Successfully estimating tensile strength by small punch testing

The Small Punch (SP) test is a relatively simple test well suited for material ranking and material property estimation in situations where standard testing is not possible or considered too material consuming. The material tensile properties, e.g. the ultimate tensile strength (UTS) and the proof strength are usually linearly correlated to the force-deflection behaviour of a SP test. However, if the test samples and test set-up dimensions are not according to standardized dimensions or the material ductility does not allow the SP sample to deform to the pre-defined displacements used in these correlations, the standard formulations can naturally not be used. Also, in cases where no supporting UTS data is available the applied correlation factors cannot be verified. In this paper a formulation is proposed that enables the estimation of UTS without supporting uniaxial tensile strength data for a range of materials, both for standard type and for curved (tube section) samples. The proposed equation was originally developed for estimating the equivalent stress in small punch creep but is also found to robustly estimate the UTS of several ductile ferritic, ferritic/martensitic and austenitic steels. It is also shown that the methodology can be further applied on non-standard test samples and test set-ups and to estimate the properties of less ductile materials such as 46% cold worked 15-15Ti cladding steel tubes. In the case of curved samples the UTS estimates have to be corrected for curvature to match the corresponding flat specimen behaviour. The geometrical correction factors are dependent on tube diameters and wall thicknesses and were determined by finite element simulations. The outcome of the testing and simulation work shows that the UTS can be robustly estimated both for flat samples as well as for thin walled tube samples. The usability of the SP testing and assessment method for estimating tensile strength of engineering steels in general and for nuclear claddings in specific has been verified.


Introduction
In a small punch (SP) test the local stresses and strains are biaxial in nature [1]. It has been shown to be a challenging task to estimate uniaxial (equivalent) stress from the force displacement curve of the SP test [2,3]. A new standard [4] is currently under preparation within the European Committee for Iron and Steel Standardization (ECISS), Technical Committee 101 (TC101), working group 1 (WG1) to replace the current CEN Workshop Agreement [5]. The new standard covers the classical Small Punch (SP) test for tensile property estimation and the Small Punch Creep (SPC) test for creep property evaluation. In this paper some new insight, gained from the SPC equivalent stress determination [6], is used for estimating the tensile strength.
In the SP test a hemispherical punch or a ball is forced at a constant displacement rate through a disc specimen (Error! Reference source not found.) that is clamped between an upper and a lower die. The main result of a SP test is the measured force F as a function of displacement v (at the punch tip) or deflection u (below the sample). The measured displacement v has to be corrected for compliance. The difference between displacement and deflection is the change of the specimen thickness at the punch tip.
Example SP force-displacement curves for the two standardized SP test set-ups and specimen sizes are shown in Error! Reference source not found.a and in normalized form in Error! Reference source not found.b.

Test rig set-ups
The new standard (presented in [4]) includes two types of SP or SPC specimen, i.e. a specimen with a diameter DS = 8 mm and an initial thickness h0 = 0.5 mm and a specimen with DS=3 mm and h0=0.25 mm. The standard test rig specifics for these two types are given in Error! Reference source not found. together with other set-ups found in literature [2,5,11]. The lower die has a receiving hole with diameter D and a chamfer of length L. Both, D and L depend on the type of specimen used (Error! Reference source not found.).

Miniature Specimen
Classical specimen

Materials
The materials assessed here are from various projects and test campaigns as given under the sub-headings below. The test materials and their room temperature (RT) ultimate tensile strengths are given in Tables 2-4. These values are estimated by SP tests later in this paper.

ECISS/TC101 round robin materials
The main materials used by ECISS/TC101/WG1 for the estimation of tensile properties were different heat treatments of P92 pipe. To study the impact of differing yield to tensile strength ratios the 316L was also tested. The TC101 test materials are given in Table 2. All the ECISS/TC101/WG1 materials, except 316L-miniature, are tested at room temperature with test specification number SNR#1 (Error! Reference source not found.) and the miniature test sample with SNR#4 . 316Lminiature 569 2) 316L 569 2) 1) As given by material supplier (MMV). 2) As measured by JRC [8].

