Scholarly article on topic 'Small punch tensile testing of curved specimens: Finite element analysis and experiment'

Small punch tensile testing of curved specimens: Finite element analysis and experiment Academic research paper on "Materials engineering"

CC BY
0
0
Share paper
OECD Field of science
Keywords
{"Small punch test" / "Cladding tube" / "Grade 91" / "Finite element" / Simulation}

Abstract of research paper on Materials engineering, author of scientific article — Igor Simonovski, Stefan Holmström, Matthias Bruchhausen

Abstract The Small Punch (SP) technique is a miniature test used for characterizing irradiated materials or when a testing material is available only in small quantities. In this work Finite Element (FE) models are developed to support the parametric analysis of SP fuel cladding tube specimens in comparison to standard flat ones. FE analysis shows that there are practically no differences between circular and rectangular flat specimens. The tube specimen results in only slightly higher maximal force (Fm). However, Fm is attained at significantly lower displacements. This is attributed to the curvature of the specimen. The friction linearly increases the Fm and to a lesser extent the displacement at Fm. FE analysis also shows that the yield stress and different hardening, while keeping ultimate tensile strength constant, practically do not affect the Fm. Significant specimen deformation can be expected at already small (0.1mm) puncher deflection, which could limit the applicability of the small punch test to ductile materials. Varying degree of clamping in the experimental procedure can cause large scatter in the yield stress estimates. In all cases good agreement between the simulation and experimental results was obtained, best with a friction coefficient of 0.2.

Academic research paper on topic "Small punch tensile testing of curved specimens: Finite element analysis and experiment"

Contents lists available at ScienceDirect

International Journal of Mechanical Sciences

journal homepage: www.elsevier.com/locate/ijmecsci

Small punch tensile testing of curved specimens: Finite element analysis and .m. experiment

CrossMark

Igor Simonovski*, Stefan Holmström, Matthias Bruchhausen

European Commission, Joint Research Centre, Nuclear Safety & Security, P.O. Box 2, NL-1755 ZG Petten, The Netherlands

ARTICLE INFO

Keywords: Small punch test Cladding tube Grade 91 Finite element Simulation

ABSTRACT

The Small Punch (SP) technique is a miniature test used for characterizing irradiated materials or when a testing material is available only in small quantities. In this work Finite Element (FE) models are developed to support the parametric analysis of SP fuel cladding tube specimens in comparison to standard flat ones. FE analysis shows that there are practically no differences between circular and rectangular flat specimens. The tube specimen results in only slightly higher maximal force (Fm). However, Fm is attained at significantly lower displacements. This is attributed to the curvature of the specimen. The friction linearly increases the Fm and to a lesser extent the displacement at Fm. FE analysis also shows that the yield stress and different hardening, while keeping ultimate tensile strength constant, practically do not affect the Fm. Significant specimen deformation can be expected at already small (0.1 mm) puncher deflection, which could limit the applicability of the small punch test to ductile materials. Varying degree of clamping in the experimental procedure can cause large scatter in the yield stress estimates. In all cases good agreement between the simulation and experimental results was obtained, best with a friction coefficient of 0.2.

1. Introduction

The Small punch (SP) technique is a miniature test developed in Japan and the US in the 1980s [1-5]. SP test can be performed for determining both tensile and creep properties [6]. It is especially suited for: (1) testing materials available only in small quantities, such as novel materials produced in laboratory quantities [7,8], (2) testing specimens from irradiated components [2,4,5], (3) testing of material with local inhomogeneities such as heat affected zones in weldments [9] and (4) estimation of neutron embrittlement [10]. In this work only tensile SP is used.

In the SP tests a small spherical tip or ball ("punch") indents a thin disc type specimen, Fig. 1. The tensile SP tests are performed at a constant displacement rate and the force is measured either as function of displacement of the puncher tip or as a function of specimen deflection i.e. the deflection of the specimen measured on the opposite side of the puncher. In the former case the displacements need to be corrected for the compliance. The latter configuration is recommended by the current European Code of Practice (CoP) [6]. The specimen deflection is measured by a ceramic rod which can also include a thermocouple for controlling the specimen temperature.

A typical force-deflection curve of a tensile SP test is characterized by several zones, e.g. [11], roughly distinguished by different deforma-

tion modes of the specimen, Fig. 2. Zone I corresponds to indenting of the specimen surface by the puncher tip and elastic bending of the specimen. In zone II plastic bending spreads through the entire sample. In zone III the specimen behaviour is dominated by membrane stretching while in zone IV necking and cracking occur, decreasing the force and, finally, resulting in a failure.

Due to the changing and non-homogeneous deformation state in the SP specimen, the extraction of the tensile material properties from the force-deflection curve is not a straightforward task and it is still a topic of research [13-16]. Finite Element Analysis (FEA) often needs to be used to better understand the experiments and supplement them. FEA has therefore been used from the beginning for analysing SP tests [1] and is now widely used to gain detailed insight into the SP tests [13,15], including evaluation of applicable theoretical equations [17], crack propagation [18], creep [19] and the significance of specimen displacement definition [20].

