Shakedown Criterion Employing Actual Residual Stress Field and Its Application in Numerical Shakedown Analysis

Construction of the static admissible residual stress field and searching the optimal field are key tasks in the shakedown analysis methods applying the static theorem. These methods always meet dimension obstacles when dealing with complex problems. In this paper, a novel shakedown criterion is proposed employing actual residual stress field based on the static shakedown theorem. The actual residual stress field used here is produced under a specified load path, which is a sequence of proportional loading and unloading from zero to all the vertices of the given load domain. This ensures that the shakedown behavior in the whole load domain can be determined based on the theorem proposed by K6nig. The shakedown criterion is then implemented in numerical shakedown analysis, The actual residual stress fields are calculated by incremental finite element elastic-plastic analysis technique for finite deformation under the specified load path with different load levels. The shakedown behavior and the shakedown limit load are determined according to the proposed criterion. The validation of the criterion is performed by a benchmark shakedown example, which is a square plate with a central hole under biaxial loading. The results are consistent with existing results in the literatures and are validated by full cyclic elastic-plastic finite element analysis. The numerical shakedown analysis applying the proposed criterion avoids processing dimension obstacles and performing full cyclic elastic-plastic analysis under arbitrary load paths which should be accounted for appearing. The effect of material model and geometric changes on shakedown behavior can he considered conveniently.

Determination of the Fracture Toughness of Optomechanical Devices

Static fracture toughness characteristics are traditionally determined in tests of standard notched specimens using a P-V curve, where P is the load and V is the notch-opening displacement. This curve has a characteristic point Q. At the load PQ corresponding to this point, the crack starts to propagate. For this load, the fracture toughness characteristics are then calculated. In brittle (elastic) fracture, the P-V curve at the onset of crack propagation has an extremum (or a local extremum), from whose ordinate PQ is determined with sufficient accuracy. In ductile and elastic-ductile fracture, P-V curves are monotonically increasing, and PQ is calculated using the 5% secant offset method without taking into account the characteristics of the material, so that the PQ is determined inaccurately. To improve the accuracy of PQ determination, we propose a thermographic method for determining the fracture toughness of metals. This method involves plotting the load P against the temperature change ΔТ over a relatively short period of time at the notch tip. This plot is then transformed to a P-ΔS curve, where ΔS is the specific entropy increment at the notch tip, which is calculated through ΔТ. This thermodynamic diagram has a characteristic step at the beginning of crack propagation, and from the ordinate of this step, PQ can be determined much more accurately. Furthermore, in the thermographic method, the preparation of test specimens can be simplified by replacing the process of growing a fatigue crack at the tip of a notch by making a sharp cut, which provides significant time savings. Statistical processing and comparison of test results of steel 20 specimens using the conventional and thermographic methods have shown the advantages of the thermographic method in accuracy and complexity.