Crack-front Constraint Research Articles

Simulation of fatigue crack growth in aluminium alloy 7075-T7351 under spike overload and aircraft spectrum loading

The trend towards virtual testing and digital-twin assisted management means that the accurate and reliable simulation of fatigue crack propagation behaviour is more important than ever. Reliable but conservative approaches to support this are in widespread use in the aerospace industry. Nevertheless, the conservatism comes at a significant cost in terms of reduced structural life and an increased ongoing inspection requirement and, as such leads to questions about the economic burden of these approaches. Recent comparisons between blind predictions and test results revealed the extent of the issue for cracking in aluminium alloy 7075-T7351 coupons with configuration and loading representative of military transport aircraft wing skins. The current models were generally conservative by a factor of two or more in terms of crack propagation life. This suggested that there was significant scope to improve the modelling to better reflect all the complex contributing factors. The current work has investigated the issue of changes in the crack front constraint as the crack progresses from a state of high constraint (close to plane strain) to a lower constraint (approaching plane stress). This issue was investigated both experimentally and with the development of an improved analytical model. A test program was conducted on several specimens, loaded under constant-amplitude, constant-amplitude with spike-overloads and a variable amplitude spectrum. Crack-opening stress levels were measured at key points in the tests and the results were used to develop and evaluate improved modelling approaches. The improved model was generally able to predict crack growth within about ± 30 % of that demonstrated along with the correct form of the crack growth, which is a significant advance and will lead to reduced costs and increased safety.

Prediction of the durability of a plate with a through crack taking into account biaxial constraints of deformations along the front of a normal rupture crack

A methodology for evaluating the durability of plate elements of structures taking into account biaxial constraints of deformations along the front of a normal rupture crack (Mode I crack) is presented. The absence of the available literature data in which the prediction of the crack growth is carried out using Txx- and Tzz-stresses which are non-singular terms in the Williams expansion for stresses at the crack tip is noted. The calculation of the fatigue crack growth rate is based on the Paris equation in which the range of the effective SIF is used instead of the range of the usual stress intensity factor (SIF). In this case, the expression for the effective SIF includes Txx- and Tzz-stresses in addition to the usual SIF. This approach provides taking into account, for example, the thickness of the plate for predicting the durability, which is impossible when only the SIF and Txx-stresses are used. The formula for the effective SIF is derived proceeding from the assumption that tangential stresses in the pre-fracture zone are equal to the local strength of the material. In this case, the size of the pre-fracture zone and the local strength of the material are determined taking into account Txx- and Tzz-stresses. The numerical simulation is based on the proprietary finite-element program which allows calculating Txx- and Tzz-stresses at the front of a through crack in a plate subjected to cyclic uniaxial and biaxial tension. It is shown that nonsingular Txx-stresses primarily describe the effect of biaxial loading on the survivability, whereas Tzz-stresses describe the effect of the plate thickness on the survivability. It is shown that with increasing thic kness of the plate the value of the effective SIF increases due to the increased constraint along the crack front, thus increasing the crack growth rate and decreasing the survivability. With an increase in the stress ratio R, under the condition of a constant stress range, the maximum effective SIF reaches the critical value equal to the fracture toughness much faster thus reducing the durability. It is shown that for uniaxial cyclic tension, the durability predicted by the proposed methodology is higher than that in the classical approach, when the conventional SIF is used in the Paris equation. For biaxial cyclic tension of a plate, an increase in stresses directed parallel to the crack banks leads to an increase of crack front constraints and therefore to a decrease in the durability compared to the classical approach. In other words, the classical theory does not always provide a conservative estimate of the durability, which indicates the expediency of using the developed method for calculating the durability taking into account biaxial constraints of deformations along the crack front.