Traditionally SP tests are performed on flat specimens. In this work the current FEA support for the SP tests is extended to the curved specimens extracted from a sectioned fuel cladding tube. These tube specimens can be used as a "component test" of nuclear fuel claddings by applying the SP test. To our knowledge FEA assessment of SP test tube specimens has not yet been reported in the literature. Systematic FEA analysis is done to assess the impact of friction, uniaxial tensile

* Corresponding author. E-mail address: Igor.Simonovski@ec.europa.eu (I. Simonovski).

http://dx.doi.org/10.1016/j.ijmecsci.2016.11.029

Received 27 May 2016; Received in revised form 26 October 2016; Accepted 28 November 2016 Available online 30 November 2016

0020-7403/ © 2016 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.Org/licenses/by/4.0/).

Fig. 1. Typical SP test setup: I. Modified SP test setup for tube specimen: II. A) puncher, B) puncher ball, C) specimen, D) clamping thread.

Fig. 2. Force-deflection curve for a tensile SP test of a Grade 91 stainless steel at — 100 °C [12].

properties (true stress-strain curves), clamping, specimen type (tube and flat) and dimensions, including different material thicknesses (0.5 and 0.45 mm). FEA simulations are compared with experimental results.

2. Methods

2.1. Material

The material used is a Grade 91 Ferritic/Martensitic steel from the European FP7 MATTER Project. Standard uniaxial tensile test and SP specimens were extracted from a 60 mm thick plate (heat 20057) acquired from ArcelorMittal and produced in full accordance with RCC-MRx nuclear requirements (STR RM 2432) [21]. Grade 91 has been chosen because the literature contains a significant amount of published results on flat specimens and it is easier to manufacture cladding tube specimens from Grade 91 than manufacturing flat specimens from the cladding tubes.

The required minimum yield stress and range of ultimate tensile strength are Rp0 2 > 445 MPa and Rm = 580-760 MPa, correspondingly. The tensile uniaxial test, conducted at room temperature (RT) with "as received" material state, measured Rp0 2 = 510 MPa and Rm = 680 MPa with a fracture strain of ef=38.7% [22]. For the FEA simulations, the

Fig. 3. P91 true stress-strain curves.

true stress-strain curve from the uniaxial test was simplified (point reduction) and labelled as Rp0 2 Orig, Fig. 3. Two additional tensile curves were created from the original curve by decreasing/increasing the yield strength by 25%. All three stress-strain curves reach the same ultimate tensile strength strain at the same strain. Ultimate tensile strength was kept constant to decrease the number of independent variables. The modified tensile curves are used for yield strength sensitivity analysis. Beyond 0.2 of strain ideal plastic response is used. The Young's modulus and Poisson ratio of 200000 MPa and 0.3 are used, respectively.

2.2. Experimental method

The SP tensile tests were conducted on an Instron hydraulic testing machine (D-11797) with a 20 kN load-cell. The test set-up allows for high temperature SP testing up to 800 °C. The load cell was calibrated to the load range 0-5 kN to suit the needs of the test type. The tests were performed at room temperature. The puncher was pressed into the specimen at a constant displacement rate of 0.3 mm/min. Force and displacements were recorded. The puncher displacement was obtained from the cross-head displacement by correcting for the temperature dependent compliance by a procedure similar to the one described in [20].

The classical methodology for determining the yield stress Rp0.2 and ultimate tensile strength Rm from SP test results is to correlate them with "yield" force Fe and the maximum force Fm, Fig. 4. Fm is the maximum force reached during the tests and Fe can for instance be obtained by the "two-secant" method, i.e. finding the intersection of two linear least squares fits for the force-displacement data in the deflection

„ 1500

Fm i I / i 1 / i i

F / i i i i i i

Fig. 4. Locations of the parameters Fm, um, Fe and ue from the force-displacement curve.

Fig. 5. Determination of Fe according to the CEN Workshop Agreement (CWA) [6] method and the two-secant method.

Fig. 6. Determination of Fe using off-set method with offsets of h0/10 and h0/100 for the same test as in Fig. 5. h0 is the original specimen thickness.

range 0-h0, where h0 is the original specimen thickness, Fig. 5. One of the functions is anchored at the coordinate origin (F = 0, u = 0). The correlations for determining tensile strength and yield stress are given in Eqs. (1) and (2). An alternative way for defining Fe is by an off-set method (Fig. 6) following the same approach used for the determination of Rp0.2 from uniaxial tensile tests.

Oy-SP = al-J + a2

^uts-SP - ßü~ + ß:

The ai, ft and parameters are test constants. These constants depend on the test-setup, i.e. ball diameter, receiving hole diameter. A comparison of different methods for estimating Fe based on the computed force-displacement curves is given in Section 4.1.

