Issue 41
V. Shlyannikov et alii, Frattura ed Integrità Strutturale, 41 (2017) 31-39; DOI: 10.3221/IGF-ESIS.41.05
From the crack front shape obtained in this way, the relations between the relative crack depth a/D and the surface crack chord length b/D can be measured using a comparison microscope (Fig. 4). In addition, based on periodically measured increments of surface crack chord length b , the curve of surface crack propagation versus cycle numbers db/dN can be obtained. Afterwards, utilizing the relation of crack depth versus surface crack chord length, it is possible to obtain the crack growth rates da/dN in the depth direction.
c
a
0.2 0.4 0.6 0.8 1 1.2 1.4
1.2
b
0.2 0.4 0.6 0.8 1 1.2 1.4
1
0.8
D16T, Т=‐60°C D16T, Т=+23°C D16T, Т=+250°C В95АТ, Т=‐60°C В95АТ, Т=+23°C В95АТ, Т=+250°C
0.6
a/c
a/c
a/c
В95АТ, Т=‐60°C В95АТ, Т=+23°C В95АТ, Т=+250°C
D16T, Т=‐60°C D16T, Т=+23°C D16T, Т=+250°C
0.4
0.2
0
0.2
0.4
0.6
0.8
0
0.1
0.2 b/D
0.3
0.4
0 0.1 0.2 0.3 0.4 0.5 0.6 b/D
a/D
Figure 4 : Aspect ratio versus crack depth (a) and crack length (b, c) for both alloys and different temperature conditions.
The evolution of the crack growth rate of the elliptical-fronted edge cracks during the tests is determined using CMOD and the microscope. Fig. 5 shows relations between CMOD and crack length b on free surface for both alloys and three temperatures. It is found strong correlation between these two parameters which can be very useful for automation of experimental studies of fatigue and fracture under multiaxial stress state. It should be noted, that the measurements of crack length b by microscope on free surface of specimens for the test in climatic chamber are impossible. For these specimens crack length b was obtained on the base of experimental relations represented on Fig. 5.
0.32
0.22
B95AT, T=+250°C B95AT, T=+23°C B95AT, T=-60°C
D16T, T=+250°C D16T, T=+23°C D16T, T=-60°C
0.17
0.22
0.12
0.12
0.07 CMOD, mm
CMOD, mm
0.02
0.02
0
5
10
15
20
0
5
10
15
20
b, mm
b, mm
Figure 5 : Relationship between CMOD and crack length on free surface of hollow specimen under different temperature conditions.
N UMERICAL STUDY
he main purpose of the present study is the interpretation of the surface crack growth rate data in terms of elastic and plastic fracture mechanics parameters. In our previous work we calculated different constraint parameters distribution along the crack front. That is the elastic constraint parameters in the form of the non-singular T -stress and T Z -factor as well as the elastic-plastic constraint parameters in the form of local stress triaxiality h and I n -factor for the specified combinations of tested material and temperature conditions [4]. FEM analysis was performed for semi-elliptical cracks in the cylindrical hollow specimens to determine the stress strain fields along the crack front. Typical finite element meshes for the cylindrical hollow specimens are illustrated in Fig. 6. The stress-strain state and constraint parameters at the crack tip for each type of the tested specimens were calculated by using the corresponding static material properties listed in Tab. 1, ranges of the testing loads and temperatures. These distributions correspond to the crack front positions at the accumulated number of loading cycles: initial front, intermediate front and final failure front (Fig. 7). One of the purposes of the work is to obtain an accurate description for the distribution along the crack front of the governing parameter of the elastic-plastic solution in the form of an I n -integral T
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