PSI - Issue 13

Jiaming Wang et al. / Procedia Structural Integrity 13 (2018) 560–565 J. Wang et al. / Structural Integrity Procedia 00 (2018) 000–000

562

3

usually do not provide su ffi cient microstructure data. In the second method, X-ray computed tomography (XCT) is used to obtain the meso-structure. A series of 2D images are reconstructed into a 3D image, which can be transformed into an FE model by translating the voxel-based 3D-image into an FE mesh. In this work we use the synthetic approach to generate models (acknowledging the limited aggregate size data) and the image-based approach for mesh generation after transforming the synthetically generated 3D meso-structure into voxel-based image. This is done for consistency of meshing in view of future comparison between results from the two approaches. The detailed ’take and place’ procedure for synthetic model generation can be found in Wang et al. (2016). Spheri cal particles are used for simplicity. Aggregate particle size distribution is applied with minimum size of 2.36 mm and maximum size of 12.7 mm. After each new particle is generated with size from the distribution function, overlapping conditions are checked. If no overlapping is established, the new particle is placed in the specimen. The procedure is repeated until a prescribed aggregate volume fraction is achieved. The synthetic model is then tessellated into voxels. Tessellations with three voxel sizes, 0.25, 0.2 and 0.15 mm are used to investigate potential e ff ect of resolution on results. The voxel-based models are reconstructed and meshed by Simpleware or Aviso. Zero-thickness cohesive ele ments are inserted between aggregates and mortar using an in-house programme to represent ITZ. 50 mm cubes with 30% aggregate volume fraction and 1% porosity are generated. The majority of the results presented are from models with meshes of 0.25 mm voxel size. The detailed CDP model description can be found in Huang et al. (2015). CDP model is originally designed for concrete. As the softening behaviour of mortar in tension and compression is similar to that of concrete [Du et al. (2014); Grote et al. (2001)], the CDP model is adopted here for mortar matrix. For normal strength concrete, Young’s modulus of mortar ranges from 19 to 35 GPa [Unger et al. (2011); Lu and Tu (2011); Wriggers and Moftah (2006); Snozzi et al. (2012)]. Poisson’s ratio is 0.2 and density is 2000 kg / m 3 . Compressive strength of 45 MPa [Grote et al. (2001)] and tensile strength of 4 MPa are adopted here. The tensile and compressive damage scale factors are calculated by equations given by Guo (2004). Five other parameters of the CDP model are: dilation angle of 35 degree, flow potential eccentricity of 0.1, biaxial / uniaxial compression plastic strain ratio of 1.16, invariant stress ratio of 0.667 and viscosity parameter of 0.0005. These are default values for normal strength concrete in Abaqus [Huang et al. (2015)]. The detailed cohesive zone model description can be found in Wang et al. (2016). The zero-thickness cohesive elements for ITZ follow a bi-linear traction-separation law. Damage can be initiated in normal as well as in two shear directions. Traction stress and relative displacement (or opening displacement) define the damage initiation point. Cohesive sti ff ness ranges from 10 4 to 10 9 MPa / mm [Lo´pez et al. (2008); Trawin´ski et al. (2018); Caballero et al. (2006a); Wang et al. (2016)]. Traction stress is between 2 to 3 MPa in normal direction [Lo´pez et al. (2008).] The fracture energy, total area under stress-relative displacement curve, ranges from 0.01 to 0.1 N / mm in normal direction [Lo´pez et al. (2008)]. The ratio between properties in shear and normal directions varies from 2 to 10 [Lo´pez et al. (2008); Trawin´ski et al. (2018); Caballero et al. (2006a); Wang et al. (2016)]. Simulations are performed with displacement boundary conditions applied to the surface nodes in tension and to a rigid plate in compression. The tensile experiment of Hordijk (1991) and the compressive experiment of Lowes (1999) are used for calibration and validation. Since the tensile and compressive results available for calibration are obtained with di ff erent concrete constitutions, Young’s moduli of mortar and aggregate are calibrated separately for the two cases. According to experiments, the overall Young’s modulus to be achieved for tension is 19 GPa [Hordijk (1991)], while the one to be achieved for compression is 36 GPa [Lowes (1999)]. Considering published values for the Young’s modulus aggregate and that concrete Young’s modulus was found to be more sensitive to mortar’s for the studied aggregate volume fraction, the calibrated values are shown in Table 1. Other parameters were tried during model calibration and test numbers used in this section figures are also given in Table 1 (i.e. parameters of ’Model 1 6’ tension results are mortar elasticity of 60 GPa, aggregate elasticity of 18 GPa, mortar compressive strength of 45 MPa, mortar tensile strength of 4 MPa, ITZ traction stress of 2, 4 and 4 MPa from normal / shear / shear mode, ITZ fracture energy of 0.01 / 0.02 / 0.02 N / mm and cohesive sti ff ness of 10 5 MPa / mm). It should be noted that ’Model 1 6’ and ’Model 1 3’ are correspondingly adopted in tension and compression results of Figure 2, 3(b,d) and 4. 3. Results and discussion