Structural Effects in Dynamic Testing of Brittle Materials Gérard Gary

Structural effects in dynamic testing of brittle materials Gérard Gary To cite this version: Gérard Gary. Structural effects in dynamic testing of brittle materials. First International Conference on Rock Dynamics and Applications, Jun 2013, Lauzanne, Switzerland. hal-00968931 HAL Id: hal-00968931 https://hal.archives-ouvertes.fr/hal-00968931 Submitted on 4 Apr 2014 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Structural effects in dynamic testing of brittle materials G. Gary LMS, Ecole Polytechnique, 91128 PALAISEAU, France ABSTRACT: Dynamic testing of brittle materials obviously involves the specificities of dynamics and of the special kind of behaviour that describes brittle material. The interaction of both aspects is much more important than for materials like metals which exhibit a plastic behaviour. This interaction is described in the present paper, with a special focus on the Split Hopkinson bar technique commonly used in these fields. 1 INTRODUCTION So called “brittle materials” first show a brittle behaviour in tension – sometimes in simple compression – and usually a plastic-like behaviour under confined compression. This plastic- like behaviour is more often the response of a damaged material that does not recover its integ- rity after unloading. It then appears that the notion of behaviour, when applied to brittle materials, is strongly dependant on the loading. It is also dependant on the size of the elementary ele- ment in which it will be introduced for the (FEM) modeling of a real structure. Basic physical phenomena may involve a very small scale while a much large scale is required for modeling. The same situation occurs in the case of testing when, in the opposite way of thinking, one has to go from global measurements to stress-strain relations. Accounting for structural effects in testing is then an evidence as any specimen tested is nothing else than a structure. It will appear in an evident manner for many tests used in brittle material testing (like flexion tests for instance), especially for concrete often requiring big specimens (in “10 cm” range, minimum). For this reason, we will especially focus on tests for which this aspect does not clearly appear as simple compression and tension tests that are safely processed in a standard way in the case of metals. In quasi-static testing, going from global measurements – force, displacement, gauge meas- urement – to the stress-strain relations requires the homogeneity of mechanical fields within the tested area, basically the strain field. Such an assumption cannot exactly be verified in dynamic testing, especially with brittle materials generally described in the range of small strains. This leads to specific approaches that are investigated in the present paper. This idea can be simply quantified, following Forquin (2013). Considering for example the case of HS-Concrete (High performance) in compression, at an average strain rate of 100/s (ra- ther small in dynamics) it would take 10 µs to reach the failure strain of 0.1%. In order to as- sume equilibrium, waves should run at least 5 round-trips within the specimen during this time, corresponding to a distance of 4 cm (if the speed of wave is 4000 m/s) leading to a maximum specimen size of 0.4 cm which could not be, in any case, representative of the material. The larger the representative size, the smaller the failure strain, the more difficult dynamic testing. Table 1. Mechanical properties of common brittle materials from Forquin (2013), Materials: Glass S-SiC Limestone UHS- HS- ceramic rock Concrete Concrete Tensile strength (σt): ∼ 50 MPa ∼ 400 MPa ∼ 25 MPa ∼ 20 MPa ∼ 5 MPa Elastic failure strain (σt /E): ∼∼∼ 0.1% ∼∼∼ 0.1% ∼ 0.03% ∼ 0.04% ∼ 0.01% in Inelastic tensile failure strain (εf ): 0 0 0 0 ∼ 0.02% Compressive strength (σc): - ∼ 6000 MPa ∼ 150 MPa ∼ 200 MPa ∼ 40 MPa Elastic failure strain (σc /E): ∼∼∼ 1.5% ∼ 0.2% ∼ 0.2% ∼ 0.1% Inelastic compressive failure strain: 0 0 0 ∼ 0.2% Yield stress (Hugoniot Elastic Limit): ∼ 4000 MPa ∼ 12 GPa - - ∼ 350 MPa C Toughness (KI ): ∼ 1 MPa√m ∼ 3.2 MPa√m ∼ 2 MPa√m ∼ 1.6 MPa√m ∼ 2 MPa√m Size of microstructure < nm 2-5 µm 0.1 mm 0.2-0.5 mm 2-5 mm 1.1 Meaning of the word “dynamic” As distinct from the term “static”, ”dynamic” implies the influence of time. A test is said to be “quasi-static” – while a purely static test cannot exist – when the effects of time can be ne- glected. For any real test, the effects of time are typically expressed in two ways: - by inertia forces resulting from the non null acceleration to which elements of structures are submitted. - by the behaviour of each elementary volume of the material depending on evolution in time of the elementary mechanical values (stress and strain) and possibly of their time derivatives. This dependence is described by the generic name of viscosity. This distinction is strictly linked to the notion of elementary volume underlying the definition of the behaviour. Actually, the fact that viscosity effects can be the manifestation of inertial mi- croscopic phenomena cannot be excluded. The behaviour that experimentalists are looking for, to be used in modeling, is supposed to refer to any elementary volume of the studied material free of internal forces. 