Materials under vibration experience internal stress waves that can cause material failure or energy loss due to inelastic vibration. Traditionally, failure is defined in terms of material acceleration, yet this approach has many drawbacks, principally because it is not invariant with respect to scale, type of vibration, or material choice. Here, the likelihood of failure is instead considered in terms of the maximum vibration or particle velocity for various metals, polymers, and structural materials. The exact relationship between the maximum particle velocity and the maximum induced stress may be derived, but only if one knows the details of the vibration, material, flaws, and geometry. Statistical results with over thousands of individual trials are presented here to demonstrate a wide variety of vibrations across a sufficient variety of these choices. Failure in this context is defined as either fracture or plastic yield, the latter associated with inelastic deformation and energy loss during vibration. If the maximum permissible cyclical stress in material vibration is known, to at least an order of magnitude, the probability of this type of failure may be computed for a range of vibration velocities in each material. The results support the notion that a maximum particle velocity on the order of 1 m/s is a universal and critical limit that, upon exceeding, causes the probability of failure to become significant regardless of the details of the material, geometry, or vibration. We illustrate this in a specific example relevant to acoustofluidics, a simple surface acoustic wave device. The consequences of particle velocity limit analysis can effectively be used in materials and structural engineering to predict when dynamic material particle velocity can cause inelastic losses or failure via brittle fracture, plastic deformation, or fatigue failure.