Prediction of crack opening stress levels for 1045 quenched and tempered steel under service loading spectra

The opening stresses of a crack emanating from an edge notch in a 1045 quenched and tempered steel specimen were measured under two different Society of Automotive Engineers (SAE) standard service load histories having different average mean stress levels. The two spectra are the Grapple Skidder history (GSH), which has a positive average mean stress, and the Log Skidder history (LSH), which has a zero average mean stress. To capture the behaviour of the crack opening stress in the material, the crack opening stress levels were measured at 900X using an optical video microscope, at frequent intervals for each set of histories scaled to two different maximum stress ranges.A crack growth analysis based on a fracture mechanics approach was used to model the fatigue behaviour of the steel specimens for the given load spectra and stress ranges. Crack growth analysis was based on an effective strain‐based intensity factor, a crack growth rate curve obtained during closure‐free loading cycles and a local notch strain calculation based on Neuber's rule.The crack opening stress (S_op) was modelled and the model was implemented in a fatigue notch model, and the fatigue lives of the specimens under the two different spectra scaled to several maximum stress levels were estimated. The average measured crack opening stresses were between 6 and 12% of the average calculated crack opening stresses. In the interest of simplifying the use of S_op in design, the average S_op was correlated with the frequency of occurrence of the cycle reducing the S_op to the average crack opening stress level. The use of an S_op level corresponding to the cycle causing a reduction in S_op to a level reached once per 10 cycles gave a conservative estimate of average crack opening stress for all the histories.     

Loading‐rate dependence of mode I crack growth in concrete

Mode I crack propagation process of concrete under relatively low loading rates which cover four orders of magnitude (0.2 μm/s to 2.0 mm/s) is investigated with three‐point bending (TPB) beams. All measured material properties exhibit rate sensitivity and follow a log‐linear relationship with the loading rate. A rate‐sensitive softening curve is established. The complete load‐crack mouth opening displacement (P‐CMOD) curve, crack propagation length, and fracture process zone (FPZ) length are simulated based on crack growth criterion with the fitted material parameters under those loading rates. Results show that the simulated P‐CMOD curves agree well with those of experimental measurements. It is clear that the peak load increases with the loading rate and so is the critical crack mouth opening displacement. Moreover, under the same load level, the length of the FPZ and the cohesive stress at the initial crack tip also increase with the increasing loading rate.     

Observation of deformation and damage at the tip of cracks in adhesive bonds loaded in shear and assessment of a criterion for fracture

The evolution of damage at the tip of cracks in adhesive bonds deforming in shear was monitored in real time using a high-magnification video camera. Brittle and a ductile epoxy resins were evaluated, with the bond thickness t being an experimental variable. An extensive zone of plastic deformation developed ahead of the crack tip prior to fracture. In the case of the brittle adhesive, for relatively thick bonds tensile microcracks formed within that zone. Increased loading caused the microcracks to grow from the interlayer to the interface, which led to a complete bond separation after interface cracks emanating from adjacent microcracks linked. In contrast, for the ductile adhesive the crack always grew from the tip. Strain gradients tended to develop there when the bond thickness was large.The adhesive shear strain was determined from fine lines scratched on the specimen edge. For both adhesives, the average crack tip shear strain at crack propagation rapidly decreased with increasing t. This effect was attributed to the changing sensitivity of the bond to the presence of flaws; thicker bonds can accommodate larger microcracks or microvoids which cause greater stress concentration. For a given bond thickness, the critical crack tip shear strain agreed well with the ultimate shear strain of the unflawed adhesive previously determined using the napkin ring shear test [12]. This suggests that the ultimate shear strain is a key material property controlling crack growth. The critical distortional strain energy/unit area of the unflawed adhesive W _s was determined from the area under the stress-strain curve in the napkin ring test. Good agreement between W _s and the adhesive mode II fracture energy was found for all joints tested except for relatively thick bonds. For the particular case of an elastic-perfectly plastic adhesive, the agreement above implies % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGak0dh9WrFfpC0xh9vqqj-hEeeu0xXdbba9frFj0-OqFf% ea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr% 0-vqpWqaaeaabaGaciaacaqabeaadaqaaqaaaOqaaGqaciaa-Deada% WgaaWcbaacbaGaa4xsaiaa+LeacaGFdbaabeaakiabg2da9iaa-Dfa% daWgaaWcbaGaa83CaaqabaGccqGHHjIUcaWF0bGaeqiXdq3aaSbaaS% qaaiaa-LhaaeqaaOGaeq4SdC2aaSbaaSqaaiaa-zgaaeqaaaaa!463A!\[G_{IIC} = W_s \equiv t\tau _y \gamma _f \].     

