Crack Velocity Data Research Articles

Analysis of dynamic fracture propagation in steel pipes using a shell-based constant-CTOA fracture model

In this paper, a finite element (FE) model with shell elements using a constant crack tip opening angle (CTOA) as fracture criterion was implemented for the simulation of dynamic fracture propagation in steel pipes. The new model was developed to improve computational efficiency over current CTOA models while retaining a high level of numerical accuracy. The commercial FE code ABAQUS was used to generate the meshes and perform the analyses. The proposed model was first used to reproduce data from an existing CTOA model of an American Petroleum Institute (API) X65 steel, matching the steady-state fracture velocity within a maximum difference of 5% while drastically reducing the computational time required. The model was then used to analyze recent experimental data from a full-scale pipe burst test of a Japanese Industrial Standard (JIS) steel STPG370, matching the crack velocity data within 4%. It was thereby demonstrated that FE analysis using this shell-based constant-CTOA model is an efficient method for describing dynamic fracture propagation in steel pipes and can be used as an engineering tool to develop fracture driving force based on CTOA.

Dynamic and static characterization of compact crack arrest tests of navy and nuclear steels

Recent experimental and computational work by Link and associates has demonstrated that relatively small ( W = 150 mm) single edge notched tension specimens (SE(T)) can be used to obtain crack arrest data high in the ductile-to-brittle transition of ferritic structural steel using dynamic computational techniques if a thermal gradient is utilized to aid in the crack arrest. Testing has been reported on two important navy structural steels that clearly defines the relative capability of the two materials to arrest rapidly growing cracks. The HY100 material demonstrated the expected large difference between the initiation and crack arrest toughnesses which has made it impossible in the past to measure crack arrest toughness for this material using the standard ASTM procedure (E1221). The HSLA-100 steel, however demonstrated a much higher crack arrest toughness and a correspondingly smaller drop in toughness below the initiation toughness. This small difference between initiation toughness and arrest toughness suggested that the E1221 procedure, using wedge loaded, compact crack arrest (CCA) specimens would be applicable to this material. Two important issues could then be investigated using this material. First, having completed the expensive and relatively complex testing of the SE(T) specimens using tensile loading and a thermal gradient, a second, quite different geometry could be tested using the E1221 procedure, allowing an important comparison between the crack arrest measurements made using these two distinct geometries. Historically, obtaining crack arrest results using one test configuration has been so difficult, that there have been very few reports of results for the same material using two different test geometries. Transferability of the laboratory results to structural applications has thus been a matter of conjecture. Furthermore, if the E1221 CCA specimens were strain gaged to obtain crack velocity data, and analyzed using the dynamic computational procedure used by Link on the SE(T) specimens, it would be possible to compare the results the E1221 static analysis with the results of the dynamic computation procedure to determine the degree of conservatism present in the E1221 standard procedure. The results of this work have shown that the crack arrest toughness results obtained on these two specimen geometries are similar and hence insensitive to the test geometry and the difference resulting from the application of the complex dynamic computational procedure or the E1221 static analyses is small.

Crack arrest testing of high strength structural steels for naval applications

The crack arrest fracture toughness of two high strength steel alloys used in naval construction, HSLA-100, Composition 3 and HY-100, was characterized in this investigation. A greatly scaled-down version of the wide-plate crack arrest test was developed to characterize the crack arrest performance of these tough steel alloys in the upper region of the ductile–brittle transition. The specimen is a single edge-notched, 152 mm wide by 19 mm thick by 910 mm long plate subjected to a strong thermal gradient and a tensile loading. The thermal gradient is required to arrest the crack at temperatures high in the transition region, close to the expected service temperature for crack arrest applications in surface ships. Strain gages were placed along the crack path to obtain crack position and crack velocity data, and this data, along with the applied loading is combined in a “generation mode” analysis using finite element analysis to obtain a dynamic analysis of the crack arrest event. Detailed finite element analyses were conducted to understand the effect of various modeling assumptions on the results and to validate the methodology compared with more conventional crack arrest tests. Brittle cracks initiation, significant cleavage crack propagation and subsequent crack arrest was achieved in all 15 of the tests conducted in this investigation. A crack arrest master curve approach was used to characterize and compare the crack arrest fracture toughness. The HSLA-100, Comp. 3 steel alloy had superior performance to the HY-100 steel alloy. The crack arrest reference temperature was T KIA = −136 °C for the HSLA-100 plate and T KIA = −64 °C for the HY-100 plate.

