Subproject B6

Director

Dr.-Ing. Mike Richter
Institute of Mechanics and Shell Structures

Staff

Prof. Dr.-Ing. Bernd W. Zastrau (advisory)
Dipl.-Ing. Daniela Bayer (until Dec.2009)
M.Sc.-Ing. Aussama Azzam (from Feb.2010)

Objectives

The main objective of B6 is the continuum mechanics analysis of load transfer mechanisms between the individual fibers and the matrix and their influence on the overall behavior of textile reinforced concrete (TRC), in addition to determining the required anchoring end lengths of the textile reinforcement. Moreover, the stress transfer and the damage mechanisms in the areas of the overlapping lengths of the fibers are investigated. The analysis of the stress transfers and the damage mechanisms are carried out by means of the continuum mechanics analysis, the numerical simulations, and the fracture mechanics approaches.

The objectives of this subproject are:

Development of mechanical models for determining the load transfer mechanisms between the textile reinforcement and the fine concrete matrix under multiaxial loading
Determination of local stress concentrations for the detection of damages and the initiation of cracking in the concrete matrix
Investigation of the damage evolution developed by the mechanism of matrix cracking
Analysis of the stress transfer behavior in the areas of reinforcement splices and determining the required overlapping lengths for a wide range of parameters
Investigation of the load transfer from the textile reinforcement to the fine concrete matrix and determining the required anchorage (development) lengths.

Results

IDENTIFICATION OF STRESS CONCENTRATIONS IN TRC AND DETECTING THE INITIATION OF MATRIX CRACKING

The experimental work conducted on the tensile behavior of TRC specimens indicates a final crack pattern corresponds to macro cracks located along the directions of the transverse reinforcements normal to the direction of the applied elongation loads. This comes from the absence of the transverse stiffness of these fibers which create hole-like volumes in the matrix, which lead to concentrated stresses at these locations. The conducted heterogeneous Finite Element modeling in this step gives clear indications for stress concentrations and cracks initiation in the matrix. Figure 1 shows a Finite Element model that considers the structural components of the TRC: the matrix, and both the main and the transfers textile reinforcement fibers.

[Removed image: http://imf.tu-dresden.de/forschung/sfb528/b6bilder/model4_a3d_5_2_geometry.png Alternative text: Geometry and mesh of Finite Element modeling for investigating the stress concentration and the intiation of the matrix cracking Image caption: ]

Figure 1: Geometry and mesh of Finite Element modeling for investigating the stress concentration and the initiation of the matrix cracking

Figure 2 illustrates the stresses in the matrix and gives clear indication to damage initiation an stress concentrations at the locations of the transverse fibers.

[Removed image: http://imf.tu-dresden.de/forschung/sfb528/b6bilder/model4_a3d_5_2_s33_ma_all.png Alternative text: Stress S33 in the matrix under tension loading Image caption: ]

Figure 2: Stress S33 in the matrix under tension loading

INVESTIGATION OF BOND BEHAVIOR BETWEEN FIBERS AND MATRIX IN TRC COMPOSITE

The bond behavior between fiber reinforcements and the concrete matrix is a main characteristic material property of the textile reinforced concrete TRC composite and it affects the overall behavior of this composite. The bond behavior in the fiber-matrix interface is mainly characterized by an initial elastic behavior (the adhesion) until the critical bond stress is reached, then a degradation of bond stresses between the fiber and the matrix is developed (debonding process) until the full breakage of the bond occurs. After that the frictional shear stresses between the fiber and the matrix are dominated.

Mechanical model for the bonding in fiber-matrix interface and Finite Element simulation of the pullout experiments:

The bonding behavior in the fiber-matrix interface can be characterized by a slip-based interfacial model defined by shear stress - shear slip material law, the degradation of the bond shear stresses (debonding process) is regarded in this model by a scalar damage variable. This material law is affected by the mechanical properties of the TRC composite, in addition to the layout of the used textile reinforcement. This bond law is usually deduced by the inverse analysis on the pullout force - pullout displacement obtained from the fiber pullout experiment.

