Finite element cohesive fracture modeling of airport pavements at low temperatures

Low temperature cracking induced by seasonal and daily thermal cyclic loads is one of the main critical distresses in asphalt pavements. The safety of aircraft departure and landing becomes a crucial issue in runways when thermal cracks occur in airport pavements. The low-temperature fracture behavior of airport pavements was investigated using a bilinear cohesive zone model (CZM) implemented in the finite element method (FEM). Nonlinear temperature gradients of pavement structures were estimated based on national weather data and an integrated climate prediction model. Experimental tests were conducted to obtain the numerical model inputs such as viscoelastic and fracture properties of asphalt concrete using creep compliance tests, indirect tensile strength tests (IDT), and disk-shaped compact tension (DC(T)) tests. The finite element pavement fracture models could successfully predict the progressive crack behavior of asphalt pavements under the critical temperature and heavy aircraft gear loading conditions.     

Micromechanical fracture modeling of asphalt concrete using a single-edge notched beam test

Cracks in asphalt pavements create irreversible structural and functional deficiencies that increase maintenance costs and decrease lifespan. Therefore, it is important to understand the fracture behavior of asphalt mixtures, which consist of irregularly shaped and randomly oriented aggregate particles and mastic. A two-dimensional clustered discrete element modeling (DEM) approach is implemented to simulate the complex crack behavior observed during asphalt concrete fracture tests. A cohesive softening model (CSM) is adapted as an intrinsic constitutive law governing material separation in asphalt concrete. A homogenous model is employed to investigate the mode I fracture behavior of asphalt concrete using a single-edge notched beam (SE(B)) test. Heterogeneous morphological features are added to numerical SE(B) specimens to investigate complex fracture mechanisms in the process zone. Energy decomposition analyses are performed to gain insight towards the forms of energy dissipation present in fracture testing of asphalt concrete. Finally, a heterogeneous model is used to simulate mixed-mode crack propagation.     

Cohesive Modeling of Fracture in Asphalt Mixtures at Low Temperatures

Low temperature cracking is the major distress observed in asphalt pavements in the northern US and Canada. In the past years fracture mechanics concepts were introduced to investigate the fracture properties of asphalt mixtures at low temperatures. In this paper the cohesive zone model (CZM) is used to describe the fracture behavior of asphalt mixtures at low temperatures and the interface element is used to numerically simulate the material response under monotonic loading. The simulation is calibrated with the experimental results from a newly proposed semi circular bend (SCB) test. A parametric analysis of the input material properties indicates that the tensile strength has a significant effect on the peak load in the SCB configuration, the modulus has a strong effect on the calculated stiffness of the SCB specimen, and the fracture energy influences the post-peak behavior of the asphalt mixtures. The calibrated numerical model was applied to simulate the low temperature cracking in a simplified asphalt pavement and to study the influence of these material parameters on the performance of asphalt pavements.     

δ25 Crack opening displacement parameter in cohesive zone models: experiments and simulations in asphalt concrete

Recent work with fracture characterization of asphalt concrete has shown that a cohesive zone model (CZM) provides insight into the fracture process of the materials. However, a current approach to estimate fracture energy, i.e., in terms of area of force versus crack mouth opening displacement (CMOD), for asphalt concrete overpredicts its magnitude. Therefore, the δ₂₅ parameter, which was inspired by the δ₅ concept of Schwalbe and co‐workers, is proposed as an operational definition of a crack tip opening displacement (CTOD). The δ₂₅ measurement is incorporated into an experimental study of validation of its usefulness with asphalt concrete, and is utilized to estimate fracture energy. The work presented herein validates the δ₂₅ parameter for asphalt concrete, describes the experimental techniques for utilizing the δ₂₅ parameter, and presents three‐dimensional (3D) CZM simulations with a specially tailored cohesive relation. The integration of the δ₂₅ parameter and new cohesive model has provided further insight into the fracture process of asphalt concrete with relatively good agreement between experimental results and numerical simulations.     

FRP-混凝土三点受弯梁损伤粘结模型有限元分析

该文采用双线形损伤粘结模型研究带切口FRP-混凝土三点受弯梁(3PBB)I型加载下的界面断裂性能。通过有限元参数分析,详细讨论了界面粘结强度、界面粘结能、混凝土抗拉强度、混凝土断裂能对3PBB受力性能的影响。数值模拟表明,FRP-混凝土界面有两种破坏形式,包括FRP-混凝土界面的损伤脱粘和界面混凝土的损伤脱粘破坏,与实验所观察到的现象一致。两种破坏形式尽管在宏观上均表现为界面脱粘,但破坏机制却不同。FRP-混凝土界面的损伤粘结模型与混凝土的拉伸塑性损伤模型相结合,不但再现了3PBB的宏观力学性能,数值分析得到的荷载-位移曲线接近实验结果,而且还能详细展示FRP-混凝土界面的损伤、断裂破坏过程以及损伤在FRP-混凝土界面和界面混凝土之间的转移,能够预测构件的承载力,有助于界面优化设计,这是单纯以能量判据预测裂纹发展的经典断裂力学方法所无法做到的。     

