基于虚拟裂缝模型的混凝土断裂过程区研究

利用虚拟裂缝模型对混凝土断裂过程区进行了研究.以无限大板中心拉伸裂缝模型为例,将过程区裂缝张开位移采用多项式级数形式表示,求得了断裂过程区上的位移分布和粘聚力分布.进而分析了材料参数对断裂过程区上的位移、粘聚力、断裂过程区长度以及峰值外荷载的影响.结果表明：断裂过程区上的位移和粘聚力均为非线性分布.断裂过程区长度随骨料最大粒径增大而逐渐增大,随抗压强度增大而逐渐减小.峰值外荷载随骨料最大粒径和抗压强度增大均逐渐增大.     

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.     

Finite fracture mechanics analysis of crack onset at a stress concentration in a UD glass/epoxy composite in off-axis tension

The presence of stress concentrations at holes and notches is known to reduce the strength of composite materials. Due to complexity of the damage processes at a stress raiser in a composite, different modeling approaches have been developed, ranging from empirical point and average stress criteria to involved damage mechanics or cohesive zone-based models of failure. Finite fracture mechanics approach with a coupled stress and energy failure criterion, recently developed and applied mainly to cracking in homogeneous isotropic materials, allows predicting the appearance and propagation of a crack using material strength and toughness characteristics obtained from independent tests. The present study concerns application of the finite fracture mechanics to the analysis of cracking at a notch in a UD glass/epoxy composite subjected to tensile off-axis loading. Based on UD composite strength and intralaminar toughness characterized by separate tests, finite fracture mechanics analysis provided conservative estimates of crack onset stress at the notch.     

Three‐dimensional finite‐element simulation of the dynamic Brazilian tests on concrete cylinders

We investigate the feasibility of using cohesive theories of fracture, in conjunction with the direct simulation of fracture and fragmentation, in order to describe processes of tensile damage and compressive crushing in concrete specimens subjected to dynamic loading. We account explicitly for microcracking, the development of macroscopic cracks and inertia, and the effective dynamic behaviour of the material is predicted as an outcome of the calculations. The cohesive properties of the material are assumed to be rate‐independent and are therefore determined by static properties such as the static tensile strength. The ability of model to predict the dynamic behaviour of concrete may be traced to the fact that cohesive theories endow the material with an intrinsic time scale. The particular configuration contemplated in this study is the Brazilian cylinder test performed in a Hopkinson bar. Our simulations capture closely the experimentally observed rate sensitivity of the dynamic strength of concrete in the form of a nearly linear increase in dynamic strength with strain rate. More generally, our simulations give accurate transmitted loads over a range of strain rates, which attests to the fidelity of the model where rate effects are concerned. The model also predicts key features of the fracture pattern such as the primary lens‐shaped cracks parallel to the load plane, as well as the secondary profuse cracking near the supports. The primary cracks are predicted to be nucleated at the centre of the circular bases of the cylinder and to subsequently propagate towards the interior, in accordance with experimental observations. The primary and secondary cracks are responsible for two peaks in the load history, also in keeping with experiment. The results of the simulations also exhibit a size effect. These results validate the theory as it bears on mixed‐mode fracture and fragmentation processes in concrete over a range of strain rates. Copyright © 2000 John Wiley & Sons, Ltd.     

The prediction of dynamic fracture evolution in PMMA using a cohesive zone model

A cohesive zone model was used in conjunction with the finite volume method to model the dynamic fracture of single edge notched tensile specimens of PMMA under essentially static loading conditions. In this study, the influence of the shape of the cohesive law was investigated, whilst keeping the cohesive strength and separation energy constant. Cohesive cells were adaptively inserted between adjacent continuum cells when the normal traction across that face exceeded the cohesive strength of the material. The cohesive constitutive law was therefore initially rigid, and the effective elasticity of the material was unaltered prior to insertion of the cohesive cells. Notch depths ranging from 2.0 to 0.1 mm were considered. The numerical predictions were compared with experimental observations for each notch depth and excellent qualitative and quantitative agreement was achieved in most cases. Following an initial period of rapid crack tip acceleration up to terminal velocities well below the Rayleigh wave speed, subsequent propagation took place at a constant rate under conditions of increasing energy flux to an expanding process region. In addition, attempted and successful branching was predicted for the shorter notches. It was found that the shape of the cohesive law had a significant influence on the dynamic fracture behaviour. In particular, the value of the initial slope of the softening function was found to be an important parameter. As the slope became steeper, the predicted terminal crack speed increased and the extent of the damage decreased.     

