Simulation of Thermal Effects for the Analysis of Micro Laser Assisted Machining

By

Saurabh R Virkar

Under guidance of Dr. John A Patten

ICOMM 2010

Venue: University of Wisconsin, Madison

Introduction:

Silicon Carbide (SiC) is an advanced engineered ceramic and an alternative to semiconducting Silicon (Si) for operation at elevated temperatures and high power applications. Some of SiC’s beneficial properties include: chemical resistance, high temperature resistance, extreme hardness and high stiffness

Hardness of SiC: 26 GPa

The machining of SiC is difficult due to its high hardness and brittle nature.

Ductile mode µ-LAM has been studied to replace grinding and polishing processes and to increase the material removal rates and maintaining the workpiece surface quality

In µ-LAM, the laser beam passes through the diamond tool, thus heating the surface just below the tool tip in the chip formation zone

SiC

Schematic of µ-LAM

Diamond tool

High Pressure Phase Transformation

The ductile material removal can be attributed to a High Pressure Phase Transformation (HPPT) at the tool-chip interface and the resultant phase is metallic or amorphous

The HPPT occurs due to contact between the sharp tool and workpiece at or below critical depth of cut, i.e., below the ductile to brittle transition

Why Simulations?

Silicon Carbide (SiC) is very expensive semiconductor Measurement of temperatures at nano-scale is practically not

possible Also the rate of heat transfer and pressures on tool and

workpiece can be studied There is a metallic phase at tool chip interface due to high

pressure phase transformation

Software used: AdvantEdge version 5.4 Commercial software for machining solutions in metals

developed by Third Wave Systems Inc.

Objective:

To simulate different heating conditions over a temperature range for studying the laser heating effect

To study the change in chip formation, cutting forces and pressures with changes in heating/temperature conditions

Mathematical model:

Drucker Prager Yield Criterion:

…(1)

…(2)

Where I1 is first invariant of stress tensor

…(3)

Where J2 is second invariant of deviatoric stress tensor

Hence initial yield stress is given by:

…(4)

For uniaxial stress, σ2 = σ3 = 0 and also σc = σ1 = H= 26 GPa

σt = H/2.2 = 11.82 GPa (for ceramics)

Hence, К= 16.25 GPa and Drucker-Prager coefficient (α) = 0.375

213

232

2212 6

1 J

ct

ct

2

03 12 IJ

3211 I

Simulation Model

Material properties Value UnitsElastic Modulus, E 330 GPaPoisson’s ratio 0.212 -Hardness, H 26 GPaInitial yield stress, σ0 16.25 GPa

Reference plastic strain, ε0p 0.049 -

Accumulated plastic strain, εp 1 -Strain hardening exponent, n 50 -

Low strain rate sensitivity exponent, m1 100 -

High strain rate sensitivity exponent, m2 100 -

Threshold strain rate, εtp 1E7 sec-1

Drucker-Prager coefficient (DPO) 0.375

Workpiece Material properties:

Thermal Softening Curve

Properties ValueThermal Conductivity (W/cm K) 3.21*Thermal Cutoff temperature ( C)⁰ 1500*Melting temperature ( C)⁰ 2830Initial reference temperature ( C)⁰ 20

* Note: The values for temperature from 20° C to 1500° C which is thermal cutoff temperature are estimated based on various references. The value for melting temperature of SiC is also estimated from a reference.

Workpiece Thermal properties:

Tool parameters and geometries:

Cutting Edge Radius, r, (nm) 100

Rake angle, α - 45º

Relief angle, β 5º

Width of tool (µm) 20

Tool geometry:

Thermal Conductivity, W/m C⁰ 1500Heat Capacity, J/kg C⁰ 471.5Density, kg/m³ 3520Elastic Modulus, GPa 1050Poisson's ratio 0.2

Tool Properties:

The -45 rake angle creates a high pressure sufficient to accommodate the HPPT, ⁰thus the chip formation zone is conducive for ductile deformation

Simulated Thermal Effect Conditions

Tooltip Boundary Condition Rake and Clearance face Heated Boundary Condition Workpiece Boundary Condition

Tooltip Boundary Condition

A thermal boundary condition was provided on the tool tip about 2µm on rake and clearance face from cutting edge

Workpiece Boundary Condition

A thermal boundary was provided on the workpiece top surface

Simulation parameters

Parameters Values

Feed (nm) 500

Cutting speed (m/s) 1

Width of cut (mm) 0.02

Co-efficient of friction 0.3

• Temperature range of the simulation work:20° C, 700° C, 1500° C, 2200° C and 2700° C where 1500° C is the thermal cutoff point in the material model.

• From 20° C till 1500° C, the thermal softening curve has a 3rd order polynomial fit in the material model

• From the thermal cutoff point (1500° C) till melting point (2830° C) the curve is linear

Constraints:

AdvantEdge does not provide for the direct incorporation of the laser heat source, thus the heating effect is modeled with these thermal conditions

For this study, the crystalline dependency of the brittle behavior of SiC is not included in the model

Note: The temperature scale changes in each figure, as the minimum temperature is set slightly above and below the boundary condition temperature

Tooltip Boundary Condition at 20° C

Tooltip Boundary Condition at 2200° C

Rake and Clearance face at 20° C

Rake and Clearance face heated at 2200° C

Workpiece Boundary Condition at 20° C

Workpiece Boundary Condition at 2200° C

Results:

Temperatures (° C)

Cutting Force (mN)

Thrust Force (mN)

Chip formation Pressure (GPa)

Tooltip Boundary Condition simulation

20 500 900 Yes 50

700 460 890 No 46

1500 370 610 No 37

2200 200 300 No 20

2700 80 130 Yes 8

Workpiece Boundary Condition simulation

20 470 1040 Yes 47

700 450 1000 No 45

1500 390 570 No 39

2200 200 260 No 20

2700 30 40 No 3

Toolface Boundary Condition

20 500 1060 Yes 50

700 450 1000 No 45

1500 380 620 No 38

2200 200 300 No 20

2700 60 90 Yes 6

Force plots (All simulation conditions)

20 700 1500 2200 27000

200

400

600

800

1000

1200

Cutting and Thrust Forces

Tooltip Cutting force (mN)

Tooltip Thrust force (mN)

Toolface BC Cutting Force (mN)

Toolface BC Thrust force

WBC Cutting Force (mN)

WBC Thrust force (mN)

Temperature (° C)

For

ces

(mN

)

Cutting Pressure Plots (All Boundary Conditions)

20 700 1500 2200 27000

10

20

30

40

50

60

Cutting Pressures

Tooltip Cutting Pressure (GPa)Toolface BC Cutting Pressure (GPa)WBC Cutting Pressure (GPa)

Temperature (° C)

Cut

ting

Pre

ssur

e (G

Pa)

Conclusions:

The thermal effects successfully simulated the laser heating effect

Decrease in cutting forces and pressures is studied with increase in temperature

The change in chip formation due to change in temperature above and below the thermal cutoff point is studied is studied

On-going work:

To determine the effect of interaction between temperature and compressive stress on the cutting forces and pressures from room temperature till melting point of SiC

3D scratch test simulations for comparison with experiments

Acknowledgement

• Support from NSF (CMMI-0757339)

• Support from ThirdWave Systems