Middle-crack Tension Specimens Research Articles

Effects of shot peening with different coverage on surface integrity and fatigue crack growth properties of 7B50-T7751 aluminum alloy

Engineering design methods based on the assumption of crack growth and the application of fracture mechanics principles are commonly used in aerospace engineering for the design of aluminum structures. In aerospace manufacturing, surface shot peening is one of the most widely used techniques for improving the fatigue performance of structural components. This work reviews the effect of different shot peening coverage on surface integrity and fatigue crack growth (FCG) properties of 7B50-T7751 aluminum alloy. The shot peening was applied to middle-crack tension (MT) specimens with four kinds of peening coverage: 100%, 300%, 600% and 1000%, respectively. The results showed that shot peening treatment reduced specimen surface roughness, moreover, surface shot peening promoted a maximum microhardness increased by 28.1% and induced compressive residual stresses in order of −412 MPa compared to untreated specimens. FCG experiment results showed that the effect of shot peening coverage on da/dN-ΔK curves was quite limited at constant amplitude loading. With the increase of shot peening coverage from 100% to 1000%, the FCG rate decreases first and then increase. At 300% of surface shot peening coverage, the FCG rate is the lowest, which results in the longest fatigue crack growth life.

Fatigue crack growth in a laser shock peened residual stress field

Laser Shock Peening is a surface treatment technique used in the aerospace sector to increase fatigue life, as well as resistance to fretting fatigue and stress corrosion cracking. In this study, laser shock peening was applied to a 6-mm-thick middle-crack tension specimen made of aluminium 2524-T351. Residual stress was measured with neutron diffraction and the contour method, along the predicted crack path prior to fatigue testing. Fatigue crack growth test results showed that fatigue life improved by a factor of 4 compared to an untreated component, owing to a significant crack growth rate reduction inside the laser peened area. A linear-elastic finite-element crack growth prediction model was also developed, obtaining predicted results in excellent agreement with the experimental data.

Comparison of the Fatigue Crack Propagation Behavior of Two Different Forms of PMMA Using Two-Stage Zone Model

The fatigue crack propagation behavior of two different forms of PMMA was studied using two-stage zone model. First, the fatigue crack length and fatigue crack propagation velocities of different specimens were obtained experimentally. Then the effect of material forms and specimen types on the fatigue crack propagation velocities was analyzed. Finally, the data scatter of da/dN-ΔK curves in different forms and different types of specimens was analyzed. The results show that the expressions of fatigue crack propagation velocities of middle crack tension (MT) specimens and compact tension (CT) specimens in the same form PMMA are similar. And the scatter of MT specimens is larger than CT specimens in two forms of PMMA.

Extent of the Surface Region in Notched Middle Cracked Tension Specimens

This article aims at evaluating the extent of the surface region in notched Middle Cracked Tension specimens. Firstly, a fully automatic fatigue crack growth technique is developed to obtain stable crack shapes. After that, the stress triaxiality along the crack front is evaluated for different notch shapes. Then, objective criteria are defined to quantify the extent of the surface region from the stress triaxiality data collected. Next, the extent of the surface region is related to the elastic stress concentration factor of the uncracked geometry by a linear relationship. Finally, empirical two-constant equations able to evaluate the extent of the surface region from the thickness, notch radius, notch depth and elastic stress concentration factor are formulated.

Fatigue crack propagation into the residual stress field along and perpendicular to laser beam butt‐weld in aluminium alloy AA6056

ABSTRACTLaser beam butt welds in Al‐alloys are very narrow and are accompanied by steep residual stress gradients. In such a case, how the initial crack orientation and the distance of the notch tip relative to the weld affect fatigue crack propagation has not been investigated. Therefore, this investigation was undertaken with two different crack orientations: along the mid‐weld and perpendicular to the weld. Fatigue crack propagation ‘along the mid‐weld’ was found to be faster in middle crack tension specimens than in compact tension specimens. For the crack orientation ‘perpendicular to the weld’, the relative distance between the notch tip and the weld was varied using compact tension specimens to generate either tensile or compressive residual stresses near the notch tip. When tensile residual stresses were generated near the notch tip, fatigue crack propagation was found to be faster than that in the base material, irrespective of the difference in the initial residual stress level and whether the crack propagated along the mid‐weld or perpendicular to the weld. In contrast, when compressive weld residual stresses were generated near the notch tip, fatigue crack arrest, slow crack propagation, multiple crack branching and out of plane deviation occurred. The results are discussed by considering the superposition principle and possible practical implications are mentioned.

