Crack Velocity Measurements Research Articles

Size Selection of Crack Front Defects: Multiple Fracture-Plane Interactions and Intrinsic Length Scales.

Material failure is mediated by the propagation of cracks which, in realistic 3D materials, typically involves multiple coexisting fracture planes. Multiple fracture-plane interactions create poorly understood out-of-plane crack structures, such as step defects on tensile fracture surfaces. Steps form once a slowly moving, distorted crack front segments into disconnected overlapping fracture planes separated by a stabilizing distance h_{max}. Our experiments on numerous brittle hydrogels reveal that h_{max} varies linearly with both a nonlinear elastic length Γ(v)/μ and a dissipation length ξ. Here, Γ(v) is the measured crack velocity v-dependent fracture energy, and μ is the shear modulus. These intrinsic length scales point the way to a fundamental understanding of multiple-crack interactions in 3D that lead to the formation of stable out-of-plane fracture structures.

Fracture mechanics properties of fused silicas used for international space station windowpanes

AbstractThe fracture toughness and slow crack growth (SCG) parameters of a quartz‐based silica and a high‐purity fused silica were measured as part of a program to review the reliability of the International Space Station windows. The materials exhibit the same fracture toughness (.75 MPa m1/2 in N2) and very similar SCG parameters. The literature on fused silica indicates excellent agreement of fracture toughness, but a very wide range of SCG parameters, even from the same institution, with strength‐based methods usually yielding a lower power law exponent than direct crack velocity measurements. Use of the exponential function is shown to provide better agreement between test methods, with velocity curves derived from strength tests of bare fiber and polished or ground test specimens paralleling those from wide‐range, direct crack velocity observations, implying that constant stress rate tests can predict long lifetime via the exponential function. However, much variation still exists. SCG parameters for soda–lime silicate are much less sensitive to the test method than fused silica. Static load tests and stress intensity measurements resulted in a fatigue threshold of .3 MPa m1/2 for fused silica.

Correction to: Crack velocity measurements through continuous stiffness monitoring of cyclically loaded notched micro-beams of thin graded Pt–Ni-Al bond coats

Correction to: Crack velocity measurements through continuous stiffness monitoring of cyclically loaded notched micro-beams of thin graded Pt–Ni-Al bond coats

Crack velocity measurements through continuous stiffness monitoring of cyclically loaded notched micro-beams of thin graded Pt–Ni-Al bond coats

The notched clamped beam geometry has proven to be a useful geometry in evaluating local mechanical properties like fracture and fatigue of thin graded platinum nickel aluminide bond coats. Cyclic fatigue tests performed on different zones of these coatings have shown that the structural stiffness of the beam is a useful parameter in estimating localized damage in front of the notch root, which can arise either due to cyclic softening from micro-crack nucleation and propagation in the crack wake or due to work hardening in the plastic zone surrounding the crack tip. This paper describes the use of finite element method-based analysis to quantify different geometrical factors that affect cyclic stiffness data in the micro-beam bending methodology employed in the present study. Variations in the stiffness values measured at the beginning of each loading cycle can occur due to factors such as the effect of loading line offsets (both lateral and angular) and the notch length to width ratio (a/W). Using this analysis, it was found out that lateral offsets affect the starting stiffness of the beam more profoundly compared to angular offsets. It has also been shown that for beams having lengths of $$\sim $$ $$80-90\,\upmu \mathrm{m}$$ and an a/W ratio of $$\sim $$ 0.3–0.4, the starting stiffness variations can be kept under 10%. The stiffness can also be used to estimate crack velocities (da/dN) in an approximate sense using the finite element method. Detailed finite element analysis has been performed to estimate through thickness crack lengths from cyclic stiffness drops. The applied stress intensity factor for real crack geometries observed during testing have been computed using the extended finite element methodology and da/dN vs $$\Delta $$ K plots have been generated for two cases. This paper highlights the importance of using computational analysis in optimizing and augmenting micro-scale fatigue testing data and thus providing for a richer dataset through such analysis.

