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

CML 26 th Annual Sponsors’ Meeting January 27 th , 2014 Peridynamics Analysis of the Wear Process of Thin Films of Hard ‐ Disk Drives Sayna Ebrahimi Advisors: Professors K. Komvopoulos and D. Steigmann

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: Molecular Dynamics: o Cannot apply PDEs directly in the presence of a structural discontinuity (e.g., defect). o Its accuracy depends on the assumed o Significant discretization refinement is potential function necessary at large strain ‐ gradient locations(e.g., contact region and film interface). o Time consuming o A pre ‐ existing defect or specified crack path must be assumed to model material removal o Size (scale) and boundary condition restrictions o 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

What is Peridynamics? Peridynamics is a continuum version of Molecular Dynamics � �� � , �� � � � � � � � � , � � � � � �� � � � � ��� � , �� �  Each particle x interacts with a finite number of Horizon 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 z � �  For particles more than the horizon radius apart � � � (similar to the cutoff radius in MD) x y

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

Peridynamics Fundamentals � � � � � � � Relative position vector: � � ��� � , �� � ��� � , �� Relative displacement vector: � : Original bond length in reference configuration � � � : Bond length in current configuration � �, �, � � � � � � � Bond stretch: � Peridynamic Horizon

Bond ‐ based Peridynamics � �� � �� � , �� � � � � � � � � , � � � � � �� � � � � ��� � , �� ��� �� � � �, � � � � �, �, � Pair ‐ wise force function: �� � �� � � � � �, �, � � Bond Stretch: � �: represents linear or ��� � � Micro ‐ modulus function: K: bulk modulus �� � nonlinear bond stretching (elastic stiffness ) Critical Bond Stretch: � � �, �, � � � �� � �� ��� � , �, � � �� and � are material ‐ � ��� � � ��� � � , �, � in � dependent properties. Brittle material Ductile material

State ‐ based Peridynamics � �� � �� � , �� � � � � � , � �� � � � � � � � � � , � �� � � � � � �� � � � � ��� � , �� ��� � � � � �� � �� � � � � � 0 Deformed direction vector state: ���� = � 0 ��������� � � 3�� � � �� � � � � Scalar state field: � � � � � ������� ������ Weighted volume: � � � � �, � ��� � � � � � � Extension scalar state: 3 Dilation: � �, � � � � � � ������� ������ � � � � � 15� �

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 But other numerical methods?! to run first numerical experiment with PD: two weeks

PD Simulations of Asperity Sliding Contact Moving layer and asperity • 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 = �� Fixed layer and asperity • Time step : �. ���� ��

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)

Conclusions Advantages of Peridynamics • 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

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!