Prediction Of Stresses On Orifices And Evaluation Of Constraints On Crack-tips

Stress concentration is a main cause of the damage in engineering structures, and the evaluation of stress concentration factors is important to engineering analysis. In the first part of this paper, the investigation of gray model approach and the application of gray model to some stress concentration problems were studied.According to the exponential form of GM (1,1 ) model, a new formula about the background value was established by a definite integral. The application domain and the prediction precision of the consequent improved GM(1, 1) model were discussed. In addition, considering the spacing interval in the primary accumulating generating of primitive data sequence, a approach for establishing a GM(1,1) model for non-equidistant sequence was presented. Furthermore, the gray model was applied in the stress concentration test. The strain electrical measurement tests were taken on six typical components. The test data were obtained to establish the gray models, which was applied to predict the maximun stress values of stress concentration problems. It is shown that the predicted data agree very well with the experimental data. The gray modeling method need less test data and is of high precision in prediction. Therefore, the gray model is feasible to a real time test of the strain or stress concentration problem.Fierce stress concentration occurs on the crack-tip. In the second part of this paper, the two parameters J-A₂ theory in fracture mechanics was used to analyze the elastic-plastic stress fields and to evaluate the constraint levels on the crack-tips. The transferability of constraint was discussed.The elastic-plastic stress fields on the crack-tips were obtained by use of the finite element analysis to the single edge notched bend(SENB) and single edge notched tension(SENT) specimens at the different temperatures and the various loading levels. SENT specimens were loaded with different eccentricity tension to simulate different loading configurations and the constraint levels. The relation between eccentricity e and parameter A₂ is obtained. Over the ductile-brittle transition region, the relationship between constraint parameter A₂ and reference temperature T₀ of the master curve was obtained. Therefore, according to the constraint level on the crack-tip one can forecast the fracture toughnesses K_JC at different timperatures. A bending correction factor was included in the J-A₂ asymptotic solution by two points matching method to improve the theoretical prediction of the stress field for deep cracks under large scale yielding condition. As a result, the valid region for J-A₂ controlled crack growth is extended, and the ASTM specimen size requirements for fracture toughness testing can be relaxed. And then, the functional dependence of J_R curves on A₂ was established and the predicted J_R curves agree very well with the experimental curves. This ensures the transferability of laboratory test data to an actual structure provided the constraint level A₂ of the cracked structure is known or determined. Farther, the constraint parameters A₂ as a function of the crack lengths were presented for the SENT samples and the SENB samples for convenience in actual application. Also, the conversion formula of the crack lengths was obtained between them. According to the fracture rule with two parameters J and A₂, the fracture press values of some cracked inner-pressed-pipelines were forecasted. Finally, the J-A₂ theory was performed to study the collinear two cracks in plate under biaxial loading. The influence to J-integral and constraint parameter A₂ of the main crack were researched with the different sizes and the different distances of adjacent crack in biaxial loading condition for different load ratios. The influence coefficients were also presented.