Crack Extension Curves Research Articles

A novel method to calculate the load vs. crack extension curve based on the load vs. load-line displacement curve

In order to obtain the crack growth resistance curve, a typical fracture test must measure the load vs. crack extension (F-Δa) curve. Apart from the basic measurement of the load vs. load-line displacement (F-vLL) curve, additional instruments or tedious test operations such as partial unloading are necessary to measure the amount of crack extension. This paper proposed a novel method of calculating the F-Δa curve directly from the F-vLL curve, in which no additional instrument or test operations are required. The proposed method can be easily applicable to these non-standard specimens. Several examples of C(T) and M(T) specimens are adopted to verify this method. Thus, this method is expected to simplify these available standards for measuring crack length.

Characterization of fracture behavior under impact-like loading conditions of elastomeric grades for high-pressure gas applications

Rapid gas decompression (RGD) is a major concern for elastomeric sealing components in cyclic gas exposure conditions as it generates cracks and can even cause total mechanical damage threatening the sealing integrity. Therefore, to analyze the fracture behavior of elastomeric grades under impact-like loading conditions, a test methodology was developed using a single edge notch in tension (SENT) specimen. To gain more insights into the behavior of differently formulated four nitrile butadiene rubber (NBR) grades (carbon black (CB) or Silica-filled, with different curing characteristics), tests were conducted at a wide range of temperatures, −20, 23, and 80 °C and under a wide range of loading rates (0.2–5 m/s). The single fracture parameters, strain energy release rate (G) at stable crack initiation and G at maximum load, as well as multiple fracture parameters from crack resistance curves (R-curves), G–Δa and crack growth rate vs crack extension curves, da/dt–Δa, were derived. All the grades showed distinct temperature and loading rate sensitivity on fracture behavior, however, the effect was more pronounced in sulfur-cured grades. Higher cross-link density, delivered a lower resistance to fracture and a uniform higher crack growth rate, conversely higher filler loading improved the fracture resistance. Within the tested conditions, the component-level instrumented tests on RGD failure revealed a similar ranking to the tested grades and it emphasizes the importance and relevance of intrinsic fracture properties. The generated information on single fracture parameters and crack growth kinetics is vital in phenomenological modeling attempts of the actual failure of components as well.

Effect of Shape and Distribution of Secondary Voids on Ductile Crack Path

Ductile fracture in structural metals and alloys comprises of three distinct stages: namely nucleation, growth, and coalescence of voids. In this failure mode voids, either pre-existing in the material or nucleated during deformation grow until they coalesce to form a continuous fracture path. The larger voids nucleating early in the deformation history are often referred to as the primary voids whereas the smaller ones (typically around 0.1 to 0.01 times the size of the primary voids) nucleate much later and are described as the secondary voids. As the imposed deformation increases, voids grow, and the ductile crack path is influenced by the interaction and coalescence of the two-scale voids. The present work numerically models the interaction between the two populations of pre-existing voids lying ahead of the crack tip. The influence of secondary voids attributes, in particular, the shape and distribution of secondary voids on ductile crack propagation is analysed. A plane-strain modified boundary layer (MBL) model, under small-scale yielding condition, subjected to remote mode-I loading is analysed. Both primary and secondary voids lying near the crack tip are modelled explicitly. In the absence of secondary voids, as expected, the crack path is controlled by the distribution of primary voids. The presence of small secondary voids, however, influences the crack growth and, hence, the crack driving force. Various initial configurations of secondary voids are modelled and some details of crack propagation and the numerically computed driving force versus crack extension (J-Δa) curves are presented.

Fracture Characterization of Base Metal, Seam Weld, and Girth Weld of Welded Line Pipe Steel at Room and Low Temperatures

For fitness-for-service assessment of pipeline cracks, it is necessary to examine toughness values of pipeline steels and their variations with temperature. In this study, experimental values of toughness (KJC) at room temperature have been obtained for base metal (BM), seam weld (SW), and girth weld (GW) in an API X65 gas transportation pipeline in order to investigate the structural integrity of whole structure. The toughness tests employed side-grooved compact tension specimens, obtained from the original pipe, to characterize the resistance to crack extension curves based on the unloading compliance technique. The values of JIC for tested specimens were found, and then, KJC values are obtained using ASTM E1820 guideline as 302, 262, and 166 MPam1/2 for BM, SW, and GW materials, respectively. Charpy V-notch (CVN) impact tests at room and low temperatures were also conducted to determine low-temperature effects on the toughness, and to examine ductile–brittle transition temperature values in the samples under study. The capability of CVN test for prediction of toughness in the tested specimens was also investigated. The error values in using CVN test results are large enough to justify that the CVN test is not suitable for prediction of toughness accurately.

