The design of new grips for multiaxial fatigue tests

21ème Congrès Français de Mécanique Bordeaux, 26 au 30 août 2013

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The design of new grips for multiaxial fatigue tests

V. I. PRISACARIa, P. GABORITa, M. PONCELETa, B. RAKAa, J.M. VIRELYa

a. Laboratoire de Mécanique et Technologie (LMT-Cachan), ENS de Cachan / UMR 8535 CNRS / Univ. Paris 6 / PRES UniverSud Paris,

61 Avenue du Président Wilson, F-94235 Cachan Cedex

Résumé: L’amélioration des simulations numériques de tenue à la fatigue nécessite des modèles multiaxiaux et leurs essais d’identification. Nombre d’entre eux se font sur des éprouvettes « en croix » depuis la démocratisation des machines de traction biaxiale [1]. La majorité des mors utilisés actuellement pour ce type d’essai a plusieurs avantages : robustesse vis-à-vis des charges radiales, montage simple et rapide des éprouvettes. Généralement, ils ont comme défauts communs une précision d’alignement insuffisante (induisant une flexion statique au montage) et potentiellement une flexion sous charge. Ces défauts sont évidemment de première importance lorsque des essais de fatigue sont réalisés. D’autres mors suppriment une partie de ces inconvénients, mais habituellement au prix d’un encombrement significatif. En outre, les techniques de mesure mises en place au sein des machines biaxiales ont beaucoup évolué depuis leur apparition [2-7]: Corrélation d’Images Numériques, Stéréo-corrélation, Thermographie, DRX. Il est donc nécessaire de prendre en compte ces nouvelles contraintes en plus des défauts des mors actuels. La solution proposée offre une plus grande raideur en flexion tout en conservant un encombrement très réduit, permettant de nombreuses instrumentations. En outre, elle permet l’alignement du mors par rapport à son palier pour diminuer au maximum les mouvements hors plan (ce qui est vérifié avec une éprouvette étalon instrumentée). Plusieurs capteurs peuvent être embarqués sur le mors pour répondre à différentes fonctions, en particulier des capteurs de déplacement LASER offrent une mesure directe de l’écart entre mors et de leur inclinaison relative.

Abstract: Most of the planar biaxial machine grips currently used for cross-shaped specimens have several advantages: stiffness to radial loads, fast and easy sample mounting. Generally, they lack a sufficient alignment precision (inducing a static bending during clamping) and might exhibit flexion during load. These shortcomings are obviously of major importance when it comes to fatigue tests. Other types of grips avoid some of these problems, but usually at the cost of a significantly larger size. Moreover, measurement techniques used with biaxial testing machines have evolved considerably: Digital Image Correlation, Stereo Correlation, Thermography, X-Ray Diffraction. It is thus necessary to take into account these new requirements along with the defects of the existing grips. The considered solution offers a higher bending stiffness without considerable increase in size, permitting significant additional instrumentation. Also, it allows the measurement and the adjustment of the alignment of the grip with respect to its hydrostatic bearing, thus reducing considerably the out of plane motions. Auxiliary devices can be attached to the grips, particularly LASER displacement sensors that provide direct measurement of the distance between the grips and of their relative tilt.

Keywords: multiaxial, fatigue, testing machine, grips

1 Introduction Due to the increasing complexity of systems used in aeronautics, spatial, automobile industries, etc. the need for more sophisticated fatigue models to describe their behavior has grown in the past years [1]. This implies that experiments manage to get as close as possible to the multiaxial loading states encountered in service. In this sense, studies performed on biaxial samples have grown in number and in complexity.


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The LMT Cachan laboratory owns a tri-tension/compression testing machine named ASTREE. It has three orthogonal axes, each of them containing two hydraulic actuators working in pairs. This machine is particularly interesting because of its mobile architecture, allowing the mounting of considerably large samples and permitting experiments where the center of the specimen is kept motionless. Most of the experiments performed in ASTREE are biaxial tension-compression tests on planar cross-shaped samples [2-7]. Many sets of grips have been used for these experiments [3-7] but the majority fails in terms either of stiffness, size, or ultimate load. The design of new grips for ASTREE aims to fulfill the following needs: improving the stiffness of the grips, controlling unexpected solicitations, evaluating the quality of the alignment of the actuator lines, mounting of smaller and thicker samples. Moreover, the instrumentations and types of tests performed in the laboratory have evolved considerably making it necessary to adapt the grips to these complex conditions. This study will first provide a brief description of the existing grips and the reasons why they fail the aforementioned criteria. The architecture of the new grips will be then presented along with their innovations. Finally, the validation procedure and conclusions are stated.

