Experimental database with full field measurements for mixed-mode crack propagation in concrete: comparison between experimental and numerical results

The present work is focused on the development of new experimental tests to better characterize the concrete behavior during mixed-mode crack propagation and to validate damage and fracture models. Rich and discriminating tests are performed by using state of the art techniques where the experimental boundary conditions are measured during crack propagation. The crack path complexity is obtained by performing an interactive experimental test, where digital image correlation is performed on regular time intervals to assess crack propagation. At chosen crack tip positions the loading is manually changed to reorient the crack. The experimental results are compared to numerical simulations carried out with a nonlocal damage model and also with a linear elastic fracture mechanics (LEFM) within the X-FEM framework. The present work underlines the importance of using accurate boundary conditions, which are estimated from full field measurements, to perform numerical simulations that reproduce the experimental results. Moreover it is shown that crack reorientation and crack branching are required to create discriminant crack propagation tests. 1 INTRODUCTION The concrete damage and fracture models are continually evolving, increasing in number, in complexity, and most of the existing nonlinear models depend on an important number of parameters that have to be identified [1]. The choice between different models is not trivial and has to be validated. Therefore, to experimentally validate these numerical models, to identify their parameters and to better characterize the concrete behavior during mixed-mode crack propagation, multiaxial tests are developed. Inspired by the work of Nooru-Mohamed [2] DOI 10.21012/FC9.149 A. Carpiuc-­‐Prisacari et al. 2 rich and discriminating tests are conducted by using state of the art techniques. Digital image correlation (DIC) [3] is used to measure the experimental boundary conditions during crack propagation, which are subsequently used in numerical simulations. The mechanical loading is applied using a 6degree-of-freedom testing machine controlled by a 3D displacement measurement system [4] and the cracking state is analyzed via DIC. The major difficulty when performing this type of tests is given by the important difference between the sample dimensions (of the order of tens of centimeters) and the applied displacement at fracture (of the order of few micrometers). With the proposed experimental setup several loading histories are analyzed, namely, proportional and non-proportional loading histories with or without crack closure and friction. The test detailed in the sequel was subjected to a non-proportional loading history. To obtain a more complex shape of the crack path, DIC computations are performed during the test to determine the crack front and in certain key positions of the crack tip the loading is changed in order to reorient the crack. To show the complexity and richness of the presented test, the experimental results are further compared with two numerical models, namely, a nonlocal damage model and an LEFM model; two very different types of models very often used to characterize concrete behavior. The experimental test is considered challenging not only for the presented models but also for a wider class of damage and fracture models. 2 EXPERIMENTAL SETUP The test is performed using a hexapod testing machine with a 3D control system. Therefore complex loading conditions can be applied to a specimen in order to obtain different mixed-mode crack propagations. The 3D control system has been added to overcome the flexibility of the machine and it consists of using three cameras observing three targets attached to the upper mobile part of the machine, and calculating the corresponding actuators length with an integrated digital image correlation algorithm implemented on Graphical Processing Units (GPUs). The control loop frequency is equal to 20 Hz. To check the applied boundary conditions a second measurement setup composed of 6 LVDTs is installed. The cracking state is analyzed on each face of the sample using in plane DIC and to determine the out-of-plane motions stereoDIC is also utilized. The test is performed on a 200 × 200 × 50 mm mortar sample with a 5 × 25 × 50 mm notch. The mortar characteristics (Tab. 1) are obtained by performing 3-point flexural tests on 40 × 40 × 160 mm samples and compressive tests. During the experimental test a combination of shear, tension and rotation is applied to the specimen in a displacementcontrolled history. Each loading component has a well-defined role in the propagation and orientation of the crack. The shear loading allows for the reorientation of the crack, the tension step enables for the crack propagation and the rotation is inducing a gradient of tension/compression in the sample ensuring the stability of the propagation. Table 1: Mechancial properties of the studied material (Young’s modulus, Poisson’s ration, Tensile strength, Compressive strength, Fracture energy) E ν σt σc Gf [GPa] [ ] [MPa] [MPa] [J/m] 21 0.2 3.9 80 100 A. Carpiuc-­‐Prisacari et al. 3 3 EXPERIMENTAL RESULTS The experimental test is composed of seven loading steps (numbered from 1 to 7 in Fig. 1) and a pre-test step (0 in Fig. 1). The pre-test phase is an elastic proportional tension-shear loading-unloading cycle. This step enables the functionality of the experimental setup to be checked. As it is the first motion performed under loading, some spurious movements may be observed due to the positioning of the sample and of all the components used to apply the loading. During the first loading step a proportional rotation/shear displacement is applied to the sample and a crack is initiated (Fig. 2(a)). The shear force, which is equal to 4 kN, has an important influence on the crack propagation angle. Therefore in order to reorient the crack during the second phase the shear force is changed from 4 kN to −4 kN (Fig. 3(a)). The third loading phase consists of applying a combination of rotation and tension that enables for the propagation of the crack in the desired direction. The rest of the steps is a succession of rotation/tension and shear loading phases (Fig. 1) resulting in a crack path having 3 reorientations (Fig. 2(a-c)) and one branching (Fig. 2(d)) resulting in the final fracture profile shown in Fig. 2(d). The forces (Fig. 3(a)) and the moments (Fig. 3(b)) developed during the test are measured using the six-axis load cell of the machine. Therefore no information concerning the applied loading is missing. The displacement fields are measured on each face of the specimen using global RT3-DIC code [5] with a regularization length of 250 pixels inducing a standard displacement uncertainty of 0.7 μm. (a)