Uncertainty modelling and code calibration for composite materials

Uncertainties related to the material properties of a composite material can be determined from the micro-, meso- or macro-scales. These three starting points for a stochastic modelling of the material properties are investigated. The uncertainties are divided into physical, model, statistical and measurement uncertainties which are introduced on the different scales. Typically, these uncertainties are taken into account in the design process using characteristic values and partial safety factors specified in a design standard. The value of the partial safety factors should reflect a reasonable balance between risk of failure and cost of the structure. Consideration related to calibration of partial safety factors for composite material is described, including the probability of failure, format for the partial safety factor method and weight factors for different load cases. In a numerical example, it is demonstrated how probabilistic models for the material properties formulated on micro-scale can be calibrated using tests on the meso- and macro-scales. The results are compared to probabilistic models estimated directly from tests on the macro-scale. In another example, partial safety factors for application to wind turbine blades are calibrated for two typical lay-ups using a large number of load cases and ratios between the aerodynamic forces and the inertia forces.

[1]  D. J. Lekou,et al.  Mechanical property variability in FRP laminates and its effect on failure prediction , 2008 .

[2]  John Dalsgaard Sørensen,et al.  Reliability-Based Design of Wind Turbine Blades , 2011 .

[3]  Henrik O. Madsen,et al.  Load Combinations in Codified Structural Design , 1980 .

[4]  B. D. Agarwal,et al.  Analysis and Performance of Fiber Composites , 1980 .

[5]  Andrew Shaw,et al.  A critical reliability evaluation of fibre reinforced composite materials based on probabilistic micro and macro-mechanical analysis , 2010 .

[6]  N. J. Tarp-Johansen.  Partial Safety Factors and Characteristic Values for Combined Extreme Wind and Wave Load Effects , 2005 .

[7]  Niels C. Lind,et al.  Methods of structural safety , 2006 .

[8]  Kim Branner,et al.  Investigating the impact of non‐linear geometrical effects on wind turbine blades—Part 1: Current status of design and test methods and future challenges in design optimization , 2011 .

[9]  Theodore V. Galambos,et al.  Probability-based criteria for structural design , 1982 .

[10]  Michael Shiao,et al.  Probabilistic Evaluation of Fuselage-Type Composite Structures , 1999 .

[11]  R. Bennett,et al.  Statistical Characterization of Fiber-Reinforced Polymer Composite Material Properties for Structural Design , 2006 .

[12]  Marios K. Chryssanthopoulos,et al.  Probabilistic Models for Spatially Varying Mechanical Properties of In-Service GFRP Cladding Panels , 2009 .

[13]  M. Hinton.  Failure Criteria in Fibre-Reinforced-Polymer Composites: The World-Wide Failure Exercise , 2004 .

[14]  J. C. H. Affdl,et al.  The Halpin-Tsai Equations: A Review , 1976 .

[15]  Jack W. Baker,et al.  On the assessment of robustness , 2008 .

[16]  John Dalsgaard Sørensen,et al.  Optimal, Reliability-Based Code Calibration , 1994 .

[17]  Vistasp M. Karbhari,et al.  Sources of uncertainty and design values for field-manufactured FRP , 2009 .

[18]  S. Sriramula,et al.  Quantification of uncertainty modelling in stochastic analysis of FRP composites , 2009 .

[19]  Brian Hayman,et al.  Approaches to Damage Assessment and Damage Tolerance for FRP Sandwich Structures , 2007 .

[20]  R. A. Shenoi,et al.  Size and scale effects in composites: I. Literature review , 1999 .

[21]  Norman A. Fleck,et al.  Compressive Failure of Fiber Composites , 1997 .

[22]  Bruce R. Ellingwood,et al.  Toward Load and Resistance Factor Design for Fiber-Reinforced Polymer Composite Structures , 2003 .

[23]  Galib H. Abumeri,et al.  Probabilistic dynamic buckling of composite shell structures , 2005 .

[24]  Henrik Stensgaard Toft,et al.  Defect Distribution and Reliability Assessment of Wind Turbine Blades , 2011 .

[25]  Christos C. Chamis,et al.  Probabilistic Simulation of Multi-Scale Composite Behavior , 2012 .

[26]  Michael R Wisnom,et al.  Size effects in the testing of fibre-composite materials , 1999 .