Theoretical and Applied Fracture Mechanics

Published by Elsevier
Print ISSN: 0167-8442
The fatigue and damage tolerance behaviour of pre-corroded 2024 T351 aluminum alloy specimens has been investigated and compared to the behaviour of the uncorroded material. The experimental investigation was performed on specimens pre-corroded in exfoliation corrosion environment and included the derivation of S–N and fatigue crack growth curves as well as measurements of fracture toughness. The fatigue crack growth tests were performed for different stress ratios R. To obtain reference material behaviour all mechanical tests were repeated under the same conditions for uncorroded specimens. For the corroded material an appreciable decrease in fatigue resistance and damage tolerance was obtained. The results of the experimental investigation were discussed under the viewpoint of corrosion and corrosion-induced hydrogen embrittlement of the 2024 aluminum alloy. The need to account for the influence of pre-existing corrosion on the material’s properties in fatigue and damage tolerance analyses of components involving corroded areas was demonstrated.
This paper presents experimental results on the application of Microsecond Plasma Opening Switch (MPOS) technology to Al alloy surface modification. The main objective of the experiments presented here was to study the change in the tensile and fatigue properties of the MPOS-treated Al2024, Al7075 alloy samples. The bending fatigue test was carried out both in air and in corrosive media. The measurements indicate significant improvement of fatigue properties for the treated 7075 alloy in corrosive media (1.5 times higher in fatigue limit). For the 2024 alloy the enhancement in fatigue lifetime for higher stresses was measured. Anodic polarization curve measurements were carried out at various values of fatigue cycles.
Evaluation was made for the corrosion susceptibility of aircraft structure aluminum alloys 2024 T351, 6013 T6, 8090 T81 and 2091 T84. Tensile and energy density data were obtained. Stereoscopic and metallographic corrosion analysis were made as well. The specimens were pre-corroded using accelerated laboratory corrosion tests or out-door atmospheric conditions before testing. Noticeable decrease of yield and ultimate tensile stress were detected when the specimen surface was corroded. Dramatic volumetric embrittlement was observed even after short exposure times that were not sufficient for the appreciable development of surface corrosion attack. Observed material degradation behavior is attributed to hydrogen penetration and absorption.
Constant amplitude fatigue tests at R = 0.1, conducted on the aircraft aluminum alloy 2024 T3, have revealed an appreciable surface hardness increase of the alloy at the nano- and meso-scale during fatigue. The observed surface hardness changes could be monitored with confidence by means of nanoindentations. The degree of hardening increases with increasing number of fatigue cycles following exponential relations. With increasing fatigue stress level degree of hardening increases as well. The observed results provide a basis for developing concepts to early detect and also monitor fatigue damage accumulation in aluminum aircraft structures based on measurements of the material’s hardness changes by means of nanoindentations.
The present investigation aims to inquire whether Al cladding of 2024 aluminum alloy specimens could provide, additionally to the expected protection against corrosion damage, also a protection against the corrosion induced hydrogen embrittlement of the alloy. The latter is observed when bare 2024 material is subjected to laboratory exfoliation corrosion exposure also in the absence of mechanical loading. Furthermore, the study aims to ponder on the question whether local Al cladding at small regions of the specimen surface might suffice for protecting the specimen against corrosion damage and hydrogen embrittlement. The work comprises the results of an extensive experimental investigation including tensile tests on precorroded 2024 specimens protected through both complete and local surface Al cladding, metallographic and fractographic analyses as well as measurements of the hydrogen uptake during the corrosion process.
During the high cycle fatigue of aluminium alloys, an energy dissipation occurs. This dissipation is hard to be estimated because of the high diffusivity of such alloys and the importance of the thermoelasticity effects in comparison with others standard metallic materials (e.g., steels). Nevertheless the study of the energy balance gives valuable information about the nature of deformation mechanisms facilitating the construction of constitutive models associated with the microplasticity and damage of the aluminium alloy. In this work, the different energies involved in the energy balance were deduced from two complementary imaging techniques. The dissipation and thermoelastic sources were derived from an infrared thermography system, while the deformation energy was estimated from a digital image correlation system. Three tests with various loading blocks were carried out and a comparison between deformation and dissipation energies was systematically performed.
The concept of pressure proof testing of fuselage structures with fatigue cracks to insure structural integrity was evaluated from a fracture mechanics viewpoint. A generic analytical and experimental investigation was conducted on uniaxially loaded flat panels with crack configurations and stress levels typical of longitudinal lap-slice joints in commercial transport aircraft fuselage. The results revealed that the remaining fatigue life after a proof test was longer than that without the proof test because of crack growth retardation due to increased crack closure. However, based on a crack length that is slightly less than the critical value at the maximum proof test stress, the minimum assured life or proof test interval must be no more than 550 pressure cycles for a 1.33 proof factor and 1530 pressure cycles for a 1.5 proof factor to prevent in-flight failures.