Crack Arrest Testing Using Small Wide Plate SE(T) Specimens

Abstract A greatly scaled-down version of the wide plate crack arrest test has been developed to characterize the crack arrest performance of a high strength, low alloy (HSLA) steel alloy in the upper region of the ductile-brittle transition. The specimen is a single-edge notched, 152 mm wide by 19 mm thick by 910 mm long plate subjected to a strong thermal gradient and a tensile loading. The thermal gradient is required to arrest the crack at temperatures high in the transition region, close to the expected service temperature for crack arrest applications in surface ships. Strain gages are placed along the crack path to obtain crack position and crack velocity data, and this data, along with the applied loading is combined in a “generation mode” analysis using finite element analysis to obtain a dynamic analysis of the crack arrest event. A prior investigation demonstrated the feasibility of the technique and this investigation was devised to obtain a larger dataset of crack arrest toughness values of an HSLA-100 steel plate to better characterize the upper transition crack arrest performance of this alloy. Brittle crack initiation, significant cleavage crack propagation, and subsequent crack arrest was achieved in all eight of the tests conducted in this investigation. The cleavage cracks were observed to propagate at nearly constant velocity, typically in the range of 350–400 m/s before arresting abruptly. A crack arrest master curve approach was used to characterize the fracture toughness and a crack arrest reference temperature, TKIA=−136°C was determined for the HSLA-100 plate. This corresponded to a shift in the crack initiation reference temperature of +36°C. The shift in reference temperature was much less than that observed for low Ni steel alloys.

Mode mixity and nonlinear viscous effects on toughness of interfaces

This paper examines steady-state crack growth at interfaces between polymeric materials and hard substrates under quasi-static conditions. The polymeric material is taken to be an elastic nonlinear viscous solid while the substrate is treated as a rigid material. Void growth and coalescence in the rate-dependent fracture process zone is modeled by a nonlinear viscous porous strip of cell elements. In the first part of this paper, the polymeric background material surrounding the process zone is assumed to be purely elastic. Under fixed mode mixity, the computed interface toughness is found to be a monotonically increasing function of crack velocity; toughness also increases rapidly with higher rate sensitivity. This behavior can be explained in terms of voids growing in a strain-rate strengthened process zone. In the second part of the paper, the background material is also treated as an elastic nonlinear viscous solid. The competition between work of separation in the process zone and energy dissipation in the background material leads to a U-shaped toughness–crack velocity curve. Effects of mode mixity, initial porosity, rate sensitivity, as well as the initial yield strain on toughness are studied. The simulations produce trends that agree with interface toughness vs. crack velocity data reported in experimental studies for rubber toughened epoxy-paste adhesive and urethane acrylate adhesive.

Rate effects on toughness in elastic nonlinear viscous solids

A micromechanics-based constitutive relation for void growth in a nonlinear viscous solid is proposed to study rate effects on fracture toughness. This relation is incorporated into a microporous strip of cell elements embedded in a computational model for crack growth. The microporous strip is surrounded by an elastic nonlinear viscous solid referred to as the background material. Under steady-state crack growth, two dissipative processes contribute to the macroscopic fracture toughness—the work of separation in the strip of cell elements and energy dissipation by inelastic deformation in the background material. As the crack velocity increases, voids grow in the strain-rate strengthened microporous strip, thereby elevating the work of separation. In contrast, the energy dissipation in the background material decreases as the crack velocity increases. In the regime where the work of separation dominates energy dissipation, toughness increases with crack velocity. In the regime where energy dissipation is dominant, toughness decreases with crack velocity. Computational simulations show that the two regimes can exist in certain range of crack velocities for a given material. The existence of these regimes is greatly influenced by the rate dependence of the void growth mechanism (and the initial void size) as well as that of the bulk material. This competition between the two dissipative processes produces a U-shaped toughness–crack velocity curve. Our computational simulations predict trends that agree with fracture toughness vs. crack velocity data reported in several experimental studies for glassy polymers and rubber-modified epoxies.

Subcritical crack growth in CVI SiC f/SiC composites at elevated temperatures: dynamic crack growth model

A dynamic crack-growth model has been developed to predict slow crack growth in ceramic composites containing nonlinear, creeping fibers in an elastic matrix. Mechanics for frictional bridging and nonlinear fiber-creep equations are used to compute crack extension dynamically. Discrete, two-dimensional fiber bridges are employed, which allows separate bridge “clocks”, to compute slow crack-growth rates for composites containing Nicalon-CG and Hi-Nicalon fibers. Predictions for activation energies, time-temperature exponents, crack lengths, and crack-velocity data for composites in bending at 1173 K to 1473 K in inert environments are in good agreement with experimental data. In addition, calculated creep strains in the bridges agree with experimental damage-zone strains. The implications of multiple-matrix cracking are discussed.

