Indentation modelling of heterogeneous materials

The computational modelling of the indentation response of heterogeneous materials is studied using the finite element method. The material system consists of hard particles embedded within a soft matrix. Two material models with exactly the same overall stress-strain characteristics are simulated: one specifically incorporating dispersed elastic particles in an elastic-plastic matrix and the other a simple elastic-plastic continuum having a homogenized constitutive response of the particle-containing material. The material model with particles explicitly included shows a harder response than that of the homogenized model, even when the particle size is much smaller than the indent size. This is primarily due to the local increase in particle concentration directly underneath the indentation, which cannot be easily accounted for in the homogenized model. As a consequence, treating a heterogeneous material as a simple continuum in a straightforward manner appears to be an invalid approach in indentation modelling.

[1]  W. Fränzel,et al.  Dynamic ball hardness tests on polymers , 1999 .

[2]  Yang-Tse Cheng,et al.  Scaling approach to conical indentation in elastic-plastic solids with work hardening , 1998 .

[3]  N. Chawla,et al.  On the correlation between hardness and tensile strength in particle reinforced metal matrix composites , 2001 .

[4]  John W. Hutchinson,et al.  The mechanics of size-dependent indentation , 1998 .

[5]  Subra Suresh,et al.  A new method for estimating residual stresses by instrumented sharp indentation , 1998 .

[6]  Huajian Gao,et al.  Indentation size effects in crystalline materials: A law for strain gradient plasticity , 1998 .

[7]  D. Bahr,et al.  Elastic loading and elastoplastic unloading from nanometer level indentations for modulus determinations , 1998 .

[8]  Mark Bush,et al.  A phase mixture model of a particle reinforced composite with fine microstructure , 2000 .

[9]  B. Lawn,et al.  A simple indentation stress strain relation for contacts with spheres on bilayer structures , 1998 .

[10]  G. J. DeSalvo,et al.  On the Plastic Flow Beneath a Blunt Axisymmetric Indenter , 1970 .

[11]  Norman A. Fleck,et al.  Spherical indentation of elastic–plastic solids , 1999, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[12]  Alexei Bolshakov,et al.  Influences of stress on the measurement of mechanical properties using nanoindentation: Part II. Finite element simulations , 1996 .

[13]  G. Pharr.  Measurement of mechanical properties by ultra-low load indentation , 1998 .