Experimental Study of Crack Branching Velocity in Polymers

One of the little-studied problems of modern mechanics and the physics of destruction is crack branching, which is observed in materials of varying nature. In order to study this phenomenon, the criteria and mechanisms for crack branching are analyzed. Studies of crack branching in polymers and steel, as well as fractographic studies of the fracture surface, are considered. It is found that the crack at branching in brittle plastics reaches the limiting propagation velocity V* = 500–800 m/s. Tensile tests of flat samples made of polymethyl methacrylate (PMMA) at temperatures of +20 and –60°C are carried out with measurement of crack velocity by the method of rupture of conductive strips. A measuring device based on a TERCON precision converter of signals of resistance thermometers and thermocouples connected to a computer is created. Crack velocity is measured for (i) rectilinear crack propagation in the mirror, matte, and feather zones of PMMA fracture surface, (ii) single branching of the crack, and (iii) multiple crack branching with parallel movement of the front of several cracks. A hypothesis for the physical mechanism of crack branching is proposed.

Thermal activation effects in crack propagation and reliability of fused silica

AbstractThe thermal activation energy u1 characterizing changes in crack velocity with temperature for fused silica in water is determined. The determination is based on a new analysis that incorporates the familiar Arrhenius term for thermally activated processes and a term characterizing the departure of the propagating crack system from fracture equilibrium. In determining u1 from experimental data, the Arrhenius term and the nonequilibrium term are of approximately equal magnitude. The analysis is applied to an extensive compilation of crack velocity measurements in fused silica to arrive at an estimate of u1 = (69 ± 11) kJ mol−1, where the value represents the multi‐laboratory mean ± variability. This value is greater than that assumed in some earlier works and characterizes a typical within‐laboratory increase in crack velocity of a factor of approximately 102 in fused silica between freezing and boiling water conditions and a decrease of a factor of 103 in component time to failure for the same change in conditions. The multi‐laboratory variation in velocity at fixed temperature is comparable to the within‐laboratory maximum increase, perhaps obscuring temperature effects.

Experimental Study of Fracture Characterizations of Rocks under Dynamic Tension Test with Image Processing

To investigate the fracture characterizations of rocks under high strain rate tensile failure, a series of dynamic Brazilian tests was conducted using Split Hopkinson pressure bar (SHPB), and a high‐speed digital camera at a frame rate of 50,000 frames per second (FPS) with a resolution of 272 × 512 pixels was adopted to capture the real‐time images and visualize the failure processes. Using the extracted cracks and image processing technique, the relationship between loading condition (impact velocity), crack propagation process (crack velocity, crack fractal characteristic, and crack morphological features), and dynamic mechanical properties (absorbed energy and strain‐stress parameters) was explored and analyzed. The experimental results indicate that (1) impact velocity plays a critical role in both crack propagation process and dynamic mechanical properties, (2) the crack fractal dimension is positively correlated with crack propagation velocity and has a linear relationship with the proposed morphological feature of crack, (3) mean strain rate and max strain of rocks under SHPB loading both decrease with the increase of crack propagation velocity, and (4) the energy absorbed by the rocks increases with increasing impact velocity and has a strong negative correlation with a proposed novel crack descriptor. Experimental studies pertaining to the measurement of crack propagation path and velocity, in particular, some crack feature extraction approaches, present a promising way to reveal the fracture process and failure mechanisms of rock‐like materials.

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%.

Decompression wave speed and crack velocity measurements during S4 test in water pressurized plastic pipes: Part 2. Criteria for onset of rapid crack propagation

The rapid crack propagation behavior in pressurized plastic pipes was investigated to establish the criteria for onset of rapid crack propagation in terms of the relationship between decompression wave speed and crack velocity. The study was performed by using an instrumented S4 test apparatus, the methodology for which is described in Part 1 of this paper. To establish the criteria for the onset of rapid crack propagation in water-filled plastic pipes, PVC pipes of 440 mm outside diameter having dimensional ratios of 14, 18 and 25 were tested following the procedure described in ISO 13477. From the measurements made on decompression wave speed and crack velocity, it was determined that, for rapid crack propagation to occur in the S4 test, two conditions were required. The decompression wave speed, Cw,S4, needs to be lower than the rapid crack velocity, a˙. Also, the crack velocity must be equal to or above the critical crack velocity, a˙crit. That is,Cw,S4≤a˙a˙≥a˙critIt was shown that this critical crack velocity is always greater than the theoretical decompression wave speed in water filled pipes. Until now, the criterion for rapid crack propagation in S4 was understood to only involve the former condition in water pipes. With this and the latter condition proposed, more complete criteria for rapid crack propagation in water filled plastic pipes using the S4 method is now established.

