Incubation Time Fracture Criterion Research Articles

Predicting impact strength of perforated targets using artificial neural networks trained on FEM-generated datasets

The paper considers application of artificial neural networks (ANNs) for fast numerical evaluation of a residual impactor velocity for a family of perforated PMMA (Polymethylmethacrylate) targets. The ANN models were trained using sets of numerical results on impact of PMMA plates obtained via dynamic FEM coupled with incubation time fracture criterion. The developed approach makes it possible to evaluate the impact strength of a particular target configuration without complicated FEM calculations which require considerable computational resources. Moreover, it is shown that the ANN models are able to predict results for the configurations which cannot be processed using the developed FEM routine due to numerical instabilities and errors: the trained neural network uses information from successful computations to obtain results for the problematic cases. A simple static problem of a perforated plate deformation is discussed prior to the impact problem and preferable ANN architectures are presented for both problems. Some insight into the perforation pattern optimization using a genetic algorithm coupled with the ANN is also made and optimized perforation patterns which theoretically enhance the target impact strength are constructed.

Fracture delay effect: Analogy between crack initiation due to short pulse loads and mass-spring system failure

The incubation time fracture criterion (ITFC) is used to analytically investigate dynamic crack initiation under short pulse loads. Particular attention is paid to the phenomenon of delayed fracture – a fundamental fracture effect which can be observed in experiments with short pulse loads. The effect can be described in the following way: the material failure occurs after local stresses reached their maximum values, meaning that the fracture takes place at a drop stage of the local stress field and thus delay is present. It is shown that the fracture delay effect manifests itself when minimal required critical loads are applied to the system. Such loads are called threshold loads being a key tool for experimental investigation of the dynamic fracture effects. It is found that the experimentally registered fracture delay can be clearly explained within the incubation time framework. The conditions for the delay are found, threshold load parameters are evaluated and the corresponding analytical formulas are given. Additionally, a simple analogy based on a mass-spring model is discussed. Analytical formulas available for the oscillator model are used to find some non-obvious similarities between the crack instability under short pulse loads and the oscillator failure when analogous loads are applied: the dynamic fracture process in the crack vicinity appears to exhibit inertial behavior.

Analogy between crack initiation due to dynamic pulse load and mass-spring system failure: fracture delay effect

In this short communication application of the incubation time fracture criterion (ITFC) for analysis of crack initiation under short pulse loading conditions is discussed. It is shown that the ITFC can be used to predict and investigate one of the key effects of the dynamic fracture – the fracture delay. The fracture delay phenomenon manifests itself when fracture occurs at a drop stage of local stress fields. In addition to this an analogy between crack instability under pulse loads and linear oscillator failure is drawn in the work. It is shown that the fracture process exhibits inertia when intensive loads are applied and a virtual oscillator with a particular eigen frequency can be formally attributed to a cracked sample. The applied theoretical models are calibrated against experimental data on crack onset under pulse loading conditions.

The Influence of Background Ultrasonic Field on the Strength of Adhesive Zones under Dynamic Impact Loads.

The influence of background ultrasonic field on the ultimate dynamic strength of adhesive joints is studied using fracture mechanics analysis. Winkler foundation-type models are applied to describe the cohesion zone, and the incubation time fracture criterion is used. The challenging task is to study whether relatively weak ultrasound is able to decrease the threshold values of the external impact load depending on a joint model, such as an “elastic membrane” or “beam” approximation, and various boundary conditions at the ends. The specific task was to investigate the case of short pulse loading through application of time-dependent fracture criterion instead of the conventional principle of critical stress. Three different load cases, namely, step constant force, dynamic pulse, and their combination with ultrasonic vibrations, were also studied. The analytical solution to the problem demonstrates that background vibrations at certain frequencies can significantly decrease threshold values of fracture impact load. Specific calculations indicate that even a weak background sonic field is enough to cause a significant reduction in the threshold amplitude of a dynamic short pulse load. Additionally, non-monotonic dependency of threshold amplitude on pulse duration for weak background field was observed, which demonstrates the existence of optimal regimes of impact energy input. Moreover, this phenomenon does not depend on the way in which the beam edges mount, whether they are clamped or hinged, and it could be applied for micro-electro-mechanical switch design processes as an additional tool to control operational regimes.

Instability effects of the dynamic crack propagation process

Dependencies and parameters describing the crack propagation process can often exhibit unstable behavior which is not predicted by classic fracture mechanics. Here such phenomena as the crack velocity oscillations and floating stress intensity factor (SIF) values for the initiation of a pulse loaded crack can be mentioned. This paper considers SIF – crack velocity dependence (KI-ȧ dependence, mode-I fracture is considered in the paper) for dynamically propagating cracks as another example of instabilities observed in the crack propagation. Uniqueness, related to a given material, and even existence of this dependence has been a matter of discussion among researchers, since contradicting experimental results were reported in the literature over the last decades. Experiments with different loading regimes and specimen types demonstrated various shapes of the KI-ȧ curve for a particular material. However, common theoretical tools for the crack propagation prediction and simulation imply the KI-ȧ dependence to be a material property and thus suppose it to be unique for a particular material. In this work crack propagation is simulated using incubation time fracture criterion, which provides possibility to avoid the a priori given KI-ȧ dependence. A computational scheme based on finite element method and the incubation time fracture criterion was developed and various types of the KI-ȧdependence were numerically obtained for various loading conditions and materials.

