It's beeen a while since we have waxed theoretical. In this blog-post from January we explore some of the benefits and weaknesses of the empirically-minded approaches to composites analysis. Enjoy.
In a previous blog, we talked about the importance of learning from failure in materials testing. For better or worse, theoreticians have, in some ways, tried taken the burden of “learning from failure” off the plate of the common engineer. Instead, they try to capture the insights gained from failure into flexible analytical theories; theories that (theoretically) allow us to predict a parts behavior, without knowing anything more than some material properties and part dimensions. In computer science, this is known as abstraction.
The question is, Can composite failure theories sufficiently abstract all the nuance out of composites design? Do you need to understand the origins of a failure theory in order to use it properly?
Collectively evaluating individual failure theories:
In 1991, amid growing interest in composite materials, a group of material experts, organized by the science and engineering council of the UK, convened a meeting. The organizers set out to assemble a comprehensive unbiased evaluation of all major composites failure theories. At the time, even for simple lamina or laminate, there was a lack of evidence to show whether any theories could definitively provide meaningful predictions of the ultimate strength of a structure.
Further, at the onset of the trials, and still to some extent today, extensive materials testing was required in order to determine global material allowable’s, which were typically set at levels less than 30% of the ultimate material strength.
The organizers called this ambitious competition the World Wide Failure Exercises (WWFE) and its goals included:
- To establish the level of accuracy of the theories used for establishing the failure responses of fiber reinforced plastic laminates (FRP)
- To bridge the gap between the theoreticians and design practitioners in the engineering field.
- To help train design engineers with more robust and accurate methods of failure prediction.
Most importantly, these evaluations were to be carried out in a thorough, objective, and dispassionate manner.
World Wide Failure I:
The first world-wide failure exercise (WWFE) kicked off in 1996 and came to an end in 2004. It focused on studying fiber-reinforced lamina under biaxial stresses. The results of this study were published here in a 1200 page compendium.
If the study uncovered nothing else,it revealed that all theories are good for some applications, but no failure theories are good for all application
WWF I was a pioneering effort that exposed the strengths and weaknesses of 19 popular theories, and more importantly provided an index of evidence as to each theory’s bounds of applicability and levels of confidence.s. The most impressive part of the publication is their summary of all the strong and weak points of each theory, found here. These organizers demonstrated that understanding the reasons why a theory is successful and unsuccessful is crucial to knowing whether it will be relevant to your unique application.
World Wide Failure II and III:
Despite the achievements of WWF I, the exercise provided little guidance in the two significant areas, critical for real world composites design:
- The behavior of materials under triaxial stresses
- Damage/matrix crack development, initiation of matrix-driven delamination and ultimate failure.
For these reasons, the organizers initiated a two more competitions, which attempted to analyze these theories against a number of triaxial test-cases (WWFEII), and gain more insight into the prediction of evolving composite damage (WWFEIII).
The results of the WWFEII were similar to those obtained in the first exercise. The designers, wishing to use the models benchmarked in WWFE-II, can only expect a few theories to give acceptable correlation (within 50%) with test data for 75% of the test cases used. This again proved that an non-superficial understanding of available theories is very much required if one is to expect accurate prediction results. A special issue of the Journal of Composite materials detailed the results.
To evaluate the theories predicting damage and failure mechanisms, WWFE-III is currently being conducted and is expected to run for another couple of years.
As stated by the organizers “It is widely accepted that, in designing structures with laminated fiber-reinforced composites, there is a need to understand damage initiation, damage propagation and ultimate fracture and how each relate to the state of stress–strain behavior and modes of failure.” The folks at MultiMechanics couldn’t agree more.
After 25 years since the exercises inception, there is one thing we know for sure: you cannot let theoreticians blindly abstract what has been learned through decades of trial-and-error (and research). Any time you are using an analytical tool to solve a real-world problem, the assumptions of that tool need to be clearly understood, and the pros and cons carefully weighed.If you’d like help understanding the nuances of different composite failure theories, reach out to us at email@example.com