برآورد مجازی قابل قبول ارزش B ورقه های کامپوزیت
Abstract
1- Introduction
2- Methodology
3- Case study
4- Sensitivity analysis
5- UQ&M framework validation
6- Applications
7- Conclusions
References
Abstract
The design of composite structures relies on the accurate determination of design allowables, which are statistically based material parameters that take into account manufacturing, geometrical and microstructure variability. The accurate determination of these design parameters requires extensive experimental testing, which makes the certification process of a composite material extremely costly and time consuming. To increase the efficiency of the design process, there is the need to develop alternatives to the mostly experimental material characterization process, ideally based on accurate and quick modelling analysis combined with powerful statistical tools. In this work an analytical model to compute the notched strength of composite structures based on three ply-based material properties (elastic modulus, unnotched strength and -curve) is combined with an uncertainty quantification and management (UQ&M) framework to compute the B-basis design allowables of notched configurations of CFRP laminates. The framework is validated with open-hole tension experimental results for the IM7/8552 material. Given the analytical nature of the developed framework and consequent computational efficiency, the UQ&M methodology is applied to the generation of design charts for notched geometries, whose generation would otherwise be impractical, using experimental test based methods.
Introduction
The design and certification of composite structures is based on the building block approach [1]. This approach relies on the accurate determination of design allowables that drive the design of structures at larger scales. These design allowables are statistically based material parameters that define an acceptable stress value for a material and, therefore, ensure their safe and efficient use. Design allowables have to account for the variability of the material properties and of the manufacturing process, and are a function of the structural details and loading conditions [2] and, consequently, their experimental determination is an extremely costly and time-consuming process. The standard design allowable used in the aeronautical industry for fail safe structures is the B-basis [1, 3], which is defined as the 95% lower confidence bound on the tenth percentile of a specified population of measurements. This is a conservative allowable that ensures with 95% confidence that 90% of the population will have a given property, e.g. strength, higher than the B-value allowable. It is of key importance to accurately determine these design allowables, however, time consuming processes are not ideal during preliminary design. For this reason, alternatives to fully experimental material characterization have been proposed, namely, the use of statistically based numerical and analytical models [4, 5, 6, 3]. These models include the influence of the uncertainty related to the determination of the input parameters and their intrinsic variability on the global response of the model. A convenient way to describe these uncertain quantities is to describe them using a probability distribution which can be defined through experimental measurements or assumed based on empirical evidence. The stochastic finite element method [7, 5] is a powerful tool to address the influence of the uncertainty related to the determination of the material and geometrical properties and loading conditions on the global response of composite structures. Nam et al. [7] proposed a methodology to determine the design allowables of composite laminates using lamina level test data and finite element analysis and validate the proposed methodology for both un-notched and open hole strength. However, stochastic finite element method solutions rely on computationally expensive procedures, which makes the consideration of the variability of the input parameters an extremely time consuming and, therefore, impracticable process quick design.