Issue 39

S. Seitl et alii, Frattura ed Integrità Strutturale, 39 (2017) 110-117; DOI: 10.3221/IGF-ESIS.39.12 113 Figure 2 : (a) 3PBT numerical model in ANSYS; (b) detailed view of the mesh near the crack tip. Results Neither d a /d N nor ∆ K , used in the Paris-Erdogan law, can be directly measured during a 3PBT or WST, and must therefore be obtained using a combination of finite element analysis and several calculation procedures. First, a mathematical relationship between the relative crack length α (= a/W ), the dimensionless ratio between the crack length a and the specimen height W, and the CMOD was calculated through inverse analysis. This was achieved by calculating the CMOD for fixed values of α , at intervals of 0.1. In the WST, the relative crack length is defined as the vertical distance between the point where the splitting force is exerted and the support of the specimen. For α = 1, the total crack length a is therefore 145 mm; 5 mm shorter then the total WST specimen height. Fig. 3.a depicts the calculated CMOD values of the VC 3PBT geometry, under the four tested stress ratios, for α between 0.3 and 0.7. The plotted fitting curve (for VC 90%) shows an exponential relationship between the CMOD and the relative crack length can be found. Hence the great value for R 2 it can be stated that the exponential fitting curve is very accurate. Similar graphs for the WST can be obtained, also showing an exponential relationship between CMOD and α. Exponential fitting curves for the 3PBT and WST were calculated for all stress ratios. The inverse functions, which relate the relative crack length ⍺ to the CMOD where then used in further calculations. Figure 3 : (a) CMOD calculations for different stress ratios; (b) ∆ K calculations for 70% of the ultimate static load. CMOD 90% = 0.0022e 5.7259 ⍺ R² = 0.9964 0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,2 0,3 0,4 0,5 0,6 0,7 0,8 Ccalculated CMOD [mm] Relative crack length α [-] VC 70% VC 75% VC 80% VC 90% ∆K 10-70 = 0.1671e 4.2133 ⍺ R² = 0.94935 0 5 10 15 0 0,2 0,4 0,6 0,8 1 Stress intensity factor ∆K [MPa.√m] Relative crack lenght ⍺ [-]