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Reconfiguring Steel Structures: Energy Dissipation and Buckling Mitigation Through the Use of Steel

Foams

Principal Investigators:

Sanjay R. Arwade (University of Massachusetts)

Jerome F. Hajjar (Northeastern University)

Benjamin W. Schafer (Johns Hopkins University

Project Proposal

Authors:

Sanjay R. Arwade

Jerome F. Hajjar

Benjamin W. Schafer

Date: 12/6/10

Grants: CMMI-1000334, CMMI-1000167, CMMI-0970059

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Collaborative Research: Reconfiguring Steel Structures: Energy Dissipation and Buckling Mitigation Through the Use of Steel Foams

1 Introduction

Steel buildings and bridges are designed such that elastic or inelastic buckling occurs in key components during major loading events (AISC 2005a, 2005b; AISI 2007; AASHTO 2009). However, such buckling has complications such as (a) low-cycle fatigue failures in the buckling components (Uriz and Mahin 2004), (b) requirements for expensive local stiffening to control where the buckling occurs, and (c) limited energy dissipation in the buckling modes triggered. Cellular and foamed steel (Fig. 1) is a new and potentially revolutionary material that allows for (i) components to be replaced with elements capable of large energy dissipation, or (ii) components to be stiffened with elements which will generate significant supplementary energy dissipation when buckling occurs. Steel foams provide a means to explore reconfiguring steel structures to mitigate cross-section buckling in many cases and dramatically increase energy dissipation in all cases.

Though aluminum and titanium foams are utilized in aerospace and automotive applications that require materials that are light and stiff, stiff and permeable, or energy absorbent, the potential application of steel foams in civil structures has not been adequately explored. Steel foams offer the following key advantages for use in civil structures:

• Steel foams have a high stiffness-to-weight ratio and therefore can be designed as stockier members having similar weight but much lower local slenderness ratios than comparable steel members. Members that commonly buckle now, such as steel braces or flanges of girders in flexure may be replaced by energy-dissipating steel foams. These members will not be exposed to the low cycle fatigue fractures and irregular load-deformation curves that are common in current steel members that now buckle cyclically, with this cyclic local or member buckling now being fundamental to the primary energy dissipation mechanism in a large majority of present-day steel structures.

• Steel foams absorb large amounts of energy at lower stress levels and will not attract large additional loads through increased strength making steel foams ideal to use in energy-dissipating devices.

• Steel foams are weldable to other steel components (Kremer et al. 2004) using comparable if not identical methods to current steel. This puts steel foams in stark contrast to other methods that are being investigated for enhancing ductility (e.g., shape memory alloys).

• Steel foams should have enhanced thermal properties compared with regular steel on a pound-for-pound basis, due to the internal voids and increased conductive path.

• Steel foams have low specific weight, thus these components will not add undue weight to the structure in comparison to their energy-dissipation capabilities.

Mass production of steel foam does not yet exist, yet recent key advances in the manufacture of steel foams present the first opportunity to develop practical applications for metallic foams in civil structures. Through an agreement with the American Iron and Steel Institute, the investigators can obtain the necessary steel foam members and components as produced by a powder metallurgy process developed by Kremer et al. (2004). This process has, for the first time, produced steel foam of high enough quality that it can be considered for use as a structural material, and the investigators will have ample access to the specimens necessary to conduct this research. By utilizing a less expensive base material (i.e., steel as opposed to titanium) the cost penalty of using foamed materials will be reduced. Further, by providing

!"# $

!%# $

! $

Figure 1: Steel foam (a)-(b) microstructures ~ 4cm and (c) sections (Kremer et al. 2004).

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initial characterization and applications, the case for developing mass production methods and more dramatic cost reductions can be established as a necessary step towards common use.

The goal of this work is to provide the foundational experimental results, validated complementary simulations, and an initial assessment of appropriate implementation strategies to enable the basic engineering of steel foam as a structural component in steel structures. This project, through physical testing and computational simulation, will deliver (1) a constitutive model for the complete, quasistatic, monotonic and cyclic response of steel foam; (2) computational tools for the simulation of the micromechanical response of steel foams; (3) candidate designs of steel foam elements that can serve as energy dissipators in civil structures; (4) quantitative demonstration of the ability of steel foam to mitigate buckling instability in steel structural components; and (5) recommendations on possible new designs for the microstructure of steel foam to render it more suitable for civil structural applications.

The research team is described in Tab. 1. See Section 5 for additional details.

Table 1: Research team participants, affiliation and expertise

Researcher Affiliation Expertise/Role

Asst. Prof. Sanjay R. Arwade

University of Mass. Amherst

PI: Materials characterization, micro-scale modeling, constitutive models, stochastic simulation

Assoc. Prof. Benjamin W. Schafer

Johns Hopkins University

co-PI: Cold-formed steel structures, structural stability, component modeling, modeling energy dissipation

Prof. Jerome F. Hajjar

University of Illinois Urbana-Champaign

co-PI: Hot-rolled steel structures, fuse-based structural systems, structural system modeling, experimental testing

To ensure the developed work has maximum impact on industry and practice, an Industrial Advisory Board (IAB) has been created for this proposal (Tab. 2). See Section 5 for additional details. The individuals named in the table, representing essentially all the major organizations in the steel construction industry, have agreed to participate in the IAB. The American Iron and Steel Institute (AISI) and the American Institute of Steel Construction (AISC) have provided supporting letters (included in the supplementary docs). AISI specifically endorses the “potential in the application of steel foam for structural use,” and states that the proposal “takes genuine steps towards providing analytical tools and specific real applications,” that will motivate the adoption of steel foam in practice. AISC advises of the need for a “product form that would eliminate the buckling” that often causes failure in steel structures.

