{"title":"Dislocations","authors":"A. Sutton","doi":"10.1093/oso/9780198860785.003.0006","DOIUrl":"https://doi.org/10.1093/oso/9780198860785.003.0006","url":null,"abstract":"Plastic deformation involves planes of atoms sliding over each other. The sliding happens through the movement of linear defects called dislocations. The phenomenology of dislocations and their characterisation by the Burgers circuit and line direction are described. The Green’s function plays a central role in Volterra’s formula for the displacement field of a dislocation and Mura’s formula for the strain and stress fields. The isotropic elastic fields of edge and screw dislocations are derived. The field of an infinitesimal dislocation loop and its dipole tensor are also derived. The elastic energy of interaction between a dislocation and another source of stress is derived, and leads to force on a dislocation. The elastic energy of a dislocation and the Frank-Read source of dislocations are also discussed. Problem set 6 extends the content of the chapter in several directions including grain boundaries and faults.","PeriodicalId":236443,"journal":{"name":"Physics of Elasticity and Crystal Defects","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131139956","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Stress","authors":"A. Sutton","doi":"10.1093/oso/9780198860785.003.0002","DOIUrl":"https://doi.org/10.1093/oso/9780198860785.003.0002","url":null,"abstract":"The concept of stress is introduced in terms of interatomic forces acting through a plane, and in the Cauchy sense of a force per unit area on a plane in a continuum. Normal stresses and shear stresses are defined. Invariants of the stress tensor are derived and the von Mises shear stress is expressed in terms of them. The conditions for mechanical equilibrium in a continuum are derived, one of which leads to the stress tensor being symmetric. Stress is also shown to be the functional derivative of the elastic energy with respect to strain,which enables the stress tensor to be derived in models of interatomic forces. Adiabatic and isothermal stresses are distinguished thermodynamically and anharmonicity of atomic interactions is identified as the reason for their differences. Problems set 2 containsfour problems, one of which is based on Noll’s insightful analysis of stress and mechanical equilibrium.","PeriodicalId":236443,"journal":{"name":"Physics of Elasticity and Crystal Defects","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114492595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Strain","authors":"A. Sutton","doi":"10.1093/oso/9780198860785.003.0001","DOIUrl":"https://doi.org/10.1093/oso/9780198860785.003.0001","url":null,"abstract":"A discussion of the continuum approximation is followed by the definition of deformation as a transformation involving changes in separation between points within a continuum. This leads to the mathematical definition of the deformation tensor. The introduction of the displacement vector and its gradient leads to the definition of the strain tensor. The linear elastic strain tensor involves an approximation in which gradients of the displacement vector are assumed to be small. The deformation tensor can be written as the sum of syymetric and antisymmetric parts, the former being the strain tensor. Normal and shear strains are distinguished. Problems set 1 introduces the strain ellipsoid, the invariance of the trace of the strain tensor, proof that the strain tensor satisfies the transformation law of second rank tensors and a general expression for the change in separation of points within a continuum subjected to a homogeneous strain.","PeriodicalId":236443,"journal":{"name":"Physics of Elasticity and Crystal Defects","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130216145","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Open questions","authors":"A. Sutton","doi":"10.1093/oso/9780198860785.003.0010","DOIUrl":"https://doi.org/10.1093/oso/9780198860785.003.0010","url":null,"abstract":"Four areas requiring further research are introduced and possible PhD projects are identified. They are (i) workhardening, (ii) electroplasticity, (iii) mobility of dislocations and (iv) hydrogen-assisted cracking. In each case the topic is introduced and key questions are identified. Self-organised criticality and slip bands are considered in the discussion of work hardening. The impact of drag forces is considered in the discussionof dislocation mobility. Possible mechanisms for hyfrogen-assisted cracking include hydrogen-enhanced decohesion (HEDE), adsorption-induced dislocation emission (AIDE) and hydrogen-enhanced localised plasticity (HELP).","PeriodicalId":236443,"journal":{"name":"Physics of Elasticity and Crystal Defects","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125347681","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Point defects","authors":"A. Sutton","doi":"10.1002/9783527809080.cataz13200","DOIUrl":"https://doi.org/10.1002/9783527809080.cataz13200","url":null,"abstract":"Examples of intrinsic and extrinsic point defects are discussed. Models of point defects in a continuum as misfitting spheres are solved for rigid and deformablemisfitting spheres. Free surfaces alter significantly the formation volume of a point defect even when the point defect is far from any free surface. Many point defects have non-sperical symmetry, and it is then better to consider defect forces exerted by the point defect on neighbouring atoms. Defect forces capture the symmetry of the point defect in its local environment. Interaction energies between point defects and between point defects and other sources of stress are expressed conveniently and with physical transparency in terms of dipole, quadrupole etc. tensors of point defects and derivatives of the Green’s function. The dipole tensor is experimentally measurable through the lambda-tensor, which measures the derivative of the macroscopic strain of a crystal with concentration of the point defect.","PeriodicalId":236443,"journal":{"name":"Physics of Elasticity and Crystal Defects","volume":"37 13","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141211511","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Cracks","authors":"A. Sutton","doi":"10.1007/978-3-662-55771-6_300136","DOIUrl":"https://doi.org/10.1007/978-3-662-55771-6_300136","url":null,"abstract":"","PeriodicalId":236443,"journal":{"name":"Physics of Elasticity and Crystal Defects","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123973499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}