High Crack Velocities Research Articles

Kinetics, stages and fracture modes of stress-corrosion cracking in ZK60 and AZ31 alloys

The kinetics and fractographic features of stress corrosion cracking (SCC) in ZK60 and AZ31 alloys was investigated. It is established that ZK60 alloy possesses higher SCC resistance and fracture toughness compared to those of AZ31 alloy as is evidenced by the higher threshold stress intensity factors K1SCC and Kc. However, the lower average velocity of the stable SCC is observed in AZ31 alloy than in ZK60 one. Stable SCC occurs in two sub-stages, the first of which is featured by the lower crack growth rate and brittle fracture mode, while the higher crack velocity and quasi-cleavage fracture mode herald the second sub-stage. The crack growth velocities at specific SCC stages as well as stress intensity factor Kf associated with the alternation of the fracture mode are evaluated.

Peridynamic investigation of dynamic brittle fracture

AbstractIn this study, we investigate the dynamic fracture process in amorphous brittle materials using 3D peridynamic analyses of dynamic crack propagation in PMMA plates subjected to quasi‐static loads. This loading condition allows one to assume, that the crack will accelerate to a steady‐state velocity and will continue propagating straight forward at a constant velocity. Dynamic crack instability and its effect on the fracture surface creation as well as the dissipated energy is analyzed numerically for cracks propagating at different velocities. Simulations reproduce many salient features of experimental observations, such as instabilities occurring at the crack tip for cracks propagating above a certain critical velocity. It is shown from the simulations, that increasing crack velocity results in excessively repeated micro‐branching. An increased energy dissipation is also observed at higher crack velocities in the simulations, which correspond to the well known velocity toughening effect. Simulations also reproduce a limiting crack speed, which is below the theoretical limit, i.e. the Rayleigh wave speed.

VISCOELASTIC RESPONSE DURING CRACK PROPAGATION OF UNFILLED AND FILLED SBR

ABSTRACT The crack propagation behavior of unfilled and filled styrene–butadiene rubber (SBR) in steady and dynamic tearing was investigated using tensile tests on trousers samples and tear fatigue measurements on single edge notched tension (SENT) samples, respectively. For the unfilled sample, both types of measurements indicated that the tearing energy is dominated by the viscoelastic response of the polymer. This was demonstrated by the creation of crack growth master curves using the horizontal shift factors obtained from mastering the complex modulus. The tearing energy increased with increasing crack velocity and decreasing temperature as required by the time-temperature superposition principle. The crack growth master curves followed a power law with the same exponent for steady and dynamic tearing. This exponent agrees fairly well with the exponent predicted by linear viscoelastic crack propagation theory. For steady tearing at high crack propagation rates, systematic deviations from the master curves appeared, which were attributed to flash temperature effects. For the filled SBR, which contained 50 phr carbon black, only dynamic tearing was found to be dominated by the viscoelastic response of the polymer. For steady tearing, filler networking seemed to alter crack propagation rates significantly, so that the viscoelastic fingerprint was no longer visible. For the filled sample, additional measurements with a high preload were conducted. It was demonstrated that a single master curve can be constructed, only if the (static) preload contribution is neglected and the dynamic contribution of the energy density is used for the evaluation of the tearing energy. This master curve showed two distinct slopes at high and low crack velocities. It is argued that the higher slope at low crack speeds is relevant for lifetime predictions based on the integration of the Paris–Erdogan power law. Under conditions in which the viscoelastic crack propagation holds, very slow crack growth rates can be explored at reasonable testing times by measurements at elevated temperatures.