In order to have a better understanding of stress distributions and damage behavior observed in the pullout experiments, three -dimensional Finite Element models are performed on the meso-scale with regard to the TRC material heterogeneity by means of modeling the main structural components: the matrix, the fiber, and the interface between matrix and fibers. The constitutive behavior of the cohesive elements is defined in terms of traction-separation law representing the initial elastic behavior (the adhesion), the damage initiation, and the damage evolution in the interface. Figure. 3 shows the shear tress - shear slip relation and the evolution of the scalar damage variable D of a cohesive element near the crackin addition to the pullout force - crack opening relation up to 1 mm of crack opening.

[Removed image: http://imf.tu-dresden.de/forschung/sfb528/b6bilder/model3_5_t_s_3.png Alternative text: Shear stress - shear slip relation and the scalar damage evolution variable in a cohesive element near the crack Image caption: ]

[Removed image: http://imf.tu-dresden.de/forschung/sfb528/b6bilder/model3_5_p_w_1mm_3.png Alternative text: Pullout force - crack opening relation up to 1 mm of crack opening Image caption: ]

(a) Shear stress - shear slip relation and the evolution of the scalar damage variable in a cohesive element near the crack

(b) Pullout force - crack opening relation up to 1 mm of crack opening

Figure 3: Results of Finite Element modeling of the fiber pullout experiment

The conducted Finite Element simulation allows for capturing the stress distribution during the accumulation of damages along the interface. Figure. 4 shows the shear stress distribution along the interface in three different situations with regard to the pullout force (i.e point P1, P2, and P3 in Figure 3(b))

[Removed image: http://imf.tu-dresden.de/forschung/sfb528/b6bilder/model3_5_l1_l2_contour_3.png Alternative text: Geometry and mesh of Finite Element modeling for investigating the stress concentration and teh intiation of the matrix cracking Image caption: ]

Figure 4: Shear stresses in the model at 0.15 mm crack opening

[Removed image: http://imf.tu-dresden.de/forschung/sfb528/b6bilder/model3_5_l1_l2_tx_3.png Alternative text: Geometry and mesh of Finite Element modeling for investigating the stress concentration and teh intiation of the matrix cracking Image caption: ]

Figure 5: Shear stresses along the interface at points P1, P2, P3 in Figure 3(b)

Pullout fracture energy:

Fiber pullout from a matrix and the corresponding debonding process between the fiber and the surrounding matrix is actually a mode II fracture mechanism. The pullout fracture energy depends on the bond properties (i.e. the bond law). The total pullout fracture energy is plotted in Figure 6 with regard to the developing crack opening w.

[Removed image: http://imf.tu-dresden.de/forschung/sfb528/b6bilder/model3_5_psi_w_1.png Alternative text: The evolution of the total pullout fracture energy in the interface according to the developing crack opening w Image caption: ]

Figure 6: The evolution of the total pullout fracture energy in the interface according to the developing crack opening w

MODELING OF THE MULTIPLE MATRIX CRACKING IN TRC UNDER TENSION LOADING

Textile reinforced concrete is a brittle composite, and it shows damage behavior represented by a multiple crack bridged by fiber reinforcement. In order to investigate the damage behavior accompanied by the multiple cracking process in TRC, 3D Finite Element simulation are made on the meso-scale using the discrete cracking concept and fracture mechanics approaches. The conducted Finite Element models consider the cohesive behavior of the fine concrete matrix within the discrete cracks, in addition to the pullout mechanism of fibers from the concrete matrix. The numerical simulation procedures are accomplished by conducting different models. The first model is an investigation of the structural behavior of a single discrete crack bridged by fibers. While another model is made for analyzing the overall multiple cracking behavior and with regard to the combination of all fracture mechanism (i.e. fiber pullout and matrix cracking).

Investigation of damage mechanisms in a single discrete bridged crack:

A modeling procedure is made toward simulating the fiber crack bridging behavior and the corresponding damages. Therefore, a simple discrete crack model is presented by considering the interaction between all potential damage mechanisms represented by cracking of the concrete matrix and the fiber pullout. Figure 7 illustrates the stresses in the matrix in a single discrete crack model, and by considering the mode I fracture mechanism of the matrix cracking

[Removed image: http://imf.tu-dresden.de/forschung/sfb528/b6bilder/subm4_cohc_s33_contour_long.png Alternative text: Stresses in the matrix in a single discrete crack and by considering cohesive layer between the coupled crack surfaces Image caption: ]

Figure 7: Stresses in the matrix in a single discrete crack and by considering cohesive layer between the coupled crack surfaces

Modeling the overall multiple cracking under tensile loading:

The modeling procedure in this step considers the modeling of all potential cracks in a TRC specimen under tensile loading. Figure 8 shows the main stress - main strain relation according to both the Finite Element simulation and the experimental results, a good matching between the modeling and the experiment is observed.