Fig. 7. Typical specimens: A) flat specimen (before and after test) and B) curved tube specimen (before and after test).

Table 1

Flat 6.55x11 mm FEA specimen. Part Dimensions

Specimen Thickness 0.45 or 0.5 mm, width 6.55 mm, length 11 mm.

Top die Thickness 0.45 mm, width 6.55 mm, length 13 mm. Circular hole

with 1.4 mm radius, no chamfer. Bottom die Thickness 0.45 mm, width 6.55 mm, length 13 mm. Circular hole

with 2 mm radius and 0.2x0.2 mm flat chamfer. Puncher Ball radius 1.25 mm.

manufacture one with a simple drilling tool. Due to the curvature of the tube specimen, the drill would either create a partial chamfer, Fig. 8a), or a chamfer with a cut-through area, Fig. 8b), depending on which end one would like to manufacture a chamfer. The bottom die of a tube specimen therefore does not have a chamfer. Increase of Fm values can be expected when using a bottom die without a chamfer. Simulations indicate 2-3% increase in Fm values for the flat and tube specimens, respectively [23].

2.4. The finite element model

Finite Element (FE) models, full 3D and 1/4 symmetry, of flat 6.55x11 mm, flat 0 = 8 mm disc (Fig. 9) and tube (Fig. 10) SP specimen were created. They consist of the top die (red), specimen (blue), bottom die (grey) and the spherical puncher (green). The puncher is modelled as analytical, infinitively rigid body. It is an analytical surface that can not be deformed and does not require elastic/plastic material properties. Other parts are modelled as deformable bodies. ABAQUS FE [24] package is used for modelling and simulation.

2.3. Specimens

The SP specimens used for testing (Fig. 7) and simulation are flat 6.55x11 mm, flat 0 = 8 mm disc and tube specimen with an inner diameter of 5.65 mm. Flat specimens with a thickness of 0.45 and 0.5 mm are used while all the tube specimens have a thickness of 0.45 mm. In the experiment the specimens are placed between the top and bottom die, cf. Fig. 9, and are clamped towards the lower die by tightening a thread. In the CoP [6] the clamped version of the SP test is referred to as a "bulge" test. Table 1 through Table 3 provide an overview of the dimensions. The bottom die of a flat specimen has a chamfer of 0.2x0.2 mm which contributes to the flow of material during the punching. The chamfer is manufactured using a simple drill tool. The tube specimen does not have a chamfer as it is not possible to

2.4.1. FEA material parameters

Uniaxial tensile test material properties as defined in Section "2.1 Material" are used for the specimens. Rigid body material properties are assumed for the two dies by using 1000x higher Young modulus compared to the specimens. This results in sufficiently stiff response of the two dies.

In the FEA material anisotropy is neglected since none can be expected due to the manufacturing process. The tube specimens were cut from the plate using electro-discharging machine and not by extrusion. However, since the flat specimens were polished and tube not, a difference in the friction coefficient between the flat and tube specimens can be expected, cf. roughness in Tables 2 and 3.

Fig. 9. 1/4 symmetric FE model of a flat disc 0=8 mm disc SP specimen. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 10. 1/4 symmetric FE model of a tube small punch specimen. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

2.4.2. Loads and boundary conditions

A vertical displacement of —1.8 mm is applied to the puncher to press it against the specimen. The chosen displacement is roughly the displacement at which ductile SP specimens (0.5 mm thick, puncher

Table 2

Flat 0=8 mm disc FEA and test specimen.

Part Dimensions

Specimen Top die Bottom die Puncher Thickness 0.45 or 0.5 mm, diameter 8 mm, roughness Sq=0.12 |im, Rq = 0.08 |im. Thickness 0.45 mm, width 6.55 mm, length 13 mm. Circular hole with 1.4 mm radius, no chamfer. Thickness 0.45 mm, width 6.55 mm, length 13 mm. Circular hole with 2 mm radius and 0.2x0.2 mm flat chamfer. Ball radius 1.25 mm.

Table 3 Tube FEA and test specimen.

Part Dimensions

Specimen Top die Bottom die Puncher Thickness 0.45 mm, internal diameter 5.65 mm, length 11 mm, roughness Sq = 0.81 |im, Rq = 0.69 |im. Thickness 0.45 mm, length 13 mm. Circular hole with 1.4 mm radius, no chamfer. Thickness 0.45 mm, length 13 mm, circular hole with 2 mm radius, no chamfer. Ball radius 1.25 mm.

diameter 2.5 mm, receiving hole radius 2 mm) typically fail. A displacement rate of 1.8 mm/s is used. However, since the material properties used in the simulation are rate independent, the FE results are not affected by the loading rate. The specimen is placed between the two dies and it is allowed to slide between them but not to bend upwards. The top surface of the top die and the bottom surface of the bottom die are constrained in all directions. This enables the simulation of the clamped SP "bulge" test. Symmetrical boundary conditions are applied to the symmetrical models where 1/4 of the geometry is modelled.