Modeling delamination growth in composites under fatigue loadings of varying amplitudes

A numerical model was developed to simulate the progressive delamination of a composite subjected to mode I fatigue loading regimes of varying amplitude. The model employs a cohesive zone approach, which combines damage mechanics and fracture mechanics, and requires only standard material data as input, namely the delamination toughness and the fatigue delamination growth curve. The proposed model was validated against delamination growth data obtained from a fatigue test conducted on a DCB specimen. The model predictions agree very well with the experimental results. This model is an initial step toward life prediction of composite structures subjected to complex fatigue regimes.     

Fracture loads for ceramic samples with rounded notches

Fracture loads of ceramic components with rounded notches cannot be computed by linear elastic fracture mechanics techniques because no stress singularity exists. We propose a procedure to estimate such fracture loads, which is based on the cohesive zone model and supported by experimental evidence with alumina, zirconia and silicon ceramics. Data from 18 ceramic materials and different notched geometries were used. The only material parameters needed were the tensile strength and the fracture toughness.     

A meso-mechanical model for concrete under dynamic tensile and compressive loading

We present a computational model, which combines interface debonding and frictional contact, in order to investigate the response of concrete specimens subjected to dynamic tensile and compressive loading. Concrete is modeled using a meso-mechanical approach in which aggregates and mortar are represented explicitly, thus allowing all material parameters to be physically identified. The material phases are considered to behave elastically, while initiation, coalescence and propagation of cracks are modeled by dynamically inserted cohesive elements. The impenetrability condition is enforced by a contact algorithm that resorts to the classical law of Coulomb friction. We show that the proposed model is able to capture the general increase in strength with increasing rate of loading and the tension/compression asymmetry. Moreover, we simulate compression with lateral confinement showing that the model reproduces the increase in peak strength with increasing confinement level. We also quantify the increase in the ratio between dissipated frictional energy and dissipated fracture energy as the confining pressure is augmented. Our results demonstrate the fundamental importance of capturing frictional mechanisms, which appear to dissipate a similar amount of energy when compared to cracking under compressive loading.     

Computational model for predicting nonlinear viscoelastic damage evolution in materials subjected to dynamic loading

Many inelastic solids accumulate numerous cracks before failure due to impact loading, thus rendering any exact solution of the IBVP untenable. It is therefore useful to construct computational models that can accurately predict the evolution of damage during actual impact/dynamic events in order to develop design tools for assessing performance characteristics. This paper presents a computational model for predicting the evolution of cracking in structures subjected to dynamic loading. Fracture is modeled via a nonlinear viscoelastic cohesive zone model. Two example problems are shown: one for model validation through comparison with a one-dimensional analytical solution for dynamic viscoelastic debonding, and the other demonstrates the applicability of the approach to model dynamic fracture propagation in the double cantilever beam test with a viscoelastic cohesive zone.     

Notch sensitivity of orthotropic solids: interaction of tensile and shear damage zones

The macroscopic tensile strength of a panel containing a centre-crack or a centre-hole is predicted, assuming the simultaneous activation of multiple cohesive zones. The panel is made from an orthotropic elastic solid, and the stress raiser has both a tensile cohesive zone ahead of its tip, and shear cohesive zones in an orthogonal direction in order to represent two simultaneous damage mechanisms. These cohesive zones allow for two modes of fracture: (i) crack extension by penetration, and (ii) splitting in an orthogonal direction. The sensitivity of macroscopic tensile strength and failure mode to the degree of orthotropy is explored. The role of notch acuity and notch size are assessed by comparing the response of the pre-crack to that of the circular hole. This study reveals the role of the relative strength and relative toughness of competing damage modes in dictating the macroscopic strength of a notched panel made from an orthotropic elastic solid. Universal failure mechanism maps are constructed for the pre-crack and hole for a wide range of material orthotropies. The maps are useful for predicting whether failure is by penetration or kinking. Case studies are developed to compare the predictions with observations taken from the literature for selected orthotropic solids. It is found that synergistic strengthening occurs: when failure is by crack penetration ahead of the stress raiser, the presence of shear plastic zones leads to an enhancement of macroscopic strength. In contrast, when failure is by crack kinking, the presence of a tensile plastic zone ahead of the stress raiser has only a mild effect upon the macroscopic strength.     