The effect of corrosion on the mechanical behavior of the aircraft aluminum alloys 2024 and 6013 has been investigated experimentally. It is shown that corrosion exposure leads to moderate reduction in yield and ultimate tensile stress. Dramatic reduction in elongation to failure and strain energy density are observed even after relatively short exposure times. Mechanical removal of the corroded areas restored the yield and ultimate tensile stress but not the tensile ductility. The latter was stepwise restored to the values for the uncorroded materials after heat treatment of the alloys at temperatures corresponding to thermal desorption of certain hydrogen trapping sites. The findings clearly suggest that corrosion of the above alloys is associated with volumetric hydrogen embrittlement. The corrosion-induced reduction of tensile ductility was associated with the reduction of the residual strength of corroded components. A model, based on a multiscaling concept, was used to relate the reduction of fracture toughness and residual strength to the reduction of the strain energy density obtained from tensile tests for corroded and uncorroded coupons. It has been shown that the strain energy density can be used to reliably predict the residual strength of corroded components.
A fatigue crack growth retardation model is developed. It considers a strip plastic zone with material hardening effect which is taken as one of the basic mechanisms controlling fatigue crack growth. Crack growth is treated incrementally and corresponds to the failure of material elements ahead of an existing crack after a certain critical number of low cycle fatigue. Computed curves are correlated to test data obtained from the 2024-T3 and 6061-T6 aluminium specimens. Deviations from test data increase with increasing crack length.
The synergetic effect of corrosion and corrosion induced hydrogen embrittlement damage processes which occur at local scale has been found to result in a dramatic macroscopic tensile ductility loss of the 2024 aluminum alloy. In the present work, the tensile behaviour of corroded 2024 T351 specimens has been estimated on the basis of FE analysis by taking into account the local material properties in the damaged areas. A parametric study is involved to account for the effect of thickness in the results. Calculated tensile properties obtained with the analysis agree well with experimental data.
Experiments were designed to determine the failure characteristics of AISI 304L stainless steel under different stress triaxialities and temperatures up to 70% of melt. The data show that as temperature increases the displacement to failure of notched tensile specimens increases. The complex interaction of deformation mechanisms, such as twinning and dynamic recrystallization, appears to negate the damage accumulation at higher temperatures. Microstructural analyses and finite element simulations indicate that voids nucleate, grow, and coalesce more rapidly as temperature and triaxiality increase. Finite element simulations were performed to analyze temperature dependence on the Cocks–Ashby void growth model. The finite element simulations qualitatively show a double-knee that was observed in the notched experimental specimens after loading. The combined experimental–numerical study indicates that failure can be defined at several points in the notch tests when: (1) macrovoids starts to form, (2) the load drop-off occurs, and (3) total perforation of the specimen occurs. These three points occur simultaneously in ambient conditions but occur at different displacements at higher temperatures.
Optimization of 3D sharp high speed impactors with given form of a longitudinal contour, length, and volume, penetrating into layered ductile targets, both for conical and thin non-conical strikers using approximate models is studied. It is found that the impactor with the minimum drag moving in a homogenous target with a constant velocity penetrates to the maximal depth into a semi-infinite target and has the minimal ballistic limit when it penetrates into a finite thickness target, regardless of the distribution of the material properties of the target along its depth, the number of the layers, etc. Using the analogy with the hypersonic flow over the flying projectiles it is predicted that the optimal impactor should have a star-shaped form of the cross section. If an impactor has a polygonal cross sections allowing the inscribed circles, the ballistic limit and maximum depth of penetration are independent not only of the properties of the target but also of the form of the polygon in the cross section and equal to the corresponding values for the inscribed body of revolution.
Friction stir welding (FSW) is a solid-state joining process which emerged as an alternative technology to be used in high strength alloys that were difficult to join with conventional techniques. Notwithstanding the widespread interest in the possibilities offered by FSW, data concerning the fatigue behaviour of joints obtained using this process still is scarce. In this work, a comparative study between fatigue crack growth behaviour of friction stir welds of 6082-T6 and 6061-T6 aluminium alloys is carried out. Fatigue crack growth curves were determined for cracks growing in different locations of the weldments, including the base material, the heat affected zone and the welded material. Generally, friction stir material exhibited lower strength and ductility properties than the base material. However, an enhanced crack propagation resistance is observed in the welded material. The 6082-T6 and 6061-T6 base materials exhibit very similar crack propagation behaviours. On the other hand the friction stir 6061-T6 material shows lower crack propagation rates than corresponding 6082-T6 friction stir material. Particular features of the distinct microstructures of the welded and surrounding material are illustrated using scanning electron microscopy.
Unlike vibration and fatigue, repeated impact has not received the attention it deserves. Response of many of the military equipment falls into this category. It involves not only high intensity time-dependent disturbances but also damage accumulation that can lead to premature failure if these effects are not properly accounted for in the design. To this end, the Ordnance Production Service (OPS) of the Republic of China (ROC) has made an effort to develop the methodology for analyzing the dynamic wave propagation history and life expectancy of structural components subjected to repeated impact. This capability will be demonstrated in this work for the XT-75 20 mm cannon support.The design of a cannon support involves knowing the transient load transmission characteristics. In particular, both the location and time corresponding to the maximum dynamic stress and/or energy must be determined. A dynamic finite element computer program using mode superposition is applied in conjunction with the strain energy density failure criterion for determining the structural integrity of the cannon support. More specifically, dynamic stresses, displacements and shape modes are obtained for nine (9) time steps starting from inclusfive and firing angles of −15° to 85° with reference of the 0° horizontal line. Contours of constant volume energy density are plotted to illustrate how the locations of maximum and minimum shift with time. The most detrimental position corresponds to a firing angle of −15° and occurs at approximately seven o'clock on the outer wall of the pivot hole where the recoil force gives rise to high energy intensification. Based on accumulative energy density calculation for an aluminum support, an impact load can be repeated about 90 × 103 time for a cannon firing at 1500 rounds/min. A more conservative estimate would be to assume the existence of a small defect of 10−2 cm in size. This reduces the number of impact to approximately 9 × 103 time.