Development of Automated Model Generation and Analysis of Surface-Cracked Plates in Bending for Interpolated Elastic–Plastic J-Integral Solutions

Abstract NASA’s Tool for Analysis of Surface Cracks (TASC) has been used since 2014 to perform elastic–plastic J-integral (J), crack mouth opening displacement (CMOD), crack front constraint, and deformation limit calculations for plates in tension. To date, no comparable database or tool exists for surface-cracked plates in bending. Existing tools and prior ASTM standards are limited to linear-elastic materials or simpler 2-D crack geometries. TASC uses a database of 600 models for interpolated solutions over a wide range of semielliptical surface crack geometries (0.2≤a/c≤1.0, 0.2≤a/t≤0.8) and material properties (100≤E/Sys≤1,000, 3≤n≤20). Here, a is the crack depth, c is the half-width of the crack, and t is the plate thickness, so that a/c is the crack aspect ratio and a/t is a normalized measurement of crack depth. E, Sys, and n are the plate’s elastic modulus, yield strength, and the Ramberg–Osgood power law hardening exponent, respectively. This report details the development of a bending model database covering the same range of crack geometries and material properties. It includes developing new criteria to determine if a model has reached sufficient plastic deformation and modifications to model boundary conditions to accurately capture the behavior of deeply cracked plates in bending. Python is the primary automation tool used in this process, including running FEACrack to create meshes, modifying material properties, iterating WARP3D boundary conditions to meet plastic deformation requirements, and converting WARP3D output into a reduced set of MATLAB-compatible data files. Bending model results from WARP3D are validated against Abaqus results for identical meshes. This report then shows the initial integration of bending models and results into the existing TASC code, laying the groundwork for a single tool for analysis of surface-cracked plates in tension or bending.

Phase II Results of an Analytical Round Robin for Elastic-Plastic Analysis of Surface Cracked Plates

Abstract The second phase of an analytical round robin for the elastic-plastic analysis of surface cracks in flat plates was conducted under the auspices of ASTM Interlaboratory Study 732. The interlaboratory study (ILS) had ten participants with a broad range of expertise and experience, and experimental results from a surface crack tension test in 4142 steel plate loaded well into the elastic-plastic regime provided the basis for the study. The participants were asked to evaluate a surface crack tension test according to the version of the surface crack initiation toughness testing standard published at the time of the ILS, ASTM E2899-13, Standard Test Method for Measurement of Initiation Toughness in Surface Cracks under Tension and Bending. Data were provided to each participant that represented the fundamental information that would be provided by a mechanical test laboratory prior to evaluating the test result. Participants were asked to interpret the test according to E2899, including evaluation of crack-front constraint, determination of a critical initiation angle along the crack front, determination of the deformation regime of the test, and determination of the critical J-integral value. The choice of finite element analysis constitutive models and treatment of the stress-strain data was left to the discretion of the participants. The hope was that this process would familiarize participants with the standard and provide the task group with very helpful feedback regarding the interpretation of the requirements as they are written. Overall the participants’ test analysis results were in good agreement and constructive feedback was received that has resulted in an improved published version of the standard E2899-15.

Fatigue and crack-growth behavior in a titanium alloy under constant-amplitude and spectrum loading

A titanium alloy (Ti-6Al-4V STOA) plate material was provided by the University of Dayton Research Institute from a previous U.S. Air Force high-cycle fatigue study. Fatigue-crack-growth tests on compact, C(T), specimens have been previously performed at Mississippi State University on the same material over a wide range in rates from threshold to near fracture for several load ratios (R = Pmin/Pmax). These tests used the compression pre-cracking method to generate fatigue-crack-growth-rate data in the near-threshold regime. Current load-reduction procedures were found to give elevated thresholds compared to compression pre-cracking methods. A crack-closure model was then used to determine crack-front constraint and a plasticity-corrected effective stress-intensity-factor-range relation over a wide range in rates and load ratios. Some engineering estimates were made for extremely slow rates (small-crack behavior), below the commonly defined threshold rate. Newly-developed single-edge-notch-bend, SEN(B), fatigue specimens were machined from titanium alloy plates. These specimens were fatigue tested at two constant-amplitude load ratios (R = 0.1 and 0.5) and a modified Cold-Turbistan engine spectrum. All of the tests were conducted under laboratory air and room temperature conditions. Calculated fatigue lives from FASTRAN, a fatigue-life-prediction code, using small-crack theory with an equivalent-initial-flaw-size (semi-circular surface flaw) of 9-μm in radius at the center of the semi-circular edge notch fit the constant-amplitude test data fairly well, but under predicted the spectrum loading results by about a factor of 2–3. The reasons for the large under prediction were discussed. Life predictions made with linear-cumulative damage (LCD) calculations agreed fairly well with the spectrum tests.