Role of structural relaxations in the fracture of vitreous silica

The double cleavage drilled compression fracture mechanics specimen was used to obtain crack velocity data for vitreous silica in vacuum conditions at temperatures of 100 and 300 K. We observed stable crack propagation over a velocity range between 10−9 and 10−2 m/s. The measured fracture rate dependence with applied stress was modeled using a global energy balance approach that incorporated energy losses due to the anelastic response of the material in the stress field of the propagating crack. Measured mechanical loss data for vitreous silica were incorporated into an anelastic fracture model to produce qualitative agreement with the measured fracture behavior. These results indicate that the anelastic response of silicate glasses can contribute significantly to the measured fracture energy. This interpretation of silicate glass fracture suggests a new approach to design glass compositions for improved mechanical performance and provides a more complete picture of the atomic scale processes that control the macroscopic fracture energy of amorphous materials.

Effect of Humidity on Small‐Crack Growth in Silica Optical Fibers

Subcritical small‐crack growth in silica optical fibers was measured directly in air at 25°C for several humidity conditions from 30% to 90% relative humidity. The crack velocity data were shown to be closely fitted by a power function of the stress intensity factor. It was found that the power n is independent of humidity and takes a value of 21.7. It was also revealed that crack velocity varies with relative humidity to a power of 2.5, which agrees with estimates from the published dynamic fatigue data concerning the humidity dependence of the strength of pristine silica fibers.

Subcritical crack growth along epoxy/glass interfaces

Subcritical crack growth behavior along polymer/glass interfaces was measured for various epoxy adhesives at different relative humidities. A four-point flexure apparatus coupled with an inverted microscope allowed for observation in situ of the subcritical crack growth at the polymer/glass interface. The specimens consisted of soda-lime glass plates bonded together with epoxy acrylate, epoxy (Devcon), or epoxy (Shell) adhesives. Above a threshold strain energy release rate, the subcritical crack velocity was dependent on the strain energy release rate via a power law relationship where the exponent was independent of the adhesive tested and the test humidity (n = 3). However, the multiplicative constant A in the power law relation varied by over three orders of magnitude between the various adhesives with epoxy (Shell) having the smallest value and the epoxy (Devcon) the greatest value; in addition, A was very sensitive to humidity, decreasing by over two orders of magnitude from 80% to 15% relative humidity. At high strain energy release rates, the subcritical crack velocity reached a plateau at approximately 10−6 m/s. The use of this subcritical crack velocity data in predicting thin film delamination is discussed.

Mechanical Properties of SiO2vs. SiO2-TiO2Bulk Glasses and Fibers

ABSTRACTThe mechanical properties of silica and titania-doped silica glasses, in bulk and fiber forms, are presented. These include the elastic properties (E and ν), strength distribution (in tension and bending), fatigue behavior (dynamic and static loading) and fracture toughness. Following a brief review of above properties for fused silica and ULE™ glasses (Coming Codes 7940 and 7971), used primarily for space applications, the mechanical properties data for silica and titania-doped silica-clad optical fibers are presented. The enhancement of mechanical performance of titania-doped silica clad fiber is also discussed.The effect of titania doping on fundamental properties like stress-free activation energy, crack tip pH, and deformation mode of Si-O-Si bond is discussed. In addition, the crack velocity data obtained from DCDC specimens of homogeneous silica and titania-doped silica glasses are compared in an attempt to understand the role titania plays in improving the fatigue resistance of optical fibers.

Subcritical Crack Growth of Glass Under Combined Modes I and II Loading

The glass plate specimens with inclined cracks introduced by Vickers microhardness indentation were subjected to sustained bend stress in water. Subcritical crack growth behaviors were investigated under combined Modes I and II loading. The crack velocity dc/dt can be described as a function of coplanar energy release rate G. The experimental results show that the dc/dt which is initially high decreases and thereafter increases with G. The crack velocity data are found to be influenced by the residual stress and the presence of a lateral crack. Inclined cracks in the increasing region tend to show the crack velocity higher than would be expected from the Mode I results of β = 90 deg on the basis of G as the β between the loading axis and the crack plane decreases. The dc/dt-G curves in this region have a steeper portion at low velocities and thereafter tend to a shallower portion.

