Fracture Process in Silicate Composite Specimens – X-ray Dynamic Observation and Numerical Modelling

Tensile failure in quasi-brittle materials is connected with formation and evolution of what is referred to as the Fracture Process Zone (FPZ) at the tip of propagating crack. Not only the very existence of the material damage area but also its descriptive parameters (volume, shape and energy dissipation distribution) have to be identified in order to validate approaches on both numerical modelling of quasi-brittle behaviour and experimental determination of fracture properties. Radiographic techniques and Digital Image Correlation method are used in the presented research as being very appropriate for analysing of the FPZ evolution during specimen loading. The experimental results are accompanied with predictions of the FPZ size and shape via semi-analytical technique serving as a part of developing comprehensive method for evaluation of the real fracturemechanical characteristics of quasi-brittle materials from records of loading tests on laboratory-sized specimens. Introduction The field of determination of characteristics of quasi-brittle building materials (most commonly cementitious composites) which should describe their ability to resist the fracture propagation has been thoroughly researched for several decades [1],[2],[3],[4]. However, some aspects that can be considered as crucial are still among the topics of intensive research. Effects of the size and geometry of the test specimen [5] regarded also as the effect of the specimen free boundaries [6],[7] seems to be the most relevant. An approach incorporating the parameters of the zone of material failure developing at the propagating macroscopic crack tip (fracture process zone, FPZ) has been proposed and (partially) employed recently [8]. The development of this approach is motivated by capturing of the above-mentioned effects in order to provide values of the fracture-mechanical parameters of the tested material independent of these effects. This methodology works with the reconstruction of the current size and shape of the FPZ (and perhaps also the intensity of the cohesive behaviour over the FPZ volume) [9] to which the amount of energy dissipated during the current step of fracture process should be related. The development of the methodology is in a stage of testing, verification by numerical simulations [10],[11] and experimental validation [12] at present. It has to be emphasized that sound experimental evidence the FPZ size and shape (and possibly other characteristics) is published rather rarely. Techniques based on acoustic emission ([13],[14],[15],[16]), holographic interferometry, X-ray imaging (in combination with Digital Image Analysis − [17]) and infrared thermography were reported to be used to determine the FPZ in quasi-brittle materials (summarized e.g. in [3],[2]). Investigation of the material failure employing X-ray imaging is presented in this paper. Notched beams prepared from silicate-based composite were loaded in three point bending in a specially designed loading device. Crack length and FPZ shape/size during loading were analyzed using Digital Transmission Radiography and X-ray Computed Tomography (XCT). Visualization of the FPZ was enabled using tools of the Digital Image Correlation (DIC) method. Experiments Tested material and specimens. The radiographic investigations of the material failure have limits in the dimensions of the test specimens. In our case, the length of the beam subjected to three point bending is limited by the chamber diameter of the loading device in which the specimen was placed. As a material for the specimen preparation, a fine-grained cementitious composite was chosen to simulate the failure process of normal-sized building structures/structural members made of concrete. Commercial dry plaster mix with maximum aggregate size equal to 1.2 mm (limestone debris) was selected. The bonding agent of this mix consists of both cement and calcium hydroxide. Minimal value of modulus of rupture quoted by the producer is 0.7 MPa. The mix was prepared according to the producer’s instructions. The presented experiment was made as a pilot test to develop appropriate methodology of the FPZ and crack analysis intended for future experimental campaign. Series of 9 specimens were casted into the moulds: Specimen height W and length L are equal to 40 and 150 mm, respectively; three specimens’ breadths B (12, 20 and 30 mm) were selected; three different notch lengths a (4, 10 and 16 mm) were taken into account for each specimen breadth B. The notches were cut using diamond saw after demoulding. It provides the relative notch length  = a/W equal to 0.1, 0.25 and 0.4. From this series the specimen with breadth B = 20 mm and notch length a = 10 mm was selected for the pilot test and is presented hereafter. The loading span S of the test geometry was set to 120 mm. Schematic picture of the specimen and related bending test is depicted in Fig. 1. Fig. 1: Three point bending geometry; indication of dimensions of the specimen Instrumentation. The modular tomographic system [18] provides an experimental setup allowing positioning adjustment of the X-ray tube, motorized positioning of the detector and the operational movement of the observed object fixed on a motorized stage. The linear axis of this stage enables to set the projective magnification of the object. The rotation axis is used for tomographic data acquisition. The setup is equipped by the motorized revolver holder of the filters used for the fully automated acquisition of data needed for beam hardening correction, using the Signal to Equivalent Thickness (SET) method [19]. Hamamatsu microspot tube is employed as X-ray source in the tomographic system. This tube has a 5 m spot size and cone beam. The pixelated Hamamatsu flat panel was utilized as X-ray imager in our work. This detector has active area 120 × 120 mm with 50 m pixel size. Binning of 2 × 2 pixels was used in our work, so effective pixel pitch was equal to 0.1 mm. Highly stiff loading compressive device was used for the specimen loading. This device allows very low loading velocity while it’s relatively low weight and dimensions enable X-ray observation of the specimen in the radiographic cabin. Loading device generally consists of the actuating part and of the chamber in which specimen is placed. This chamber was manufactured from two parts. Top one is from the Certal aluminium alloy and bottom one from the 0.6 mm thick carbon epoxy laminate, which is practically transparent for X-rays. These parts are connected using bayonet mechanism. Support pins of the bending mechanism were also prepared from the carbon material. This solution enables radiographic observation of the analyzed specimen without any influence of the loading device for X-ray measurement. Whole setup is depicted in Fig. 2 left. Disassembled chamber with the specimen is in Fig. 2 right. Fig. 2: Radiographic/mechanical test setup: disassembled chamber with the specimen (left); completely arranged testing device (right) Test procedure details. Specimen was loaded with velocity 0.1 m/min (that holds true for the displacement imposed by the engine of the loading device, deng, which is not equal to the mid-span deflection of the tested beam, d). Exposure time of one X-ray radiogram was 5 × 0.48 seconds (it corresponds to the 0.5 m displacement increment due to read out time). These radiograms were recorded continuously during loading while CT measurement was done in two load levels. For the CT measurement, 240 snapshots (180° rotation) were taken. Total time of one CT measurement was 50 minutes. The specimen rotation axis was at a distance of 188 mm from the X-ray tube spot and the flat panel was at distance 429 mm from the tube spot. Therefore, the projected magnification was 2.3. The X-ray tube was operated at 80 kV and 125 A. CT reconstruction was done considering divergent X-ray beam [20]. Results. It is clearly visible from load−displacement diagram (LD diagram) plotted in Fig. 3a) that the used loading device enables to study processes with very high loading precision. Measured force P as a function of both the displacement imposed by the engine deng and the estimation of the real deflection of the beam d (without displacements taken place at the contacts of the loading chain parts and the push-in of supports into the specimen) is showed. The real displacement d was not measured directly, it was determined from optical measurements using DIC. The radiogram of the specimen taken 1.5 m after surpassing maximal loading force (point A in LD diagram) is in Fig. 3b) (only middle part of the specimen is showed, overturned upside down). Significant internal structure can be observed, which corresponds to the material inhomogeneity. It is almost impossible to observe FPZ directly in the investigated specimen due to this structure. DIC tools were used to avoid this difficulty; the actual and initial radiograms were subtracted (resulting in subtraction image) to find changes of the specimen density considering specimen movement during its loading. Such image are shown in Fig. 3c) (three blue diamond shape spots occurred due to the flat panel local noise, one of them in the middle of the crack path, unfortunately). It is apparent that FPZ has significant role for the fracture mechanics description.