Center-cracked Tension Specimens Research Articles

On the predictive capabilities of non‐local models for ductile crack propagation under different levels of stress triaxiality

AbstractDuctile materials are used in many applications such as hydrogen storage and transport, energy plants and additively manufactured components. High safety standards are vital for such applications, which underline the necessity of thoroughly investigating ductile failure to ensure safety and increase components efficiency. Ductile failure is mainly prompted by the evolution of the so‐called ductile damage, characterized by the nucleation, growth and coalescence of microvoids due to plastic deformation. Moreover, the plastic zones formed at the crack tip of ductile materials exhibit high sensitivity to the stress triaxiality level, which in turn distinctly depends on the geometry of the considered component. The quantification of the stress triaxiality at the crack tip is therefore essential to better understand and predict ductile crack propagation and failure. For that reason, a non‐local ductile damage model is employed in this work to simulate the ductile crack propagation under different stress triaxiality conditions. Different geometries are considered, such as constrained geometries of notched bending specimens and unconstrained geometries of center cracked tension specimens, which characterize the different triaxiality levels. To address the effects of thickness and initial crack length, three‐dimensional geometries are simulated, which account for the out‐of‐plane crack‐tip constraints. Finally, to evaluate the prediction quality of the simulations, corresponding experiments have been carried out and direct comparisons are conducted, with respect to the crack length, ductile crack propagation and resistance curves.

Predicting failure of cracked aluminum plates with one-sided composite patch

Composite patch repairs are an alternative to weld repair methods to arrest crack growth in metal plates. While these repairs have been effective, it has been difficult to use basic linear elastic fracture mechanics (LEFM) theories and design methods based on LEFM to predict the efficacy of patch repairs because the repaired plate exhibits bending and significant crack tip plasticity. In this investigation, we have studied the effect that one-sided low modulus composite patch repairs have on the development of crack tip plasticity on the free surface and through the thickness using large strain area and volume, total axial stress balance, and the free surface J-integral. Digital Image Correlation (DIC) and three-dimensional finite element analysis with first order elements were used to understand the evolution of crack tip plasticity and strain energy release rate to develop a simplified prediction method identifying a characteristic crack opening displacement prior to crack tip behavior of a one-sided composite patch repaired Center-Cracked Tension (CCT) specimen transitioning from Small Scale Yielding (SSY) to Large Scale Yielding (LSY), and eventually the re-initiation of crack growth. This method was then validated by comparing the predicted characteristic transition load to observed ultimate patched CCT specimen load capacity. Results correlated well with predictions when the composite patch was perfectly bonded to the aluminum and predicted characteristic transition loads more than 90 $$\%$$ greater than LEFM based failure predictions and 25 $$\%$$ lower than observed ultimate failure loads, demonstrating the potential to use this method for patch repair optimization.

Study on Fatigue Crack Growth of Laser Melting Deposited 12CrNi2 Alloy Steel Based on XFEM

Based on the Paris model of fatigue crack growth theory, the fatigue crack growth behaviour of Center Crack Tension (CCT) specimens of laser melting deposited 12CrNi2 alloy steel is studied by extended finite element method (XFEM). The crack growth rules and fatigue life are analyzed by experiment and finite element simulation. The experimental results are in good agreement with the finite element results, which verifies the accuracy of XFEM method to simulate the fatigue crack growth behaviour of laser melting deposited 12CrNi2 alloy steel components. Based on this, the effects of initial crack direction and load amplitude on fatigue crack growth behaviour are discussed. The results indicate that even if the initial crack direction is different, the crack will finally propagate in a direction perpendicular to the load. With the increase of the load amplitude, the fatigue life of the specimen with initial crack decreases exponentially.

Crack-tip-opening-displacement-based description of three-dimensional elastic-plastic crack border fields

Characterization of elastic-plastic crack-tip fields has been great developed in the framework of the classical dominating parameter J-integral, which has a limit of the basic assumptions of small deformation and simple proportional loading. A stable and effective parameter is still a challenge for three-dimensional (3D) elastic-plastic fracture problems. Based on the crack-tip-opening-displacement (CTOD) conception and out-of-plane stress constraint factor Tz, a new elastic-plastic stress intensity factor Kδ-Tz is proposed to dominate the 3D elastic-plastic crack border fields. Detailed 3D finite element simulations are performed for four typical testing specimens, which are the centre-cracked tension specimens, compact specimens, single-edge cracked tension specimens and single-edge-notched bending specimens under three-point bending. It is shown that for specimens with different geometries and thicknesses, Kδ-Tz is proven to be more stable than the classical J-integral via the experiment data and simulation results, in which the maximum change in J-integral can be over 340% while the change in Kδ-Tz is within 7.78%. Good agreements are obtained between the CTOD-based Kδ-Tz description and simulation results for the 3D elastic-plastic crack border stress fields under all the simulated conditions.