Instability of critical characteristics of crack propagation

The paper presents the numerically evaluated dependence of the stress intensity factor (SIF) on crack velocity ( $$K_{I}-{\dot{a}}$$ dependence) in Homalite-100 specimens subjected to pulse loading. Experiments on crack propagation (Ravi-Chandar and Knauss in Int J Fract 25:247–262, 1984. https://doi.org/10.1007/BF00963460 ; Int J Fract 26:65–80, 1984. https://doi.org/10.1007/BF01152313 ; Int J Fract 26:141–154, 1984. https://doi.org/10.1007/BF01157550 ; Int J Fract 26:189–200, 1984. https://doi.org/10.1007/bf01140627 ) were simulated using the finite element method and incubation time fracture criterion. According to (Ravi-Chandar and Knauss in Int J Fract 26:141–154, 1984. https://doi.org/10.1007/BF01157550 ), experimental data on the SIF–crack velocity dependence exhibit unstable behavior, i.e. considerable scattering of the SIF values: a broad range of SIF values corresponds to a single crack velocity. This way, the conventional approach based on a $$K_{I}-{\dot{a}}$$ dependence being a material property is not applicable in this case. Such a phenomenon is also observed in a numerically obtained $$K_{I}-{\dot{a}}$$ dependence, meaning that the developed approach makes it possible to evade the known ambiguity of the $$K_{I}-{\dot{a}}$$ relation to predict the crack propagation.

Instabilities encountered in the dynamic crack propagation process under impact loading as a natural consequence of the dynamic fracture discreetness

Dependence of stress intensity factor (SIF) on crack velocity (KI−ȧ dependence) in Homalite-100 specimens subjected to pulse loading was numerically studied. The numerical scheme is based on finite element method and incubation time fracture criterion. Experimental results from works by Ravi-Chandar and Knauss (1984a,b,c) were used. Experimentally obtained KI−ȧ dependence is characterized by considerable scatter of the SIF values.Application of the incubation time based approach made it possible to qualitatively describe scattering of the SIF values since the used fracture condition does not rely neither on critical SIF value, nor on a a priori given KI−ȧ dependence.

Experimental observation and numerical modelling of unstable behaviour of a fast crack velocity

Dynamic crack propagation due to quasistatic loading in PMMA plates with a notch is considered. Both experimental data and results of numerical simulations are presented. The crack tip position was registered using slit-scan photography. Numerical simulations were performed using the finite element method and the incubation time fracture criterion. Special attention was paid to the unstable behaviour of the crack velocity. Processing of the experimental data revealed oscillations of the crack velocity, which were qualitatively obtained using the numerical model.

Investigation of strength characteristics of aluminum alloy under dynamic tension

The study presents the results of experimental-theoretical analysis for aluminum alloy subjected to static and dynamic tension on samples of different types. The material was tested under initial coarse-grained (CG) and in ultrafine-grained (UFG) condition. The time dependence of the tensile strength is calculated using an incubation time fracture criterion based on a set of fixed constants of the material.

Structural-time nature of the dynamic instability of the fracture process

Principal effects of dynamic instability of the fracture process are investigated. Particularly an issue of a dependence of stress intensity factor (K) on crack velocity (v) is discussed. Uniqueness, related to the given material, and even existence of this dependence has been a matter of discussion among researchers, since contradicting experimental results have been reported in the literature over last decades. In this paper results of numerical simulations of the crack propagation process are presented. A numerical scheme based on finite element method and incubation time fracture criterion was developed. Scattering of the K values during the propagation process is considered to be a feature principally related to a spatial-temporal nature of the fracture process. It is found that quasistatic loading is characterized by a small scatter of the K values and fitting of the data can be performed in order to obtain some well-known K - v curve. In the case of a pulse loading the scatter is much higher and it can be concluded that a wide range of K values correspond to a particular crack velocity and no unique continuous K - v curve can be associated with the process. These results are supported by well-known experimental observations. Thus, it is proved that the incubation time fracture criterion makes it possible to investigate dynamic crack propagation for a wide variety of loading conditions (quasistatic, high rate and short pulse loading) and only one extra material parameter – the incubation time is needed to predict a big variety of effects of the dynamic instability of the fracture process. This is a huge advantage comparing to a widespread approach, which involves complicated experimental determination of material strain rate dependencies and an a priori given K - v relationship.

Dependence of strength characteristics of aluminum alloys on strain rate under tension

The study presents the results of investigation for different aluminum alloys. Small samples of these materials were subjected to static and dynamic tension. A numerical analysis using an incubation time fracture criterion has been carried out. For each material a set of fixed constants were obtained that allows determine the dependencies of the tensile strength of material in a wide range loading conditions.