Interface crack initiation at V-notches along adhesive bonding in weakly bonded polymers subjected to mixed-mode loading

In this paper, interface crack initiation at V-notches along adhesive in bonded Polycarbonate (PC) and Poly Methyl Methacrylate (PMMA) subjected to mixed-mode loading conditions was investigated based on a combined experimental, finite element and matched asymptotic analysis. The V-notch specimens with an adhesive interface starting from its tip made at different notch angles were tested under three-point bending conditions. The experimental observations show that the specimens mainly fail by cracks along the interface. Also, the load at the crack initiation increases when the notch angle increases. The computational results are then used to explain and to correlate with the experimental data. A two-fold criterion developed by Leguillon (Eur J Mech A/Solids 21:61?C72 2002) that requires a simultaneous satisfaction of both Griffith energy and stress conditions for the crack initiation at a notch in the specimen made of a homogeneous brittle material is first extended for V-notch specimens under mixed-mode loading conditions and then used to estimate the crack initiation load. The estimated loads appear to agree well with the experimental data. Finally, an inverse method is proposed to estimate the values of fracture toughness at different mode mixity ratios.     

Parameters affecting the damage tolerance behaviour of railway axles

The paper provides a discussion on damage tolerance options applied to railway axles and factors influencing the residual lifetime as well as the required inspection interval. These comprise material properties such as the scatter of the da/dN–ΔK curve, the fatigue crack propagation threshold ΔK_th and the toughness of the material. Parameters affecting axle loading such as the press fit, rotating bending, load history and mixed crack opening modes are discussed. Finally the influence of the initial crack geometry on residual lifetime is simulated.     

Micromechanics of shear deformations in cracked bonded joints

Experiments and analytical analysis were carried out to elucidate the process of crack propagation in adhesively bonded joints loaded in mode II. The adhesive used was a toughened epoxy resin, with the bond thickness varying from a few micrometers to 0.6 mm. The development of a plastic deformation zone at the crack tip was monitored in real-time using a high-magnification video camera. Within the plastic zone the adhesive shear strain, determined from scratch marks applied to the specimen edge, was uniform across the bond except for several bond thicknesses long region just ahead of the crack tip where, depending on bond thickness, noticeable strain gradients may develop. The experimental results suggest that the critical shear strain at the crack tip is a viable fracture criterion. A simplified analysis for the cracked bond which is based on the technical theory of beams/plates and which considers nonlinear adhesive behavior was developed. The model prediction for the increase in the plastic deformation zone with load and the distribution of shear strain within the zone agreed well with the experimental results. An expression for the energy dissipated by the advancing crack was derived which accounted for the nonlinearity in the load vs. deflection curve observed in the fracture experiments and allowed G _IIC to be calculated from easily measurable test parameters.     