Table 2: Industrial Advisory Board participants, title and organization

Participant Title Organization

Jay Larson Director Construction and Technical American Iron and Steel Institute

Don Allen Technical Director Steel Stud Manufacturers Association

Lee Shoemaker Director of Research Metal Building Manufacturers Association

Tom Schlafly Director of Research American Institute of Steel Construction

David Mar Principal Tipping Mar Associations, Berkeley, CA

Tom Trestain Principal Trestain Structural Engineering, Toronto, ON

2 Background

In the seminal edited volume Metal Foams A Design Guide, (Ashby et al. 2000) Ashby, Gibson and others argue that industrial take-up of advanced materials lags far behind research development, and that the route to accelerating the take-up of advanced materials is to focus early in material development on “development of design rules, research targeted at characterizing the most useful properties, and demonstrator projects” (Ashby et al. 2000, Fig. 1.2). Ashby and co-authors (Salimon et al. 2005) specifically identified the wide range of possible transformative applications for steel foam. This proposal is a direct response to the opportunity the identify, and is focused specifically on “characterizing the most useful properties”, and developing “demonstrator” applications for the new material, steel foam.

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2.1 Mechanics of metal foams

The mechanics of low-density (relative density less than 0.2) open- and closed-cell foams is essentially mature at this point, with results available for important material properties such as the elastic and shear moduli, Poisson’s ratio, yield stress and plasticity parameters (Gibson & Ashby 1997, and, selected from a very deep literature, Silva & Gibson 1995, Gong et al. 2005, Jang et al. 2008, Warren & Kraynik 1987, 1997, Luxner et al. 2007, Papka 1994, Papka & Kyriakides 2008a,b, Silva et al 1995). The mechanics indicate that relative density of the foam controls virtually all of the material properties. The mechanics, however, are developed from the beam or plate-like behavior of the cell ligaments and walls in low-density metallic foams, this behavior does not predominate in steel foams, which have relative densities between 0.3 and 0.8 (Kremer et al. 2004). For higher density foams bending does not dominate the local microstructural response, and further study is needed.

Nevertheless, the knowledge base from low-density foams provides a strong foundation from which we will develop our treatment of steel foams. For example, the engineering community now knows that material stiffness decreases less rapidly than weight when a metal is foamed so that foams have high stiffness to weight ratios, that foams are able to develop very large compressive strains at low stress levels, that response is asymmetric in tension and compression, and that relative density is the most important, if not the only, parameter that determines material properties.

Basic design guides are provided for low density foams subject to fatigue loads (Ashby et al. 2000), and some experimental investigations of the fatigue response of metal foams have been published (Harte et al. 1999, Ingraham et al. 2008) but there remain significant gaps in our understanding of metal foam mechanics (Tab. 3). To apply steel foams to civil structures these gaps must be filled because steel foams are high density and seismic fatigue loads are low cycle.

2.2 Steel foams

Metallurgists and materials scientists in Europe and the United States have fabricated steel foams using three main: powder metallurgy (Kremer et al. 2004, Park & Nutt 2000, 2001a,b, 2002, Motz et al. 2005), sintering hollow steel spheres (Tuchinsky 2005), and chemical reduction of ceramic foams (Verdooren 2005 a,b). These methods are similar to those reviewed by Banhart (2001) for the processing of metal foams, and each yield different microstructures. We will focus on steel foams prepared by the powder metallurgy method developed by Fraunhofer USA (Kremer

et al. 2004; Fig. 1 a,b,c in this proposal) in a project supported by the Dept. of Energy and the American

Iron and Steel Institute. The close association of the investigators with AISI is evidenced by the letter of

support, which states, “AISI strongly supports the goals of this research and will work with the

researchers to help them achieve those goals, including securing samples, should the project be funded.”

This firm support of the group that participated in the development of the Fraunhofer process assures that

this project will have access to sufficient material

samples, and also that the work will remain firmly

grounded in the realities of the production process.

Kremer et al. (2004) completed preliminary experimental characterization of the tensile and compressive properties of steel foam and the response of hollow steel tubes filled or partially filled with foam. The material characterizations indicate substantial differences between the response of high density steel foams (relative

Table 3: Summary of state of knowledge of foam mechanics.

Foam

Monotonic

Fatigue

Medium-High Cycle

Fatigue

Low Cycle

Low density Well understood

Several experimental results

Fewer than 10 tests reported, no models

High density Preliminary experiments

No known character-izations or models

No known character-izations or models

Figure 2: Bending tests on tubes filled (green, higher load and ductility) and empty (blue) (Kremer et al. 2004)

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density about 0.5) and low density foams made of other metals. The tests on filled tubes demonstrate the potential of foam to shift buckling modes in the direction of higher strength and ductility (Fig. 2)

3 Material Characterization and Constitutive Modeling

The steel foams that we propose to investigate have microstructures that are qualitatively different from those in currently produced metal foams. The key difference is the high relative density, in the range of 0.5, and the resulting thick cell walls (Fig 1). The thickness of the cell walls renders invalid the assumption of beam- or plate-like behavior for the cell walls. Since essentially all previous analytical and computational work on the mechanics of metal foams has been built upon the assumption of beam- or plate-like behavior of the cell walls, we must develop novel models for the microstructure and mechanics of steel foams. Our material characterization efforts concentrate in four areas:

1. Experimental characterization of the material microstructure

2. Experimental characterization of the mechanical properties

3. Numerical modeling of the material and material response

4. Development of constitutive models for the material

Development of validated numerical modeling techniques will enable, (a) careful examination of steel foam applications as described in Section 4 and (b) the extension of this work from material characterization to material design, in which simulation will be used to optimize the material microstructure to specific structural applications.

Working with AISI (see support letter), who have previously performed research on steel foams, we will secure a variety of steel foam samples for testing. Because steel foam is not in regular commercial production, bars and cold-reduced sheet are selected as sample components for this project due to their relative ease of manufacture. Based on the work sponsored by AISI and DOE at Fraunhofer (Kremer et al. 2004) it is anticipated that a carbon-strontium carbonate composition will be used for the foaming agent and hot uniaxial pressing for mechanical drawing of the specimens. Many of the developed procedures are proprietary to AISI, but AISI’s support of this project insures that successful steel foam samples can be created and explored for structural use herein. AISI has specifically stated in their supporting letter that it will “ensure those companies [that produce steel foams] are receptive to material requests.”

