Showing papers on "Crack closure published in 2008"

Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements

Abstract: A method is presented in which fracture mechanics is introduced into finite element analysis by means of a model where stresses are assumed to act across a crack as long as it is narrowly opened. This assumption may be regarded as a way of expressing the energy adsorption GC in the energy balance approach, but it is also in agreement with results of tension tests. As a demonstration the method has been applied to the bending of an unreinforced beam, which has led to an explanation of the difference between bending strength and tensile strength, and of the variation in bending strength with beam depth.

Shear Strength of Members without Transverse Reinforcement as Function of Critical Shear Crack Width

Abstract: This paper investigates the shear strength of beams and one-way slabs without stirrups based on the opening of a critical shear crack. The shear-carrying mechanisms after the development of this crack are investigated. On this basis, a rational model is developed to estimate the shear strength of members without shear reinforcement. The proposed model is based on an estimate of the crack width in the critical shear region, taking also into account the roughness of the crack and the compressive strength of concrete. The proposed model is shown to properly describe a large set of available test data. A simplified method adopted by the Swiss code for structural concrete (SIA 262) is also introduced. Comparisons with other codes of practice are finally presented, with a highlight on the main differences between them.

An interacting micro-crack damage model for failure of brittle materials under compression

Abstract: A model is developed for brittle failure under compressive loading with an explicit accounting of micro-crack interactions. The model incorporates a pre-existing flaw distribution in the material. The macroscopic inelastic deformation is assumed to be due to the nucleation and growth of tensile “wing” micro-cracks associated with frictional sliding on these flaws. Interactions among the cracks are modeled by means of a crack-matrix-effective-medium approach in which each crack experiences a stress field different from that acting on isolated cracks. This yields an effective stress intensity factor at the crack tips which is utilized in the formulation of the crack growth dynamics. Load-induced damage in the material is defined in terms of a scalar crack density parameter, the evolution of which is a function of the existing flaw distribution and the crack growth dynamics. This methodology is applied for the case of uniaxial compression under constant strain rate loading. The model provides a natural prediction of a peak stress (defined as the compressive strength of the material) and also of a transition strain rate, beyond which the compressive strength increases dramatically with the imposed strain rate. The influences of the crack growth dynamics, the initial flaw distribution, and the imposed strain rate on the constitutive response and the damage evolution are studied. It is shown that different characteristics of the flaw distribution are dominant at different imposed strain rates: at low rates the spread of the distribution is critical, while at high strain rates the total flaw density is critical.

The simulation of dynamic crack propagation using the cohesive segments method

Abstract: The cohesive segments method is a finite element framework that allows for the simulation of the nucleation, growth and coalescence of multiple cracks in solids. In this framework, cracks are introduced as jumps in the displacement field by employing the partition of unity property of finite element shape functions. The magnitude of these jumps are governed by cohesive constitutive relations. In this paper, the cohesive segments method is extended for the simulation of fast crack propagation in brittle solids. The performance of the method is demonstrated in several examples involving crack growth in linear elastic solids under plane stress conditions: tensile loading of a block; shear loading of a block and crack growth along and near a bi-material interface.

Low-speed fracture instabilities in a brittle crystal

Abstract: Multiscale models predict detailed features of surfaces left by crack propagation and rationalize the occurrence of fracture instabilities in a technologically important material, silicon. As a crack propagates along the most stable cleavage plane in silicon at relatively low speeds (800 metres per second), an instability suddenly appears. The authors find that beyond the very tip of the crack, when fracture speed is slow enough, bonds are broken one atomic layer below the fracture plane leading to a systematic downward deflection of the crack. Conversely, deflecting of fracture on another cleavage plane of silicon occur when the fracture speed is very high. Preliminary simulations reveal that similar instabilities could occur in diamond and silicon carbide. When a brittle material is loaded to the limit of its strength, it fails by the nucleation and propagation of a crack1. The conditions for crack propagation are created by stress concentration in the region of the crack tip and depend on macroscopic parameters such as the geometry and dimensions of the specimen2. The way the crack propagates, however, is entirely determined by atomic-scale phenomena, because brittle crack tips are atomically sharp and propagate by breaking the variously oriented interatomic bonds, one at a time, at each point of the moving crack front1,3. The physical interplay of multiple length scales makes brittle fracture a complex ‘multi-scale’ phenomenon. Several intermediate scales may arise in more complex situations, for example in the presence of microdefects or grain boundaries. The occurrence of various instabilities in crack propagation at very high speeds is well known1, and significant advances have been made recently in understanding their origin4,5. Here we investigate low-speed propagation instabilities in silicon using quantum-mechanical hybrid, multi-scale modelling and single-crystal fracture experiments. Our simulations predict a crack-tip reconstruction that makes low-speed crack propagation unstable on the (111) cleavage plane, which is conventionally thought of as the most stable cleavage plane. We perform experiments in which this instability is observed at a range of low speeds, using an experimental technique designed for the investigation of fracture under low tensile loads. Further simulations explain why, conversely, at moderately high speeds crack propagation on the (110) cleavage plane becomes unstable and deflects onto (111) planes, as previously observed experimentally6,7.