2.4.3. Contacts

The puncher applies the load to the specimen through the contact, defined between the two. Contact is also defined between the top die and the specimen and the bottom die and the specimen. ABAQUS [24] general contact settings are used with Coulomb friction, Table 4. The same friction coefficient is used for all the contacts. The friction coefficients are in the range reported in the literature [13,17].

2.4.4. FE mesh

In all cases ABAQUS C3D20R elements were used for meshing. C3D20R are 20-node quadratic brick, reduced integration elements [24]. Mesh sensitivity study was done to make sure the calculated force-displacement curves are mesh independent [23]. Force is defined here

Table 4

Contact settings.

Parameter Value

Sliding formulation Finite sliding

Discretization method Surface-to-surface

Slave adjustment Adjust only to remove overclosure (Tube FEM only)

Tangential behaviour

Friction formulation Penalty

Friction coefficient 0.001, 0.01, 0.1, 0.15, 0.2, 0.3, 0.4

Normal behaviour

Pressure-overclosure "Hard" contact

Fig. 11. FE mesh of the flat (top) and tube (bottom) specimen. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

as the force applied to the puncher. Displacement is defined as the displacement of the point at the centre of the specimen, on its top surface.

The flat 6.55x11 mm specimen was partitioned into Region 1 (2 mm radius) and Region 2 (2.3 mm radius), see Fig. 11 top. The Region 1 radius corresponds precisely to the radius of the bottom die hole. Along the red lines (Region 1) element size varied from 0.1 mm at the edge of the Region 1 to 0.02mm at the centre of the specimen. Element size of 0.1 mm was used along the thick black lines (Region 2). Elsewhere, a general element size of 0.3 mm was used. In the thickness direction models with 4 up to 8 elements were used. The same partitioning and element sizes were also used for the flat 0 = 8 mm disc specimen.

The tube specimen was partitioned into Region 1 (0.8 mm radius), Region 2 (1.9 mm radius) and Region 3 (2.3 mm radius), see Fig. 11 bottom. Along the red lines (Region 1) element size varied from 0.033 mm at the edge of the Region 1 to 0.01mm at the centre of the specimen. Element size of 0.0275 mm was used for the green lines (Region 2) and 0.02 mm along the brown lines (Region 3) where significant bending was expected. 30 elements were assigned to the 90° arc perimeters of Regions 1-3. Elsewhere, a general elements size of 0.3 mm was used. In the thickness direction models from 4 up to 12

elements were used. In all the cases the top and the bottom dies used larger elements compared to the specimens. The mesh of the symmetric models was the same as in the corresponding region of a full 3D model.

For the flat 6.55x11 mm and tube specimen at least 4 elements in the thickness direction should be used, while for the flat 0=8 mm disc specimen 6 elements or more should be used [23]. Symmetric models give practically the same force-displacement response as the full 3D models, albeit at a significantly lower (at least a factor of 5) computational cost (within one hour).

2.4.5. Solution settings

Geometric non-linearity is accounted for during the loading step as large deformations are expected. Coulomb friction results in unsym-metric stiffness matrix during the FE model solution [24]. Requesting a symmetric stiffness storage scheme with small Coulomb friction may still result in a converged solution albeit with increased number of iterations since the matrix will have some non-symmetric terms. Requesting symmetric matrix storage did not lead to convergence problems with the flat specimen. However, it severely decreased the convergence rate in the case of the tube specimen. Nonsymmetric matrix storage was therefore requested for all the models. To improve the efficiency for severely discontinuous behaviour, such as frictional sliding, the number of iterations prior to beginning of convergence rate checks was increased by applying "^Controls, analysis = discontinuous" setting [24]. Finally, for the tube specimen, small amount of artificial damping was employed by using "*Static, stabilize = 1.0E-8" [24]. Without this small amount of artificial damping the tube models did not converge. The impact of artificial damping on the force-displacement response was checked by also running analysis with 100x smaller damping ("*Static, stabilize = 1.0E-10"). The force-displacement curves were identical.

3. Results

Some laboratories also use a rectangular flat specimen (10x10 mm) since it is easier to manufacture than a circular flat specimen. The results from the two should, however, be similar [10]. The FEA simulations performed on the 6.55x11 mm and 0 = 8 mm disc specimen enable us to check for possible differences in the response. The flat rectangular and the disc force-displacement responses are nearly identical, Fig. 12. The maximal forces (Fm) forces are within 0.6% while the difference between the displacements at the maximal force (um) is somewhat higher (6.5%), Table 5. The width of the flat specimen

1800 -1-1-1-1-1-'-'-1-

1600 -

1400 - Jfr—*-

1200 - j/fjf Z 1000 - AiT yr

£ 800 - / 600 - J? jf

400 - M jf? _-

—*— FEM tube

—©— FEM tube, inverted

—B—FEM flat 6.55x11mm

X FEM: flat 0=8mm

of-1-1-1-1-'-1-1-1-1-

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Displacement [mm]

Fig. 12. Computed force-displacement responses of tube and flat specimens. Friction ^=0.001, specimen thickness 0.45 mm.

