Erich H. Kisi and Christopher J. Howard
- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780198515944
- eISBN:
- 9780191705663
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198515944.003.0011
- Subject:
- Physics, Condensed Matter Physics / Materials
This chapter highlights a different but significant application of neutron diffraction in the measurement of engineering strains. It begins by defining the stress and strain tensors, and their ...
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This chapter highlights a different but significant application of neutron diffraction in the measurement of engineering strains. It begins by defining the stress and strain tensors, and their connection via tensors of elastic constants or compliances. Next the relationship between the elastic constants of individual crystallites to those of the polycrystal are developed by averaging according to micromechanical (Voigt, Reuss, Hill, Kröner self-consistent) and texture models. Different diffraction peaks respond differently to stress, and the strains measured from the peak positions are related to the stresses by a set of diffraction elastic constants. The later sections are devoted to practical applications: (i) in engineering where residual stress is estimated from the observed strains using known (or computed) diffraction elastic constants; and ii) in materials science where measurement of the diffraction elastic constants allows the single crystal elastic constants to be derived in favourable circumstances (e.g., ceria-tetragonal zirconia polycrystal, Ce-TZP).Less
This chapter highlights a different but significant application of neutron diffraction in the measurement of engineering strains. It begins by defining the stress and strain tensors, and their connection via tensors of elastic constants or compliances. Next the relationship between the elastic constants of individual crystallites to those of the polycrystal are developed by averaging according to micromechanical (Voigt, Reuss, Hill, Kröner self-consistent) and texture models. Different diffraction peaks respond differently to stress, and the strains measured from the peak positions are related to the stresses by a set of diffraction elastic constants. The later sections are devoted to practical applications: (i) in engineering where residual stress is estimated from the observed strains using known (or computed) diffraction elastic constants; and ii) in materials science where measurement of the diffraction elastic constants allows the single crystal elastic constants to be derived in favourable circumstances (e.g., ceria-tetragonal zirconia polycrystal, Ce-TZP).
Erich H. Kisi and Christopher J. Howard
- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780198515944
- eISBN:
- 9780191705663
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198515944.001.0001
- Subject:
- Physics, Condensed Matter Physics / Materials
This book covers the theory, practicalities, and the extensive applications of neutron powder diffraction in materials science, physics, chemistry, mineralogy, and engineering. Various highlight ...
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This book covers the theory, practicalities, and the extensive applications of neutron powder diffraction in materials science, physics, chemistry, mineralogy, and engineering. Various highlight applications of neutron powder diffraction are outlined in the introduction, then the theory is developed and instrumentation described sufficient for a return to the applications. The book covers the use of neutron powder diffraction in the solution (hard) and refinement (more straightforward) of crystal and magnetic structures, applications of powder diffraction in quantitative phase analysis, extraction of microstructural information from powder diffraction patterns, and the applications of neutron diffraction in studies of elastic properties and for the measurement of residual stress. Additional theory to underpin these various applications is developed as required.Less
This book covers the theory, practicalities, and the extensive applications of neutron powder diffraction in materials science, physics, chemistry, mineralogy, and engineering. Various highlight applications of neutron powder diffraction are outlined in the introduction, then the theory is developed and instrumentation described sufficient for a return to the applications. The book covers the use of neutron powder diffraction in the solution (hard) and refinement (more straightforward) of crystal and magnetic structures, applications of powder diffraction in quantitative phase analysis, extraction of microstructural information from powder diffraction patterns, and the applications of neutron diffraction in studies of elastic properties and for the measurement of residual stress. Additional theory to underpin these various applications is developed as required.
Alain Goriely and Derek Moulton
- Published in print:
- 2011
- Published Online:
- September 2011
- ISBN:
- 9780199605835
- eISBN:
- 9780191729522
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199605835.003.0006
- Subject:
- Physics, Soft Matter / Biological Physics
This chapter is concerned with the modelling of growth processes in the framework of continuum mechanics and nonlinear elasticity. It begins by considering growth and deformation in a one-dimensional ...
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This chapter is concerned with the modelling of growth processes in the framework of continuum mechanics and nonlinear elasticity. It begins by considering growth and deformation in a one-dimensional setting, illustrating the key relationship between growth, the elastic response of the material, and the generation of residual stresses. The general three-dimensional theory of morphoelasticity is then developed from conservation of mass and momentum balance equations. In the formulation, the multiplicative decomposition of the deformation tensor, the standard approach in morphoelasticity, is derived in a new way. A discussion of continuous growth is also included. The chapter concludes by working through a sample problem of a growing cylindrical tube. A stability analysis is formulated, and the effect of growth on mucosal folding, a commonly seen instability in biological tubes, is demonstrated.Less
This chapter is concerned with the modelling of growth processes in the framework of continuum mechanics and nonlinear elasticity. It begins by considering growth and deformation in a one-dimensional setting, illustrating the key relationship between growth, the elastic response of the material, and the generation of residual stresses. The general three-dimensional theory of morphoelasticity is then developed from conservation of mass and momentum balance equations. In the formulation, the multiplicative decomposition of the deformation tensor, the standard approach in morphoelasticity, is derived in a new way. A discussion of continuous growth is also included. The chapter concludes by working through a sample problem of a growing cylindrical tube. A stability analysis is formulated, and the effect of growth on mucosal folding, a commonly seen instability in biological tubes, is demonstrated.
