Fracture Strength of Silicon Carbide Microspecimens Versus Weibull Size Effect Predictions Noel...

Fracture Strength of Silicon Carbide Microspecimens Versus Weibull Size Effect Predictions

Noel Nemeth

Laura Evans

Osama Jadaan

William Sharpe

George Quinn

Mark Trapp

Glenn Beheim

TMS 2005 Annual MeetingSymposium: Mechanical Behavior of Thin Films and Small Structures:

Fatigue, Fracture, and Reliability of MEMS and Thin Structures I

February 14-17, 2005,

San Francisco, California

Glenn Research Centerat Lewis Field

Outline

ObjectiveWeibull size-effect relationship Specimen design, testing & fractographyRoom-temperature size-effect study of a

polycrystalline SiCRoom-temperature size-effect study of a

single crystal SiC

- Effect of dimensional variation using ANSYS/PDS & CARES/Life

Objective

Examine the capability of Weibull statistics to predict the stochastic strength behavior of brittle SiC structures at the appropriate size scale for designing PowerMEMS. Weibull Size-effect study

Demonstrate the ANSYS Probabilistic Design System (PDS) with NASA CARES/Life

- predict the effect of stochastic variables (component geometry in this case) on the strength response of a structure.

Technical Approach:

• SiC microfabrication technology (Glenn Beheim (PI), RIS0) - Develop deep reactive ion etching (DRIE) process for fabrication of high aspect ratio SiC microstructures.

• Reliability model for SiC microstructures (Noel Nemeth, RSL0) - Test SiC microstructures and analyze using CARES to establish a probabilistic design methodology for microscale turbomachinery fabricated using SiC.

Structures for microengines have high aspect ratios (vertical dimension oretch depth divided by lateral feature size), which makes microfabricationdifficult. Highly directional etch processes are required.

Advanced Micromachining Technology for SiC Microengines

MIT radial inflow turbine, fabricated in silicon.Rotor diameter = 4 mm, Blade span (height) = 200 m,Bearing gap = 10 m (between rotor and stator baseplate).Must hold bearing gap to within 1 m whileetching though 300-m-thick stator baseplate.

What does Weibull behavior & size-effect mean? Material strength displays stochastic behavior.

Strength depends on size, load configuration, and geometry of structure (size effect).

mf

e

mf

m

fA

mf

f

A

dAyx

P

exp1

exp1

),(exp1

0

0

m

e

e

f

f

A

A/1

1,

2,

2,

1,

Size-Effect:

1 2

f is the peak stressfound in the specimen

3.1 mm1.3 mm

0.2mm

1.179 mm

0.675 mm

(a) (b) (c) (d)

0.1 mm

Curved Double-Notch Circular-hole Elliptical-hole

Size-effect study with test specimens designed withvarious levels of stress concentration

Tests a fundamental premise of Weibull theory – that strength increases as the area (or volume) under highest stress decreases.

BaselineGeometry

DRIE Process Parameters

FABRICATION RUN

SUBSTRATE MECHANISM GAS RATE

Batch 3Batch 4

Polycrystalline SiC Chemical / Physical (A) SF6

Ar

0.22 µm/min

Batch 6 Single crystal SiC TMEP (B) etch SF6

passivate C4F8 0.2 µm/min

etch: F ions CFx, SiFxpassivate: CxFy

maskSiC

etch: F ions CFx, SiFx

mask

(B) Time-Multiplexed Etch-Passivate (TMEP)

(A) Chemical/PhysicalEtch mechanisms:

Materials Fabricated with DRIESingle Crystal SiC

• Hexagonal crystal n-type 6H-SiC • TMEP process

Polycrystalline SiC• Cubic -phase • Chemical/physical process

Note side-wall roughness from etching

Notice the roughness and grooving in the notch and all the twist hackle in the single large columnar SiC grain.

Fractography of polycrystalline SiC

The critical flaws were in most cases a combination of the sidewall grooves, which probably acted as stress concentrators, and a favorably oriented large grain.

