17 June 2011

A toppling failure in a lemon meringue

Posted by Dave Petley

Dessert at Michele’s house last night was a rather wonderful lemon meringue cooked by her mother, Christine (thanks!).  The meringue had already been cut; when we started upon it this was what found:

The strawberries give the game away – the outer edge of the meringue had undergone what initially appeared to be a classic toppling failure, with clear evidence of rotation outwards as the collapse developed.  At first glance this is about as close to a textbook example as you are ever likely to get, as per this BGS illustration:

An aerial view of the situation provides some clarity regarding the process:

This allows us to start to understand what has gone on here.  Note the weaker lemon curd and soft basal meringue below the more cohesive cream topping.  After erosion of the toe of the slope (removal of the previous slice), the soft basal meringue has not been able to withstand the combined load of the (dense) cream and the strawberries, and has flowed outwards.  This has put the cream under tension (and I think that as with many cohesive materials, its tensile strength is probably low ), allowing a crack to develop.  At that point disaster became inevitable.

In the interests of science (as you can see, I am willing to suffer for this blog)! we decided we should test the hypothesis by cutting a cross-section through it:

The toppled block is clearly visible on the right.  Note the thinning from left to right of the lower layer of the less brittle meringue, which has allowed the topple to develop.  However, close inspection suggests that here is one additional thing of interest here though.  The upper (cohesive) cream layer has also moved forward (note the tension crack on the left side just behind the leftmost strawberry), suggesting an additional complexity to the process.  Unfortunately, this suddenly means that the mechanism is not a simple topple but is instead a complex mix of translational motion, deep-seated ductile deformation and toppling.  A hypothesis would be that the order of events was:

  1. Erosion of the toe (removal of the previous piece)
  2. Ductile deformation of the basal layer
  3. Development of a tension crack
  4. Sliding of the cream layer on the lemon curd layer, which pushed the frontal block forward
  5. Toppling of the frontal block
  6. Continued sliding of the main block

Unfortunately, it could also be that the topple preceded the translational movement, but at the moment there is no way of knowing.  Clearly further research is needed.  It is however fair to say that after all this science we had developed an appetite, such that future investigations will need a new meringue…

The lessons here are of course that toppling failures are dominated by the combination of the physics of the system and the mechanics of the materials and that, as in most landslides, systems that initially appear to be simple prove to be rather more complex once investigated properly.

Comments welcome!