短纤维复合材料宏微观内聚力模型参数测量的实验与数值混合法

提出了一种改进的实验与数值混合法。该方法采用随机短纤维增强复合材料的紧凑拉伸实验,首先得到材料的宏观内聚力模型,进而确定该材料纤维基体界面微观内聚力模型参数。通过有限元法和基于场投影的反解法得到了宏观内聚力模型结果,对比分析这两个方法的结果,得出该反解法对误差的容忍度较低。随后采用改进的反解法,用数字图像相关法(DIC)直接获取宏观内聚力模型分离量,减少了该反解法未知数的数量,提高了容错率。再将DIC和改进的反解法结合,对该材料裂纹尖端宏观内聚力区的牵引力进行了反解。采用双线性内聚力模型,根据Mori-Tanaka方法,将求得的宏观内聚力定律与纤维基体界面微观内聚力定律关联起来,从而求得了纤维基体界面微观内聚力模型参数。该方法和结果可为短纤维增强复合材料纤维基体界面的微观力学分析提供实验基础。     

Modelling cohesive crack growth using a two-step finite element-scaled boundary finite element coupled method

A two-step method, coupling the finite element method (FEM) and the scaled boundary finite element method (SBFEM), is developed in this paper for modelling cohesive crack growth in quasi-brittle normal-sized structures such as concrete beams. In the first step, the crack trajectory is fully automatically predicted by a recently-developed simple remeshing procedure using the SBFEM based on the linear elastic fracture mechanics theory. In the second step, interfacial finite elements with tension-softening constitutive laws are inserted into the crack path to model gradual energy dissipation in the fracture process zone, while the elastic bulk material is modelled by the SBFEM. The resultant nonlinear equation system is solved by a local arc-length controlled solver. Two concrete beams subjected to mode-I and mixed-mode fracture respectively are modelled to validate the proposed method. The numerical results demonstrate that this two-step SBFEM-FEM coupled method can predict both satisfactory crack trajectories and accurate load-displacement relations with a small number of degrees of freedom, even for crack growth problems with strong snap-back phenomenon. The effects of the tensile strength, the mode-I and mode-II fracture energies on the predicted load-displacement relations are also discussed.     

界面应力传递重新分析及Cohesive模型参数的确定

在经典剪滞理论中引入双线性cohesive模型表征纤维/基体之间的非理想界面,重新分析了纤维增强复合材料中的应力传递机理,得到了考虑界面因素的应力分布。用上述结果解释了单丝段裂实验过程中的现象,讨论了界面参数和材料性能对应力分布的影响。基于上述理论,建立了用cohesive单元表征界面的模拟单丝段裂实验的三维有限元模型,结合单丝段裂实验结果,提出了一种估测cohesive界面刚度参数的新方法。数值和理论分析结果与实验结果对比,吻合良好,可以为材料的界面性能分析和材料设计提供参考依据。     

Simulation of mixed-mode I/III stable tearing crack growth events using the cohesive zone model approach

A cohesive zone model (CZM) approach is applied to simulate mixed-mode I/III stable tearing crack growth events in specimens made of 6061-T6 aluminum alloy and GM 6208 steel. The materials are treated as elastic–plastic following the \(J_{2}\) flow theory of plasticity, and the triangular cohesive law is employed to describe the traction-separation relation in the cohesive zone ahead of crack front. A hybrid numerical/experimental approach is employed in simulations using 3D finite element method. For each material, CZM parameter values are chosen by matching simulation prediction with experimental measurement (Yan et al. in Int J Fract 144:297–321, 2009), of the crack extension-time curve for the \(30^{\circ }\) mixed-mode I/III stable tearing crack growth test. With the same sets of CZM parameter values, simulations are performed for the \(60^{\circ }\) loading cases. Good agreements are reached between simulation predictions of the crack extension-time curve and experimental results. The variations of CTOD with crack extension are calculated from CZM simulations under both \(30^{\circ }\) and \(60^{\circ }\) mixed-mode I/III conditions for the aluminum alloy and steel respectively. The predictions agree well with experimental measurements (Yan et al. in Int J Fract 144:297–321, 2009). The findings of the current study demonstrate the applicability of the CZM approach in mixed-mode I/III stable tearing simulations and reaffirm the connection between CTOD and CZM based simulation approaches shown previously for mixed-mode I/II crack growth events.     