Subcritical crack growth behavior of a perovskite‐structured Ba0.5Sr0.5Co0.8Fe0.2O3−δ oxygen transport membrane

AbstractThis paper herein studies subcritical crack growth (SCG) behavior of a perovskite‐structured Ba0.5Sr0.5Co0.8Fe0.2O3−δ (BSCF) as an oxygen transport membrane material. The SCG behavior of BSCF is evaluated by a constant load method and constant stress rate method at room temperature (RT) and 800°C in air, respectively. The low crack velocity measurements are carried out by ring‐on‐ring bending tests while the high crack velocity measurements by compact tension tests. The stress rates vary approximately from 0.1012 to 101.2 MPa/min. The fracture stress increases with increasing stress rate at 800°C. The SCG parameter, n, of BSCF is determined to be 24.32 and 13.83 at RT and 800°C in air, respectively. This indicates that BSCF is more susceptible to SCG at 800°C. The strength‐probability‐time (SPT) diagram is constructed for design proposes. The stress for a lifetime of 40 years should not exceed 27.21 MPa at RT or 4.53 MPa at 800°C to assure a failure probability below 1%.

The roles of cohesive strength and toughness for crack growth in visco-elastic and creeping materials

A cohesive-zone analysis for crack propagation in a linear visco-elastic/creeping material is presented. The concept of a viscous fracture length is defined; this serves an analogous role to the elastic fracture length in determining the conditions under which fracture is controlled by the continuum crack-tip stress field. It is shown that there are two regimes for viscous crack growth. The first regime occurs in the limit of small viscous fracture lengths, when the crack-tip stress field has a region exhibiting the inverse square-root dependence expected from classical linear fracture mechanics. In this regime, the crack velocity is proportional to the fourth power of the stress-intensity factor. This is consistent with an existing analytical model developed for crack growth in linear polymers. The second regime occurs for large viscous fracture lengths, where classical fracture mechanics is not appropriate. In this regime, the crack velocity has a weaker dependence on the applied load, and can be modeled accurately by the solution to the problem of a viscous beam on an elastic foundation. At higher crack velocities, when the viscous fracture length exceeds the elastic fracture length, the expected transition to elastic fracture occurs.

Mode I fracture of a biopolymer gel: Rate-dependent dissipation and large deformations disentangled

We have designed a new experimental setup able to investigate fracture of soft materials at small scales. At high crack velocity, where energy is mostly dissipated through viscoelastic processes, we observe an increasingly large high strain domain in the crack tip vicinity. Taking advantage of our ability to determine where linear elasticity breaks down, we derive a simple prediction for the evolution of the energy release rate with the crack velocity.

Calculation of Dynamic Stress Intensity Factors for Pipes During Crack Propagation by Dynamic Finite Element Analysis

A dynamic finite element analysis method was proposed for calculating the dynamic stress intensity factors for pipes during crack propagation. The proposed method can directly calculate the stress intensity factors without the simplification used in theoretical analyses, and it can consider the effects of the crack velocity and gas decompression. It was found that the stress intensity factors of long propagating cracks in pipes saturated at a certain value in the case of a high crack velocity. However, the stress intensity factors for pipes were in good agreement with those of band plates in the case of a high crack velocity, the stress intensity factors for pipes were different from those of band plates in the case of a low crack velocity. This result could be explained by the effect of bulging on the stress distribution around a crack tip. The effect of bulging was more prominent for pipes with smaller diameters. In contrast, the dynamic stress intensity factors for band plates were in good agreement with the theoretical values that consider the dynamic effects and tended to decrease monotonically with increasing crack velocity. Additionally, the effects of gas decompression, caused by leakage from opened cracks, on the stress intensity factors for pipes were investigated. An explanation of the change in crack direction, reflecting a change from an axial crack to a circumferential crack, which is observed in actual pipeline fractures, was given by analyzing the ratio of the longitudinal stress to lateral stress.

