Applied stress [MPa]

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Load Sharing in Tungsten Continuous Fiber Reinforced Kanthal MMC’s

B. Clausen

^†

, M.A.M. Bourke

^‡

and E. Üstündag

^†

†

Materials Science, California Institute of Technology

‡

MST-8, Los Alamos National Laboratory

Annual Meeting New Orleans, Louisiana February 11-15, 2001

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Outline

z Tungsten Continuous Fiber Reinforced Kanthal Metal Matrix Composites

z Neutron Diffraction

z Finite Element Modeling

z Self-consistent Modeling

z Conclusions

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Metal Matrix Composites (MMC)

z

Thermal Residual Stresses (TRS)

z Influence mechanical behavior

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Tungsten Continuous Fiber Reinforced Kanthal MMC

z Kanthal has good high temperature properties

z Inherent corrosion/oxidization protection by forming an alumina case

z 73.2% Fe, 21.0% Cr, 5.8% Al and 0.04%C

z Tungsten fibers increase creep resistance

z Samples

z Monolithic Kanthal.

• Reference sample. No TRS.

z 10, 20 and 30 volume percent Tungsten fibers

• Various levels of TRS due to the differences in CTE

• Different yield points in tension due to the TRS z Manufacture technique

z Arc-sprayed, NASA Lewis, Tufts University

z Mixed cubic and hexagonal stacking observed

10%

20%

30%

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Neutron Diffraction (ND)

λ = 2dsinθ

z

TOF technique: Measure diffracted intensity as function of time-of-flight

z

Differences in lattice spacing => Elastic Lattice Strain

z

Unique method to non-destructively determine internal strains in bulk samples

z

Phase specific measurements - ideal for composites

Ki Q Kd

d 2θ

0 1

0

0 = −

= −

hkl hkl hkl

hkl el hkl

hkl d

d d

d

ε

d

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Neutron Diffraction

+ 90°

Detector Bank Incident Neutron Beam

- 90°

Detector Bank Tensile Axis

Q_⊥ Q_||

z

Neutron Powder Diffractometer (NPD) at LANSCE

z

Schematic set-up for in-situ loading measurements

z

Measurement time is about 2-4 hours per load level

z

Measure elastic strains in two directions simultaneously

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Neutron Diffraction

z The NPD load frame

z 48 kN maximum load in tension or compression

z Mirror furnace, 350°C maximum temperature

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Neutron Diffraction

SMARTS: Spectrometer for Materials Research at Temperature and Stress

z

SMARTS; First neutrons by May 2001

z Order of magnitude lower count times than NPD (10-20 min)

z 1 cubic millimeter gauge volume

z Combined ±250kN, 1500°C and translation/rotation

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Neutron Diffraction

Perpendicular Parallel

z Monolithic Kanthal

z Random (texture index is 1.04)

z 30% Tungsten fibers

z Kanthal matrix is still random (1.05)

z The fibers are highly textured (5.87)

z Rietveld refinement provides an empirical lattice elastic mean phase (LEMP) strain

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Neutron Diffraction

z

Measured macroscopic stress/strain curves

z

10 and 20% N/A due to extensometer problems

z

Difference in curves?

z

Young’s modulus?

z

Yield point?

0 100 200 300 400 500 600

0.0 0.5 1.0 1.5 2.0

Macro, Neat Macro, 30%

Ap plied s tress [ M Pa]

Total strain [%]

Macro Measurements

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Neutron Diffraction

z Measured LEMP strains

z Monolithic Kanthal. The LEMP strain is not linear in the plastic region due to build-up of intergranular strains.

10%. Co-deformation until 200 MPa.

Load sharing as Kanthal becomes plastic.

20%. Co-deformation until 100 MPa.

30%. Region with co-deformation is very limited (about 50 MPa).

z Initial stiffness; Appears to be the same in all samples

z Elastic region ?

z Neutron diffraction is the only tool that can provide us with this type of

0 1000 2000 3000 4000 5000

data

0 100 200 300 400 500 600

Kanthal, Neat Kanthal, 10%

Tungsten, 10%

Kanthal, 20%

Tungsten, 20%

Kanthal, 30%

Tungsten, 30%

Elastic lattice strain [µε]

Ap pl ied s tre ss [ M Pa ]

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Finite Element Modeling (FEM)

z 3D model to accommodate the “out-of-plane” loading

z Unit-cell assumptions

z Outer surfaces with x=constant or y=constant are kept as planes with x=constant or y=constant, respectively

z Plane strain assumption

z Outer surfaces with z=constant are kept as planes with z=constant.