Table 5

Maximal forces and displacements. Friction ^ = 0.001, specimen thickness 0.45 mm.

Case Fm [N] Fm/Fm FEM: tube um [mm] um/um FEM: tube

FEM:tube 1426.0 1 1.020 1

FEM:tube, inverted 1775.1 1.245 1.247 1.222

FEM:flat 6.55x11 mm 1371.8 0.962 1.465 1.436

FEM:flat 0 = 8 mm 1363.6 0.956 1.375 1.348

(6.55 mm) could be a reason for this difference. Also, the scatter in experimental data is often higher than this, thus it seems to be reasonable to allow for this specimen type. Since the differences are small and the 0=8 mm disc type specimen is the one recommended by the CoP [6], the coming sections only refer to the 0 = 8 mm disc specimen.

Load-displacement curves with higher Fm and lower um can be expected for the tube specimen because the curved specimen is pushed through a hole in a tube. Tubular shape in itself results in a higher constraint. Since the hole is also curved (due to the tube radius) the flow of material is anisotropic as it is easier for the material to flow in the Z symmetry plane than in the X symmetry plane. There are no such effects for the flat specimen. The simulations on the tube specimen do result in marginally higher Fm force, about 4%, compared to the two flat specimens. However, the Fm is obtained at considerably lower displacements due to the specimen curvature which produces a higher deformation constraint compared to the flat specimens. The marginal difference in the Fm indicates that the same methodology to estimate the tensile strength, i.e. correlating Fm with Rm, can be used.

For the tube specimen the experiment is performed in a way that the puncher is placed at the inner side of the tube specimen, Fig. 10. Simulations follow the same set-up. In principle the puncher could also be placed at the outer side of the tube and then moved along the positive Y direction to press against the specimen from the bottom up, resulting in an inverted set-up. The puncher would then first flatten the convex specimen underneath the contact. With further puncher movement the specimen under the contact would become concave. This would result in high shear stresses in the specimen at the perimeter of the die hole. Consequently one could expect initially stiffer force-displacement response, earlier damage evolution and failure of the specimen. In the simulations without incorporation of damage, one would obtain higher Fm values as seen in Fig. 12. Since the experimental work on the inverted set-up is still on-going such a case is not further explored here.

Fig. 13. Yield strength and hardening effect. Friction ^=0.001, specimen thickness 0.45 mm.

Fig. 14. The effect of friction on force-displacement curves.

3.1. Yield strength and hardening

SP test response is sensitive to both the yield strength and the hardening of the material involved, Fig. 13. The lower (higher) yield strength causes the transition from the zone I (elastic bending, see Fig. 2) to the zone II (larger plastic deformation) to occur at lower (higher) force. Simulations therefore confirm the logical dependence of the elastic-plastic transition force Fe on the yield stress. This is more pronounced for the flat than for the tube specimen. On the other hand, the simulations show that the maximal force Fm is mostly related to the ultimate true yield strength which is the same in all three used material curves, Fig. 3. Fm is slightly influenced by the yield strength and hardening but this effect is so small that it can almost be neglected. Note that ultimate tensile strength is kept constant in all these cases. Similar results were also obtained for friction coefficients of 0.1, 0.15 and 0.2 and flat 0 = 8 mm disc specimen with 0.5 mm thickness [23].

3.2. Friction effect

Friction between the specimen, the two dies and the puncher has almost no effect on the force-displacement response until approximately half way into the Zone II, Fig. 14, irrespective of the specimen type and its thickness. This is in line with [20,25] where it is reported that the friction coefficient affects the force-displacement curve only around the maximal force. For the tube 0.45 mm thick specimen, the friction changes the force-displacement curve after (800 N, 0.3 mm), for the flat 0.45 mm thick specimen after (800 N, 0.61 mm) and for the flat 0.5 mm thick specimen after (1000 N, 0.65 mm) point. Friction linearly increases the maximal force up to ^ = 0.2, beyond which the deformation around the cap starts to localize, Fig. 15, resulting in smaller volume of high strain area and resulting in smaller increase of Fm, Fig. 16. Overall, Fm increases up to 22% within the observed range of friction coefficient. Displacement at maximal force does not exhibit such a good linear dependence on the friction, Fig. 17. However, as soon as friction is not negligible the dependence is close to being linear. Force-displacement curves with ^ = 0.01 were also calculated. Since the results were almost the same as the ones with ^ = 0.001, the results with ^ = 0.01 are omitted from Fig. 14. The results with ^ = 0.15 are also omitted as not to clutter the figure. However, they are accounted for in Figs. 16 and 17.

