Stress Intensity Factor Rate Research Articles

Computation of two dimensional mixed-mode stress intensity factor rates using a complex-variable interaction integral

The well-known interaction integral, also known as the M-integral or I-integral, is a method to compute the mixed-mode stress intensity factors (SIFs) for fracture mechanics problems. The capabilities of the M-integral are extended here to compute derivatives of the SIFs with respect to the crack extensions for an isotropic linear elastic material under static loading. These derivatives were calculated using the complex Taylor series expansion (CTSE) numerical differentiation method. The derivatives of the auxiliary fields are calculated by applying CTSE directly to the M-integral formulation. The derivatives of the actual displacement fields are computed using a hypercomplex-variable finite element method (ZFEM) that also employs CTSE. SIF rates with respect to all crack tips are computed in a single analysis. The method is general and can be easily extended to other two-dimensional loading scenarios and different material models in a straightforward manner through the use of the appropriate auxiliary fields. The complex-variable M-integral was implemented within the commercial finite element software Abaqus through a user-defined element subroutine (UEL). Numerical examples demonstrate the high accuracy of the method.

Investigation of Mode I Notch Toughness of Zr41.2Ti13.8Cu10Ni12.5Be22.5 Metallic Glass under Dynamic Loading Conditions

Based on dynamic three-point bending tests, the dynamic notch toughness ( $$ K_{\text{Q}}^{\text{d}} $$ ) of Zr41.2Ti13.8Cu10Ni12.5Be22.5 (Vit 1) bulk metallic glass (BMG) was found to be sensitive to stress intensity factor rate ( $$ \dot{K}_{\text{Q}}^{\text{d}} $$ ), which varied from 5.21 to 31.90 MPa m1/2. The number of shear bands (Ns) in the notch tip plastic zone was quantitatively analyzed. The phenomenon wherein Ns decreased with increasing loading rate was explained based on the theory of the shear transformation zone and the softening mechanism. Then, power law relationships were established among Ns, $$ K_{\text{Q}}^{\text{d}} $$ and $$ \dot{K}_{\text{Q}}^{\text{d}} $$ . The results showed that shear bands can affect $$ K_{\text{Q}}^{\text{d}} $$ and $$ \dot{K}_{\text{Q}}^{\text{d}} $$ and act as a bridge connecting $$ K_{\text{Q}}^{\text{d}} $$ and $$ \dot{K}_{\text{Q}}^{\text{d}} $$ . The sensitivity of $$ K_{\text{Q}}^{\text{d}} $$ to $$ \dot{K}_{\text{Q}}^{\text{d}} $$ in BMGs can be well explained by the variation of Ns with loading rate.

Quantitative In Situ Studies of Dynamic Fracture in Brittle Solids Using Dynamic X-ray Phase Contrast Imaging

We demonstrate the use of X-ray phase contrast imaging with sub-microsecond temporal resolution to obtain quantitative visualization of dynamic fracture processes in brittle solids. We examine an amorphous solid (fused silica), a ceramic single crystal (single-crystal quartz), and a polycrystalline ceramic (boron carbide), in the form of single-edge notched specimens loaded using a three-point apparatus at nominal strain rates up to $\sim $ 800 s−1. We observe that the crack tip speed for boron carbide is relatively independent of mode I stress intensity factor rate ( $\dot {K}_{\mathrm {I}}$ ) for these rates of loading, while that of fused silica and single-crystal quartz increases with $\dot {K}_{\mathrm {I}}$ . Further, for the amorphous and single crystal cases, we observe the development of a crack tip instability in the form of crack branching as the crack tip speed approaches 45% of the Rayleigh wave speed. This suggests that strain-rate-dependent mechanisms contribute to crack branching. Such mechanisms may, in turn, affect the macroscopic fracture properties of these materials.