The steel foam bars will be 41mm x 92mm (essentially equivalent to a timber “2x4” or a 362S162 cold-formed steel stud, SSMA 2001 nomenclature) in cross-section with length dependent on the test of interest. Such a specimen size is within the known capabilities of the specimens produced at Fraunhofer (Kremer et al 2004). Void density ranges between 43% and 55% were demonstrated in that work, target void densities of 50%, 65% and 80% will be sought for the bar specimens here.

3.1 Microstructure characterization

Characterization of the microstructure of steel foam requires imaging of the complex three-dimensional geometry of the solid and void phases of the material. We will employ two techniques at opposite ends of the technological spectrum to obtain such images, serial sectioning and x-ray computed tomography (CT), and will follow the recommendations of Banhart (2001) to establish a systematic characterization plan. In serial sectioning, two-dimensional images of cross sections through the material microstructure are obtained by grinding the material to reveal successive sections. The advantages of serial sectioning are that it requires no specialized equipment and the grinders and imaging tools are readily available at UMass. The disadvantages are that considerable skill is required to grind material so as to reveal successive layers, reconstruction of the three-dimensional geometry from the serial sections is a subtle operation, and the process is extremely time consuming, cannot be automated, and is destructive. X-ray CT imaging, on the other hand, is fully automated, non-destructive, and directly delivers a three-dimensional reconstruction of the microstructure. The disadvantage of CT imaging is that it requires highly specialized equipment usually available only at medical institutions, and can be expensive. Access

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to CT scanning equipment is available at UMass through arrangement with Cooley-Dickinson Hospital. Given the relative advantages and disadvantages of the two methods we propose to investigate CT scanning as the primary imaging tool, with serial sectioning available as a backup method to ensure viability of the project. Successful CT scanning of steel foams has already been demonstrated (Fig. 3)

In characterizing the microstructure we will evaluate the following features: void size distribution, void shape, and spatial distribution of the voids. Quantification of the void size can be conducted by a relatively straightforward thresholding operation because of the high contrast ratio between the solid and void phases in the material. Quantifying the shape of the voids is somewhat more challenging since the shape of the voids is in general random. Recent work on the analysis has indicated that moment invariants are the best way to characterize the shape of irregular three-dimensional volumes (MacSleyne et al. 2008). We will employ standard methods for characterizing the spatial distribution of the void phase including 2- and 3- point correlation functions and the lineal path and chord length density functions (Torquato 2002).

3.2 Mechanical property experiments

A thorough investigation of the mechanical properties of steel foams is proposed since the high relative density of steel foams renders their mechanics qualitatively different from those conventionally understood for low density metal foams. We propose to characterize the compressive, tensile, and cyclic response of steel foams, and make preliminary investigations into the thermal and vibrational characteristics. Furthermore, we will make preliminary investigations into the dependence of mechanical properties on average void size and will determine whether any size effect can be discerned in the response of the material. The tests described here will allow us to develop constitutive models for steel foams that will then be implemented in the finite element analysis packages ABAQUS and ADINA. These models are a major contribution of this project because no constitutive models currently exist for the class of high density foams such as steel foam.

3.2.1 Tension tests: We will conduct tension testing on specimens designed to conform to ASTM standard E8 (ASTM 2008) for tension testing of metallic materials. The specimens have reduced cylindrical cross sections in the gage length. The tension tests are designed to define the overall stress-strain response of the material during tensile loading, to establish the elastic modulus and ultimate stress of the material and the dependence of the modulus and ultimate stress on the void size and specimen size. Also important are the strain at ultimate stress and the post-peak response of the foam. We propose to conduct tension tests on specimens with the three target relative densities, 50%, 65%, and 80%. At each relative density we will investigate specimens with three different diameter to void size ratios, 5, 10, 20. These values are chosen because for low density aluminum foams a specimen to void diameter ratio of 10 is usually treated as a minimum. Our goal is to determine whether this lower bound on specimen size also applies to high density steel foams. We will determine in conjunction with the manufacturer whether variation in the diameter to void size ratio will be varied by changing the specimen diameter or the average void size. If the material characterization tests reveal substantial orthotropy in the void structure we will conduct the full set of experiments in each of the three principal material directions. With three test replications for each specimen design we will conduct 27 tests if the material is found to be isotropic, and 81 tests if the material is found to be anisotropic. The test matrix for

Figure 3: X-ray CT image of steel foam (Kremer et al. 2004)

Table 4: Test matrix for tension tests on steel foams. Numbers in the table cells indicate number of test replications at each specimen design

Specimen diameter/void size

Relative density 5 10 20

50% 3 3 3

65% 3 3 3

80% 3 3 3

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each relative density and material direction is summarized in Tab. 4.

3.2.2 Compression tests: The compression testing program has essentially the same objectives as the tension testing program so the experimental design is similar. These tests are necessary because the response of metallic foams is highly asymmetric in tension and compression. The test matrix is identical to that shown in Tab. 4. The specimen geometry is as specified in ASTM E9 (ASTM 1989). An additional parameter to be studied in the compression tests is the strain to densification.

3.2.3 Shear tests: Shear deformation is the primary local deformation mode used in energy dissipating devices in civil structures. We will therefore conduct an investigation of the shear properties of steel foams, again following the test matrix of Tab. 4. We will use the compact shear specimen proposed by Barr & Liu (1983) due to the small volume of material required and robust performance cited in the paper. The specimen diameter / void size ratio for the shear specimens should be interpreted as the ratio of the minimum specimen dimension to the void size.

