Crack Modeling Approach Research Articles

Fictitious Rough Crack Model (FRCM): A Smeared Crack Modelling Approach to Account for Aggregate Interlock and Mixed Mode Fracture of Plain Concrete.

The intention of this paper is to clarify the mechanisms of mixed mode fracture and shear stress transfer in plain concrete. To capture these scarcely explored phenomena, a new mechanical formulation is proposed called the fictitious rough crack model (FRCM). The FRCM considers mode I deformations to control crack formation and residual tensile stress transfer, while mode II deformations are assumed to induce shear stress transfer along the crack surfaces and compressive normal stresses attributed to aggregate interlock. The fundamental idea of the FRCM is to combine these tension-softening and shear-transfer laws and to superimpose the emerging shear and normal stresses of both mechanisms in the crack. The paper illustrates the analytical development of the FRCM and its numerical implementation. Three well-known experimental benchmark problems (concrete panel test series by Nooru-Mohamed and by Hassanzadeh as well as aggregate interlock test series by Paulay and Loeber) are numerically addressed to test plausibility of FRCM results. The numerical implementation of the FRCM is capable of simulating the transition from mode-I fracture to mixed-mode fracture in the structural response and is also able to predict the crack path with reasonable agreement.

Interrogating failure mechanisms of notched composites through a discrete crack modeling approach

The prediction of compressive failure of composite laminates is generally more challenging than tensile failure, due to more complex failure mechanisms and nonlinear effects. This work presents an extension of a previously developed numerical framework utilizing discontinuous solid-shell elements and enriched cohesive elements for the simulation of damage growth of open-hole laminates under compression. Unlike tension, compressive loading may result in inclined matrix cracks due to localized shear damage. An approximate but efficient modeling technology was adopted by formulating an assumed vertical cohesive crack with the inclined crack coordinate system. The proposed approach explicitly represents damage as discrete cracks and leads to more accurate prediction of brittle and push-out failure patterns for sublaminate-scaled and ply-scaled laminates, respectively, including size and lay-up effects. These failure events of open-hole compression are believed to be captured with discrete crack analysis for the first time.

A continuum damage and discrete crack-based approach for fatigue response and residual strength prediction of notched laminated composites

This paper presents a combined continuum damage and discrete crack (CDDC) modelling approach for fatigue damage characterization and post-fatigue residual strength prediction of laminated composite components with a hole. In order to capture both the fatigue cycle-driven material degradation and discrete damage-induced stress concentration and redistribution, an overlapped element approach is developed based on a combined user-defined material (UMAT) and user-defined element (UEL). An Abaqus element coupled with UMAT for fatigue damage characterization is used to detect the location of failure initiation, while the discrete crack network-based (DCN) UEL is applied to insert a crack without remeshing. The intensified stress field induced by the newly inserted matrix crack is used for the evaluation of failure initiation and stiffness degradation. The UMAT for the fatigue analysis has incorporated the stress-cycle ( S-N) curves for the damage evolution characterization associated with matrix and fiber based on the tested S-N curves for plies at their different orientations. A continuum damage mechanics (CDM) approach is used for the fatigue-driven delamination initiation and propagation by insertion of a finite thickness interface layer at each ply interface. Both the blind and recalibrated predictions are performed for specimens of three different layups under the Air Force Tech Scout 1 program. The predicted fatigue failure progression and the stiffness against cycle curves are compared with the test data provided by the Air Force Research Lab (AFRL). In addition, post-fatigue residual strength predictions are performed for these notched specimens under tension and compression.

Failure Predictions for Graphite Reflector Bricks in the Very High Temperature Reactor with the Prismatic Core Design

Graphite is used in nuclear reactor cores as a neutron moderator, reflector and structural material. The dimensions and physical properties of graphite change when it is exposed to neutron irradiation. The non-uniform changes in the dimensions and physical properties lead to the build-up of stresses over the course of time in the core components. When the stresses reach the critical limit, i.e. the strength of the material, cracking occurs and ultimately the components fail. In this paper, an explicit crack modeling approach to predict the probability of failure of a VHTR prismatic reactor core reflector brick is presented. Firstly, a constitutive model for graphite is constructed and used to predict the stress distribution in the reflector brick under in-reactor conditions of high temperature and irradiation. Fracture simulations are performed as part of a Monte Carlo analysis to predict the probability of failure. Failure probability is determined based on two different criteria for defining failure time: A) crack initiation and B) crack extension to near control rod channel. A significant difference is found between the failure probabilities based on the two criteria. It is predicted that the reflector bricks will start cracking during the time range of 5–9years, while breaching of the control rod channels will occur during the period of 11–16years. The results show that, due to crack arrest, there is a significantly delay between crack initiation and breaching of the control rod channel.