Decompression wave speed and crack velocity measurements during S4 test in water pressurized plastic pipes: Part 1. Experimental methods

In a Small Scale Steady State (S4) test apparatus of ISO 13477, instrumentations were designed and successfully adapted to determine decompression wave speed and crack velocity during rapid crack propagation event in water-filled plastic pipes. The basic design for decompression wave speed measurement involved the use of high-frequency dynamic pressure transmitters, located external to the water-filled pipe and connected to pressure measurement positions inside the pipe, by means of stainless steel tubes. For the crack velocity measurements, timing wire system with the required circuitry capable of giving the precise temporal indication of the propagating crack was designed and employed. In this paper, detailed design of instrumentations adapted to the S4 test apparatus and the assessment techniques used to obtain decompression wave speed and crack velocity are described. It was also demonstrated that the methods developed were viable for these measurements which are known to affect the rapid crack propagation behavior in water-filled plastic pipes.

Crack and Damage Velocities in Ballistic Experiments

A series of ballistic impact experiments were conducted against a borosilicate glass (Borofloat®33) bonded to a polycarbonate substrate. Two of the objectives of the experiments were to measure crack velocities in the glass, and to measure the damage velocity in the glass. The speed of distinct propagating cracks was found to be 1.92 ± 0.03 km/s, independent of impact velocity. The maximum rate of damage propagation was found to be a function of impact velocity, but the damage velocity plateaued at 2.07 ± 0.04 km/s.

Photomultiplier tube failure under hydrostatic pressure in future neutrino detectors

Failure of photomultiplier tubes (PMTs) under hydrostatic pressure is a concern in neutrino detection, specifically, in the proposed Long-Baseline Neutrino Experiment (LBNE) project. Controlled hydrostatic implosion tests were performed on prototypic PMT bulbs of 10-inch diameter and recorded using high-speed filming techniques to capture failures in detail. These high-speed videos were analyzed frame-by-frame in order to identify the origin of a crack, measure the progression of individual crack along the surface of the bulb as it propagates through the glass, and estimate crack velocity. Crack velocity was calculated for each individual crack and an average velocity was determined for all measurable cracks on each bulb. Overall, 32 cracks were measured in 9 different bulbs tested. Finite element modeling (FEM) of crack formation and growth in prototypic PMT shows stress concentration near the middle section of the PMT bulbs that correlates well with our crack velocity measurements in that section. The FEM model predicts a crack velocity value that is close to the terminal crack velocity reported. Our measurements also reveal significantly reduced crack velocities compared to terminal crack velocities measured in glasses using fracture mechanics testing and reported in literature.

Optical method for measuring slow crack growth in cementitious materials

The double-torsion (DT) test is commonly used to calculate slow or subcritical crack velocities in (quasi-)brittle engineering materials directly from the measured load relaxation of notched DT-specimens. In cementitious materials a significant part of the recorded load relaxation in the DT-test may be due to specimen creep deformation, and this would then lead to overestimated crack velocities. In this paper we describe a method to optically measure slow crack growth in cementitious materials by carrying out DT-tests under the optical microscope or inside the environmental SEM. Crack tip detection is facilitated by digital image correlation of the time-lapse microscope recordings. DT-tests at 10 % relative humidity in hardened cement paste (with w/c-ratio of 0.4, 0.5 and 0.6) showed that optically measured crack velocities were significantly lower than those calculated from the DT-specimen relaxation. In many experiments the subcritical crack growth rapidly stopped, while an ongoing specimen load relaxation was recorded. At 90 % relative humidity, load-relaxation in the DT-test was much stronger than at 10 % relative humidity, because subcritical cracking and creep-induced relaxation both increase with moisture content.

Subcritical crack growth and long-term strength in rock and cementitious material

High-strength and ultra low-permeability concrete (HSULPC) is a strong candidate for a radioactive waste package containing transuranic radionuclides (TRU waste) for geological disposal. Knowledge of the time-dependent fracturing of HSULPC and surrounding rock mass is essential to assess the long-term stability of such underground repositories. We have measured crack velocity in andesite and HSULPC both in air and water to examine subcritical crack growth by the Double-Torsion method. In air, the crack velocity in andesite increased when the temperature and relative humidity increased. On the other hand, the temperature and relative humidity had little effect on the crack velocity in HSULPC in air. In water, the crack velocity increased when the temperature was higher for both andesite and HSULPC. Using these experimental results, the long-term strength was estimated. It was shown that the long-term strength of HSULPC was higher than that of andesite. In air, the long-term strength for andesite was affected by the temperature and relative humidity. The long-term strength for andesite decreased when the temperature or relative humidity increased. For HSULPC, the change of the long-term strength with varying temperature or relative humidity was smaller than andesite in air. In water, the long-term strength for both materials decreased with increasing the temperature. Comparing the long-term strength of andesite and HSULPC at the same environmental conditions, it was recognized that the decrease of the long-term strength of HSULPC is smaller than that of andesite. The long-term strength in water was smaller than that in air for both materials.