3.2.4 Fatigue tests, low and high cycle: In many of the example applications discussed in Section 4 the steel foam must sustain non-monotonic loads, such as are generated in an earthquake. The response of metal foams to cyclic loading is much less well understood than their response to monotonic loads, and the initial report on steel foam fabrication and properties (Kremer et al. 2004) did not report any cyclic tests. Our objective is to obtain characterizations of the mechanical response of steel foams to cyclic loading of large and small amplitudes, corresponding to low and high cycle fatigue cases respectively. The responses of interest are the fatigue life and also the hysteretic behavior of the material which is critical to evaluating the potential cyclic energy dissipating performance of the material. We will perform fatigue tests under strain control at strain amplitudes ranging from 0.05% to 2% strain, for three values of relative density, 50%, 65%, and 80%, and for fully reversed loading, compression-compression loading, tension-tension loading and fully reversed shear loading.

3.2.5 Size effect: Statistical size effect is known to occur in materials with heterogeneous microstructures such as steel foams. The tests described above interrogate specimens of three different sizes relative to the average void size in the material to provide an indication of the size of the representative volume element and any tendency for the material to exhibit a size effect. Any potential size effect in the material is important to our study because, as is described in the following sections, some of our example applications use relatively large volumes of steel foam to directly absorb energy and some use small volumes of steel foam to attempt to beneficially modify the response of thin-walled steel members.

3.2.6 Other properties: Steel foams have potentially advantageous thermal, vibrational, and acoustic properties. They should prove less thermally conductive than solid steel, and foams are known to substantially dampen vibrations. To investigate vibrational properties we will conduct free vibration tests on steel foam beams to evaluate the damping coefficient by logarithmic decrement methods. The beams tested will have span to depth ratio of about 15, will be square in cross section, and will be fabricated at the three relative densities of interest, 50%, 65%, and 80%. They will be instrumented with an accelerometer during the test so that the damping coefficient can be estimated. A full fledged thermal conductivity study is beyond the scope of this project, but we will make some preliminary measurements of the conductivity by heating one end of one of the beams and measure the heat conduction using thermocouples.

3.2.7 Weldability: Connection design will be a major challenge in the eventual commercialization of steel foam for civil structural applications. Kremer et al (2004) demonstrated the feasibility of welding steel foams, but used filler wire and rods more typical in aerospace applications. UMass has an established relationship with a steel fabricator where a small scale program of test welding will be conducted. The program will consist of cutting five to ten specimens of the same geometry as the tensile specimens, welding them back together. The specimens will be returned to UMass to undergo the tensile testing protocol to evaluate the tensile strength of welded butted connections. Results of this preliminary

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evaluation will include the quantitative tensile testing results and the qualitative report of the welder on material weldability.

3.3 Material modeling

Our material modeling efforts are focused on developing models that can predict the macroscopic material properties of a steel foam from an explicit representation of the material microstructure. In addition to these homogenization efforts, which we propose to conduct both by numerical simulation and approximate analytical methods, we will use numerical simulation to evaluate the thermal and vibrational properties, as well as bolt bearing, a problem that arises in a many structural steel connections. We build our modeling on the experience of Prof. Arwade with modeling random microstructures and simulating their response (Arwade & Grigoriu 2003,2004; Schafer & Arwade 2004; Tan & Arwade 2008; Louhghalam & Arwade 2009).

3.3.1 Material microstructure model: The microstructure of steel foams consists of solid and void phases. The void phase is often spherical, and is typically at least approximately elliptical. The problem of generating sample microstructures for use in analysis, therefore, amounts to placing voids of random size and shape in a defined domain that is otherwise filled with the solid phase. Many packing algorithms are available for performing such simulations in two and three dimensions, including the Poisson hard core field (Torquato 2002). We prefer the Poisson hard core field as a model on which to base simulations because of its straightforward implementation and flexibility in allowing for control of the void shape, void size distribution, and void spatial distribution. Figure 4 shows some of the degrees of control available in simulating microstructures using a Poisson hard core field. The illustrations are two dimensional, and the algorithm is easily extended to three dimensions. If voids of random shape are desired, as opposed to elliptical voids with random size, we will use a recently developed method for generating three dimensional volumes of arbitrary shape with specified statistical properties (Grigoriu et al. 2006). Although the Poisson hard core field is very flexible, it is not well suited to generating microstructures that match statistical measures of phase spatial distribution such as the n-point correlation functions, lineal path and chord length density functions. Iterative methods are, however, available for simulating such microstructures with specified higher order statistics (Graham-Brady & Xu 2008), and these will be adapted to our purpose.

3.3.2 Analytical approaches to homogenization: In the applications we describe in the following sections, plastic deformation in the steel foam is used as an energy absorbing mechanism. The homogenization problem, therefore, involves the plastic and elastic properties of the steel foam microstructure. Although homogenization for elastic properties of heterogeneous microstructures are well developed, only recently have techniques become available for homogenization of plastic properties (Acton & Graham-Brady 2009). While these techniques are suitable for characterizing the elastic properties and compressive plastic properties, no techniques are currently available for homogenization of fracture properties or ultimate stress. We will investigate adapting the method of Acton & Brady for homogenization of ultimate stress of the steel foam microstructures so that a full characterization of the elastic and inelastic properties of the foam can be approximated by analytical methods. The research challenges posed by applying approximate analytical homogenization techniques to steel foam microstructures include:

1. The void phase has zero material stiffness, and this zero value can pose numerical challenges to averaging based homogenization methods.

2. Homogenization for ultimate stress is even more challenging than for yield stress since ultimate stress of a heterogeneous material with voids in it is highly dependent on the local arrangement of

Figure 4: Simulated 2D steel foam

microstructures; circular and

elliptical voids, both with 70%

relative density and random void

size.

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the phases, and consideration of such local geometry is particularly difficult to include in homogenization methods.

3.3.3 FE mechanics modeling: To the degree that analytical homogenization approaches do not provide the necessary characterization of the steel foam material properties we will seek recourse to finite element analysis of steel foam microstructures to establish the link between the steel foam microstructures and macroscopic properties. Such simulations can be treated as quasi-static and must incorporate material nonlinearity to capture yielding of the base metal and geometric nonlinearity to account for the large displacements that occur at the cell walls. Figure 5 shows simulations of the tensile elasto-plastic response of a steel foam with oriented elliptical voids.

