Dynamic Fracture Experiments Research Articles

Dynamic crack kinking from a PMMA/Homalite interface

The behavior of a pre-existing, dynamically loaded, interfacial crack kinking away from the interface separating two materials was experimentally investigated under dynamic loading conditions. Dynamic fracture experiments were performed on pre-cracked bimaterial panels of PMMA bonded with Homalite-100 impact loaded using a high-speed gas gun. By varying the location of impact, a large range of mixed mode loading at the crack tip was produced. Information about the stress state surrounding the crack tip was obtained through use of the lateral shearing interferometer of coherent gradient sensing in conjunction with high-speed photography. The high-speed interferogram corresponding, to the time of crack initiation was analyzed in each case to find the preinitiation mode mixity at the crack tip. Measurement of both the local initiation mode mixity and the crack kink angle allows for possible extension of existing quasi-static interface crack kinking criteria, such as maximum opening stress or maximum energy release rate, to the case of dynamic loading. It was found that for bimaterial systems with small material property mismatch, such as the PMMA/Homalite system, the maximum opening stress criterion accurately predicts the relation between crack tip mode mixity and resulting kink angle for small initial crack kinking speeds.

A statistics and energy based theory of dynamic fragmentation

Mott [1] developed a statistical theory of fracture and fragmentation to account for the frequency and statistical distribution of fracture in impulsively loaded rapidly expanding metal cylinders. In the present work the dynamic fracture and fragmentation theory of Mott is extended to account for fracture dissipation within the failure zone. Dynamic fracture and fragmentation experiments were performed on rings of uranium-6%-niobium (U6N). Comparisons between experiment and theoretical predictions are systematically explored.

Dynamic crack propagation in large steel specimens

Dynamic fracture experiments on crack initiation and crack growth in single edge bend specimens are performed. The impact velocity is in the range of 14 to 50 m/s and the specimen size is 320×75 mm with a thickness varying from 18 to 40 mm. The experiments are recorded by high speed photography. Two different steel qualities are investigated and their constitutive characterisation are obtained from uni-axial tension tests and shear tests with strain rates in the range 10 −4 to 10 3 s −1 and tension tests at temperatures between −196 and 600°C. One of the materials exhibits a transition from a ductile dimple fracture to a brittle cleavage fracture as the loading velocity increases and as the specimen thickness increases. Scanning electron microscope fractographs show that the density of plastic bridges within cleavage ligaments decreases with increasing impact velocity and with increasing specimen thickness. It is also noted that the local crack propagation direction deflects from the global one in cleavage fracture areas with a high density of plastic bridges. The other material fails in a ductile mode in all the investigated cases.

Role of plasticity in heat generation during high rate deformation and fracture of polycarbonate

Abstract The role of plastic deformation in generating heat during dynamic compression and fracture of polycarbonate was examined in a combined experimental and numerical investigation. Split Hopkinson pressure bar (SHPB) experiments and opening mode dynamic fracture experiments were performed to measure the thermomechanical response of polycarbonate at various loading conditions. A companion set of dynamic, thermomechanically coupled explicit finite element simulations of the tested geometries was performed to isolate the temperature increase of the polymer due to plasticity effects only, and these were then compared to the experiments to identify the role of plasticity in the overall heating of the polymer. Temperature measurements during the experiments were made with a remote sensing technique that utilizes the detection of infrared radiation. Polycarbonate was observed to have a rate dependent yield and plastic deformation response under uniaxial compression. For the strain rates tested in the SHPB experiments (400 to 3000 s−1), the fraction of plastic work rate converted to heat was found to be approximately 0.5. The dynamic fracture experiments indicated that the maximum temperature increase in the region surrounding the propagating crack was over 100 K, and the crack tip velocity was limited to approximately 60% of the Rayleigh wave speed. The numerical simulations used the plastic behavior of polycarbonate observed during the compression SHPB experiments as inputs for an incremental plasticity model that uses a rate dependent Mises yield surface and isotropic hardening. Plastic deformation was the only source of material heating in the simulations. Good agreement between the SHPB experiments and the numerical simulations was seen for both stress and temperature during the compression event. Crack growth during the dynamic fracture simulations was imposed by a manual node release technique that duplicated the crack growth speed observed in the experiments. The dynamic fracture simulations which only included the thermoplastic effect significantly under-predicted the temperature increase in the region surrounding the propagating crack. The results indicate that plastic deformation is not the dominating source of heat generation during the dynamic fracture of polycarbonate, it only accounts for about 8% of the measured heating. Additional effects, such as thermofracture coupling, must be considered in the simulations if a more accurate comparison is to be made with experiments.

