Application of an energy balance and an energy method to dynamic crack propagation

The speeds of fast running cracks in a range of quasi-brittle materials are measured as a function of the dynamic strain energy release rate. From the results, the heat output associated with the plastic work at the crack tip is calculated as a function of crack speed using an energy balance, and compared with the heat outputs determined experimentally using an energy method. A generally good agreement is found between the calculated and the experimentally measured variation of heat output with crack speed.

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Zusammenfassung Die Geschwindigkeiten schnell-laufender Brüche werden als Funktion der dynamischen Energiefreisetzungsrate für eine Anzahl unterschiedlich spröder Materialien gemessen. Aus diesen Ergebnissen wird mit Hilfe einer Energiebilanz die durch die plastischen Deformationen an der Rißspitze entstehende Wärme berechnet und mit der durch eine Energiemethode experimentell gemessenen Wärme verglichen. Es wird eine im allgemeinen gute Übereinstimmung zwischen dem berechneten und gemessenen Verlauf der Wärme als Funktion der Bruchgeschwindigkeit gefunden.

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Résumé Les vitesses de propagation des fissures en développement rapide dans une gamme de matériaux quasi-fragile sont mesurés en fonction de la vitesse de relaxation de l'énergie de déformation dynamique. A partir des résultats obtenus, on calcule la dissipation de chaleur associée au travail de formation plastique à l'extrémité de la fissure en fonction de la vitesse de la fissure correspondant à un équilibre énergétique. On compare ces valeurs calculées avec les dissipations de chaleur déterminées expérimentalement à l'aide d'une méthode énergétique. En général, on trouve un bon accord entre les variations de dissipation de chaleur calculées et mesurées par voie expérimentale en fonction de la vitesse de fissuration.

     

Multiscale modeling of dynamic crack propagation

A multiscale approach is employed to investigate a center-cracked specimen with the purpose to redefine fracture toughness from the atomistic perspective and to simulate different modes of crack propagation. The specimen is divided into three regions: (1) far field, modeled by classical fracture mechanics, (2) near field, modeled by a multiscale field theory and analyzed by a generalized finite element method, and (3) crack tip atomic region, modeled by molecular dynamics (MD). The exact and analytical solution of the far field is utilized to specify boundary conditions at the interface between the far field and the near field. The interaction between the near field and the crack tip region is described by full-blown interatomic forces. In this work, crystals of perovskite (Barium Titanate) and rocksalt (Magnesia) have been studied. Fracture toughness is defined as a material property associated with instability of the MD simulation. Mode I, Mode II, and mixed mode fracture have been investigated and numerical results will be presented and discussed.     

A low-cycle fatigue approach to fatigue crack propagation

The damage accumulation hypothesis is used to derive a fatigue crack growth rate equation. The fatigue life of a volume element inside the plastic zone is evaluated by using low-cycle fatigue concepts. Crack growth rate is expressed as a function of cyclic material parameters and plastic zone characteristics. For a given material, crack growth increment, is predicted to be a fraction of the plastic zone size which can be expressed in terms of fracture mechanics parameters,K andJ. Hence, the proposed growth rate equation has a predictive capacity and is not limited to linear elastic conditions.     

Influence of dynamic fracture toughness on dynamic crack propagation

A dynamic finite element code was used in its “propagation mode” to assess the differences in dynamic crack propagation in a wedge-loaded (WL) single-edged notch (SEN) specimen, a tapered double cantilever beam (TDCB) specimen and a rectangular double cantilever beam (RDCB) specimen. The dynamic fracture toughness, K_ID, vs the crack velocity, a, relations determined experimentally for WL-SEN, WL-TDCB and WL-RDCB specimens machined from Araldite B were used as dynamic fracture criteria and the resultant k_id variations with crack propagations in the three specimens were compared with the corresponding experimental results. While the specific K_ID vs /.a relations established for each specimen obviously yielded calculated k_ID which were in best agreement with the experimental K_ID for the respective specimen, the K_ID vs /.a relation for the large WL-SEN specimen provided the best overall fit between the calculated and measured K_ID variations with crack propagation in all three specimens.     

