Introduction
A substantial problem which is not well studied or understood with regard to growth stress is the characterization of the stress field existing within the stem. There is currently no known technology which has the ability to directly or indirectly measure either the surface or volume stress field with a degree of accuracy which would provide insight into the scale of local inhomogeneity. It is suspected, once a reliable technology is developed to investigate the field our understanding and way of thinking about growth stress from both a theoretical and applied view will change significantly. Various hypothetical stress fields based on conservation of energy etc. have been suggested, for a review see Chapter 1.
Currently rudimentary testing technologies such as strain gauges are limited to measuring surface strains with an unknown level of accuracy. There are no current testing procedures which are non-destructive, and hence repeated testing on a unique (all wooden samples are unique) samples is imposable. Most techniques use multiple measurements of surface strain around the stem which are then averaged \cite{Archer1987,Kubler1987} to provide a single quantification of 'growth strain' however, the accuracy of any one of these given testing procedures can not be tested as measurement error and variation on the stem surface are completely confounded. The same problem exists for the splitting test as was discussed in Chapter 5, the splitting test is the only growth strain testing procedure fast enough to be used for tree breeding, so calculating its reliability is of practical importance.
A more fundamental problem also exists; the idea that growth strain is usefully quantifiable as a mean surface strain, whether obtained through multiple surface tests or through some geometric averaging as is implicit in the splitting tests. This assertion is particularly problematic for wood scientists who are interested in identifying pieces of timber which are unlikely to bend during sawing whether that be developing in-line screening technology for mills or to assist breeders identifying favorable genetics in breeding programs. In a rudimentary way, the first step to investigating this problem is taken here, by investigating the relationship between surface strain variation with individuals and mean surface strain variation between individuals. Unlikely surface strain profiles are identified and removed and estimates on the reliability of the splitting test and strain gauge tests are made.
Method
Simulating an individual sample
In order to investigate the roll differing surface stress profiles play on the reliability of both the rapid splitting test procedure and 'point' based procedures such as using strain gauges or CIRAD an orthotropic elastic mathematical model of a typical very early selection stem sample was developed. This generic sample was assumed to be a truncated cone with a length of 400 mm, a small end diameter of 34.8 mm and a big end diameter of 39.55 mm. The material of the sample was amused to be orthotropic with longitudinal stiffness coming from Eucalyptus argophloia (Chapter 5) the remainder being taken from \citet{Gon_alves_2013}, or derived as a ratio from the E. argophloia longitudinal value. Salome and Netgen \cite{Ribes_2007,Schöberl1997} was used to create a mesh of 6436 verticies and 22506 cells to approximate the sample using 3 dimensional tetrahedrons, and a slit from the big end, though the pith with a width of 0.9 mm and a length of 300 mm was added to simulate the splitting test, as can be seen in Figure \ref{518491}. Further the slit was rotated 90 degrees about the pith and a second mesh created to provide multiple splitting test measurements from each modeled sample.