Large Crack Growth Research Articles

A Griffith description of fracture for non-monotonic loading with application to fatigue

With the fundamental objective of establishing the universality of the Griffith energy competition to describe the growth of large cracks in solids not just under monotonic but under general loading conditions, this paper puts forth a generalization of the classical Griffith energy competition in nominally elastic brittle materials to arbitrary non-monotonic quasistatic loading conditions, which include monotonic and cyclic loadings as special cases. Centered around experimental observations, the idea consists in: (i) viewing the critical energy release rate Gcnot as a material constant but rather as a material function of both space X and time t, (ii) one that decreases in value as the loading progresses, this solely within a small region Ωℓ(t) around crack fronts, with the characteristic size ℓ of such a region being material specific, and (iii) with the decrease in value of Gc being dependent on the history of the elastic fields in Ωℓ(t). By construction, the proposed Griffith formulation is able to describe any Paris-law behavior of the growth of large cracks in nominally elastic brittle materials for the limiting case when the loading is cyclic. For the opposite limiting case when the loading is monotonic, the formulation reduces to the classical Griffith formulation. Additional properties of the proposed formulation are illustrated via a parametric analysis and direct comparisons with representative fatigue fracture experiments on a ceramic, mortar, and PMMA.

Stiffening-resistant composite TBCs counteracting the substrate constraint effect during thermal exposure

Thermal barrier coatings (TBCs) endow metal components with an increased capacity to endure exposure to high temperatures. Plasma-sprayed TBCs exhibit excellent thermal insulation performance and are widely used in land-based thermal protection systems. However, plasma-sprayed TBCs are more prone to cracking during usage, significantly limiting their applications. The main issue is the sintering-induced stiffening that enhances the cracking driving force. In this work, stiffening-resistant TBCs were fabricated using a composite structure that counteracts the substrate constraint effect. First, the substrate constraint effect on the TBCs was studied based on the surface roughness. The results revealed that stiffening was the primary cause of substrate constraint-related failure. Two-dimensional (2D) interface gaps were spontaneously formed during thermal exposure, which could reduce stiffening by 20%. Moreover, the healing behavior of the 2D gaps was analyzed and used to explain the stiffening-resistant behavior. Finally, the effect of the newly formed 2D gaps on the lifespan of the TBCs was analyzed. Detailed simulations suggested that the newly formed 2D gaps were capable of reducing the strain energy release rate and led to the growth of large in-plane cracks. For future applications, it is necessary to fully take advantage of the newly-formed 2D gaps by avoiding their negative effects on TBC life span.

Fatigue behavior of low-temperature hot isostatic pressed electron beam powder bed fusion manufactured Ti-6Al-4 V

Ti-6Al-4 V finds application in the fan and compressor modules of gas turbine engines due to its high specific strength. Ti-6Al-4 V components manufactured using one of the additive manufacturing (AM) techniques, the electron beam powder bed fusion (PBF-EB) process, has been an active area of research in the past decade. The fatigue life of such PBF-EB built Ti-6Al-4 V components is improved by hot isostatic pressing (HIP) treatment typically performed at about 920 ˚C. The HIP treatment at 920 ˚C results in coarsening of α laths and reduced static strength and therefore a low-temperature HIP treatment is performed at about 800 ˚C to limit the impact on static mechanical properties. In the present work, the low cycle fatigue and fatigue crack growth behavior of such a modified HIP (low-temperature HIP) treated material is assessed and compared with the respective data for the standard HIP-treated material. The modified HIP-treated material has fatigue performance comparable to the standard HIP-treated material. This work suggests that the modified HIP treatment improves the static mechanical properties without significantly impacting the fatigue performance. Also, fatigue life predictions were made from the measured defect size at the crack initiation site using a linear elastic fracture mechanics tool. The life predictions show good agreement with the experimental values for defects greater than the intrinsic crack length, where life is well predicted by large-crack growth methodology.

