The endochronic cyclic plasticity with finite element analysis (EndoFEM) is employed to simulate plasticity-induced crack closure phenomenon of Al 2024-T3 CCT specimens under maximum cyclic stress of 80MPa and 0.1 stress ratio (R). Various fatigue crack lengths are generated by a rc dominated-node-released strategy. The suitability of element-mesh planning around crack tip is supported by the real simulations in the decreasing tendencies of crack opening load (Pop) with increased distance behind the crack tip, and the enough elements to reflect the reversed plastic responses at minimum load.EndoFEM results of vertical stress ahead of the crack tip show a typical distribution of small scale yield (SSY) in the realm of fracture mechanics; and Pop/Pmax ratio determined at 1mm behind crack tip is kept constant i.e. Kmax-independent. In these cases, fatigue parameters based on either the far field loading parameter ΔK, the effective ΔK (ΔKeff) with crack closure effect, or the mechanical responses ahead of crack tip (e.g. stress parameter, reversed (plastic) strain at 1mm) are all equivalent and are linearly correlated with the stage II fatigue crack growth (FCP) rate. However, for longer crack length with the ligament bending effect or shorter crack length with the starter notch effect, the Pop/Pmax ratio decreases and changes the SSY stress distribution. This result reduces the usefulness of the above fatigue parameters. As a consequence, a nonlinear correlation of FCP rates with ΔK or ΔKeff are purely empirical. The Kmax-dependent ΔKeff must be considered in the correlation as suggested by the present study of EndoFEM.

Applications of the EndoFEM with node-released methods had been used successfully to simulate the plastic wakes left behind the advancing fatigue crack. In this paper, employing the plastic zone size estimated by LEFM as a guideline, four strategies with various plans of node-released rates and two plans of finite element discretization near crack tip, are proposed to generate various fatigue cracked lengths of A12024-T3 CCT specimen under all tensile-cyclic loading. Evaluations based on the mechanical responses near crack tip and the crack opened/closure behaviors, it can be concluded that the EndoFEM with the rc dominant node-released strategy can lead to not only economical but also reliable results.

In this paper, the FEM with the incremental endochronic cyclic plasticity (EndoFEM) and the r c controlled node-released strategy are employed to study the fatigue crack opened/closed load (P op ) of Al 2024-T3 CCT specimens provided by Mageed and Pandey under several crack lengths and the constant amplitude with various load ratio (R). After statisfactory results are achieved by comparisons of computed P op values and cited experimental data, the simulations will be extended to the crack lengths with significant bending effect due to short ligaments or high peak (P max ) or high positive or very low negative R cyclic loads. Through these simulations, the complete map of P op /Pmax vs. K max and R can be constructed and thereafter its correspondant empirical formulae can be proposed. Using these formulae and selecting the traditional fatigue crack growth parameter AK eff , the Al 2024-T3 fatigue crack growth rate da/dN vs. AK and R data, provided by Hiroshi and Schijve, can be employed to proposed empirical formulae of da/dN vs. AK eff and R. After integration, fatigue-crack-growth length a vs. N curves computed by EndoFEM can be obtained. The results are agreed very well with the existing experimental curves.According to the above procedures of simulation and steps of comparions with experiment, this paper may provides an integrate methodology of numerical simulation in the studies of fatigue crack growth for academic and industrial researches and design analysis.Keywords : EndoFEM with r c controlled node-released strategy, Crack opened/closed load, Bending effect of short ligament, Crack closure model, Fatigue crack rate vs. AK eff .

Enhancing self-efficacy for calorie control and exercise is a crucial strategy for successful weight management. This study developed and psychometrically tested a 13-item quick checklist for assessing self-efficacy for calorie control and exercise (QCSE-CCE). A convenience sample of 425 adults between 18 and 69 years old completed the QCSE-CCE online. The principle axis factor analysis and a parallel analysis demonstrated a three-factor structure that accounts for 72.8% of the total variance. The confirmatory factor analysis indicated a good model fit (χ2/ df = 2.168, GFI = .913, AGFI = .873, RMR = .049, RMSEA = .073, CFI = .959). The predictive validity was adequate (.38 <  r < .39, p < .000), with Cronbach’s alphas ranging from .87 to .91. The test-retest demonstrated good stability ( r = .69; p < .001). The QCSE-CCE is a valid and reliable instrument for assessing self-efficacy for calorie control and exercise for weight management purposes.