Modern Experimental Stress Analysis

Modern Experimental Stress Analysis

This book is based on the assertion that, in modern stress analysis, constructing the model
is constructing the solution—that the model is the solution. But all model representations
of real structures must be incomplete; after all, we cannot be completely aware of every
material property, every aspect of the loading, and every condition of the environment,
for any particular structure. Therefore, as a corollary to the assertion, we posit that a
very important role of modern experimental stress analysis is to aid in completing the
construction of the model.

What has brought us to this point? On the one hand, there is the phenomenal growth
of finite element methods (FEM); because of the quality and versatility of the commercial
packages, it seems as though all analyses are now done with FEM. In companies
doing product development and in engineering schools, there has been a corresponding
diminishing of experimental methods and experimental stress analysis (ESA) in particular.
On the other hand, the nature of the problems has changed. In product development,
there was a time when ESA provided the solution directly, for example, the stress at a
point or the failure load. In research, there was a time when ESA gave insight into the
phenomenon, for example, dynamic crack initiation and arrest. What they both had in
common is that they attempted to give “the answer”; in short, we identified an unknown
and designed an experiment to measure it. Modern problems are far more complex, and
the solutions required are not amenable to simple or discrete answers.

In truth, experimental engineers have always been involved in model building, but the
nature of the model has changed. It was once sufficient to make a table, listing dimensions
and material properties, and so on, or make a graph of the relationship between quantities,
and these were the models. In some cases, a scaled physical construction was the model.
Nowadays the model is the FEM model, because, like its physical counterpart, it is a
dynamic model in the sense that if stresses or strains or displacements are required, these
are computed on the fly for different loads; it is not just a database of numbers or graphs.
Actually, it is even more than this; it is a disciplined way of organizing our current
knowledge about the structure or component. Once the model is in order or complete, it
can be used to provide any desired information like no enormous data bank could ever
do; it can be used, in Hamilton’s words, “to utter its revelations of the future”. It is this
predictive and prognostic capability that the current generation of models afford us and
that traditional experimental stress analysis is incapable of giving.

There are two main types of stress analyses. The first is conceptual, where the structure
does not yet exist and the analyst is given reasonable leeway to define geometry, material,
loads, and so on. The preeminent way of doing this nowadays is with the finite element
method (FEM). The second analysis is where the structure (or a prototype) exists, and it
is this particular structure that must be analyzed. Situations involving real structures and
components are, by their very nature, only partially specified. After all, the analyst cannot
be completely aware of every material property, every aspect of the loading, and every
condition of the environment for this particular structure. And yet the results could be
profoundly affected by any one of these (and other) factors. These problems are usually
handled by an ad hoc combination of experimental and analytical methods—experiments
are used to measure some of the unknowns, and guesses/assumptions are used to fill in
the remaining unknowns. The central role of modern experimental stress analysis is to
help complete, through measurement and testing, the construction of an analytical model
for the problem. The central concern in this book is to establish formal methods for
achieving this.

Experimental methods do not provide a complete stress analysis solution without additional
processing of the data and/or assumptions about the structural system. Figure I.1

shows experimental whole-field data for some sample stress analysis problems—these
example problems were chosen because they represent a range of difficulties often encountered
when doing experimental stress analysis using whole-field optical methods. (Further
details of the experimental methods can be found in References [43, 48] and will be elaborated
in Chapter 2.) The photoelastic data of Figure I.1(b) can directly give the stresses
along a free edge; however, because of edge effects, machining effects, and loss of
contrast, the quality of photoelastic data is poorest along the edge, precisely where we
need good data. Furthermore, a good deal of additional data collection and processing is
required if the stresses away from the free edge is of interest (this would be the case in
contact and thermal problems). By contrast, the Moir´e methods give objective displacement
information over the whole field but suffer the drawback that the fringe data must be
spatially differentiated to give the strains and, subsequently, the stresses. It is clear from
Figure I.1(a) that the fringes are too sparse to allow for differentiation; this is especially
true if the stresses at the load application point are of interest. Also, the Moir´e methods
invariably have an initial fringe pattern that must be subtracted from the loaded pattern,
which leads to further deterioration of the computed strains. Double exposure holography
directly gives the deformed pattern but is so sensitive that fringe contrast is easily lost
(as is seen in Figure I.1(c)) and fringe localization can become a problem. The strains
in this case are obtained by double spatial differentiation of the measured data on the
assumption that the plate is correctly described by classical thin plate theory—otherwise

it is uncertain as to how the strains are to be obtained.


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