One Numerical Simulation Method and its Applications for Fatigue Crack Growth

Abstract: Based on the Miner′s linear accumulative damage theory and the low cycle fatigue damage parameter that is relative to the total strain amplitude and the mean stress of the plastic zone near crack tip, a new numerical simulation method to predict the fatigue crack growth (FCG) of materials is presented. The numerical FCG results for middle-cracked tension (MT) specimens of Cr2Ni2MoV steel, TA12 and TC4 alloys by ANSYS are closed to those by tests. Therefore, the new method has capability to give good FCG prediction accuracy for different materials. Furthermore, the Paris FCG models of TA17 and TC11 alloys were predicted by this method and can be referred to the key engineerings.

A mechanics based study of crack closure measurement techniques under constant amplitude loading

An elastic–plastic finite element model was used to simulate a growing fatigue crack in a middle-crack tension specimen made of an aluminum alloy. The finite element analysis provided the load–displacement curve at various locations as is commonly done in experimental work, and the crack opening stress intensity factor (Kop) was determined with ASTM standard methods, Elber’s method, and the Adjusted Compliance Ratio (ACR) method. The performance of ACR was compared against the established standard methods. Measurement location effects on Kop and ACR were investigated. ASTM (2% offset) and ACR methods gave values that were dependent upon measurement location. Whereas, Elber’s method (0% offset) gave values that were independent of measurement location.

Computations of energy release rate under monotonic and cyclic loading conditions

Abstract In case of an elastic–plastic fracture mechanics analysis, the determination of the energy release rate distribution is a crucial point. In the present paper, three numerical techniques: the virtual crack closure technique (VCCT), J-integral and energy derivative technique (EDT), are used to compute the energy release rate in a middle-crack tension specimen with the combined isotropic/kinematic hardening model. The results obtained by these methods are compared with each other under monotonic and cyclic loading conditions. Finally, it comes out that the difference of the VCCT method to the J-integral is rather insensitive to load increasing, especially when the traction >40% of yield stress, however, the deviation of the VCCT and J-integral results are within 10%, suggesting that one may use the VCCT for plastic cracked specimen analysis. The computations show that the EDT provides the same values for the monotonic as the J-integral if the plastic deformations are not large, but for high plastic loading the EDT overestimates the fracture energy. For cyclic loading case, VCCT method offers closer results as the elastic analytical results, also suggesting that the whole plastic dissipated energy in the loading process should be integrated. While EDT method gives the smaller results than the J-integral because of the energy dissipated in the unloading phase is considered in the loading process.

Fatigue crack growth performance of peened friction stir welded 2195 aluminum alloy joints at elevated and cryogenic temperatures

The effects of various surface treatments on fatigue crack growth and residual stress distributions in friction stir welded 2195 aluminum alloy joints were investigated. The objective was to understand the degree to which residual stress treatments can reduce fatigue crack growth rates, and enhance fatigue life of friction stir welded components. Specimens were fabricated from 12.5 mm thick 2195-T8 aluminum plate, with a central friction stir weld along their length. Residual stresses were measured for three specimen conditions: as-welded (AW), welded then shot peened (SP), and welded then laser peened (LP). Crack growth rate tests were performed in middle-cracked tension specimens under constant amplitude load for each of the three conditions (AW, SP, LP) and at three temperatures (room, elevated, and cryogenic). At room and elevated temperature, crack growth rates were similar in the AW and SP conditions and were significantly lower for the LP condition. At cryogenic temperature, it was difficult to discern a trend between residual stress treatment and crack growth rate data. Laser peening over the friction stir welded material resulted in the fatigue crack growth rates being comparable to those for base material.