Embedded Shape-Memory Alloy Wires for Improved Performance of Self-Healing Polymers**

Abstract: We report the first measurements of self-healing polymers with embedded shape-memory alloy (SMA) wires. The addition of SMA wires shows improvements of healed peak fracture loads by up to a factor of 1.6, approaching the performance of the virgin material. Moreover, the repairs can be achieved with reduced amounts of healing agent. The improvements in performance are due to two main effects: (i) crack closure, which reduces the total crack volume and increases the crack fill factor for a given amount of healing agent and (ii) heating of the healing agent during polymerization, which increases the degree of cure of the polymerized healing agent.

The extended finite element method in thermoelastic fracture mechanics

Abstract: The extended finite element method (XFEM) is applied to the simulation of thermally stressed, cracked solids. Both thermal and mechanical fields are enriched in the XFEM way in order to represent discontinuous temperature, heat flux, displacement, and traction across the crack surface, as well as singular heat flux and stress at the crack front. Consequently, the cracked thermomechanical problem may be solved on a mesh that is independent of the crack. Either adiabatic or isothermal condition is considered on the crack surface. In the second case, the temperature field is enriched such that it is continuous across the crack but with a discontinuous derivative and the temperature is enforced to the prescribed value by a penalty method. The stress intensity factors are extracted from the XFEM solution by an interaction integral in domain form with no crack face integration. The method is illustrated on several numerical examples (including a curvilinear crack, a propagating crack, and a three-dimensional crack) and is compared with existing solutions. Copyright © 2007 John Wiley & Sons, Ltd.

Strain controlled cyclic deformation behavior of an extruded magnesium alloy

Abstract: Fatigue properties of an extruded AZ31B magnesium alloy were evaluated using strain-controlled push–pull cyclic tests at different total strain amplitudes at room temperature. The alloy exhibited an asymmetric sigmoidal-shaped hysteresis loop due to twinning in compression during the unloading phase and detwinning during the loading phase. As the total strain amplitude increased, the asymmetry of hysteresis loops, plastic strain amplitude, mean stress, and stress amplitude increased, while the ratcheting strain and pseudoelastic modulus decreased. As the cyclic deformation progressed at a given total strain amplitude (greater than 0.3%), an abrupt increase in the plastic strain amplitude was observed, representing the onset of fatigue crack initiation. The extent of this increase process, which decreased with increasing total strain amplitude, corresponded to the fatigue crack propagation prior to the final fast failure. Fatigue crack initiation was observed to occur at the specimen surface, and fatigue crack propagation was characterized by typical striations. The smaller spacing of fatigue striations and larger fatigue crack propagation zone at the lower total strain amplitude gave rise to a longer fatigue life. The Coffin–Manson and Basquin's relationships can be used to describe the fatigue lifetime of this alloy.

The role of twinning-detwinning on fatigue fracture morphology of Mg-3%Al-1%Zn alloy

Abstract: Typical fracture morphology of Mg–3%Al–1%Zn (AZ31) alloy after low cycle fatigue was investigated using SEM and optical microscope. It is shown that prolific lamellar structure in the crack initiation and crack stable propagation zone mainly results from twinning, while dimple structure formed in the unstable crack propagation and final rupture zone is mainly due to slip. The formation mechanisms of corresponding morphologies are proposed based on twinning and detwinning processes during compressive and tensile loading half cycles, respectively, for this alloy.