Quantitative Visualization of Human Cortical Bone Mechanical Response: Studies on the Anisotropic Compressive Response and Fracture Behavior as a Function of Loading Rate

Blast and impact events regularly cause damage to human tissues. Efforts to improve protective gear are made through numerical simulation of these events where human tissues are exposed to high-rate loading conditions. Accurate simulation results can only be obtained if constitutive models are used that are based on precisely carried out experimental studies. Experimental studies on bone are challenging because of the relatively brittle nature of bone as well as the importance of the bone being in a hydrated state prior to experiments to avoid changing the mechanical properties. Past studies have utilized strain gages which require a period of drying time to bond strain gages to the surface of the bone. In this study, rate dependent fracture and compressive responses of wet human femur bone are investigated with in situ quantitative visualization. The fracture properties of cortical bone are studied transverse to the longitudinal axis of the bone up to high stress intensity factor rates, and the rate dependent compressive response is investigated in both longitudinal and transverse directions. The rate dependent nature of the fracture response, and the compressive behavior of human cortical bone over a range of rates from 0.001–1000 s-1 is discussed with the aid of quantitative visualization.

Rate-dependent fracture modes in human femoral cortical bone

An accurate understanding of fracture in human bone under complex loading scenarios is critical to predicting fracture risk. Cortical bone, or dense compact bone, is subject to complex loading due to the inherent multi-axial loading conditions, which are also influenced by the anisotropy of the microstructure. When determining critical fracture parameters, bone is traditionally idealized as isotropic. This paper presents a method to examine rate-dependent mode mixity associated with cortical bone crack initiation. Four-point bend experiments have been conducted on cortical femoral bone samples from three human donors at quasi-static (slow), intermediate, and dynamic loading rates. Digital image correlation was used to obtain full-field displacement maps at the crack tip during the experiments. An over-deterministic least squares method is presented and used to evaluate Mode I (opening) and Mode II (shear) stress intensity factors (SIF) for fracture initiation at slow (10 $$^{-2}$$ MPa-m $$^{1/2}$$ s $$^{-1}$$ ), intermediate (15 MPa-m $$^{1/2}$$ s $$^{-1}$$ ), and high ( $$4.5^{4}\,\hbox {MPa-m}^{1/2}\,\hbox {s}^{-1}$$ ) stress intensity factor rates. Results show that under dynamic loading, the critical SIF in Mode I assuming material anisotropy is approximately 50 % lower than fracture toughness assuming isotropy. Additionally, critical Mode I and II SIFs had the lowest values at the highest rate of loading examined, decreasing to one third of the values under quasi-static loading. Crack growth in the low and intermediate SIF rates appears to be Mode II dominant, and shows a transition to completely mixed-mode at the high rate of loading. These results suggest that the conventional assumption of isotropy is a conservative estimate at low and intermediate rates, but overestimates fracture strength at dynamic rates.

Characterization of the Master Curve Based Fracture Toughness of ORNL TSE5 Steel and Unirradiated and Irradiated ASTM A203D 3.5 % Ni Steel by the IGCAR Procedure

Abstract The Indira Gandhi Centre for Atomic Research (IGCAR) procedure for predicting the master curve (MC) reference temperature T0 has been further validated via its application to ORNL thermal shock experiment (TSE) 5 steel, an A508 Cl.2 steel that has been widely characterized in the literature. The procedure also was applied to ASTM A203D 3.5% Ni steel tested at IGCAR in virgin and irradiated states. The IGCAR procedure involves the application of the inverse Wallin strain rate equation to TQSchdy, the dynamic reference temperature obtained from Charpy tests using the modified Schindler procedure corresponding to a stress intensity factor rate of ∼106 MPa√m.s−1. A direct correlation of TQSchdy to T0 is also used. The larger of the estimates from these two, namely, TQSchW, provides an accurate and acceptably conservative estimate of the reference temperature TQ-est for steels with TQSchdy ≤ 60°C; for steels with TQSchdy>60°C, TQ-est=the larger of TQSchW and TQM2. The value of TQ-est obtained via the IGCAR procedure is termed TQ-IGC. Mostly, TQM2 gives the most conservative estimate, and TQBT (based on the value of TD obtained from instrumented Charpy V-notch impact tests) has a tendency toward accuracy, provided a robust estimate of TD can be obtained (which is not always the case). The IGCAR procedure was compared with two other conservative lower-bound (LB) procedures (Schindler-LB and Merkle-LB procedures), and it was shown that the IGCAR procedure with a 1% MC provides an LB curve without the difficulties involved in using the more tortuous calculations necessary for applying the Schindler- and Merkle-LB procedures. For the irradiated A203D steel, the shift in the estimated T0 was ΔTQ-IGC=340°C.