Void nucleation, growth, and coalescence in A356 aluminum notch specimens was determined from a combination of experiments, finite element analysis, nondestructive analysis, and image analysis. Notch Bridgman tension experiments were performed on specimens to failure and then other specimens were tested to 90%, 95%, and 98% of the failure load. The specimens were evaluated with nondestructive X-ray tomography and optical image analysis. Finite element simulations of the notch tests were performed with an elastic–plastic internal state variable material model that incorporated the pertinent microstructures (silicon particle volume fraction and size distribution and porosity volume fraction and size distribution). Parametric finite element simulations were performed to give insight into various initial conditions and responses of the notch tensile bars. The various methods all corroborated the same damage progression.
The solid state diffusion bonding process is performed using a liquid film protection (LFP) method for AA8090 aluminum alloy in contrast to the more costly vacuum environment. After chemical etching and prior to bonding, aluminum sheets were immersed in dehydrated alcohol to isolate surface from air. Two sheets are then joined with a special clamp to form a specimen which is press-deformed and heated in a salt bath. Protecting liquid film completely volatilizes on heating to bonding temperature thus keeping bonding surface free from oxidation. Effectiveness of the LFP-method is demonstrated in various combinations of process parameters. The contact ratio, in particular, is an important index for bonding strength.
Acoustic Emission (AE) sensing technique is used as a tool for on-line monitoring of hydro-abrasive erosion (HAE) of pre-cracked multiphase materials. As reference materials, five types of concrete materials were used for the experimental study. Compression tests were performed to determine the mechanical properties and the failure behavior of these materials. Erosion parameters, such as abrasive particle velocity, local exposure time, and abrasive mass flow rate were varied during the experiments and AE-signals were acquired. The trends exhibited by the time domain and frequency domain AE-signals with change in process parameters and material properties were analyzed. The results indicate that acoustic emission signal is capable of revealing the different material removal mechanisms occurring in pre-cracked multiphase materials when subjected to hydro-abrasive erosion. Visualization studies performed on the erosion site provide more insight into the physics of the process and verify the observations made from the AE-signals. Finally, it is concluded that due to its capability to quantify the amount of material removed, AERMS could be considered as a parameter for monitoring the material removal process.
Energy dissipation at the macroscopic scale, applied to large bodies, relies on using the average bulk or global properties. The normal procedure is to load/unload a uniaxial tensile specimen, and account for the difference of the area under the stress and strain curve, even though unloading does not occur in reality. The same procedure, however, is not feasible for treating the energy dissipation at the microscopic scale, applied to small bodies, where the space/time dependency of the local material properties plays a role. That is the transient character of the energy transfer between the specimen surface and surrounding can no longer be neglected. Moreover, there is no way to simulate microscopic unloading. Besides, the coupon test scheme of load/unload, an artifact, that has been used because of no other choice.
Analyzed in this work is the four-point bending of a concrete slab supported by a steel beam. An edge crack is assumed to prevail on the tension side of the concrete that would grow gradually while the overall stiffness and local fracture toughness of the concrete would also degrade as damage accumulates. The latter two quantities are assumed to decrease with increasing deflection of the composite system. These effects are incorporated into the strain energy density criterion that can simultaneously predict crack initiation and growth including the event of final termination. Numerical results on load and deflection are obtained for two different composite concrete/steel beam systems such that the prevailing geometric material and loading parameters are accounted for as a combination. The distances between the local and global stationary values of the volume energy density are also determined as an indication of fracture instability. An edge crack tends to extend more stably as the compressive zone ahead increases with deflection of the composite beam.
A pseudo-elastic damage-accumulation model is developed by application of the strain energy density theory. The three-point bending specimen is analyzed to illustrate the crack growth characteristics according to a linear elastic softening constitutive law that is typical of concrete materials. Damage accumulation is accounted for by the decrease of elastic modulus and fracture toughness. Both of these effects are assessed by means of the strain energy density functions in the elements around a slowly moving crack. The rate of change of the strain energy density factor S with crack growth as expressed by the relation dS/da = constant is shown to describe the failure behavior of concrete. Results are obtained for different loading steps that yield different slopes of lines in an S versus a (crack length) plot. The lines rotate about the common intersect in an anti-clockwise direction as the load steps are increased. The intersect shifts upward according to increase in the specimen size. In this way, the combined interaction of material properties, load steps and specimen geometry and size are easily analyzed in terms of the failure mode or behavior that can change from the very brittle to the ductile involving stable crack growth. An upper limit on specimen or structural size is established beyond which stable crack growth ceases to occur and failure corresponds to unstable crack propagation or catastrophic fracture. The parameters that control the failure mode are the threshold values of the strain energy density function (dW/dV)c and the strain energy density factor Sc.