Smeared crack modelling approach for corrosion-induced concrete damage

In this paper a smeared crack modelling approach is used to simulate corrosion-induced damage in reinforced concrete. The presented modelling approach utilizes a thermal analogy to mimic the expansive nature of solid corrosion products, while taking into account the penetration of corrosion products into the surrounding concrete, non-uniform precipitation of corrosion products, and creep. To demonstrate the applicability of the presented modelling approach, numerical predictions in terms of corrosion-induced deformations as well as formation and propagation of micro- and macrocracks were compared to experimental data obtained by digital image correlation and published in the literature. Excellent agreements between experimentally observed and numerically predicted crack patterns at the micro and macro scale indicate the capability of the modelling approach to accurately capture corrosion-induced damage phenomena in reinforced concrete. Moreover, good agreements were also found between experimental and numerical data for corrosion-induced deformations along the circumference of the reinforcement.

An analytical cohesive crack modeling approach to the edge debonding failure of FRP-plated beams

This paper focuses on the prediction of edge debonding for a beam retrofitted with a Fiber-Reinforced Polymer plate. This failure mechanism, also known as plate-end debonding, stems from the concentration of interfacial stresses arising at the termination of the strengthening plate. Early models of edge debonding adopted failure criteria based on interfacial stresses. However, due to the typically catastrophic nature of this failure mechanism, approaches based on Linear Elastic Fracture Mechanics (LEFM) became increasingly established. In this paper, the problem is addressed by means of the Cohesive Crack Model (CCM) and of the Finite Fracture Mechanics (FFM). These models are able to bridge the gap between the stress- and the energy-based approaches and nevertheless have been used in a limited number of analytical studies to date. Based on a cohesive interface law with linear softening, closed-form solutions are derived for the interfacial stresses and the load–displacement curves, as well as for the ultimate load. It is found that LEFM usually overestimates the debonding load, thus justifying the need for the proposed approach; on the other hand, debonding load estimates based on FFM are in excellent agreement with the CCM predictions. Finally, a parametric analysis highlights the effect of the geometry/material properties on the structural response, as well as the ductile-to-brittle transition and the possible occurrence of structural instabilities depending on the test controlling parameters.

A computational model for the simulation of dynamic fracture in laminated composite plates

A mesoscopic, time-dependent finite element model for the simulation of dynamic fracture in laminated composite plates is presented. The computational model allows for the simulation of mesh-objective multiple matrix cracking and delamination in laminated composite plates. The analyses are performed with an emphasis on the quantification of the effect of the loading rate on interacting damage mechanisms, i.e. matrix cracking and delamination. In particular, rate effects on damage initiation, propagation, and interaction between matrix cracking and delamination under low and high velocity impact are studied. Moreover, the paper addresses computational issues related to time continuity in stress/strain and velocity fields, during dynamic simulation, at the time of incorporation of new degrees of freedom in a mesh-objective crack modeling approach. Illustrative numerical examples are presented to show the performance of the model. The model is validated with a fast crack growth simulation in a unidirectional laminate. An impact test on a cross-ply laminated plate is performed in order to study the rate effects on structural response and damage mechanics.

Finite separation method: an efficient boundary element crack modeling technique

In computational fracture mechanics, great benefits are obtained from the reduced modeling dimension order and the accurate integral formulation of the boundary element method (BEM). However, the direct representation of co-planar surfaces (i.e., cracks) causes a degeneration of the standard displacement BEM formulation which can only be circumvented with special modeling techniques. Aiming to simplify the generalized application of the BEM to fracture mechanics problems, this paper presents a two-dimensional crack modeling approach. The method uses the direct BEM displacement formulation within a single-domain model to efficiently and precisely calculate any mixed mode crack tip stress intensity factor. Details of the application of the method are presented, while its accuracy and reliability are demonstrated through numerous comparisons with benchmark results.