Radiation response of the overlay cladding from the decommissioned WWER-440 Greifswald Unit 4 reactor pressure vessel

The Results of tensile and crack extension testing conducted on irradiated austenitic overlay cladding material are presented. The specimens were machined from three trepans sampled from the decommissioned WWER-440/V-230 reactor pressure vessel of the nuclear power plant Greifswald Unit 4. Crack extension curves were measured with Charpy size SE(B) specimens using the unloading compliance technique according to ASTM E1820-11 at different temperatures. Provisional crack initiation fracture toughness values JQ and KJQ are determined. The highest KJQ values were found in the temperature range from 20 to 80°C. A significant scatter was observed in the initiation values. This is due to the inhomogeneous structure of the welded overlay cladding. During the loading the crack moves through regions with different tearing strength, thus the J–Δa values show discontinuities caused by fast crack propagation or crack jumps. The comparison of the measured KJQ values and conservatively estimated stress intensity factors at an assumed surface crack shows that the cladding would remain intact during pressurized thermal shock transient.

Industrial application of Instrumented DWTT in evaluating material resistance to ductile fracture for modern pipeline steels

CTOA C of typical X70, X80 and X90 pipeline steels plates were evaluated by using energy based regression method upon their single specimen. Clear difference in the material resistance to ductile cracking could be distinguished by the values of CTOA C and their characteristic fracture surface. The region of stable cracking on the fracture surface could be identified from the dynamic crack extension curve, with the help of key-curve method. In the meanwhile, the crucial material based parameter required by many other CTOA C algorithm, (A ∗ σ f ) of present X70, X80 and X90 plates were experimentally determined, also proving the validity of theoretical geometric factor A ∗ to be 0.30–0.34, close to the commonly cited constant of 1/3.

Residual crack extension resistance of post-fire wedge-splitting normal strength concrete specimen based on the cohesive force function

A comparative study on determining the crack extension resistance curves (KR-curves) for the complete fracture process associated with two functions of the cohesive stress distribution, i.e. Peterson’s softening curve and CEB-FIP Model, 1990 softening curve using an analytical method and the weight function approach is presented in this paper. Fifty wedge-splitting normal strength concrete specimens were prepared to sustain ten different elevated temperatures up to 600°C. The stress intensity factor curves (K-curves) were calculated from the load–displacement curves obtained on these post-fire specimens. At each temperature, the residual fracture toughness KR(Δa) increased with the crack extension length Δa, whereas the KR-curves became lower and flatter with the increasing heating temperatures Tm. It was found that the KR-curve calculated from the weight function method coincided well with the one from the analytical method, whereas different softening curves had observable effects on the KR-curves. The stability of the KR-curve and the influence of temperatures on the crack tip opening displacement–crack extension curves (CTOD–Δa curves) were also analyzed.

An inverse analysis of cohesive zone model parameter values for ductile crack growth simulations

Abstract An inverse analysis using a modified Levenberg–Marquardt method is carried out to identify cohesive zone model parameter values for use in 3D finite element simulations of stable tearing crack growth events in Arcan specimens made of 2024-T3 aluminum alloy. The triangular cohesive law is employed in the simulations. The set of cohesive parameter values is determined in the inverse analysis by minimizing the difference between simulation predictions of key points on the load–crack extension curve with experimental measurements. From three different initial values, similar cohesive parameter value sets are reached. Using these sets of values, the predicted load–crack extension curves and the variation of a generalized crack tip opening displacement (CTOD) with crack extension for mixed-mode loading cases are compared with experimental measurements, which provide a validation of the cohesive parameter values and of the finite element simulation predictions.

