DTIC ADA495119: High-Temperature Material Lattice Combining Low Thermal Expansion, High Stiffness and Strength

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by  Defense Technical Information Center

High-Temperature Material Lattice Combining Low Thermal
Expansion, High Stiffness and Strength

by

Pamela L. Fetchko

A dissertation proposal submitted in partial fulfillment of the requirements for the
degree of Master of Science
(College of Engineering – Department of Materials Science and Engineering)
in the University of Michigan
2008
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High-Temperature Material Lattice Combining Low Thermal Expansion,
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High Stiffness and Strength
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Abstract

Low or near zero thermal expansion is a desirable property for structures undergoing high
heat fluxes and thermal stresses. A number of lattice concepts have been investigated to solve
this issue. Unfortunately they do not display high stiffness and strength, are too complicated to
allow for ease of fabrication, or are not proven at high enough temperatures from practical use on
extreme temperature environments. A bi-material lattice that combines low or near zero thermal
expansion with high stiffness over a wide temperature range has been introduced and discussed
in previous research. This concept was effectively modeled and tested using an aluminum alloy,
7075-T6, and a titanium alloy, Ti-6Al-4V. The main objective of this research is to prove this
bi-material lattice concept can be applied to higher temperature combinations of material capable
of 1000oC while still maintaining high strength and stiffness. Criteria for materials selection are
presented. Three configuration concepts are analyzed via finite element calculations. Results
show that the bi-material lattice can be used with high temperature materials up to 1000oC but
some adjustments in topology are required to achieve that temperature in a Ni – Nb metallic
lattice.

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Table of Contents

List of Figures……………………………………………………………………………………..5
List of Tables……………………………………………………………………………………...6
1. Introduction……………………………………………………………………………………7
2. Design Analysis……………………………………………………………………………...10
2.1. Topology Concept………………………………………………………………………10
2.2. Materials Selection…………………………………………………………...…………12
2.3. Modeling/Simulation……………………………………………………………………15
2.4. Cell Geometry...…………………………………………………………………………18
3. Results………………………………………………………………………………………..18
3.1. Dove-tail configuration………………………………………………………………….18
3.2. Keyhole configuration…………………………………………………………………..19
3.3. Rounded dove-tail configuration………………………………………………………..21
4. Conclusions…………………………………………………………………………………..23
5. Future Work………………………………………………………………………………….24
6. References…………………………………………………………………………………....25
7. Figures………………………………………………………………………………………..27
8. Appendix A…………………………………………………………………………………..43

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List of Figures
Figure 1: Curved rib diagram similar to one used by Lakes………………………………….….27
Figure 2: Lakes lattice for thermal expansion via lateral bending displacement…………….…..27
Figure 3: Sigmund & Torquato’s zero expansion lattice created by topology optimization
methods……………………………………………………………………………………….….27
Figure 4: Steeves et al. topology concept and calculations……………………………………...28
Figure 5: Schematic illustration of the triangular zero-thermal expansion lattice concept……...28
Figure 6: Pin-jointed lattice used in the study by Steeves and co-workers……………………...29
Figure 7: Coefficient of thermal expansion vs. temperature comparison of high temperature
materials………………………………………………………………………………………….29
Figure 8: Specific Strength vs. Temperature comparison among several alloy classes…………30
Figure 9: Comparison chart of nickel-cobalt alloys showing yield strength vs temperature……30
Figure 10: Comparison chart of nickel-cobalt alloys showing coefficient of thermal expansion
vs. temperature………………...…………………………………………………………………31
Figure 11: Comparison chart of Haynes 188 and Wah-Chang C-103 showing yield strength vs.
temperature………………………………………………………………………………………31
Figure 12: Comparison chart of Haynes 188 and Wah-Chang C-103 showing coefficient of
thermal expansion vs. temperature………………………………………………………………32
Figure 13: Binary phase diagram of nickel-niobium interdiffusion within Haynes 188………...32
Figure 14: Boundary conditions applied to the lattice model in ABAQUS simulation….……...33
Figure 15: Stress-strain curves for Haynes 188 at 1000oC………………………………………33
Figure 16: Stress-strain curve for Wah-Chang C-103 at 1000oC……………………………..…34
Figure 17: Dovetail configuration of lattice cell…………………………………………………34
Figure 18: Highest stress concentrations in Haynes 188………………………………………...35
Figure 19: Highest stress concentrations in Wah-Chang -103…………………………………..35
Figure 20: Mises stresses in dovetail configuration at 200oC……………………………………36
Figure 21: Overall displacement, U, of dovetail configuration at 1000oC………………………36
Figure 22: Keyhole configuration of lattice cell…………………………………………………37
Figure 23: Mises stresses in keyhole configuration at 300oC……………………………………37
Figure 24: Overall displacement, U. of keyhole configuration at 1000oC…………………….…38
Figure 25: Rounded dovetail configuration of lattice cell…………………………………….....38
Figure 26: Mises stresses for rounded dovetail at 1000oC……………………………………….39
Figure 27: Equivalent plastic strain for rounded dovetail at 1000oC…………………………….39
Figure 28: Displacement of rounded dove configuration at 1000oC…………………………….40
Figure 29: Stress comparison of Haynes 188 for three configurations…………………………..40
Figure 30: Stress comparison of Wah-Chang C-103 for three configurations…………………..41
Figure 31: Phase fraction diagram of niobium-nickel interdiffusion within Haynes 188……….42

