Plastic Zone Size Research Articles

Experimental Verification and Estimation of Fatigue Crack Growth Delay due to Single Overload

A novel crack driving force parameter based on the plastic zone size for overload/constant amplitude loading is proposed to estimate the fatigue crack growth (FCG) and the beneficial fatigue life due to overload. By considering the stress distribution in the plastic zone, the effective stress intensity factor (SIF) integrated from equivalent residual stress is presented. It is illustrated that the FCG rate decreases rapidly after overload and then gradually returns to the baseline FCG rate. Besides, the overload ratio Rpic has a significant influence on the affected length ad and the beneficial fatigue life Nd.

Effect of the notch depth on fracture behavior of TC4 titanium alloy sheets

To evaluate the low-stress brittle fracture of TC4 titanium alloy sheet structures, the effect of notch depth (d) on the fracture behavior of the 1.8 mm thick TC4 titanium alloy sheets was investigated combied with tensile tests and digital image correlation method. The results show that the ductile–brittle transition (DBT) occurs with increasing notch depths. Ductile fracture occurs for the notched samples with d = 0.5–1.5 mm, and a uniform plastic deformation stage is observed in the load–displacement (P-L) curves, and there are stretch zone and the stable crack propagation zone in the fracture surfaces. Brittle fracture occurs for the notched samples with d = 3.0–5.0 mm, and there is only the linear elastic stage in the P-L curves, and no stretch zone in the fracture surfaces. The samples at the middle notch depths (d = 2.0–2.5 mm) are in the transition from ductile to brittle fracture, and there exists the elastoplastic deformation stage in the P-L curves, and the stretch zone and stable crack propagation zone are both decreased. The analysis of notch fracture parameters shows that fracture of notched samples is controlled by the stress concentration and the stress field intensity of an imaginary crack with the same notch depth. The effect of crack gradually increases with increasing d, which results in increased brittle fracture tendency. Moreover, the fracture energy γf can characterize the DBT of notched TC4 titanium alloy sheets, and the γf is proportional tothe ratio of critical plastic zone size to d (rpc/d). Finally, the rpc/d is proposed to characterize the DBT of the notched TC4 titanium alloy sheets, and the criterion of the DBT for the notched TC4 titanium alloy sheets is obtained.

A 2D numerical modelling of plasticity induced crack closure on MT specimens

In many engineering fields, structures are often subjected to fatigue loading that initiate and propagate cracks. The development of fracture mechanics studies has enabled the tolerance of a substantial amount of damage and the ability to predict failure in fatigue damaged structures, extending their service life safely. This can bring social impacts from economics, public-safety, or an environmental point of view. These damage tolerance analyses can be performed using linear elastic fracture mechanics (LEFM), where the Stress Intensity Factor (SIF) is a chief key, or under elastoplastic fracture mechanics (EPFM), where plasticity induced crack closure (PICC) plays a major role on fatigue crack growth (FCG). This study deals with the computational modelling developed consisting in the simulation of a two-dimensional model to predict FCG under PICC conditions. Extremely fine meshes were generated around the crack tip, in order to predict PICC loads, SIF and plastic zone size. The results showed good agreement with the experimental model, allowing for accurate damage tolerance assessments.

Effect of Constraint and Crack Contact Closure on Fatigue Crack Mechanical Behavior of Specimen under Negative Loading Ratio by Finite Element Method

Mechanical behaviors at fatigue crack tips of cracked specimens under negative loading ratios are studied in detail by the finite element method in this paper. Three factors induced by specimen type and loading type on fatigue crack field are discussed, including constraint, compressive loading effect (CL effect) and crack contact closure. For mode I crack under negative loading ratios, the effects of the CL effect and crack contact closure on plastic strain accumulations are dominant, with the constraint effect being minor. The constraint effect has effects on the monotonous plastic zone, while the CL effect and contact closure both have effects on the reversed plastic zone (RPZ) and residual tensile plastic zone (RTPZ). That is, the higher the constraint, the smaller the size of the monotonous plastic zone; the greater the CL effect, or the smaller the contact degree, the larger the size of RPZ and RTPZ. For mode II crack, there is only CL effect on the crack tip field without the effect of constraint and contact closure, so plastic strain accumulation at the mode II crack tip is much greater than that at the mode I crack tip when they are under the same loading level.

