphasized the interaction of grain boundaries and triple junctions and their relationship to interface stress which results from the deformed state of the interface; these interface stresses must be equilibrated by homogeneous bulk stresses or analogously macrostresses. The bulk stresses brought on by interface stresses in polycrystalline materials are rather low; however, when the volume fraction of intercrystal defects is high, as in the case of nanocrystalline materials and especially at grain sizes less than 20 nm, these interface stresses become significant. Birringer et al. (2002) developed a method based on the theory of Weissmuller and Cahn (1997) for experimentally measuring the interface stress, f. The calculation relies on the detection of a lattice parameter change which is related to the strain in the material that is induced on the order of f / d. Birringer et al. (2002) analyzed nanocrystalline Pd samples produced by the inert gas condensation method and determined an interface stress of 1.2 N/m. The lattice parameters were found to decrease with decreasing grain size which indicates the presence of a compressive bulk stress.

This is consistent with the compressive macrostresses identified in the current study for the electrodeposited nanocrystalline Ni and Ni-Fe samples.

Pages:     | 1 |   ...   | 15 | 16 || 18 | 19 |

Similar works:

«Title: A framework for e-government success from the user’s perspective Name: Obaid Almalki This is a digitised version of a dissertation submitted to the University of Bedfordshire. It is available to view only. This item is subject to copyright.A FRAMEWORK FOR E-GOVERNMENT SUCCESS FROM THE USER’S PERSPECTIVE OBAID ALMALKI PhD UNIVERSITY OF BEDFORDSHIRE A Framework for e-Government Success from the User’s Perspective by Obaid Almalki A thesis submitted to the University of Bedfordshire...»

«HAGIOGRAPHY AND THE CULT OF SAINTS IN THE DIOCESE OF LIÈGE, C. 700-980 Matthew Zimmern A Thesis Submitted for the Degree of PhD at the University of St. Andrews 2007 Full metadata for this item is available in Research@StAndrews:FullText at: http://research-repository.st-andrews.ac.uk/ Please use this identifier to cite or link to this item: http://hdl.handle.net/10023/358 This item is protected by original copyright Hagiography and the Cult of Saints in the diocese of Liège, c. 700-980 By...»

«Increasing Shared Understanding of a Design Task Between Designers and Design Environments: The Role of a Specification Component by Kumiyo Nakakoji B.S., Osaka University, Japan, 1986 M.S., University of Colorado, Boulder, 1990 A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Computer Science 1993 This thesis for the Doctor of Philosophy degree by Kumiyo...»


«Phonetic and Cognitive Bases of Sound Change by Reiko Kataoka A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Linguistics in the Graduate Division of the University of California, Berkeley Committee in charge: Professor John J. Ohala, Co-Chair Professor Keith Johnson, Co-Chair Professor Andrew Garrett Professor Yoko Hasegawa Fall 2011 Phonetic and Cognitive Bases of Sound Change © 2011 by Reiko Kataoka 1 Abstract Phonetic and...»

«ADOLESCENT MALE DANCERS’ EMBODIED REALITIES by Zihao Li A thesis submitted in conformity with the requirements For the degree of Doctor of Philosophy Department of Curriculum, Teaching and Learning Ontario Institute for Studies in Education of the University of Toronto © Copyright by Zihao Li, 2010 ADOLESCENT MALE DANCERS’ EMBODIED REALITIES Doctor of Philosophy, 2010 Zihao Li Department of Curriculum, Teaching and Learning University of Toronto Abstract This dissertation looks at...»

«Test Algebra for Concurrent Combinatorial Testing by Guanqiu Qi A Dissertation Presented in Partial Fulfillment of the Requirement for the Degree Doctor of Philosophy Approved October 2014 by the Graduate Supervisory Committee: Wei-Tek Tsai, Chair Hasan Davulcu Hessam Sarjoughian Hongyu Yu ARIZONA STATE UNIVERSITY December 2014 ABSTRACT A new algebraic system, Test Algebra (TA), is proposed for identifying faults in combinatorial testing for SaaS (Software-as-a-Service) applications. In the...»

«Avian Responses to Predator Communities in Fragmented, Urbanizing Landscapes DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Laura J. Kearns, M.S. Graduate Program in Environment and Natural Resources The Ohio State University Dissertation Committee: Amanda D. Rodewald, Advisor Stanley D. Gehrt P. Charles Goebel Mazeika S. P. Sullivan Copyright by Laura J. Kearns Abstract Behavioral...»

«Genesis of a Discourse: The Tempest and the Emergence of Postcoloniality By Judith Anne Pocock A thesis submitted in conformity with the requirements for the degree of Doctor Philosophy, Graduate Department of English, University of Toronto © Copyright by Judith Pocock 2010 Genesis of a Discourse: The Tempest and the Emergence of Postcoloniality Judith Anne Pocock Degree of Doctor of Philosophy Graduate Department of English University of Toronto Abstract This dissertation contends that The...»

«The Role of Imageability in Word Learning Efficiency and Transfer among First and Second Graders At-Risk for Reading Disabilities By Laura M. Steacy Dissertation Submitted to the Faculty of the Graduate School of Vanderbilt University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY in Special Education May, 2015 Nashville, Tennessee Approved by: Donald L. Compton, Ph.D. Douglas Fuchs, Ph.D. Lynn S. Fuchs, Ph.D. Christopher J. Lemons, Ph.D. Sonya K. Sterba,...»

«Fetal Testosterone and Early Autism Spectrum Disorder Related Neurodevelopmental Outcomes Bo Y. Park, MPH A Thesis Submitted to the Faculty of Drexel University by Bo Y. Park in partial fulfillment of the requirements for the degree of Doctor of Philosophy June 2015 ©Copyright 2015 Bo Y. Park. All Rights Reserved. Dedication For Eleanor and Evelyn. Tough moments are the beautiful ones. Acknowledgements I am very fortunate to have had the opportunity to learn and grow surrounded by great...»

«The Process of Salvation I. Foundational Premises The conclusions one draws are heavily influenced by the basic and foundational assumptions or premises one brings to the question at issue. The premises which underlie this study are as follows: 1) That there is an objective right and wrong. We live in a philosophical climate dominated by the theory of evolution which holds that life is a product of blind chance. There is no plan behind man’s existence and, hence, ultimately no purpose to it....»

<<  HOME   |    CONTACTS
2016 www.dissertation.xlibx.info - Dissertations, online materials

Materials of this site are available for review, all rights belong to their respective owners.
If you do not agree with the fact that your material is placed on this site, please, email us, we will within 1-2 business days delete him.