TY - JOUR
T1 - Surface effect in axisymmetric Hertzian contact problems
AU - Jia, Ning
AU - Yao, Yin
AU - Peng, Zhilong
AU - Yang, Yazheng
AU - Chen, Shaohua
N1 - Publisher Copyright:
© 2018
PY - 2018/10/1
Y1 - 2018/10/1
N2 - Surface effect in three different axisymmetric Hertzian contact models is investigated in this paper with a recently developed elastic theory for nanostructured materials, including a Boussinesq problem, contact problem between a rigid flat-ended cylindrical indenter and an elastic half space as well as contact problem between a rigid spherical indenter and an elastic half space. With the help of the Love's strain function method and Hankel integral transformation, closed-form solutions of the stress and displacement fields at the surface of an elastic half space subjected to a concentrated force are achieved, based on which the interface tractions and displacements in the three different axisymmetric contact problems can be further obtained. It is found that surface effect in these contact problems can be characterized only by an intrinsic length, i.e., the ratio of the bulk surface energy density to the bulk shear modulus of the indented material. When the contact radius is comparable with the intrinsic length, surface effect is much obvious, leading to a serious deviation between the two solutions predicted respectively by the theoretical model developed for nanomaterials and the classical contact model. A more interesting phenomenon is about surface effect on the indentation hardness, which is found to increase with the reduction of the indenter radius when the external load is fixed, or to increase with the decrease of the external load when the indenter radius keeps unchanged. All the results in this paper should be helpful not only for deep understanding of the surface effect on nano-contact behaviors but also for further revealing the nature of surface effect of nano-indentation hardness.
AB - Surface effect in three different axisymmetric Hertzian contact models is investigated in this paper with a recently developed elastic theory for nanostructured materials, including a Boussinesq problem, contact problem between a rigid flat-ended cylindrical indenter and an elastic half space as well as contact problem between a rigid spherical indenter and an elastic half space. With the help of the Love's strain function method and Hankel integral transformation, closed-form solutions of the stress and displacement fields at the surface of an elastic half space subjected to a concentrated force are achieved, based on which the interface tractions and displacements in the three different axisymmetric contact problems can be further obtained. It is found that surface effect in these contact problems can be characterized only by an intrinsic length, i.e., the ratio of the bulk surface energy density to the bulk shear modulus of the indented material. When the contact radius is comparable with the intrinsic length, surface effect is much obvious, leading to a serious deviation between the two solutions predicted respectively by the theoretical model developed for nanomaterials and the classical contact model. A more interesting phenomenon is about surface effect on the indentation hardness, which is found to increase with the reduction of the indenter radius when the external load is fixed, or to increase with the decrease of the external load when the indenter radius keeps unchanged. All the results in this paper should be helpful not only for deep understanding of the surface effect on nano-contact behaviors but also for further revealing the nature of surface effect of nano-indentation hardness.
KW - Axisymmetric Hertzian contact
KW - Intrinsic length
KW - Nano-indentation hardness
KW - Surface effect
KW - Surface energy density
UR - http://www.scopus.com/inward/record.url?scp=85052109722&partnerID=8YFLogxK
U2 - 10.1016/j.ijsolstr.2018.06.019
DO - 10.1016/j.ijsolstr.2018.06.019
M3 - Article
AN - SCOPUS:85052109722
SN - 0020-7683
VL - 150
SP - 241
EP - 254
JO - International Journal of Solids and Structures
JF - International Journal of Solids and Structures
ER -