2 Existing grips The current configuration contains four grips (fixed and mobile part), each one connected to the hydraulic actuator by means of a spacer (Fig 1a). These grips (Fig 2a), designed by J. Lemaitre and J.M. Virely (and called in the following L&V grips), have been used for most biaxial tests on ASTREE because of their clear advantages: sufficient effort transmission, small size and easy sample mounting. Nevertheless, some tests have shown non-negligible bending values (Fig. 1b). Moreover, the alignment of the actuators is not properly evaluated (inducing static bending during mounting) and the compatibility with other types of samples is quite limited both in size and thickness. On the grips developed by Instron and used at the Centre des Matériaux laboratory an extra tightening, perpendicular to the load axis, has been added in order to ensure the contact between the fixed and the mobile part. The MTS standard grips used in uniaxial tensile machines have a more complex design: two wedges supported on the fixed part, with a mobile shaft which clamps these wedges. They are available in “hydraulic” or "mechanical" versions. As shown in Fig. 1b, these types of grips endure high loads and induce almost no bending. However, their large diameter prevents the use of a stereo-DIC setup or a mobile X-ray diffraction (XRD) machine that was developed in LMT Cachan.

Fig. 1 – (a) Current configuration used in ASTREE, (b) Basic specifications of existing grips

L&V LMT

Instron CdM

MTS Hydr.

MTS Mech.

Diameter (mm) 150 225 204 170

Axial efforts (kN)

250 100 100 100

- 250 - 100 - 100 - 100

Radial efforts (kN) 200 110 - -

Bending (mm) > 0,1 ≈ 0 ≈ 0 ≈ 0

(a) (b)


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3 Chosen design Different architectures have been investigated. The chosen one is a combination between the L&V grips (Fig. 2a) and to the Instron ones. It is simple (only two main parts) and stiff (because of its nearly symmetric geometry (Fig 2b), compactness and large ribs) despite its small size. Its rough shape and size derive directly from the collision limits with the neighboring devices or their size.

(a) (b)

Fig. 2 – (a) L&V grips (b) Diagram of the new grips

The upper mobile part will be attached during tests to the lower fixed one directly, using 8 M12 screws, and through sample contact using 8 M8 screws or less depending on the specimens. The height of the grips allows the XRD machine to be used. This machine will be mounted above the horizontal plane of the grips in order to measure the stress state and phase changes while performing biaxial tension tests. The seemingly trivial aspect of the “steep” front end makes the region of interest more accessible in terms of visibility (lighting, XRD) and allows the use of shorter samples (no collision with neighboring grips). Another aspect that had to be taken into account was the cooling of the grips (controlling the heat flux from the grips to the samples or in the opposite way in case of high temperature tests). The four cooling pipes that go right through the grips allow maintaining their temperature at 20°C (the temperature of the actuator being about 60°C) without noticeably reducing their stiffness. Another clear improvement is the wider range of possible sample thicknesses (from 3 to 10mm) that allows coherence between the sample mid-plane and the actuators plane. One need only use the corresponding jaws. These jaws, which complement the tightening M8 screws in terms of adherence, can be designed with different contact surfaces (smooth, spiked, striated, etc.) depending on the material and on the loading type.

4.1 Alignment solution The design of the grips aims to accomplish two purposes: on the one hand to allow the alignment of each grip with respect to its bearing in order to reduce as much as possible the out of plane movements that come from bearing rotation and on the other hand to allow the alignment of the grip assembly to avoid sample bending. Because of the inability to rigorously position the actuators vertically, these two conditions cannot be stricto sensu satisfied. An alternative is to verify the relative position of the actuators and then to modify the position of the grips with respect to the spacers. For the relative position verifications, one of the proposed solutions is to use a cross-shaped gauge with cylindrical ends placed on specific surfaces of the grips (Fig 2). Using this method, the measure is independent with respect to the rotation of each bearing and simplified (no iterations between each possible combination of grips).


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(a) (b)

Fig. 2 – Alignment measuring system: (a) Support for the alignment cross which is coaxial with respect to the axis of the grip (b) Alignment cross gauge

4.2 Out of plane motion measurement In order to measure the relative position of each grip with respect to its opposite neighbor, LASER sensors (Fig 3a) have been chosen. They offer high precision (e.g. 2 microns of measure incertitude at 10Hz, for a working range of 300-500 mm) without interfering with the other measurements. Because of their considerable size they could only be placed on top and on the bottom of the grips. Such a pair of sensors along with their corresponding “screen” on the opposing grip would allow the monitoring of the distance between the grips and the system’s alignment during loading (Fig 3).

(a) (b) (c)

Fig. 3 – Distance measuring using LASER: (a) Principle of LASER triangulation (b) Side view (c) Top view

4.3 Numerical validation of the design In order to quantify the gain in stiffness with respect to the L&V LMT grips, numerical simulations of the two systems were performed. The purpose was to find the critical areas and to compare the way each set of grips distributes efforts. Thus, the two systems are elastically loaded up to the maximum service values. To come closer to the real behavior, the efforts weren’t directly applied onto the grips but through a quarter of a typical cross-shaped sample. For the L&V grips an assembly with the fixed part, the mobile part and a sample in between was created (perfect contacts were used). For the new grips, in order to simulate the worst


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clamping scenario, a clearance was introduced between the upper grip and the lower one so that the efforts are only transmitted through the 5 M12 screws. The first simulation was simple tension, i.e. the most commonly encountered solicitation during grips usage. Thus, a force of 100 kN (the maximum load that can be induced by one actuator) was applied on the tip of the quarter sample (Fig. 4). The upper limit of the represented stress range was set to 150MPa, i.e. far lower than the fatigue limit of the material (about 600 MPa). The new grips are below this value once optimization was done, whereas the L&V ones are considerably above in the connecting area and the lower ribs. Moreover, the deflection of the new grips is approximately 15 times smaller than of the L&V ones (Tab. 1).