Finite element modelling and analysis of crack shape evolution in mode-I fatigue Middle Cracked Tension specimens

A numerical procedure was employed to study the shape evolution of fatigue cracks in Middle Cracked Tension specimens. This iterative procedure consists of a 3D finite element analysis to obtain the displacement field in the cracked body, calculation of stress intensity factors along crack front and definition of local crack advances considering the Paris law. Numerical predictions were compared with experimental crack shapes with a good agreement. The evolution of crack shape was analysed for different propagation conditions considering robust dependent parameters. Two main propagation stages were identified: an initial transient stage highly dependent on initial crack shape and a stable stage where the crack follows preferred paths. Mathematical models were proposed for transient and stable stages consisting of exponential and polynomial functions, respectively. The transition between both stages was defined considering two criteria: the rate of shape variation and the distance to stable shape. Finally, the crack shape change was linked with the distribution of stress intensity factor along crack front.

Effect of plastic anisotropy of weld on limit load of undermatched middle cracked tension specimens

ABSTRACTPlastic anisotropy may have a significant effect on the limit load of structures. The present paper shows its effect on the limit load of well‐undermatched middle cracked tension specimens assuming that the base material is elastic and the weld material obeys Hill's quadratic orthotropic yield criterion in rigid‐perfect plasticity. The solution is based on a kinematically admissible velocity field, which is compatible with a stress field satisfying the equilibrium equations and the yield criterion in the plastic zone. The velocity field is singular in the vicinity of the bi‐material interface, which is typical for isotropic materials.

Effects of crack closure on fatigue crack-growth predictions for 2024-T351 aluminum alloy panels under spectrum loading

Effects of plasticity induced crack closure on the calculated fatigue crack-growth behaviour of middle-crack tension specimens made of 2024-T351 alloy subjected to variable amplitude fatigue loading were examined. The specified loadings were four distinct aircraft spectra: (1) “modified” center-wing spectrum performed as part of this study; (2) fighter aircraft maneuver spectrum; (3) lateral gust spectrum; and (4) pressurized fuselage gust and maneuver spectrum. The experimentally observed crack-growth lives were compared with crack-growth predictions obtained using the crack closure concept in FASTRAN. Fatigue crack-growth material data extracted from the NASGRO materials database and the literature follows two distinct paths possibly due to different transitions from flat-to-slant (single or double shear) fracture. The material baselines for the FASTRAN code were selected to fit the two different paths. The two baseline curves were used to predict crack-growth life under four spectra to assess how the observed differences in the crack-growth rate trajectories affect the results. Using the lower bound baseline curve, which is suspected to be characterized by the double shear fracture mode, the FASTRAN model was able to predict crack- growth behaviour within ±25% of the test data for all four spectra.

Modeling of ductile fracture: Application of the mechanism-based concepts

This paper summarizes our recent studies on modeling ductile fracture in structural materials using the mechanism-based concepts. We describe two numerical approaches to model the material failure process by void growth and coalescence. In the first approach, voids are considered explicitly and modeled using refined finite elements. In order to predict crack initiation and propagation, a void coalescence criterion is established by conducting a series of systematic finite element analyses of the void-containing, representative material volume (RMV) subjected to different macroscopic stress states and expressed as a function of the stress triaxiality ratio and the Lode angle. The discrete void approach provides a straightforward way for studying the effects of microstructure on fracture toughness. In the second approach, the void-containing material is considered as a homogenized continuum governed by porous plasticity models. This makes it possible to simulate large amount of crack extension because only one element is needed for a representative material volume. As an example, a numerical approach is proposed to predict ductile crack growth in thin panels of a 2024-T3 aluminum alloy, where a modified Gologanu–Leblond–Devaux model [Gologanu, M., Leblond, J.B., Devaux, J., 1993. Approximate models for ductile metals containing nonspherical voids – Case of axisymmetric prolate ellipsoidal cavities. J. Mech. Phys. Solids 41, 1723–1754; Gologanu, M., Leblond, J.B., Devaux, J., 1994. Approximate models for ductile metals containing nonspherical voids – Case of axisymmetric oblate ellipsoidal cavities. J. Eng. Mater. Tech. 116, 290–297; Gologanu, M., Leblond, J.B., Perrin, G., Devaux, J., 1995. Recent extensions of Gurson’s model for porous ductile metals. In: Suquet, P. (Ed.) Continuum Micromechanics. Springer-Verlag, pp. 61–130] is used to describe the evolution of void shape and void volume fraction and the associated material softening, and the material failure criterion is calibrated using experimental data. The calibrated computational model successfully predicts crack extension in various fracture specimens, including the compact tension specimen, middle crack tension specimens, multi-site damage specimens and the pressurized cylindrical shell specimen.