Specimen n Avg. strength(GPa)

m

(GPa)

Aesw

mm2

Curved 22 0.47 0.16 3.2 0.53 0.184

Notched 26 0.68 0.19 3.8 0.75 0.0143


m

(GPa)

Aesw

mm2

Curved 23 0.47 0.15 3.4 0.53 0.197

Notched 25 0.79 0.28 3.1 0.88 0.0157

Size-effect study of polycrystalline SiC Batches 3 & 4

Both fabricated using the same processing recipe

Batch 3 - Weibull parameters:

Batch 4 – Weibull parameters:

Fracture stresses determined with stress concentration factors computed from FEA using average-specimen dimensions

CARES/Life & FEA used to calculate effective side-wall area Aesw

Batch 3

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.5 1.0 1.5 2.0

Strength (GPa)

Pro

bab

ility

of

Fa

ilure

Curved experimental

Notched Experimental

Curved Weibull Plot

Notched (side-wall)

Batch 4

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.5 1.0 1.5 2.0

Strength (GPa)

Pro

ba

bili

ty o

f F

ailu

re

Curved Experimental


Curved Weibull Plot

Notched (side-wall)

Size-effect study of polycrystalline SiCExperimental data shows a clear size-effect

Size-effect more pronounced in batch 4 (because of better dimensional control (?) )

CARES/Life Weibull predictions over predicted observed size effect

Deviation from continuum behavior (?) - Large grains, deep etching grooves, less well-defined notches

Baseline Baseline

Predicted:Notched Predicted:

Notched

Batch 3 – predictions are based on side-wall area Batch 4 – predictions are based on side-wall area

Size-effect study of single crystal SiC Batch 6 – fabricated 2004

fabricated with an improved process than previous batches 3 & 4

Nickel Mask Side (Top)

Circular-hole specimencross-section

Side-wall

Circular-hole example 1

Circular-hole example 2

Elliptical-hole example 1

Elliptical-hole example 2

Curved t Top Width Bottom Width

Batch 6 127 2 111 3 125 7

Circular hole t Top Width Top Diameter Bottom Width Bottom Diameter

Batch 6 126 2 210 3 91 2 223 7 77 5

Ellipse t Top Width

Top Maj. Axis

Top Min. Axis

Bottom Width

Bottom Maj. Axis

Bottom Min. Axis

Batch 6 127 1 210 4 91 4 42 3 225 7 73 5 26 8

Batch 6

Circular-hole Specimen

Curved Specimen

Elliptical-hole Specimen

2:1 3:1Degree of ellipticity changesfrom top to bottom surface

Top Bottom

Size-effect study of single crystal SiC

Random inputvariables


Finite-ElementModel

Finite-ElementModel

Material• Strength• Material

Properties

Loads• Thermal• Structural

Geometry/Tolerances

Boundary Conditions

• Gaps• Fixity

ANSYS/PDS & CARES/Life (Probabilistic Design System)

Bringing Probabilistic Design into Component life prediction

Probabilistic Life Prediction

Probabilistic Life Prediction

CARESANSYS PDS SimulationsPDS Simulations

Using ANSYS macros, CARES/Life evaluates component failure probability for each trial within an ANSYS/PDS simulation.

Normal distribution assumed for dimensional variationMonte-Carlo method used for PDS simulationIsotropic properties assumed – anisotropy not modeled

baselinem

ifiesw

baselineeswbaselineif P

nA

A1

,,

,,, 1

1

ANSYS/PDS & CARES/Life simulation procedure Simulate the effect of dimensional variation

CARES/Life & FEA calculates effective side-wall area Aesw,i using baseline mbaseline and Aesw,baseline

Random number generator chooses Pf,i

Calculate f,i ;

Result : a collection of n ranked fracture strengths;f,1 , f,2 , … f,i , …, f,n. That can be plotted according to :

n

iP irankedf

5.0,,

For the ith trial within the simulation:

Max. Max.