Moving polarization saturation crack in ferroelectric solids

A moving polarization saturation (PS) model is proposed to study the plane problem of a Yoffe-type crack moving with constant velocity in ferroelectric materials considering electric saturation. Based on the extended Stroh formalism, the model is solved using complex function method. The closed-form expressions for the electroelastic fields are obtained in a concise way. Results are shown to converge to known solutions for static PS model and the moving linear piezoelectric model. Numerical results for PZT-5H material are given graphically. It can be deducted that the dynamic intensity factors are dependent of the electric field and the velocity. It predicts that crack propagation may be promoted by a positive applied electrical field and inhibited by the negative one. For high crack velocity, 0.28 times minimum body wave speed, the hoop stress is maximal for an angle qs0.

Dynamic toughness in elastic nonlinear viscous solids

This work addresses the interrelationship among dissipative mechanisms—material separation in the fracture process zone (FPZ), nonelastic deformation in the surrounding background material and kinetic energy—and how they affect the macroscopic dynamic fracture toughness as well as the limiting crack speed in strain rate sensitive materials. To this end, a micromechanics-based model for void growth in a nonlinear viscous solid is incorporated into a microporous strip of cell elements that forms the FPZ. The latter is surrounded by background material described by conventional constitutive relations. In the first part of the paper, the background material is assumed to be purely elastic. Here, the computed dynamic fracture toughness is a convex function of crack velocity. In the second part, the background material as well as the FPZ are described by similar rate-sensitivity parameters. Voids grow in the strain rate strengthened FPZ as the crack velocity increases. Consequently, the work of separation increases. By contrast, the inelastic dissipation in the background material appears to be a concave function of crack velocity. At the lower crack velocity regime, where dissipation in the background material is dominant, toughness decreases as crack velocity increases. At high crack velocities, inelastic deformation enhanced by the inertial force can cause a sharp increase in toughness. Here, the computed toughness increases rapidly with crack velocity. There exist regimes where the toughness is a non-monotonic function of the crack velocity. Two length scales—the width of the FPZ and the ratio of the shear wave speed to the reference strain rate—can be shown to strongly affect the dynamic fracture toughness. Our computational simulations can predict experimental data for fracture toughness vs. crack velocity reported in several studies for amorphous polymeric materials.

Ductile–brittle transitions in the fracture of plastically deforming, adhesively bonded structures. Part II: Numerical studies

To enable the effective and reliable use of structural adhesive bonding in automotive applications, the cohesive properties of a joint need to be determined over a wide range of loading rates. In this paper, a strategy for determining these properties has been described and used to analyze a set of experimental results presented in a companion paper. In the particular system studied, a crack growing in a toughened quasi-static mode could make a catastrophic transition to a brittle mode of fracture. The cohesive parameters for both the toughened and brittle modes of crack growth were determined by comparing numerical predictions from cohesive-zone simulations to the results of experimental tests performed using double-cantilever beam specimens and tensile tests. The cohesive parameters were found to be essentially rate-independent for the toughened mode, but the toughness dropped by a factor of four upon a transition to the brittle mode. The results of wedge tests were used as an independent verification of the cohesive parameters, and to verify that the quasi-static properties remained rate-independent to very high crack velocities corresponding to conditions of low-velocity impact. The effects of friction, and the use of the wedge test to determine cohesive parameters, were also explored.

Ductile Crack Propagation Characteristics in Thin Steel Tubes

Static ductile crack propagation tests were conducted using two pressurised thin carbon-manganese steel tube specimens, and the crack tip opening angle (CTOA) was measured using digital images captured on specimen surface. The critical values of CTOA for static crack propagation decreased with crack extension while propagating crack was short. After the crack grew up to the distance of the tube specimen thickness, the critical CTOA exhibited nearly constant. These tendencies were the same as those of referential data in the thin single edge notched tension (SENT) specimens of the same tubes. Using the data of both tube specimens and SENT specimens, it was noted that the higher crack velocities slightly reduced the constant CTOA. A global constraint factor was calculated for each tube specimen, and the constant CTOA decreased with the increase of the global constraint factor. In addition, a dynamic ductile crack propagation test of a tube specimen was carried out, and a crack velocity was measured. The estimation of the constant CTOA for dynamic crack propagation in the tube specimen was performed by using the crack velocity.

