Scaling relations for viscoelastic – cohesive conical indentation

Abstract Most geomaterials exhibit both viscoelastic and plastic material response when indented by a sharp conical tip. Lacking analytical solutions for viscoelastic – plastic material response, a numerical approach based on the finite element method is proposed for backcalculation of model parameters from indentation data. Departing from the analytical solutions recently obtained by Vandamme and Ulm, viscoelastic – cohesive conical indentation of a homogeneous material halfspace is dealt with in this paper. Results from finite element analysis, i. e., the load – penetration history for a rigid, conical indenter with linearly increasing load, are presented in dimensionless form. From the results, scaling relations are constructed for application to materials exhibiting viscoelastic – cohesive behavior.

[1]  J. Radok,et al.  Visco-elastic stress analysis , 1957 .

[2]  A. E. H. Love,et al.  BOUSSINESQ'S PROBLEM FOR A RIGID CONE , 1939 .

[3]  Roman Lackner,et al.  Constitutive modeling of cementitious materials in the framework of chemoplasticity , 2002 .

[4]  G. Pharr,et al.  An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments , 1992 .

[5]  En-Jui Lee,et al.  The Contact Problem for Viscoelastic Bodies , 1960 .

[6]  I. N. Sneddon.  The relation between load and penetration in the axisymmetric boussinesq problem for a punch of arbitrary profile , 1965 .

[7]  Franz-Josef Ulm,et al.  Dual-indentation technique for the assessment of strength properties of cohesive-frictional materials , 2006 .

[8]  En-Jui Lee,et al.  Stress analysis in visco-elastic bodies , 1955 .

[9]  Roman Lackner,et al.  Identification of viscoelastic properties by means of nanoindentation taking the real tip geometry into account , 2007 .

[10]  Yang-Tse Cheng,et al.  Scaling, dimensional analysis, and indentation measurements , 2004 .

[11]  Franz-Josef Ulm,et al.  Grid indentation analysis of composite microstructure and mechanics: Principles and validation , 2006 .

[12]  Roman Lackner,et al.  Microscale characterization of bitumen – back-analysis of viscoelastic properties by means of nanoindentation , 2007 .

[13]  Alexei Bolshakov,et al.  A critical examination of the fundamental relations used in the analysis of nanoindentation data , 1999 .

[14]  Franz-Josef Ulm,et al.  Viscoelastic solutions for conical indentation , 2006 .

[15]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[16]  P. Germain.  Mécanique des milieux continus , 1962 .