fem modeling of instrumented indentation

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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]

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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] - PowerPoint PPT Presentation

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Microstructural Flaws in Bone Associated with Bone Remodeling

FEM Modeling of Instrumented IndentationMAE 5700: Finite Element Analysis for Mechanical and Aerospace Design

Joseph Carlonia, Julia Chenb, Jonathan Mathenyc, Ashley TorrescaMaterials Science PhD program, [email protected] Engineering PhD program, [email protected] Engineering PhD program, [email protected], [email protected]

Introduction to instrumented indentationA 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

2Because of this advantage, instrumented indents are commonly used... Especially at the small scale... i.e. nanoindentation

2A Real Nanoindentation Experiment1. Load Application2. Indentation3. Load Removal

3Here is a schematic of a real nanoindentation experiment. The instrument applies a load, the indenter penetrates the surface, and then the load is removed. The collected load-displacement data is usually plotted like so (load on y vs. displacement on x). After some critical load, the material plastically deforms (that is doesnt return to its initial displacement), but elastic properties can still be calculated from a linear fit to the initial unloading. Alternatively, you can try to to stay below the critical load for plasticity.3Nanoindentation EquationsThe 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:

4Sneddon, 1948 W.C. Oliver and G.M. Pharr (1992). For contact between 2 different materials, the reduced modulus is a function of the materials Youngs moduli.Sneddons equation (originally derived in 1948, and applied to nanoindentation in the early 90s) relates the reduced modulus to a measured contact stiffness and contact area4Motivation / Problem StatementSneddons equation was derived for contact between a rigid indenter and a semi-infinite half spaceWe 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 AxisymmetricPEi, viEs, vshw5The analytical solution for indentation was derived for...In practice, this is not possible, so we want to model it using FEA and see how close we can approximate the analytical solution by varying dimensional parameters and boundary conditions.5Solid Body ContactAssume: strains are small, materials are elastic, surfaces are frictionlessContact is a changing-status nonlinearity. The stiffness, depends on whether the parts are touching or separatedWe 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.6Normal Lagrange FormulationAdds 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 DOFOnly applies to forces in directions Normal to contact surfaceDirect solvers are used

ANSYS Academic Research, Release 14.5, Help System, Introduction to Contact Guide, ANSYS, Inc.7Penalty-Based FormulationsConcept of contact stiffness knormal is used in bothThe higher the contact stiffness, the lower the penetration As long as xpenetration is small or negligible, the solution results will be accurate

The Augmented Lagrange method is less sensitive to the magnitude of the contact stiffness knormal because of (pressure)

Pros (+) and Cons (-)ANSYS Academic Research, Release 14.5, Help System, Introduction to Contact Guide, ANSYS, Inc.88ANSYS Detection MethodAllows you to choose the location of contact detection in order to obtain convergence Normal Lagrange uses Nodal Detection, resulting in fewer pointsPure 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.9ANSYS Contact StiffnessNormal stiffness can be automatically adjusted during the solution to enhance convergence at the end of each iteration The Normal Contact Stiffness knormal is the most important parameter affecting accuracy and convergence behavior Large value of stiffness gives more accuracy, but problem may be difficult to convergeIf knormal 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.10Nonlinear Finite Element Approach

Newton-Raphson Iterative MethodLoading Incrementation ProcedureBecker, A.A. An Introductory Guide to Finite Element Analysis. p.109-125.

11Initial problem set-upMaterialsIndenter- DiamondYoungs Modulus=1.14E12 PaPoissons Ratio=0.07

Tested Material- CalciteYoungs Modulus=7E10 PaPoissons Ratio=0.3

Both Materials Type Isotropic Elasticity

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Initial problem set-upAxisymmetric ModelBoundary ConditionsFixed displacement (in x) along axis of symmetryFixed support on bottom edge of materialLoadingPressure (1E8 Pa) applied normal to top edge of indenter 13Automated Calculations

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ANSYS Default Mesh (10 divisions)

Quadrilateral Elements15ANSYS Default Results (-13.4% error)

16Refined Mesh (160 divisions)

Quadrilateral Elements17Refined Results (2.74% error)

18Mesh Convergence

The magnitude of the error converges Now we change other parameters19Normal Lagrange(9.29% error, 5e-17 m penetration)

20Augmented Lagrange(2.74% error, 1e-9 m penetration)

21Final setupContact Type: Frictionless Target Body: indenterContact Body: materialBehavior: SymmetricContact Formulation: Augmented LagrangeUpdate Stiffness: Each IterationStiffness factor: 1Auto time step: min 1, max 10Weak springs: off

22PressureToo high of a pressure increases the error23Sneddons equation is derived for purely elastic, small deformations. We chose a pressure of 1e8 based on experimental results. As the pressure increases, we will eventually have large deformations that should result in plasticity. Therefore, we expect the error to increase after some critical pressure.23Dimension of materialToo small of a sample increases the error24Sneddons equation is derived assuming contact with a semi-infinite half space. As the material size decreases, we will eventually have a geometry that cannot be accurately approximated as infinite. Therefore, we expect to see an increase in the error below some critical material size.24Different modulusTesting a high modulus material increases the error25Sneddons equation was initially derived for contact by an perfectly rigid indenter. The concept of reduced modulus was introduced as a correction for indenters with some finite stiffness. As we increase the stiffness of the material being indented, eventually the ratio between the stiffness of the material and that of the indenter becomes too high to be accurately corrected. Therefore, we expect the magnitude of the error to increase with increasing material modulus.25ConclusionIndentation can be accurately modeled using ANSYS and a well-refined mesh

The validity of Sneddons equation has been explored:Lower pressure More accurateLarger sample More accurateMore compliant sample More accurate26Questions?27