3.3. Comparison with experiments

The calculated force-displacement response of the tube specimen is in very good agreement with the experimental data, Fig. 18. Up to

Fig. 15. Localization in the deformation of the cap of the specimen develops beyond [r = 0.15. Tube specimen, thickness 0.45 mm.

Fig. 16. Relation between the maximal force Fm and friction coefficient. Dashes indicate linear fit to the data.

1000 N the effect of friction does not impact the force-displacement curve. For a given trues stress-strain curve (Fig. 3), friction coefficient can be estimated by comparing the maximal calculated force with the measured one. With the friction coefficient of 0.2 the calculated maximal force is in good agreement with one of the experimental curves and since the scatter in the measured maximal force is only 4.5%, one can consider a friction coefficient of 0.2 as a good estimate. Best fit with the experimental data using a friction coefficient of 0.2 was also reported in [17].

The calculated force-displacement response of the flat 0 = 8 mm disc specimen with a thickness of 0.45 mm is in a good agreement with the experimental data, Fig. 19. Up to 800 N the calculated force is higher than the measured force in the two out of the three measurements. The calculated maximal force, using previously estimated value of friction coefficient (0.2), falls within the small scatter (2%) of the measured maximal forces. This confirms that the friction coefficient of 0.2 is indeed a good estimate.

Fig. 20 compares the calculated with the experimental results for

Fig. 17. Relation between displacement at Fmax and friction coefficient.

the flat 0=8 mm disc specimen with a thickness of 0.5 mm. Here as well, the calculated results agree well with the experimental data. Exp. 1 matches perfectly the results of simulation with friction coefficient of 0.2.

It can be seen that the force-displacement response of the test data (and the simulated curves) are not always overlapping in the beginning of the curve, Figs. 19 and 20. Since the Grade 91 is known to have little variation in the material properties within one heat, the difference in the measured force-deflection curves could be a result of possible eccentricity of the puncher ball in the relation to the receiving hole, the resulting compliance differences or higher than usual variation in the material properties within one heat. This is a good example of how difficult it is to get a good estimate of the yield properties from a SP test (see Eq. (1)).

It is sometimes reported that more advanced material models (e.g. with damage) need to be incorporated in order to compute a good estimate of the maximal force [17]. This is a logical conclusion since significant plastic deformation (see next section) and damage can

Fig. 18. Comparison of model with experimental results. Tube specimen, thickness 0.45 mm.

Fig. 19. Comparison of model with experimental results. Flat 0 = 8 mm disc specimen, thickness 0.45 mm.

Fig. 20. Comparison of model with experimental results. Flat 0 = 8 mm disc specimen, thickness 0.5 mm.

initialize early in the SP specimen. However, in this work even a simple elastic-plastic material model resulted in maximal forces, comparable to the experimental data.

3.4. Initialization of significant deformation

In an SP test the specimen exhibits significant levels of deformation already at small puncher displacements. Maximal principal strains reach ~10% already at a beginning of a test with a puncher displacement of just 0.1 mm, Fig. 21. This indicates that SP test could be problematic for brittle materials that can start to crack at strains below 2.5% strain. In such cases cracking would be initialized already at the beginning of the test. This would be followed by the ball being pushed through the specimen. Crack initiation is visible as a drop in the force signal and can easily be detected [4]. However, in the case of small cracks, the overall shape of the force-displacement curve would still look very similar to that of a ductile material [4]. Nevertheless, the measured displacement would then have two components of which one can be ascribed to bending and stretching (as in the case of ductile materials) whereas the other contribution to the displacement could be caused by crack growth. It is questionable if in that case the same data evaluation procedures can be applied as for ductile materials. Fig. 22 shows an example of the difference between ductile and brittle specimen.

4. Discussion and open issues

The SP simulations show that the tensile strength determination assuming linear proportionality with maximum force can be extended to the curved specimen. For the estimation of yield, the Eq. (1) methodology seems to be very susceptible to the inherent scatter in the SP data. For instance insufficient/varying degree of clamping can cause large scatter in the extracted Fe values whereas it seems that the maximum force Fm is much less affected. Simulated force-displacement response of an unclamped specimen in relation to a clamped one shows that using an unclamped specimen results in underestimation of the yield stress by more than 25%, Fig. 23. Table 6 lists the maximal clamping forces, defined here as the total reaction force acting on the top die in the vertical direction, including the force required for preventing the specimen to bend upwards. To see the effect of reduced clamping the displacement boundary condition on the top die was replaced by a vertical downwards force of 5%, 10%, 20% and 50% of the maximal clamping force as given in Table 6. One can see that as soon as even 10% of maximal clamping force is applied, the force-displacement curves are very close to the ones where a full clamping force is applied. This implies that a reasonably small amount of clamping is sufficient for flat specimens.

Tube specimens have significantly higher area moment of inertia compared to the flat specimens. Consequently they are much more difficult to bend and the resulting clamping forces in the vertical direction are therefore expected to be significantly lower. Clamping is therefore expected to be less important for the tube specimens.