Simulation of stable tearing crack growth events using the cohesive zone model approach

A cohesive zone model (CZM) approach is applied to simulate Mode I and mixed-mode I/II stable tearing crack growth events in Arcan specimens made of 2024-T3 aluminum alloy. The material is treated as elastic–plastic following the J2 flow theory of plasticity, and the triangular cohesive law is employed to describe the traction-separation relation in the cohesive zone ahead of the crack front. Simulations are carried out using the 3D finite element method. CZM parameter values are chosen based on considerations of values suggested in the literature and by matching simulation predictions with experimental data of the load–crack extension curve for a Mode I stable tearing crack growth event. With the same set of CZM parameter values, simulations are performed for mixed-mode I/II stable tearing crack growth events. A good agreement is reached between simulation predictions of the load–crack extension curve and experimental results. To connect with a simulation approach based on the crack tip opening displacement (CTOD) at a fixed distance behind the current crack front, the variation of CTOD with crack extension is examined under both Mode I and Mode I/II conditions. It is found that CZM simulation predictions of the CTOD variation with crack extension agree well with experimental measurements. The results of this study suggest that CZM based simulations can predict the critical CTOD value which, in CTOD based simulations, is used as an input and is conventionally obtained from experimental measurements. The findings of the current study demonstrate the applicability of the CZM approach in mixed-mode stable tearing simulations and establish a connection between the CTOD and CZM based simulation approaches.

Microscale digital image correlation study of irradiation induced ductile-to-brittle transition in polyethylene

The transition from ductile-to-brittle (DTB) response in polymers can be triggered by many factors such as temperature, strain rate, and environmental effects. The focus of this paper is on investigating the DTB transition that occurs in a polyethylene carbon monoxide copolymer (ECO) under the influence of ultraviolet (UV) irradiation. As ECO is subjected to increased amounts of UV light it becomes stiffer and more brittle because of increased cross-linking and simultaneous chain scission. Consequently, its failure processes also change with UV irradiation transitioning from a shear yielding mechanism typical of ductile polymers to a crazing mechanism typical of brittle polymers. An in-house built microtensile tester placed under a microscope is used to image at the microscale (1–10 µm/pixel) the failure processes of ECO irradiated for 0, 10, and 50 h. The full-field optical method of digital image correlation is used to image the area around a crack tip in a microscale fracture sample. The results show a significant region of K-dominance very near the crack tip in both the shear yielding (10 h irradiation) and the crazing (50 h irradiation) samples. Crack extension curves are also obtained and are seen to be consistent with macroscopic data obtained elsewhere.

Hybrid experimental and computational studies: combined compression‐bending fracture of edge‐cracked polypropylene specimens

ABSTRACTA four‐camera system is employed to measure three‐dimensional (3D) displacements on both the front and back surfaces of a single‐edge‐notched polypropylene plate undergoing combined compression and out‐of‐plane bending. A methodology was developed to ensure that both systems employed a common coordinate system for defining the deformations on the front and back surfaces. Using the image pairs obtained simultaneously by both stereo‐vision systems, the full 3D displacement and strain history on both sides of the specimen are measured during the loading process by using the 3D digital image correlation (DIC) technique, including the crack path, load‐surface crack extension curve, load versus actuator displacement curve, crack front profiles and 3D displacement and strain fields. It is found that crack growth only occurs on the front side of the specimen where tensile stresses are present; there is no crack growth on the back side where compression occurs. A computational model is also established to reconstruct the failure process based on a simplified geometry model and nodal release technique. Good agreements are reached on the measured and predicted results on deformation, strain fields, load‐crack extension curves.

Experimental characterization of the crack-tip-opening angle in fibre metal laminates

Although the crack-tip-opening angle (CTOA) has been shown to be well suited for modelling stable crack growth in monolithic sheet aluminium alloys, its applicability for fibre metal laminates has not been fully analyzed yet. Fracture test were performed on M(T) panels made of Glare 2-3/2-0.4, Glare 3-3/2-0.4 and laminated 2024-T3 3/2-0.4. Different fatigue pre-crack lengths were created to study the effect of bridging fibres on the CTOA measured on the external layer. The effect of bridging fibres resulted in small deviations of the CTOA vs. crack extension curve with respect to the reference panel made of metal laminate. The CTOA criterion could be successfully used for predicting the residual strength in fibre metal laminates.