In modeling the large deformation response of steel foams in tension and compression, some significant challenges are presented, namely:

1. Densification of the foam is caused by self-contact of the material as the voids close and the cell walls come into contact with one another. This is a challenging phenomenon to model since the geometry of the contact and target surfaces is not known a priori for a steel foam with random void geometry.

2. Fracture of the foam under tensile loading occurs by progressive fracture or tearing of the cell walls. Modeling this phenomenon is challenging because the locations of the local fractures are not known a priori. Two options are available for simulating the tensile failure of steel foams, the use of cohesive elements at all possible locations of fracture (Ortiz & Pandolfi 1999) or the use of a strain based element rupture criterion to determine when fracture occurs in individual elements. We will investigate both of these methods to gauge their suitability to this modeling problem.

The primary purpose of the finite element modeling is to develop a model for the mechanical response of steel foam that has been validated against the experimental results described in the previous section. This modeling capability will be used in the successive parts of the proposal, specifically in efforts to design steel foam microstructures that are optimized to the desired structural performance and as plug-in components to the simulations used to explore possible structural applications of steel foams. For example, the structural advantages of forming the web of a steel plate girder from steel foam cannot be evaluated if constitutive models for the steel foam are not available. While the material characterization experiments will provide constitutive models for the as-produced foams, the computational models are critical to evaluating the constitutive relations of novel candidate microstructural designs.

3.3.4 Constitutive modeling: The ultimate goal of the material testing program is to motivate and calibrate constitutive models for steel foams that can be used in the computational simulations of steel foam applications. Standard material properties (E, Est, fy0.2, !y, fu, !u, etc.) as well as phenomenological

properties (Ramberg-Osgood parameters, etc.) will be developed from the test results. Models for the monotonic constitutive response and the cyclic constitutive response are required to allow investigation of the intended breadth of applications. Ramberg-Osgood, crushable foam (similar to von Mises plasticity), and hyperfoam models (energy functionals similar to Mooney-Rivlin models), all of which are readily available in commercial finite element codes such as ABAQUS/ANSYS/ADINA, will be investigated as potential monotonic models. The challenges in fitting a model to the monotonic response center on the asymmetric response of foams to tensile and compressive loading.

Figure 5: Simulated stress strain curves for steel

foam microstructures with elliptical voids. Bold

(red) line is reference continuum stress-strain

curve. Dashed lines are stress strain curves for

different material orientations. Light solid line is

reference stress strain curve for steel foam with

circular voids.

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Preliminary tests performed at UMass on aluminum foams show a reasonably straightforward, symmetric, cyclic hysteretic response under fully reversed loading, but under tension-tension and compression-compression loading strain ratcheting has been observed (Harte et al. 1999). This ratcheting is not reproduced by the classical cyclic plasticity models. Bari and Hassan (2000) report on the suitability of the Prager, Armstrong and Frederick, Chaboche, Ohno-Wang and Guionnet models for modeling ratcheting, and indicate that the Chaboche, Ohno-Wang, and Guionnet models perform well. We will use these results to guide our cyclic constitutive modeling in response to the experimental results.

3.3.5 Bolt bearing: A critical step in making steel foams useful as a structural material is developing strong and ductile connection details. Although preliminary studies on the structural use of steel foam (Kremer et al. 2004) have shown that good quality welds can be achieved and that adhesives provide another possible connection method, the bolting of steel foams has not yet been investigated. Because this proposal is focused on material characterization and the demonstration of possible structural applications, the scope does not include comprehensive testing of connection details. The simulation tools described in the above sections, which allow the comprehensive inelastic modeling of steel foam response far past the elastic limit in tension and compression, provide an opportunity to conduct preliminary numerical investigations into the possibility of using bolts to connect steel foam components to other steel foam components or to solid steel components. We will investigate through simulation the multiple bolt configuration shown in Fig. 6, with and without the steel face sheets. Only the relatively high density of steel foams makes bolted connections conceivable.

3.3.6 Model validation: The material characterization tests described above provide the data required for validation of the computational models we propose to develop. The models must be validated with respect to their ability to predict the elastic properties, yield points, densification strains, and tensile failure strains measured in the experiments.

3.4 Computational material design

One of the objectives of this project is to demonstrate that structural elements can be made of steel foam that deliver better performance characteristics than their solid steel counterparts. We intend that this demonstration, disseminated to the steel industry through AISI and AISC, our industrial partners, will spur more intense research and development on the metallurgical and manufacturing aspects of steel foam. The materials design research task makes preliminary exploration into the possibility of designing the material microstructure to deliver desired macroscopic material properties. Three specific material design parameters are of interest to us in this project, the void size distribution, void orientation distribution, and the possibility of functionally grading the void size distribution and volume fraction within a steel foam component.

For low density metallic foams the properties have been shown to depend nearly completely on the relative density. This has not been verified for higher density foams such as steel foams, leaving open the possibility that, at the same relative density, different void size distributions may deliver different macroscopic properties. This seems particularly likely for fracture properties which are known to depend on defect size. In steel foams the voids play the role of defects. Figure 1 shows that anisotropic voids can be generated in steel foams, and Fig. 5 shows how the properties differ in the material directions of steel foams with anisotropic voids. There may arise applications in which anisotropy of steel foams with anisotropic voids can be advantageous to the material performance. Finally, and potentially most importantly, functional grading of the void size distribution could significantly enhance the performance of steel foam components. For example, functional gradation opens the possibility for tailoring the stiffness, strength, and energy dissipation potential to the demands not only component by component, but within components. Furthermore, the possibility of generating, during the manufacturing process, regions of very low or zero porosity would solve many challenges relating to painting, corrosion

Fig. 6: Schematic bolt testing arrangement

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resistance, and fireproofing of the material. Figure 1 shows a steel foam cylinder that is functionally graded by virtue of having the foam expanded within a solid steel tube so that the porous steel foam transitions to nonporous steel at the surface. Our objective is to demonstrate how functional grading of a steel foam could be beneficial to performance, and motivate development of a process for directly manufacturing steel foams with functionally graded void structures.

