The Pin-Loaded Small One-Bar Specimen in Use to Determine Uniaxial and Multiaxial Creep Data

Introduction

Many of the engineering components in chemical plants, power generation plants, aero-engines and oil refineries operate at temperatures and/or stresses which are high enough to cause creep to occur [1–3]. Creep failure of these components normally leads to significant damage financially, environmentally as well as the loss of human lives in most cases. In order to improve safety, efficiencies and lower emissions and fuel consumption, new materials are being introduced to the industries mentioned above and these materials are being subjected to increasingly severe loading conditions (see [4–6]). In order to ensure the safe operation of components, improved understanding of the creep behaviour of the materials being used to manufacture them and improved inspection techniques are required [1, 7, 8]. One effect of the desire to improve understanding of material behaviours and to obtain better inspection techniques is the need, in some cases, to uses small material samples [9–10]. This comes about because small scoop samples (see Figures 1 and 2) with depth of 3 mm and radius of 15 mm can be removed from some components, for example, steam pipes and pipe bends in the power plants, without adversely affecting their safe operation. Also, for some material zones, for example, the heat-affected zones (HAZ) of welds, only small amounts of material are available for testing.

Figure 1:

Photographs of scoop sampling in process on stem pipe (a), and image of a typical scoop sample (b).

Figure 2:

Dimensions of a typical scoop sample.

A conventional cylindrical uniaxial creep test specimen (see Figure 3) with total length of about 130 mm and diameter of 16 mm, or the Bridgeman notched specimen (see Figure 8) cannot be manufactured out of a typical scoop sample or from the HAZ region of weld because the scoop samples and the HAZ region are far too small to allow these specimens to be extracted from them. Therefore, it has become necessary to develop small specimen creep testing techniques, whereby reliable creep data can be obtained using small material samples [11–13]. The limitations associated with the previous small specimens creep testing techniques made them unable to replace the uniaxial and the Bridgeman notched specimens when there is not enough material for creep assessment. However, pin-loaded small one-bar specimen (OBS) and the small notched specimen with four loading pins (SNS4) presented in this paper are designed to overcome the limitations associated with the previous small specimen creep testing techniques.

Figure 3:

Conventional uniaxial creep test specimen.

Specimen geometries and dimensions

The primary objective of this research is to develop the non-destructive small specimen creep testing technique which can be used to assess creep strength and to determine the remaining lifetimes for the high-temperature components using small material samples. The proposed pin-loaded small OBS and the SNS4 are designed to determine the creep strength and the remaining lifetime for the high-temperature engineering components, using small material samples. The OBS type (see Figures 4 and 5) and SNS4 (see Figures 6 and 7) have simple geometries, therefore they can be easily manufactured using, for example, electric discharge machining (EDM). The OBS specimen dimensions are defined by L_o, b, d, h, R and k, where L_o is “bar” length, i.e. the distance between the centres of the loading pins in the loading direction, b is the bar width, d is the specimen thickness, h is the specimen height, R is the radius of the loading pins and k is the length of the loading pin supporting end, as shown in Figure 4. The small OBS is designed to replace the uniaxial creep test specimen (see Figure 3) when there is not enough material available for testing. The OBS is capable of obtaining uniaxial creep strain and creep rupture data using small material samples. The OBS is unlike other small specimen creep testing techniques, it is capable of obtaining the full creep strain-time curves, i.e. primary, secondary and tertiary regions, similar to the strain-time curves obtained from the uniaxial creep test specimens.

Figure 4:

The pin-loaded small one-bar specimen (OBS) shape and dimensions, where L_o is the distance between the centres of the loading and constraining pins (~(5–13) mm), K is the supporting material behind the loading pins (~(2–4) mm), R is the loading pin radius (~(1–2) mm), b is the bar thickness (~(1–2) mm), d is the specimen depth (~(1–2) mm) and h is the specimen height (~(3.5–7) mm).

Figure 5:

The pin-loaded small one-bar specimen (OBS) with the loading and constraining pins in position.

