Multiaxial creep deformation investigation of miniature cruciform specimen for type 304 stainless steel at 923 K using non-contact displacement-measuring method

2.1 Miniature specimen

The shape and dimensions of the cruciform specimen [10,11] are shown in Figure 1(a). The entire specimen had dimensions of 50 mm × 50 mm, with a 1 mm thickness center gauge section. An finite element (FE) analysis confirmed that the von Mises equivalent stress varies within a ±5% range at the center gauge section and because the σ _z stress component is zero at the center gauge section, a plane stress condition is achieved with this particular shape and dimensions of the miniature cruciform specimen. Multiaxial stress testing was conducted using X- and Y-axis load settings for the cruciform specimen. Because the cruciform specimen does not have a definite cross-section, the relationship between the applied load and the generated stress was obtained by the FE analysis in advance. The designed cruciform specimen has a tensile loading arm length of approximately 20 mm, which is a relatively large ratio of its length to its overall dimensions. The reason for the large length is that bending deformation of the loading arms is inevitable when tensile load is applied to them, and this deformation generates bending stresses that may affect the stress distribution at the center gauge section. By setting the loading arm length to Figure 1(a), the effect of the bending mode of the arm on the stress distribution at the gauge section can be reduced. Figure 1(b) shows the shape and dimensions of the uniaxial testing specimen. Uniaxial data were obtained for the same material.

Figure 1

Shape and dimensions of miniature specimen for creep testing (mm): (a) cruciform specimen and (b) plate specimen for uniaxial loading.

2.2 Specimen surface observation method

Figure 2 shows an appearance of the multiaxial creep testing machine for the cruciform specimen. Figure 2(a) shows the configuration and the main dimensions of the testing machine, which was installed with dimensions of 600 mm × 600 mm and a height of 1,000 mm. Figure 2(b) shows a photograph of the electric furnace of the biaxial tensile creep testing machine developed for the miniature cruciform specimens. The furnace has a 1 kW heating capacity and is of the upper and lower two-split type. The figure shows the lower part of the furnace, which was installed with quartz glass at the bottom to observe the inside of the furnace. Figure 2(c) shows the setup of the furnace and the optical camera used to observe the interior of the furnace. The deformation of the specimen was visualized by observing it in an electric furnace and periodically capturing photographs. In addition, the displacement was measured using a non-contact method by quantifying the trajectory of target marks marked on the specimen.

Figure 2

Appearance of tensile creep testing machine for miniature cruciform specimen: (a) schematic figure of the testing machine, (b) electric furnace with observation window (lower part), and (c) setup of an electric furnace and an optical camera for observation.

The verification results of the non-contact displacement measurement method are shown in Figure 3. The tensile tests described below were performed using a conventional tensile testing machine and a high-temperature tensile testing machine with an electric furnace with an observation window. Figure 3(a) shows the results of the tensile test of the aluminum alloy plate specimen at room temperature. The strain in the direction of the tensile axis (Y-axis) and the strain perpendicular to the tensile axis were measured using the strain gauges. In addition, the target marks on the specimen were photographed and measured using the non-contact displacement measurement method described earlier, and the trajectories were quantified. The circular plots in the figure show the Y- and X-axis strains obtained by the non-contact displacement measurement method. The solid lines represent the strain gauge results. The strain obtained by the non-contact displacement measurement method is almost the same as that obtained by the strain gauges, and it can even measure large deformations that are difficult to measure using strain gauges.

Figure 3

Verification results of non-contact displacement measurement methods: (a) strain measurement results of aluminum alloys at room temperature and (b) displacement measurement results of stainless steel at high temperature.