4 Application of Steel Foams to Steel Components and Systems

To understand the potential transformative benefits of steel foams, the second major part of this proposal focuses on applications, both at the component and system level. The materials characterization and constitutive models from Section 3 provide a means to meaningfully simulate steel foam. This ability will be integrated with our existing research expertise in performing material and geometric nonlinear analysis of steel components and systems to provide accurate simulations demonstrating the resulting behavior of structural systems comprised of, or modified by, steel foams. The use of steel foams to significantly increase energy dissipation and to mitigate local (cross-section) stability modes will be the focus at the component level. The integration of steel foams into braced frame systems (both cold-formed and hot-rolled) and modern fuse-based framing systems will be the focus at the systems level. The objective here is to use computational simulation to explore and identify the most promising

applications for steel foams and then use these findings to

motivate future experimental studies in a continuing

collaboration with the industrial partners.

The primary activities within this task include:

• Calibration of baseline archetypes: A series of baseline archetype steel structures will be defined, and parametric variations will be established for a computational study of both member archetypes and system archetypes that will benefit from steel foam. Specific instances of what will be explored are discussed below.

• Development of comparative performance metrics: Metrics will be established to compare progression of damage and performance of traditional steel structures versus those with foam. Future cost/benefit assessments will also be included. Through this study, the most effective uses of steel foam will be identified based on the material characterizations of Section 3.

• Computational analysis of steel foam alternatives: We will conduct both three-dimensional continuum analysis of members and components as well as system-level analyses based on fiber analysis procedures to study the detailed progression of damage, comparing existing steel construction to the proposed, optimized use of steel foam.

• Identification of target alternatives for future testing: This research will establish a clear basis for the necessary next steps in structural system testing needed to facilitate broader adoption of steel foams.

The research team has significant experience both modeling and testing the member archetypes: including steel plates, (e.g., Moen and Schafer 2009; Schafer et al. 1998; Yu and Schafer 2006b; Hajjar et al. 1998; Ye et al. 2000; Tort and Hajjar 2007), hot-rolled W-sections (e.g., Schafer et al. 2000; Schafer and Seif 2008), and cold-formed C-sections (e.g., Moen and Schafer 2008; Yu and Schafer 2003; Yu and Schafer 2006a; Yu and Schafer 2007) as illustrated in Fig. 7. This experience will be utilized to build baseline

(a) FE model of hot-rolled steel FR

connection using shell and solid elements (Schafer et al. 2000)

(b) Testing and simulation of purlin-metal

shheeting, distortional failure (Yu and Schafer 2007)

Figure 7: FE modeling examples

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models (ABAQUS and/or ADINA FE models utilizing predominately shell elements) for the performance of the archetypes that will subsequently be modified through the use of steel foams.

The team also has extensive experience in static and dynamic system analyses using stress-resultant space distributed plasticity formulations that discretize the cross section into a grid of fibers and track uniaxial stress-strain constitutive relations at each fiber (Hajjar et al. 1998; Tort and Hajjar 2007). This formulation includes a comprehensive bounding surface steel plasticity model, already calibrated to baseline models of steel beam-column strength, including the debilitating effects of local buckling (Tort and Hajjar, 2007). The formulation will be recalibrated to the constitutive response found in Section 3 for appropriate foamed materials, thus enabling parametric differentiation of the global static and dynamic response of complete systems with and without the use of foamed components. In the applications below, both static and dynamic loadings may be investigated depending on the specific needs of the application. To provide a basis for comparison, solutions that are generally equivalent or lesser in weight (i.e., amount of material employed) will be investigated. Detailed simulation will track damage progression for example through the use of incremental dynamics analysis (e.g., Vamvatsikos and Cornell 2004) in line with ATC-63 protocols (ATC 2009) to assess damage up to and include collapse potential. We will examine the relative effects of mitigation of buckling modes and favorable tension, compression, and shear cyclic yielding capabilities for energy dissipation as compared to traditional structural systems.

4.1 Member archetypes

To provide a means for baseline comparison a series of member archetypes are selected for analysis and simulation: plate/sheet steel, a hot-rolled steel W-section, and a cold-formed steel C-section. Plate steel is a fundamental building block for existing steel structures and provides a means to examine local buckling in an isolated context. The W-section and C-section are the most commonly used sections in hot-rolled and cold-formed steel construction, respectively.

Two major modifications will be explored for the member archetypes: (1) foaming the basic shape, and (2) adding foam inserts to the member at critical locations. The local slenderness of a steel plate in compression may be defined as

where ! = 0.7 typically defines the slenderness limit at which

plates can develop their full yield capacity (! > 0.7 implies a plate

with reduced capacity due to local buckling) and is found to be a function of material properties: E, ", fy; loading and boundary

Figure 8: Hot-rolled W-section (a) standard, (b) equal area foamed to

50% relative density

Figure 10: (a) BRB braced frame after Sabelli et al. (2003) with (b) BRBs replaced with steel foam links (c) buckling of a hollow tube brace and (d) buckling of a steel foam filled brace – note shorter wavelength buckling and a buckling resistance increased by more than a factor of two.

Figure 9: Cold-formed steel stud buckling modes and potential steel foam modifications: (a) global flexural-torsional buckling, (b) distortional buckling, (c) local buckling, (d) full height foam core insert, (e) end-only foam insert, and (f) intermediate foam insert.

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conditions, k; and the basic geometry width, w, and thickness, t. A foamed plate can have a significantly reduced ! for the same amount of base material – consider the ratio of the slenderness of a foamed plate,

!*, to the original plate, !.

While the effective properties (E*, "#, fy*) of the foamed plate all change (and exact determination of this

change is an important outcome of the work of Section 3) the dominant change is of the thickness, resulting in a stockier plate for the same amount of material. As Fig. 8 illustrates for a W-section foaming a cross-section can provide a steel member with remarkably different properties: chief among them an increased resistance to local buckling and the potential for much greater energy dissipation.

