Consider an infinitely extended elastic solid in which a domain {Ω:r ≤ a} is defined in cylindrical polar coordinates. The geometry of the problem is illustrated in Fig. 6.1 for a = 1. The problem is formulate
It is found that the ratcheting rate of elbow mainly depends on internal pressure, bending moment and material parameters, etc. Subsequently, the ratcheting behavior of elbow is simulated by using the constitutive model and compared with the experimental results. In addition, for the ratchet ...
Eshelby's tensors for plane strain and cylindrical inclusions based on a simplified strain gradient elasticity theory. Acta Mech. 211, 115-129.Ma H.M., Gao X.-L.: Eshelby’s tensors for plane strain and cylindrical inclusions based on a simplified strain gradient elasticity theory. Acta ...
The radial (i.e., depth below the surface) dependence of the residual strain tensor within shot-peened samples of cylindrical geometry is measured nondestructively using high-energy synchrotron radiation (80 keV). Transmission geometry is employed in combination with a triangulation slit and area ...
The radial (i.e., depth below the surface) dependence of the residual strain tensor within shot-peened samples of cylindrical geometry is measured nondestructively using high-energy synchrotron radiation (80 keV). Transmission geometry is employed in combination with a triangulation slit and area ...
The infinitesimalstrain tensoris asymmetric tensorcharacterised by nine components that in three-dimensional rectangularCartesian coordinatesreads: εij=[εxxεxyεxzεyxεyyεyzεzxεzyεzz] where the diagonal componentsεkk[-] are called normal strains and represent stretching of an element and the...
whereCijklareelastic constants, which are the components of the fourth-orderstiffness tensororelastic tensor. Since the indicesi,j,kandlmay each take the values 1, 2 or 3, there are all together 81 constantsCijkl. However, some of these vanish, and others are equal by symmetry, so that ...
In a similar fashion, the local-overall relation for the strain rate tensor is assumed in the effective configurations as follows: (7.5)dε¯ij=c¯Mdε¯ijM+c¯Fdε¯ijF where ε¯ijM and ε¯ijF are the components of the effective matrix and fiber strain tensors, respectively...
Conseqently, an isotropic tensor function of two symmetric tensors involves in the most general case nine response functions, ϕ1, …,ϕ9, which depend in turn on the six moment invariants of the stress and strain rate tensors below, (60)I―1σ=trσ,I―2σ=trσ2,I―3σ=trσ3...
The RVE strain tensors were computed in the Cartesian coordinate system which needed to be transformed into the Cylindrical coordinate system to compare with the 2D SXRD fibre lattice strains in the radial and axial directions. A schematic overview of the interaction between the meso- and ...