Modeling viscoelastic-damping-for-dampening-adhesives

© 2014 ANSYS, Inc. May 1, 2014 ANSYS Confidential

Modeling Viscoelastic Damping for Dampening Adhesives

ANSYS REGIONAL CONFERENCE SANTA CLARA 2014 Can Ozcan & Metin Ozen Ozen Engineering Inc.


ABSTRACT Dampening adhesives are widely used in high sensitivity

manufacturing equipment design in order to minimize vibration. Dampening adhesives exhibit viscoelastic behavior and needs to be modeled properly to achieve high quality design criteria.

This presentation discusses the importance of viscoelastic material modeling, how it is tested and used to design for vibration control. Ansys Structural nonlinear capabilities are needed to analyze for time-transient response of structural damping adhesives with accuracy.

The presentation includes a test case for electronic device manufacturing equipment design.


AGENDA ● VISCOELASTICITY ● DAMPENING ADHESIVES ● TESTING METHODS - NO TEMPERATURE DEPENDENCY

• Experimental Static Test Methods – Uniaxial Tension and Compression – Equibiaxial Method – Planar and Simple Shear Methods

• Experimental Dynamic Test Methods – Creep and Stress Relaxation Methods – Torsion Pendulum Method – Forced Vibration Non-Resonance Methods – Resonance Methods – Wave Propagation Methods

● INCORPORATING TEMPERATURE DEPENDENCY ● ANSYS MODELING ● DESIGN FOR VISCOELASTIC DAMPING


Use of Viscoelastic Materials ● Viscoelastic materials are widely used for vibration, shock and noise

control in the automotive, marine, aerospace, electronics, defence, instrumentation and home appliance industries.

Image: http://www.trelleborg.com/en/Media/Products-and-Solutions-News/Archive/Silence-included/


Automotive Application ● Dampening adhesives applied in automotive body to minimize vibration

induced sound

Image : http://2.bp.blogspot.com/_U2C8LB0alAM/SffrG46Fm4I/AAAAAAAAABs/Yo0KB-7ghyA/s400/Latio+spare+tyre+well+before+SP.JPG


Electronics Application

http://solutions.3mcanada.ca/wps/portal/3M/fr_CA/electronics/home/productsandservices/products/TapesAdhesives/ViscoelasticDampingPolymers/

● Used in electronic devices to minimize vibration


VISCOELASTICITY ● Viscoelastic materials are made up of long-chain molecules. ● Their properties are determined by the degree of mobility or

entanglement of the long-chain molecules. ● Three regimes of viscoelastic behavior

• The rubbery regime • The rubber-to-glass transition regime • The glassy regime

● These regimes encompass rubbers, elastomers, polymers, epoxies and plastics


VISCOELASTICITY ● Classification of a viscoelastic material is dependent on it’s temperature ● A viscoelastic material which is classed as rubber at 20C can be made to

behave as a glassy or plastic material at a relatively low temperature of -40C or less.

● Similary, a material defined as plastic at 20C can be made to behave as rubbery material at higher temperatures of 150C or more.


VISCOELASTICITY ● Unlike most metallic materials, mechanical properties of viscoelastic

materials are temperature, frequency and time dependent. ● While the mechanical properties of most metallic materials can be

obtained from material data handbooks, the temperature-, frequency- and time-dependent characteristics of the mechanical properties of viscoelastic materials have to be determined experimentally.


LINEAR VISCOELASTICITY ● Behavior of viscoelastic materials is in between elastic solids and viscous

liquids. ● A first approximation can be Hooke’s law of elasticity plus Newton’s law

of viscosity

under simple shear

conditions


SHEAR RELAXATION MODULUS ● Shear Relaxation Modulus is obtained from response of a viscoelastic

material subjected to a step change in strain as shown below ● Shear Relaxation Modulus is direct input to Ansys simulations through a

Prony series definition so it is important definition to understand


SHEAR RELAXATION MODULUS ● Shear relaxation modulus is time dependent ● Under very short times of the order 10-3s or less, ie timescale for shock

and impact, modulus is very high as the time is too short for the long-chain molecules of viscoelastic material to re-arrange

● At very long times of order 10s or more, ie timescale for creep, modulus becomes relatively low since long chains have time to re-arrange


COMPLEX MODULUS ● Analyzing viscoelasticty in frequency domain, gives us the concept of

complex modulus ● Under repetitive loading, viscoelasticity can be defined as:

Storage Modulus Loss Modulus

Loss Factor


EFFECT OF TEMPERATURE ON VISCOELASTICTY ● Effects of temperature on complex modulus can be divided into three

distinct regions as shown below (glassy, transition, rubbery) ● At very low temperatures, the motion of the long polymer chains of the

material is highly restricted ● The temperature at which the loss factor attains its maximum value is

known as the transition temperature

E0: instantaneous modulus

Ee: long term/equilibrium modulus


EFFECT OF FREQUENCY ON VISCOELASTICITY ● Frequency effect on dynamic properties is similar but inverse to the

effect of temperature

E0: instantaneous modulus

Ee: long term/equilibrium modulus


DAMPING ADHESIVES ● Most applications use the damping adhesive as part of a damped metal

laminate (DML) or as part of a Constrained Layer Damper (CLD) ● DML: Viscoelastic layer is sandwiched in between a metal/plastic layer

formed into finished product (valve cover, oil pan, brackets) ● CLD: Constraining layer of metal or plastic/viscoelastic damper is

attached via polymer layer to the structure to be damped (car panels, disk drive covers)