Foaming the archetypal shape itself may not be necessary or cost-effective in some situations. Instead, targeted application of the steel foam may provide a more efficient use. In deep W-sections or plate girders it may be advantageous to make the stiffeners of steel foam bars, so that when buckling of the flanges occurs compression in the stiffening bars will be engaged and significant energy expended. In cold-formed steel sections a number of potential uses for supplementary steel foams are envisioned as shown in Fig. 9. Different foam inserts may be appropriate for mitigation of each of the dominant cross-section buckling modes and provide a means to stabilize the offending buckling modes, and to expend far greater energy in such deformation modes when they occur.

4.2 System (braced frame) archetypes

A systems-level archetype selected for additional study is the braced frame. Hot-rolled steel braced frames suffer from a number of difficulties that may be removed through innovative inclusion of steel foam components. Similarly, cold-formed steel strap braced shear walls (the braced frame analog in low-rise construction) have poor seismic performance and deserve attention.

In seismic zones the conventional hot-rolled steel Special Concentrically-Braced Frames (SCBF) suffer from having their primary energy dissipation include cyclic buckling and tensioning of the brace, often resulting in low cycle fatigue fractures (Uriz and Mahin 2004; Uriz 2005). For this reason, buckling-restrained braces (BRBs) have gained popularity in recent years (Sabelli 2004; Xie 2005), including being incorporated into the national seismic specifications for steel structures (AISC 2005). BRBs are highly resilient members with strong potential to improve seismic performance as compared to SCBFs. However, they are found to fail, sometimes prematurely, either due to overall buckling of the brace (Takeuchi et al. 2009) or, more likely, due to premature buckling of the gusset plate (e.g., Takeuchi et al. 2004). Preliminary exploration of an SCBF where steel foam links replace the brace or BRB (Fig. 10) show the potential for excellent performance. In addition, eccentrically braced frames currently rely upon heavily stiffened shear links to dissipate energy. Recent research has shown sensitivity of these links to premature fracture (Okazaki et al. 2005). Preliminary assessment of the use of foamed links without stiffeners, spliced into the girder outside link region, will be conducted to explore an attractive alternative to the fabrication and alleviation of stress concentrations seen in current shear links.

For cold-formed steel construction the braced frame analog is the strap braced shear wall (Fig. 11). Though a commonly used system the failure mode in the absence of careful weld details or reduced section braces is connection fracture. Even when the strap remains intact, large strap deformations lead to severe pinching in the hysteretic loops under even low numbers of cycles (Al-Kharat and Rogers 2008). The inclusion of steel foams introduces the possibility to provide inelastic deformations in the chords as well as the diagonals. More radically, rather than include interior studs, a foamed track distribution

strap braced shear wall

Figure 11: Light steel frame shear walls (Al-Kharat and Rogers 2008)

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member along with an optimally designed foam core might be utilized in the plane of the shear wall. A variety of options will be explored, including steel foam modifications to the corrugated sheet steel shear wall pioneered by Tipping-Mar (Tipping and Stojadinovic 2008) from our Industrial Advisory Board.

4.3 System (fuse-based) archetypes

The second system-level archetype selected for study is the new modular fused-based framing system. A number of these new structural systems have recently been proposed as alternatives to conventional lateral-resistance systems in building structures, particularly for seismic force resisting systems (SFRS). Modular fused-based systems offer an attractive and robust alternative to traditional systems concentrating damage in replaceable fuse elements. The SFRS may often be decomposed into modular components, permitting both the fuses and the SFRS as a whole to be optimized for desired performance at progressively higher intensities of loading. These systems are frequently coupled with a self-centering mechanism, such as post-tensioning, thus eliminating residual lateral drifts, facilitating replacement of the damaged fuses, and ensuring the integrity of the lateral-resistance system after major seismic events.

The use of modular, fused-based systems in steel structures represents a fundamental departure from current seismic design methods in which the girders, braces, columns, walls, and their connections, all made from construction-grade materials, are relied upon to absorb energy through inelastic deformations. Fused systems are being explored both in hot-rolled and cold-formed steel construction, we will explore the use of foamed material to form the primary fuse mechanisms, as these can depend fundamentally on reliable cyclic yielding for energy dissipation. Since the damage is focused within the fuses, these fuses permit optimization for the desired performance. Specifically, the fuse systems enable tuning of the structural system to achieve stiff response (minimal damage) under frequent loadings, inelastic energy dissipation under moderate loadings, and pinched degrading response that preserves self-centering under large (rare) loadings. Outside of the fuses, the remainder of the SFRS structural system is then detailed to avoid structural damage. With appropriate design and detailing a variety of modular subassemblies may be developed to offer new capabilities for efficient construction and safe designs. Fuse-based systems thus offer a new opportunity for developing simple design strategies and optimized configurations that ensure outstanding structural performance with high reliability. An example of a fused-system was studied by Prof. Hajjar and others (Deierlein et al. 2009), consisting of two braced frames with energy-dissipating fuses bolted between them and absorbing the energy through cyclic inelastic shear (see Fig. 12). The fuses consist of steel plates with diamond-shaped cutouts used to enhance shear ductility. This research provides a foundation for computational exploration in this work of fuse topologies that will capitalize on the specific characteristics of steel foams to provide primary energy dissipation in steel structures.

5 Administration

Work Plan: The research tasks are shown in Tab. 5. Prof. Arwade’s primary tasks are materials characterization and constitutive modeling of steel foams, while Profs. Schafer and Hajjar focus on

Figure 13: Research team composition

Figure 12: Example of fuse-based structural system, (a) schematic, (b) under test at Illinois, (c) hysteretic performance and time history

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computational simulations to demonstrate the advantages of introducing steel foams into conventional steel construction and entirely new members and systems that fully utilize the advantage of steel foams.

