Product fragility and damage boundary theory

The theoretical basis for the widely accepted Damage Boundary Curve approach to product fragility and the applicability of its associated ASTM fragility assessment test procedure are first discussed. The basic assumption that the product can be modelled as a collection of linear spring/mass systems is shown to lead to specific characteristics of the product's damage boundary curve which are not borne out by the results of shock tests performed on some common consumer products. Discrepancies between theoretical predictions and experimental results are attributed to the inability of the model to account for progressive failure due to plastic deformation accumulated as a result of repeated shocks. An alternative damage boundary curve for a rigid/perfectly‐plastic model is then developed and shown to be a better estimate of fragility for a broader class of products based on the results of shock tests. Modifications to the standard ASTM test procedure required to obtain the damage boundary curve for this type of product are suggested. Finally, the damage boundary theory for a generalized model which incorporates both elastic and plastic properties is developed. The feature of the damage boundary curve which are shown to survive regardless of the choice of model for the product are the critical velocity change and critical acceleration parameters. Those which do not are the shape of the damage region and the associated test procedures.