Dynamics Of Crack Propagation In Brittle Materials [UPDATED]

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Numerical investigations are conducted to simulate high-speed crack propagation in pre-strained PMMA plates. In the simulations, the dynamic material separation is explicitly modeled by cohesive elements incorporating an initially rigid, linear-decaying cohesive law. Initial attempts using a rate-independent cohesive law failed to reproduce available experimental results as numerical crack velocities consistently overestimate experimental observations. As proof of concept, a phenomenological rate-dependent cohesive law, which bases itself on the physics of microcracking, is introduced to modulate the cohesive law with the macroscopic crack velocity. We then generalize this phenomenological approach by establishing a rate-dependent cohesive law, which relates the traction to the effective displacement and rate of change of effective displacement. It is shown that this new model produces numerical results in good agreement with experimental data. The analysis demonstrates that the simulation of high-speed crack propagation in brittle structures necessitates the use of rate-dependent cohesive models, which account for the complicated rate-process of dynamic fracture at the propagating crack tip.

The objective of this paper is to propose a simple physical basis to understand under which conditions rate-independent cohesive models become unrealistic representations of the cracking process. Recalling that the fracture energy is experimentally observed to be an increasing function of crack velocity, people may assume that rate-dependent cohesive models are the exclusively rigorous models. Nevertheless, rate-independent cohesive models have been successful in simulating many dynamic fracture experiments. Camacho and Ortiz [20] argued that, even within a rate-independent cohesive model there exists an intrinsic time scale, which is linked to the critical cohesive opening displacement and the elastic stress wave velocity of the bulk material. As a result, the simple rate-independent cohesive model can capture many dynamic fracture/fragmentation phenomena that appear rate-dependent. Our previous work supports this argument. We have shown that a rate-independent cohesive law, in conjunction with a rate-dependent bulk material constitutive law, is able to simulate the apparent rate-dependent fracture of ductile metallic materials [28]; additionally, we have showed in tensile tests of ceramics [29] that rate dependence can be obtained as the product of a rate-independent cohesive law combined with a multi-microcracking (nucleation and growth) mechanism.

Although successful in many cases, a rate-independent cohesive law loses effectiveness in some situations. For ductile materials, it is well known that due to the existence of an intrinsic time scale, rate-independent laws are successful in reproducing experimental results. However, for brittle materials, as it is computationally challenging to fully simulate the process zone at the crack tip, the effectiveness of a simpler rate-independent cohesive law is lost. This paper will demonstrate that while a rate-independent cohesive law fails to reproduce experimental results of crack propagation in PMMA, a rate-dependent cohesive model significantly improves the results. The rate dependence will be captured in a simple and novel formalism.

In this section we recall the experimental results of crack propagating in a pre-strained brittle PMMA strip. Part of the experimental results has been published in [46]. A detailed description can be found in [47].

In this section we use the rate-independent cohesive law to simulate the dynamic crack propagation process. Our aim is to check whether the experimentally observed G(v) curve can be successfully reproduced.

In this section we will use a rate-dependent cohesive model to perform the crack propagation analysis. To be consistent with the numerical methodology outlined previously, we use the linear-decaying irreversible cohesive law, which will be modified by the rate parameter. Motivated by the experimental observations, we assume that the crack velocity, v, is the factor that controls the rate-process in the crack-tip zone. Because the crack velocity is a macroscopic quantity, we call this cohesive

Experimental work of crack propagation in a pre-strained PMMA strip [47] is analyzed by numerical approach. Explicit dynamic FEM incorporating cohesive element technique is used to simulate the experimental work. It is found that a rate-independent cohesive model fails to reproduce the experimentally observed velocity-toughening effect. A detailed analysis of the dynamic fracture process demonstrates that the multi-microcracking mechanism happening at the crack-tip zone is the origin of the

The failure of materials due to slow crack growth, under dynamic loading conditions, is analyzed in terms of crack velocity, stress intensity relationships. It is shown that this type of analysis can fully describe the failure characteristics for both constant strain-rate and constant stress-rate loading. The analysis is used to predict the variations of strength and subcritical crack growth with strain-rate and stress-rate. Application of the analysis to several ceramic systems give data which are entirely consistent with available experimental data.