Investigations on fracture characteristics of Aluminium 6082-T6 alloy by Using Single Edge Notch Bending

Aluminium 6082-T6 is a structural alloy having high strength has seen replacing 6061 alloy in engineering applications. During manufacturing process geometric discontinuities are inevitable. The presence of notch in the component is more dangerous. In this paper, the influence of notch length on miniature fracture characteristics of aluminium 6082-T6 alloy has been studied. Experiment was carried in accordance with ASTM standard and specimens were tested by varying the notch length within the specified constraint. Single edge notch bending test was performed on each of specimens under mode-I condition. Results showed that the specimen with minimum notch length has high crack tip initial instability, further increase in the notch length leads to decrease the load carrying capacity, extended portion of crack length and nature of fracture. On experimental observation, plastic zone size near the end of the cut is majorly dependent on notch length of the specimen. The fractured surface analysis also carried on selected specimen with the help of scanning electron microscope. Overall results shows that crack growth and crack propagation vary as a function of notch length and is different in each of the specimens.

A unified approach for describing metallic fatigue short and long crack growth behaviors via plastic accumulated damage

This work investigated the crack growth behaviors of EH36 joints, 316H steels, 6063-T6 and TC4 alloys at room temperature, proposing a unified approach. This model was achieved via the product of monotonic tensile crack tip displacement (φmt) and cyclic crack tip displacement (φc), in which φmt also considered the metallic capability to affect crack propagation behavior to eliminate the effect of material factor on crack growth rate (da/dN). Cyclic plastic zone size (rcp) in φc could describe short crack process and K in φmt could be used for the presentation of long crack behavior. Based on this method, metallic da/dN were linearly related to φmtφc under several variables, such as stress, microstructures, crack scale and loading ratio.

Investigating the transfer of toughness from rubber modified bulk epoxy polymers to syntactic foams

Syntactic foams are lightweight, high specific strength materials used in the aerospace and naval industries. Their utility is limited by their brittleness. The epoxy polymer matrix in an epoxy/hollow glass microsphere (GMS) syntactic foam was modified using carboxyl-terminated butadiene-acrylonitrile (CTBN) rubber with the aim to increase fracture toughness. The microstructure and fracture properties were investigated, and compared to CTBN modified bulk epoxy polymers. The formation of complex CTBN microstructures was responsible for the increase in fracture energy, from 193 J/m2 for the unmodified syntactic foam, to 296 J/m2 at 12 wt% CTBN modification. However, this increase is much smaller than for the CTBN modification of bulk epoxy polymers, where an increase from 101 J/m2 to 1112 J/m2 was measured for the same CTBN concentration. There is little toughness transfer from the bulk epoxy polymers to the syntactic foams, attributable to small interstitial regions between the GMS, restricting plastic zone size. A statistical approach to the analytical modelling of fracture energy in the bulk epoxy polymers highlights the importance of considering the underlying distribution of rubber particle and void sizes. The increase in fracture energy achieved in this work can increase the overall usefulness of syntactic foams in structural applications.

Evaluation of in situ hot-rolling forming effect on plastic zone of wire + arc additively manufactured 5087 alloys using digital image correlation technique

The fatigue crack growth (FCG) rates and crack-tip plastic zone size data for wire + arc additive manufacturing (WAAM)-processed 5087 alloys before and after in situ hot-rolling treatment were investigated and compared. After hot-rolling, the WAAM-processed alloys possessed higher strength. During the FCG tests, the crack-tip field was monitored using a digital image correlation (DIC) technique. The improved FCG resistance and smaller plastic zone area of the WAAM-processed alloys after hot-rolling were responsible for the grain refinement. Therefore, in situ hot-rolling treatment is a promising technique for optimising the properties of WAAM-processed alloys.

Stress intensity-dependent relation between overload plastic zone and fatigue retardation in Al-alloy

Unveiling tensile overload (OL) influence during constant amplitude fatigue is fundamental to life prediction of random fatigue load. Although the same OL results in the same plastic-zone size for a material, subsequent fatigue retardation strongly depends on applied stress intensity, e.g. stress ratio R. This study attempts to separate the contributions of OL-induced residual stress (RS) related to crack closure and applied stress, crack-tip damage zone (DZ), and R-ratio depended crack deflection. To this end, fatigue tests are comparatively analyzed based on combination of different R ratios, the same OL condition, and removing DZ and crack-tip plastic zone. The results show that the fatigue retardation induced by the same OL decreases with increasing R, and the delay retardation disappears after removing DZ at R = 0.7 case. In addition, the OL-induced crack deflection is more obvious at low R = 0.1–0.4 cases than that at R = 0.7 case.

