High Strain, Multiaxial Stress, and Non-Proportional Load Investigations
Inclusive Dates: 07/22/09 Current
Background - Fracture mechanics is the engineering discipline used to assess the integrity of structures containing crack-like flaws, and it is widely applied by many industries to define initial sizes of pre-existing flaws that would grow during service to cause failure. It is required that nondestructive examination (NDE) methods be able to detect these initial flaws to avoid potentially catastrophic environmental, economic, and safety consequences resulting from failures. Accurate methods for calculating initial flaw sizes are needed, as over-conservative values can result in predicted flaw sizes that are excessively small and difficult and costly to detect. The current level of fracture mechanics assessment technology is being tested by situations involving strains exceeding 2 percent, such as occur when pipes are subjected to reeling, frost-heave and thermal buckling. Assessment of these situations presents challenging problems related to high-strain, non-proportional loading (e.g., when multiple loads are applied in sequence rather than in parallel), multiaxial stressing (e.g., when pressure stresses and axial stresses are superposed), and local yielding (e.g., when unexpectedly high plasticity effects are observed at cracks at relatively low loads). Little is known on how to properly account for these in fracture mechanics under plastic conditions where a parameter called J is used to assess the severity of the crack loading. An analytical formulation for J is required that accurately captures the foregoing effects to facilitate the structural integrity assessment of highly strained pipes.
Approach - The adopted technical approach to developing a practical formulation for J relies on performing a large matrix of finite element analyses (FEA) to calculate J for circumferential cracks in pipes subjected to bending, pressure, axial forces, and combinations of these, and analyzing the FEA J results using an optimized scheme previously developed by SwRI that accurately determines key parameters governing the plastic behavior of J, such as the net section yield loads for pipes under combined loading. (The net section yield load is the load at which all strains on the load bearing section in a pipe first become plastic, indicating the onset of high strain behavior for further load increases.)
Accomplishments - The main objectives of the work have been achieved. Expressions for net section yield loads of cracked pipes under combined bending, axial force, and pressure have been developed from the FEA J results at high strains. These loads have been integrated into an analytical formulation for the crack tip driving force J that accurately captures fracture behavior in the following regimes: linear elastic (where plastic strains are not significant); fully plastic (where high strain behavior dominates); and the transition region between these two extremes. The J formulation has been validated against FEA solutions generated as part of this research for cracked pipes subjected to proportional and non-proportional loads consisting of bending, axial forces, and pressure. In addition, the developed J formulation is applicable to materials that undergo arbitrary stress-strain behaviors — a necessary pre-requisite for practical structural integrity applications.