Elliptical-hole principal stress Circular-hole principal stress

Elliptical-hole ¼ symmetry mesh Circular-hole ¼ symmetry meshFinite element models using average specimen dimensions


m

(GPa)

Curved 19 0.66 0.12 5.9 0.71

Circular hole 19 1.26 0.34 3.8 1.38

Elliptical hole 18 1.53 0.84 2.0 1.74


Specimen # Simulated specimens,n

m

(GPa)

Curved (baseline) --- 6.5 0.71

Circular hole 200 5.9 1.24

Elliptical hole 200 4.1 1.87

Batch 6 - Weibull parameters from experimental data calculated fracture stresses:

PDS simulated data – estimated Weibull parameters:

Simulations for the circular-hole and elliptical-hole specimen types were run. The curved-specimen was used as the baseline. The simulations were generated using a Weibull modulus mbaseline of 6.5, which was the value obtained from the fracture forces for the curved specimen and ,baseline of 0.71 GPa.

Batch 6

0.0

0.2

0.4

0.6

0.8

1.0

0.0 1.0 2.0 3.0 4.0 5.0

Strength (Gpa)

Pro

ba

bil

ity

of

Fa

ilu

re

Curved (avg. dim.)

Circ.-hole (avg. dim.)

Ellip.-hole (avg. dim.)

Circ.-hole (PDS)

Ellip.-hole (PDS)

Curved (Exp. data)

Circ.-hole (Exp. data)

Ellip.-hole (Exp. data)

Batch 6 – Predictions are based on side-wall area


Baseline

PDS Predicted:Circular-hole

PDS Predicted:Elliptical-hole

Weibull plot of elliptical-hole specimen PDS simulation

Batch 6


Experimental data showed a clear size-effect

Good correlation between prediction and experimental data for the circular-hole specimen

CARES/Life Weibull predictions over predicted size-effect for the elliptical-hole specimen

PDS simulation for the elliptical-hole specimen correlated better to the experimental data than the prediction based on average specimen dimensions

Conclusions The strength response of room-temperature SiC polycrystalline and single crystal microtensile

specimens with various stress concentrations was investigated. Strength controlling flaws were assumed to reside on surfaces that were exposed etching. Both materials showed a size-effect. The Weibull distribution tended to over predict the strength of the polycrystalline material but had

better success predicting the strength response for the single crystal material. Large columnar grains and rough side-walls likely caused deviation from continuum behavior and

therefore affected the accuracy of the analysis for the polycrystalline material . The single crystal material did not have (or had less of) these complications because of an

improved fabrication process that produced smoother side-walls. The microtensile specimens had significant specimen-to-specimen variations in dimensions. We

demonstrated with the single crystal SiC specimens that ANSYS-PDS and CARES/Life could be used to account for this variation.

These results tend to support using the Weibull distribution for design and analysis purposes of SiC MEMS – as long as the material can be modeled as a continuum and size-effect extrapolation from a baseline is kept modest.

Acknowledgments:The authors would like to acknowledge NASA Alternate Fuel Foundation Technologies (AFFT),The Ultra Efficient Engine Technology (UEET) program, DOE, and the generous cooperation and support of ANSYS Incorporated.

Extra Material

Room-temperature test setup at JHU

Specimen: SCGN-14 (notched) Polycrystalline SiC

Fracture started at the notch root from a side wall groove that popped in a crack into a large columnar SiC grain (white arrows) that ran the entire length of the specimen from top to bottom.

Notice the roughness and grooving in the notch and all the twist hackle in the single large columnar SiC grain.

260 MPa nominal gage section stress

Fractography of polycrystalline SiCThe primary fracture sources were grooves in the side walls of the specimens

caused by the etching procedure. These grooves tended to spread out and get deeper away from the nickel mask and probably acted as stress concentrators.

Large grains were often (but not always) at the origin. Presumably the large grains were susceptible to a sharp crack popping in from the etch groove, due to cleavage along a preferred crystallographic plane in the SiC. Other grooves had large grains located next to them, but these may have had orientations resistant to fracture.

In short the critical flaws were in many cases a combination of the sidewall grooves and a favorably oriented large grain.

The colored ellipses show the direction of the elongated columnar SiC grains relative to the specimen geometry. Sometimes they were tilted a little bit.

