Microstructural characterization of in situ MXCT images of high density foams under large strains
- Los Alamos National Laboratory
- UCSB
Foams are used in numerous applications, such as vibration damping and energy mitigation (e.g., packaging and helmets), wherein their mechanical properties are of critical importance. A typical compressive response of a high density elastomeric foam, shown in Fig 1, generally contains three regions of interest: (I) a linear-elastic region, governed by strut bending; (II) a relatively flat, or slowly increasing stress-strain response, accompanied by strut buckling and the localized collapse of pores; and (III) an exponentially increasing stress-strain curve wherein the collapse of the pore matrix leads to densification. Two material properties of interest, upon which considerable research has focused are the foam's Young's modulus, E{sub f}, defined as the slope of the stress-strain response in region I, and the collapse stress, {sigma}{sub f}, defined as the stress at which the response begins to deviate from linearity. It has been observed [1, 2, 3] that Young's modulus and the collapse stress are dependent on the material properties of the strut material and the non-dimensional relative-density of the foam, {rho}* = {rho}{sub f}/{rho}{sub m}, where {rho}{sub r} is the gross density of the foam and {rho}{sub m} is the density of the strut, or matrix, material. For foam of low relative-density, i.e, {rho}* < 0.1, the collapse stress and Young's modulus obey the relations {sigma}{sub c}/E{sub m} {proportional_to} ({rho}*){sup m} and E{sub f}/E{sub m} {proportional_to} ({rho}*){sup n} where E{sub m} is Young's modulus of the strut material and the bounds on the parameters m and n are 0.05 {le} m {le} 0.2 and 1 {le} n {le} 4 [4]. For open-celled foams, n = 2, whereas for closed-celled foams, n = 3. Theoretically, n = 1 for foams with an ''ideal strut'' configuration [6]. Foams of high relative-density ({rho}* > 0.1) require correcting terms to account for the axial contributions of the ''thick'' struts [5]. The above equations relate important foam properties to the relative-density of the foam; however, there exists a gap in the understanding of how the foam microstructure affects the mechanical response of the foam. This is due in large part to the difficulty of characterizing foam structures in 3D, especially foams of high relative-density. Most elastomeric foams are manufactured by the introduction of a gas into a cross-linking polymer. The developing foam microstructure has a complex dependence on the polymer viscosity and rate of polymerization, resulting in a randomly arranged pore structure with a large distribution of pore sizes. One approach is to characterize foam microstructures solely in terms of the cross-sectional shape and vector arrangement of the strut matrix, since it is this matrix that supports the stresses upon loading of the foam; yet as the density of a foam is increased, the very definition of what constitutes a strut brakes down. Another, perhaps easier to visualize, characterization of foam microstructure can come from a description of the pore shape and arrangement. Given the random nature of the microstructures of blown foam, both approaches are useful and valid. This paper describes our work aimed at linking the mechanical response and microstructural evolution of high relative-density foam as it undergoes large deformation. This work consists of several inter-related parts, including (i) measuring the compressive stress-strain response, as illustrated in Fig. 1, (ii) obtaining in situ micro X-ray computed tomography (MXCT) images of high relative-density foams undergoing large strains, and (iii) developing mathematical, computer aided, methodologies to perform image analysis and calculations of parameters that characterize the pores and struts. By using MXCT, a non-invasive technique for imaging the internal structure of materials, we are able to observe, internally, individual struts and pores as they undergo large deformation. Here we describe our computer aided image analysis methodologies and present examples of their application to the MXCT images of foams. Operations of the computer program include noise removal (smoothing), thresholding [7], edge detection [8], distance transformation [9, 10], pore detection via a Hough transformation [11], and skeletonization [12]. Strut parameters, such as the strut cross-sectional area and strut arrangement, are calculated from a skeleton-based model of the MXCT images. The Hough transform is a feature detection method used primarily in image analysis applications. We use this transform to detect and calculate pore parameters, such as pore arrangement and pore size distribution. The experiments and calculations are performed in order to develop data for the formulation of theory that links foam mechanical behavior specifically to the microstructure of high relative-density foams, not just simply to the relative-density of the foam.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC52-06NA25396
- OSTI ID:
- 992192
- Report Number(s):
- LA-UR-09-05131; LA-UR-09-5131; TRN: US201022%%179
- Country of Publication:
- United States
- Language:
- English
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