Repeated loading of the outer strut leg of the Björk–Shiley 60° convexo-concave (BSCC) valve results in fatigue crack propagation, with a duration from a few months to a few years. Sound and vibration analysis emitted from the strut of the BSCC valve due to impact is used to monitor the propagation of the fatigue crack before it would lead to the failure of one or both legs of the outlet strut. Analytical and experimental results established that the range of the fundamental natural frequency is 4000–8000 Hz. Analysis of sound emitted from the strut of the valve due to impact may be used to monitor the propagation of the fatigue crack before it would lead to the failure of the one or both legs of the outlet strut.
One of the major problems confronted by the designer of submersibles is to minimize the weight of the pressure hull for increasing the payload of a crew and necessary equipment and to simultaneously enhance the strength of the pressure hull for withstanding hydrostatical pressure, underwater explosive loading and other environmental loading. Hence, this paper presents the optimal design of a small-scale midget submersible vehicle (MSV) pressure hull with a ring-stiffened cylinder and two hemispherical ends subjected to hydrostatic pressure, using a powerful optimization procedure combined the extended interior penalty function method (EIPF) with the Davidon-Fletcher-Powell (DFP) method. According to the above optimum design results, we built up midget submersible vehicle finite element model. Then, the coupled acoustic–structural arithmetic from the widely used calculation program of the finite element – ABAQUS, was used to simulate and analyze the transient dynamic response of a midget submersible vehicle pressure hull that experiences loading by an acoustic pressure shock wave resulting from an underwater explosion (UNDEX). The analytical results are presented which will be used in designing stiffened optimum submersible vehicle so as to enhance resistance to underwater shock damage.
Compliance change and crack tip stress intensity factor are applied to study the failure behavior of a reinforced beam with an edge crack in the matrix. Equal and opposite forces are applied to the crack surfaces to simulate the constraint of the reinforcement. Defined is a brittleness number that reflects the relative influence of the critical moment to trigger fracture and that to yield the reinforcement and hence the stability of crack propagation. Minimum reinforcement for stable failure corresponds to the condition when these two threshold moments are nearly equal. Numerical results are displayed graphically so that specific values of the loading and geometric parameters for a given failure behavior can be determined.
In previous work, the stresses of a mode I elastic–plastic fracture mechanics problem were analytically continued across a prescribed elastoplastic boundary for plane stress loading conditions involving a linear elastic/perfectly plastic material obeying the Tresca yield condition. Immediately across the elastic-plastic boundary, a nonlinear parabolic partial differential equation governs the plastic stress field. The present solution deals with stresses extending beyond the parabolic region into the hyperbolic region of the plastic zone. This analytical solution is obtained through a tranformation of the original system of nonlinear partial differential equations into a linear system with constant coefficients. The solution, so obtained, is expressible in terms of elementary transcendental functions. It also exhibits a limiting line which passes through the crack tip. This feature of the solution suggests the formation of a plastic hinge in the material.
Under general loading conditions, there is no guarantee that the crack surfaces will be fully open. Complete or partial closure of the crack could occur if the surrounding material is compressed. Such a phenomenon is illustrated for the situation of a single crack engulfed by a remote but uniform compressive stress field while tensile forces are applied at isolated points so that the material can counteract against the compressive field. Examples are provided illustrating partial crack closure with or without symmetry about the mid-plane normal to the crack surface. Considered will be mechanical and thermal loadings.
The peridynamic theory is advantageous for problems involving damage since the peridynamic equation of motion is valid everywhere, regardless of existing discontinuities, and an external criterion is not necessary for predicting damage initiation and propagation. However, the current solution methods for the equations of peridynamics utilize explicit time integration, which poses difficulties in simulations of most experiments under quasi-static conditions. Thus, there is a need to obtain steady-state solutions in order to validate peridynamic predictions against experimental measurements. This study presents an extension of dynamic relaxation methods for obtaining steady-state solutions of nonlinear peridynamic equations.
In summary, the susceptibility to embrittlement during thermal ageing of the three classes of steel discussed is determined by the concentration of impurities, notably phosphorus. In some cases for steels and 9Cr steels, which operate at higher temperatures, additional embrittlement susceptibility is due to microstructural changes during heat treatment or ageing. In both cases, the silicon content plays an important role: in the case of steels silicon stabilises the formation of Cr-rich M6C which, in turn, promotes P segregation and interfacial embrittlement; in the case of 9Cr steels, silicon promotes Laves phase formation at grain boundaries which leads to a rise in DBTT and a lowering of upper shelf energy at intermediate ageing times.
Presented in this work is a qualitative assessment of microstructure damage caused by thermal shock fatigue for steels tested at different elevated temperatures. Subgrains are developed prior to the nucleation of microcracks. Changes in the metallurgical structure are also identified. Quantitative assessment of these observed events remains to be done. A possible candidate as a criterion is the Absorbed Specific Fracture Energy.