Dynamic crack propagation: quasistatic and impact loading

Simulation of dynamic crack growth under quasistatic loading was performed using finite element method with embedded incubation time fracture criterion. The uniqueness of the stress intensity factor – crack velocity relationship (K-v) is discussed. It is shown that the use of the structural–time approach and the fracture incubation time criterion enables us to predict successfully the results of experiments both on quasistatic and on impact loading of samples with cracks. Comparison of calculated K-v relationships with experimental data for various loading conditions leads to the conclusion that the dependence of the crack velocity on the stress intensity factor cannot be considered as a unique material law because the properties of this dependence are strongly determined by the sample configuration, the history, and the loading method.

Numerical implementation of the incubation time fracture criterion

The paper is discussing problems connected with embedment of the incubation time criterion for brittle fracture into finite element computational schemes. Incubation time fracture criterion is reviewed; practical questions of its numerical implementation are extensively discussed. Several examples of how the incubation time fracture criterion can be used as fracture condition in finite element computations are given. The examples include simulations of dynamic crack propagation and arrest, impact crater formation (i.e. fracture in initially intact media), spall fracture in plates. Applicability of the approach to model initiation, development and arrest of dynamic fracture is claimed.

Structural-temporal approach for dynamic strength characterization of gabbro-diabase

This paper presents some of the results of dynamic compression, splitting and direct-tensile tests of gabbro-diabase using two split Hopkinson bar apparatus. The results of laboratory experiments on specimens without and with notch for a wide range of loading parameters are given. Strength and deformation characteristics of gabbro-diabase were determined experimentally at high strain rates up to 10 3 s −1 . Mechanical characteristics were found to be strongly depended on the strain rate. A uniform interpretation of the rate effects of fracture of the tested gabbro-diabase is given on the basis of structural-temporal approach based on a set of fixed material constants. It is shown that temporal dependences of both the compressive and tensile strengths of the tested material can be effectively calculated using the incubation time fracture criterion.

Simulation of Dynamic Crack Propagation under Quasistatic Loading

Simulation of dynamic crack growth under quasistatic loading was performed using finite element method with embedded incubation time fracture criterion [. Experimental data, used for comparison was taken from [. ANSYS finite element software package was used in order to receive FEM solutions. The fracture criterion was implemented as an external procedure written in C++. The developed model is not using and trimming parameters. Only initial experimental conditions and material properties measured in separate experiments are used. Received dependencies for crack velocities as a function of time closely follow those observed in experiments by J.Finberg. Simulation results provide a possibility to conclude that the incubation time approach is an effective method to predict fracture initiation as well as crack propagation at various loading rates. Dependencies of an instant crack velocity on the current level of stress intensity factor received in this work for quasistatic loads and in [ for high-rate loads is discussed and compared to those experimentally observed by K. Ravi-Chandar and W.G. Knauss [ and J. Finberg [.

Threshold fracture energy in solid particle erosion

The effect of geometrical shape of eroding absolutely rigid particles on the threshold rate of failure has been studied. The Shtaerman–Kilchevsky theory of quasi-static blunt impact, which generalizes the Hertzs classical impact theory, is used for modelling the frictionless contact interaction of an axially-symmetric particle with an elastic half-space. The incubation time fracture criterion is applied for predicting surface fracture. It is shown that there exists a critical value of the particle shape parameter such that for all its lower values, the fracture energy possesses a non-zero minimal value.

Incubation time fracture criterion for FEM simulations

The paper is discussing problems connected with embedment of the incubation time criterion for brittle fracture into finite element computational schemes. Incubation time fracture criterion is reviewed; practical questions of its numerical implementation are extensively discussed. Several examples of how the incubation time fracture criterion can be used as fracture condition in finite element computations are given. The examples include simulations of dynamic crack propagation and arrest, impact crater formation (i.e. fracture in initially intact media), spall fracture in plates, propagation of cracks in pipelines. Applicability of the approach to model initiation, development and arrest of dynamic fracture is claimed.

Evaluation of energy saving operational modes for industrial fracture connected processes on the basis of incubation time fracture criterion

A problem for a central crack in a plate subjected to plane strain conditions is investigated. Mode I crack loading is created by a dynamic pressure pulse applied at a large distance from the crack. It was found that for a certain combination of amplitude and duration of the pulse applied, the energy transmitted to the sample has a strongly marked minimum, meaning that with the pulse amplitude or duration moving away from the optimal values, minimum energy required for initiation of crack growth increases rapidly. The results obtained indicate a possibility to optimise energy consumption of different industrial processes connected with fracture. Much could be gained in, for example, drilling or rock pounding where energy input accounts for the largest part of the process cost. Presumably further investigation of the effect observed can make it possible to predict optimal energy saving parameters, i.e. frequency and amplitude of impacts, for industrial devices, e.g. bores, grinding machines, and hence significantly reduce the process cost. The prediction can be given based on the parameters of the media fractured (material parameters, prevalent crack length and orientation, etc.).