Research Team: The research team is described in Tab. 1 and Fig. 13. The Postdoctoral Researcher will be co-mentored by Profs. Schafer and Hajjar (see supplementary mentoring plan). The research team will utilize web conferencing, i.e., Adobe Acrobat Connect, and virtual research spaces, e.g., Groupsite, (JHU provides free subscriptions to both) to ensure smooth collaboration within the research team.

Industrial Advisory

Board: An Industrial Advisory Board (IAB) has been assembled for this project (Tab. 2). (All members have agreed to serve on the IAB.) The IAB includes the major parties involved in constructional steel for building structures (AISC, MBMA, AISI, SSMA), as well as practicing engineers with significant expertise in cold-formed steel structures (Trestain) and in hot-rolled steel structures, rocking systems, and fused-based systems (Mar). The IAB will meet in-person once a year and quarterly via web conference to ensure: (a) industry feedback is provided and incorporated throughout the project, (b) research findings are immediately shared with key impacted industries, and (c) an initial consensus is achieved for continuing this intensive two year project into a 2nd phase with significant member and systems testing, and meaningful financial involvement from industry.

6 Broader Impacts

The research team strongly believes in the importance of both intellectual and sociological broader impacts. The intellectual broader impacts stem from integration with engineering practice and industry. The sociological broader impacts focus on an organized cohort of undergraduate researchers and specific efforts to include underrepresented minorities in the research team. A vertically integrated research team spanning from high school (JHU), undergraduate researchers (an organized cohort from all 3 universities), a Ph.D. student (UMass), a postdoctoral researcher (Hopkins) and faculty at the Assistant (Arwade), Associate (Schafer), and Full (Hajjar) levels is realized.

Integration with engineering practice and industry: The research will be specifically disseminated outside of academia to practicing engineers through the research team’s involvement with the IAB and the specification committees that create the building design standards for hot-rolled steel (AISC) and cold-formed steel (AISI), which will be provided regular updates on the research, and have indicated their support, specifically promising to support “commercial delivery to the marketplace” (AISI), and to “help provide fabrication expertise” (AISC). The research seeds an intellectual partnership across the institutions, and across the steel (hot-rolled and cold-formed steel) industry and research communities. This project will demonstrate the practical application of steel foams, jump starting their uptake in industry and helping to bring an important material manufacturing development to the civil infrastructure.

Table 5: Project GANTT Chart

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Undergraduate research cohort: an undergraduate will be part of the research team at each school (UMass, JHU, UIUC). In addition to working with their research mentor during the year, during the summer after the first and second year the 3 students will be combined and spend 1 month, as a cohort, at each of the three schools. The students will therefore be engaged with the entire project. The investigators will support this experience with other funds if supplemental REU funds cannot be obtained.

Baltimore Polytechnical High School (Poly) Students Research Practicum: a high school student from Poly will be included on the research team at JHU. Prof. Schafer has a strong working relationship with Ms. Sally Kutzer who runs the Research Practicum program at Poly, a majority-minority public high school in Baltimore City. This program pairs Poly students with research experiences in universities. The students spend 20 hours a week in the laboratory for an entire academic year. At the end of the two semester sequence they provide an original research paper and oral presentation. Prof. Schafer has hosted students in the past three years, and is working with a student this academic year. The two graduates from the program in Prof. Schafer’s group, both minority women, contributed original research and are enrolled as full scholarship students at JHU. Ms. Kutzer will help us identify a Poly student for the research team.

Northeast Alliance for Graduate Education and the Professoriate (NEAGEP): Recruiting for the graduate research positions at UMass-Amherst will include a specific focus on underrepresented minorities through UMass’s role as the lead institution in NEAGEP. The NSF-funded NEAGEP includes dedicated staff for recruitment and retention, funds for recruiting, summer programs, stipend support, and support in mentoring programs, amongst other activities.

7 Results of Prior NSF support

Prof. Arwade: DMI-0423582 (9/04-8/07, $286,000) A framework for microstructural design using Bayesian classifiers. The project aims to develop techniques based on pattern recognition algorithms that can be used in the rapid evaluation of the mechanical response of material microstructures. Prof. Arwade, and co-PI T. Igusa and one M.S. and one Ph.D. student (one a woman), developed reduced order representations of random material microstructures that can render microstructural design approaches more efficient. The project, has resulted in 4 journal publications, 8 articles in peer-reviewed conference proceedings, 8 conference presentations, and 4 invited departmental seminars at various universities.

Prof. Schafer: CMMI-0448707 (5/2005-6/2010, $400,000) CAREER: Structural Stability and Thin-walled Structures. The project investigates (i) a novel decomposition technique of use in model reduction and modal identification in structural stability problems, and (ii) the practical extension and verification of computational structural stability into design of thin-walled steel members. Publications include fundamental advances in stability as well as a re-examination of coupled instabilities in thin-walled members and inelastic buckling of thin-walled bending members totaling 7 journal publications and 13 refereed conference proceedings. This grant supports 2 Ph.D. students, high school and undergraduate researchers, and has led to the construction of a new testing facility for thin-walled members.

Prof. Hajjar: CMS-0084848 (9/2000-8/2006, $206,142) Performance Based Design Methodology for Composite Construction with Application to Concrete-Filled Steel Tube Structural Systems. A 3D fiber-based distributed plasticity mixed finite beam element formulation was developed to simulate the nonlinear dynamic response of rectangular concrete-filled steel tube (RCFT) beam-columns, steel girders, and steel braces as part of frame structures. The finite element has separate translational degrees-of-freedoms defined for the concrete core and the steel tube to simulate slip deformation. Cyclic constitutive relations were derived accounting for slip, confinement and local buckling. The work was validated against over one hundred experiments in the literature. Representative composite frames were analyzed under a suite of ground motion records to quantify the demand imposed on the RCFT columns. The project supported one Ph.D. student and one M.S. student and 6 journal articles have appeared.

See the investigator biographical sketches for representative publications resulting from these projects.

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