Time dependent crack tip enrichment for dynamic crack propagation

We study several enrichment strategies for dynamic crack propagation in the context of the extended finite element method and the effect of different directional criteria on the crack path. A new enrichment method with a time dependent enrichment function is proposed. In contrast to previous approaches, it entails only one crack tip enrichment function. Results for stress intensity factors and crack paths for different enrichments and direction criteria are given.     

Studies of dynamic crack propagation and crack branching with peridynamics

In this paper we discuss the peridynamic analysis of dynamic crack branching in brittle materials and show results of convergence studies under uniform grid refinement (m-convergence) and under decreasing the peridynamic horizon (δ-convergence). Comparisons with experimentally obtained values are made for the crack-tip propagation speed with three different peridynamic horizons. We also analyze the influence of the particular shape of the micro-modulus function and of different materials (Duran 50 glass and soda-lime glass) on the crack propagation behavior. We show that the peridynamic solution for this problem captures all the main features, observed experimentally, of dynamic crack propagation and branching, as well as it obtains crack propagation speeds that compare well, qualitatively and quantitatively, with experimental results published in the literature. The branching patterns also correlate remarkably well with tests published in the literature that show several branching levels at higher stress levels reached when the initial notch starts propagating. We notice the strong influence reflecting stress waves from the boundaries have on the shape and structure of the crack paths in dynamic fracture. All these computational solutions are obtained by using the minimum amount of input information: density, elastic stiffness, and constant fracture energy. No special criteria for crack propagation, crack curving, or crack branching are used: dynamic crack propagation is obtained here as part of the solution. We conclude that peridynamics is a reliable formulation for modeling dynamic crack propagation.     

An experimental investigation of dynamic crack propagation

The dynamic fracture behavior of polymethylmethacrylate (bdPMMA) has been investigated. The specimens were in the form of rectangular sheets with sharp notches. The elastodynamic crack tip stress field and the crack velocity were determined by the use of resistance strain gauges. An analytic expression for the dynamic crack tip stress field was used to evaluate the dynamic stress intensity factors, and the dynamic arrest toughness was also determined.The dynamic response of the stresses at the notch tip at varying loading rates was considered and some “hysteresis” fracture phenomena were observed.     

Effect of crack layer on dynamic crack propagation behaviour in polystyrene

Dynamic crack propagation in thin, edge-notched polystyrene specimens was studied by the method of dynamic caustics. During crack propagation, an intensive zone of crazing surrounds and precedes the propagating crack. Therefore, an active zone ahead of the crack tip is developed. This active zone is related to the velocity of crack propagation and the strain rate of loading. The velocity of the crack and the stress intensity factor, K_I, or the energy release rate, G_I, were strongly influenced by the development of the active zone at the crack tip.     

Numerical analysis of dynamic crack propagation in rubber

In the present paper, dynamic crack propagation in rubber is analyzed numerically using the finite element method. The problem of a suddenly initiated crack at the center of stretched sheet is studied under plane stress conditions. A nonlinear finite element analysis using implicit time integration scheme is used. The bulk material behavior is described by finite-viscoelasticity theory and the fracture separation process is characterized using a cohesive zone model with a bilinear traction-separation law. Hence, the numerical model is able to model and predict the different contributions to the fracture toughness, i.e. the surface energy, viscoelastic dissipation, and inertia effects. The separation work per unit area and the strength of the cohesive zone have been parameterized, and their influence on the separation process has been investigated. A steadily propagating crack is obtained and the corresponding crack tip position and velocity history as well as the steady crack propagation velocity are evaluated and compared with experimental data. A minimum threshold stretch of 3.0 is required for crack propagation. The numerical model is able to predict the dynamic crack growth. It appears that the strength and the surface energy vary with the crack speed. Finally, the maximum principal stretch and stress distribution around steadily propagation crack tip suggest that crystallization and cavity formation may take place.     

Environmental dynamic fatigue crack propagation in high density polyethylene: an empirical modelling approach

Part of a programme to study environmental dynamic fatigue crack propagation in engineering thermoplastics is presented. High density polyethylene has been studied in terms of its stress cracking properties under dynamic loading conditions in detergent. This work complements previous investigations on stress cracking in detergent under static loading. The stress cracking was found to vary according to loading conditions and in conclusion, a dependence of crack growth rate on test frequency, amplitude and level of stress intensity factor is reported. An emperical model describing environmental fatigue crack propagation is proposed which adequately represents the experimental results of high density polyethylene, Nylon 66 and which, it is suggested, may be suitable for use with other polymers.     

