Internal Stresses in Tungsten Fiber Reinforced Bulk Metallic Glass Matrix
Composites
B. Clausen
†, S.-Y. Lee
†, E. Üstündag
†, and M.A.M. Bourke
‡†Department of Materials Science, California Institute of Technology
‡Materials Science and Technology Division, Los Alamos National Laboratory
Supported by DARPA and NSF-MRSEC
Outline
z BMG matrix tungsten fiber composites
z Neutron diffraction
z Finite element modeling
z Results
z Conclusion
BMG matrix tungsten fiber composites
z
Vit1: Zr
41.2Ti
13.8Cu
12.5Ni
10Be
22.5z
BMG/Tungsten fiber composites
z
Same ultimate stress as monolithic Vit1
z
Large increase in ductility
z
Knee in stress strain curve as tungsten fibers yield
R. D. Conner, R. B. Dandliker and W. L. Johnson, Acta Mater., vol. 46(17), pp. 6089-6102, 1998
BMG matrix tungsten fiber composites
20% (21.0%) 40% (42.4%) 60% (61.9%) 80% (84.2%)
z
Measured volume fractions deviates slightly compared to nominal volume fractions
z
“Agglomeration” seen for all volume fractions
z
“Stacking faults” seen for the 80% sample
Neutron diffraction
Incident Neutron Beam
+90° Detector Bank
-90° Detector Bank
Q⊥
Q
Compression axis
z Spectrometer for MAterials Research at Temperature and Stress (SMARTS)
z Schematic set-up for in-situ compression loading
z Measurement time is about 10-20 minutes per load level
z Measure elastic strains in two directions simultaneously
z Bulk measurement contrary to conventional X-ray measurements
Neutron diffraction
λ = 2dsinθ
z Fixed λ; Reactor (steady state). Measure intensity as function of angle
z Fixed θ: TOF (spallation). Measure intensity as function of time-of-flight
z Differences in lattice spacing => Only Elastic Lattice Strain of Crystalline Phase Ki Q Kd
d 2θ
0 1
0
0 = −
= −
hkl hkl hkl
hkl el hkl
hkl d
d d
d ε d
Neutron diffraction
Parallel Perpendicular
z Diffraction patterns from BMG tungsten fiber composite sample (80%)
z Highly textured fibers; hh0 texture for wire drawn bcc metals
z Good statistics from short count times
z Rwp ≈ 6-8%, strain error bar ≈ 15 µε
Finite element model input
z
BMG
z Young’s modulus: 96 GPa
z Poisson’s ratio: 0.36
z Yield stress (Mohr-Coulomb):
τc = 946 - 0.04σn [MPa]
z No hardening
z
Tungsten
z Young’s modulus: 410 GPa
z Poisson’s ratio: 0.28
z Yield stress (Von Mises):
σy = 1305 [MPa]
z Hardening as shown in plot
-2000 -1500 -1000 -500 0
-1.6 -1.2 -0.8 -0.4 0
Von Mises yield stress [MPa]
Plastic strain [%]
Hardening of tungsten fibers
R. D. Conner, R. B. Dandliker and W. L. Johnson, Acta Mater., vol. 46(17), pp. 6089-6102, 1998
Lewandowski J. J. and Lowhaphandu P., Phil. Mag. A., in print
A. Saigal and G.G. Leisk, Mat. Sci & Eng. A, vol. 237, pp. 65-71, 1997
Finite element model
z Full 3D model due to loading along fibers
z Unit cell model
z Plane strain by keeping planes perpendicular to fibers plane
z Brick 2nd order elements
z Hexagonal stacking in all models to accommodate high volume fractions
z Thermal cooling cycle
z Same ∆T as previously found to give good comparison with measured thermal residual stresses (same for all volume fractions)
20% Mesh 80% Mesh
Thermal residual strains
-1000 -500 0 500 1000 1500 2000
0 0.2 0.4 0.6 0.8 1
W, L, ND W, T, ND W, L, FEM W, T, FEM BMG, L, FEM BMG, T, FEM
Thermal residual strain [µε]
W volume fraction
Neutron measurements and FEM calculations
-600 -400 -200 0 200 400
0 0.2 0.4 0.6 0.8 1
W, L, FEM W, T, FEM BMG, L, FEM BMG, T, FEM
Thermal residual stress [MPa]
W volume fraction FEM calculations
0 5 10 15 20
-200 -100 0 100 200 300 400 500 αW
αBMG
Coefficient of linear expansion (CTE) [x10-6 ]
Temperature [°C]
CTE used in the FEM calculations
z