As PWR (Pressure Water Reactor) components are submitted to mechanical and thermal loadings in addition to being exposed to aggressive chemical and nuclear environments, thay are subject to damage. Safety and reliability connected with operation of nuclear power plants are a concern. Undertaken in France is evaluating and monitoring the degradation process of PWR components for the nuclear steam supply syste (NSSS).Discussed are the schemes for in-service surveillance and transient monitoring which could assist in decision making. Nondestructive inspection is applied to evaluate damage due to cracking enhanced by corrosion, irradiation and fatigue.
The effects of physical aging on fracture and yielding behavior are polycarbonate are considered. Two groups of Bisphenol A-based polycarbonate, consisted of extruded PC sheets (thickness of 0.25 mm) and injection molded PC bars (thickness of 3.18 mm) are used. These samples were annealed at various temperatures ranging from 60 to 120 °C, for different times varying up to 240 h. For PC sheets the essential work of fracture (EWF) method was used to analyze fracture behavior. The results are compared to the strain energy density with aging time and aging temperature in the ranges investigated. This effect is confirmed by the change in fracture toughness, as measured by three-point bending tests. The concept of fictive temperature (Tf) was used to characterize the degree of aging in the sample. Tf of a glass in an aged state at a time t is defined as the temperature at which the volume would be equal to the equilibrium volume at Tf if the sample were instantaneously removed to that temperature. Differential scanning calorimetry (DSC) was used to determine Tf. The variations of Tf with aging time and aging temperature are in agreement with both the strain energy density measurement and the three-point bending tests. These results contradict the effects of aging on fracture toughness observed by the essential work of fracture approach. The latter showed anomalous regions of increasing fracture toughness with aging, leading to spurious conclusions. The brittle–ductile transition in fracture behavior is analyzed by an activation energy approach. Aging increases the brittle–ductile transition temperature and the effect is more pronounced for the lower molecular-weight sample. Fracture tests also showed a decrease in the entropy with aging, confirming the results observed previously from tension and compression tests.
In contrast to the notion that heating prevails in the material when stressed, a period of cooling followed by heating is predicted to occur in the cracked speciment upon loading. This findings does not only confirm with the recent experiments made on AISI 316 steel [1] but it supports the existence of a damage free zone ahead of the crack within which the energy dissipation is extremely low as compared with those outside. The size of this zone can be macroscopic or otherwise depending on the scale level of observation. It is not uniquely determined by material type as it can change with the local crack tip strain rate that obviously depends on the load-time history. The idea of the material process zone that has been widely referred to in fracture mechanics must, therefore, be seriously questioned.
The fracturing of glass and tearing of rubber both involve the separation of material but their crack growth behavior can be quite different, particularly with reference to the distance of separation of the adjacent planes of material and the speed at which they separate. Relatively speaking, the former and the latter are recognized, respectively, to be fast and slow under normal conditions. Moreover, the crack tip radius of curvature in glass can be very sharp while that in the rubber can be very blunt. These changes in the geometric features of the crack or defect, however, have not been incorporated into the modeling of running cracks because the mathematical treatment makes use of the Galilean transformation where the crack opening distance or the change in the radius of curvature of the crack does not enter into the solution. Change in crack speed is accounted for only via the modulus of elasticity and mass density. For this simple reason, many of the dynamic features of the running crack have remained unexplained although speculations are not lacking. To begin with, the process of energy dissipation due to separation is affected by the microstructure of the material that distinguishes polycrystalline from amorphous form. Energy extracted from macroscopic reaches of a solid will travel to the atomic or smaller regions at different speeds at a given instance. It is not clear how many of the succeeding size scales should be included within a given time interval for an accurate prediction of the macroscopic dynamic crack characteristics. The minimum requirement would therefore necessitate the simultaneous treatment of two scales at the same time. This means that the analysis should capture the change in the macroscopic and microscopic features of a defect as it propagates. The discussion for a dual scale model has been invoked only very recently for a stationary crack. The objective of this work is to extend this effort to a crack running at constant speed beyond that of Rayleigh wave. Developed is a dual scale moving crack model containing microscopic damage ahead of a macroscopic crack with a gradual transition. This transitory region is referred to as the mesoscopic zone where the tractions prevail on the damaged portion of the material ahead of the original crack known as the restraining stresses, the magnitude of which depends on the geometry, material and loading. This damaged or restraining zone is not assumed arbitrarily nor assumed to be intrinsically a constant in the cohesive stress approach; it is determined for each step of crack advancement. For the range of micronotch bluntness with 0 < β < 30° and 0.2 ⩽ σ∞/σ0 ⩽ 0.5, there prevails a nearly constant restraining zone size as the crack approaches the shear wave speed. Note that β is the half micronotch angle and the applied stress ratio is σ∞/σ0 with σ0 being the maximum of the restraining stress. For σ∞/σ0 equal to or less than 0.5, the macrocrack opening displacement COD is nearly constant and starts to decrease more quickly as the crack approaches the shear wave speed. For the present dual scale model where the normalized crack speed v/cs increases with decreasing with the one-half microcrack tip angle β. There prevails a limit of crack tip bluntness that corresponds to β ≅ 36° and v/cs ≅ 0.15. That is a crack cannot be maintained at a constant speed if the bluntness is increased beyond this limiting value. Such a feature is manifestation of the dependency of the restraining stress on crack velocity and the applied stress or the energy pumped into the system to maintain the crack at a constant velocity. More specifically, the transitory character from macro to micro is being determined as part of the unknown solution. Using the energy density function dW/dV as the indicator, plots are made in terms of the macrodistance ahead of the original crack while the microdefect bluntness can vary depending on the tip geometry. Such a generality has not been considered previously. The macro-dW/dV behavior with distance remains as the inverse r relation yielding a perfect hyperbola for the homogeneous material. This behavior is the same as the stationary crack. The micro-dW/dV relations are expressed in terms of a single undetermined parameter. Its evaluation is beyond the scope of this investigation although the qualitative behavior is expected to be similar to that for the stationary crack. To reiterate, what has been achieved as an objective is a model that accounts for the thickness of a running crack since the surface of separation representing damage at the macroscopic and microscopic scale is different. The transitory behavior from micro to macro is described by the state of affairs in the mesoscopic zone.