裂纹止裂技术及裂纹动态扩展规律研究

为了对动态荷载作用下水泥粉煤灰砂浆的裂缝动态扩展行为进行研究,提出了一种大尺寸带V型底边的半圆边裂纹(SECVB)试件,其V形底部具有止裂功能。SECVB试件的V形底部设计为180°,150°和120°三个角度。采用落锤冲击装置进行了冲击试验,并使用裂纹扩展计(CPG)用于测量裂纹扩展的相关参数。利用有限差分程序AUTODYN对裂纹扩展行为进行了数值模拟,并用有限元程序ABAQUS计算了裂纹的动态应力强度因子(DSIF);根据CPG测量的裂纹萌生时间和扩展时间来确定临界应力强度因子。试验和数值模拟结果表明,SECVB试件适合于研究动态荷载作用下水泥粉煤灰砂浆的裂纹扩展行为和止裂行为。在裂纹扩展过程中,裂纹可能在一段时间内止裂,并且裂纹在起始时刻的断裂韧度高于裂纹扩展时的断裂韧度。     

Environmental dynamic fatigue crack propagation in nylon 66

The introduction of plastics into the structural materials market necessitates careful study of their fatigue behaviour in different environmental conditions. Standard samples of nylon 66 were pre-treated in either air, water, or dilute sulphuric acid and then notched and examined for fatigue crack propagation in the various environments. Tensile dynamic fatigue tests under constant sinusoidal load amplitudes were carried out at different frequencies. Linear fracture mechanics concepts were found to be a useful tool when interpreting the results.     

Transient analysis of dynamic crack propagation in piezoelectric materials

Abstract

In this paper, the transient analysis of semi‐infinite propagating cracks in piezoelectric materials subjected to dynamic anti‐plane concentrated body force is investigated. The crack surface is assumed to be covered with an infinitesimally thin, perfectly conducting electrode that is grounded. In analyzing this problem, it has characteristic lengths and a direct attempt towards solving this problem by transform and Wiener‐Hopf techniques (Noble, 1958) is not applicable. In order to solve this problem, a new fundamental solution for propagating cracks in piezoelectric materials is first established and the transient response of the propagating crack is obtained by superposition of the fundamental solution in the Laplace transform domain. The fundamental solution to be used is the responses of applying exponentially distributed traction in the Laplace transform domain on the propagating crack surface. Taking into account the quasi‐static approximation, exact analytical transient solutions for the dynamic stress intensity factor and the dynamic electric displacement intensity factor are obtained by using the Cagniard‐de Hoop method (Cagnard, 1939; de Hoop, 1960) of Laplace inversion and are expressed in explicit forms. Numerical calculations of dynamic intensity factors are evaluated and the results are discussed in detail. The transient solutions for stationary cracks have been shown to approach the corresponding static values after the shear wave of the piezoelectric material has passed the crack tip.     

A numerical approach to subsurface crack propagation assessment in rolling contact

Subsurface crack mode II propagation parallel to the contact surface is a damage mechanism leading to dramatic failure in many components subjected to cyclic loading. A weight function (WF) was elaborated for calculating the applied mode II stress intensity factor (SIF) of a crack in a two‐dimensional half‐space in plane strain condition, for crack completely closed and frictionless contact between the crack faces. With respect to other methods, the WF allows faster SIF calculation, thus being suitable for simulation of many repeated load cycles and fatigue crack propagation. The WF was applied for simulating a case of rolling contact experiments found in the literature, and good agreement between experimental and numerical results was obtained, showing the effectiveness of the WF method in damage tolerant design.     

A continuum mechanics approach to some problems in subcritical crack propagation

The results of the so-called energetic approach to fracture for the cases of a sharp crack without and with a cohesive zone are briefly reviewed with particular attention to the crack tip singularity analysis and to the issue of energy dissipation due to crack propagation. The case of a crack with a cohesive zone removing all thermomechanical singularities is then further analyzed, focusing the attention on the question of the thermodynamic admissibility of subcritical crack growth, and on some of the hypotheses that lead to the derivation of subcritical crack growth laws. A two-phase cohesive zone model for discontinuous crack growth is presented and its thermodynamics analyzed, followed by an example of its possible application.