Fracturing behaviors of FRP-strengthened concrete structures

In this paper, we focus on the study of concrete cracking behavior and interfacial debonding fracture in fiber reinforced polymer (FRP)-strengthened concrete beams. An experimental program is systematically reviewed according to the observed failure modes, in which it is found that the interfacial debonding may propagate either within the adhesive layer or through concrete layer in the vicinity of bond interface. A finite element analysis is performed to investigate the different types of debonding propagation along FRP-concrete interface and crack distribution in concrete. For the numerical fracture models, interfacial debonding that initiates and propagates in adhesive layer is modeled by fictitious interfacial crack model. And concrete cracking, including the debonding fracture through interfacial concrete, is modeled by smeared crack model. Properties of the interfacial adhesive layer and concrete are considered to significantly influence the debonding propagation types and crack distribution. The interactions between interfacial bond strength, interfacial fracture energy of bond adhesive layer and tensile strength, fracture energy of concrete are discussed in detail through a parametric study. According to the results, the effects of these properties on different types of interfacial debonding, concrete cracking behavior and structural load-carrying capacity are clearly understood.     

Physical meaning of ΔKRP and fatigue crack propagation in the residual stress distribution field

Previous papers have shown ΔK_RP to be a useful parameter describing fatigue crack propagation behavior, where ΔK_RP is an effective stress intensity factor range corresponding to the excess RPG load (re-tensile plastic zone's generated load) in which the retensile plastic zone appears under the loading process. In this paper, the relationship between ΔK_RP and the zone size ( ) (which is smaller between the tensile plastic zone at maximum load and the compressive plastic zone at minimum load) was investigated using a crack opening/closing simulation model so as to consider a physical meaning of ΔK_RP. As a result, it becomes clear that ΔK_RP dominates the zone size where fatigue damage mostly occurs. This result supports the following crack propagation equation

where C and m are material constants.Simulation and fatigue crack propagation tests were then carried out for compact tension (CT), center cracked tension (CCT) and four points bend (4PB) specimens under constant amplitude loading to obtain C and m values for HT-50 steel. Fatigue crack propagation tests were also carried out under constant amplitude loading using CCT specimens with residual stress distribution due to flame gas heating at the center line or edge lines. The T specimen introduced tensile residual stress at the tip of a notch, and the C specimen introduced compressive residual stress. It therefore becomes clear that tensile residual stress leads to a decrease in RPG load, while compressive residual stress leads to increase in RPG load, and that the simulation results are in good agreement with the experimental RPG load. It also becomes clear that simulated crack growth curve using the simulated and the above equation is in good agreement with the experimental curve. It is understood that tensile residual stress creates only a slight increase in crack propagation rate and compressive residual stress create a big decrease a crack propagation rate.     

Steel-to-concrete bond after concrete splitting: test results

The definite trend towards the use of large-diameter rebars and the introduction of high-strength steels (f _y=500 to 600 MPa) make it necessary to study the effects of longitudinal splitting on the steel-to-concrete bond. The study of splitting effects requires firstly basic tests to be performed in order to gather experimental information on bond and confinement stresses acting at the bar-to-concrete interface. For this purpose, three series of tests were recently carried out at the Politecnico di Milano. The results make it possible to ascertain a few basic properties of the bond after concrete splitting, and to formulate empirical constitutive laws regarding the stresses and the displacements (bar slip and opening of the splitting crack). All specimens consisted of a short deformed bar embedded in a concrete block, which had a preformed splitting crack in the plane passing through the bar axis: twelve specimens (Tests A and C) were fitted up with a round deformed bar having crescent-shaped lugs (D_b=18 mm); seven specimens (Tests B) were fitted up with a specially machined deformed bar having a rectangular cross-section and straigth, lugs, so that concrete deterioration close to the bar could be investigated at the surface of the specimen, by means of the moiré technique. The tests were carried out at constant slip rate, up to very large slip values ( ); both the ascending and the descending branches of the stress-slip curves were measured, for four different values of the opening of the splitting crack. The agreement among the results of the three series is generally satisfactory and often very good: consequently, constitutive laws regarding the four main variables (crack opening and bar slip, shear and confinement stresses) can be worked out, as will be shown in a companion paper on constitutive relationships and on concrete deterioration at the bar-to-concrete interface.     

