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 8 Fig. 1 — Elimination of compliance measurements in the load displacement curve for the normalization method compared with the elastic unloading compliance method. 2 ' ' ' pli pli Ni pli a bv cv P d v + + = + (3) where a , b , c , and d are fitting con- stants. The normalization function shall fit all data points described above with a maximum deviation less than 1% of the final normalized load. The normalization function is used to calculate crack lengths between ini- tial and final crack sizes such that when the calculated crack sizes are plugged into Eq. (1) to derive normalized load, the deviation between the resulting value and the normalized load from Eq. (3) is within ±0.1%. The final J-R curve can be determined after crack siz- es between the initial and final crack sizes are calculated. SOFTWARE DEVELOPMENT As mentioned previously, despite the advantage in testing, analysis pro- cedures for the normalization method are complicated and require both man- ual data analysis and computer pro- graming. To facilitate the application of the normalization method in J-R curve testing, the authors developed an open source software with a user-friendly graphic interface to perform automat- ed J-R curve analysis. The software can analyze the four most commonly used fracture toughness specimen geome- tries; i.e., compact tension (C(T)), disk compact tension (DC(T)), single edge bend with load line displacement mea- surement (SEB(LLD)), and single edge bend with crack mouth opening dis- placement measurement (SEB (CMOD)). MATLAB was used to write the program due to its ease of use and wide applica- tion in engineering and science. One of the most challenging as- pects of developing the software was how to let the program draw a tangent line (Fig. 2), because MATLAB does not have any function or module to auto- matically perform such a task. An iter- ative process was designed to achieve this goal. Process details: The program first fits normalized load displacement data from ν ' pl i >0.001 up to, but not includ- ing, the maximum load and the final load-displacement pair using the nor- malization function in Eq. (3). The re- sidual value between the normalization function fit and the final normalized load is then calculated. The program proceeds to the next round of normal- ization fitting using the previous fitting dataset subtracting the load displace- ment pair prior to the final load-dis- placement pair and recalculates the residual value between the normaliza- tion function fit and the final normal- ized load. The same iterative process is repeated until the deviation between the normalization function fit and the final normalized load is less than 0.5% of the final normalized load. The process fulfills the ASTM E1820 requirement that the maximum deviation between the normalization function fit and the final normalized load should be less than 1% of the final normalized load. At that point, the load displacement pair prior to the final load displacement pair in the fitting dataset is equivalent to the point of tangency manually obtained in Fig. 2. In addi- tion, the normalization function fitting process was optimized, because occa- sionally the default least square curve fitting in MATLAB does not yield opti- mal fitting constants for Eq. (3). More details are available in the technical manual for automated J-R curve analy- sis software [8] . After completing coding in MAT- LAB, the MATLAB Application Com- piler was used to create a standalone executable file, which is readily com- patible with modern Windows operat- ing systems. Users can begin using the software to perform J-R curve analysis after installing the executable file. The software offers a streamlined and self- explanatory operation process, which can be completed by clicking com- mand buttons from pop-up windows. At first, a pop-up window gives general Fig. 2 — Illustration of the tangent line from the final load displacement pair to the remaining data. The red point highlights the tangent point.