Bias in Linear Regression Analysis of Compliance Measurements in Fatigue Crack Growth and Fracture Toughness Tests

• Published in: Materials performance and characterization 2018-06, Vol.7 (2), p.26-46
• Main Authors: Brazill, Richard L., Donald, J. Keith
• Format: Article
• Language: English
• ISSN: 2379-1365; 2165-3992
• DOI: 10.1520/MPC20170118

When compliance methods are used to determine specimen crack size in fracture mechanics testing, accurate and unbiased determination of the slope of the linear region of the force versus the crack opening displacement (COD) curve is required. Often, the region of interest is isolated by truncation of data that lie outside either force or COD limits. Two decisions are required: which parameter to use for the truncation and which to use as the independent variable in the linear regression analysis. This article will demonstrate that the incorrect choice of independent variable for truncated data sets can lead to a systematic bias in the determination of the linear regression slope and intercept. It will be shown with Monte Carlo simulations that the independent variable for linear regression should always be the same as the truncation variable, and in this case the variation in slope will be random, with a zero mean. The magnitude of the slope bias is related to the relative noise in each variable. Not only will this lead to a bias in determining crack size, but large errors can occur when determining nonlinearity associated with crack-opening force and in the crack-compliance method for determining the crack driving force due to residual stress, Kres.