High velocity penetration of a rigid conical impactor into a ductile target with air gaps between the plates is studied using the cylindrical cavity expansion approximation describing impactor–target interaction. It is showed that the latter model predicts improvement of the ballistic performance of the target with the increase of air gaps. It is found analytically that the ballistic limit velocity of the target consisting of N plates with a fixed total thickness with large air gaps increases with the increase of N. The conditions are discussed when the predicted effects can be most pronounced.
In this paper, the incremental theory of plasticity is used in conjunction with the strain energy density criterion to determine the stress field in 4-in. wide test specimens containing 3 holes. These specimens, made from 0.04-in. thick sheets of 2024-T3 aluminum, also contained small collinear cracks emanating from the holes. The initial crack sizes varied from 0.15 to 0.26 in. Residual strength tests conducted with these specimens revealed that stable tearing occurred before failure. Analyses were performed to predict the stable crack extension and failure by plastic collapsed. Because of the complexities involved with nonlinear stress analysis combined with subcritical crack extension, the finite element method was used with the grid pattern adjusted for each increment of stable tearing. Reasonable correlation between the experimental data and predicted results was achieved.
The BFRP crack-patching technique has been applied to the field repair of fatigue cracks in the aluminium alloy wing skins of Mirage III fighter aircraft. Finite-element procedures were used in patch design. The repair was qualified using fatigue-crack propagation studies on panels simulating the cracked and repaired area. A field support unit was designed to allow repairs to be carried out by air force personnel during routine maintenance of the aircraft. To date over 150 patches have been applied and nearly three years of operational history gained. While some crack growth was observed after repair of a few wings, the patch stopped further growth and no wing skin has required further repair.
The use of composite patches on cracked portions of metallic aircraft structures is an accepted means of improving fatigue life and attaining high structural efficiency. As more and more advanced composite materials are beng developed, the wider use of the repair technology is anticipated even for the reinforcement of primary aircraft structure. The objective of this work is to illustrate how the composite patch repair technology can be successfully applied to restore the structural integrity of cracked components.The Phosphoric Acid Anodize (PAA) surface treatment on aluminum when applied in conjunction with the AVI13/HV998 adhesive were essential for achieving the appropriate patch bonding strength. Such a process was done without immersing the component into the PAA tank; dismantling the component from the aircraft was not necessary. Boron/epoxy and carbon/epoxy patches were applied at room temperature to the 7075-T6511 cracked specimens and tested under fatigue simulating the load spectrum for the upper longeron attached to the access door of the electronic equipment bay. Considerable improvement in the fatigue life was observed after the repair. Equivalent flight test hours were increased from approximately two thousand hours at which the component fractured completely when not repired to twelve thousand hours when the repair was made with only a small amount of crack growth. A six times increase fatigue life is obtained. The laboratory developed technique has been applied to several in-service aircraft which have now been flown for more than 700 h without detection of crack growth.
This paper discusses an analytical and experimental investigations of the fatigue crack growth behavior in attachment lugs subjected to a randomized flight-by-flight spectrum. In the analysis, the stress intensity factors for through-the-thickness cracks initiating from lug holes were compared by weight function method, boundary element method (BEM), the interpolation of Brussat’s solution. The stress intensity factors of a corner crack at a transition region were obtained using two parameter weight function method and correction factors. Fatigue life under a load spectrum was predicted using stress intensity factors and Willenborg retardation model considering the effects of a tensile overload. Experiments were performed under a load spectrum and compared with the fatigue life prediction using the stress intensity factors by different methods. Changes of fatigue life and aspect ratio according to the clipping level of the spectrum were discussed through experiment and prediction. Effect of the spectrum clipping level on the fatigue life was experimentally evaluated by using beach marks of fractured surface.