Numerical Study of the Crack-Front Constraint for SENT Specimens of X80 Pipeline Steel

This work presents a numerical study of crack-front constraint for SENT specimens of X80 pipeline steel, to examine geometry effect on the correlation of crack-front stress field and constraint. An average measure of constraint over crack-front Am was employed to characterize the crack-front constraint. SENT specimens with varying geometries (different crack depth to specimen width ratio, a/W, and different specimen width and thickness, W/B) were analyzed by Gurson-Tvergaard-Needleman model (GTN model). Results showed that the stress triaxiality Am can characterize the crack-front constraint of X80 pipeline steel very well. The level of the Am-△a curve rises with the decrease of crack depth, and increases first and then decreases with the increase of SENT specimen thickness.

Prediction of fatigue-crack growth for 7075-T7351 aluminum alloy under various flight-load spectra

A plasticity-induced crack-closure model was used to calculate fatigue-crack-growth lives of middle-crack-tension, M(T), and compact, C(T), specimens made of 7075-T7351 aluminum alloy subjected to nine different simulated aircraft flight-load spectra. Experimental crack-growth results from the literature were compared to crack-growth calculations or predictions made using the FASTRAN life-prediction code, employing material property data extracted from material databases, such as the NASGRO database. In order to account for a loss of crack-front constraint (flat-to-slant crack-growth transition) during crack growth, crack-growth-rate dependent constraint factors were selected to correlate large crack-growth-rate data as a function of the effective stress-intensity-factor range under constant-amplitude loading. FASTRAN calculations or predictions with and without the constraint-loss option, through appropriate specification of constraint factors, resulted in about ±30% difference from the test lives on all nine spectrum loading. Some tests showed as much as 20% scatter between two test lives. Linear-cumulative damage life predictions also did very well on about one-half of the spectrum tests.

Leak-Before-Break assessment of a welded piping based on 3D finite element method

The paper studies the effects of the load reduction (discrepancy between designing and real loadings), strength match of the welded piping joint (WPJ), welding width, crack size and crack tip constraint on the Leak-Before-Break (LBB) assessment of a welded piping. The 3D finite element (FE) method is used in the study of a surge line of the steam generator in a nuclear power plant. It is demonstrated that the LBB margin is dependent on the loading level and the load reduction effect should be considered. When the loading is high enough, there is a quite large deviation between the J-integral calculated based on the real material property of WPJ and that calculated based on the engineering method, e.g. Zahoor handbook of Electric Power Research Institute (EPRI). The engineering method assumes that the whole piping is made of the unique welding material in the calculation. As the influence of the strength matching and welding width is ignored in the engineering method for J-integral calculation, the engineering method has a sufficient precision only if the width of welding is comparable to the crack depth. Narrower welding width leads to higher constraint of the plastic deformation in the welding and larger high stress areas in the base for the low strength-match WPJ. Higher strength matching of WPJs has higher crack-front constraints.