[Removed image: http://imf.tu-dresden.de/forschung/sfb528/b6bilder/multiple_cracking_sa_ea_contour_1.png Alternative text: main stress - main strain relation of the Finite Element simulation and the result of an experimental investigation of the tensile behavior of TRC specimen Image caption: ]

Figure 8: main stress - main strain relation of the Finite Element simulation and the result of an experimental investigation of the tensile behavior of TRC specimen

IINVESTIGATION OF STRESS TRANSFER BETWEEN THE FIBERS AND THE MATRIX AND DETERMINING THE REQUIRED REINFORCEMENT DEVELOPMENT LENGTHS

Stress transverse behavior between fiber reinforcement and the matrix is analyzed and investigated by means of Finite Element simulations. 3D heterogeneous models are used for simulating the experimental investigation performed for determining the required development length Le. Figure 9 illustrates the Finite Element model in addition to the fiber force - crack opening relation, while Figure 10 represents the fiber force - crack opening relation.

[Removed image: http://imf.tu-dresden.de/forschung/sfb528/b6bilder/le-model-no1-geometry-mesh.png Alternative text: Geometry and mesh of Finite Element model for determining the required fiber development length Image caption: ]

Figure 9: Geometry and mesh of Finite Element model for determining the required fiber development length

[Removed image: http://imf.tu-dresden.de/forschung/sfb528/b6bilder/le-model-120mm-f-w-final_1.png Alternative text: Fiber force - crack opening relation for a reinforcement development length of Le=120 mm Image caption: ]

Figure 10: Fiber force - crack opening relation for a reinforcement development length of Le=120 mm

Figure. 11 shows the shear stress distributions along the interface between the fiber and the matrix

[Removed image: http://imf.tu-dresden.de/forschung/sfb528/b6bilder/le-model-tx-final-incr120_1.png Alternative text: Shear stress in the fiber - matrix interface layer along the development length Image caption: ]

Figure 11: Shear stress in the fiber - matrix interface layer along the development length

ANALYZING of STRESS TRANSFER BEHAVIOR OF REINFORCEMENT SPLICES AND DETERMINING THE REQUIRED OVERLAPPING LENGTHS

Material behavior in the locations of reinforcement splices is analyzed. Moreover, investigations of the required overlapping length Lu in the reinforcement splices are conducted by building 3D Finite Element models for simulating the associated experimental work. Figure 12 illustrates Finite Element modeling of reinforcement splices of overlapping length of Lu= 60 mm.

[Removed image: http://imf.tu-dresden.de/forschung/sfb528/b6bilder/lu-model-60mm--S23-contour.png Alternative text: Shear stress in the model in the overlapping region Image caption: ]

Figure 12: Matrix Stresses in the fibers overlapping region

Puplications

2010

Richter, M.; Bayer, D.: On the Crack Opening in Textile Reinforced Concrete with Regard to Fiber Bridging. In: Proceedings of the International RILEM Conference on Material Science (MatSci) Vol. 1: 2nd ICTRC: Textile Reinforced Concrete, Aachen

2009

Bayer, D.; Richter, M.: Zur Anwendung bruchmechanischer Konzepte für die Modellierung der rissüberbrückenden Wirkung von Rovings. In: Curbach, M. (Hrsg.), Jesse, F. (Hrsg.): Textile Reinforced Structures : Proceedings of the 4th Colloquium on Textile Reinforced Structures (CTRS4) und zur 1. Anwendertagung, Dresden, 3.-5.6.2009. SFB 528, Technische Universität Dresden, D–01062 Dresden : Eigenverlag, 2009, S. 325-336 – ISBN 978-3-86780-122-5 URN: urn:nbn:de:bsz:14-ds-1244047456442-11748
Richter, M.; Bayer, D.: On the Calculation of Crack Face Opening Displacements in Fiber Reinforced Composites under Plane Loading. In: Proceedings in Applied Mathematics and Mechanics, Weinheim