Analysis of Surrounding Rock Pressure of Deep Buried Tunnel considering the Influence of Seepage

This paper takes the surrounding rock of deep tunnel as the research object and considers the action mechanism under the influence of seepage. Based on the Mohr-Coulomb criterion, the stress mechanism of surrounding rock of deep buried tunnel is analyzed by a convergence constraint method. Based on the elastic-plastic solution, the nonlinear elastic-plastic solution of the interaction between surrounding rock and lining structure considering the effect of seepage force is proposed, and the radius of surrounding rock plastic zone is obtained. The relationship between surrounding rock stress and displacement, radial deformation of lining, and support reaction force was observed. At the same time, considering the effects of seepage, strain softening, and intermediate principal stress, the surrounding rock is divided into a plastic residual zone, plastic softening zone, and elastic zone, and the stress distribution expressions of the plastic zone and each zone of surrounding rock of circular tunnel are derived. The results show that with the change of nonuniform permeability coefficient, the seepage shows anisotropy in different directions, and the closer to the horizontal or vertical direction, the more obvious the influence of nonuniform permeability coefficient on pore water pressure distribution. Seepage and material softening have different effects on the distribution of surrounding rock stress field and the size of plastic zone. Material softening is more unfavorable to the stability of surrounding rock than seepage. The intermediate principal stress coefficient has a significant impact on the tangential stress and plastic zone of surrounding rock. When the intermediate principal stress effect is not considered, the calculation results are relatively conservative and cannot give full play to the strength of surrounding rock effectively. The research conclusion can provide a theoretical reference for studying the stability of surrounding rock in tunnel excavation under water-bearing rock.

Essential work of fracture studies of 3D Printed PEEK (Poly-ether-ether-ketone) polymer

The concept of essential work of fracture is implemented for characterizing the raster-orientation-dependent fracture behavior of 3D printed PEEK polymer for the first time. The fracture tests are carried out on various 3D printed double-edge-notched-tension specimens of constant thickness but different raster orientations. It is observed that the fracture initiation energy has a strong dependence on the raster orientation and attains the highest value for 0° raster orientation (printing direction perpendicular to the crack plane) and the lowest value for 90° raster orientation (printing direction parallel to crack plane). The fracture tests have indicated that the ductility levels of the samples and size of plastic zone developed within the ligament region are also controlled by the raster orientation. In addition to fracture tests, the fractured surfaces of the test samples are also examined to identify the dominant failure mechanisms. The detailed analysis carried out in this study provide guidelines in making fracture resistant 3D printed PEEK components.

Plastic anisotropy and twin distributions near the fatigue crack tip of textured Mg alloys from in situ synchrotron X-ray diffraction measurements and multiscale mechanics modeling

In spite of many potential applications due to their superior mechanical properties, magnesium alloys still find many practical restrictions primarily due to our limited knowledge of their failure mechanisms. In situ and non-destructive strain measurements on the microstructural scales are critical in understanding the fatigue crack behavior, which has greater advantages than the macroscopic measurements based on replica technique and the small-scale mechanical testing that cannot easily provide a complete view on the synergy of many scale-dependent deformation and failure mechanisms. This work exploits the state-of-the-art synchrotron X-ray diffraction technique to attain in situ strain mapping results, with high spatial resolution, near a fatigue crack tip in the highly textured ZK60 Mg alloy. The accurate measurements in the plastic zone are compared to a micromechanical modeling framework, in which the steady fatigue crack is simulated by an irreversible, hysteretic cohesive interface model and the surrounding plasticity by Hill anisotropic plasticity. The general agreement in the anisotropic deformation fields is reached down to half of the plastic zone size towards the crack tip, while the discrepancy right at the crack tip can be used to develop an inverse model to extract the material-specific fatigue damage evolution in our future work. It is surprisingly noted that twin activities are localized in a narrow band from the tip to the wake of the fatigue crack, irrespective of the crack growth direction of this textured alloy. Such twin-crack interactions are understood here by our crystal plasticity finite element simulations with several representative crystallographic orientations.

Numerical Modeling of Fracture Height Propagation in Multilayer Formations Considering the Plastic Zone and Induced Stress.