Experimental visualization of the wear and scuffing evolution of a flake graphite cast iron cylinder liner

Scuffing is a wear mechanism that can lead to catastrophic failure of various technical applications. Even though the mechanism has been researched in countless publications for decades, it is not fully understood yet. An experimental approach was used in this paper to investigate the origin and evolution of scuffing in a ring-on-liner contact. For this purpose, test runs in an application-oriented test rig were stopped at different points in time. A linear tribometer was used to transfer a reciprocating motion of a real piston ring segment to a specimen made from a real cylinder liner. Based on a comprehensive analysis, a four-stage scuffing hypothesis for a ring-on-liner contact was developed. In the first stage, smearing of the honing structure and the formation of surface cracks lead to the development of a scaly structure on the liner surface. Crack growth induced by adhesive shear forces leads to the formation of breakouts in the liner surface in the second stage. Both stages are stable and only the specific load increase of the used test strategy causes the transition to stage three. Here, large crack growth induced breakouts result in the local destruction of tribofilms and, subsequently in local metallic contact between the specimens. When this local destruction becomes rampant and expands to a macro scale, adhesive bonds lead to macroscopic scuffing. It can be deduced that the first occurring damage stage is a result of a surface fatigue process.

Probabilistic Risk Assessment for Life Extension of Turbine Engine Rotors

Maintaining the component service life beyond its historical limits requires the ability to accurately quantify component reliability and address the uncertainties in material responses. A probabilistic method for predicting the total fatigue life was developed and applied to determine the probability of failure of a Ti-6Al-4V turbine disk component. The total fatigue life incorporates a dual mechanism approach including the crack initiation life and propagation life while simultaneously determining the associated initial flaw sizes. A microstructure-based model was employed to address the uncertainties in material response and relate the crack initiation life with crack size. The propagation life was characterized using both small and large crack growth models to ensure accurate fatigue life prediction. Fatigue life predictions were found to correlate with experimental data at high stress levels. The risk assessment can be used to estimate the expected initial crack sizes from variability in material properties, which can further be used to establish an enhanced inspection planning.

Fatigue and Crack Growth under Constant- and Variable-Amplitude Loading in 9310 Steel Using “Rainflow-on-the-Fly” Methodology

Fatigue of materials, like alloys, is basically fatigue-crack growth in small cracks nucleating and growing from micro-structural features, such as inclusions and voids, or at micro-machining marks, and large cracks growing to failure. Thus, the traditional fatigue-crack nucleation stage (Ni) is basically the growth in microcracks (initial flaw sizes of 1 to 30 μm growing to about 250 μm) in metal alloys. Fatigue and crack-growth tests were conducted on a 9310 steel under laboratory air and room temperature conditions. Large-crack-growth-rate data were obtained from compact, C(T), specimens over a wide range in rates from threshold to fracture for load ratios (R) of 0.1 to 0.95. New test procedures based on compression pre-cracking were used in the near-threshold regime because the current ASTM test method (load shedding) has been shown to cause load-history effects with elevated thresholds and slower rates than steady-state behavior under constant-amplitude loading. High load-ratio (R) data were used to approximate small-crack-growth-rate behavior. A crack-closure model, FASTRAN, was used to develop the baseline crack-growth-rate curve. Fatigue tests were conducted on single-edge-notch-bend, SEN(B), specimens under both constant-amplitude and a Cold-Turbistan+ spectrum loading. Under spectrum loading, the model used a “Rainflow-on-the-Fly” subroutine to account for crack-growth damage. Test results were compared to fatigue-life calculations made under constant-amplitude loading to establish the initial microstructural flaw size and predictions made under spectrum loading from the FASTRAN code using the same micro-structural, semi-circular, surface-flaw size (6-μm). Thus, the model is a unified fatigue approach, from crack nucleation (small-crack growth) and large-crack growth to failure using fracture mechanics principles. The model was validated for both fatigue and crack-growth predictions. In general, predictions agreed well with the test data.