Characterization of mixed-mode fracture based on a complementary analysis by means of full-field optical and finite element approaches

This paper focuses on the characterization of mixed-mode fracture parameters through use of two formalisms based on Crack Relative Displacement Factors and Stress Intensity Factors, respectively. The evaluation of Crack Relative Displacement Factors is based on a kinematic approach that integrates the experimental displacement field measured by a digital image correlation method. In parallel with this step, the stress intensity factor is calculated from a finite element analysis. The coupling between these two approaches allows for the identification of fracture parameters in terms of an energy release rate without any prior knowledge of material elastic properties. Depending on the mixed-mode configuration, the proportion of the energy release rate corresponding to opening and shear modes can be calculated. Moreover, the proposed formalism allows determining, in addition to fracture parameters, the local elastic properties in terms of reduced elastic compliance directly from the test sample. Experimental protocols are carried out using a Single-Edge notched specimen made from a rigid Polyvinyl Chloride polymer loaded at various mixed-mode ratio values.     

用扩展有限元方法模拟混凝土的复合型开裂过程

用扩展有限元法对混凝土梁复合型开裂过程进行了数值模拟。裂纹面间的力学行为采用粘聚裂纹模型来描述,通过引入切向保留刚度考虑剪力分量的影响。开裂方向的计算采用了一种简化的最大切向应力准则。对Arrea和Ingraffea的混凝土梁复合开裂实验进行了数值模拟。计算给出了裂纹萌生、扩展的过程及破坏形态,并获得了与实验结果对比良好的荷载-裂纹开口滑移曲线。结果表明,扩展有限元法通过附加特定的位移模式,使裂纹两侧不连位移场的表达独立于网格划分,是一种能够模拟准脆性材料复合开裂问题的有效方法。     

Numerical study of mixed-mode fracture in concrete

In the present paper, a finite element code based on the microplane model for concrete is used for the analysis of typical mixed-mode geometries: a Single-Edge-Notched beam, a Double-Edge-Notched specimen and a Dowel-Disk specimen. A local smeared fracture finite element analysis is carried out. As a regularization procedure, the crack band method is used. The principal objective of the study was to investigate whether the smeared fracture finite element code is able to predict mixed-mode fracture of concrete with no optimisation of the material model parameters. Comparison between experimental and numerical results shows that the used code predicts structural response and crack patterns realistically for all cases investigated. Moreover, it is shown that for most of the studied geometries a mixed-mode fracture mechanism dominates at crack initiation, however, with increase of the crack length mode-I fracture becomes dominant and the specimens finally failed in mode-I fracture.     

基于扩展有限元法的钢筋混凝土梁复合断裂过程模拟研究

针对钢筋混凝土梁裂纹扩展问题,基于扩展有限元法,建立了预置裂纹的简支混凝土梁三维模型,用粘聚裂纹模型描述裂纹面间的力学行为,采用线性的软化曲线表示裂纹尖端断裂过程区的应变软化行为,分别对素混凝土梁和钢筋混凝土梁的复合断裂过程进行模拟,分析了纵向钢筋对裂纹扩展路径、荷载-挠度和荷载 -CMOD (裂缝开口处张开位移)曲线的影响,并与文献中的试验结果进行对比,计算结果与试验结果吻合良好,展示了扩展有限元法在结构断裂破坏分析方面的独特优势。     

Simulation of delamination by means of cohesive elements using an explicit finite element code

This paper presents the formulation of a tri-dimensional cohesive element implemented in a user-written material subroutine for explicit finite element analysis. The cohesive element simulates the onset and propagation of the delamination in advanced composite materials. The delamination model is formulated by using a rigorous thermodynamic framework which takes into account the changes of mixed-mode loading conditions. The model is validated by comparing the finite element predictions with experimental data obtained in interlaminar fracture tests under quasi-static loading conditions.     

Extrinsic cohesive modelling of dynamic fracture and microbranching instability in brittle materials

Dynamic crack microbranching processes in brittle materials are investigated by means of a computational fracture mechanics approach using the finite element method with special interface elements and a topological data structure representation. Experiments indicate presence of a limiting crack speed for dynamic crack in brittle materials as well as increasing fracture resistance with crack speed. These phenomena are numerically investigated by means of a cohesive zone model (CZM) to characterize the fracture process. A critical evaluation of intrinsic versus extrinsic CZMs is briefly presented, which highlights the necessity of adopting an extrinsic approach in the current analysis. A novel topology‐based data structure is employed to enable fast and robust manipulation of evolving mesh information when extrinsic cohesive elements are inserted adaptively. Compared to intrinsic CZMs, which include an initial hardening segment in the traction–separation curve, extrinsic CZMs involve additional issues both in implementing the procedure and in interpreting simulation results. These include time discontinuity in stress history, fracture pattern dependence on time step control, and numerical energy balance. These issues are investigated in detail through a ‘quasi‐steady‐state’ crack propagation problem in polymethylmethacrylate. The simulation results compare reasonably well with experimental observations both globally and locally, and demonstrate certain advantageous features of the extrinsic CZM with respect to the intrinsic CZM. Copyright © 2007 John Wiley & Sons, Ltd.     