Hydraulic fracturing and acid fracturing are very effective stimulation technologies and are widely used in unconventional reservoir development. Fracture height, as an essential parameter to describe the geometric size of a fracture, is not only the input parameter of two-dimensional fracturing models but also the output parameter of three-dimensional fracturing models. Accurate prediction of fracture height growth can effectively avoid some risks. For example, petroleum reservoirs produce a large amount of formation water because wrong fracture height prediction leads to the connection between the oil or gas reservoir and the water layer. Although some fracture height prediction models were developed, few models considered the effects of the plastic zone, induced stress, and heterogeneous multilayer formation and its interaction. Therefore, considering the influence of many factors, an improved fracture-equilibrium-height model was developed in this study. The successive over-relaxation iteration method and the displacement discontinuity method were used to solve the model. We investigated the effects of the geological and engineering factors on fracture height growth by using the model, and some important conclusions were obtained. The higher the fracture height, the larger the plastic zone size, and the more obvious its influence on fracture height propagation. High overlying or underlying in situ stress and fracture toughness and low fluid density played a positive role in limiting the growth of the fracture height. Induced stress caused by fracture 1 could not only inhibit the height growth of fracture 2 but also promote its growth. The model established in this paper could be coupled to a fracturing simulator to provide a more reliable fracture height prediction.

Can the finite fracture mechanics coupled criterion be applied to V-notch tips of a quasi-brittle steel alloy?

Structures made of steel alloys with V-notches may fracture at the V-notch tip at which a small plastic zone usually evolves. Failure criteria for predicting fracture loads for such quasi-brittle alloys, as a function of the V-notch opening angle are very scarce and have not been validated, to the best of our knowledge, by a set of experimental observations.Herein we provide a database of experiments performed on AISI 4340 steel alloy specimens with three different V-notch opening angles and three different tempering temperatures, loaded in mode I. Material properties, failure load and plastic area at the V-notch tip are detailed.The experimental observations are used to investigate to which extent the finite fracture mechanics coupled criterion (FFMCC) for brittle materials may predict the failure load of quasi-brittle steel alloys, depending on the plastic zone size. Finite element analyses were used to compute the parameters required by the FFMCC. We compared the predicted versus the experimental fracture load for the different V-notch opening angles and tempering temperatures.For small opening angles (30°) for which the plastic area is very small, the FFMCC under-predicts the fracture load by about 20% which is within the experimental error range. The under-prediction of the failure load constantly increases to ∼ 50% as the V-notch angle increases to 90° and plastic zone area on the surface increases to ∼0.5mm2 (for a V-notch depth of 5 mm).The detailed experimental database is suggested to be used for validation purposes when new failure criteria for quasi-brittle materials are developed.

Finite Element Modeling of Indentation Behavior of Dual Phase Steels: Role of Plastic Zone Size in Property Mapping

Finite Element Modeling of Indentation Behavior of Dual Phase Steels: Role of Plastic Zone Size in Property Mapping

Fracture Behavior and Reliability of Low-Silver Lead-Free Solder Joints

Abstract Low-silver solders are increasingly being used because silver improves the tensile strength. In this study, the variation in fracture behavior with silver content in lead-free solder joints was studied using double cantilever beam specimens. Fracture tests were done with solder joints made with Sn-0.7Cu, SACX0307, and SAC305 solder materials. The critical energy release rate for crack-initiation (Gci) of the joint was correlated with the plastic zone just ahead of the precrack tip, intermetallic compound layer thickness, energy dispersive spectroscopy analysis, and scanning electron microscopy based fractography study. The Gci for Sn-0.7Cu solder joint was observed to be significantly higher than the other two solder joints. The fractography study revealed that the failure was ductile for Sn-0.7Cu and a mix of ductile and brittle for the other two solder joints. The extent of the plastic zone ahead of the crack tip, obtained from finite element modeling, was found to be significantly larger and the intermetallic compound layer was relatively thinner for Sn-0.7Cu solder joint compared to the other two solder joints. The ductile failure, significantly larger plastic zone size and thinner intermetallic compound layer resulted in significantly higher Gci for Sn-0.7Cu solder joint.

