Peridynamics Analysis of the Wear Process of Thin Films of Hard Disk - - PowerPoint PPT Presentation

Peridynamics Analysis of the Wear Process of Thin Films of Hard‐Disk Drives

Sayna Ebrahimi Advisors: Professors K. Komvopoulos and D. Steigmann

CML 26th Annual Sponsors’ Meeting January 27th, 2014

Outline

• Motivation
• Introduction
• Peridynamics Theory
• Asperity Sliding Contact Simulations
• Conclusions

Motivation

• Why wear analysis of thin films ?

The key role of the thin‐film overcoat is to:

 protect the magnetic medium from wear and corrosion  reduce frictional interaction between surface asperities

• Why contact of asperities matters?

It controls the longevity of the thin‐film overcoat It may cause surface damage/wear and, in turn, data loss It affects the operation efficiency and lifetime of the hard drive

Computational Methods

Continuum Mechanics:

• Cannot apply PDEs directly in the presence of a

structural discontinuity (e.g., defect).

• Significant discretization refinement is

necessary at large strain‐gradient locations(e.g., contact region and film interface).

• A pre‐existing defect or specified crack path

must be assumed to model material removal

• Breaks down at the nanoscale

Why Peridynamics?

 No potential function dependency  No assumption of a pre‐existing defect; damage occurs when the material

is energetically favorable to fail

 No mathematical difficulty caused by solving PDEs  Ideal for cyclic deformation/fatigue analysis

Molecular Dynamics:

• Its accuracy depends on the assumed

potential function

• Time consuming
• Size (scale) and boundary condition

restrictions

What is Peridynamics?

 Each particle x interacts with a finite number of particles (family of x) in the body within a certain distance, referred to as the “horizon”  Replaces PDEs with integral equations and utilizes same set of equations everywhere  When bonds stretch beyond a critical distance, they break, simulating material separation  Force function contains the constitutive model  For particles more than the horizon radius apart (similar to the cutoff radius in MD) Peridynamics is a continuum version of Molecular Dynamics , ,

,

• x

y z

• Horizon

Bond‐based & State‐based Peridynamics (PD) Elastic, Elastic‐Plastic, and Plastic Materials

• Bond‐based PD: The interaction between each

pair of particles is independent of all the others.

• State‐based PD: It incorporates features of the

material response, including damage evolution, that involve the collective behavior of all the points with which a given point interacts.

• High‐accuracy description of irreversible

permanent deformation.

State‐based A “State of order ” is a function T . ∶ → denotes the set of all tensors of order

Peridynamics Fundamentals

, , , ,

• Relative position vector:

Relative displacement vector: Bond stretch: Peridynamic Horizon

: Original bond length in reference configuration : Bond length in current configuration

, ,

,

• Bond‐based Peridynamics

: represents linear or nonlinear bond stretching (elastic stiffness)

Pair‐wise force function: , , , Bond Stretch: , ,

• Micro‐modulus function:
• K: bulk modulus

Critical Bond Stretch:

, , , , , , in

and are material‐ dependent properties.

Brittle material Ductile material

State‐based Peridynamics

Scalar state field: , , ,

,

• 3

=

Deformed direction vector state:

15

• ,

, 3

• Dilation:

Extension scalar state: Weighted volume:

Peridynamics Discretization

Theory lends itself to a mesh‐free numerical method

No elements Changing connectivity Bond breakage occurs irreversibly when a bond

exceeds its prescribed critical stretch Velocity‐Verlet Algorithm to track particles:

∆ . ∆ 1 2 . ∆ ∆/2 1 2 . ∆ 1

• ,

Computational Tools for PD

• LAMMPS (Large‐scale Atomic/Molecular Massively Parallel Simulator)

open‐source (http://lammps.sandia.gov) Provides (nonlocal) continuum mechanics simulation capability within an MD code Fast parallel implementation capability Capable of modeling prototype microelastic brittle (PMB), Linear peridynamic solid

(LPS) models and viscoplastic model

General boundary conditions Material inhomogeneity

• Costume‐made codes: Can be easily parallelized through different processors: reduces

computational expenses drastically.

A personal observation… Time from starting implementation of LAMMPS to run first numerical experiment with PD: two weeks But other numerical methods?!

PD Simulations of Asperity Sliding Contact

• Asperity deformation due to sliding contact
• Asperities have the same and 
• Periodic boundary conditions in x‐y plane
• Lattice constant: .
• Asperity Radius =
• Radius of neighborhood:
• Critical Bond stretch =
• Time step : .

Fixed layer and asperity Moving layer and asperity

Sliding Speed Effect on Asperity Deformation

. . . ⁄ . ⁄

Sliding Speed Effect on Asperity Deformation (Animated File)

/ /

Asperities Mass Reduction After Each Sliding Pass

Asperity Radius Effect

t = t = . t = . t = .

⁄

Asperity Interference Effect (Animated Files)

• Continuum mechanics cannot model nanoscale damage phenomena (e.g., wear)
• Damage is self guided!
• No material separation (crack) path is needed; local material separation occurs

whenever it is energetically favorable

• No mesh, no elements!
• Can model heterogeneous materials exhibiting high complexity
• Can model complex-fracture systems without the need to keep track of each crack
• Can be easily implemented in LAMMPS or custom-made codes and be parrallelized

to minimize computational cost

Conclusions

Advantages of Peridynamics

Future Work

• Simulate asperity contact to study the effect of local surface

interference at the head‐disk interface (HDI) on the resulting deformation and atomic‐scale wear using Peridynamics, a continuum version of Molecular Dynamics (MD).

• Simulate the wear process of thin‐film media at the HDI.
• Develop a criterion of atomic‐scale material removal including

statistical parameters, such as average asperity size, interference distance, and media nanomechanical properties.

Thank You!