Hopkinson Bar Loaded Fracture Experimental Technique: A Critical Review of Dynamic Fracture Toughness Tests

Hopkinson bar experimental techniques have been extensively employed to investigate the mechanical response and fracture behavior of engineering materials under high rate loading. Among these applications, the study of the dynamic fracture behavior of materials at stress-wave loading conditions (corresponding stress-intensity factor rate ∼106 MPam/s) has been an active research area in recent years. Various Hopkinson bar loading configurations and corresponding experimental methods have been proposed to date for measuring dynamic fracture toughness and investigating fracture mechanisms of engineering materials. In this paper, advances in Hopkinson bar loaded dynamic fracture techniques over the past 30 years, focused on dynamic fracture toughness measurement, are presented. Various aspects of Hopkinson bar fracture testing are reviewed, including (a) the analysis of advantages and disadvantages of loading systems and sample configurations; (b) a discussion of operating principles for determining dynamic load and sample displacement in different loading configurations; (c) a comparison of various methods used for determining dynamic fracture parameters (load, displacement, fracture time, and fracture toughness), such as theoretical formula, optical gauges, and strain gauges; and (d) an update of modeling and simulation of loading configurations. Fundamental issues associated with stress-wave loading, such as stress-wave propagation along the elastic bars and in the sample, stress-state equilibrium validation, incident pulse-shaping effect, and the “loss-of-contact” phenomenon are also addressed in this review.

An investigation of the loading rate dependence of the Weibull stress parameters

This paper examines the dependence of the Weibull stress parameters on loading rate for a 22NiMoCr37 pressure vessel steel. Extensive fracture tests, including both quasi-static and dynamic tests, are conducted using deep- and shallow-cracked SE(B) specimens. The fracture specimens are carefully prepared to ensure the crack fronts are placed at the location where the material is homogeneous. Three dynamic loading rates (in terms of the stress intensity factor rate, K ˙ J ) in the low-to-moderate range are considered. The load-line velocities for the dynamic tests are chosen so that the resulted K ˙ J values for the deep- and shallow-cracked specimens are the same. Independent calibrations performed at each loading rate (quasi-static and the three dynamic loading rates) using deep- and shallow-cracked fracture toughness data show that the Weibull modulus, m, is invariant of loading rate. The calibrated m-value is 7.1 for this material. Rate dependencies of the scale parameter ( σ u ) and the threshold parameter ( σ w-min) are computed using the calibrated m and the results indicate that σ u decreases and σ w-min increases with higher loading rates. The demonstrated loading rate invariant of m, when combined with the master curve for dynamic loading, can provide a practical approach which simplifies the process to estimate σ u as a function of loading rate.

ICONE15-10531 APPLICATION OF FRI MODEL TO SCC GROWTH ANALYSIS IN BWR COMPONENTS

Two methods of applying Fracture Research Institute Theoretical Stress Corrosion Cracking model (FRI model), the theoretical SCC model developed by Shoji and Suzuki, to SCC growth analysis in a cylindrical component with stress distribution are proposed. FRI model has rarely been adapted to estimate SCC growth behavior in a real structural component in which the changing rate of stress intensity factor with time (dK/dt) naturally changes as the crack grows. One of the reasons might be the difficulty of solving the equation consisting of many parameters including dK/dt. In this paper, the authors propose two methods to conduct SCC growth analysis using FRI model. In Method 1 (Once-through method), the authors successfully applied FRI model to SCC growth analysis of 360 degree circumferential crack in a cylinder under the stress distribution by replacing dK/dt with the changing rate of stress intensity factor with crack length (dK/da). Method 1 is so easy that it can be achieved only using Worksheet functions of EXCEL. Method 2 (Iteration method) is relatively difficult solving the complex equation at each crack growth step. The authors performed Method 2 using originally developed codes with VBA, Visual Basic for Applications, for EXCEL. Method 2 is applicable to two-dimensional crack (semi-elliptical crack) contrary to Method 1 that is only for a one-dimensional crack. The details of Method 1 and Method 2, an example of application of FRI model to SCC growth analysis and the parameter study for FRI model are shown in this paper.