Temperature dependent fatigue crack growth in electrical steel laminates with μm-thick epoxy layers

The effect of adhesive layer thickness on monotonic roll peel strength and fatigue crack-growth kinetics was investigated for electrical steel laminates with bond line thickness values ranging from 7 to 48 μm. Roll peel strength was increasing with epoxy layer thickness up to 20 μm. In contrast, roll peel strength was leveling at higher thickness values. The fatigue fracture mechanics approach in mode I delivered an equivalent ranking such as roll peel testing. However, energy-based fracture mechanics analysis was much more sensitive than monotonic roll peel testing, also at thicker bond lines. The different failure modes were correlated with the plastic deformation zone size developing at the propagating crack. In case of a constrained plastic zone, cohesive failure mainly within the epoxy layer was ascertained. In contrast, interfacial failure and interestingly also a better fatigue crack growth resistance was deduced for a weakly or non-constrained plastic zone. Regarding the temperature dependency, an enhanced fatigue crack resistance was obtained at 60 °C. At this temperature about 50 °C below the maximum of the loss factor of the epoxy adhesive, the effect of epoxy layer thickness was much smaller than at 23 °C. At testing temperatures slightly below or above the glass transition temperature, the fatigue crack propagation rate was a factor of 10 to 100 higher.

On the slow crack growth process and associated structure–property relationships in polyamide 12 grades

AbstractThe influence of micro‐structural changes within polyamide 12 (PA12) grades on their resistance against crack initiation and subsequent Slow Crack Growth (SCG) was examined. Possible micro‐deformation mechanisms and processes guiding slow crack extensions in PA12 are discussed. Special focus was put on the formation of plastic zones as predecessors to microscopic cracks prior to crack initiation via crack freezing analysis. Simultaneously, variations in the pure SCG resistance after a recorded craze‐crack transition were determined via cyclic Cracked Round Bar (CRB) tests. In that context, a homologous series of PA12 grades of increasing molecular weight (MW), as well as a systematically developed series of PA12 grades incorporating a pigment and/or an impact modifier, were selected for this study. Results show a good correlation between the crack initiation resistance and the disentanglement resistance of PA12 chains as well as the size of the plastic zone. In that context, an increasing average MW, leads to increasing disentanglement resistances due to hydrogen bond effects. An impact modification promotes the development of notably larger plastic zones. Contrarily, colored grades exhibit a reduced plastic zone size, rendering a lower amount of dissipated energy before physical crack initiation. Pure SCG resistance follows a similar trend and is improved by high average MW as well as the use of impact modifier. Crack growth acceleration, however, is assumed to occur alongside the relatively weak interfaces between polymer matrix and pigments.

Fatigue crack growth under overload/underload in different strength structural steels

Aiming at the different strength-level structural steels, fatigue crack growth rate (FCGR) tests were conducted under a series of loading conditions, i.e., constant amplitude load (CAL), single overload (OL), single underload (UL), or periodic underloads (PULs). Meanwhile, the effects of various baseline loading stress ratios on the FCGR were considered. To analyze the effects of crack-tip behavior on the crack propagation following an OL/UL, the crack-tip strain fields and crack opening displacement were obtained by digital image correlation (DIC). It was found that when the OL/UL-amplitude was constant, the fatigue crack propagations under the OL/UL were affected by both steel strengths and baseline loading stress ratios. In general, an increase in the steel strength grade indicated a lower crack retardation/acceleration during the OL/UL process, which was more evident under the lower baseline stress-ratio condition. The higher the strength, the lower the crack-opening stress level, the smaller the plastic zone size, and the higher the crack-tip residual strain. Correspondingly, there were different variations in the instantaneous FCGR and OL/UL-affected cycles. When the OL/ULs are considered in the design stage, our work can guide the steel strength grade selection and provide a better understanding of the crack growth retardation/ acceleration mechanisms.

An improved small-time-scale crack growth rate model considering overloading and load-sustaining effects for deep-sea pressure hulls

The fatigue life assessment of deep-sea pressure hulls needs to consider its load characteristics reasonably, including short-term overloading and load-sustaining at a certain depth in a load cycle lasting several hours. In this case, the traditional reversal-based crack growth rate model is no longer applicable while the small-time-scale model which can consider the crack growth process in any small interval highlights its advantages. This paper presents an improved small-time-scale crack growth rate model with consideration of overloading and load-sustaining effects as well as the stress/strain constraints. The formula for crack tip opening angle is modified to more accurately demonstrate its changing tendency from crack opening to final fracture. A concept of plastic zone influence range is proposed to express the effect of the plastic zone size and the overload ratio. Creep effects at load-sustaining period at high stress level are included into calculation. Finally, model validation and parametric analysis are conducted. The improved model can be reasonably applied for fatigue life prediction of deep-sea pressure hulls.