Three-dimensional finite element simulations of mixed-mode stable tearing crack growth experiments

Mixed-mode stable tearing crack growth events in Arcan plate specimens made of aluminum alloy 2024-T3 are simulated using three-dimensional (3D) finite element methods. A modeling/simulation procedure utilizing a mixed-mode CTOD fracture criterion and the custom 3D crack growth simulation software, CRACK3D, with an automatic local re-meshing option is demonstrated. Simulation predictions of the load–crack extension curve and the in-plane curvilinear crack growth path are compared with experimental measurements for various mixed-mode loading cases. Issues such as the effects of near-tip finite element size and crack extension increment size on simulation predictions are investigated.

A ϑ method-based numerical simulation of crack growth in linear elastic fracture

This paper presents a method for the automatic simulation of quasi-static crack growth in 2D linear elastic bodies with existing cracks. A finite element algorithm, based on the so-called ϑ method, provides the load vs. crack extension curves in the case of rectilinear crack propagation. Since the approach is both theoretically general and simple to be performed from a computational point of view, it could be extended for describing the phenomenon of crack growth in different fracture mechanics contexts.

Prediction of the Shape of the K J Ductile-to-Brittle Transition Temperature Curve for Ferritic Pressure Vessel Steels Using the Material's Resistance to Crack Extension K J versus Δa Curve

Abstract Fracture toughness (KJ (cleavage)) measurements made within the ductile-to-brittle transition region for ferritic pressure vessel steels are not always described by the shape of the Master Curve currently given in ASTM Standard E 1921. The objective of this paper is to show how the shape of the transition toughness curve may be related to the shape of the material's resistance to crack extension curve (KJR) once the crack tip starts to blunt and ductile crack extension precedes cleavage failure. Using an empirical relationship between the mean ductile crack extension (Δa) prior to the onset of cleavage failure and temperature (Δa=λ exp(ϕT)), then the relationship between KJ and T may simply be given by KJ=KA+α[λ exp(ϕT)]β, where KA, α, and β are simply the coefficients to an offset power law to KJ versus Δa data given by KJR=KA+α(Δa)β. For specimens of different sizes, a reference temperature TK may be defined for a given reference level of Δa or equivalent KJ. Unique curves may be defined for materials with differing crack extension resistance curves through plots of KJ versus (T−TΔa(ref)) or (T−TK(ref)). The generalized form of the transition curve may be given by KJ=KA+α{Δa(ref) exp[ϕ(T−TΔa(ref) >β or KJ=KA+(K(ref)−KA){exp[ϕ(T−TK(ref) >β. Experimentally, ϕ has been estimated as approximately 0.08 for nuclear pressure vessel materials such as A533B/A508. Using a specific situation wherein the value of KA=30MPa√m,K(ref)=100MPa√m, and β=0.25 then, for a B=25-mm specimen, within experimental scatter this provides an almost exact match to the Master Curve given by KJ=30+70 exp[0.019(T−TK100)]. The predictions of transition curve shape using the material's resistance to crack extension curve are believed to be complementary to the Master Curve method, and may describe the shape of the transition curve when there is ductile crack extension prior to cleavage failure. Further work is recommended to investigate the relationship between the predicted ductile-to-brittle transition curve and the Master Curve for probabilities of cleavage failure post-initiation.

Three-dimensional modeling of ductile crack growth: Cohesive zone parameters and crack tip triaxiality

For 10 mm thick smooth-sided compact tension specimens made of a pressure vessel steel 20MnMoNi55, the interrelations between the cohesive zone parameters (the cohesive strength, T max, and the separation energy, Γ) and the crack tip triaxiality are investigated. The slant shear-lip fracture near the side-surfaces is modeled as a normal fracture along the symmetry plane of the specimen. The cohesive zone parameters are determined by fitting the simulated crack extensions to the experimental data of a multi-specimen test. It is found that for constant cohesive zone parameters, the simulated crack extension curves show a strong tunneling effect. For a good fit between simulated and experimental crack growth, both the cohesive strength and the separation energy near the side-surface should be considerably lower than near the midsection. When the same cohesive zone parameters are applied to the 3D model and a plane strain model, the stress triaxiality in the midsection of the 3D model is much lower, the von-Mises equivalent stress is distinctly higher, and the crack growth rate is significantly lower than in the plane strain model. Therefore, the specimen must be considered as a thin specimen. The stress triaxiality varies dramatically during the initial stages of crack growth, but varies only smoothly during the subsequent stable crack growth. In the midsection region, the decrease of the cohesive strength results in a decrease of the stress triaxiality, while the decrease of the separation energy results in an increase of the triaxiality.