(a) (b)

Fig. 4 – Simple tension numerical simulations (100kN): (a) L&V grips (b) New grips

Secondly, accidental radial loads were simulated, where a force of 200kN was applied in the loading plane but perpendicular to the axis of the grip (Tab. 1 - Radial force 1). Although the found efforts are unrealistic, they validate qualitatively the gain in stiffness. Finally, system behavior was tested in the case of an accidental load perpendicular to the loading plane (Tab. 1 - Radial force 2). The considered load was 500kN, representing the maximum impact of an actuator from the vertical axis. As before, it can be seen that the compact design and the contribution of the mobile part are responsible for the considerably better response of the new system. In both cases, it is clear that the weakest link will be the M12 screws in such accidental loadings.

Measured value Axial force

(100 kN) Radial force 1

(200 kN) Radial force 2

(500 kN)

L&V grips Deflection (mm) 0.3 - -

Maximum stress (MPa) 350 2000 10000

New grips Deflection (mm) 0.02 - -

Maximum stress (MPa) 140 600 4000

Tab. 1 – Numerical simulations results for the L&V grips and the new grips

5 Conclusions and perspectives The study has presented the design of new grips for biaxial tension tests. The main focus was to resolve the issues found in most existing grips: improving the stiffness of the grips, controlling unwanted solicitations, evaluating the quality of the alignment of the actuator lines, mounting of smaller and thicker samples. Moreover, the complex techniques used while performing biaxial tests (Digital Image Correlation, Stereo Correlation, Thermography, XRD) created further needs that were partially covered (providing cooling pipes, easy LASER sensor attachment, mobile XRD machine accessibility, etc.). At the writing time of this proceeding, a validation procedure for the new grips was foreseen in a few weeks. The main purpose of the validation is to quantify the bending due to loading for the L&V and the new grips.


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This comparison will be performed using different measuring techniques (strain gauge rosettes, Digital image correlation, LVDT) during cyclic proportional loadings with a stress ratio of -1 using two loading frequencies (20 Hz and 1 Hz). In order to perform these tests, two reference test samples [8] were machined. One of them will be instrumented with 10 strain gauge rosettes (5 on each side) thus obtaining the averaged plane strain field in these areas of interest (Fig. 5a). The surface of the second one will be painted with a black and white speckle in order to obtain the full displacement field using Digital Image Correlation (Fig. 5b).

(a) (b)

Fig. 5 – Reference test samples used for grip validation using different measuring techniques: (a) strain gauge rosettes (b) Digital Image Correlation. The positioning system using centering pins is represented:

primary contact (red) and secondary contact (blue).

(1)

References [1] Hannon, A. & Tiernan, P. A review of planar biaxial tensile test systems for sheet metal. Journal of Materials Processing Technology 198, 1-13 (2008). [2] Wu, X.-D., Wan, M., & Zhou, X.-B. Biaxial tensile testing of cruciform specimen under complex loading. Journal of Materials Processing Technology, 168(1), 181–183. doi:10.1016/j.jmatprotec.2004.11.003 (2005). [3] Bonnand, V., Chaboche, J.L., Gomez, P., Kanouté, P. & Pacou, D. Investigation of multiaxial fatigue in the context of turboengine disc applications. International Journal of Fatigue 33, 1006-1016 (2011). [4] Bedkowski, W., Determination of Critical Plane and Effort Criterion in Fatigue Life. Evaluation for Materials under Multiaxial Random Loading. Experimental Verification Based on Fatigue Tests of Cruciform Specimens. Proc. 4th ICB/MF, May 31 - June 3, Paris, 435 – 447 (1994). [5] Sermage, J.-P., Lemaitre, J., Desmorat, R., 2000. Multiaxial creep fatigue under anisothermal conditions, Fatigue and Fracture of Engineering Materials & Structures. 23(3), 241–252. [6] Doudard, C., Poncelet, M., Calloch, S., Boue, C., Hild, F., & Galtier, A. Determination of an HCF criterion by thermal measurements under biaxial cyclic loading. International Journal of Fatigue, 29(4), 748–757. (2007). [7] Poncelet, M., Barbier, G., Raka, B., Courtin, S., Desmorat, R., Le-Roux, J. C., & Vincent, L. Biaxial High Cycle Fatigue of a type 304L stainless steel: Cyclic strains and crack initiation detection by digital image correlation. European Journal of Mechanics - A/Solids, 29(5), (2010). [8] J. Lemaitre , J.-L. Chaboche , A. Benallal , R. Desmorat, Mécanique des matériaux solides (3e édition), (2008)

The design of new grips for multiaxial fatigue tests

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