Measured and calculated thermal residual stresses
z Pure elasticity
z Good agreement for the tungsten fibers
z
Predict thermal residual stresses in both phases
D. Dragoi, E. Üstündag, B. Clausen and M. A. M. Bourke, Scripta Mater., vol. 45, pp. 245-252, 2001 Y. He, R. B. Schwarz and D. G. Mandrus, J. Mater. Res., vol. 11, p. 1836, 1996
Finite element model
20% Von Mises 20% Von Mises Matrix only
80% Von Mises 80% Von Mises Matrix only
z Von Mises stresses at highest load level (1000MPa for 20, 1600MPa for 80%)
z Stress concentration for the 80% - precursor for shear band formation
z No appreciable variation of Von Mises stress in fibers
Measured lattice strains and predicted stresses, 20% sample
ND and FEM for W fiber ⇒ FEM, Load partitioning
-1000 -800 -600 -400 -200 0
-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3
ND FEM
Applied Stress [MPa]
Strain [%]
2180 µε 2665 µε
-1500 -1000 -500 0 500 1000 1500
-1 -0.8 -0.6 -0.4 -0.2 0
Macro BMG W
Phase stress [MPa]
Macro strain [%]
-285 MPa 1065 MPa
z Good agreement with loading data; Residual strain is overestimated
z Calculated loading and unloading slopes are slightly shallower than the measured slopes
Measured lattice strains and predicted stresses, 40% sample
ND and FEM for W fiber ⇒ FEM, Load partitioning
-1000 -800 -600 -400 -200 0
-0.4 -0.3 -0.2 -0.1 0 0.1
ND FEM
Applied Stress [MPa]
Strain [%]
700 µε
790 µε
-1500 -1000 -500 0 500
-0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
Macro BMG W
Phase stress [MPa]
Macro strain [%]
-230 MPa
310 MPa
z Good agreement with loading data; Reasonable agreement with residual data
z Good agreement with measured slopes
Measured lattice strains and predicted stresses, 60% sample
ND and FEM for W fiber ⇒ FEM, Load partitioning
-1600 -1400 -1200 -1000 -800 -600 -400 -200 0
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2
ND FEM
Applied Stress [MPa]
Strain [%]
115 µε and 1110 µε
150 µε and 1085 µε
-2000 -1500 -1000 -500 0 500
-1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0
Macro BMG W
Phase stress [MPa]
Macro strain [%]
-700 MPa 425 MPa
-90 MPa 63 MPa
z Overestimates strains at high load; Good agreement for residual data
z Good agreement with measured slopes
Measured lattice strains and predicted stresses, 80% sample
ND and FEM for W fiber ⇒ FEM, Load partitioning
-1600 -1400 -1200 -1000 -800 -600 -400 -200 0
-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1
ND FEM
Applied Stress [MPa]
Strain [%]
246 µε
222 µε
-2000 -1500 -1000 -500 0 500
-1 -0.8 -0.6 -0.4 -0.2 0
Macro BMG W
Phase stress [MPa]
Macro strain [%]
-480 MPa 90 MPa
z Good agreement with both loading and residual data
z Good agreement with measured slopes
Yielding in BMG
0 500 1000 1500 2000 2500
0 1 2 3 4 5 6
20%
40%
60%
Applied compressive stress [MPa] 80%
Compressive strain [%]
z Predicted yield stress in the BMG using Mohr-Coulomb yield criteria
z All samples predicted to have about the same ultimate stress
z Measured ultimate stress varies as a function of fiber volume fraction
Lewandowski J. J. and Lowhaphandu P., Phil. Mag. A., in print
R. D. Conner, R. B. Dandliker and W. L. Johnson, Acta Mater., vol. 46(17), pp. 6089-6102, 1998
Conclusions
z
Neutron diffraction
z
10-20 minutes count times gives adequate statistics
z
Finite element modeling
z
Predictions of elastic strains in the tungsten fibers are in good agreement with the diffraction data
⇒
FEM provides phase stresses, residual stresses and load partitioning
z
The Von Mises yield stress used in FEM is the same for all volume fractions and there is good agreement with the onset of non-linearity in the diffraction data for all volume fractions
⇒