TASTE project materials
In the EERA JPNM pilot project TASTE [11][12][13] the main material of interest was the nuclear grade titanium stabilized 15-15Ti (DIN 1.4970) stainless steel cladding [14]. The 15-15Ti is the primary choice for fuel cladding of several current fast spectrum research reactor projects. The main test material was the 24% cold worked (24%CW) 15-15Ti cladding tube material, manufactured by Sandvik on behalf of SCK•CEN. The material batch has passed tight quality control, i.e. stringent composition, grain sizes and mechanical properties (yield strength, tensile strength and elongation at rupture) control and tight product tolerances (diameters, straightness and ovality), roughness and defect controls. A smaller batch with a cold-work level of 46% (46%CW) was also produced and tested. For the 46%CW the deformation level is intended to simulate irradiation damaged material in the sense of work-hardening saturation demonstrated by the small difference between the proof stress and the ultimate tensile strength. The 46%CW also has markedly decreased total elongation [15,16].
The 15-15Ti material properties (axial) at RT performed on full tubes (no waist) and on sections cut from the wall (with waist) are given in 3 together with the properties of the reference material P91. All the JRC curved specimens analyzed for this paper were tested with a test-set-up with D=4 mm, r=1.25 mm and no chamfer (SNR#7 in Error! Reference source not found.). The chamfer cannot be manufactured on a curved surface. The flat reference P91 specimens were tested with the standard test set-up (SNR#1 in Error! Reference source not found.), with the standard thickness (h0=0.5 mm), and with a reduced thickness to comply with the tube specimen, i.e. h0=0.45 mm. The flat test set-up always has a chamfer ( Table 3). 1) As given by the material supplier [11], tested on full tube.
3) As measured from standard size uniaxial samples [17]. 4) Inner surface as from EDM cut.

ASTM round robin materials
In the US the American Society for Testing and Materials (ASTM) has an ongoing work item [18] for the development of a SP standard. The scope of the work is to enable estimates of yield and tensile strength up to a temperature of 450°C for metallic materials. JRC has taken part in this effort as a member of an inter-laboratory round-robin testing. The tested steels are given in Table 4. The measured UTS and proof stresses were not provided until after the delivery of the test data and the tensile property estimates.

Classical and recently developed estimation procedures for force to stress conversion
The simplest force to stress conversion can be found in the CEN Work Shop Agreement (CWA, Code of Practice) [5]. The conversion is meant for small punch creep (SPC) test giving a constant force to stress ratio =F/, allowing for different test set-up dimensions and specimen thicknesses. The CWA equivalent creep stress  SPC can be calculated as: where FSPC (in N) is the SPC test force (load), h0 the initial specimen thickness, kSP a "ductility" parameter and r, R are the puncher radius and receiving hole radius (in mm) as given in Error! Reference source not found.. For the standard test set-up (SNR#1) the CWA=1.895 when kSP=1. This conversion factor works well for steels like P91, where the minimum deflection rate is reached at a deflection of around 1 mm. The draw-back of this method is that kSP is not a constant and it can be both temperature and force dependent [18].
The CWA model is based on the Chakrabarty [1] membrane stretch equations. The Chakrabarty (CHA) model gives the CHA as a function of displacement v. Full CHA curves can be defined for each test set-up using the equations given in [1]. The maximum CHA-max at vCHA-max can be calculated with Eq. (1). The CHA=CWA at a displacement vmax=1.58 mm for the standard test set-up and specimen size (sNR#1).
The corresponding classical equation (CLA) in [5] for estimating the (uniaxial) ultimate tensile strength Rm with small punch "tensile" tests (SP) is: where F m (in N) is the maximum force reached during the test and β Rm-CLA is a geometry dependent correlation coefficient which needs to be determined. The main draw-back of this method is that the Rm-CLA has to be established by correlation to actual uniaxial tensile tests or by Finite Element Analysis (FEA) simulation with the right constitutive equations in place. It has been found that the correlation factor seems to be somewhat materia l dependent but mainly test-setup and specimen thickness dependent. In this paper the classical model (CLA) is used for estimating tensile strength as in Eq. (2), with a constant value for βRm-CLA = 0.276, optimized in the MATTER project [19] for P91 steel for the standard test set-up and a specimen thickness of 0.5 mm.
The above method seemingly works well for ductile materials but does not give adequate results for less ductile materials failing at deflections well below vCHA-max. For less ductile materials other methods have to be applied.
A new promising method for both ductile and less ductile materials has been proposed by Altstadt et al. [3] and it has been included in the new standard as an Annex. The Altstadt method (ALT), optimized on finite element simulated materials, correlates the force Fi to the ultimate tensile strength at a much lower displacement vi in the force-displacement curve. The ALT model correlation to the tensile strength is: The Fi (in N) of the ALT method is extracted from the test data at the displacement vi=0.645 mm or a deflection of u i =0.55 mm. The model parameters are to date only defined for the S NR #1 and S NR #4 test set-ups (see Error! Reference source not found.). The correlation coefficient βRm-ALT is 0.179 for SNR#1. This is an average value for a range of simulated materials with different tensile strengths and ductilities.
In [6] the Empirical Force to Stress (EFS) model and the Modified Chakrabarty (MCH) model was shown to robustly estimate the equivalent creep stresses for equal creep rupture times of SPC and uniaxial creep tests. The MCH is a simplification of the EFS model that can be recalculated for different test set-ups since the model parameters can be determined analytically using the CHA as base.
The MCH is: where v is the displacement (or deflection) and A and B are test set-up dependent constants. In the case of small punch creep v is replaced by umin, i.e. the deflection where a minimum deflection rate is reached in a test. The SPC data determined constants (from [6]) for A and B which are applied unchanged on the SP test data with the standard test-setup and specimen thickness, i.e. A=0.6143 and B=1.2954 for the SNR#1 set-up. For the curved specimen, the miniature sample and the 0.45 mm thick standard SP specimen the constants have been recalculated using the methodology given in [6]. For the curved specimen further correction factors have to be applied as described in section 3.2 in this paper.
In Figure3a it is shown that the calculated Fi and vi (and corresponding ui) from [3] that was the base for Eq. (3) are in good agreement with the MCH curve for the standard specimen and standard test-set up. In Figure3b it can be seen that for the miniature specimen the MCH slope is representative of the Fi/vi (and Fi/ui) but the analytically calculated MCH intercept is somewhat high. It is to be noted that MCH curve for this specimen size and test-setup (SNR#4) has not been verified up to now by creep tests and the few SP tests indicate that the model overpredicts the UTS (see section 4). The discrepancy is likely to be caused by the assumed fixed point for the MCH set by the CHA model vmax, i.e. MCH(vmax)= CHA(vmax)(1+h/r). This factor was optimized on P91 steel [18]. If another more reliable fixed point can be found, such as using the ALT data or actual test data (both SP and SPC data) it is foreseen that the MCH model for the miniature specimen can be improved. It is to be emphasized that the MCH model is not restricted to the location of maximum force as the CLA model even if it has been used that way in this paper. It can be used as the ALT model at lower displacements. This feature will be studied in future work.
All the above stress conversion models for the SNR#1 test-setup are shown in Figure4 with P91 SP data from the MATTER project.
Unification of reference stress estimation between SPC and SP tests would have a beneficial effect on the credibility of the SP and SPC determined material properties.