The subject of crack propagation, which is related to the subject of how things break, is an important area of research in material science. Despite the technological importance of crack propagation the subject has, only recently, received some theoretical attention. This neglect occurred, partly, because the subject is too difficult to deal with (theoretically or experimentally). In part, this difficulty stems from the fact that the crack propagation is a non-equilibrium process. In fact, atoms near a crack tip are under tremendous amount of stress and moving so fast that the concept of temperature is not defined clearly. Many of the solid-state physics models are applicable to a perfect crystalline solid and do not apply to a crystal with a defect (crack). The main motivation for the study of crack propagation is because materials fail through the propagation of cracks.

With the advent of powerful computers, sophisticated molecular dynamics codes, and advanced visualization techniques it is now possible to tract the dynamics of the crack propagation in materials. A crack in a material includes a long-range strain/stress field. This indicates that for any computer simulation of the crack to converge, satisfactorily, a large number of atoms need to be included.

Materials are classified into two categories brittle or ductile. A brittle material shatters with a strike (like a glass), while in a ductile material, the strike causes it to deform (like a metal). In the brittle materials, the failure is believed to be due to the breaking of chemical bonds, while in ductile materials, the failure is believed to be due to the emission of dislocations. Most solids make a transition from a brittle to a ductile phase at a certain temperature. Presence of defects near a crack tip could lead to the strengthening of the material and prevent propagation of the crack tip.

A summary of some of the important questions concerning the crack propagation in materials are as follows: (a) What is the mechanism of crack propagation in a brittle material, (b) what is the mechanism of crack propagation in a ductile material, (c) can a crack propagate through breaking bonds in a material that is originally ductile, (d) is there a critical tensile load that will initiate the propagation of a crack, (e) what is the ultimate speed of a crack, (f) what kind of effects the defects have on the strength of a material, (g) what is the effect of interface on the propagation of the crack. In order to answer some or the entire above questions one need to employ an efficient molecular dynamics code coupled to a visualization tool.

The data generated by a molecular dynamics computer simulation of crack propagation includes positions and velocities of all the atoms in the system at each time step. The data can be fed into a graphic engine for visualization and animation. Due to the specific application at hand, one requires to consider a very large system size. However, most of the important dynamics take place near the crack tip and, therefore, majority of the atoms that are far away from the crack tip are doing the usual vibrations about their equilibrium sites. By visualizing only those atoms that are dynamically important (atoms near the crack tip), one could reduce the memory need as well as image processing time. The data generated from the simulation could be screened and store only those that are relevant to the atoms close to the crack.

One improvement to the visualization/animation described in the previous paragraph is to map not only the propagation of the crack but also its temperature. This is important, because in most of the computer simulations of crack propagation, energy density deposited near the crack tip is so immense that could lead to the melting of the crack tip ( Holland 98). This is an unrealistic artifact of the interatomic interaction model that is employed in the simulation and can hardly occur in real crack propagation.

Dynamic crack propagation drives catastrophic solid failures. In many amorphous brittle materials, sufficiently fast crack growth involves small-scale, high-frequency microcracking damage localized near the crack tip. The ultrafast dynamics of microcrack nucleation, growth, and coalescence is inaccessible experimentally and fast crack propagation was therefore studied only as a macroscale average. Here, we overcome this limitation in polymethylmethacrylate, the archetype of brittle amorphous materials: We reconstruct the complete spatiotemporal microcracking dynamics, with micrometer/nanosecond resolution, through post mortem analysis of the fracture surfaces. We find that all individual microcracks propagate at the same low, load-independent velocity. Collectively, the main effect of microcracks is not to slow down fracture by increasing the energy required for crack propagation, as commonly believed, but on the contrary to boost the macroscale velocity through an acceleration factor selected on geometric grounds. Our results emphasize the key role of damage-related internal variables in the selection of macroscale fracture dynamics. 2b1af7f3a8