Modelling and estimation of critical fracture energy, Gfr in ductile to brittle transition zone for characterising crack growth phenomenon in 20MnMoNi55 RPV steel

One of the methods for describing the phenomenon of stable crack growth in ductile materials is the estimation of critical fracture energy, Gfr as proposed by Marie and Chapuliot. These methods of calculation of Gfr are applicable for large crack growth. However, the method for estimating Gfr was re-investigated for short crack growth. It was observed in the previous works that the Gfr values obtained for short crack growth gradually increases and saturates to the value at large crack growth. This saturated Gfr value can be claimed to be a material property. It was also shown that a correction factor (function of critical CTOD and crack growth) when introduced to this saturated value of Gfr helps in obtaining the unsaturated values of Gfr. In the present work, an attempt is made to estimate Gfr using the above mentioned re-investigated idea at the upper part of ductile to brittle transition temperature regime (0 °C to-60 °C). At sub-zero temperatures stable crack growth is much less when compared to the room temperature. The correction factor which is a function of saturated Gfr value, CTOD and crack growth is found to be suitable for the CT specimen results even at low temperature. The values of unsaturated Gfr values thus obtained using the correction factor are then used to simulate load versus load line displacement curves. The simulated load versus load line displacement curves at different temperatures are in good agreement with the experimental results irrespective of change in a/W ratios of the CT specimen.

Growth of gas-filled penny-shaped cracks in decompressed hydrogels.

We report that the decompression of soft brittle materials can lead to the growth of internal gas-filled cracks. These cracks are oblate spheroids ('penny shape'), whose major radius grows linearly in time, irreversibly fracturing the surrounding material. Our optical measurements in hydrogels characterise and quantify the three-dimensional crack geometry and growth rate. These results are in good agreement with our analytical model coupling fracture mechanics and gas diffusion, and predicting the dependence on the mechanical properties, gas diffusivity and super-saturation conditions (gas pressure, solubility, temperature). Our results suggest a new potential mechanism for decompression sickness in scuba diving and for indirect optical measurements of the fracture properties of hydrogels.

Size Effect on FRP External Reinforcement and Retrofit of Concrete Structures

The size effect on the strength of reinforced concrete (RC) beams flexurally strengthened by surface bonded sheets of fiber-reinforced polymer (FRP) is studied. As the failure is neither ductile nor brittle, but quasibrittle, occurring after stable growth of large cracks with large damage zones, the transitional size effect governed by the energetic size effect law (SEL) must be expected, which the present analysis confirms. Owing to scarcity of size effect experimental data, finite element (FE) analysis is used. A powerful microplane damage constitutive model M7 for concrete, coupled with the crack band model to suppress spurious mesh sensitivity, is calibrated by fitting the existing test data to FRP-strengthened RC specimens of diverse types, and consequently is trusted to simulate the size effect. The analysis captures the debonding near the concrete–FRP interface starting at midspan or at the end of the FRP sheet. It also captures the debonding between adjacent concrete shear cracks, and the delamination of concrete cover. The causes of these different delamination modes are explained. Simple beam-type formulas, in which the size characteristic is not the beam depth but the length of the shear span, are proposed and validated by FE results. The use of single-lap shear tests to determine the bond strength is critically discussed. Finally, a good fit of a few existing limited test data on the size effect of FRP-strengthened specimens is demonstrated.

Relationships among Charpy impact toughness, microstructure and fracture behavior in 10CrNi3MoV steel weld joint

Charpy impact toughness of 10CrNi3MoV steel weld joint was investigated, and microstructure and fracture behavior were considered as reasons for differences in Charpy impact toughness. Charpy impact toughness of fusion zone (FZ) was lower than that of heat affected zone (HAZ) due to combinations of microstructure and fracture behavior. Acicular ferrite (AF) and grain boundary ferrite (GBF) with granular bainite (GB) in columnar dendrite pattern of FZ and a mixed mode of quasi cleavage fracture and ductile fracture was responsible for the low toughness; while tempered martensite with some bainite in fine dispersed equiaxed dendrite pattern of HAZ was contributed to absorb crack energy and improve the toughness. Tortuous crack propagation path of zigzag pattern confirmed the crack deviated at large angle grain boundary and depressed crack growth.

Customized weight function for cracks initiated from semi-circular notches

A new weight function is analytically derived for calculating the stress intensity factor of a crack initiated from a semi-circular notch root. This function is dependent on crack size and notch radius and independent from loading condition. The employed method is based on the solution of the weight function for an edge crack. A proper modification factor is applied to considering the effect of the notch and crack geometry on the weight function of the edge crack. It is initially assumed that the notch is a part of the crack. This assumption is used in an analytical method to obtain accurate solution for the weight function. The modification factor is obtained in terms of dimensionless parameters for the ease of application. The provided weight function is examined for different geometries under different loading conditions, and the results are compared with finite element solutions. The weight function is found accurate and reliable. Accuracy is not altered by crack size, notch geometry, and loading conditions. Therefore, the weight function can be used to study the different stages of the initiation and growth of short and large cracks with suitable accuracy.