Correction for curvature for thin walled tube samples
When SP testing curved samples [11,21] it is evident that the force-displacement curves are different from those of flat specimens. To find the right way of correcting the deflections (and marginally the force) a number of 3D FEA simulations using ABAQUS [22] have been performed on ¼ of the geometry for simulated flat and curved specimens. The curved sample studied in this paper is a section of the aforementioned SCK-CEN tube. The geometrical configuration consisting of the top die (red), specimen (blue), bottom die (grey) and the spherical punch (green) is shown in Figure 5. Example of computed force-displacement curves for the studied materials is shown in Figure 6. A more detailed description of the methodology and resulting correction factors are given in [23].  To obtain the equivalent force and displacement of a flat specimen, the measured force and displacement of a SCKCEN tube specimen should be divided by a factor of 1.07 and 0.71, respectively. The given factors are averages on the results acquired from the two 15-15Ti materials and the reference material P91.

Results
The ultimate tensile strengths estimated by SP tests are given in Tables 5-7 as relative errors of the uniaxial UTS values given in Tables 2-4. The relative error Erel is calculated as: Where Rm-UA is the uniaxial tensile strength, Rm-SP the estimated UTS calculated by the CLA, ALT and MCH models.
Note that for the curved samples there are currently no calculated vi values at which one could extract the Fi values for the ALT model. Potentially the same correction factors could be used as for correcting the vmax and Fmax but this has not been attempted in this work. Note that the Rm estimates from CLA and the MCH are more or less the same. This is to be expected if the displacement at maximum is around 1.6 mm. The ALT estimates are for some materials more accurate but the model seems to be prone to larger deviations, especially for ductile material.  Table at RT using the MCH model.  (2)) 3) MCH model parameters as in Figure 7.
The ALT and MCH models are for these sets of data better than the CLA model, except for the miniature specimen estimate. It is to be noted that the MCH is generally over-predicting the stress though less so than the CLA model.  In addition to the RT tests the MCH method was also applied to the full range of test temperatures, i.e. RT-800C. The results are very encouraging as can be seen in Figure 8. In the previous assessments on the TASTE data [11] the SP estimates were based on a displacement corrected CLA model, with inherently more scatter in the estimated UTS. The CLA model also predicts somewhat lower strengths for P91 and clearly over-predicts the RT strength for the 46%CW 15-15Ti steel. In Figure 9 the reference P91 SP estimates are plotted against the measured uniaxial strength for the temperature range RT-650C. It can be seen that the P91 flat specimens give robust predictions and the spark erosion manufactured curved samples show more scatter. The MCH seems to under-predict the tensile strength for the curved P91 samples. This could be an artefact caused by the manufacturing route, i.e. the inner surface was not polished. a b In Figure 10 and Figure 11 the SP estimated strengths are plotted as a function of temperature together with both uniaxial UTS results and hoop direction ring tension results for 24%CW and 46%CW samples correspondingly.

