Fracture testing of spectacle lenses
SOLA International is working with MI*Net to develop mathematical models that will predict the impact strength of new lens designs.
New lenses are tested by dropping a steel ball onto them. Can we predict the impact strength of a new lens design?
Before new lenses are allowed to be sold, USA and European authorities demand they meet certain safety standards. In particular, they must be resistant to fracturing. In the USA lenses are tested by dropping a steel ball of specified size from a predetermined height onto the centre of the lens; in Europe a similar ball is pushed against the lens at a prescribed pressure.
SOLA International, founded in Adelaide in 1960, is now the world's largest manufacturer and supplier of plastic spectacle lenses, and makes more than 20,000 different types of plastic lens. Since the early days in Adelaide, the company's business success has depended on innovation. Over 60% of SOLA's current sales derive from new products, which means that safety testing is a significant activity for the company.
The current test methods are laborious and costly. The drive towards thinner, lighter lenses with multilayered coatings to reduce scratching and glare makes lens design a difficult problem.
Creating a new product range is a nightmare. Qualifying a new material for lenses is an even bigger nightmare.
SOLA believe that accurate numerical models of the impact process and subsequent lens fracture will save time, effort and money in laboratory testing. At the very least, the process of building such models would provide greater insight into the lens fracture process.
The company needed a model to predict from the geometry of a lens, and the force of the impact, whether or not the lens would fracture. The idea was to reduce the amount of laboratory testing by focusing attention on those types of lenses which were likely to be most at risk of breakage.
A suitable model might also provide a means to predict stresses in the back surface coating, and a capacity to predict crack initiation and propagation. The very process of constructing the model provides insight into those factors which affect fracture.
SOLA presented their problem at the Mathematics in Industry Study Group (MISG) 2000 workshop. The MISG team was able to construct and solve an equation to calculate the stress at the back of a cylindrical lens for a given force on the front. It is this stress that causes a lens to fracture. The stresses predicted by the model were comparable with empirical figures obtained from the company.
The group also calculated the characteristics of the vibrations set up in a flat plastic plate when hit by a steel ball. The period of transverse and compressive waves was about a millionth of a second, bending and flexing of the plate took less than a thousandth of a second, whereas the duration of impact was about two thousandths of a second. The group showed that the forces imparted by the USA drop ball test and the European static test were almost equal, and yet lenses tend to fracture more easily in the American test.
Enough was achieved in a week to show that development of the kinds of models requested by SOLA International is possible with further work. SOLA and MI*Net are continuing the work.
We've had a fascinating week. It is a difficult problem, and we were not sure how far people would get, but we are very encouraged by the results.
|MI*Net consultant:||Professor Jim Hill
University of Wollongong