Research of large scale mechanical structure crack growth method based on finite element parametric submodel

With the development of mechanical structure in large scale, the dimension difference between whole structure and part damage-crack can be widely further. In order to get a precise analytic result of crack structure the grid of crack structure finite element model should be meshed very dense so that the calculation scale is very large and calculation efficiency is lower even the calculation cannot be completed. To solve this multi scale problem of crack structure, presently the submodel method is used, but in the method crack growth trajectory need to be supposition and the crack model also need to be built by man-made, which is not satisfied with need of mix-mode crack growth especially for continuously reconstructing of crack model. In this paper the parametric submodel will be put forward. The method describes crack coarse model and submodel data by parameter way, including meshing, load, boundary condition etc. In the method dynamic relationship of analytical results between coarse model and submodel is built, so that crack stress intensity factor and growth angle can be automatically calculated for every crack tip. According to the dynamic modification of crack coarse model and submodel, the crack growth trajectory simulation can be calculated through iterative steps instead of the traditional supposition growth trajectory and crack propagation life calculation can also be finished. The method gets the accuracy crack growth trajectory and improves analytical efficiency. At last the case of the crack growth trajectory and life analysis in gantry crane verifies the validity of this method.

Simulation of ductile behaviour of 20MnMoNi55 steel using unsaturated Gfr′ values for short crack growth estimated by introduction of correction factor to critical fracture energy, Gfr

Marie and Chapuliot proposed a new fracture parameter, critical fracture energy, Gfr, to characterise stable crack growth. The idea of critical fracture energy was re-investigated and it was found that the critical fracture energy is not a single valued parameter, when estimated for short crack growth. It was claimed that the values of Gfr increases and then saturates to a single value when a large crack growth is reached. In the present work, it is found that the saturated value of Gfr is the critical fracture energy, Gfr and is a material property. However, the increasing unsaturated values of Gfr obtained from ductile stretch is not a material property. Therefore, an attempt is made to introduce a correction factor to this saturated value of Gfr. The correction factor is found to be a function of saturated value of Gfr (material property) CTOD and crack growth. The values of increasing Gfr obtained, using this correction factor is then used to predict the load versus load line displacement curve which matches well with experimental load versus load line displacement curve. The work is carried out for different a/W ratios and for both half CT and full CT.

Behavior of small cracks under negative stress ratio fatigue loading

In this paper we analyze growth of small cracks initiated from microscopic notches and loaded near the growth threshold under different stress ratios. The results of in-situ optical measurements during high cycle fatigue testing show that small cracks initiate and grow quickly after which there is a long period of slow growth until the large crack growth threshold is reached. The crack growth rate data from different loading ratios indicates that the positive portion of the stress amplitude or the maximum stress intensity factor can be used to compare crack growth rates. The test data also shows that increasing only the compressive stress portion of the loading will cause an arrested small crack to grow again.

Explosive blast damage resistance of three-dimensional textile composites

The damage resistance of 3D textile composites when subjected to shock wave loading caused by an explosive blast is experimentally investigated. Non-crimp 3D orthogonal textile carbon-epoxy composites with different volume contents of through-thickness z-binder yarns are subjected to explosive blasts of increasing intensity, and the resultant damage is compared to a 2D woven carbon-epoxy laminate. At high blast impulse, the 3D textile composites are highly effective at resisting large delamination crack growth, and display superior damage resistance compared to the 2D laminate. The delamination resistance of the 3D textile composites at high blast impulse increases with their z-binder yarn content, and this correlates with higher modes I and II interlaminar fracture toughness properties. Furthermore, the 2D laminate completely shatters under high blast impulse whereas the 3D textile composites remain intact, which is also evidence of higher explosive damage resistance.

