TY - JOUR
T1 - Some issues concerning the use of a single, material specific length scale parameter in theories of higher order strain gradient plasticity
AU - Guruprasad, Thimmappa Shetty
AU - Basu, Sumit
N1 - Publisher Copyright:
© 2019 Elsevier Ltd
PY - 2019/9
Y1 - 2019/9
N2 - Higher order strain gradient plasticity theories extend conventional ones with a view to explain the observed elevation of plastic flow stress in micron-sized structures. The essential elements of this modifications are the definition of a measure of plastic strain gradients, introduction of a conjugate higher order stress and introduction of one or more length scale parameters. We adopt a particular elasto-viscoplastic version of the higher order strain gradient theory based on a single scalar length scale parameter, formulate a large deformation based Finite Element model capable of handling strain gradients and higher order boundary conditions and simulate for three different materials, two sets of experiments where size effects manifest. The experiments differ in the level of plasticity that is induced during deformation — ranging from the order of the yield strain to approximately ten times its value. The materials, namely Cu, Al and Ni, have grain sizes that differ widely. We determine the scalar length scale parameter by demanding that the simulations match the experimental load deformation responses closely. The results indicate that single, scalar length scale parameter based higher order strain gradient theories cannot describe experimental observations across a wide range of geometries, boundary conditions, and plastic strain levels. The length scale is not intrinsic to the material but depends on the level of plastic strain induced by the deformation and also possibly on the number of grains involved in the deformation.
AB - Higher order strain gradient plasticity theories extend conventional ones with a view to explain the observed elevation of plastic flow stress in micron-sized structures. The essential elements of this modifications are the definition of a measure of plastic strain gradients, introduction of a conjugate higher order stress and introduction of one or more length scale parameters. We adopt a particular elasto-viscoplastic version of the higher order strain gradient theory based on a single scalar length scale parameter, formulate a large deformation based Finite Element model capable of handling strain gradients and higher order boundary conditions and simulate for three different materials, two sets of experiments where size effects manifest. The experiments differ in the level of plasticity that is induced during deformation — ranging from the order of the yield strain to approximately ten times its value. The materials, namely Cu, Al and Ni, have grain sizes that differ widely. We determine the scalar length scale parameter by demanding that the simulations match the experimental load deformation responses closely. The results indicate that single, scalar length scale parameter based higher order strain gradient theories cannot describe experimental observations across a wide range of geometries, boundary conditions, and plastic strain levels. The length scale is not intrinsic to the material but depends on the level of plastic strain induced by the deformation and also possibly on the number of grains involved in the deformation.
UR - http://www.scopus.com/inward/record.url?scp=85067682619&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85067682619&partnerID=8YFLogxK
U2 - 10.1016/j.mechmat.2019.103076
DO - 10.1016/j.mechmat.2019.103076
M3 - Article
AN - SCOPUS:85067682619
SN - 0167-6636
VL - 136
JO - Mechanics of Materials
JF - Mechanics of Materials
M1 - 103076
ER -