This work attempts to assess the available data concerning reversed temper embrittlement (RTE) effects in low alloy ferritic steels and to evaluate the influence of this embrittlement phenomena on the environmental assisted crack (EAC) growth, behaviour of low alloy steels in pressurised water reactor, (PWR) environments.It has been demonstrated that RTE could be anticipated in reactor pressure vessel (RPV) steels with the worst effects occuring in the heat affected zone (HAZ) regions. The segregation of residual elements to gain boundary locations can promote enhanced EAC growth processes in low alloy steels, viz., stress corrosion cracking (SCC) hydrogen assisted cracking (HAC) and corrosion fatigue (CF). Hence, the possibility that RTE effects in RPV steels can enhance EAC growth processes cannot be overlooked and studies including RTE-EAC growth interactions are required to determine the future long term safe operation of working PWR facilities.
Fatigue crack growth behaviour from a lack of penetration (LOP) defect in austenitic stainless steel weld metals of cruciform joints made of a low alloy high strength (Q & T) steel has been studied to understand the effect of two welding processes, namely, shielded metal arc welding (SMAW) and flux cored arc welding (FCAW). Fatigue crack growth studies were carried out at a stress ratio of R = 0 and a frequency of 90 to 110 Hz in a resonant testing equipment (Rumul, Model:8601). Crack growth rates were relatively lower in the weld metal obtained by flux cored arc welding process. Microstructural features observed revealed marked difference in the morphology of delta ferrite for the welded joints obtained from the above two welding processes. Long streaks of delta ferrite in austenite matrix were found in case of SMAW-weld metal which seem to have lowered the resistance to the fatigue crack propagation. A discontinuous network of delta ferrite found in austenite matrix in the case of FCAW-weld metal seems to have contributed to slower propagation of fatigue crack. Fractographic features also substantiate the observed trends in the fatigue crack growth behaviour.
An energy approach has been used in the study of the coalescence or linkage of multiple cracks in aluminum alloy sheets. The study was motivated by concern for the structural integrity of aging aircraft. Forty reported tests for 2024-T3 aluminum panels with a major crack and several multiple-site damage (MSD) cracks have been analyzed via a simple computational model with a Dugdale–Barenblatt [D.S. Dugdale, J. Mech. Phys. Solids 8 (1960) 100–104; G.I. Barenblatt, in: H.L. Dryden, Th. VonKarman (Eds.), Advances in Applied Mechanics, vol. II, 1962, pp. 55–130] type of plastic or inelastic deformation. For simplicity, the computational model considers only the plastic interaction between the major crack and two symmetrically adjacent MSD cracks in an infinite sheet under remote tensile stress. By following the approach given in [B. Cotterell, J. K. Reddel, Int. J. Fract. 13 (1977) 267–277], the specific work to cause ligament failure is found to be a linear function of the normal extent of the confined plastic region for most tests considered. A few exceptions to this linear relation are attributed to the limitation of the employed computational model. A new criterion and an engineering method to predict crack link-up in an MSD sheet are proposed based on this specific work concept, and they have been demonstrated through application to stiffened panels.
The study reported in this paper deals with the experimental determination of the effect of the two-phase microstructure of an aluminum-silicon alloy on the propagation of fatigue-induced fracture. The work involved the use of a computerized apparatus which applied four-point bending loads to test specimens inside the vacuum chamber of a scanning electron microscope (SEM). The use of the SEM allowed for the in-situ monitoring of the progression of the fatigue crack with respect to the microstructure of the material.A constant load amplitude fatigue test was established for the experimental system and an analytic model is proposed to predict the growth of the crack in the specimen using compliance measurements. In-situ tests were performed on a variety of test aluminum-silicon alloy specimens. Preliminary results show that a relationship exists between the silicon phase in the aluminum matrix and propagating fatigue crack. Data from these tests were used to evaluate both the model mentioned above and an analytic relation for the stress intensity factor for a beam containing a crack subjected to four-point bending.
Internal state variable rate equations are cast in a continuum framework to model void nucleation, growth, and coalescence in a cast Al–Si–Mg aluminum alloy. The kinematics and constitutive relations for damage resulting from void nucleation, growth, and coalescence are discussed. Because damage evolution is intimately coupled with the stress state, internal state variable hardening rate equations are developed to distinguish between compression, tension, and torsion straining conditions. The scalar isotropic hardening equation and second rank tensorial kinematic hardening equation from the Bammann–Chiesa–Johnson (BCJ) Plasticity model are modified to account for hardening rate differences under tension, compression, and torsion. A method for determining the material constants for the plasticity and damage equations is presented. Parameter determination for the proposed phenomenological nucleation rate equation, motivated from fracture mechanics and microscale physical observations, involves counting nucleation sites as a function of strain from optical micrographs. Although different void growth models can be included, the McClintock void growth model is used in this study. A coalescence model is also introduced. The damage framework is then evaluated with respect to experimental tensile data of notched Al–Si–Mg cast aluminum alloy specimens. Finite element results employing the damage framework are shown to illustrate its usefulness.
Transmission electron microscopy was used to investigate the reorientation of crystal lattice during the formation of ultrafine-grained (UFG) copper, nickel, and an alloy of Ni–18% Al–8% Cr–1% Zr–0.15% B (at.%) under severe plastic deformation by equal-channel angular (ECA) pressing and twisting at a high quasi-hydrostatic pressure. The crystal lattice was found to transform into a UFG state; it is fragmented at the nano-, micro-, and mesoscale levels. Possible mechanisms for the reorientation of the crystal lattice under deformation at the micro- and mesoscale level are discussed.