Figure 3(b) shows the tensile test results for the Type 304 stainless steel at 573 K. Displacement at the gauge part is measured in an electric furnace using a non-contact displacement measurement method through an observation window of the furnace. Multiple verifications showed that the relationship between the displacement measured by the LVDT (δ _LVDT) and the displacement measured by the optical camera (δ _CCD) was 0.96 and 1.06. The reasons for the differences in the calculated values may be due to the long distance between the camera lens and the specimen gauge part in the electric furnace, or errors in the results due to the small number of tensile testing datasets verified. Although the reasons for the differences in the calculated values are not clear, it is considered that the non-contact displacement measurement method can be used in high-temperature environments when applying this method to creep tests for the miniature cruciform specimens, because the distance between the camera lens and the specimen point is small, as shown in Figure 2(c).

2.3 Experimental conditions

Multiaxial creep tests were conducted using the cruciform specimen and the biaxial tensile creep testing machine. Type 304 austenitic stainless steel was used for the tests; its chemical composition is listed in Table 1. The testing temperature was 923 K (650°C). The testing temperature was increased from room temperature to the target temperature within approximately 2 h, and the tests were started after approximately 30 min of heat equalization. We verified that the temperature distribution at the center gauge section of the cruciform specimen is within a tolerance of ±1.1 K at 923 K in advance.

The principal stress ratio (λ) defined by Eq. (1) was used to express the multiaxiality in this study. The ratio is calculated as the ratio of the maximum principal stress (σ ₁) to the minimum principal stress (σ ₃) and is equal λ to 0 for uniaxial tension and λ = 1 for equi-biaxial tension:

3.1 Fracture direction of cruciform specimen

Creep testing was conducted at two levels of Mises-type equivalent stress (σ _eq); 200 MPa and 180 MPa, for λ = 0 and λ = 1 conditions. The creep rupture lifetimes are presented in Table 2. There were no significant differences in the creep rupture lifetimes when compared at the same equivalent stress, although the results for λ = 1 were slightly shorter than those for λ = 0.

Figure 4 shows the photographs of the specimen after the creep testing. The results for λ = 0 are shown in Figure 4(a) and (b). The specimen fractured ductility in a direction perpendicular to the tensile axial direction. Figure 4(c) shows the results at σ _eq = 200 MPa for λ = 1. Crack initiation will be described later, but several cracks at the center gauge section grew in the direction perpendicular to the principal direction of maximum stress, leading to rupture. Figure 4(d) shows the results for σ _eq = 180 MPa at λ = 1. Similar to the σ _eq = 200 MPa results, the specimen ruptured owing to crack propagation at the center gauge section, but the direction of macroscopic propagation was approximately 45° to the direction of the principal stress. The macrocrack propagation direction of the main crack was different depending on the equivalent stress; however, this difference and its propagation mechanism are not yet understood. Further studies, such as measurement of the fracture surface angle and numerical analysis of the difference in stress distribution in the specimen thickness direction with increasing or decreasing stress and duration of the test, are required in the future.

Figure 4

Overall photographs of ruptured specimens: (a) λ = 0, σ = 200 MPa, (b) λ = 0, σ = 180 MPa, (c) λ = 1, σ _eq = 200 MPa, and (d) λ = 1, σ _eq = 180 MPa.

3.2 Multiaxial creep deformation

Figure 5 shows an example of a series of observation photographs of the specimen placed in the electric furnace during the creep test. Figure 5(a) shows the results at λ = 1 and σ _eq = 200 MPa, expressed as the rupture lifetime ratio. The center gauge section of the specimen was polished with emery paper up to #2000 and buffed with alumina powder before the test, and a metallic luster was observed in the early stage of its life (0.1 t _r, 0.2 t _r). However, high-temperature oxidation can be observed over time. The unevenness at the center gauge section can be observed from approximately 0.4 t _r, suggesting that the grain boundary has been damaged and small cracks have appeared. The main cracks, which may have been caused by the propagation of small cracks and their linkage, were observed from 0.9 t _r onward.

Figure 5

Example of time series variation of the miniature cruciform specimen in the electric furnace. : (a) λ = 1, σ _eq = 200 MPa and (b) λ = 1, σ _eq = 180 MPa.