Constitutive models for cohesive zones in mixed-mode fracture of plain concrete

Discrete mixed-mode fracture (modes I and II) of plain concrete is investigated using a coupled and an uncoupled cohesive zone constitutive model in a finite element context. Fracture surfaces are confined to inter-element boundaries that are not necessarily coincident with the actual fracture surfaces. For this reason, traction components on the cohesive zone do not correspond to actual values either. In this work is demonstrated that only the coupled model is able to cope with these spurious traction components, that must decrease with crack opening. It is shown also that, in this regard, the key variable is the plastic potential adopted in the integration of tractions. Three mixed-mode fracture examples were tested in this work: a three-point single-edge notched beam, double-edge notched plates under variable lateral and normal deformation and four-point double-edge notched beams. A good fitting with experiments was obtained only for the coupled model. Mode II parameters can change in a large range without noticeable change in results, at least in the tested examples.     

An embedded atom hyperelastic constitutive model and multiscale cohesive finite element method

Based on embedded atom method (EAM), an embedded atom hyperelastic (EAH) constitutive model is developed. The proposed EAH constitutive model provides a multiscale formalism to determine mesoscale or macroscale material behavior by atomistic information. By combining the EAH with cohesive zone model (CZM), a multiscale embedded atom cohesive finite element model (EA-cohesive FEM) is developed for simulating failure of materials at mesoscale and macroscale, e.g. fracture and crack propagation etc. Based on EAH, the EA-cohesive FEM applies the Cauchy-Born rule to calculate mesoscale or macroscale material response for bulk elements. Within the cohesive zone, a generalized Cauchy-Born rule is applied to find the effective normal and tangential traction-separation cohesive laws of EAH material. Since the EAM is a realistic semi-empirical interatomic potential formalism, the EAH constitutive model and the EA-cohesive FEM are physically meaningful when it is compared with experimental data. The proposed EA-cohesive FEM is validated by comparing the simulation results with the results of large scale molecular dynamics simulation. Simulation result of dynamic crack propagation is presented to demonstrate the capacity of EA-cohesive FEM in capturing the dynamic fracture.     

Prediction of tensile capacity based on cohesive zone model of bond anchorage for fiber-reinforce dpolymer tendon

In this paper, analytical solutions based on a cohesive zone model (CZM) are developed for the bond fiber-reinforce dpolymer (FRP) tendon anchorage under axial load. With bilinear cohesive laws, the analytical solutions of tensile capacity of anchorages are derived. The concept of the minimum relative interface displacement s_m is introduced and used as the fundamental variable to express all other parameters, such as external tensile load. Experimental and analytical results show that the thickness of the anchoring material is main factor affecting tensile capacity. The characteristic bond strength depends mainly on the properties of the bonding agent-anchoring material, the geometry and surface conditions of the tendon, and the radial stiffness of the confining medium. A comparison of the calculated and experimental results showed good agreement. Formulas based on fracture energy of the tension load capacity derived in the present work can be directly used in the design of FRP tendon anchorage.     

Analysis of mixed-mode interlaminar fracture and damage behavior of GFRP woven laminates at cryogenic temperatures

The objective of this work is to investigate the interlaminar fracture and damage behavior of glass fiber reinforced polymer (GFRP) woven laminates loaded in a mixed-mode bending (MMB) apparatus at cryogenic temperatures. The finite element analysis (FEA) is used to determine the mixed-mode interlaminar fracture toughness of MMB specimen at room temperature (RT), liquid nitrogen temperature (77 K) and liquid helium temperature (4 K). A FEA coupled with damage is also employed to study the damage distributions within the MMB specimen and to examine the effect of damage on the mixed-mode energy release rate. The technique presented can be efficiently used for characterization of mixed-mode interlaminar fracture and damage behavior of woven laminate specimens at cryogenic temperatures.     

Modeling of cohesive crack growth using an adaptive mesh refinement via the modified-SPR technique

In this paper, an adaptive finite element procedure is presented in modeling of mixed-mode cohesive crack propagation via the modified superconvergent path recovery technique. The adaptive mesh refinement is performed based on the Zienkiewicz–Zhu error estimator. The weighted-SPR recovery technique is employed to improve the accuracy of error estimation. The Espinosa–Zavattieri bilinear cohesive zone model is applied to implement the traction-separation law. It is worth mentioning that no previous information is necessary for the path of crack growth and no region of the domain is necessary to be filled by the cohesive elements. The maximum principal stress criterion is employed for predicting the direction of extension of the cohesive crack in order to implement the cohesive elements. Several numerical examples are analyzed numerically to demonstrate the capability and efficiency of proposed computational algorithm.