Optimal ligament lengths in impact fracture toughness estimation by the essential work of fracture method

This work presents a statistical analysis of the confidence in fracture parameters of polymers estimated through the essential work of fracture (EWF) methodology under impact conditions. Fracture toughness parameters-essential, we, and non-essential work of fracture, wp-are obtained from the experimental relationship between specific total work of fracture wf and ligament length of the tested samples l: we is obtained from the y-intercept and wp from the slope of wf versus l in cases where a linear fit is suitable. The distribution of ligament lengths within a fixed number of samples to be tested under impact loading conditions is determined in order to minimize the uncertainty of the estimated parameters when linear reduction of the data is assumed. The statistical approach applied to two different polymeric materials shows that the uniform ligament length distribution along the ligament range is not the optimal one. We propose an optimal distribution of ligament lengths to be tested that depends on the distribution of error standard deviations of the measured work of fracture along the l-axis.