Experimentally determined key curves for fracture specimens

Crack extension during fracture toughness tests of ferritic structural steels cannot be determined from measurements of unloading compliance or electric potential change when the specimen is dynamically tested. Measurements of crack extension in fracture toughness tests are also very difficult when the test temperature is high or the test environment is aggressive. To circumvent this limitation, researchers for years have been developing key curve and normalization function methods to estimate crack extension in standard elastic-plastic fracture toughness test geometries. In the key curve method (Ernst et al., 1979; Joyce et al., 1980) a load-displacement curve is measured for a so-called `source' specimen that is sub size or has a blunt notch so that the crack will not initiate during elastic-plastic loading. The load and displacement are then converted to normalized stress-strain units to obtain a key curve that can be used to predict crack extension in geometrically similar `target' specimens of same material loaded at similar loading rates and tested under similar environmental conditions. More recently Landes and coworkers (Herrera and Landes, 1990; Landes et al., 1991) proposed the normalization data reduction technique – Annex A15 of ASTM 1820 specification – that presents an alternative to the standard E1820 unloading compliance procedure. Although the normalization method works well in many cases, it has serious drawbacks: the load, displacement and crack length at the end of the test must be measured; the prescribed functional form that is fitted to the initial and final data may not be accurate for all materials; and the iterative method of inferring crack length from the combination of the data and the normalization function is complex. The compliance ratio (CR) method developed in this paper determines key curves for predicting crack extension as follows. First, a statically loaded source specimen with the unloading compliance procedure specified in ASTM 1820. Second, the so-called CR load-displacement curve is calculated for the source specimen, which is the load-displacement record that would have been obtained if the crack had not extended. Third, non-dimensionalizing the CR load by the maximum load and the displacement by the elastic displacement at the maximum load, P ^* _i/P _max and v _i/v _{el max} from the source specimen yields the adjusted key curve. Analysis of extensive data shows that the key curve is independent of notch type, initial crack length and temperature. But it is dependent on specimen size and steel type. Assuming that the key curves of the source and target specimens are one and the same, the compliance of the target specimens are calculated with a reverse application of the compliance ratio method, and the crack length is obtained using the equations in ASTM E1820. The CR Method is found to be much simpler than the normalization method described in the Annex A15 of ASTM 1820. With the compliance ratio method, Joyce et al. (2001) successfully predicted crack extension in dynamically loaded specimens using a key curve of a statically loaded specimen.     

Effect of acid corrosion on crack propagation of concrete beams

The effect of acid corrosion on crack propagation of concrete beams was theoretically studied by the method of crack extension resistance curve. Based on this method, a calculation approach was proposed to determine fracture stress intensity factors in crack propagation of concrete beams. Loop iteration analysis was carried out to calculate maximum bearing capacity load, unstable crack toughness, resistance toughness curve, cohesive toughness curve and load–crack mouth opening displacement. Both bilinear and nonlinear softening traction–separation curves were adopted for each of these calculation parameters. The analysis results of each showed the effect of acid corrosion degrees. The influence of acid corrosion on fracture properties was discussed through the calculated results of cohesive toughness curves. These five kinds of simulated results were basically consistent, before the load attained the maximum value. However, with further crack propagation, cohesive toughness of nonlinear softening model was significantly larger than that of bilinear softening model, and the descending branch of P–CMOD curve by nonlinear law is higher than that by bilinear law. To validate the approach, tests of specimens under six different corrosion periods were experimentally studied, using three-point bending notched concrete beams soaked in sulphuric acid solution. The Double-K fracture parameters were investigated based on the test results, and load–crack mouth opening displacement curves for different acid conditions were obtained using synchronous sampling of a load sensor and clip-gauge. Numerical results by bilinear softening model showed a good correlation with the experimental ones.     