Thresholds and reversibility in brittle cracks: An atomistic surface force model

A new picture of environmentally-enhanced fracture in highly brittle solids is presented. It is asserted that the fundamental relations for crack growth are uniquely expressible in terms of the surface force functions that govern the interactions between separating walls in an intrusive medium. These functions are the same, in principle, as those measured directly in the newest submolecular-precision microbalance devices. A fracture mechanics model, based on a modification of the Barenblatt cohesive zone concept, provides the necessary framework for formalizing this link between crack relations and surface force functions. The essence of the modification is the incorporation of an element of discreteness into the surface force function, to allow for geometrical constraints associated with the accommodation of intruding molecules at the crack walls. The model accounts naturally for the existence of zero-velocity thresholds; further, it explains observed shifts in these thresholds in cyclic load-unload-reload experiments, specifically the reduction in applied loading needed to propagate cracks through healed as compared to virgin interfaces. The threshold configurations emerge as thermodynamic equilibrium states, definable in terms of interfacial surface energies. Crack velocity data for cyclic loading in mica, fused silica and sapphire are presented in support of the model. Detailed considerations of the theoretical crack profiles in these three materials, with particular attention to the atomic structure of the “lattice” (elastic sphere approximation) at the interfaces, shows that intruding molecules must encounter significant diffusion barriers as they penetrate toward the tip region. It is concluded that such diffusion barriers control the fracture kinetics at low driving forces. At threshold the barriers become so large that the molecules can no longer penetrate to the tip region. This leads to a crucial prediction of our thesis, that the cohesive zone consists of two distinct parts: a “protected” primary zone adjacent to the tip, where intrinsic binding forces operate without influence from environmental influences; and a “reactive” secondary zone more remote from the tip, where extrinsic interactions with intruding chemical species are confined. The prevailing view of chemically enhanced brittle fracture, that crack velocity relations are determined by a concerted reaction with reactive species at a single line of crack-tip bonds, is seen as a limiting case of our model, operative at driving forces well above the threshold level. The new description offers the potential for using brittle fracture as a tool for investigating surface forces themselves.

The Influence of Displacement Rate on Environmentally Assisted Cracking of Precracked Ductile Steel Specimens

Sustained load and rising displacement tests were performed on precracked specimens to investigate the environmentally assisted cracking (EAC) behavior of AISI 4340, σ0 = 1095 MPA (159 ksi), in flowing synthetic seawater. J-R resistance curves were generated in environment over four orders of magnitude in displacement rate and KIJ (from JIC) from the slowest test was found to agree closely with the KIEAC (KISCC) value determined from cantilever beam tests. Crack velocity data from the slowest rising displacement test and constant stroke—decreasing KI—tests fall on the same line suggesting that there is a unique a˙-KI curve for EAC in this system. A method is suggested to determine the displacement rate needed to obtain a good estimate of KIEAC from a rising displacement test.

Stress corrosion crack propagation in α-brass and copper exposed to sodium nitrite solutions

Crack growth in α-brass and 99.99% copper exposed to NaNO 2 solutions has been studied as a function of solution composition, potential, temperature and strain rate. The observed crack velocities under some conditions may be accounted for on the basis of a continuous dissolution or a discontinuous cleavage-like mechanism and so distinction between these mechanisms on the basis of crack velocity data does not currently appear appropriate. The fractographic characteristics and the effects of strain rate upon cracking appear more consistent with the discontinuous cleavage-like mechanism, but this requires further development and data acquisition before its applicability can be taken as unequivocally established.

Strength and Fatigue Properties of Optical Glass Fibers Containing Microindentation Flaws

The inert strength and dynamic fatigue properties of fused‐silica optical fibers are studied using subthreshold indentation flaws, i.e., flaws without radial cracks. These subthreshold properties differ from those obtained in comparative tests on silica rods containing postthreshold indentation flaws in three major respects: (1) the inert strengths are significantly higher than predicted by extrapolation of the postthreshold data; (2) the slopes of the dynamic fatigue plots are likewise greater, indicating a greater susceptibility of the subthreshold flaws to chemical kinetic effects; and (3) the scatter in strengths is wider. These trends reflect the change in mechanical response reported for optical fibers with “natural” flaw populations in going from ordinary to ultra‐high‐strength regions. Direct observations of the indentation sites up to the point of failure indicate that the property differences can be interpreted in terms of a transition from propagation‐controlled to initiation‐controlled fracture instabilities at reduced contact loads. The subthreshold instability condition is modeled qualitatively as a two‐step, deformation‐fracture process, with strong emphasis on the importance of residual stress fields in parametric evaluations. The relevance of the results to the practical issue of fiber reliability, most notably in connection with the potential dangers of using macroscopic crack velocity data to predict long‐lifetime characteristics, is addressed.