Figure 6:

The small notched specimen with four loading pins (SNS4) shape and dimensions, where L_o is the distance between the centres of the loading and constraining pins (~(6–13) mm), K is the supporting material behind the loading pins (~(2–4) mm), R is the loading pin radius (~(1–2) mm), r is the notch radius (~(0.5–1) mm), b is the bar thickness (~(1–2) mm) and d is the specimen depth (~(1–2) mm).

Figure 7:

The small notched specimen with four loading pins (SNS4) with the loading and constraining pins in position.

Most of the high-temperature components in the power plants operate under multiaxial stress state condition and not just under uniaxial condition, therefore the multiaxial stress state for the material needs to be defined in order to obtain accurate creep assessment for the components. Traditionally the Bridgeman notched specimen is used (see Figure 8) to determine the multiaxial stress state parameter; however, in many cases the material available for creep assessment is not enough to manufacture this specimen type; the proposed SNS4 specimen can be used instead in such cases. The SNS4 dimensions are defined by L_o, r, b, d, h, R and k, where L_o is “bar” length, i.e. the distance between the centres of the loading pins in the loading direction, r is the small notch radius, b is the bar width, d is the specimen thickness, h is the specimen height, R is the radius of the loading pins and k is the length of the loading pin supporting end, as shown in Figures 6 and 7. Most of the components operating under creep condition are subject to multiples stresses, not only stresses in the directions of X–Y coordinate, but also subject to stresses in many other directions, normally referred to as the multiaxial stress. The SNS4 has been designed to obtain only the multiaxial stress state parameter for the high-temperature material. The multiaxial stress state parameter for the material at a particular temperature can be obtained by comparing the SNS4 experimental failure times with the corresponding finite element (FE) analyses failure time; this procedure has been explained and published in Ref. [14].

Figure 8:

Conventional Bridgeman notched bar specimen.

Data conversion method

Determination of reference parameters

If an analytical solution can be obtained, substituting two values of n in the expression f₁ (n)/ηⁿ and equating the two resulting expressions allow the value of η to be determined. Hence, σref=(ησnom) and D can be obtained. This approach was proposed by MacKenzie [18]. However, analytical solutions only exist for a small number of, usually, relatively simple components and loadings. If FE solutions to a creep problem are obtained (Δ˙ssc) using several n values, but keeping all other material properties, loading and component dimensions the same, then σ_r can be obtained. This is done by taking several values of α, normalising the steady-state value of displacement rate, Δ˙ssc, with respect to A(ασnom)n and hence finding the value of α which renders Δ˙ssc/(A(ασnom)n) independent of n. This process is most easily visualised by plotting log Δ˙ssc/(A(ασnom)n) for various values of α against n, as illustrated in Figure 9. Also from Figure 9 it can be seen that, for very small n value, i.e. (n≈0), the straight lines produced using all of the α values have the same intercept on the log Δ˙ssc/(A(ασnom)n) axis. This intercept is equal to the logarithm of the reference multiplier, D.

Figure 9:

Variation of log steady-state creep displacement rate for various α values against n.

Summary of the SNS4 and the OBS test procedure

The OBS testing method is based on the principle of converting the specimen load line displacement, displacement rate and displacement–time curves, to the corresponding uniaxial strain, strain rate and strain–time curves, using conversion relationships defined by eqs (6), (8) and (9). The conversion relationships, which are used to convert the specimen displacements and displacement rate to equivalent uniaxial strains and strain rate, are functions of specimen dimensions and deformations. The OBS and the SNS4 can be loaded using four loading pins, two of them are used to constrain the specimen and the other two are to apply tensile loading to the specimen as shown in Figures 5 and 7. The loading pins have to be attached to the loading machine using flexible joint, in order to allow good alignment to be achieved during the loading application. The loading fixtures generally have a much higher stiffness, compared to the specimen, and are generally manufactured from a material which has a much higher creep resistance than the tested material. The OBS and the SNS4 testing methods can be summarised as in the following points:

1. Small material samples are removed from the component surface or from the critical small regions, such as the HAZ or weld metal (WM) of weld, this small material sample is used to manufacture the SNS4 or the OBS.

