Mixed-mode Fracture Of Concrete Research Articles

Investigation of driving forces in a phase field approach to mixed mode fracture of concrete

Concrete, with its heterogeneous internal structure of cement mortar and grains, exhibits complex quasi-brittle cracking where a gradual decrease in the material integrity is observed. In practical engineering, concrete structures are commonly under loading conditions that cause complex mixed mode fracture patterns. Hence, the prediction of failure mechanisms and patterns in concrete is a demanding task. In the past decades, computational fracture modeling of concrete has proven to be a suitable substitute for costly experimental testing. Among many fracture models, the phase field approach, owing to its ability to capture various crack phenomena without a need for ad hoc criteria, has gained significant attention. Although there exist phase field models applied to various failure mechanisms ranging from brittle to ductile fractures, only a limited number of them deal with the quasi-brittle cracking observed in concrete. Hence, in this work, a thermodynamically consistent phase field approach for quasi-brittle fracture is presented, and its performance for capturing the mixed mode failure patterns of concrete is investigated. Starting from a purely geometric approach, the evolution of fracture is associated with a constitutive crack driving functional. The crack driving force is related to an equivalent effective stress measure leading to a simple, yet versatile, framework in which various failure criteria can be implicitly incorporated into the framework. In particular, equivalent effective stresses based on the Rankine, Drucker–Prager, modified von Mises, and three-parameter failure criteria are derived. A unified form of the equivalent effective stress encompassing all the models is also proposed, which offers flexibility in choosing an appropriate driving force, and allows a simple implementation into a finite element framework. Utilizing this unified form, the effectiveness of the aforementioned driving forces in capturing complex mixed mode cracking in concrete is investigated by comparing the results obtained from computational simulations to existing experimental data. In particular, the load–displacement curves and the crack propagation paths are compared with the corresponding experimental observations, and a systematic study of the performance of different driving forces is detailed in this study.

Phase field model for mixed mode fracture in concrete

Concrete is a quasi-brittle material and generally fails in mixed mode I-II fracture. The fracture energy release in mode I and mode II during crack propagation is usually different. However, the tensile test fracture toughness has generally been considered in most of the numerical models to study fracture in concrete. In this paper, a phase field model is presented which considers the fracture energy of mode I and mode II for mixed mode I-II fracture simulation in concrete. In addition, it uses a fracture mode controlling parameter χ which, in a sense, controls the governing failure criterion. The post-peak material response is modeled using a cohesive zone approach. The effect of the length scale parameter, mesh size and χ is investigated. For validation, a single-edge notch beam with a notch at various eccentricities is considered. It is shown that the model is mesh independent for a sufficiently fine mesh in cracking region. Also, the effect of the length scale parameter on global response is insignificant. It is observed that χ≥1 gives satisfactory results both for mode I and mixed mode I-II fracture in single edge notch concrete beam. The numerical results for the load–displacement curve are compared with the experimental data both qualitatively and quantitatively. It is concluded that the proposed phase field model can simulate mode I and mixed mode I-II fracture in concrete with sufficient accuracy.

Simulation of cohesive crack growth by a variable-node XFEM

A new computational approach that combines the extended finite element method associated with variable-node elements and cohesive zone model is developed. By using a new enriched technique based on sign function, the proposed model using 4-node quadrilateral elements can eliminate the blending element problem. It also allows modeling the equal stresses at both sides of the crack in the crack-tip as assumed in the cohesive model, and is able to simulate the arbitrary crack-tip location. The multiscale mesh technique associated with variable-node elements and the arc-length method further improve the efficiency of the developed approach. The performance and accuracy of the present approach are illustrated through numerical experiments considering both mode-I and mixed-mode fracture in concrete.

