Abstract
The objective of this paper is to use two-parameter fracture mechanics to adjust a material J-R resistance curve (i.e. toughness) from the test specimen geometry to the cracked component geometry. As most plant equipment is designed and operated on the “upper shelf”, a ductile tearing analysis may give a more realistic assessment of flaw tolerance. In most cases, tearing curves are derived from specimen geometries that ensure a high degree of constraint, e.g., SENB and CT Therefore, there can be significant benefit in accounting for constraint differences between the specimen geometry and the component geometry.
In one-parameter fracture mechanics a single parameter, K or J-integral, is sufficient to characterize the crack front stresses. When geometry dependent effects are observed, two-parameter fracture mechanics can be used to improve the characterization of the crack front stress, using T-stress, Q, or A2 constraint parameter. The A2 parameter was be used in this study.
The usual J-R power-law equation has two coefficients to curve-fit the material data (ASTM E1820). The adjusted J-R curve coefficients are modified to be a function of the A2 constraint parameter. The measured J-R values and computed A2 constraint values are related by plotting the J-R test data versus the A2 values. The A2 constraint values are computed by comparing the HRR stress solution to the crack front stress results of the test specimen geometry using elastic-plastic FEA. Solving for the two J-R curve coefficients uses J values at two Δa crack extension values from the test data. A closed-form solution for the adjusted J-R coefficients uses the properties of natural logarithms. The solution shows the adjusted J-R exponent coefficient will be a constant value for a particular material and test specimen geometry, which simplifies the application of the adjusted J-R curve.
A different test specimen geometry can be used to validate the adjusted J-R curve. Choosing another test specimen geometry, having a different A2 constraint value, can be used to obtain the adjusted J-R curve and compare it to the measured J-R curves.
The geometry of the component is also expected to have a different A2 constraint compared to the material test specimen. The example examined here is an axial surface flaw in a pipe. The A2 constraint for an axial surface cracked pipe is computed and used to obtain an adjusted J-R curve. The adjusted J-R curve shows an increase in toughness for the pipe as compared to the CT measured value. The adjusted J-R curve can be used to assess flaw stability using the driving force method or a ductile tearing instability analysis.