Inelastic deformation and energy dissipation in ceramics: A mechanism-based constitutive model

Abstract: A mechanism-based constitutive model is presented for the inelastic deformation and fracture of ceramics. The model comprises four essential features: (i) micro-crack extension rates based on stress-intensity calculations and a crack growth law, (ii) the effect of the crack density on the stiffness, inclusive of crack closure, (iii) plasticity at high confining pressures, and (iv) initial flaws that scale with the grain size. Predictions of stress/strain responses for a range of stress states demonstrate that the model captures the transition from deformation by micro-cracking at low triaxiality to plastic slip at high triaxialities. Moreover, natural outcomes of the model include dilation (or bulking) upon micro-cracking, as well as the increase in the shear strength of the damaged ceramic with increasing triaxiality. Cavity expansion calculations are used to extract some key physics relevant to penetration. Three domains have been identified: (i) quasi-static, where the ceramic fails due to the outward propagation of a compression damage front, (ii) intermediate velocity, where an outward propagating compression damage front is accompanied by an inward propagating tensile (or spallation) front caused by the reflection of the elastic wave from the outer surface and (iii) high velocity, wherein plastic deformation initiates at the inner surface of the shell followed by spalling within a tensile damage front when the elastic wave reflects from the outer surface. Consistent with experimental observations, the cavity pressure is sensitive to the grain size under quasi-static conditions but relatively insensitive under dynamic loadings.

J-integral and crack driving force in elastic–plastic materials

Abstract: This paper discusses the crack driving force in elastic–plastic materials, with particular emphasis on incremental plasticity. Using the configurational forces approach we identify a “plasticity influence term” that describes crack tip shielding or anti-shielding due to plastic deformation in the body. Standard constitutive models for finite strain as well as small strain incremental plasticity are used to obtain explicit expressions for the plasticity influence term in a two-dimensional setting. The total dissipation in the body is related to the near-tip and far-field J-integrals and the plasticity influence term. In the special case of deformation plasticity the plasticity influence term vanishes identically whereas for rigid plasticity and elastic-ideal plasticity the crack driving force vanishes. For steady state crack growth in incremental elastic–plastic materials, the plasticity influence term is equal to the negative of the plastic work per unit crack extension and the total dissipation in the body due to crack propagation and plastic deformation is determined by the far-field J-integral. For non-steady state crack growth, the plasticity influence term can be evaluated by post-processing after a conventional finite element stress analysis. Theory and computations are applied to a stationary crack in a C(T)-specimen to examine the effects of contained, uncontained and general yielding. A novel method is proposed for evaluating J-integrals under incremental plasticity conditions through the configurational body force. The incremental plasticity near-tip and far-field J-integrals are compared to conventional deformational plasticity and experimental J-integrals.

Evaluation of crack opening performance of a repair material with strain hardening behavior

Abstract: One of the novel mechanical properties of strain hardening cementitious composites (SHCC) is that they exhibit multiple fine cracks and strain hardening in tension. This promotes the use of SHCC as an effective repair material, because penetration of substances through the fine cracks is greatly reduced. Most research on SHCC has focused on its behavior and results obtained from uniaxial tensile tests. However, the crack distribution of the repair material (SHCC) layer is more concentrated adjacent to an existing crack in a substrate. So the design procedure considering the crack opening, which represents the potential for localized fracture, should be established for appropriate material selection. In this paper, the performance of SHCC as a repair material was assessed through three tests: uniaxial tensile tests; zero-span tensile tests; and flexural tests of RC beams repaired with SHCC. Comparisons between crack opening performances and the observed crack patterns of the three tests were conducted. The crack opening and crack pattern obtained from the zero-span tensile tests were similar to those of the repaired beam specimens. According to the zero-span tensile tests, the performance of cracking behavior of the repair material on an existing crack can be estimated. On the other hand, the deformation capacity of SHCC obtained from the uniaxial tensile tests cannot be directly applied to the design of surface repair application.

A Three-dimensional Damage Model for Transversely Isotropic Composite Laminates

Abstract: This article proposes a fully three-dimensional continuum damage model, developed at the sub-ply level, to predict in an integrated way both the intralaminar and the interlaminar failure mechanisms that occur in laminated fiber-reinforced polymer composites The constitutive model is based on the assumption that the composite material is transversely isotropic, and accounts for the effects of crack closure under load reversal cycles The damage model is implemented in an implicit finite element code taking into account the requirement to ensure a mesh-independent computation of the dissipated energy The comparison between the model predictions and published experimental data indicates that the model can accurately predict the effects of transverse matrix cracks on the residual stiffness of quasi-isotropic laminates, the interaction between transverse matrix cracks and delamination, and final failure of the laminate