February AMP_Digital

A D V A N C E D M A T E R I A L S & P R O C E S S E S | F E B R U A R Y / M A R C H 2 0 1 9 2 7 *Member of ASM International T he J -integral versus crack-growth resistance curve ( J-R curve) is a useful tool for evaluating material fracture toughness in the ductile region [1] . A widely accepted practice for conduct- ing J-R curve testing is ASTM standard E1820 [2] , which introduces the normaliza- tion method. This method does not re- quire compliance measurements during testing, significantly simplifying J-R curve testing compared with the convention- al elastic unloading compliance (EUC) method. Despite the advantage in testing, analysis procedures for the normaliza- tion method are very complicated. Also, there is no open source software current- ly available to perform such analysis. The authors developed an open source automated J-R curve-analysis software based on the normalization method inASTME1820-18. Source codes were written in MATLAB and the com- piled software, in the form of a stand- alone executable, has a user-friendly graphic interface and is readily com- patible with modern Windows operat- ing systems. Both source codes and the compiled executable file are available for download at https://code.ornl.gov/ xc8/ANJR.git. Comparisons between re- sulting J-R curves from the software and manual analysis procedures show essentially identical results, indicating the suitability of applying the automat- ed software for J-R curve analysis. NORMALIZATION METHOD PRINCIPLES The normalization method was initially developed by Herrera and Lan- des et al. [3,4] and later studied by Joyce [5] and Lee [6] . The method requires only load displacement data, initial and final crack size measurements, and speci- men dimensional and physical prop- erties to derive the J-R curve. With the elimination of compliance mea- surements in testing, the normaliza- tion method significantly simplifies J-R curve testing and reduces testing time compared with the EUC method (Fig. 1). Procedures for applying the nor- malization method to derive the J-R curve are described in detail in Annex A15 of ASTM E1820. Experimental load displacement data up to, but not in- cluding, the maximum load and the final load displacement pair are con- verted into the normalized load ( P Ni ) and normalized plastic displacement ( ν ’ pli ) according to Eq. (1) and (2): ( ) pl i Ni bi P P W a WB W η = − (1) ' i i i pli v PC v W − = (2) where P i = load at the ith data point, W = specimen width, B = specimen thickness, a b i = blunting corrected crack size at the ith data point, η pl = dimen- sionless parameter that relates plastic work done on a specimen to crack growth resistance defined in terms of deformation theory J -integral [7] , ν i = dis- placement at the ith data point, and C i = specimen elastic load line compli- ance based on crack size a b i . A line is drawn from the normal- ized final load displacement pair tan- gent to the remaining data as shown in Fig. 2. The final normalized load displacement pair and data between ν ' p li >0.001 and the tangent point are fitted with the following normaliza- tion function: USING AUTOMATED J-R CURVE ANALYSIS SOFTWARE TO SIMPLIFY TESTING AND SAVE TIME Newly developed automated software based on the ASTM standard E1820-18 normalization method is user friendly and yields results that match the manual analysis method. Alberto Esteban Linares, Oak Ridge Institute for Science and Education, Oak Ridge, Tenn., and Vanderbilt University, Nashville, Tenn. Logan Clowers, Oak Ridge Institute for Science and Education and University of Tennessee, Knoxville Xiang Chen and Mikhail Sokolov, Oak Ridge National Laboratory Randy Nanstad, FASM,* R&S Consultants LLC, Knoxville, Tenn.