Softening and snap-back instability in cohesive solids

The nature of the crack and the structure behaviour can range from ductile to brittle, depending on material properties, structure geometry, loading condition and external constraints. The influence of variation in fracture toughness, tensile strength and geometrical size scale is investigated on the basis of the π-theorem of dimensional analysis. Strength and toughness present in fact different physical dimensions and any consistent fracture criterion must describe energy dissipation per unit of volume and per unit of crack area respectively. A cohesive crack model is proposed aiming at describing the size effects of fracture mechanics, i.e. the transition from ductile to brittle structure behaviour by increasing the size scale and keeping the geometrical shape unchanged. For extremely brittle cases (e.g. initially uncracked specimens, large and/or slender structures, low fracture toughness, high tensile strength, etc.) a snap-back instability in the equilibrium path occurs and the load–deflection softening branch assumes a positive slope. Both load and deflection must decrease to obtain a slow and controlled crack propagation (whereas in normal softening only the load must decrease). If the loading process is deflection-controlled, the loading capacity presents a discontinuity with a negative jump. It is proved that such a catastrophic event tends to reproduce the classical LEFM-instability (K_I = K_IC) for small fracture toughnesses and/or for large structure sizes. In these cases, neither the plastic zone develops nor slow crack growth occurs before unstable crack propagation.     

Notch sensitivity of thermoset and thermoplastic laminates loaded in tension

Inplane tensile fracture of unnotched and notched thermoset graphite-epoxy and thermoplastic graphite-PEEK composite laminates is examined. Both fibre-dominated quasi-isotropic and matrix dominated ±45 angle-ply layups were investigated.Classical lamination theory predictions of elastic and strength properties of unnotched specimens are compared with experiments. Several notched geometries, i.e. centre-notched, double-edge notched and open-hole specimens subjected to tensile loading to fracture were examined. The notched strength of the quasi-isotropic laminates was analysed by a damage zone model, where damage around the notch is represented by an equivalent crack with cohesive force acting between the crack surfaces.Good agreement between experimental and calculated strength was observed for the graphite-epoxy laminates which failed in a collinear manner. For the graphite-PEEK laminates discrepancies between predicted and experimental strength are related to observed deviations from collinear crack growth. The angle-ply graphite-PEEK laminates showed larger notch sensitivity than the corresponding graphite-epoxy, probably due to less degree of stress relieving damage formation around the notch.     

Numerical modelling of failure of cement concrete using a unit cell approach

In this paper, a unit cell based approach is followed, where a unit cell consisting of one aggregate surrounded by mortar matrix is used for numerical simulation of mechanical response of cement concrete. Unit cell approach is a simple mathematical approximation that helps us to simplify the simulation of mechanical response of multi-phase composites. To model the failure of matrix, brittle cracking model is used, where the entire fracture zone is represented by a band of micro cracked material. Current study involves; (a) failure analysis of the concrete unit cell when it is subjected to tensile loads, and (b) parametric study of variation of peak strength with shape and volume fraction of aggregate. In this study, circular and square aggregates at various orientations are modelled. The simulation results predict that the peak tensile stresses are not very sensitive to the volume fraction of aggregates, when the unit cell is subjected to tensile loads. This paper effectively demonstrates the power of unit cell model in simulating the nonlinear mechanical response of cement concrete when it is subjected to tensile loading.     

A cohesive edge crack

The nucleation and growth of a cohesive edge crack is studied. This topic is germane to the initiation and early stage of crack growth during unnotched beam testing, the growth of short edge cracks in finite test pieces, and the formation of tension cracks of geological origin. This paper focuses on an edge crack in a semi-infinite plane, under a uniform far-field tensile stress acting parallel to the plane boundary. Expressions for the Mode I stress-intensity-factor and crack-opening-displacement for an edge crack subjected to arbitrary crack face loading are determined via the weight function method. All of the constants needed to define the weight function and associated integrals are themselves explicit functions of just two constants: f_r and ψ. Two types of softening behavior in the cohesive zone are examined: rectangular softening, and linear softening. In each case the process zone size, energy-release-rate, crack-opening displacement and load-ratio are examined. The different test behavior exhibited under load-control versus fixed-grip displacement control is explored. The test control conditions alter the fracture behavior significantly. For a linear softening cohesive edge crack, it is found out that under fixed-grip control (load-control), the process zone size decreases (increases) steadily with increasing traction-free crack length, approaching the semi-infinite crack asymptote from above (below). The differences between load-control versus fixed-grip control decrease rapidly with increasing traction-free crack length.     

