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Title

INVESTIGATION AND MODELING OF PRESSURE DEPENDENT YIELD BEHAVIOR OF 3D STOCHASTIC AND PERIODIC FOAMS

Creator

Ayyagari Venkata S, Ravi Sastri

Date

2013, 2013-07

Description

With growing potential of cellular solids in a multitude of diverse engineering applications including but not limited to automotive,...
Show moreWith growing potential of cellular solids in a multitude of diverse engineering applications including but not limited to automotive, aerospace, naval and biomed- ical industries as lightweight alternatives and space lling cores in sandwich struc- tures, need for predictive yield/failure criteria for these load bearing members under multiaxial stress states becomes critical. Although there exist several yield criteria proposed in the literature for highly porous solid foams, they are all phenomenolog- ical in nature, rely on relatively long list of model parameters that require di cult experimentation not readily available to end user, and none of them can handle the anisotropy observed in the majority of commercially available solid foams. Further, it is by now well established that, unlike commonly used engineering bulk solids, the yield behavior of highly porous solid foams is signi cantly in uenced by the hydro- static component of stress. In majority of phenomenological yield criteria proposed for solid foams this dependence is expressed by a quadratic pressure term. The scope of this study is quite comprehensive in the sense that it integrates analytical and computational investigation of yield behavior in solid foams along with extensive validation by recent experimental results produced in our lab. Present study proposes a physics based approach by hypothesizing that the yielding of stochastic foams is governed by the total elastic strain energy density, which leads to an energy based yield criterion for transversely isotropic foams and also provides a physical basis for the quadratic pressure dependence commonly adopted in existing phenomenolog- ical models. An added bene t of the analytical framework proposed in this work is that it introduces new scalar measures of stress and strain, which are referred to as characteristic stress and characteristic strain, that function in an analogous way to e ective (von Mises) stress and strain commonly used in analyzing the yield and post- yield behavior of bulk metals. Besides accommodating anisotropy, this energy-based xii yield criterion renders a unique advantage by relying only on the elastic properties and uniaxial yield strengths of the material, which makes the proposed yield criterion extremely practical for end user. Results from experimental data obtained from multiaxial testing of Divinycell H100 and H130 foams (Sha q, 2009; Ehaab, 2011) as well as a series of extensive com- putational simulations performed in this study on: a) periodic Kelvin foam models (both isotropic and transversely isotropic) of varying relative densities, b) stochastic Voronoi foams (both isotropic and transversely isotropic), point out to an additional linear pressure dependence in the yield behavior of solid foams, from a load-sharing viewpoint. This dependence is observed to be more pronounced at lower relative den- sities. A simple quantitative technique which is based on the partition of elastic strain energy into bending and stretch components is used to identify the distribution of deformation modes at microstructural level, along with its in uence on load sharing as a function of stress path. Furthermore, a plasticity model that incorporates a ow rule and hardening law are presented which allows the analysis of inelastic deforma- tions in solid foams in a continuum framework. Such models facilitate development of user de ned material model (UMAT) that allow evaluating the performance of proposed yield criterion under complex loading scenarios, such as indentation and punch loading.
PH.D in Mechanical and Aerospace Engineering, July 2013
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