4.1. Re-calculation of the yield stress from simulations

To test the precision of methods for determining Rp0.2 from the SP tensile data, the yield stress 0y-SP, Eq. (1), was recalculated from the FEA simulations for a 0=8 mm disc where true yield stress was decreased/increased by 25%, see red curves in Fig. 13. The Fe loads were extracted from the simulations by the two-secant, the CWA (Fig. 5) and the two offset (Fig. 6) methods. In line with [13] an assumption was made that a2 = 0. Furthermore, it was assumed that a1 is material independent. If all these assumptions were true and Fe was a true measure of yield stress, one should see a ± 25% change in the ratio in the extracted Fe values and consequently re-calculated yield stresses. The results show that none of the methods give an exact prediction of

Fig. 21. Maximal principal strains at a puncher displacement of 0.1 mm. The maximum tensile strain (negative in blue) is located on the outer surface of the specimen, directly under the puncher. Specimen thickness 0.45 mm, friction coefficient ^=0.001. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 22. X-ray computed tomography scans of a ductile (Grade 92) SP tensile specimen interrupted at maximum force (left) and a fractured SP creep specimen of a brittle ODS steel (right).

the ± 25% yield stress change, Table 7. The two-secant method gives the best 0y-SP estimate for the Rp0.2 when yields stress is decreased by 25%, while the method with an offset of h0/100 gives the best 0y-SP estimate for the Rp0.2 when yields stress is increased by 25%. A perfect fit would give ratios of 75% and 125%. The average ratio of all methods with one standard deviation is 83.6 ± 2.4% for the lower yield stress and 121.4 ± 4.0% for the higher one.

The scatter in the measured Fe and therefore estimation of Rp02 is clearly susceptible to more scatter than in the case of Fm and Rm. This was also shown to be the case for the SP-tensile tests conducted in [10] where comparing results between different laboratories showed that the standard deviation for measured Fe is 20.7% and 1.6% for Fm at room temperature.

Since the deformation is non-homogeneous, direct determination of the yield stress is difficult. This is the reason why up to now the SP is primarily used as a screening test.

5. Conclusions

Small punch test finite element models have been developed in this work. The models have been validated against flat 6.55x11 mm, flat 0 = 8 mm disc (both 0.45 and 0.5 mm thick) and tube (0.45 mm thick) experimental data. In all cases good agreement between the simulation and experimental results was obtained. No significant differences between the flat 6.55x11 mm and flat 0 = 8 mm disc force-displacement curves were found. Due to the curvature, the tube specimen results in higher maximal force (Fm) which is attained at lower displacements. The friction linearly increases the Fm and to a lesser extent displacement at Fm. On the other hand the yield stress and the hardening, while keeping ultimate tensile strength constant, practically do not affect the Fm. Significant specimen deformation can be expected at already small (0.1 mm) puncher deflection, which could limit the applicability of the small punch test to ductile materials. A reasonable amount of clamping is sufficient to limit the scatter in the yield stress

Fig. 23. Simulations with and without top die (clamping) showing negligible impact on maximum force but large impact on estimated yield force Fe. Flat 0=8 mm disc specimen, thickness 0.5 mm.

Table 6

Maximal clamping forces obtained from the FEM model. Flat 0=8 mm disc specimen, thickness 0.5 mm.

Friction ц Maximal clamping force [N]

0.001 3259

0.01 3161

0.1 2608

0.15 2457

0.2 2333

0.3 2118

0.4 2010

Table 7

The influence of the method for determining Fe on the yield stress oy-SP estimation.

Method (oy-SP with -25% yield) / (°y-SP with +25% yield) / a1, a2[13]

(°y-SP Orig) (Oy-SP Orig)

oy-SP two-secants 80.5% 117.9% 0.442, 0.0

Oy-sp CWA 82.4% 121.1% 0.476, 0.0

oy-SP offset h0/10 84.2% 118.5% 0.346, 0.0

oy-SP offset ho/100 87.2% 128.1% n.a.

estimates. Further work is required to ascertain the effect of ultimate tensile strength and elongation on the small punch test force-displacement curves and quantities, estimated from them.

Acknowledgments

This work has been carried out within the multiyear program of the European Commission's Joint Research Centre under the auspices of the PreMaQ and MaCoSyMa institutional projects.

References

[1] Manahan MP, Argon AS, Harling OK. The development of a miniaturized disk bend test for the determination of postirradiation mechanical properties. J Nucl Mater 1981;103 104:1545-50.

[2] Misawa T, Adachi T, Saito M, Hamaguchi Y. Small punch tests for evaluating ductile-brittle transition behavior of irradiated ferritic steels. J Nucl Mater 1987;150:194-202.

[3] Baik J-M, Kameda J, Buck O. Small punch test evaluation of intergranular embrittlement of an alloy steel. Scr Matall 1983;17:1443-7.

