Sample Sizes Based on Weibull Distribution and Normal Distribution for FRP Tensile Coupon Test

Area of Science:

• Materials Science
• Mechanical Engineering
• Statistical Analysis

Background:

• Current guidelines for fiber reinforced polymer (FRP) tensile coupon testing recommend a sample size of five, assuming normal distribution and a coefficient of variation (COV) of 0.058.
• Research increasingly supports the Weibull distribution for characterizing FRP tensile properties, yet its impact on sample size determination remains under-explored.
• Practical COVs for FRP properties can range significantly, from 5% to 15%, potentially challenging the adequacy of the current sample size recommendation.

Purpose of the Study:

• To compare sample size requirements for FRP tensile testing using a two-parameter Weibull distribution versus the traditional normal distribution.
• To evaluate whether the Weibull distribution yields a more conservative sample size for FRP tensile properties.
• To assess the prediction error associated with the current guideline of five samples across a range of practical COVs.

Main Methods:

• Statistical comparison of sample size calculations based on two-parameter Weibull and normal distributions.
• Analysis of sample size requirements for FRP tensile properties with varying coefficients of variation (COVs) from 0.05 to 0.20.
• Quantification of prediction errors for material properties when using a fixed sample size of five across different COVs.

Main Results:

• The Weibull distribution generally results in a sample size comparable to that of the normal distribution, indicating the current normal distribution-based sample size is broadly applicable.
• For COVs ranging from 0.05 to 0.20, the required sample sizes varied significantly, from less than 10 to over 60 specimens.
• Utilizing only five specimens can lead to substantial prediction errors in material properties, ranging from 6.2% to 24.8% for the tested COV range.

Conclusions:

• The sample size derived from normal distribution assumptions is generally applicable for fiber reinforced polymer (FRP) tensile testing, even when a Weibull distribution is more appropriate.
• A sample size of five is insufficient for FRP tensile coupon tests when the coefficient of variation exceeds 0.058, leading to significant prediction errors.
• Further research may be needed to refine sample size guidelines for FRP composites, considering the practical variability in material properties and the suitability of different statistical distributions.