Higher Order Mode-I Elastodynamic Stress and Displacement Fields of Dynamic Crack Propagation in Brittle Materials

Higher order Mode-I elastodynamic stress and displacement fields at the tip of a crack are calculated by the perturbation method up to the 1-st order. The present method of derivation utilizes a certain condition at the crack tip and resolves the difficulty encountered otherwise. Including the 1-st order stress field we find that the well known hoop stress maximum at high crack velocity, which is considered to determine the direction of the branching, disappears when the crack is accelerated.

Hot Cracks in Rubber: Origin of the Giant Toughness of Rubberlike Materials

We study crack propagation in rubberlike materials and show that the nonuniform temperature distribution which occurs in the vicinity of the crack tip has a profound influence on the crack propagation, and may strongly enhance the crack propagation energy G(v) for high crack velocities v. At very low crack-tip velocities, the heat produced at the crack tip can diffuse away, but already at moderate crack-tip velocities a very large temperature increase occurs close to the crack tip resulting in a "hot-crack" propagation regime. The transition between the low-speed regime and the hot-crack regime is very abrupt and may result in unstable crack motion, e.g., stick-slip motion or catastrophic failure.

Evolution of dynamic fractures in poly(methyl methacrylate)

The results from single edge notched tension tests support the idea that the nucleation, growth, and coalescence of penny shaped microcracks govern the fracture evolution in poly(methyl methacrylate) (PMMA). The density of the microcracks (seen as parabolic markings on the fracture surface), and therefore the roughness of the fracture surface, increases with the crack velocity. The damage beneath the main fracture surface also increases with crack velocity and the crack length. This damage is formed by attempted and successful crack branches originating from the main fracture and other cracks propagating alongside the main fracture. Microscopy of the virgin material and fractured surfaces showed no consistent evidence of pre-existing flaws, dust particles, or other impurities that would provide nucleation sites for the microcracks. It can therefore be argued that the material microstructure, chain length in particular, must play a significant role in the nucleation of microcracks. This can be supported by an earlier work in which strong dependence of the microcrack density on the molecular weight of PMMA was reported. Crack velocity measurements show rapid initial acceleration of the crack followed by nearly constant mean velocity. The mean velocity is found to increase with decreasing initial notch depth. Oscillations in the crack velocities were also observed and they were more pronounced at higher crack velocities. To a large extent the degree of crack velocity oscillation is dependent on the filtering technique applied to process the raw data. Therefore, no conclusive correlation between the fracture history and surface was obtained.

Crack Growth in the High Crack Velocity Region for Binary Sodium Silicate Glasses.

The crack growth behavior in the high crack velocity region (region III) for binary sodium silicate glasses was investigated by using a DCDC (double cleavage drilled compression) specimen under compressive stress. For 15mol% Na2O glass, despite the anomalous characteristic of the bulk modulus, subcritical crack growth in region III was detected. The slope of stress intensity factor (KI)-crack velocity (v) curve for silicate glass depended on the number of non-bridging oxygen per SiO4 tetrahedron rather than on the alkali content in the glass. This compositional dependence of the slope of KI-v curve for silicate glasses could not be explained in terms of thermally activated crack growth process where the crack-tip shape would vary with the pressure derivative of bulk modulus. The smaller KI-v slope and the higher KIC value of 35mol% Na2O glass may be related to the structural change from a three-dimensional network to a two-dimensional network because of the introduction of many non-bridging oxygens into the silica network.