The industrial application of dynamic testing for the study of metallic strength and toughness properties

The specific type of specimens were prepared from X80 pipeline steel with perpendicular sampling orientation for the dynamic testing of impact tensile at given strain rate, 10 2 /s and instrumented pendulum impact with the given stress intensity factor rate, 5×10 5 MPa m 1/2 /s in the present paper. The comparison of the yield stress and tensile strength corresponding to quasi static and dynamic loading clearly indicates that the strength of X80 steel is sensitively dependent of the strain rate change. The correlation of σ yd and F gy obtained from instrumented impact by means of Server equation was proved to be satisfactory. Moreover tensile toughness index LST is also proposed as the plastic energy distribution throughout the cross section area under static and impact tensile loading, reveling the dependence of strength and plasticity combination of structural steel on the loading variation. In addition, dynamic crack extension resistance curve, J-Δ a , was acquired for the evaluation of toughness property, also effectively revealing the mechanism of crack initiation and growth under dynamic loading.

封圧下における岩石のき裂進展抵抗曲線

According to the core-based methods proposed by the authors, fracture toughness testing under confining pressure was carried out for Inada granite and Ogino tuff by using SR and C-RCT specimens, and K-resistance curves of the rocks were measured under confining pressure up to 29.4 MPa. The surfaces of a chevron-notch were sealed with a flexible and tough bellows-shaped film of copper and vinylchloride and other surfaces with a film of vinyl-chloride. In the C-RCT specimen, a fracture propagated parallel to the weakest plane (the bedding plane for the tuff and the rift plane for the granite) while, in the SR specimen, a fracture propagated perpendicular to the weakest plane to evaluate the anisotropy in the Kresistance curve under confining pressure.For both of the rocks, the K-resistance increased remarkably with confining pressure and the increase rate of the K-resistance with crack extension also became greater with confining pressure. Furthermore, the difference in the K-resistance between the two directions became greater with confining pressure. These phenomena were explained by the effects of confining pressure on the formation of process zone ahead of the crack tip. These effects are to reduce the tensile stress ahead of the crack tip by the component perpendicular to the crack plane, to decrease the rate of stress intensity factor with respect to crack extension by the same component of the confining pressure and to close pre-existing microcracks by the components parallel to the crack plane.

Determination of Dynamic Fracture-Initiation Toughness Using a Novel Impact Bend Test Procedure

A novel impact bend test procedure is described/or determining the dynamic fracture-initiation toughness, KId, at a loading rate (stress intensity factor rate), K˙I, of the order of 106MPam/s. A special arrangement of the split Hopkins on pressure bar is adopted to measure accurately dynamic loads applied to a fatigue-precracked bend specimen. The dynamic stress intensity factor history for the bend specimen is evaluated by means of a dynamic finite element technique. The onset of crack initiation is detected using a strain gage attached on the side of the specimen near a crack tip. The value of KId is determined from the critical dynamic stress intensity factor at crack initiation. A series of dynamic fracture tests is carried out on a 7075-T6 aluminum alloy, a Ti-6246 alloy and an AISI 4340 steel. The KId values obtained for the three structural materials are compared with the corresponding values obtained under quasi-static loading conditions.

圧力容器用鋼材の破壊じん性に及ぼす負荷速度の影響

In order to study an effect of loading rate on fracture toughness of steels for pressure vessels, static and dynamic fracture toughness tests and brittle crack arrest test were carried out. The steels used were two kinds of nuclear pressure vessel steel, A508 Cl.3 and A533B Cl.1, and an Al-killed steel.The results obtained are as follows:(1) The plane-strain fracture toughness was independent of the increase rate of stress intensity factor, K.(2) The values of plane-strain fracture toughness obtained by static and dynamic fracture toughness tests and brittle crack arrest test were the same.(3) Fracture toughness became lower as K increased in the transition region in which plastic deformation cannot be ignored.(4) The fracture toughness during brittle crack propagation, KID, became higher as the crack propagation rate increased, owing to the rise of temperature caused by the fracture of material near the crack tip.

Fracture Toughness of Bohai Bay Sea Ice

Abstract In this paper linear elastic fracture mechanics is used to evaluate the fracture toughness of sea ice, which was collected from Bohai Bay and researched experimentally in the recent 84/85 winter. The value of fracture toughness and its trend under different loading rate is analyzed. Not only the fracture toughness of mode I is discussed, but also the fracture criterion of II and combined mode is firstly investigated. If the rate is not too low, the critical stress intensity factor KIIC does not vary with the variation of stress intensity factor rate K˙II. Experimental results of sea ice under combined fracture mode coincide well with the criterion obtained from the strain energy density factor theorem. But this theorem cannot be employed so well to determine the orientation of crack propagating tendency.