Influence of anisotropy on a limit load of weld strength overmatched middle cracked tension specimens

ABSTRACT A plane‐strain upper bound limit load solution for weld strength overmatched middle cracked tension specimens (M(T) specimens), is found. It is assumed that the weld material is isotropic, but the base material is orthotropic and its axes of orthotropy are straight and parallel to the axes of symmetry of the specimen. A quadratic orthotropic yield criterion is adopted. The solution is based on a simple discontinuous kinematically admissible velocity field and is an extension of the corresponding solution for the specimen made of isotropic materials. These two solutions are compared to demonstrate the influence of anisotropy on the magnitude of the limit load.

Finite element modeling of plasticity-induced crack closure with emphasis on geometry and mesh refinement effects

Two-dimensional, elastic–perfectly plastic finite element analyses of middle-crack tension (MT) and compact tension (CT) geometries were conducted to study fatigue crack closure and to calculate the crack-opening values under plane-strain and plane-stress conditions. The behaviors of the CT and MT geometries were compared. The loading was selected to give the same maximum stress intensity factor in both geometries, and thus approximately similar initial forward plastic zone sizes. Mesh refinement studies were performed on both geometries with various element types. For the CT geometry, negligible crack-opening loads under plane-strain conditions were observed. In contrast, for the MT specimen, the plane-strain crack-opening stresses were found to be significantly larger. This difference was shown to be a consequence of in-plane constraint. Under plane-stress conditions, it was found that the in-plane constraint has negligible effect, such that the opening values are approximately the same for both the CT and MT specimens.

Residual strength analyses of stiffened and un-stiffened panels––Part I: laboratory specimens

This paper presents the results of residual strength analyses on stiffened and un-stiffened panels using the STructural Analysis of General Shells (STAGS) finite-element shell code and the critical crack-tip-opening angle (CTOA) fracture criterion. Previous analyses of wide, flat panels have shown that high-constraint conditions around a crack front must be modeled in order for the critical CTOA fracture criterion to predict wide panel failures from small laboratory tests. Thus, the STAGS code with the “plane-strain” core option was used in all analyses. In the present study, the critical CTOA ( Ψ c) value and the plane-strain core height were determined from a fit to the experimental load-against-crack-extension results from a series of middle-crack tension specimens (76–1016 mm wide) tested with anti-buckling guides. In the residual strength analyses of the 305-mm wide stiffened panels with a single crack, modeling of the sheet, stiffeners, rivet flexibility and buckling were based on methods and criteria, like that currently used in industry. STAGS and the CTOA criterion were used to predict load-against-crack extension for the single stiffened panels for both intact and cut stiffeners. Analyses were able to predict stable crack growth and residual strength of the single stiffened panels within about ±5% of the test failure loads.

A thin-sheet, combined tension and bending specimen

Validating stress intensity factor solutions for combined tension and bending is an arduous task because the necessary experimental data are not readily available. Toward this end, a tension and bending test specimen was designed to produce controllable levels of both tension stress and bending stress at the crack location. The specimen was made from 2024-T3 clad aluminum, which is commonly used in aircraft structures. The need for testing multiple specimens of various geometries and stress levels prompted the development of an analytical tool for specimen design. An extention of the Schijve line model, based on simple beam theory, was developed to calculate the stress distributions of tension and bending through the length of the specimen. A comparison of measured static strain levels with those predicted by the model showed the model to be accurate to within 5 percent, confirming its efficacy for specimen design. As expected, for the same remote stress (100 MPa), cracks in the tension and bending specimens grew faster than those in middle-cracked tension specimens.