Energy dissipation and path instabilities in dynamic fracture of silicon single crystals

Brittle fracture usually proceeds at crack driving forces which are larger than those needed to create the new fracture surfaces. This surplus can lead to faster crack propagation or to the onset of additional dissipation mechanisms. Dynamic fracture experiments on silicon single crystals reported here show several distinct transitions between different dissipation mechanisms. Cleavage fracture is followed by the propagation of a faceted crack front, which is finally followed by a path instability and the propagation of multiple cracks. The fracture surface qualitatively corresponds to the mirror, mist, and hackle morphology of amorphous materials. However, the corresponding fracture mechanisms, which remain largely unknown in the amorphous materials, can clearly be identified here.

Experimental investigation of transient thermoplastic effects in dynamic fracture

In a recent paper, we investigated the extent to which transient thermoelastic effects could affect dynamic crack initiation [Rittel, D., 1998a. Experimental investigation of transient thermoelastic effects in dynamic fracture. Int. J. Solids and Structures 35(22), 2959–2973]. In the present paper, we pursue this line of investigation by investigating transient thermoplastic effects. Three characteristic experiments are described which address the assumptions of the isothermal nature of dynamic crack initiation in two representative materials: ‘ductile’ polycarbonate and ‘brittle’ polymethylmethacrylate. First, by varying the global (baseline) temperature of dynamic fracture experiments, it is shown that these two materials react quite differently. The crack-tip temperature of the PC specimen rises significantly as evidenced from the failure mode at both the macroscopic and microscopic scales. By contrast, the failure mode of PMMA is apparently unaffected by temperatures below its Tg. This experiment demonstrates further that the local crack-tip temperature is likely to be different from the baseline temperature. Next, we investigate the bulk thermomechanical behavior of these two materials to quantitatively assess the temperature rise which accompanies transient adiabatic deformations. This behavior is deemed to be characteristic of that of the process zone material ahead of the crack-tip. Finally, we present thermal and fractographic results about transient temperature recordings ahead of an adiabatic shear band in a PC specimen loaded in mode II. These results show that thermomechanical couplings must be taken into account in dynamic fracture investigations. These couplings are related to the loading mode, to the strain levels reached in a typical process zone and also to the thermomechanical response of the specific material at such strain levels.

Numerical simulation of a mixed-mode dynamic fracture experiment

A time-domain boundary element method is applied to simulate mixed-mode dynamic fracture experiments performed on compact compression specimens (CCS) in a split Hopkinson bar. This numerical investigation addresses the time histories of the mode I and II stress intensity factors for the precracked CCS, the instant and angle of crack initiation as well as the resulting crack paths in dependence upon the external load. The aim of the study is two-fold: to gain deeper insight into the mixed-mode dynamic fracture process under investigation and to test the applicability of our recently developed numerical method. Numerical results are compared to experimental data reported in the literature. Furthermore, aspects of modelling the experimental set-up in the framework of the boundary element method are discussed, and advantages and shortcomings are analyzed.

Ideal Brittle Fracture of Silicon Studied with Molecular Dynamics

Dynamic fracture experiments measure crack velocity versus energy flux to the tip. We report here the first calculation of this quantity in a realistic setting, using molecular dynamics to study silicon. The results require relating the short length and time scales of simulations to the long length and time scales of experiments.

An experimental study of dynamic delamination of thick fiber reinforced polymeric matrix composites

Dynamic delamination of thick fiber reinforced polymeric matrix composite laminates is investigated using optical techniques and high-speed photography. The laminates used in this work are graphite/epoxy fiber reinforced, 65 percent fiber volume fraction, composite plates consisting of 48 plies (6 mm plate thickness). Two different laminate layups are tested: a quasi-isotropic arrangement and a unidirectional arrangement. The experimental setup consists of 152 mm×152 mm square plates impact loaded in an outof-plane configuration using a high-speed gas gun. Impact speeds range from 1 m/s to 30 m/s. Real-time imaging of the laminate out-of-pane displacement is performed using the lateral shearing interferometer of coherent gradient sensing (CGS) in conjunction with high-speed photography. Onset of dynamic delamination can be observed, and quantities such as delamination speeds (in some cases up to 1800 m/s) are measured and reported. A brief comparison is made with dynamic fracture experiments of the same material conducted in a separate study.