2. Determine the conversion factors β and η, using FE analyses method for the particular OBS dimensions.

3. The OBS and the SNS4 are loaded using a tensile loading P, the load magnitude for the OBS is calculated for the required stress using η value for the specimen and specimen dimensions, i.e. eq. (6). For the SNS4 the applied load can be determined based on the required stress and the notched region dimensions.

4. The specimens are creep tested at the same practical operating temperature and stress levels much higher than the operating stress, this is to make the specimen fail in a shorter time.

5. The deformation of the SNS4 and the OBS is recorded throughout the test until the failure of the specimens.

6. The OBS deformation is converted to the corresponding uniaxial strain and strain rate using β value for the specimen and the conversion relationship, i.e. eqs (8) and (9).

7. These data then can be used to determine the creep strength for the components or the remaining lifetime, also it can be used to determine the creep constants for any creep model.

Finite element analysis

Specimen modelling

Three-dimensional FE analyses were carried out for the OBS using meshes which consist of 20-noded brick elements. Because of the symmetry, it was only necessary to model one quarter of the specimen and half of the specimen thickness, d, as shown in Figure 10. The boundary conditions, i.e. u_x=0 on plane A, u_y=0 on plane B and u_z=0 on plane C, are also indicated in Figure 10. The specimen is loaded and constrained through four loading pins which are assumed to be “rigid” in the FE model. The applied load for the OBS was calculated for the required stress using eq. (6). FE analyses have been carried out to obtain full creep deformation–time curves using the OBS and the Liu and Murakami model.

Figure 10:

Finite element mesh and the boundary conditions for the OBS.

Determination of the reference stress parameters for the OBS

The FE analyses were used to determine the conversion factors η and β for the OBS. Accurate determination of the conversion factors allows the EGL and the corresponding uniaxial stress for the specimen to be accurately obtained. Using a Norton material model, i.e. ε˙c=Aσn, FE analyses were performed to obtain the steady-state deformation rates between the loading pins for a range of n values, i.e. (n=8.2, n=8.4, n=8.6, n=8.8, n=9, n=9.2). Similar to Figure 11, the steady-state deformation rates between the loading pins, Δ˙ssc are normalised by LoAηPbdn, where P is the applied load. As only quarter of the specimen is used in the FE analyses and half of the specimen thickness, (see Figure 10), the obtained minimum deformation rates have to be doubled and the nominal stress will be P0.25bd. Several η values were considered for all of the deformation rate values, with different n values, i.e. (n=8.2, n=8.4, n=8.6, n=8.8, n=9, n = 9.2). The value of η which makes log2Δ˙cssLoAηP0.25bdn practically independent of n is the required η value for the particular OBS geometry and dimensions. This value corresponds to the solid, horizontal line in Figure 11. The value of β can then be obtained from the intercept of the same solid line in Figure 11, with the vertical line, i.e. log2Δ˙cssLoAηP0.25bdn. This procedure is described in more detail in Ref. [14]. Using the same procedure the conversion factors, i.e. η and β, were fund to be 0.99 and 1.2, respectively, for the OBS with the dimensions of 13.0, 4.0, 2.0, 2.0, 7.0 and 5.0 mm, for L_o, k, b, d, H and D_i, respectively.

Figure 11:

Determination of β and η parameters for the OBS.

Validation

Initial validation of the OBS testing technique was carried out using 3D-FE analyses and Norton’s law, to assess the accuracy of the conversion relationships, i.e. eqs (6), (8) and (9), and the conversion factors, i.e. η and β. The OBS steady-state deformation rates were obtained numerically using FE analyses for several n values, using Norton’s model and FE analyses. The specimen steady-state deformation rates were converted to the MSR using eq. (9). The OBS dimensions, L_o, k, b, d, H and D_i, were 13.0, 4.0, 2.0, 2.0, 7.0 and 5.0 mm, respectively. These specimen dimensions result in conversion factors β and η values of 1.2 and 0.99, respectively. For this study the magnitude of the material constant A in Norton’s law was 1.029E-20 for all cases, and the applied load corresponded to a constant stress of 50 MPa. The load was calculated using eq. (6) and the η value for the specimen which is 0.99. Using the same material properties, i.e. (A, n), and stress level, the MSRs have been obtained theoretically using Norton’s model for several n values. The theoretical and numerical MSRs are plotted together in Figure 12;remarkably good correlation is found between the two sets of results.

