Assurance of reliable time limits in fatigue depending on choice of failure simulation: Energy density versus stress intensity

• Published in: Theoretical and applied fracture mechanics Vol. 55; no. 1; pp. 39 - 51
• Main Authors: Sih, G.C., Tang, K.K.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.02.2011; Elsevier
• Subjects: Applied sciences; Bridges; Buildings. Public works; Cable-stayed bridge; Crack length; Crack propagation; Energy density; Exact sciences and technology; Fatigue (materials); Fatigue failure; Fracture mechanics; Fracture mechanics (crack, fatigue, damage...); Fundamental areas of phenomenology (including applications); Least variance; Life time; Load frequency; Mathematical models; Mean stress; Measurement and testing methods; Physics; R-integrals; Reliability; Solid mechanics; Static elasticity (thermoelasticity...); Strain; Strain energy density (SED); Stress amplitude; Stress intensity factor (SIF); Stresses; Structural and continuum mechanics; Suspension bridges. Stayed girder bridges. Bascule bridges. Swing bridges; Variance; Weighted functions; Stress intensity factor (SIF); Mean stress; Stress amplitude; Weighted functions; Cable-stayed bridge; R-integrals; Least variance; Strain energy density (SED); Crack length; Life time; Reliability; Load frequency; Metallic structure; Measurement; Ultimate limit; Fatigue fracture; Modeling; Energy intensity; Variance; Crack propagation; Stress intensity factor; Stayed girder bridge; Precracked specimen; Size effect; Root mean square value; Monitoring; Mean field approximation; Probabilistic approach; Strain energy; Energy density; Durability; Fatigue; Fatigue limit; Variance analysis; Fatigue crack; Crack bridging; Steel bridge; Weight function
• ISSN: 0167-8442; 1872-7638
• DOI: 10.1016/j.tafmec.2011.01.004

The principle of least variance is applied to evaluate the reliability of the design conditions of the Runyang cable-stayed bridge. Monitored fatigue load in service data are analyzed in conjunction with the specimen fatigue crack growth data for bridge steel. Aside from size differences, the interactive effects of material behavior with load amplitude and frequency would vary with the depicted physical model for the reliability of life prediction. Based on the same crack growth history in time or cycle, the two choice selected for comparison are stress intensity factor (SIF) range, and the strain energy density (SED) range. Reliability is found to depend on the trade off between load amplitude and frequency. Considered are high-amplitude; low-frequency and low-amplitude; high-frequency. In each case, the chances are the reliable time span of fatigue crack growth will not coincide with the useful portion of bridge life, simply because the load frequency must be anticipated as an educated estimate. It is subject to change. Conversion of the crack length fatigue cycle history to the corresponding time history requires the specification of load frequency that can set the time span of the useful life. This is demonstrated for the Runyang bridge, where approximately 30 MPa and 8 MPa would correspond to the high and low fatigue load, respectively. Significant variances were found for the SIF and SED models. The difference can be attributed to the inclusion of the mean stress in the SED that is more forgiving since it accounts for both the stress and strain effects, in contrast to the SIF model that leaves out the strain and the mean stress. Since the principle of least variance refers to the average of the R-integrals, the results based on the linear sum (LS) and root mean square (RMS) will differ quantitatively, but not qualitatively. The obvious mismatch of the fatigue load used to determine the material property and that for the bridge design can be adjusted and absorbed into the appropriate choice for the load frequency, a compensating factor not realized up to now. To this end, the weighted functions in the R-integrals further emphasize long run effects of the least variance reliability analysis. Attention is called to Changeability in addition to determinability and probability for predicting the time to failure. That is to better anticipate the change in the fatigue load frequency, to which the assistance of health monitoring should provide.