High ResolutionR-Curve Characterization of the Fracture Toughness of Thin Sheet Aluminum Alloys

AbstractThe plane-strain initiation fracture toughness and plane-stress stable crack growth resistance were determined with a single small compact tension (C(T)) specimen for each of three precipitation hardened aluminum alloy sheets (AA2024-T3, AA2519-T87 (+Mg+Ag), and AA2650-T6). Crack length was monitored precisely with direct current potential difference (DCPD) measurements, and specimen plasticity was accounted for with the J-integral. The DCPD technique resolves a small amount of crack-tip process-zone damage (≈20 µm) that constitutes crack initiation under plane-strain constraint. Two measures of initiation toughness are calculated: the elastic-plastic fracture toughness detected by DCPD (JICi, KJICi) and the toughness based on ASTM Standard E 813 () and the toughness based on ASTM Standard E 813 (JIC, KJIC). High resolution of fracture initiation is necessary to obtain a lower bound initiation toughness,). High resolution of fracture initiation is necessary to obtain a lower bound initiation toughness, KJICi, because plane-strain constraint is present ahead of the fatigue precrack but is rapidly lost with crack extension in thin sheet. KJIC overestimates toughness due to constraint loss coupled with the offset blunting line definition of fracture initiation. The J-integral/DCPD method provides a reproducible measure of the plane-stress linear-elastic resistance curve (KJ − Δa) that compares reasonably to R-curves determined for large middle-cracked tension specimens. The small specimen method is effective for studies pertaining to alloy development, environmental effects, and fracture mechanisms.

CTOA and crack-tunneling measurements in thin sheet 2024-T3 aluminum alloy

The stable tearing behavior of 2.3-mm thick sheets of 2024-T3 aluminum alloy was experimentally investigated for middle crack tension specimens having initial flaws that were: (a) flat fatigue cracks (low fatigue stress) and (b) 45-deg through-thickness slant cracks (high fatigue stress). The critical CTOA values during stable tearing were measured by two independent methods, optical microscopy and digital-image correlation. Results from the two methods agree well. The CTOA measurements and observations of the fracture surfaces have shown that the initial stable tearing behavior of low and high fatigue stress tests is significantly different. The cracks in the low fatigue stress tests underwent a transition from flat-to-slant crack growth, during which the CTOA values were high and significant crack tunneling occurred. After crack growth equal to about the thickness (Δa>B), CTOA reached a constant value of 6 deg and after crack growth equal to about twice the thickness (Δa>2B), crack tunneling stabilized. The cracks in the high fatigue stress tests reach the same constant CTOA value after crack growth equal to about the thickness, but produced only slightly higher CTOA values during initial crack growth. The amount of tunneling in the high fatigue stress tests was about the same as that in the low fatigue stress tests after the flat-to-slant transition. This study indicates that stress history has an influence on the initial portion of the stable tearing behavior. The initial high CTOA values, in the low fatigue crack tests, coincided with large three-dimensional crack front shape changes due to a variation in the through-thickness crack-tip constraint. The measured CTOA reached a constant value of 6 deg for crack growth of about the specimen thickness. This coincided with the onset of 45-deg slant crack growth and a stabilized, slightly tunneled (about 20 percent of the thickness) crack-front shape. For crack growth on the 45-deg slant, the crack front and local field variables are still highly three dimensional.

Three-dimensional elastic-plastic finite-element analyses of constraint variations in cracked bodies

Three-dimensional elastic-plastic (small-strain) finite-element analyses were used to study the stresses, deformations, and constraint variations around a straight-through crack in finite-thickness plates for an elastic-perfectly plastic material under monotonie and cyclic loading. Middle-crack tension specimens were analyzed for thicknesses ranging from 1.25 to 20 mm with various crack lengths. Three local constraint parameters, related to the normal, tangential, and hydrostatic stresses, showed similar variations along the crack front for a given thickness and applied stress level. Numerical analyses indicated that cyclic stress history and crack growth reduced the local constraint parameters in the interior of a plate, especially at high applied stress levels. A global constraint factor α g was defined to simulate three-dimensional effects in two-dimensional crack analyses. The global constraint factor was calculated as an average through-the-thickness value over the crack-front plastic region. Values of α g were found to be nearly independent of crack length and were related to the stress-intensity factor for a given thickness. Using the global constraint factors, crack-tip-opening displacements calculated from a modified Dugdale model compared well with the finite-element results from small- to large-scale yielding conditions for both thin and thick bodies. An application of the global constraint factor concept to model fatigue-crack growth under aircraft spectrum loading is presented.