Presentation on theme: "FEM Modeling of Instrumented Indentation"— Presentation transcript:
1 FEM Modeling of Instrumented Indentation MAE 5700: Finite Element Analysis for Mechanical and Aerospace DesignJoseph Carlonia, Julia Chenb, Jonathan Mathenyc, Ashley TorrescaMaterials Science PhD program,bMechanical Engineering PhD program,cBiomedical Engineering PhD program,
2 Introduction to instrumented indentation A special form of indentation hardness testing where load vs. displacement data is collected continuouslyThe resulting load-displacement data can be used to determine the plastic and elastic properties of the materialCommonly used to test the elastic properties of a material, especially at a small scale “nanoindentation”Because of this advantage, instrumented indents are commonly used... Especially at the small scale... i.e. nanoindentation
3 A Real Nanoindentation Experiment 1. Load Application2. Indentation3. Load RemovalHere 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 doesn’t 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.
4 Nanoindentation Equations The reduced modulus of contact between two materials is a function of the Young’s moduli:Sneddon’s equation relates the reduced modulus of a contact to the contact stiffness and contact area:For contact between 2 different materials, the reduced modulus is a function of the materials’ Young’s moduli.Sneddon’s equation (originally derived in 1948, and applied to nanoindentation in the early 90s) relates the reduced modulus to a measured contact stiffness and contact areaSneddon, 1948W.C. Oliver and G.M. Pharr (1992).
5 Motivation / Problem Statement Sneddon’s 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 Sneddon’s equation2DAxisymmetricPEi, viEs, vshwThe 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.
6 Solid 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 compatibilityANSYS® Academic Research, Release 14.5, Help System, Introduction to Contact Guide, ANSYS, Inc.
7 Normal Lagrange Formulation Adds an extra degree of freedom (contact pressure) to satisfy contact compatibilityContact force is solved for explicitly instead of using stiffness and penetrationEnforces zero/nearly-zero penetration with pressure DOFOnly applies to forces in directions Normal to contact surfaceDirect solvers are usedANSYS® Academic Research, Release 14.5, Help System, Introduction to Contact Guide, ANSYS, Inc.
8 Penalty-Based Formulations Concept of contact stiffness knormal is used in bothThe higher the contact stiffness, the lower the penetrationAs long as xpenetration is small or negligible, the solution results will be accurateThe Augmented Lagrange method is less sensitive to the magnitude of the contact stiffness knormal because of λ (pressure)Pros (+) and Cons (-)ANSYS® Academic Research, Release 14.5, Help System, Introduction to Contact Guide, ANSYS, Inc.
9 ANSYS Detection Method ANSYS® Academic Research, Release 14.5, Help System, Introduction to Contact Guide, ANSYS, Inc. Allows you to choose the location of contact detection in order to obtain convergenceNormal Lagrange uses Nodal Detection, resulting in fewer pointsPure Penalty and Augmented Lagrange use Gauss point detection, resulting in more detection points
10 ANSYS Contact Stiffness Normal stiffness can be automatically adjusted during the solution to enhance convergence at the end of each iterationThe Normal Contact Stiffness knormal is the most important parameter affecting accuracy and convergence behaviorLarge 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 otherANSYS® Academic Research, Release 14.5, Help System, Introduction to Contact Guide, ANSYS, Inc.
11 Nonlinear Finite Element Approach Loading Incrementation ProcedureNewton-Raphson Iterative MethodBecker, A.A. An Introductory Guide to Finite Element Analysis. p
13 Initial problem set-up Axisymmetric ModelBoundary ConditionsFixed displacement (in x) along axis of symmetryFixed support on bottom edge of materialLoadingPressure (1E8 Pa) applied normal to top edge of indenter
19 Mesh Convergence The magnitude of the error converges Now we change other parameters
20 Normal Lagrange (9.29% error, 5e-17 m penetration)
21 Augmented Lagrange (2.74% error, 1e-9 m penetration)
22 Final setup Contact Type: Frictionless Target Body: indenter Contact Body: materialBehavior: SymmetricContact Formulation: Augmented LagrangeUpdate Stiffness: Each IterationStiffness factor: 1Auto time step: min 1, max 10Weak springs: off
23 Too high of a pressure increases the error Sneddon’s 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.Too high of a pressure increases the error
24 Dimension of material Too small of a sample increases the error Sneddon’s 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.Too small of a sample increases the error
25 Testing a high modulus material increases the error Different modulusSneddon’s 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.Testing a high modulus material increases the error
26 ConclusionIndentation can be accurately modeled using ANSYS and a well-refined meshThe validity of Sneddon’s equation has been explored:Lower pressure More accurateLarger sample More accurateMore compliant sample More accurate