[4] Kameda J, Buck O. Evaluation of the ductile-to-brittle transition temperature shift due to temper embrittlement and neutron irradiation by means of a small-punch test. Mater Sci Eng 1986;83:29-38.

[5] Misawa T, Sugawara H, Miura R, Hamaguchi Y. Small specimen fracture toughness tests of HT-9 steel irradiated with protons. J Nucl Mater 1985;133-134(C):313-6.

[6] CEN Workshop Agreement CWA 15627: Small Punch Test Method for Metallic Materials: European Committee for Standardization, CWA 15627: 2007

[7] Turba K, Hurst R, Hähner P. Anisotropic mechanical properties of the MA956 ODS steel characterized by the small punch testing technique. J Nucl Mater 2012;428(1-3):76-81.

[8] Bruchhausen M, Turba K, de Haan F, Hähner P, Austin T, de Carlan Y. Characterization of a 14Cr ODS steel by means of small punch and uniaxial testing with regard to creep and fatigue at elevated temperatures. J Nucl Mater 2014;444(291):283.

[9] Gül^imen B, Durmu§ A, Ülkü S, Hurst RC, Turba K, Hähner P. Mechanical characterisation of a P91 weldment by means of small punch fracture testing. Int J Press Vessels Pip 2013;105-106:28-35.

[10] Altstadt E, Ge H, Kuksenko V, Serrano M, Houska M, Lasan M, Bruchhausen M, Lapetite J-M, Dai Y. Critical evaluation of the small punch test as a screening procedure for mechanical properties. J Nucl Mater 2016;472:186-95. http:// dx.doi.org/10.1016/j.jnucmat.2015.07.029.

[11] Contreras MA, Rodriguez C, Belzunce FJ, Betegon C. Use of the small punch test to determine the ductile-to-brittle transition temperature of structural steels. Fatigue Fract Eng Mater Struct 2008;31:727-37.

[12] Lapetite J-M, Bruchhausen M. Small punch tensile/fracture test data for Gr. 91 material at -100 °C and a displacement rate of 0.005 mm/s, version 1.0. Petten, The Netherlands: European Commission JRC Institute for Energy and Transport; 2015. http://dx.doi.org/10.5290/1900105.

[13] Garcia TE, Rodriguez C, Belzunce FJ, Suarez C. Estimation of the mechanical properties of metallic materials by means of the small punch test. J Alloy Compd 2014;582:708-17.

[14] Lacalle R, Älvarez J, Guiterrez-Solana F. Analysis of key factors for the interpretation of small punch test results. Fatigue Fract Eng Mater Struct 2008;31:841-9.

[15] Turba K, Gül^imen B, Li Y, Blagoeva D, Hähner P, Hurst R. Introduction of a new notched specimen geometry to determine fracture properties by small punch testing. Eng Fract Mech 2011;78:2826-33.

[16] Bruchhausen M, Holmström S, Lapetite J-M, Ripplinger S. On the determination of the Ductile to Brittle Transition Temperature from Small Punch tests on Grade 91 ferritic-martensitic steel, submitted to Journal of Pressure Vessels and Piping; 2015.

[17] Haroush S, Priel E, Moreno D, Busiba A, Silverman I, Turgeman A, Shneck R, Gelbstein Y. Evaluation of the mechanical properties of SS-316L thin foils by small punch testing and finite element analysis. Mater Des 2015;83:75-84.

[18] Soyarslan C, Gül^imen B, Bargmann S, Hähner P. Modelling of fracture in small punch tests for small- and large-scale yielding conditions at various temperatures. Int J Mech Sci 2016;106:266-85.

[19] Lancaster RJ, Harrison WJ, Norton G. An analysis of small punch creep behaviour in the titanium aluminide Ti-45Al-2Mn-2Nb. Mater Sci Eng A 2015;626:263-74.

[20] Moreno MF, Bertolino G, Yawny A. The significance of specimen displacement definition on the mechanical properties derived from small punch test. Mater Des 2016;95:623-31.

[21] Pillot S. Production of plates (P91 and 316LNmod material) for MATTER FP7 Project, ArcelorMittal, Technical Note CRMC - 2013 - 002; 2013.

[22] de Haan F. MATTER uniaxial tensile test for Gr. 91 steel at room temperature, version 1.1. Eur Comm JRC Inst Energy Transp. The Netherlands: Petten; 2014. http://dx.doi.org/10.5290/2500005.

[23] Simonovski I, Holmström S. Small Punch Model Validation, JRC Technical Report; 2016.

[24] ABAQUS 6.14-2, Dassault Systemes, 2015.

[25] Penuelas I, Cuesta II, Betegon C, Rodriguez C, Belzunce FJ. Inverse determination of the elastoplastic and damage parameters on small punch tests. Fatigue Fract Eng Mater Struct 2009;32(11):872-85.