Numerical Simulation Of The Tensile Strain Hardening And Multi-Cracking Behavior Of ECC

Engineered cementitious composites(ECC)is a fiber-reinforced cementitious composite material with tensile strain hardening behaviours and excellent crack control capability.As a type of fiber-reinforced composite material,the mechanical properties of ECC material are closely related to the mechanical interaction between fibers,matrix,and fiber/matrix interface,A multi-scale model from single fiber to single crack surface,and then to composites is established through the micromechanics theory.It can realize the quantification of the mechanical properties of ECC material at various scales,and then guide the design of ECC material.In this paper,numerical simulation and theoretical analysis of the ECC uniaxial tensile strain hardening and multi-crack behavior were carried out through two fiber bridging models(one ignores fiber bending and the other considers fiber bending),and systematic research has been carried out from single fiber pullout,single crack fiber bridging model,numerical simulation of ECC tensile performance and model application,and the following results have been achieved:(1)The friction pulley model(“string” model without considering the bending effect of the fiber)and the equivalent foundation beam model(“beam” model with considering the bending effect of the fiber)were introduced to simulate the pull-out behavior of a single fiber.Based on the ANSYS plane strain analysis model,the force-displacement response of the fiber subjected the lateral load under different fiber-matrix stiffness ratios was calculated.An explicit calculation method was proposed to determine the spring constraint stiffness of the equivalent continuous beam through parameter analysis and fitting,and an improved equivalent foundation beam model considering the bending stiffness of the fibers was established.(2)The axial force and lateral force of the pull-out section in the fiber pull-out process were deduced based on the “beam” model,and a program to calculate the relationship between fiber pull-out force and pull-out displacement was programmed by MATLAB.In order to verify the correctness of the model,a single fiber pull-out finite element analysis model was established based on the Coulomb friction model.The results show that the “beam” model is more consistent with the finite element results when the crack opening width is smaller than that of the “string” model.(3)Based on the “string” model and the “beam” model that simulate the pull-out of single fiber,two single-crack fiber bridging models were established considering the two-way fiber pull-out and the averaging treatment of random distribution,and the comparison and analysis of the two models were conducted.The results show that the peak bridging stress of single crack and the corresponding crack opening width obtained by the “beam” model are both larger than the “string” model,indicating that fiber bending has a significant effect on fiber bridging.(4)Based on the single-crack fiber bridging model,two numerical models of discrete crack random distribution were established to simulate the tensile strain hardening and multicrack behavior of ECC.By comparing the stress-strain curves obtained from uniaxial tensile tests of PE-ECC and PVA-ECC standard specimens,it was found that the ultimate tensile strength and tensile strain of ECC calculated by “beam” model considering the bending effect of fiber are both higher than “string” model.For ECC using PE fiber with higher elastic modulus,the calculated results based on “beam” model are in good agreement with the experimental results,while for PVA-ECC,the calculated results based on “string” model ignoring the bending effect of the fiber are in good agreement with the experimental results.For ECC using PE fiber with higher elastic modulus,the calculated results based on the equivalent foundation beam model are in good agreement with the experimental results,while for PVA-ECC,the calculated results based on the friction pulley model ignoring the bending effect of the fiber are in good agreement with the experimental results.(5)The probability distribution model of the influence of specimen width and thickness on the fiber distribution was derived,and the above two fiber bridging models were applied to simulate the tensile properties of ECC specimens with different widths/thicknesses.The validity of the model was verified by uniaxial tensile tests of ECC specimens of different sizes.The results show that the ultimate tensile strength and ultimate tensile strain of ECC can be significantly increased by the width and thickness of the specimen within a certain range.However,when the width of the specimen W≥30mm,the width of the specimen has little effect on the tensile properties of ECC.When the thickness of the specimen decreases,the fiber approaches 2D distribution,and when the thickness of the specimen increases,the fiber approaches 3D distribution.At this time,the ECC ultimate tensile strength and ultimate tensile strain decrease.Based on the model analysis,the stress-strain reduction factor considering the size of the specimen was proposed,and the reduced constitutive model was applied to the finite element simulation to analyze a group of four-point bending test beams.It was found that the finite element analysis results obtained by using the reduced tension stress-strain relationship are in good agreement with the test results.