Ductile Fracture Behavior of Small-sized CIET Specimen Considering Crack Front Constraint Effect

Ductile Fracture Behavior of Small-sized CIET Specimen Considering Crack Front Constraint Effect

Normalization method for evaluating J-resistance curves of small-sized CIET specimen and crack front constraints

Based on dimensionless load separation principle, the normalization method for estimating J-resistance curves of CIET specimen for ductile materials has been developed. Experiments of ductile crack growth resistance on a typical pressure vessel steel SA-508 are conducted by using CT, SEB and CIET specimens. The resulted J-resistance curves show outstanding influence by load configuration and specimen dimensions. J-Q-M and J-A2-M approaches are introduced to quantify the crack front constraint of the three types of specimens. According to finite element analyses (FEA) under plane strain and 3D conditions, the distance-independent constraint parameters are calibrated by matching the FEA results with the J-Q-M and J-A2-M solutions using weight average method. The analyses show that the parameters of Q and A2 are load-independent under plane strain condition, but under 3D condition, the J-A2-M approach is incapable of characterizing the stress and deformation fields ahead of crack front of CIET specimen for SA-508 steel, and the parameter Q is no longer load-independent. Because of different crack front constraint, the CIET specimen with B=10 mm, a0=5.8 mm gets the lowest fracture resistance while the SEB specimen with B=20 mm, a0=11 mm and the CT specimen with B=15 mm, a0=29 mm obtain the highest fracture resistance for SA-508 steel. The size requirements of J-Q-M dominance for each used CIET, CT and SEB specimens are got. Finally, the constraint-modified J-resistance curves of SA-508 steel based on J-Q-M approach are constructed to predict the crack growth resistance for any fracture specimens or actual flawed structures.

Elastic-Plastic Finite Element Analyses of 3D Constraint Effects in Single Edge Cracked Plate Specimens

Abstract Extensive finite element analyses have been conducted to obtain numerical solutions of the constraint parameter A, which is the second parameter in a three-term elastic-plastic asymptotic expansion for the crack-tip field for thin three-dimensional (3D) single edge cracked plate specimens under uniaxial and biaxial loading. The 3D crack geometries analyzed included shallow to deep cracks, and the biaxial loading ratios analyzed were 0.0 (uniaxial loading) and 1.0 (biaxial loading). Solutions for the parameter A were obtained for materials following the Ramberg–Osgood power law with hardening exponents of n = 3, 5, and 10. Remote tension loading was applied covering the deformation range from small-scale to large-scale yielding. Crack-front constraint effects for 3D cracked specimens under uniaxial and biaxial loading are analyzed and discussed.

Effect of residual stresses on the linear-elastic KI–T field for circumferential surface flaws in pipes

This paper describes the effect of four realistic residual stress patterns on the crack-front constraints for circumferential surface flaws in the wall of a pipe, characterized by the linear-elastic K I – T stresses. The numerical representation of the residual stresses combines a thermal-induced eigenstrain field with a local mechanical traction applied over the interface between the heat affected zone and the remaining pipe. The verification study confirms the accuracy of this approach based on the analytical K I solution for a 2-D crack under prescribed residual stresses. This study demonstrates low crack-front constraints near the deepest crack front for three typical residual stresses.

A computational framework of three-dimensional configurational-force-driven brittle crack propagation

We consider a variational formulation of quasi-static brittle fracture and develop a new finite-element-based computational framework for propagation of cracks in three-dimensional bodies. We outline a consistent thermodynamical framework for crack propagation in elastic solids and show that both the elastic equilibrium response as well as the local crack evolution follow in a natural format by exploitation of a global Clausius–Planck inequality in the sense of Coleman’s method. Consequently, the crack propagation direction associated with the classical Griffith criterion is identified by the material configurational force which maximizes the local dissipation at the crack front. The variational formulation is realized numerically by a standard spatial discretization with finite elements which yields a discrete formulation of the global dissipation in terms configurational nodal forces. Therefore, the constitutive setting of crack propagation in the space-discretized finite element context is naturally related to discrete nodes of a typical finite element mesh. In a consistent way with the node-based setting, the discretization of the evolving crack discontinuity is performed by the doubling of critical nodes and interface facets of the mesh. The crucial step for the success of this procedure is its embedding into an r-adaptive crack-facet reorientation procedure based on configurational-force-based indicators in conjunction with crack front constraints. We propose a staggered solution procedure that results in a sequence of positive definite discrete subproblems with successively decreasing overall stiffness, providing a robust algorithmic setting in the postcritical range. The predictive capabilitiy of the proposed formulation is demonstrated by means of representative numerical simulations.