Static fatigue behaviour of linear low-density polyethylenes

Various thermal histories were utilized to generate samples with the same crystalline microstructure (i.e. degree of crystallinity, supermolecular structure, tie molecule density and lamellar thickness) for linear low-density polyethylenes (LLDPEs) with the same molecular weight, molecular weight distribution and branch frequency but different branch length. The static fatigue properties were found to improve with decreasing applied load for samples with the same type of short-chain branches. The failure time of static fatigue (t _f) was found to increase dramatically as the branch length increased. An equation was used to predict t _f from the stress, the branch length and other material parameters. In addition, the initial growth rate of the crack opening displacement and the time required to reach the critical opening displacement at the notch roots of the specimens were observed to decrease and increase, respectively, with increasing branch length. This dramatic improvement in static fatigue properties is attributed to the increasing sliding resistance of the polymer chains through the crystal and through entanglements in the amorphous region as the branch length of LLDPEs increases.     

Tensile fracture of centre-notched angle ply (0/±45/0)S and (0/90)2S graphite — epoxy composites

The fracture behaviour of centre-notched (0/± 45/0)_S and (0/90)_2S laminates with increasing notch length has been studied. Two test series have been investigated: specimens of constant width (W=20 mm) and small notch length (2a 12 mm), and specimens with various notch lengths (5 2a 35 mm) and a constant relative notch length (2a/W=0.5). An X-ray technique showed that the damage at the notch tip, which is formed at increasing load, consists mainly of subcracks parallel to the fibres of the constituent layers. The damage zone causes the crack opening displacement (COD) to deviate from the original linearity. TheK _R curve concept has been applied assuming that the COD deviation from linearity is completely the result of original crack extension. This approach fails to describe the notch length effect, because a tangent point between theK _R andK curves was not found and because of a strong dependency of the maximum fracture resistanceK _Rmax on notch length. The fracture behaviour of 20 mm wide specimens could be explained with the point and average stress criteria, based on characteristic lengths which are independent of notch length. At various notch lengths at a constant 2a/W=0.5, however, the characteristic lengths increased with increasing notch length.     

Crack propagation studies and bond coat properties in thermal barrier coatings under bending

Ceramic based thermal barrier coatings (TBC) are currently considered as a candidate material for advanced stationary gas turbine components. Crack propagation studies under bending are described that were performed on plasma sprayed ZrO₂, bonded by MCrAlY layer to Ni base superalloy. The crack propagation behaviour of the coatings at room temperature in as received and oxidized conditions revealed a linear growth of the cracks on the coating till the yield point of the super alloy was reached. High threshold load at the interface between the ceramic layer and the bond coat was required to propagate the crack further into the bond coat. Once the threshold load was surpassed the crack propagated into the brittle bond coat without an appreciable increase in the load. At temperatures of 800°C the crack propagated only in the TBC (ceramic layer), as the ductile bond coat offered an attractive sink for the stress relaxation. Effects of bond coat oxidation on crack propagation in the interface region have been examined and are discussed.     

Fracture testing of Brazilian disk sandwich specimens

The reliability of a joint subjected to mechanical and thermal loads during processing and service constitutes a major technical problem. Joints contain flaws. The observed strength of a joint depends upon the location and size of the flaws, as well as the crack path through the joint. The aim of this investigation is to measure the fracture toughness of a crack in an adhesive joint, as well as to observe its path through the bond. Sandwich Brazilian disk specimens made of two aluminum adherends joined by a thin layer of epoxy are employed in the testing. A thin paraffin notch is located within the adhesive layer. Numerical analyses are carried out to calibrate the specimens. It is seen that asymptotic expressions for the energy release rate and phase angle of a sandwich specimen with a thin layer are inappropriate in this investigation. A wide range of mixed modes is attained with this specimen. Values of the critical energy release rate G _c are obtained as a function of the phase angle . A fracture criterion is compared to the results. During testing, all cracks divert from within the layer and grow toward and into the interface. Comparison of crack path direction is made to two theories.     