1.2 Specificity of dynamic testing arrangements The first difficulties encountered in dynamic testing are linked to transient effects inside the machine and the associated sensors: the balancing time of the machine and its sensor array (elastic waves moving back and forth) could be not negligible relative to the length of the test. It has also to be taken care that the acquisition frequency is far higher than the frequency of the transient signals to avoid a possible degradation of the results. Such difficulties mainly concern the faster side of machines providing a range of speeds starting from quasi-static to dynamic loadings. The response of the machine will be briefly investigated in the special case of SHPB (Split Hopkinson Pressure Bars), as matter of illustration, as it is common knowledge that Hopkinson bars have been indeed especially designed to deal with waves and provide reliable measurements at specimen boundaries. 1.3 From global testing to material behaviour. Recall that the homogeneity of mechanical fields is required in order to derive in a simple way the stress-strain relations from global measurements. This homogeneity depends on the specimen dimensions in regard of the representative size of the material tested. Transient effects in the specimen due to the finite speed of waves lead to non homogeneous stress and strain fields in an increasing manner with the specimen size (as quantified above). The homogeneity also depends on boundary conditions, as for instance friction at specimen ends in 1-D compression testing. And, last but not least for materials investigated here, it depends on the material behaviour as, for instance, a softening behaviour is supposed to induce localization. When dealing with brittle materials, especially with concrete, the representative size must be large in comparison with the size of testing devices. This size factor also gives an increased im- portance to structural forces induced by inertia effects that appear most often in addition to loading forces. 2 AVAILABLE TESTS AND MEASUREMENTS It would not be possible to give an extensive list of dynamic tests used for the experimental study of brittle materials. Our paper will then be restricted to the more common ones, with a special attention to those which are more familiar to the author. Looking for the dynamic material behaviour under compression, SHPB is commonly used (strain-rates ranging from 50 to 500 for concrete). Under such a loading, brittle material are very sensitive to lateral pressure (as shown for instance in fFigure. 1) so that three (complementary) loadings are found: simple compression, compression under controlled pressure, compression of a confined specimen preventing lateral expansion. Figure 1. Tri-axial quasi-static compression of a ceramic, from Heard & Cline (1980). The direct impact test could also be used but it is not well adapted as its processing requires the assumption of equilibrium. At higher strain rates, plate-plate impact tests have been used, but it is shown that they do not provide a direct access to the behaviour and they are limited to very high strain rates (> 105s-1) For tension testing, the two more direct approaches are the (modified) SHB for direct tension and spall tests. These last ones, as they start with a compression phase, cannot afford to avoid a transient analysis. Other tests leading to fracture in tension involve a clear structural response without homogeneity of mechanical fields: Brazilian test, flexion of beams or plates. 3 COMPRESSION 3.1 Compression with SHPB. Striker Incident bar Strain gauge A Specimen Strain Figure 2. Typical SHPB set-up. 3.1.1 Basics of the machine SHPB suffers from its historical original use introduced by Kolsky (1949). He proposed his formulas before computers had become generally available for data processing. He used identi- cal input and output bars (same length, diameter and material) and put strain gauges at the mid- dle of each bar.

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