Figure 5(b) shows the results for λ = 1 and σ _eq = 180 MPa. The deformation of the cruciform specimen in the high-temperature environment was similar to that of the σ _eq = 200 MPa specimen shown in (a), i.e., unevenness was observed at the center gauge section from mid-life, and small cracks grew into macrocracks, leading to specimen rupture. Using an optical camera to observe specimens in the electric furnace, it was possible to visualize the deformation of the specimens and the initiation and propagation of cracks from the grain boundaries and other points. The effectiveness of this method was confirmed, as it has been generally difficult to observe the deformation of specimens in a closed electric furnace.

3.3 Strain under multiaxial stress

As shown in Figure 5, the target marks of approximately 0.3 mm diameter were marked with heat-resistant ink in the direction of the tensile loading axis at the specimen center gauge section. The relative distances between the two target marks in the Y- and X-axis directions were computed using image analysis, and the displacement of the center gauge section was obtained.

Figure 6 shows the creep curve obtained using the non-contact displacement measurement method. Both σ _eq = 200 and 180 MPa, indicated by the square and circle marks, respectively, show that the nominal strain from the beginning of the testing could be drawn. In both cases, the creep curves show that the steady-state region was followed by acceleration to rupture. At σ _eq = 200 MPa, the Y-axis strain, indicated in blue, was larger than the X-axis strain, indicated in red. As shown in Figure 4(c), the main crack at λ = 1 and σ _eq = 200 MPa grew in the Y-axis direction, resulting in larger deformation in the Y-axis direction. The deformation up to creep rupture was visualized and quantified from the observation photographs of the specimen in the electric furnace.

Figure 6

Time-strain curves for the miniature cruciform specimen.

Based on the Y- and X-axis strains obtained using the cruciform specimen, as shown in Figure 6, a uniform creep curve drawing was considered. The thickness direction strain (Z-axis) was obtained using the volume invariant rule, as shown in Eq. (2).

The axial strains ε _x and ε _y in the biaxial tensile creep testing are considered to be the principal strains ε ₁ and ε ₃. Furthermore, the normal strain ε _z in the thickness direction calculated by Eq. (2) is considered to be the principal strain ε ₂, and the equivalent Mises-type strain is calculated by the following Eq. (3):

Figure 7 shows the Mises-type equivalent strain curves obtained from the multiaxial creep test at λ = 1. Figure 7(a) shows the results for σ _eq = 200 MPa, together with the results at λ = 0 using the specimen shown in Figure 2(b), and the creep curve obtained using a standard round bar specimen obtained from the same heat material. Because the creep rupture lifetimes of the miniature specimens λ = 1, λ = 0, and the standard specimens do not exactly correspond, the lifetimes are normalized to the respective rupture lifetimes. It can be observed that the equivalent strain at the early stage of the test up to approximately 5% can be uniformly expressed by the equivalent volume of the Mises-type. After 5%, the results for the standard and λ = 0 miniature specimens are almost the same, but for λ = 1, the equivalent amount at the latter stage of life is lower. The strain at the final rupture was approximately half that of other specimens at λ = 1.

Figure 7

Creep curve with Mises-type equivalent strain: (a) σ _eq = 200 MPa and (b) σ _eq = 180 MPa.

Figure 7(b) shows the results for σ _eq = 180 MPa. Although the strain in the standard specimen is slightly smaller than that in the others, the Mises-type can be evaluated uniformly up to approximately 5% of the early stage of the test, similar to the trend at σ _eq = 200 MPa. The strain at the final rupture at λ = 1 was slightly smaller than the other results, suggesting that the ductility calculated as the Mises-type equivalent may be reduced under multiaxial stress conditions. The reduction in creep rupture ductility under multiaxial stress may depend on the stress level and temperature, and more experimental data are required in the future.