Bilinear Softening Model Research Articles

Study on the member fracture and collapse performance of single-layer grid structures using discrete solid element method

In this study, the discrete solid element method (DSEM) incorporating a softening model is proposed, to accurately simulate the dynamic crack propagation and the member fracture of the single-layer grid structure. Firstly, based on the fracture criteria of strain energy release rate, the bilinear softening model and the trilinear softening model are proposed to simulate the fracture in both elastic and elastic-plastic materials. Secondly, the validity of the proposed approach is assessed through a comparison with empirical results. Furthermore, the fracture of the rectangular beam, dynamic crack propagation of the circular tube and member fracture of the hexagonal spatial rigid frame are simulated and compared with other numerical methods. Finally, the DSEM with the softening model is employed to investigate the collapse performance of single-layer grid structures, and the whole process of member fracture is captured by the DSEM. A thorough analysis is conducted to evaluate the influence of material parameters, loading methods, and rise-span ratios on the bearing capacity and fracture occurrence of single-layer grid structures. The results show that the material property of steel is superior to aluminum for single-layer grid structures. Moreover, the single-layer grid structures adopting full node loading or high rise-span ratios are shown to exhibit premature member fracture and rapid structural collapse. The obtained results exhibit remarkable agreement with the experimental results and are superior to the finite particle method (FPM) and the extended finite element method (XFEM). Therefore, DSEM with the softening model possesses the potential to evolve into an effective numerical tool capable of solving complex problems such as dynamic crack propagation and structural collapse.

Experimental Study on Crack Propagation of Concrete Under Various Loading Rates with Digital Image Correlation Method

The quantificational exploration of the propagation law of fracture process zone (FPZ) is of great importance to the research on concrete fracture. This paper performed fracture experiments on pre-cracked concrete beams under various loading rates. Digital image correlation (DIC) method was applied to obtain the whole field displacement of concrete in the fracture test. The crack opening displacement (COD) and the evolution of FPZ were determined based on the whole field displacement. The results show that the length of FPZ first increases and then decreases with the development of the effective crack length and the maximum length of FPZ is about 60 mm. It can be found that the length of FPZ corresponding to the peak load decreases with the increase of loading rates. Based on the fictitious crack model, a bilinear softening model was established. According to the proposed model, the mechanical behavior and the propagation law of FPZ were analyzed. The bilinear softening model can reflect the microcrack development and the aggregate interlocking in the FPZ.

Analysis of notch depth and loading rate effects on crack growth in concrete by FE and DIC

In this paper, the fracture characteristics of concrete specimens with different notch depths under three-point flexural loads are studied by finite element and fracture mechanics methods. Firstly, the concrete beams (the size is 700x100x150 mm) with different notch depths (a=30 mm, 45 mm, 60 mm and 75 mm respectively) are tested to study the influence of notch depths on the mechanical properties of concrete. Subsequently, the concrete beams with notch depth of 60 mm are loaded at different loading rates to study the influence of loading rates on the fracture characteristics, and digital image correlation (DIC) is used to monitor the strain nephogram at different loading rates. The test results show that the flexural characteristics of the beams are influenced by notch depths, and the bearing capacity and ductility of the concrete decrease with the increase of notch depths. Moreover, the peak load of concrete beam gradually increases with the increase of loading rate. Then, the fracture energy of the beams is accurately calculated by tail-modeling method and the bilinear softening constitutive model of fracture behavior is determined by using the modified fracture energy. Finally, the bilinear softening constitutive function is embedded into the finite element (FE) model for numerical simulation. Through the comparison of the test results and finite element analysis, the bilinear softening model determined by the tail-modeling method can be used to predict the fracture behavior of concrete beams under different notch depths and loading rates.

Strain sensing ability of metallic particulate reinforced cementitious composites: Experiments and microstructure-guided finite element modeling

This paper evaluates the capability of waste iron powder-reinforced cementitious matrices as self-sensing materials in lieu of more expensive carbon fiber and nanoparticle reinforced matrices. Electrical impedance spectroscopy coupled with equivalent circuit modeling is used to determine the bulk resistance of the composite beams containing up to 40% by volume of iron particulates under flexural loading. The fractional change in resistance and the gage factor, as functions of the applied stress, increases with increasing iron particulate content, demonstrating the ability of these composites in self-sensing. A microstructure-guided electro-mechanical finite element model is used to simulate the strain sensing response of these composites. The 2D microstructure is subjected to different applied tensile stresses, and the deformed geometry subjected to an electrical potential to simulate the change in resistance. Debonding at the inclusion-paste interface under load, which is found to significantly influence the fractional change in resistance, is accounted for by using a bilinear softening model. The model is found to correlate well with the experimental data, and has the potential to facilitate microstructural design of materials to achieve desired degrees of self-sensing.