Analysis of fatigue crack propagation in laser sintering metal

Laser sintering metal has recently been used in the manufacture of components for different applications like aerospace or medicine. The approach to engineering design based on the cracks propagation assumption applying the concepts of linear elastic fracture mechanics (LEFM) is commonly used for aerospace engineering. However, fatigue crack propagation is linked to irreversible and non-linear mechanisms at the crack tip, therefore LEFM parameters can be successfully replaced by non-linear crack parameters, namely the plastic CTOD. A model linking da/dN with plastic CTOD is proposed here to characterize fatigue crack propagation. A comparison is made with other materials showing that for the same plastic CTOD the laser sintering material has a relatively large crack growth rate.

Further Study on the Effect of Environment on Fatigue Crack Growth Behavior of 2000 and 7000 Series Aluminum Alloys

The 7000 series alloys have the highest strength in the aluminum alloys, but lower fatigue properties than 2000 series alloys. Thus, 7000 series alloys are not applied to a large proportion of the aircraft components. However, the mechanism for this has not been elucidated yet. In humid air, hydrogen embrittlement based on intergranular cracking has been known to occur in 7000 series alloys. To date, in order to explain the difference in the fatigue crack growth behavior in the two series alloys, the effect of the test environment on the fatigue crack growth of the two series alloys has been investigated in this study. A 7075-type as well as 2024-type alloy with relatively coarse equi-axed grains was T6-tempered and subjected to fatigue crack growth test in humid and dry environments. Crack growth rate at low ΔK level seemed to be larger in the 7075-type alloy than the 2024-type alloy in the humid air, when assessed by means of gradually decreasing K method. In order to clarify this result, crack growth rate of the two alloys was assessed by means of gradually increasing K method as well as decreasing K method. Crack growth rate of the 7075-type alloy in moist air was concluded to be the largest in consistent with the previous study. Thus, the large fatigue crack growth rate of the 7075-type alloy is attributable to hydrogen embrittlement.

Generalized evaluation method for determining transition crack length for microstructurally small to microstructurally large fatigue crack growth: Experimental definition, facilitation, and validation

We proposed a generalized method to determine the transition crack length from a microstructurally small to a microstructurally large crack growth, l0. Artificial errors are minimized in the data analysis process of the proposed method. In this study, we used low carbon steel specimens, each with eight micro notches (the ferrite grain size was 25μm). The micro notches were introduced by focused ion beam technique, which is regarded as pre-cracks in steel. The obtained l0 (188μm) agrees with previous studies. With the present specimen geometry, l0 can be determined using two specimens—an approach that is much easier than conventional methods.

Growth of long fatigue cracks under non-proportional loadings – experiment and simulation

An experimental campaign was carried out on thin-walled tubes under tension and torsion. The results from experiments are measured and compared. It is observed that cracks follow a shear-dominated growth pattern with increasing crack length, instead of a tension-dominated one. The experiments are performed with high amplitudes applied to the specimens, resulting in large cyclic plastic deformations and crack growth rates up to 10-3 mm/cycle. Stress intensity factors were calculated for the proportional loading case.

Characterization and analysis of surface notches on Ti-alloy plates fabricated by additive manufacturing techniques

Rectangular plates of Ti–6Al–4V with extra low interstitial (ELI) were fabricated by layer-by-layer deposition techniques that included electron beam melting (EBM) and laser beam melting (LBM). The surface conditions of these plates were characterized using x-ray micro-computed tomography. The depth and radius of surface notch-like features on the LBM and EBM plates were measured from sectional images of individual virtual slices of the rectangular plates. The stress concentration factors of individual surface notches were computed and analyzed statistically to determine the appropriate distributions for the notch depth, notch radius, and stress concentration factor. These results were correlated with the fatigue life of the Ti–6Al–4V ELI alloys from an earlier investigation. A surface notch analysis was performed to assess the debit in the fatigue strength due to the surface notches. The assessment revealed that the fatigue lives of the additively manufactured plates with rough surface topographies and notch-like features are dominated by the fatigue crack growth of large cracks for both the LBM and EBM materials. The fatigue strength reduction due to the surface notches can be as large as 60%–75%. It is concluded that for better fatigue performance, the surface notches on EBM and LBM materials need to be removed by machining and the surface roughness be improved to a surface finish of about 1 μm.