Batch # n t Top Width Bottom Width

Batch 3 22 136 5 104 2 81 6

Batch 4 23 143 3 107 2 93 2

Batch # n t Top Width Top Notch Width

Bottom Width Bottom Notch Width

Batch 3 26 138 3 202 2 156 7 176 6 146 8

Batch 4 25 144 4 207 2 160 4 193 3 156 5

Two fabrication runs 2003 Batch 3 & Batch 4

Both batches fabricated using the same processing recipe

Notched Specimen

Curved Specimen

Size-effect study of polycrystalline SiC

Batch 3

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.5 1.0 1.5 2.0

Strength (GPa)

Pro

ba

bili

ty o

f F

ailu

re

Curved experimental


Curved Weibull Plot

Notched (side-wall)



Baseline

Predicted:Notched

Batch 4

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.5 1.0 1.5 2.0

Strength (GPa)

Pro

ba

bili

ty o

f F

ailu

re

Curved Experimental


Curved Weibull Plot

Notched (side-wall)


Baseline

Predicted:Notched


• Volume flaw & surface analysis• PIA & Batdorf multiaxial models• Fast fracture reliability analysis

•Time-/Cycle-dependent analysis• Multiaxial proof testing• Works with transient FE analysis

CARES/LifePredicting the lifetime reliability of brittle material components

Reliability Evaluation• Component probability of survival• Component “hot spots” - high risk of failure

Parameter EstimationWeibull and fatigue parameter

estimates generated fromspecimen rupture data

Finite Element InterfaceOutput from FEA codes

(stresses, temperatures, volumes)read and printed toNeutral Data Base

CARES/LifePredicting the lifetime reliability of brittle material components

Reliability Evaluation• Component probability of survival• Component “hot spots” - high risk of failure

Parameter EstimationWeibull and fatigue parameter

estimates generated fromspecimen rupture data

Finite Element InterfaceOutput from FEA codes

(stresses, temperatures, volumes)read and printed toNeutral Data Base

Weibull-BatdorfStress-Volume Integration

Weibull-BatdorfStress-Volume Integration

Characterize material• Specimen rupture tests

Predict componentreliability

• General - Free for ANSYS users - works with any kind of ANSYS finite element model – including transient, static, dynamic, linear, non-linear, thermal, structural, electro-magnetic, CFD ..

•Probabilistic preprocessing - Allows large number random input and output parameters - modeling uncertainty in input parameters – Gaussian, log-normal, Weibull… - random input parameters can be defined as correlated data

• Probabilistic methods - Monte Carlo Direct & Latin Hypercube Sampling - Response Surface Method Central Composite & Box-Behnken Designs

• Probabilistic postprocessing - Histograms - Cumulative distribution functions - Sensitivity plots

• Parallel, distributed computing

ANSYS/PDS (Probabilistic Design System)

Capabilities



Finite-ElementModel

Finite-ElementModel

Material• Strength• Material

Properties

Loads• Thermal• Structural

Geometry/Tolerances

Boundary Conditions

• Gaps• Fixity

ANSYS/PDS (Probabilistic Design System)

Bringing Probabilistic Design into Finite Element Analysis

PDS SimulationsPDS Simulations• Deformations• Stresses• Lifetime

(LCF,...)

Statistical analysis of output parameters

Statistical analysis of output parameters

Extensive fractographic analysis was done on several specimens of each shape from the first processing run of the polycrystalline material – designated batch 3. The detailed examination lead to the following observations for the polycrystalline material:

Fractography of Polycrystalline SiC

• The primary fracture sources were grooves in the side walls of the specimens caused by the etching procedure. These grooves tended to spread out and get deeper away from the nickel mask and probably acted as stress concentrators.

• Large grains were often (but not always) at the origin. When this occurred, the large grain cleavage was approximately at right angles to the applied stress. Presumably the large grains were susceptible to a sharp crack popping in from the etch groove, due to cleavage along a preferred crystallographic plane in the SiC.

• There are a lot of etch grooves along the gage section of a specimen. Some probably connected to a region of normal SiC microstructure with fine grains. Other grooves had large grains located next to them, but these may have had orientations resistant to fracture. Other grooves had large grains connected to them, and if oriented the right way, a cleavage crack could propagate into the grain.

In short the critical flaws were in many cases a combination of the sidewall grooves and a large grain.

Fracture Strength of Silicon Carbide Microspecimens Versus Weibull Size Effect Predictions Noel...

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