Stress corrosion and the rate-dependent tensile failure of a fine-grained quartz rock

Pre-cracked double torsion specimens of Arkansas Novaculite were deformed (1) in the load relaxation mode, and (2) at a fast cross-head speed using an Instron deformation machine to obtain stress intensity factor ( K I)-crack velocity ( v) data for stress corrosion in liquid water. The fracture toughness ( K Ic) was found to be 1.335 ± 0.075 MN m −3/2. At temperatures from 20°C to 80°C the stress corrosion index, n( v ∞ K n I was 25.1 ± 1.5 and the activation enthalpy for crack propagation was 69.5 ± 1.7 kJ mole −1. The K I-v data at 20°C were used to generate a diagram predicting the influence of strain rate on tensile fracture stress. These predictions were in good agreement with the fracture stress determined by bend experiments in liquid water at 20°C. Both the predictions and the experimental results are consistent with a monotonie reduction in tensile fracture stress from approximately 72 MN m −2 to 39 MN m −2 as strain rate is reduced from 6 · 10 −5 s −1 down to 10 −10 s −1. At strain rates faster than approximately 6 · 10 −5 s −1 stress corrosion does not influence the tensile fracture stress. It is unlikely that Novaculite will exhibit a fundamental fracture stress during deformation at even the slowest geological strain rates.

Crack Propagation in Double-Base Propellants

Crack propagation tests were conducted on a composite modified double-base (CMDB) propellant with the use of center-cracke d strip biaxial specimens. Constant strain rate tests were conducted at several temperatures (40-105°F) and crosshead rates (0.02-200 in./min) to define the crack initiation and propagation characteristics for monotonically increasing strain history. The tests were conducted at ambient, 250, and 500 psig pressure to evaluate the effect of pressure on initiation and crack velocity. A second series of tests was conducted to evaluate the effect of a prestrain damage history on crack propagation. In the second series, the samples (without precut cracks) were initially prestrained to 15-25% and held for a period of time to induce material damage. After load release and sufficient recovery time, cracks were inserted in the specimens and they were then pulled to failure at a constant strain rate. Similar tests were conducted on round, notched tensile samples to define the critical stress intensity factor (Klc) and to provide a comparison between uniaxial and biaxial fracture initiation. Schapery's viscoelastic fracture theory was used to evaluate the crack velocity data under constant strain rate conditions. One important result of the study was the finding that the crack velocity depended rather strongly on imposed strain level. I. Introduction C RACK initiation and propagation in polymeric materials has been given considerable attention during the last 15 years, stimulated primarily by their unique viscoelastic behavior and also by the use of polymerics as solid propellant rocket fuels. Filled polymers are used extensively as solidpropellant grains which must undergo a variety of environmental loading conditions, during motor storage and handling and during actual operational firing conditions, which impose pressure loads at high rates and for relatively long times. The consequence of a crack can be the failure of the rocket motor as a result of overpressuriz ation, case burnthrough, erratic pressure-time response, or a variety of events related to structural or ballistic performance failure. The primary work over the last decade has been aimed at defining the laws which govern crack initiation, propagation, and trajectory under motorlike operational conditions to arrive at an assessment of overall crack criticality for a given rocket motor system. A number of investigators have studied viscoelastic crack propagation in polymers and solid propellants. l~l°

Applicability of Crack Velocity Data to Lifetime Predictions for Fused Silica Fibers

Applicability of Crack Velocity Data to Lifetime Predictions for Fused Silica Fibers

Strength and Failure Predictions for Glass and Ceramics

Fracture mechanics has provided the means for making failure predictions regarding the lifetime of a glass or ceramic component in service. The background necessary for making these failure calculations from crack velocity and fatigue strength data is presented. The analysis of these types of data gives conservative failure predictions for soda‐lime glass in water. Also, how these fracture mechanics concepts (with the appropriate experimental data) can be used as an index to the fatigue resistance of a material is described.