FPZ evolution of mixed mode fracture in concrete: Experimental and numerical

Abstract Digital image correlation (DIC) technique is applied to study the evolution of fracture process zone (FPZ) of mixed mode fracture in concrete. By testing a series of beams of various sizes under four-point shearing, the opening and sliding displacements on the crack surfaces are derived using the DIC technique. Meanwhile, a numerical method is employed to simulate the fracture process by introducing a crack propagation criterion. The opening and sliding displacements on the crack surfaces obtained from numerical analysis exhibit a reasonable agreement with the experimental results, which verifies the DIC technique presented in the study. By combining experimental observations with numerical simulations, the evolution of the FPZ during the whole crack propagation process of mix mode fracture is investigated and elaborated in depth. The results indicate that the ratio of crack opening to sliding displacement remains approximately constant as crack propagates before reaching a peak load. Meanwhile, the FPZ evolution during the complete fracture process is influenced by the specimen ligament length and the ratio of mode I to II stress intensity factor component. With the decrease of ligament length and the ratio of mode I to II stress intensity factor component, the full FPZ length decreases. However, when the ligament length is less than 63 mm or ratio of mode I to II stress intensity factor component is less than 0.11, the FPZ cannot fully develop, but keeps increasing as crack propagates.

Modeling Mixed Mode Fracture of Concrete by Using the Combined Discrete and Finite Elements Method

The mixed mode (I/II) fracture of concrete is investigated by using a four-point combined discrete and finite elements method. The potential fracture zone is simulated by the discrete elements (DEs) and the other zone by the finite elements (FEs). A cohesive fracture model is employed to simulate the brittle fracture only in the DE subregion. Mesh-size independency of the cohesive fracture model subjected to the DE is carefully investigated with a simple case. Subsequently, the mixed mode fracture behaviors of two simple concrete specimens are simulated and the simulation results achieve good agreements with the other simulations and experimental results.

Experimental Study on Mixed-Mode Fracture for Concrete

A new criterion (failure stress criterion) is presented for the mixed-mode fracture of concrete by comprehensively evaluating several mixed-mode crack criteria. The new criterion absorbs some results fitting in with concrete from G.C.Sih and Erdogen’s maximum circumference stress criterion and G.C.Sih’s minimum strain energy intensity factor criterion. It combines concrete material fracture property with the condition of loads at the moment of concrete fracture by Weibull theory. It is concluded that concrete crack expands neither along the direction of maximum circumference stress nor along minimum strain energy factor S. The crack extends along the direction limited in the area controlled by two criteria. The accurate crack position is determined by failure probability of the strength of concrete structure. The experimental results indicate that the new criterion has better precision and adaptability comparing with other criteria and it can be applied to engineering very well.

Impact damage assessment by using peridynamic theory

Abstract This study presents an application of peridynamic theory for predicting residual strength of impact damaged building components by considering a reinforced panel subjected to multiple load paths. The validity of the approach is established first by simulating a controlled experiment resulting in mixed-mode fracture of concrete. The agreement between the PD prediction and the experimentally observed behavior is remarkable especially considering the simple material model used for the concrete. Subsequently, the PD simulation concerns damage assessment and residual strength of a reinforced panel under compression after impact due to a rigid penetrator.

Experimental Investigation on Initial Cracking Criterion and Size Effect for I-II Mixed Mode Fracture in Concrete

Most of the previous studies utilized the maximum applied load and the initial crack length to determine the fracture criterion for Ⅰ-Ⅱ mixed mode fracture of concrete. Actually, the crack has propagated in the ultimate state due to the semi-brittle behaviors of concrete. Therefore, adopting the initial fracture toughness as the fracture criterion seems more reasonable. This subject carried out an experiment of four-point shearing notched beams of concrete with five different heights, i.e, 200mm, 300mm, 400mm, 500mm and 600mm to determine the initial cracking state according to sudden decrease of the strain gauges’ values. Then the initial cracking load ini P can be gained. Besides, the quarter point singular element approach was used to calculate the stress intensity factors ini I K and ini II K corresponding to ini P in the present study. Moreover, different combinations of ini I K and ini II K were obtained according to different positions of pre-cracks. Correspondingly, the Ⅰ-Ⅱmixed mode fracture initial cracking criterion for concrete can be gained using the curves of track formed by the different combinations of ini I K and ini II K . Through analyzing the curves of track under different specimen heights, it was found that the size effect exists significantly in the specimens with heights from 300mm to 500mm, however, the curves in the 500mm and 600mm specimens approach each other.