FE Model for 30 volume percent Tungsten fibers

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FEM Compared to ND

0 1500 3000 4500

Elastic lattice strain [µε]

Kanthal 30% W

0 1500 3000 4500

K, ND W, ND K, ∆T=630 W, ∆T=630 Elastic lattice strain [µε]

Kanthal 20% W

0 1500 3000 4500

0 100 200 300 400 500

Applied stress [MPa]

Kanthal 10% W

z Previous residual stress measurements indicate a “stress-free” temperature of 650°C

z Material behavior of Kanthal from tensile test; Tungsten fibers assumed fully elastic

z Qualitative Agreement:

z Residual strains, Yield point (region of co-deformation), Same ∆T for all volume fractions

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FEM Compared to Macro Measurements

0 100 200 300 400 500

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Macro, Neat Macro, 30%

Total strain [%]

Macro Measurements

0 100 200 300 400 500

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Neat, ∆T=630 10%, ∆T=630 20%, ∆T=630 30%, ∆T=630

Total strain [%]

Finite Element Modeling

z Initial slope is similar for all

z TRS induces micro-yielding that reduces apparent stiffness

z At least measured neat and 30% behavior agrees with FEM

z Waiting for independent tensile measurements on all volume fractions

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Self-consistent model (SCM)

z

Material parameters

z Single crystal stiffnesses and coefficients of thermal expansion

z Description of texture with discrete set of grain orientations

z Crystal structure, slip (and twinning) systems

z CRSS and hardening law

z

Model Assumptions

z Eshelby inclusion theory

z HEM properties equal to

weighted average of the grains

z

Output

z Direct comparison with neutron diffraction measurements

z Averages over grains sets representing reflections

σ σ σ

c

σ

c

HEM

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Single Crystal Elastic Constants

z Assumption of calculation of macroscopic moduli from single crystal values

z Reuss-Voigt

z Bollerath, Hauk & Müller

z de Wit (based on Eshelby theory)

z Crystal symmetry

z Slopes gives diffraction elastic constants

z E_hkland ν_hkl

-1000 -5000 0 500 1000 1500 2000 100

200 300 400

110, T 200, T 211, T 310, T 222, T

110, L 200, L 211, L 310, L 222. L

Monolithic Kanthal, elastic region

z Single crystal elastic stiffnesses from neutron diffraction data

z T. Gnäupel-Herold, P.C. Brand and H.J. Prask, J. Appl. Cryst., 1998, vol. 31, pp. 929-935

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Polycrystal versus Continuum Constitutive Description

Experimental Data

Single Crystal Properties and Deformation Mechanisms

Polycrystal Texture

Polycrystal Model Constitutive Response

Simulation of Component Loading or Forming Operations using

Finite Element Codes

Continuum mechanics

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SCM Compared to ND

0 100 200 300 400 500 600

0.0 0.5 1.0 1.5

Measured

{110}<111> slip only {211}<111> slip only {321}<111> slip only

Total strain [%]

Macroscopic stress/strain curves

z Macroscopic stress/strain curve for monolithic Kanthal

z Used to fit the macro result of the model to the measurements

z Enables direct comparison on the micro level

z Different sets of active slip systems

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SCM Compared to ND

0 1000 2000 3000 4000

0 100 200 300 400 500 600

{110}<111> slip only

0 1000 2000 3000 4000

110, ND 200, ND 211, ND 310, ND 222, ND 321, ND 420, ND

110, EPSC 200, EPSC 211, EPSC 310, EPSC 222, EPSC 321, EPSC 420, EPSC

0 1000 2000 3000 4000

z Variation of plastic anisotropy depending on active slip systems

z Best agreement with only one set of active systems is {321}<111>

z Parameter study

z Could indicate relative level of activity on different slip systems

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Conclusions

z

Neutron diffraction measurements

z Unique ability to measure in-situ phase strains in MMC’s during loading

z Directly applicable for model validation on a microstructural level

z

FEM predictions show qualitative agreement with the measurements

z Micro yielding in composites; residual strains

z Model development

• Unit cell assumptions; hexagonal, cubic, coaxial, multi fiber, …

z

SCM predictions show qualitative agreement with the measurements

z Monolithic Kanthal only

• Quantitative agreement in the elastic region

• Plastic anisotropy depends on set(s) of active slip systems