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List of Tables
Table 1: Chemical composition percentage of Wah-Chang C-103………………………...……13
Table 2: Chemical composition percentage of Haynes 188…………………………………......14
Table 3. Material properties for the candidate alloys used in the lattice model…………………15
Table 4: Ramberg-Osgood coefficients for Haynes 188 and Wah-Chang C-103……………….17
Table 5: Highest stress values for dovetail configuration………………………………………..18
Table 6: Highest stress values for keyhole configuration………………………………………..20
Table 7: Highest stress values for rounded dovetail configuration………………………………22
Table 8: Chemical composition of comparison alloys……………………………….…………..43

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1. Introduction
Structural systems that experience extreme temperature variations during service in space
applications [1-3] are subject to high thermal stresses that lead to thermo-mechanical fatigue of
components. As the material is heated and cooled cyclically, the expansion and contraction of
the material results in thermo-mechanical stresses that can eventually lead to failure of the
material and thus the structure. Hypersonic vehicles are of particular interest in this research
because the high speeds at which they operate lead to high thermal loads that in turn induce high
stresses. Since future hypersonic vehicles are intended to be used more than once, they will be
continuously subjected to thermal cyclic loading. This constant loading and unloading can lead
to thermo-mechanical fatigue if an inadequate material is used. Therefore, a low thermal
coefficient is necessary to prevent the occurrence of high thermal stresses within the material as
it heats up. However, high stiffness and strength are also required to support bending moments
and in-plane stresses that can occur in these structures during normal service conditions. Such a
combination of material properties is rarely found in a single material. For instance, metals add
weight to the structure, which is a hindrance for aerospace applications, while ceramics are
brittle and thus limit the amount of strain structures can handle before fracture.
Composite materials have long been studied in order to combine two or more materials
with differing mechanical properties that together could achieve a desired thermal property, such
as lower thermal expansion or greater stiffness. A number of researchers [4-6] have investigated
manipulating the coefficient of thermal expansion of both laminate and particle-reinforced
composites to attain negative and positive values that could exceed a single material’s
possibilities. However, zero-coefficient of thermal expansion is difficult to attain with these
types of composites.
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Lakes [7] investigated a two constituent composite in which each constituent had a
different thermal expansion coefficient and empty space was assumed to exist within the
structure. This empty space allowed the structure itself to experience higher thermal expansion
coefficients than either constituent independently. Depending on the placement of each
constituent in the composite, the overall thermal expansion could be either positive or negative.
This concept was demonstrated using a curved rib, as shown in Figure 1. If the higher thermal
expansion constituent is on the convex side an increase in temperature will cause the rib to curve
further and if it was on the concave side it will tend to straighten.
Lakes proved the importance of including void space in composites in order to alter the
thermal expansion of the composite beyond the rule of mixtures. He used a lattice, as shown in
Figure 2, that relied on lateral bending as demonstrated in the curved rib concept. The only
drawback with this configuration is that the material has low stiffness and strength since the
expansion is based on the bending of its constituents.
In the Lakes’ configuration, the structure would experience either positive or negative
thermal expansion; Sigmund and Torquato [8-9] furthered the concept by considering a net
thermal expansion of zero in the overall structure. They recognized the need for low thermal
expansion materials for structures experiencing large temperature fluctuations and thus also
considered the stiffness of their configurations. They used a numerical topology optimization
method based on previous work by Sigmund [10-11], Guedes and Kikuchi [12], and Bensoe et al
[13] to determine how each constituent and void spaces should be distributed. This same model
was later used by Sigmund [14] to create two-dimensional and three-dimensional composite
exhibiting a higher bulk modulus and a lower shear modulus than previous composite
configurations. Choosing to use a three constituent composite, two phases and a void phase as in
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Lakes’ research, their topology for the zero thermal expansion configuration is shown in Figure
3.
Topology optimization is defined by Patel et al [15] as “an iterative process that
determines the best arrangement of a limited volume of structural material within a given spatial
domain so as to obtain optimal mechanical performance of the design concept.” His paper offers
a concise comparison of three different types of methods. The topology optimization method
used by Sigmund and Torquato optimizes the distribution of phases in a configuration in order to
achieve desirable thermoelastic properties by solving finite-element problems where material
type is periodically changed within the finite elements until the appropriate overall mechanical
properties are achieved. In this case, material type and density was changed within each of the
finite elements in order to change the strain energies so that uniform strain energy could be
achieved. While it was proven to be successful in configuring optimal structures, it was also
shown that there is a tradeoff between the topology of the structure and the overall bulk modulus
of the material. Since the two materials used should have differing thermal expansion but similar
stiffness values, for a net thermal expansion of zero, the bulk modulus was found to be
approximately 7% of the bulk modulus of the constituents. Such a low bulk modulus means that
the configuration itself has a low resistance to compression and thus low overall stiffness under
compression loading conditions. In addition, the structures that were generated were too
complex to allow for ease of manufacturing of near net shape components.
Steeves [16] and co-workers explored a zero or low expansion lattice concept that was
not only capable of high strength and stiffness but also easy to manufacture. Their approach also
takes into account void spaces within a lattice to acquire the desired thermoelastic properties
while still maintaining the requisite mechanical strength of the of material structure. They
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