Effect of acid corrosion on crack propagation of concrete beams

The effect of acid corrosion on crack propagation of concrete beams was theoretically studied by the method of crack extension resistance curve. Based on this method, a calculation approach was proposed to determine fracture stress intensity factors in crack propagation of concrete beams. Loop iteration analysis was carried out to calculate maximum bearing capacity load, unstable crack toughness, resistance toughness curve, cohesive toughness curve and load–crack mouth opening displacement. Both bilinear and nonlinear softening traction–separation curves were adopted for each of these calculation parameters. The analysis results of each showed the effect of acid corrosion degrees. The influence of acid corrosion on fracture properties was discussed through the calculated results of cohesive toughness curves. These five kinds of simulated results were basically consistent, before the load attained the maximum value. However, with further crack propagation, cohesive toughness of nonlinear softening model was significantly larger than that of bilinear softening model, and the descending branch of P–CMOD curve by nonlinear law is higher than that by bilinear law. To validate the approach, tests of specimens under six different corrosion periods were experimentally studied, using three-point bending notched concrete beams soaked in sulphuric acid solution. The Double-K fracture parameters were investigated based on the test results, and load–crack mouth opening displacement curves for different acid conditions were obtained using synchronous sampling of a load sensor and clip-gauge. Numerical results by bilinear softening model showed a good correlation with the experimental ones.

Bilinear softening model and double K fracture criterion for quasi-brittle fracture of pultruded FRP composites

This study presents an experimental study on the mode I fracture property of pultruded fiber reinforced polymer (FRP) composites along the fiber direction. A quasi-brittle fracture exists for this material. The bilinear softening model is used to describe the constitutive relation in the cohesive fracture zone. Furthermore, a double K fracture criterion is applied to analyze the crack propagation and fracture property. The orthotropic effect on the fracture property of mode I along the fiber direction is rather small and ignored in this study. According to the bilinear softening model, the cohesive fracture energy is divided into two parts, the microcracking fracture energy and the fiber bridging fracture energy. The ratio between the two fracture energies and the model parameters are decided with the test results. For the double K fracture criterion, a cohesive fracture toughness in introduced to calculated the initial cracking fracture toughness. Based on the linear elastic fracture mechanics and the bilinear softening relation, the two fracture toughness of this criterion are obtained with the test results.

Three-dimensional cohesive crack model prediction of the flexural capacity of concrete slabs on soil

A three-dimensional approach to discretely account for crack initiation, crack growth, and determination of the flexural load capacity of concrete slabs on an elastic foundation under mode I loading is proposed. The finite element model incorporated cohesive crack elements along a pre-defined crack path in the concrete slab. A bilinear softening model was used to describe the stress-crack opening relationship for plain concrete and was defined solely on measured strength and fracture properties. The proposed method predicted the slab’s flexural load capacity as compared to the large-scale experimental concrete slab results for several geometries and notch configurations. The model also provided insight into stress concentration areas and crack propagation positions at different load levels.

Determination of the kink point in the bilinear softening model for concrete

The characterization of the softening curve from experimental results is essential for predicting the fracture behavior of quasi-brittle materials like concrete. Among various shapes (e.g. linear, exponential) to describe the softening behavior of concrete, the bilinear softening relationship has been extensively used and is the model of choice in this work. Currently, there is no consensus about the location of the kink point in the bilinear softening curve. In this study, the location of the kink point is proposed to be the stress at the critical crack tip opening displacement. Experimentally, the fracture parameters required to describe the bilinear softening curve can be determined with the “two-parameter fracture model” and the total work of fracture method based on a single concrete fracture test. The proposed location of the kink point compares well with the range of kink point locations reported in the literature, and is verified by plotting stress profiles along the expected fracture line obtained from numerical simulations with the cohesive zone model. Finally, prediction of experimental load versus crack mouth opening displacement curves validate the proposed location of the kink point for different concrete mixtures and also for geometrically similar specimens with the same concrete mixture. The experiments were performed on three-point bending specimens with concrete mixtures containing virgin coarse aggregate, recycled concrete coarse aggregate (RCA), and a 50–50 blend of RCA and virgin coarse aggregate. The verification and validation studies support the hypothesis of the kink point occurring at the critical crack tip opening displacement.

Concrete fracture prediction using bilinear softening

Abstract A finite element-based cohesive zone model was developed using bilinear softening to predict the monotonic load versus crack mouth opening displacement curve of geometrically similar notched concrete specimens. The softening parameters for concrete material are based on concrete fracture tests, total fracture energy (GF), initial fracture energy (Gf), and tensile strength ( f t ′ ) , which are obtained from a three-point bending configuration. The features of the finite element model are that bulk material elements are used for the uncracked regions of the concrete, and an intrinsic-based traction-opening constitutive relationship for the cracked region. Size effect estimations were made based on the material dependent properties (Gf and f t ′ ) and the size dependent property (GF). Experiments using the three-point bending configuration were completed to verify that the model predicts the peak load and softening behavior of concrete for multiple specimen depths. The fracture parameters, based on the size effect method or the two-parameter fracture model, were found to adequately characterize the bilinear softening model.

Environment induced failure of brittle and quasi-brittle materials

Since long it is known that the strength of oxide ceramics and glasses is influenced significantly by the presence of water. This not only leads to a strength reduction but also to a strain-rate effect. Conventionally, these effects are explained by the reaction of water at the crack tip with the metal–oxygen bonds. Recently, it has been shown that also adsorption can play a significant role. The relevant experiments and modelling are discussed. Moreover, the influence of various other gases, like H 2S, NH 3, NO and CO, on the strength is discussed. For materials with a process zone the influence of the microstructure has to be taken into account. This behaviour is exemplified by a quasi-brittle polymer composite using the fictitious crack model with a bi-linear softening model. Useful future extensions are indicated.