Mode I fracture of adhesive joints using tailored cohesive zone models

Cohesive zone models are explored in order to study cleavage fracture in adhesive bonded joints. A mode I cohesive model is defined which correlates the tensile traction and the displacement jump (crack faces opening) along the fracture process zone. In order to determine the traction-separation relation, the main fracture parameters, namely the cohesive strength and the fracture energy, as well as its shape, must be specified. However, owing to the difficulties associated to the direct measurement of the fracture parameters, very often they are obtained by comparing a measured fracture property with numerical predictions based on an idealized traction separation relation. Likewise in this paper the cohesive strength of an adhesive layer sandwiched between elastic substrates is adjusted to achieve a match between simulations and experiments. To this aim, the fracture energy and the load-displacement curve are adopted as input in the simulations. In order to assess whether or not the shape of the cohesive model may have an influence on the results, three representative cohesive zone models have been investigated, i.e. exponential, bilinear and trapezoidal. A good agreement between experiments and simulations has been generally observed. However, a slight difference in predicting the loads for damage onset has been found using the different cohesive models.     

Dynamic crack bifurcation in PMMA

An investigation of the branching characteristics of small PMMA single edge notched tensile (SENT) specimens is presented. The influence of notch depth and specimen thickness was examined and it was found that branching only occurred for thicker specimens and very short notch depths. The location at which successful branching occurred was very consistent for a given notch depth. Subsequently, however, a statistical variation of branching patterns was observed.A series of simulations was then performed to provide further insight into these tests and in particular to examine the evolution of the fracture process region ahead of the running crack. A finite volume/cohesive zone formulation was used to model micro-crack nucleation and dynamic interaction in the process zone. The cohesive strength and fracture resistance were estimated from unnotched tensile tests and the application of LEFM to the notch test data. Even though a very simple criterion was used to govern the insertion and subsequent behaviour of the cohesive surfaces in the model, many of the experimental observations were reproduced, including high frequency oscillations in crack velocity, the substantial increase in the fracture surface area due to the formation of subsurface micro-cracks, and the location at which successful branching took place.     

Prediction of the Work of Separation and Implications to Modeling

Following Barenblatt's idea about the modeling of cracks by the use of a cohesive zone has attracted considerable attention. Recently, this model has also been applied to the prediction of ductile crack growth. For this case the present investigation aims to compare the predictions of a cohesive zone model with the predictions of the more physically based modified Gurson relation. The results demonstrate that in case of ductile fracture the parameters cohesive strength and energy may only be regarded as material properties within a small range of stress triaxialities. This finally leads to the conclusion that special care has to be taken if a cohesive zone model is used for the analysis of ductile fracture. The use of the modified Gurson relation predicts that the cohesive energy and strength do not remain constant throughout a crack growth analysis and their change is not known a priori. Improved cohesive zone models that take a coupling to the surrounding material into account may overcome this problem. This revised version was published online in July 2006 with corrections to the Cover Date.     

Prediction of interfacial fracture between concrete and fiber reinforced polymer (FRP) by using cohesive zone modeling

Interfacial debonding between concrete and fiber reinforced polymer (FRP) is investigated through integrating experiments and computations. An experimental program is designed to evaluate interfacial fracture parameters of mode-I through cutting and bonding specimens with an FRP sheet. The evaluated fracture parameters, i.e. the fracture energy and the bonding strength, are confirmed by predicting FRP debonding failure with the cohesive zone modeling approach. In the cohesive zone model, a traction-separation relation for FRP debonding is proposed with a shape index while providing various initial descending slopes. Computational results of the cohesive zone model agree well with three-point bending test results for both FRP debonding and plain concrete fracture. Furthermore, both experimental and computational results demonstrate that the fracture energy and the cohesive strength are essential fracture parameters for the prediction of FRP debonding behavior.