Fractography of Dynamic Crack Propagation in Silicon Crystal

The phenomena occurring during rapid crack propagation in brittle single crystals were studied by cleaving silicon specimens on the low energy cleavage planes under tensile and bending. The experiments revealed new phenomena not previously reported, and new crack path instabilities in particular. The well defined boundary conditions of the tested specimens and crack velocity measurements enabled rationalization of the observed phenomena and the velocity-surface instabilities relationship in particular. In contrast to amorphous materials, the observed instabilities are generated at relatively low velocity, while at high velocity the crack path remains stable. No evidences for mirror, mist, and hackle instabilities, typical in amorphous materials, were found.

Subcritical Crack Growth and Long-Term Strength in Rock and High-Strength and Ultra Low-Permeability Concrete

High-strength and ultra low-permeability concrete (HSULPC) is a strong candidate for a radioactive waste package containing transuranic radionuclides (TRU waste) for geological disposal. The information and knowledge of the time-dependent fracturing of HSULPC and surrounding rock mass are essential to assess the long-term stability of such underground repositories. Here we measured crack velocity in andesite and HSULPC both in air and water to examine slow crack growth (subcritical crack growth) by Double-Torsion method. In air, the crack velocity in andesite increased when the temperature increased. On the other hand, the temperature had little effect on the crack velocity in HSULPC in air. In water, the crack velocity increased when the temperature was higher for both andesite and HSULPC. By using the experimental results of subcritical crack growth, the long-term strength was estimated based on the model of a single crack subjected to tension in an infinite plate. It was shown that the long-term strength of HSULPC was higher than that of andesite. When the temperature increased, the long-term strength of andesite both in air and water and that of HSULPC in water decreased. The long-term strength in water was smaller than that in air for both materials. It is concluded that water remarkably affects subcritical crack growth and the long-term strength in these materials.

Electrical technique for monitoring crack growth in thin-film fracture mechanics specimens

An accurate and reliable electrical technique for continuous monitoring of crack growth in fracture specimens containing technologically relevant thin-film device structures has been developed. Both adhesive and cohesive crack growth measurements are reported using a SiO2passivation layer and a conducting titanium film deposited on the side face of fracture specimens. Crack velocity measurements approaching 10−12m/s were achieved, representing nearly an order of magnitude improvement over commonly used compliance-based techniques. The technique may be particularly useful for elucidating near threshold crack velocity behavior, which is important for thin-film reliability.

Anomalous temperature dependence of sub-critical crack growth in silica glass

The effects of temperature, water vapor, and stress on the rate of sub-critical crack growth (SCG) in fused silica are reported. The crack velocity was measured using the double-cleavage-drilled compression method. In contrast to other inorganic oxide glasses, crack growth velocities (in region I) were found to decrease with increase in temperature. Hence a small temperature rise has the apparent effect of improving the mechanical strength of a stressed-glass part. Despite the anomalous temperature dependence, SCG in fused silica is still likely governed by the established water-enhanced stress–corrosion mechanism; another competing phenomenon is proposed to cause the observed temperature dependence. Measured crack velocities are described using an empirical model (for region I) and a mass-transport model limited by Knudsen diffusion (for region II).

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.

Subcritical Crack Growth in a Phosphate Laser Glass

The rate of subcritical crack growth in a metaphosphate Nd‐doped laser glass was measured using the double‐cleavage‐drilled compression (DCDC) method. The crack velocity is reported as a function of stress intensity at temperatures ranging from 296 to 573 K and in nitrogen with water vapor pressures ranging from 40 Pa (0.3 mmHg) to 4.7 × 104 Pa (355 mmHg). The measured crack velocities follow region I, II, and III behavior similar to that reported for silicate glasses. A chemical and mass‐transport‐limited reaction rate model explains the behavior of the data except at high temperatures and high water vapor pressures where crack tip blunting is observed. Blunting is characterized by an arrest in the crack growth followed by the inability to reinitiate slow crack growth at higher stresses. A dynamic crack tip blunting mechanism is proposed to explain the deviation from the reaction rate model.