Dynamic overshoot in -iron by atomistic simulations

We present large-scale molecular dynamic simulations of microcrack growth in -iron based on an N-body potential model which gives a good description of defect energetics, anisotropic elasticity and phonon frequency spectra. We demonstrate dynamic overshoot of a pre-existing microcrack under impact loading. We show that the basic behaviour of the simulations is in agreement with the predictions of continuum models. Dynamic phenomena, such as scattering of stress waves at crack faces, acoustic emission (due to bond breakage) and reflections of the stress waves from sample borders, are studied here in detail. The results on microcrack growth, unimpeded by the wave reflections from external sample borders, indicate that under fast loading or at high crack velocities, i.e. under high strain rates, transient twin formation is possible from the crack tip with later detwinning at free crack faces as the crack advances: a twinning equivalent to virtual Knott dislocations.

Universal features of the microbranching instability in dynamic fracture

Abstract We investigate the universality of the microbranching instability, by comparison between the characteristics of a mode I dynamic crack, in both poly(methyl methacrylate) (PMMA) and soda-lime glass. We demonstrate the existence of the instability in glass, and the similarities of its features in both PMMA and glass. In glass, as in PMMA, there is a well defined threshold for the appearance of microbranches. This threshold is higher in glass (0.44C∗R) than in PMMA (0.36C R). In both materials, the mean branch length increases linearly with increasing mean velocity of the crack and the branch profile is identical. In both materials the branches are the cause for the observed roughness of the fracture surface where, in glass, surface roughening is accompanied by fragmentation. Finally, a similar three-dimensional-to-two-dimensional transition occurs in both materials at high crack velocities.

A molecular dynamics investigation of rapid fracture mechanics

Dynamic fracture is investigated for two-dimensional notched solids under tension using million atom systems. Brittle material and ductile material are modeled through the choice of interatomic potential functions which are Lennard-Jones and embedded-atom potentials, respectively. Numerical calculations are carried out on the IBN SP parallel computer and molecular dynamics is implemented using a spatial-decomposition algorithm. Many recent laboratory findings occur in our simulation experiments. A detailed comparison between laboratory and computer experiments is presented, and microscopic processes are identified. For rapid brittle fracture, the dynamic instability of the crack growth is observed as the crack velocity approaches one-third of the Rayleigh wave speed. At higher crack velocity, the crack either follows a wavy path or branches and the anisotropy due to the large deformation at the crack tip plays the governing role in determining the crack path. Limited comparison of rapid brittle fracture process with the rapid ductile fracture process is made.

Quantitative Characterization of Indentation Crack Path in a Cubic Zirconia—10 vol% Alumina Composite

Stereological measurements were performed to characterize the indentation crack path in a cubic zirconia—10 vol% alumina (c‐ZrO2‐10 vol% Al2O3) composite. Cracks were generated using Vickers indentation, and the crack propagation behavior was characterized as a function of the indentation loading/unloading rates. Cracks that were produced by Vickers indentation formed at higher crack velocities as the loading/unloading rates increased. The amount of contact between the crack and the Al2O3 particles increased as the indentation rate decreased. The total number of crack—particle interactions per unit crack length also increased as the indentation rate decreased, because of an increase in the number of particles that were fractured per unit crack length, whereas the number of particles that were debonded remained relatively constant as the indentation rate changed. These results suggest that residual thermal mismatch stresses have predominant control of the crack path at lower crack velocities (low indentation loading/unloading rate), whereas elastic mismatch stresses predominate at higher crack velocities (high indentation loading/unloading rate).

Subcritical Crack Growth in Silica Optical Fibers in Wide Range of Crack Velocities

Crack growth in silica optical fibers was measured directly in a wide range of crack velocities da/dt (10−13 < da/dt < 10−5 m/s) by improving our previous method. The slope in log‐log plots of the crack velocity versus the stress intensity factor data was revealed to increase with the crack velocity, e.g., slope, 23.3 for da/dt < 10−10 m/s, and 39.7 for da/dt > 1(10−8 m/s. The data were also found to be fitted well by the exponential law in the whole range of da/dt, rather than the power law. Additionally, the fiber data were shown to be close to those reported for bulk silica specimens having large cracks for high crack velocities where the bulk specimens were tested.