A threshold stress intensity factor at the onset of stable crack extension of Knoop indentation cracks

Observation of the stable growth of indentation cracks in controlled bending tests is an attractive tool to study the R-curve behaviour of ceramic materials. In some crack growth experiments deviations from the ideal behaviour were observed––i.e. the cracks did not grow immediately upon application of the external load, but only after a certain applied stress is exceeded. The existence of such a threshold stress intensity for the onset of stable crack growth can be described by a disbalance of the residual stress intensity at the indentation crack tip and the fracture toughness after completion of the indentation cycle. A fracture mechanical description of this phenomenon is presented. The consequences which arise for the evaluation of crack growth data are explained by means of measured crack extension curves of Knoop indentation cracks in silicon nitride.

A threshold stress intensity factor at the onset of stable crack extension of Knoop indentation cracks

Observation of the stable growth of indentation cracks in controlled bending tests is an attractive tool to study the R-curve behaviour of ceramic materials. In some crack growth experiments deviations from the ideal behaviour were observed––i.e. the cracks did not grow immediately upon application of the external load, but only after a certain applied stress is exceeded. The existence of such a threshold stress intensity for the onset of stable crack growth can be described by a disbalance of the residual stress intensity at the indentation crack tip and the fracture toughness after completion of the indentation cycle. A fracture mechanical description of this phenomenon is presented. The consequences which arise for the evaluation of crack growth data are explained by means of measured crack extension curves of Knoop indentation cracks in silicon nitride.

Experimental validation of a microcracking-based toughening mechanism for cortical bone

It has been proposed that cortical bone derives its toughness by forming microcracks during the process of crack propagation (J. Biomech. 30 (1997) 763; J. Biomech. 33 (2000) 1169). The purpose of this study was to experimentally validate the previously proposed microcrack-based toughening mechanism in cortical bone. Crack initiation and propagation tests were conducted on cortical bone compact tension specimens obtained from the antlers of red deer. For these tests, the main fracture crack was either propagated to a predetermined crack length or was stopped immediately after initiating from the notch. The microcracks produced in both groups of specimens were counted in the same surface area of interest around and below the notch, and crack growth resistance and crack propagation velocity were analyzed. There were more microcracks in the surface area of interest in the propagation than in initiation specimens showing that the formation of microcracks continued after the initiation of a fracture crack. Crack growth resistance increased with crack extension, and crack propagation velocity vs. crack extension curves demonstrated the characteristic jump increase and decrease pattern associated with the formation of microcracks. The scanning electron micrographs of crack initiation and propagation displayed the formation of a frontal process zone and a wake, respectively. These results support the microcrack-based toughening mechanism in cortical bone. Bone toughness is, therefore, determined by its ability to form microcracks during fracture.

Ductile crack growth simulation from near crack tip dissipated energy

A method to calculate ductile tearing in both small scale fracture mechanics specimens and cracked components is presented. This method is based on an estimation of the dissipated energy calculated near the crack tip. Firstly, the method is presented. It is shown that a characteristic parameter G fr can be obtained, relevant to the dissipated energy in the fracture process. The application of the method to the calculation of side grooved crack tip (CT) specimens of different sizes is examined. The value of G fr is identified by comparing the calculated and experimental load line displacement versus crack extension curve for the smallest CT specimen. With this identified value, it is possible to calculate the global behaviour of the largest specimen. The method is then applied to the calculation of a pipe containing a through-wall thickness crack subjected to a bending moment. This pipe is made of the same material as the CT specimens. It is shown that it is possible to simulate the global behaviour of the structure including the prediction of up to 90-mm crack extension. Local terms such as the equivalent stress or the crack tip opening angle are found to be constant during the crack extension process. This supports the view that G fr controls the fields in the vicinity near the crack tip.