A computational framework of three dimensional configurational‐force‐driven crack propagation

AbstractA variational formulation of quasi‐static brittle fracture is considered and a new finite‐element‐based computational framework is developed for propagation of cracks in three‐dimensional bodies. We outline a consistent thermodynamical framework for crack propagation in elastic solids and show that the crack propagation direction associated with the classical Griffith criterion is identified by the material configurational force which maximizes the local dissipation at the crack front. The evolving crack discontinuity is realized by the doubling of critical nodes and triangular interface facets of the tetrahedral mesh. The crucial step for the success of the procedure is its embedding into an r‐adaptive crack‐facet reorientation procedure based on configurational‐force‐based indicators in conjunction with crack front constraints. We further propose a staggered algorithm which minimizes the stored energy at frozen crack state followed by the successive crack releases at frozen deformation. This constitutes a sequence of positive definite subproblems with successively decreasing overall stiffness, providing a very robust algorithmic setting in the postcritical range. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The stress-level effect on fatigue-crack growth under constant-amplitude loading

The fatigue-crack-closure concept has been successfully used with stress-intensity factors to predict the growth of cracks under a wide variety of load histories and in complex crack configurations. Both test and crack-closure analyses have shown that the stress-intensity-factor-range-against-rate curves are affected by the stress ratio ( R), the applied stress or load level ( S max or P max), and the crack-front constraint (plane-stress or plane-strain behavior). However, most life-prediction codes use only linear-elastic fracture mechanics (LEFM) concepts, which neglect stress-level effects, to make life predictions. Thus, under some loading conditions, such as negative R ratios or high-applied stress levels, non-conservative life predictions are made using only LEFM procedures. Fatigue-crack-growth tests have been conducted on middle-crack tension M(T) specimens made of 2024-T3 thin-sheet ( B = 2.3 mm) aluminum alloy over a wide range in applied stress levels (0.1–0.5 times the flow stress of the material) and for two stress ratios ( R = 0.05 and −1). The FASTRAN life-prediction code, using either the crack-closure model or LEFM procedures, and the AFGROW code, which uses only LEFM procedures, were used to make crack-growth predictions from an initial crack size to failure in the M(T) specimens. The results from AFGROW and FASTRAN, using LEFM procedures, agreed very well with each other. The crack-closure model predicted all results with ±20%, whereas, the codes using LEFM procedures (neglecting stress-level effects) resulted in non-conservative life predictions as large as a factor-of-3 from the test results.

A new constraint based fracture criterion for surface cracks

A new methodology for predicting the location of maximum crack extension along a surface crack front in ductile materials is presented. Three-dimensional elastic–plastic finite element analyses were used to determine the variations of a constraint parameter ( α h) based on the average opening stress in the crack tip plastic zone and the J-integral distributions along the crack front for many surface crack configurations. Monotonic tension and bending loads are considered. The crack front constraint parameter is combined with the J-integral to characterize fracture, the critical fracture location being the location for which the product Jα h is a maximum. The criterion is verified with test results from surface cracked specimens.

Interaction of hydrogen with crack-tip plasticity: effects of constraint on void growth

This study describes the results of finite element simulations to explore the effects of crack-front constraint variations on the distributions of hydrogen, stress, and plastic strain fields ahead of a blunting crack tip under plane-strain, small-scale yielding (SSY) conditions. Application of the non-singular T-stress in the SSY model provides a wide variety in crack tip constraint. The calculated near-tip fields drive the classical Rice and Tracey model for void growth that here couples the microscale effects of hydrogen on the local strain–stress values with this key mechanism of ductile fracture. The numerical results for a high solubility niobium system indicate that in the absence of hydrogen-induced softening, hydrogen-induced dilatation increases (decreases) void growth in low (high) constraint configurations—a result opposite of that in the absence of hydrogen. In the presence of hydrogen-induced softening, the relative resistance to ductile fracture of low and high constraint configurations depends on the initial hydrogen concentration and on the associated amount of softening. In all cases, the present model of hydrogen degradation by void growth argues for the existence of a fracture process strongly influenced by the plastic strain.