Fatigue growth of short cracks in Ti-17: Experiments and simulations

The fatigue behaviour of through thickness short cracks was investigated in Ti-17. Experiments were performed on a symmetric four-point bend set-up. An initial through thickness crack was produced by cyclic compressive load on a sharp notch. The notch and part of the crack were removed leaving an approximately 50 μm short crack. The short crack was subjected to fatigue loading in tension. The experiments were conducted in load control with constant force amplitude and mean values. Fatigue growth of the short cracks was monitored with direct current potential drop measurements. Fatigue growth continued at constant R-ratio into the long crack regime. It was found that linear elastic fracture mechanics (LEFM) was applicable if closure-free long crack growth data from constant K_Imax test were used. Then, the standard Paris’ relation provided an upper bound for the growth rates of both short and long crack.The short crack experiments were numerically reproduced in two ways by finite element computations. The first analysis type comprised all three phases of the experimental procedure: precracking, notch removal and fatigue growth. The second analysis type only reproduced the growth of short cracks during fatigue loading in tension. In both cases the material model was elastic-plastic with combined isotropic and kinematic hardening. The agreement between crack tip opening displacement range, cyclic J-integral and cyclic plastic zone at the crack tip with ΔK_I verified that LEFM could be extended to the present short cracks in Ti-17. Also, the crack size limits described in the literature for LEFM with regards to plastic zone size hold for the present short cracks and cyclic softening material.     

FRP加固混凝土构件中裂纹扩展规律的数值模拟

用材料破坏过程分析系统MFPA(MaterialFailureProcessAnalysis)对FRP(FiberReinforcedPolymer)加固混凝土梁在外荷载作用下沿FRP板和混凝土之间界面剥落的不同破坏模式以及混凝土中的裂纹分布进行了数值模拟。通过分析,发现剥落破坏可能产生在FRP板与混凝土之间的粘结层内或其上方附近的混凝土中。模拟结果与实验结果较吻合。粘结层和混凝土的特性对于剥落传播的类型及裂纹的分布有很大的影响。着重探讨了混凝土的强度参数以及粘结层的强度参数对于整个构件承载能力及最终破坏模式的影响。     

An in situ technique for the assessment of adhesive properties of a joint under load

Slow crack propagation in adhesive bonded joints has been characterised using an asymmetric wedge test. Crack position was evaluated from strain gauge measurements, both in the debonded part of the joint and in the bonded zone. Test temperature was changed during loading, giving insight into bond evolution. The technique allows accurate, and virtually continuous, determination of crack position to be made, and therefore the evaluation of crack speed versus fracture energy curves, as well as elastic properties of the adhesive layer. This technique also enables the monitoring of crack propagation in controlled environmental conditions to be performed, without interruption of exposure for measurements. By using a Winkler elastic foundation model to analyse results, the method seems to be the first to describe a process zone, or region where the adhesive is significantly strained under load, and a finite length specimen effect, manifested by crack front acceleration during the final stage of the test. The method was found to offer great potential to study in situ fracture and bulk adhesive properties.     

A hybrid method to assess interface debonding by finite fracture mechanics

Adhesive connections are potentially weak locations in many kinds of engineering structures. Since adhesive joints can be regarded locally as bimaterial notches, the assessment of the hazard of crack nucleation, initiation and propagation in the vicinity of bimaterial notches and the reliability of the junctions is an important problem. An essential requirement in this context is a sufficient criterion for crack nucleation. The present contribution proposes a modified approach based on Leguillon’s hypothesis in order to provide a feasible criterion. A crack at a notch is assumed to be initiated and to grow if and only if both the released energy and the local stresses exceed critical values. Thus, simulating virtual crack growth along an interface of two dissimilar bonded materials, the integrity of the bond is revisable. The approach enables the determination of characteristic lengths for freshly nucleated cracks forming the base for any further integrity assessment. As an example, the concept is applied to the analysis of an adhesive bond of metallic and ceramic materials under severe thermal loading conditions as they occur, among other examples, in high temperature fuel cell technology. It is shown that the failure hazard of the adhesive joint can be reduced significantly by an appropriate local design.