FEM Modeling of Instrumented Indentation MAE 5700: Finite
Element Analysis for Mechanical and Aerospace Design Joseph Carloni
a, Julia Chen b, Jonathan Matheny c, Ashley Torres c a Materials
Science PhD program, [email protected] b Mechanical Engineering
PhD program, [email protected] c Biomedical Engineering PhD
program, [email protected], [email protected] Slide 2
Introduction to instrumented indentation A special form of
indentation hardness testing where load vs. displacement data is
collected continuously The resulting load-displacement data can be
used to determine the plastic and elastic properties of the
material Commonly used to test the elastic properties of a
material, especially at a small scale nanoindentation 2 Slide 3 A
Real Nanoindentation Experiment 1. Load Application 2. Indentation
3. Load Removal 3 Slide 4 Nanoindentation Equations The reduced
modulus of contact between two materials is a function of the
Youngs moduli: Sneddons equation relates the reduced modulus of a
contact to the contact stiffness and contact area: 4 Sneddon, 1948
W.C. Oliver and G.M. Pharr (1992). Slide 5 Motivation / Problem
Statement Sneddons equation was derived for contact between a rigid
indenter and a semi-infinite half space We want to model the
elastic portion of an indentation in ANSYS so that we can vary
dimensional parameters to see how they affect the accuracy of
Sneddons equation 2D Axisymmetric P E i, v i E s, v s h w 5 Slide 6
Solid Body Contact Assume: strains are small, materials are
elastic, surfaces are frictionless Contact is a changing-status
nonlinearity. The stiffness, depends on whether the parts are
touching or separated We establish a relationship between the two
surfaces to prevent them from passing through each other in the
analysis termed, contact compatibility ANSYS Academic Research,
Release 14.5, Help System, Introduction to Contact Guide, ANSYS,
Inc. 6 Slide 7 Normal Lagrange Formulation Adds an extra degree of
freedom (contact pressure) to satisfy contact compatibility Contact
force is solved for explicitly instead of using stiffness and
penetration Enforces zero/nearly-zero penetration with pressure DOF
Only applies to forces in directions Normal to contact surface
Direct solvers are used ANSYS Academic Research, Release 14.5, Help
System, Introduction to Contact Guide, ANSYS, Inc. 7 Slide 8
Penalty-Based Formulations Concept of contact stiffness k normal is
used in both The higher the contact stiffness, the lower the
penetration As long as x penetration is small or negligible, the
solution results will be accurate The Augmented Lagrange method is
less sensitive to the magnitude of the contact stiffness k normal
because of (pressure) Pros (+) and Cons (-) ANSYS Academic
Research, Release 14.5, Help System, Introduction to Contact Guide,
ANSYS, Inc. 8 Slide 9 ANSYS Detection Method Allows you to choose
the location of contact detection in order to obtain convergence
Normal Lagrange uses Nodal Detection, resulting in fewer points
Pure Penalty and Augmented Lagrange use Gauss point detection,
resulting in more detection points ANSYS Academic Research, Release
14.5, Help System, Introduction to Contact Guide, ANSYS, Inc. 9
Slide 10 ANSYS Contact Stiffness Normal stiffness can be
automatically adjusted during the solution to enhance convergence
at the end of each iteration The Normal Contact Stiffness k normal
is the most important parameter affecting accuracy and convergence
behavior Large value of stiffness gives more accuracy, but problem
may be difficult to converge If k normal is too large, the model
may oscillate, contact surfaces would bounce off each other ANSYS
Academic Research, Release 14.5, Help System, Introduction to
Contact Guide, ANSYS, Inc. 10 Slide 11 Nonlinear Finite Element
Approach Newton-Raphson Iterative Method Loading Incrementation
Procedure Becker, A.A. An Introductory Guide to Finite Element
Analysis. p.109-125. 11 Slide 12 Initial problem set-up Materials
Indenter- Diamond Youngs Modulus=1.14E12 Pa Poissons Ratio=0.07
Tested Material- Calcite Youngs Modulus=7E10 Pa Poissons Ratio=0.3
Both Materials Type Isotropic Elasticity 12 Slide 13 Initial
problem set-up Axisymmetric Model Boundary Conditions Fixed
displacement (in x) along axis of symmetry Fixed support on bottom
edge of material Loading Pressure (1E8 Pa) applied normal to top
edge of indenter 13 Slide 14 Automated Calculations 14 Slide 15
ANSYS Default Mesh (10 divisions) Quadrilateral Elements 15 Slide
16 ANSYS Default Results (-13.4% error) 16 Slide 17 Refined Mesh
(160 divisions) Quadrilateral Elements 17 Slide 18 Refined Results
(2.74% error) 18 Slide 19 Mesh Convergence The magnitude of the
error converges Now we change other parameters 19 Slide 20 Normal
Lagrange (9.29% error, 5e-17 m penetration) 20 Slide 21 Augmented
Lagrange (2.74% error, 1e-9 m penetration) 21 Slide 22 Final setup
Contact Type: Frictionless Target Body: indenter Contact Body:
material Behavior: Symmetric Contact Formulation: Augmented
Lagrange Update Stiffness: Each Iteration Stiffness factor: 1 Auto
time step: min 1, max 10 Weak springs: off 22 Slide 23 Pressure Too
high of a pressure increases the error 23 Slide 24 Dimension of
material Too small of a sample increases the error 24 Slide 25
Different modulus Testing a high modulus material increases the
error 25 Slide 26 Conclusion Indentation can be accurately modeled
using ANSYS and a well-refined mesh The validity of Sneddons
equation has been explored: Lower pressure More accurate Larger
sample More accurate More compliant sample More accurate 26 Slide
27 Questions? 27