The 3D surface crack-front constraints in bimaterial joints

Single parameters such as the stress intensity factor K or J-integral in traditional fracture mechanics depend strongly on the geometry and loading conditions. Therefore a second parameter like the T-stress measuring the stress constraint is additionally needed to characterize general crack-tip fields. While many research works have been done to verify the J– T description of elastic–plastic crack-tip stress fields in plane strain specimens, a limited amount of work (especially for bimaterials) has been performed to describe the structural surface crack-front stress fields with two parameters. On this basis, via detailed 3D finite element (FE) analyses for surface-cracked plates and pipes of homogeneous materials and bimaterials, we investigate the extended validity or limitation of the two parameter approach. We here first develop a full 3D mesh-generating program for semi-elliptical surface cracks, and calculate elastic T-stress from the obtained FE stress field for “purely elastic” joint with modulus mismatch. We then validate the J– T methodology in characterizing the surface crack-front fields of welded plates and pipes under various loadings by comparing the J– T predictions to the “elastic–plastic” 3D FE stress fields.

Effect of specimen size and crack depth on 3D crack-front constraint for SENB specimens

Three-dimensional (3D) elastic–plastic finite element analyses (FEA) are performed to study constraint effect on the crack-front stress fields for single-edge notched bend (SENB) specimens. Both rectangular and square cross-section of the specimens with a deep crack of a/ W=0.5 are considered to investigate the effect of specimen size. A square-cross-section specimen with a shallow crack of a/ W=0.15 is also considered to examine the effect of crack depth. Stresses from FEA at the crack front on different planes of the specimen are compared with those determined by the J– A 2 three-term solution. Results show that in-plane stress fields can be characterized by the three-term solution throughout the thickness even in the region near the free surface. Cleavage fracture toughness data is compared to predict the effects of specimen size and crack depth on fracture behavior. It is found that the distributions of crack opening stress are nearly the same for the SENB specimens at the critical J which is consistent with the RKR model. Furthermore our results indicate that there is a distinct relationship between the crack-front constraint and the cleavage fracture toughness. By introducing the failure curves, the minimum fracture toughness and scatter band can be well captured using the J– A 2 approach.

Quantification of constraint on elastic–plastic 3D crack front by the J– A2 three-term solution

Three-dimensional (3D) modified boundary layer analyses are performed using the finite element method to study the crack-front constraint for an elastic–plastic thin plate. Far field loading is applied through the plane-stress displacement fields based on the elastic K I-field, and specimen constraint levels are varied through the T-stress applied on the far field boundary. Numerical stresses at the crack front at different planes of the plate are compared with those determined by the J–A 2 three-term solution. Results show that the in-plane-stress fields at the crack front for various K I– T loads possess the plane-strain nature throughout the thickness except for the region near the free surface, and can be characterized by the J–A 2 three-term solution under the small scale yielding condition. The transition of the stress field from the far field, in the plane-stress state, to the near crack-front field, dominated by the plane-strain state, is explained by the iso-contours of effective stress and the plane-strain constraint parameter. At the plane near the free surface, the crack-front field is close to the plane-stress state provided that the applied load is high and the plastic zone size is relatively large. Additional aspects of the 3D fields at the crack front through the thickness are also analyzed. In particular, a linear relationship between the constraint parameter A 2 and the hydrostatic stress is found in the 3D crack-front fields. It is also found that unlike the two-dimensional case where the J at the crack tip is not affected by the T-stress, the J-integrals at the crack front in the 3D case vary with the applied far field T-stress.