The mechanical properties of some materials (Cu, Ni, Ag, etc.) have been shown to develop strong dependence on the geometric dimensions, resulting in a size effect. Several theories have been proposed to model size effects, but have been based on very few experiments conducted at appropriate scales. Some experimental results implied that size effects are caused by increasing strain gradients and have been used to confirm many strain gradient theories. On the other hand, some recent experiments show that a size effect exists in the absence of strain gradients. This report describes a brief analytical and experimental study trying to clarify the material and experimental issues surrounding the most influential size-effect experiments by Fleck et al (1994). This effort is to understand size effects intended to further develop predictive models.
Accurate material models are fundamental to predictive structural finite element models. Because potting foams are routinely used to mitigate shock and vibration of encapsulated components in electro/mechanical systems, accurate material models for foams are needed. A viscoplastic foam constitutive model has been developed to represent the large nonlinear and rate dependent crush of a polyurethane foam throughout an application space defined by temperature, strain rate and strain levels. Validation of this viscoplastic model, which is implemented in the transient dynamic Presto finite element code, is being achieved by modeling and testing a series of structural geometries of increasing complexity that have been designed to ensure sensitivity to material parameters. Both experimental and analytical uncertainties are being quantified to ensure fair assessment of model validity. Quantitative model validation metrics are being developed to provide a means of comparing analytical model predictions with experimental observations. This paper focuses on model validation of foam/component behavior over a wide temperature, strain rate, and strain level range using a Presto viscoplastic finite element model. Experiments include simple foam/component test articles crushed in a series of drop table tests. Material variations of density have been included. A double blind validation process is described that brings together test data with model predictions.
The foam material of interest in this investigation is a rigid closed-cell polyurethane foam PMDI with a nominal density of 20 pcf (320 kg/m3). Three separate types of compression experiments were conducted on foam specimens. The heterogeneous deformation of foam specimens and strain concentration at the foam-steel interface were obtained using the 3-dimensional digital image correlation (3D-DIC) technique. These experiments demonstrated that the 3D-DIC technique is able to obtain accurate and full-field large deformation of foam specimens, including strain concentrations. The experiments also showed the effects of loading configurations on deformation and strain concentration in foam specimens. These DIC results provided experimental data to validate the previously developed viscoplastic foam model (VFM). In the first experiment, cubic foam specimens were compressed uniaxially up to 60%. The full-field surface displacement and strain distributions obtained using the 3D-DIC technique provided detailed information about the inhomogeneous deformation over the area of interest during compression. In the second experiment, compression tests were conducted for cubic foam specimens with a steel cylinder inclusion, which imitate the deformation of foam components in a package under crush conditions. The strain concentration at the interface between the steel cylinder and the foam specimen was studied in detail. In the third experiment, the foam specimens were loaded by a steel cylinder passing through the center of the specimens rather than from its end surface, which created a loading condition of the foam components similar to a package that has been dropped. To study the effects of confinement, the strain concentration and displacement distribution over the defined sections were compared for cases with and without a confinement fixture.