Crack propagation path selection and plastic deformation at a crack tip in zirconium

The crack propagation process of a center cracked tension specimen was studied in pure zirconium by quasi-in-situ microstructure characterization combined with finite element modeling (FEM). The microstructure characterization shows that as load increased, dislocations were emitted from crack-tip ledges and crystallographic planes were ‘thinned’ by accumulation of slip traces at the crack-tip. In the near-crack region, plastic deformation was achieved mainly through dislocation motion, rather than twinning. It was observed that the crack grew along grains with plastically ‘hard’ orientations (as determined by the angle between c-axis and loading axis) and that cleavage fracture planes were found to be non-basal. In addition, combined with the crack-tip stress field from a simulation, the Schmid factor was estimated for prismatic, basal and pyramidal slip systems at the crack tip; the results were compared with experimental determinations of geometrically necessary dislocation density. It was found that the existence of the crack-tip stress field slightly suppressed prismatic and pyramidal slip as compared to that determined by a far-field stress state Schmid factor analysis.

Effects of Plasticity on Patched and Unpatched Center Crack Tension Specimens

Composite patch repairs of aluminum structures are designed using linear elastic fracture mechanics, which compares crack tip predictions to a critical strain energy release rate or stress intensity. Analytical and numerical predictions are reasonable for linear-elastic behavior, but do not account for the elastic-plastic behavior observed at the crack tip of ductile materials below the ultimate load. This research used digital image correlation to study full field displacements and strains ahead of the crack tip for unpatched and patched center crack tension specimens loaded monotonically to failure. Both qualitative and quantitative comparisons show measureable effects of surface reinforcement on crack tip behavior. Free surface fracture response was an intrinsic property of the aluminum from the initial development of the plastic strain zone through crack blunting and ultimately through peak load with all stages occurring at crack opening displacements (COD) independent of the one-sided composite patch reinforcement. Patch reinforcement increased the ultimate tensile load 160% and the total achieved COD by 20% over the unpatched behavior. Increased capacity was related to an increase in accumulated large strain area and distributed plasticity measured on the free surface prior to the end of crack blunting. The direct correlation of fracture behavior indicates patched specimen failure can be predicted using unpatched specimen COD.

Crack-tip-opening-displacement-based description of creep crack border fields in specimens with different geometries and thicknesses

Creep crack growth is accompanied by strong nonlinear deformation and stress relaxation. Finding an appropriate parameter to characterize the crack tip fields, as well as the fracture resistance, has long been a challenge. Most previous studies were performed within the framework of the C(t)-integral, which is limited to the assumptions of small deformation and simple proportional loading. By using the crack tip opening displacement (CTOD), we propose a new creep stress intensity factor Kδ(t)-Tz consisting of the time-dependent CTOD, δ(t) and the out-of-plane stress constraint factor Tz to characterize the three-dimensional creep crack tip fields. Four typical specimens, single-edge cracked tension specimens, compact specimens, centre-cracked tension specimens and single-edge-notched bending specimens under three-point bending are comprehensively analysed using the power-law creeping model and three-dimensional finite element analyses. It is found that under both small-scale and large-scale creep conditions, the change in Kδ(t)-Tz along the thickness direction for different specimens is within 8.6%, whereas the change in C(t) can exceed 400%, showing that Kδ(t)-Tz is a stable parameter that governs the creep crack tip fields. With the exception of the centre-cracked tension specimens under large-scale creep conditions, good agreements are obtained between the two-parameter description δ(t)-Tz of crack border stress fields with the three-dimensional finite element results under small-scale and large-scale creep conditions. These results indicate that the CTOD-based two-parameter description δ(t)-Tz can be taken as the basis of creep fracture criteria.