An embedded cohesive crack model for finite element analysis of mixed mode fracture of concrete*

ABSTRACTAn embedded cohesive crack model is proposed for the analysis of the mixed mode fracture of concrete in the framework of the Finite Element Method. Different models, based on the strong discontinuity approach, have been proposed in the last decade to simulate the fracture of concrete and other quasi‐brittle materials. This paper presents a simple embedded crack model based on the cohesive crack approach. The predominant local mode I crack growth of the cohesive materials is utilized and the cohesive softening curve (stress vs. crack opening) is implemented by means of a central force traction vector. The model only requires the elastic constants and the mode I softening curve. The need for a tracking algorithm is avoided using a consistent procedure for the selection of the separated nodes. Numerical simulations of well‐known experiments are presented to show the ability of the proposed model to simulate the mixed mode fracture of concrete.

Numerical Analysis of Mixed-Mode Fracture in Concrete Using Extended Fictitious Crack Model

A numerical formulation of the mixed-mode (mode-I and mode-II) fracture in concrete based on the extended fictitious crack model is presented. For crack propagation, the maximum principal stress criterion is used, assuming that the mode-I condition is dominant at the tip of a mixed-mode crack. A main feature of this study is that normal and tangential tractions are applied directly to the crack surface, following specific tension-softening and shear-transfer laws. To verify the approach, two well-known experimental problems are solved. The first is the single-notched shear beam test by Arrea and Ingraffea, and the second is the scale-model test of gravity dams by Carpinteri et al. Varying the shear-transfer characteristics on the crack surface, the numerical model predicts distinct transitions from the mode-I fracture to the mixed-mode fracture in the structural response and the crack path, which both show reasonable agreement with experimental observations. The issue of stress singularity in finite-element computations of tip tensile forces is also addressed.

Experimental investigation on criterion of three-dimensional mixed-mode fracture for concrete

An investigation was carried out to establish a criterion for three-dimensional (3-D) mixed-mode fracture of concrete. Experiments on 3-D mixed-mode fracture were conducted to obtain the critical load P cr. The stress intensity factor of the specimens per unit load with different combinations of K I , , K II and K III was calculated by the mixed hybrid finite element method. Based on the stress intensity factor per unit load and the critical load, 25 groups of critical stress intensity factors were calculated, from which a criterion for the 3-D mixed-mode fracture of concrete was derived.

Dynamic mixed mode fracture of concrete

The transient moiré fringe patterns surrounding a rapidly propagating crack in an impacted three-point bend concrete specimen with an offset precrack were recorded by two IMACON 790 ultra-high speed framing cameras. The fracture parameters associated with this mixed mode fracture event were determined by driving a dynamic finite element model of the concrete specimen in its application mode with the recorded load and the crack propagation histories. The fracture process zone (FPZ), which trails the rapidly propagating crack, was characterized and the mixed modes I and lI dynamic stress intensity factors were determined. The fracture energy dissipated at the FPZ increased with crack extension and reached a constant dissipation rate toward the final phase of fracture. Under mixed mode loading, the crack kinked and propagated according to the Ramulu—Kobayashi criterion.

Mixed‐Mode Fracture of Concrete Subjected to Impact Loading

An analytical and experimental investigation of mode I (tensile) and mixed mode (combined tensile and shear) fracture of concrete subjected to impact loading was conducted. The rate of loading ranged from a slow strain rate of 10\u-\u6/s to an impact strain rate of 0.5/s. Mixed-mode tests were conducted using beams with notches at different locations along the span of the beam. A new clip gage was developed to measure crack-opening displacement at slow and impact rates of loading. A nonlinear fracture-mechanics model was developed to predict the rate sensitivity of mode I and mixed-mode fracture of concrete. This approach was based on the observation that the prepeak nonlinearity may be attributed to prepeak stable crack growth and that this prepeak crack growth decreased with an increase in the rate of loading. The mixed-mode-fracture-mechanics study used finite element analysis with singular quarter-point elements at the crack tip. Mixed-mode experimental and analytical results indicate that impact loading could result in brittle diagonal tension-shear failure of concrete structures as opposed to ductile flexural failure at a slow rate of loading.

Mixed-mode fracture of concrete

Mixed-mode fracture of concrete is encountered frequently in design of concrete structures. To accurately analyzed and design a concrete structure, it is essential to understand the failure mechanisms of concrete under mixed-mode types of loading. A model, which was originally proposed for mode I failure of concrete, is extended to characterized mixed-mode crack propagation. Crack initiation angles, final failure path, and crack instability of concrete specimens/structures are discussed. A series of mixed-mode notched beam tests were performed to verify the proposed model. The theoretical predictions were found to be in good agreement with the experimental results.