Example of DML Application Example of CLD Application


DAMPING ADHESIVES ● Selection of proper damping polymer is dependent on the temperature

and frequency of the application ● As we have seen for maximum damping, loss factor and the storage

modulus should be maximum which is dependent on both temperature and frequency for each type of viscoelastic material

● Some applications may need different types of polymers in a multi-layered setup to damp vibrations at different frequencies or temperatures


TESTING METHODS ● Hyperelastic behavior can be used to define viscoelastic materials

rubbery state ● Static test methods can be employed to determine the hyperelastic

properties ● We should remember that shear modulus and bulk modulus are required

to define elastic materials mechanical response ● Using theory of elasticity one can measure shear and Young’s modulus to

determine bulk modulus; which is hard to measure accurately for viscoelastic materials


STATIC TESTING METHODS ● Uniaxial tension and compression methods

• Usually dog bone shaped specimens of 2mm thickness and 25mm length

• Determine Young’s modulus ● Equibiaxial method

• Can be achieved by either loading a square sheet of rubber or by filling a rubber balloon with a gas and subjecting to internal pressure

● Planar and simple shear methods • Determine pure shear modulus via planar shear test • Width to Length ratio of the specimen should be 8-10


DYNAMIC TESTING METHODS ● There are several techniques for the experimental determination of

dynamics properties of viscoelastic materials (namely complex moduli) ● Methods operate either in time or frequency domain and cover different

time/frequency ranges ● Depending on the time/frequency range these methods can be listed as:

• Creep and stress relaxation methods • Torsion pendulum method • Forced vibration non-resonance methods • Resonance methods • Wave propagation methods

shorter time scales

higher frequencies


SIMULATION OF VISCOELASTICITY IN ANSYS ● Viscoelasticity brings non-linearity into finite element analysis ● Some considerations when performing viscoelastic nonlinear analysis:

• Choice of element: depends on geometry, due to common use of dampening adhesive tapes shell elements with composite properies can be preferred. 3D continuum elements may be needed for thick bulky parts (shell vs solid element types in Ansys)

• Linear vs Quadratic: since relative thickness of adhesive tapes are much thinner wrt to metal parts, quadratic elements are preferred to be able to resolve stress gradients with less elements (solid185 vs solid186 in Ansys)

• Compressible vs Incompressible: when a viscoelastic material is in its rubbery regime, its Poisson’s ratio is almost 0.5 ie when deformed the volume does not change. Hybrid elements need to be used in such case (keyopt,x,6,1: mixed u-P formulation in Ansys)


SIMULATION OF VISCOELASTICITY IN ANSYS ● Once a finite element model is build we can perform:

• Static (linear&non-linear) • Time Domain Dynamic (linear&non-linear) • Frequency Domain Dynamic (linear only)*

– For a “Full” harmonic analysis, frequency-dependent elastic and damping behaviors are supported!

analysis in Ansys ● In machine design one uses the adhesive tapes to dampen out certain

frequencies in the design either related to precision or acoustics ● Thus interest is around Dynamic analysis for adhesive tapes


COMPARISON OF ANALYSIS TYPES ● A two point bending test is usually used to assess damping performance

of adhesive tapes in a three layer laminate design ● We built the setup of such system in Ansys to compare results under

different analysis types: ● A 2-D plane-strain model with half-symmetry is used

Point fixed

invertical y

direction

Symmetry

face


COMPARISON OF ANALYSIS TYPES ● Modal analysis give same results for natural frequencies, since

nonlinearity and/or frequency dependency is not taken into account

Viscoelastic Material Definition

1st Mode: 108 Hz

Linear Material Definition

1st Mode: 108 Hz


COMPARISON OF ANALYSIS ● Harmonic analysis give different results ● Ansys takes into account frequency dependent modulus complex

modulus value for “full” solution method harmonic analysis ● Frequency dependency is applied via Prony Series ● Below results compare center displacement under repeated 1N load

Viscoelastic Material Definition

Damped solution around 70Hz

Linear Material Definition

Resonance around 108Hz


COMPARISON OF ANALYSIS ● Below time-history graph shows the center displacement of a DML plate,

2 point bending vibration under pulse input


CALCULATING FFT RESPONSE FROM TIME-HISTORY

● Time-history values can be converted to frequency domain via FFT ● Ansys CFD Post can be used to perform FFT operation ● Results compare well with harmonic analysis ● Temperature dependency is applied via WLF functions


CALCULATION PERCENT DAMPING ● Damping calculations can be performed using the frequency domain

results using “Half-power Bandwidth Methods”