Fracture Mechanics
CHAPTER – 4 THREE PARAMETER FRACTURE CRITERION
4.1 MODIFIED TWO-PARAMETER FRACTURE CRITERION K max = K F �(1 − m) � The two – parameter fracture criterion as per Newman is, σf �� σu (4.1)
Here KF and m are two fracture parameters evaluated from base line test data. σf is the failure stress normal to the direction of the crack in a body σu is the nominal stress required to produce a plastic hinge on the net section. The modified two-parameter fracture criterion is an empirical relation developed by Rao and Acharya between the failure stress and the elastic stress intensity factor at failure which is given by, K max σf σf p = K F �(1 − m) � � − (1 − m) � � � σu σu (4.2)
Here there are three parameters KF, m and p, evaluated from the baseline test data, σf is the failure stress, σu is the nominal stress and Kmax is the elastic stress intensity factor at failure. The two parameter fracture criterion of Newman explained above applies relations derived within the scope of Linear Elastic Fracture Mechanics (LEFM). In this criterion, the two fracture parameters take account of the deviation of the stress to failure from the stress calculated pursuant to LEFM principles. These parameters have to be calculated earlier in pretests known as base line tests to be conducted under identical conditions of the material. It was possible neither to find
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the failure stress of pressure vessels by means of the fracture parameter obtained from fracture mechanics specimen nor to find the failure load of the pressure vessel using the fracture parameters of pressure vessel. Rao and Acharya then developed an empirical relationship between the failure stress and the elastic stress intensity factor at failure. The results obtained using this three parameter fracture criterion is found to be in reasonable agreement with the test results. The significant parameters affecting the size of a critical crack in a structure are the applied stress levels, the fracture toughness of the
4.1 MODIFIED TWO-PARAMETER FRACTURE CRITERION K max = K F �(1 − m) � The two – parameter fracture criterion as per Newman is, σf �� σu (4.1)
Here KF and m are two fracture parameters evaluated from base line test data. σf is the failure stress normal to the direction of the crack in a body σu is the nominal stress required to produce a plastic hinge on the net section. The modified two-parameter fracture criterion is an empirical relation developed by Rao and Acharya between the failure stress and the elastic stress intensity factor at failure which is given by, K max σf σf p = K F �(1 − m) � � − (1 − m) � � � σu σu (4.2)
Here there are three parameters KF, m and p, evaluated from the baseline test data, σf is the failure stress, σu is the nominal stress and Kmax is the elastic stress intensity factor at failure. The two parameter fracture criterion of Newman explained above applies relations derived within the scope of Linear Elastic Fracture Mechanics (LEFM). In this criterion, the two fracture parameters take account of the deviation of the stress to failure from the stress calculated pursuant to LEFM principles. These parameters have to be calculated earlier in pretests known as base line tests to be conducted under identical conditions of the material. It was possible neither to find
48
the failure stress of pressure vessels by means of the fracture parameter obtained from fracture mechanics specimen nor to find the failure load of the pressure vessel using the fracture parameters of pressure vessel. Rao and Acharya then developed an empirical relationship between the failure stress and the elastic stress intensity factor at failure. The results obtained using this three parameter fracture criterion is found to be in reasonable agreement with the test results. The significant parameters affecting the size of a critical crack in a structure are the applied stress levels, the fracture toughness of the