Figure 12:

Comparison between the minimum strain rates (MSRs) obtained theoretically and numerically from the OBS.

To obtain a full deformation–time creep curve from the OBS, a continuum damage material behaviour model of Liu and Murakami has been used in the FE analysis, using the material constants for P91 and P92 steels at 650°C [19].Two high-temperature materials have been used in the validation, P91 and P92 steels, these materials are used extensively in the power plant pipework. For P91 five uniaxial creep tests have been performed at constant temperature of 650°C, under five stress levels, 70, 83, 87, 93 and 100 MPa. For P92 steel four uniaxial creep tests at constant temperature of 650°C have been performed, under four different stress levels 110, 120, 130 and 140 MPa. The OBS creep deformation–time curves are converted to the strain–time curves using the relationship given by eq. (8) and the applied load is calculated using eq. (6). The conversion factors η and β for the tested OBS were 0.99 and 1.2, respectively. The tested OBS dimensions, L_o, k, b, d, H and D_i, were 13.0, 4.0, 2.0, 2.0, 7.0 and 5.0 mm, respectively. The converted OBS strain–time curves obtained from the FE analyses are compared with the corresponding uniaxial creep strain–time curves as in Figures 13 and 14;remarkably good correlation is found between the two results.

Figure 13:

Creep strain–time curves obtained using (i) the FE converted results for the OBS and (ii) experimental uniaxial creep test results for P91 steel at 650°C.

Figure 14:

Creep strain–time curves obtained using (i) the FE converted results for the OBS and (ii) experimental uniaxial creep test results for P92 steel at 650°C.

Discussion

One of the main advantages of the OBS over other small specimen creep testing techniques is that, the specimen is capable of obtaining full creep strain–time creep curve using small material samples, such as the scoop samples removed from component surface from small material regions such as the HAZ of weld. The HAZ region is a very narrow region between the parent material (PM) and the WM, and there is no straight line boundary between the WM and HAZ also between the PM and the HAZ. Therefore, distinguishing the HAZ region from the WM and PM could be challenging. The OBS allows easy capturing of this region, because the OBS has very flexible design, the bar thickness (d) and depth (b) can be increased or decreased as required, in order to capture only the HAZ region, without increasing the risk of having significant deformation in the loading pin supporting material. This will allow accurate determination of the material creep properties. The OBS is unlike the TBS [14] where the loading pin supporting material behind the loading pins has to be large to avoid significant deformation; in the OBS the loading area, i.e. the contact area between the loading pins and the specimen, is relatively large in comparison to the bar cross-section area. This allows the OBS and the SNS4 to be machined from even smaller material samples; the specimens can be manufactured from the slides of materials removed, for example, from the HAZ region.

Conclusions

1. The OBS creep test is unlike other small specimen creep testing techniques, such as the small ring creep test and the impression creep test, where the test result is limited to the secondary creep region. The OBS creep test is capable of obtaining creep rupture data, the entire creep strain–time curve, i.e. primary, secondary and tertiary creep regions can be obtained.

2. The OBS FE results presented in Figures 12–14 indicate that the OBS is capable of obtaining full and accurate strain–time creep curves when compared with the uniaxial creep test results.

3. The OBS conversion relationships are material independent; therefore the high-temperature component creep strength can be assessed without any knowledge of its original creep properties.

4. The OBS and the SNS4 have simple geometry and they can be manufactured, loaded and tested easily.

5. The OBS and the SNS4 have the advantage of self-alignment during the loading application which increases the chance of obtaining accurate creep data.