A centre cracked plate subjected to remote tensile and shear loading is considered for the analysis. Effect of circular hole and influence of shrunk fit inclusion on stress intensity factors are studied. Multiply connected domain boundary value problem is solved using finite element alternating method (FEAM). Parametric studies involving drilled hole/inclusion sizes and locations are investigated. Energy release rates evaluated using the stress field obtained by FEAM are in good agreement with other methods. The optimum location in reducing the stress intensity factor with hole/inclusion is obtained and located at a distance 20% of semi-crack length from crack tip on the side opposite the ligament for Mode-I loading and it is also observed that the location is almost invariant of hole sizes. For Mode-II loading, the optimum location for the hole is located at a distance about 23% of semi-crack length from the middle of the crack along the transverse direction.
Microstructure and mechanical response of alumina matrix reinforced with carbon coated and uncoated SiC whiskers were examined. Carbon coating was used in order to modify the interface and possibly relax the residual thermal stresses developed on cooling from the hot-pressing temperature. Crack propagation behaviour and interfacial properties of the composite were studied using scanning and transmission electron microscopy. Resistance to fracture was assessed by using four point bend test and failure load was determined using four point chevron notched beam and double cantilever beam specimens. The improvement in fracture resistance in carbon coated whisker composites was attributed to whisker pull out, crack bridging and crack deflection.
Numerical simulations of the penetration processes in aluminium blocks by spherical-nose steel rods were performed in this study. The specific impact configuration of this study involves 152-mm diameter 6061-T651 aluminum bars impacted by spherical-nose projectiles machined from T-200 maraging steel rods at nominal impact velocities between 300 and 1000 m/s. The transient dynamic finite element code LS-DYNA2D was used for the numerical analysis. The erosion capability in LS-DYNA2D was exercised in conjunction with the maximum equivalent plastic strain criterion to carry out failure simulations in the target. Calculated results were compared to the experimental data. Good correlation was obtained.
Hypervelocity impact is a highly nonequilibrium process because the states traversed by the system cannot be described in terms of constitutive parameters that represent the system as a whole. Spontaneous changes of local material elements defy equilibrium and hence homogeneity. A consistent description of the hierarchy of damage states is made possible only by synchronizing the thermal fluctuation with mechanical deformation. This involves considering nonequilibrium dissipative effects that are beyond the scope of classical continuum mechanics and physics.The damage states of a projectile impacting a target at hypervelocity are predicted by application of the isoenergy density theory. In addition to failure by fracture and fragmentation, the analysis also includes local phase transitions where a portion of the solid may transform to liquid and/or gas. Changes in local strain rates and strain rate history are derived rather than preassumed. This enables a realistic evaluation of intense deformation, heating, melting and vaporization that occur nonhomogeneously in the projectile/target system during the course of impact. The case of a tungsten projectile impacting on an aluminum target at 9000 m/s is presented as an example. The sequence of nonequilibrium damage states is traced in nanoseconds. Within approximately 15 ns, the local strain rate in the aluminum target increased to 104 s−1 for the solid phase and 105 s−1 for the liquid phase. Phase transformation has already occured locally. The solid/liquid interface is highly unstable with a strain rate of the order of 108 to 109 s−1. The average strain rate in the tungsten projectile is 103 s−1. The size and speed of debris splashing into the empty space are also predicted. The velocity of the debris is found to be more than eight times the initial impact velocity of the projectile, a result that agrees with past observations.
This experimental study is concerned with enhancing the buckling characteristics of sandwich structure when the 6061-T6 aluminum skins are replaced by carbon fiber reinforced composite for the same aluminum honeycomb and polyurethane core. Such an improvement can be attributed to the high strength to weight ratio of the composite skin while the softer core material acts on a relative base as a better energy absorbent and hence tends to stabilize the failure. This results in much higher post-buckling loads which corresponds to the remaining strength of the structure after the onset of buckling.Sandwich structures with core made of polyurethane foam with different densities were also tested in compression. The buckling load increased with the density of polyurethane up to 280 kg/m3 while deattachment of the core and skin occurred when the density is decreased below 100 kg/m3. Compatibility of the skin and core material is shown to play an important role in the buckling behavior of sandwich structure.
An analytical approach to the cellular structure of closed-cell type Al foam for determining the mechanical properties is valuable for the development of materials. In the present work a three-dimensional model is developed taking into account the cell geometry (circular, elliptic, rectangular and square) of the foam material. The model permits the evaluation of the effect of cell geometries and their effect on two basic material properties: the Young’s modulus and the plateau stress. The proposed model simulates an experimental compression test for closed-cell Al foam allowing determination of its mechanical properties.It was found that the values of the mechanical properties determined by the model that assumes an elliptical cell structure are in good agreement with the experimental results for Al foams. These values are also in good agreement with the theoretical results of other investigators.
Top-cited authors
Filippo Berto
  • Sapienza University of Rome
Timon Rabczuk
  • Bauhaus-Universität Weimar
Xiaoying Zhuang
  • Tongji University
Majid R. Ayatollahi
  • Iran University of Science and Technology
M.R.M. Aliha
  • Iran University of Science and Technology