Modeling Masonry Shear-Compression: Role of Dilatancy Highlighted

In-plane shear and compression are important modes in masonry walls, both in load bearing structures and in framed structures. By these mechanical actions shear forces caused by wind and earthquakes are resisted. Upon shear-slipping along bed joints, brick units in masonry also undergo upward translation, or dilatancy, causing global volume increase. If this dimensional change is prevented, large compressive stresses may build up, increasing the resistance to slip by the Coulomb-friction nature. If this shear-compression interaction is not modeled correctly, large errors may be made. In the extreme case, unlimited shear resistance may be predicted by computational models. A discrete crack modeling approach for masonry, which captures the shear-compression dilatational behavior realistically, is elaborated. Shear-compression experiments on small masonry specimens as well as 1 m×1 m masonry walls are analyzed as validation.

A comparative study of numerical solutions to non-linear discrete crack modelling of concrete beams involving sharp snap-back

Numerical problems are often encountered in modelling crack propagation in concrete beams using non-linear finite element (FE) analysis, especially when sharp snap-back behaviour in load–displacement relations occurs. This paper firstly identifies 16 arc-length control based numerical strategies based on extensive literature review. They are then used to carefully model the structural behaviour of a four-point single notched shear beam using discrete crack modelling approach in which cracks are represented by interface elements with bilinear softening constitutive laws. Based on extensive FE analyses, detailed comparisons of the merits and demerits of these numerical algorithms are then made. The results indicate that the effectiveness and efficiency of different algorithms may vary considerably from one to another, with the local arc-length based procedures in conjunction with tangential stiffness strategy and reversible unloading model being the most robust.

Mesh independent modelling of cracks by using higher order shape functions

AbstractA mesh independent crack modelling approach based on displacement approximation with higher order shape functions is proposed. The Heaviside step function based local enrichment method, known as eXtended Finite Element Method, is modified by replacing the step function with a higher order shape functions approximation. Polynomial B‐spline approximation functions are used in the present paper. An advantage of the proposed method is that its implementation only involves integration of the products of original shape functions and their derivatives and does not require modification of the integration domains. A volume integral based expression is proposed to calculate the effective surface area of the crack modelled by using an approximate step function. It is shown to give the actual crack surface area in the limit of the approximate step function approaching the Heaviside function. The convergence and accuracy of the method is illustrated in examples of transverse and oblique (with respect to loading direction) crack problems in rectangular plates. Uniaxial tension of a unidirectional composite with an open hole is considered. Hoop stress relaxation due to longitudinal splitting is successfully modelled by the method proposed and compared to direct modelling by using ANSYS software. Published in 2002 by John Wiley & Sons, Ltd.

The validation of some methods of notch fatigue analysis

This paper is concerned with the testing and validation of certain methods of notch analysis which the authors have developed theoretically in earlier publications. These methods were developed for use with finite element (FE) analysis in order to predict the fatigue limits of components containing stress concentrations. In the present work we tested and compared these methods using data from standard notches taken from the literature, covering a range of notch geometries, loading types, R‐ratios and materials: a total of 47 different data sets were analysed. The greatest predictive success was achieved with critical‐distance methods known as the point, line and area methods: 94% of these predictions fell within 20% of the experimental fatigue limits. This was a significant improvement on previous methods of this kind, e.g. that of Klesnil and Lucas [(1980) Fatigue of Metallic Materials, Elsevier Science]. Methods based on the Smith and Miller [(1978) Int. J. Mech. Sci. 20, 201–206] concept of crack‐like notches were successful in 42% of cases; they experienced difficulties dealing with very small notches, and could be improved by using an ElHaddad‐type correction factor, giving 87% success. An approach known as ‘crack modelling’ allowed the Smith and Miller method to be used with non‐standard stress concentrations, where notch geometry is ill defined; this modification, with the same short‐crack correction, had 68% success. It was concluded that the critical‐distance approach is more accurate and can be more easily used to analyse components of complex shape, however, the crack modelling approach is sometimes preferable because it can be used with less mesh refinement.

Energy-Based Cohesive Crack Propagation Modeling

This paper presents an energy-based approach for the finite-element modeling of mixed-mode cohesive crack propagation. This approach predicts the propagation of a quasistatic cohesive crack based on the principle of energy conservation. The crack propagation direction is assumed to be perpendicular to the direction of the maximum tensile principal stress at the cohesive crack tip. A generalized virtual crack-extension technique including the cohesive crack model is used to efficiently evaluate the crack propagation condition. The energy-based approach is both theoretically more fundamental and numerically more accurate than the commonly used strength-based cohesive crack modeling approach. A two-dimensional automatic mixed-mode discrete crack propagation modeling program has been developed that is capable of modeling both nonlinear and linear elastic crack propagation problems. The numerical efficiency and convergence behavior of the present approach are demonstrated through two example problems: a three-point bend beam and a single edge-notched shear beam.