Fractal effects of crack propagation on dynamic stress intensity factors and crack velocities

Crack extension paths are often irregular, producing rough fracture surfaces which have a fractal geometry. In this paper, crack tip motion along a fractal crack trace is analysed. A fractal kinking model of the crack extension path is established to describe irregular crack growth. A formula is derived to describe the effects of fractal crack propagation on the dynamic stress intensity factor and on crack velocity. The ratio of the dynamic stress intensity factor to the applied stress intensity factor K(L(D, t), V)/K(L(t), 0), is a function of apparent crack velocity Vo, microstructure parameter d/Δa (grain size/crack increment step length), fractal dimension D, and fractal kinking angle of crack extension path ϑ. For fractal crack propagation, the apparent (or measured) crack velocity Vo, cannot approach the Rayleigh wave speed Cr. Why Vo is significantly lower than Cr in dynamic fracture experiments can be explained by the effects of fractal crack propagation. The dynamic stress intensity factor and apparent crack velocity are strongly affected by the microstructure parameter (d/Δa), fractal dimension D, and fractal kinking angle of crack extension path ϑ. This is in good agreement with experimental findings.

Interlaminar dynamic crack propagation

Effective computational procedures are established and used to characterize dynamic crack propagation along material interfaces between isotropic and orthotropic materials. We first simulate a dynamic fracture experiment in which crack propagation occurs along an interface between PMMA and steel in a dynamically loaded bend specimen. In the analysis, the dynamic energy release rate and mixed-mode stress intensity factors are extracted from finite element field solutions using suitably formulated conservation integrals. These variables form the basis for defining an interface fracture criterion under dynamic conditions. In order to propagate the crack according to such a criterion, an iterative procedure is utilized to determine the correct crack tip velocity history. An important computed result, which is consistent with experimental observation, is that the energy release rate decreases as the crack propagation accelerates. The physical interpretation of this result is that less energy is absorbed by the moving crack as its velocity increases. In the second part of our study, the computational procedures are modified for the dynamic fracture analysis of a thin composite panel consisting of differently oriented orthotropic laminae. Here we investigate the interplay between delamination and buckling of the more complex structure. It is assumed that the panel contains an initial finite interlaminar crack and is subjected to a uniaxial compressive load. Without any crack extension, two buckling modes are observed under quasistatic conditions. One is characterized by an overall panel buckling and the other is dominated by a local ligament buckling near the crack. Coupling of the two modes produces not only a lower critical buckling load but also an unstable post-buckling behavior. Therefore, an embedded delamination is seen to create imperfection sensitivity, leading to limit load type behavior. Such a condition is potentially troublesome for compression loaded thin composite panels. In addition, the large compressive load may also trigger a dynamic propagation of the embedded delamination. We have simulated this unstable dynamic crack growth using the iterative method and a simplified delamination criterion. In the simulation, the energy release rate, the mixed-mode stress intensity factors and the resulting crack tip speed are obtained. These results predict that an existing embedded delamination can weaken and significantly alter the post-buckling behavior of composite panel.

Dynamic fracture detection using the force-displacement reciprocity: application to the compact compression specimen

Dynamic fracture toughness is determined by impacting fracture specimens and determining the onset of crack propagation. In such experiments characteristic impedance (actuator-specimen) matching problems can affect the accuracy of the measured forces. In addition, fracture time is mostly determined by means of surface rather than bulk devices (e.g. gages). In this paper we address these issues in linear-elastic materials. Based on the H-integral we show that either the measured forces or the displacements (whichever is more accurate) can be used to calculate the evolutions of the stress intensity factors. These evolutions must be identical by virtue of the reciprocity between forces and displacements, at least until some bulk fracture process develops. Examples are presented to illustrate how these observations can be applied to 'fine-tune' dynamic fracture experiments and complement fracture gage readings.

A Compact Testing System for Dynamic Fracture Studies

Abstract Development of a compact instrumented impacting apparatus for dynamic fracture studies designed on the lines of a swing pendulum machine is described. Salient features of the system and instrumentation calibration procedures are presented. The dynamic characteristics of the system are explained with the aid of a simple inertial model. Results of dynamic fracture experiments conducted on aluminum 6061 alloy and polymethylmethacrylate (PMMA) are discussed.

An interpretation of Twyman-Green interferograms from static and dynamic fracture experiments

The application of a Twyman—Green interferometer to measurements in static and dynamic fracture mechanics is described. Twyman—Green interferometry shows the absence of a dominant singular field in the out-of-plane deformation in the vicinity of a crack. For relatively brittle fracture and except near the crack flanks, the spatial gradient of the out-of-plane displacement for a quasi-statically propagating crack is well predicted by elastostatic simulations. In addition, this method has been employed to elucidate certain transient features involving cracks propagating at large fractions of the material wave speeds. The free surface out-of-plane deformation surrounding a constant velocity dynamically propagating crack in a plate is compared with the equivalent elastostatic case. It appears that the dynamic deformation may not be obtained from the static deformation simply by a Prandtl—Glauert mapping as might be suggested by the solution for the equivalent two-dimensional generalized plane stress problem. Alternatively, the general character of the three-dimensional dynamic surface deformation may be approximately fitted by a Doppler mapping of the static deformation when scaled by the crack to plate wave speed ratio.