Discussion
The models compared in this paper for SP estimation of the UTS include a model originally optimized for SPC creep data assessment. It is encouraging to find that the same formulation gives good estimates also when applied on SP data for estimating the tensile strength. In Figure 12 the SPC data from the ECISS/TC101/WG1 round robin [6] show the =FSPC/c-UA ratio as a function of the measured deflection at minimum deflection rate (umin) for 3 different materials, i.e. a P92 pipe, a F92 forging and a 316L plate. The MCH line is calculated on the standard testsetup and a 0.5 mm specimen thickness. In Figure13 the SP data from the TASTE project (assessed in this paper) is presented as =Fm/Rm-UA as a function of displacement vm (v at Fm). In this case the MCH was modified to fit the standard test-setup with a 0.45 mm specimen.  Figure 12. The SPC creep data from the ECISS/TC101/WG1 round robin [6] plotted as  at umin together with the CHA and the MCH models. Note that the P92 SPC samples were suffering from early cracking and failure. The predicted uniaxial creep stress at equal rupture time will therefore be increased and  decreased. The specimen thickness h0=0.5 mm. Figure 13. The SP test data from the TASTE project plotted as F max /R m-UA at the test specific v max . Note that h0=0.45 mm.
It could be concluded from the above figures that the MCH could be given a slightly steeper slope, perhaps pivoting around a displacement of 1 to 1.25 mm. However, the slope should not be as steep as CLA model, having a slope of h0/Rm-CLA going through the origin. The CLA model is not giving an optimal solution if applied on SPC data replacing vmax for umin.
As stated earlier, the optimization of the MCH model parameters using both SPC and SP data would most likely improve the understanding and accuracy of predictions for both small punch test types.
Studying the Fi/Rm for the ALT model, as seen in Figure 14, for the ASTM steels it is evident that some of the materials with low proof strength did not give the expected  as was indicated by the FEA simulated SP tests on "synthetic" materials. It could be concluded that for low proof stress materials the Rm cannot be estimated at this (low) displacement. Maybe this information can instead be used for improving the SP estimates for proof strength. One of the remaining main challenges for increasing the applicability of the SP tests technique in general is to establish ductility limitations for successful assessment of both SP and SPC data. For instance what is the impact of material "necking" on the SP test curve. For some low ductility materials this could happen already at small displacement [26]. The material properties beyond the uniaxial engineering ultimate tensile strength, i.e. after necking, will naturally have an effect on vmax and Fmax. In Figure15a a SP tested 15-15Ti specimen clearly failed by plastic collapse whereas the SPC specimen in Figure15b has cracked open in a star shaped manner. The change in fracture behavior is linked to the deformation rate and differences in tensile and creep ductility.
(a) (b) Figure 15. Difference in fracture mode of a 24%CW 1515Ti A) SP "tensile" specimen after test at 600C and B) SPC creep specimen ruptured after 22 h at 600C/400N.

Conclusions
A range of different materials with differing tensile strengths have been analyzed with three different models. SP data from test set-ups that are non-standard in nature such as the curved samples from fuel cladding tubes have also been successfully assessed. The conclusions to be drawn from results from the here presented assessments are: • Good estimates on the tensile strength can be acquired by the existing conversion models, e.g. the ALT model developed for SP data and the MCH model initially developed for SPC data. • The force to stress conversion of SP and SPC test can be unified by optimizing models like the MCH.
• Curved samples such as cladding tubes can be tested by SP and analyzed successfully using curvature corrections calculated by FEA. • Tensile strength estimates for less ductile materials should be done on forces extracted at low displacement, for instance using an ALT type model. • Challenges remain in the field of improving the estimates on proof strength and ductility.
It could be claimed that the usability of the SP testing has been improved greatly by the new assessment methods, such as for estimating tensile strength in general and for nuclear claddings in specifically.