A Method for Dynamic Fracture Initiation Testing of Ceramics

An experimental method is described whereby the dynamic fracture initiation toughness of ceramics and ceramic composites can be measured in pure tension or pure torsion at stress intensity factor rates of 105 to 106 MPam/s. In this procedure, circumferentially notched cylindrical rods are subjected to uniaxial cyclic compression at room temperature to introduce a self-arresting, concentric Mode I fatigue pre-crack, following the technique presented by Suresh et al. (1987) and Suresh and Tschegg (1987). Subsequently, dynamic fracture initiation is effected by stress wave loading with a sharp-fronted pulse which subjects the specimen to a dynamic load inducing either Mode I or Mode III fracture. Instrumentation appropriate to the loading mode provides a record of average stress at the fracture site as a function of time. The capability of this method to yield highly reproducible dynamic fracture initiation toughness values for ceramics is demonstrated with the aid of experiments conducted on a polycrystalline aluminum oxide. The dynamic fracture toughness values are compared with the results obtained for quasi-static Mode I and Mode III fracture in the ceramic material at stress intensity factor rates of 10−1 to 1 MPam/s. Guidelines for the dynamic fracture initiation testing of ceramics and ceramic composites are discussed.

Ni-Cr-Mo鋼の遅れ破壊におけるき裂の伝ぱと枝分かれにおよぼす水素チャージの影響

Delayed failure tests were carried out on Ni-Cr-Mo steel quenched and tempered at 673 K in a NaCl aqueous solution in hydrogen charging condition, and the crack branching as well as crack propagation behaviors were investigated.The crack propagation rate da/dt increases with increase in cathode charging current density, i, and da/dt increases to a maximum and then decreases with increase in the increasing rate of stress intensity factor, \dotK. The stress intensity factor at crack branching, KIB, decreases to a minimum and then increases with increase in i. These results can be explained by interaction between dislocations and hydrogen atoms, such as dislocation trapping and dislocation transport of hydrogen on the slip planes near crack tip.

Dynamic Fracture Toughness and Fatigue Crack Growth Rate Properties of ASME SA508 CL 3 and SA508 CL 3a Base and Heat-Affected-Zone Materials

Abstract Dynamic fracture toughness tests were performed on ASME SA508 Cl 3 and Cl 3a base and heat-affected-zone (HAZ) materials. Linear elastic results of dynamic iniation fracture toughness obtained under fast or rapidly applied loading rates KId were obtained at low temperatures while J-integral techniques were used to evaluate dynamic fracture toughness over the transition and upper shelf temperature ranges. Loading rates in terms of stress intensity factor rate ˙K averaged 5.35 × 104 MPa · m1/2/s (4.83 × 104 ksi · in.1/2/s). Tension, Charpy impact, drop weight nil-ductility transition (NDT), and room temperature, air environment fatigue crack growth rate (FCGR) tests were also performed. From a dynamic fracture toughness as well as FCGR standpoint, SA508 Cl 3a steel can be considered as an acceptable alternative to the more commonly used SA508 Cl 2a pressure vessel steel, especially for structural applications in which underclad cracking is a potential problem.

A method for determining the stress intensity threshold level for fatigue crack propagation

The influence of a decreasing rate of stress intensity factor with crack propagation, dK/ da , on a stress intensity threshold level, δK th , below which fatigue crack propagation becomes insignificant is investigated. Specimens, 200 mm wide, 10 mm thick with a 40 mm-long central crack, are fatigued at the decreasing rates, ∥ d(δK) da∥ , of 2,44, 5 and 10 kg/mm 5/2 with a peak load control system and a pair of crack followers. In this range of d(δK)/ da , the stress intensity threshold levels, δK th , have the same value regardless of dK/ da . Therefore, the present method of decreasing the stress intensity factor at a constant rate is suitable for determining the characteristic δK th of materials. Furthermore, the influence of stress ratio, R, is investigated at the decreasing rate, ∥ d(δK)/ da] , of 10 kg/mm 5/2.