A theory of caustics for mixed-mode fast-running cracks (higher-order theory) : T. Nishioka, R. Murakami, Y. Ohishi & N. Maeda, JSME International Jpurnal, Series A: Mechanics & Material Engineering, 37(1), 1994, pp 22–30

A higher order theory of caustics for mixed mode running cracks is developed by using the general asymptotic solutions for a dynamically propagating crack tip. The analytical expressions are obtained for the Jacobian equation that determines the initial curve, and for the image equation on a screen. With the use of the higher order coefficients determined by the finite element simulations of actual dynamic fracture experiments, the effects of the higher order terms on the caustic curve are investigated on the basis of the present theory

The energy release rate for transient dynamic mode 𝐼 crack propagation in a general linearly viscoelastic body

A mathematical model of a semi-infinite mode I crack that suddenly begins to propagate at constant speed is constructed for a general linear viscoelastic body. Expressions for the Laplace transform of the stress, displacement, and stress intensity factor are derived for general loadings. A Barenblatt type process zone is incorporated into the model and used to determine the total energy flux into the crack tip. This energy release rate, G ( t ) G\left ( t \right ) , is constructed for two specific loadings: one following the advancing crack tip, the second remaining fixed as the crack tip advances. In each case G ( t ) G\left ( t \right ) is analyzed by asymptotic and numerical methods to determine its qualitative form and, in particular its rate of decay to its steady-state value. The effect of such simplifying assumptions as quasi-static propagation or an elastic material is also illustrated. The second loading is intended as an idealized model of the dynamic fracture experiments of Ravi-Chandar and Knauss [13–16].

A Theory of Caustics for Mixed-Mode Fast Running Cracks. 4th Report. Higher-Order Theory.

A higher-order theory of caustics for mixed-mode running cracks is developed using the general asymptotic solutions for a dynamically propagating crack-tip. The analytical expressions are obtained for the Jacobian equation that determines the initial curve, and for the image equations on a screen. With the use of the higher-order coefficients determined by the finite-element simulations of actual dynamic fracture experiments, the effects of the higher-order terms on the caustic curve are investigated on the basis of the present theory. It was found that the r1/2 stress field plays an important role in the formation of caustic patterns.

On the Extent of Dominance of Asymptotic Elastodynamic Crack-Tip Fields: Part I—An Experimental Study Using Bifocal Caustics

The question of the domain of dominance of mode I asymptotic elastodynamic crack-tip fields is investigated experimentally for the cases of dynamically loaded stationary cracks as well as dynamically propagating cracks. The experiments reported are on three-point bend specimens loaded dynamically using a drop-weight tower. An optical configuration leading to a bifocal high-speed camera is proposed. This is used in conjunction with the method of caustics to obtain apparent dynamic stress intensity factor measurements simultaneously from two different regions around the crack tip. The results of this study indicate that three-dimensional and transient effects necessarily have to be taken into account in the interpretation of dynamic fracture experiments.

Dynamic fracture experiment of laminated glass and its considerations.

Square plates of laminated glass, whose interlayer is the polyvinyl butyral, are impacted transversely by a circular steel ball. The impact critical energies Uc and Up, which are the energy to initiate a crack in the outerlayer glasses and penetration energy of the ball, are measured by changing the dropping height of the ball. The static bending strength and Uc are dependent on the total thickness T of glass in the laminated glass. But, Up is independent of T and dependent on the thickness of the interlayer. In the laminated glass, the crack initiates from the glass of the impact side, and the next cracks initiate from the glass of the side on the reverse of the impact side. The penetration fracture of the laminated glasses consists of three steps. The first step is until initial cracks initiate in the outerlayer glasses, the second step is the bending fracture of the laminated glass, and the third step is the fracture due to shearing of the interlayer.

A Note on Dynamic Displacement Measurements Using Hall Effect Sensors

Abstract We describe a transducer suitable for dynamic displacement measurements. The transducer uses a commercially available Hall effect sensor and a permanent magnet. Displacements are obtained by measuring the variation in magnetic field strength along the permanent magnet with the Hall effect sensor. To illustrate the capabilities of the transducer, we discuss three application examples. The first example demonstrates the good performance of the transducer under impact loading conditions and for velocities of up to 10 m/s. The other two examples illustrate the usefulness of the transducer for dynamic fracture experiments.