Finite element analysis of crack-tip opening displacement and plastic zones considering the cyclic material behaviour

Propagation and behavior of fatigue cracks are governed by strain fields in the vicinity of the crack tip. The numerical description of strains in the crack tip presents some challenges in the modelling by the multiscale involved in the fracture analysis. In this study, it is proposed a 2D finite element analysis conducted for fatigue crack propagation experiments (mode I) performed for a railway axle steel EA4T under plane stress conditions. The analysis considers a geometric approach to define a multiscale mesh on a center-crack tension (CCT) specimen for which a nonlinear material model with kinematic hardening was assumed. Crack tip opening displacement (CTOD) and plastic zones were determined for several load levels during loading and unloading states. The results show that the applied correction factors approximate better the crack propagation rate. Furthermore, the quadratic dependence of CTOD with the stress intensity factor was in good agreement with the numerical solutions.

The Possibility for Improving Damage Tolerance of Integral Airframe Structure by High Strength Bonded Straps

Integral stringer panels can attain weight reduction in primary aircraft structures, but do not contain the physical barriers for a fatigue crack growth. One of the promising techniques for prolonging a fatigue crack growth is bonded crack retarders made of materials with high stiffness. An experimental study was done on two specimens with different geometries. High strength bonded straps made of corrosion resistant steel AISI 301 were adhesively bonded to Center-Cracked Tension (CCT) specimens made of aluminium alloy 2024-T351 and fabricated by a high-speed machining process to promote fatigue crack growth retardation. Specimens were tested at a constant amplitude load. The study concludes that the fatigue crack growth life can be significantly improved. Experimental results were compared with a prediction based on the VCCT technique and the NASGRO equation.

Fatigue crack growth and probability assessment for transverse TIG welded Aluminum alloy 6013-t4

The aim of this study is to investigate the fatigue crack growth behavior with post weld heat treatments (T4) on transverse tungsten inert gas-welded Aluminum alloy 6013. All fatigue tests have been carried out using center cracked tension specimens at ambient temperature under a stress ratio of R = 0.3. The results revealed that various time of aging in T4 affects its mechanical properties, also the fatigue crack growth behavior as well. It has been observed that in the heat treated samples the crack growth rate is lower than that in the as-welded sample, but higher than the rate in the base metal. To be more specific, samples with 18 hours aging exhibit the highest tensile strength and fatigue resistance compared to the other heat treated samples. The probability assessment has also been used to determine the fatigue crack growth rate and a good linearity has been found.

A SFEM-based evaluation of mode-I Stress Intensity Factor in composite structures

The Strong Formulation Finite Element Method (SFEM) based on the Generalized Differential Quadrature (GDQ) method is applied in the present work to estimate numerically the Stress Intensity Factor (SIF) for a single edge-notched tensile specimen (SENT) with different length-to-width ratios and composite materials, as well as for a Center Cracked Tension (CCT) and a Double Edge-Notched Tensile (DENT) specimens, under a mode-I loading condition. The basis notions of the fracture mechanics are herein analyzed numerically in order to evaluate the influence of possible cracks within materials and to relate the dimensions of cracks and the applied loading to the varying stress distribution. The numerical results, in terms of stresses and SIFs, are straightforwardly compared to those ones given by the standard Finite Element Method (FEM) and theoretical predictions available from the literature. This work presents a consistent approach for the computation of the SIF using a strong form methodology. The main aim is to demonstrate the accuracy and efficiency of the proposed methodology when treating classical plane stress problems with cracks. We show and discuss results from several numerical examples, including different composite materials and varying geometries for a mode-I SENT, CCT and DENT specimens.

A systematic investigation of T-stresses for a variety of center-cracked tension specimens

In this work, a systematic investigation of three-dimensional (3D) T-stresses (T11 and T33) was conducted using detailed elastic finite element analysis (FEA). The interaction integral method was applied to extract the T-stress solutions. Standard CCT specimens with a thickness-to-width ratio of B/(2W)⩽0.0625 and a crack length-to-width ratio of a/W=0.25–0.7, as specified in ASTM E2472, were considered, and the cases of B/(2W)=0.1–1.0 and a/W=0.05–0.2 and 0.8 were also added. From the FEA results, it was found that both T11 and T33 at the specimen mid-plane showed significant changes with crack lengths and specimen thicknesses for those CCT configurations that satisfy ASTM E2472. Because both the in-plane and out-of-plane T-stresses were negative and showed large variations for all the considered CCT specimens which was true even for the CCT specimens complying with the ASTM E2472 standard, it was noted that these CCT specimens that complying with the standard might show the test specimen size effect (including the crack length and specimen thickness effect) on the fracture toughness if tested.

J-integral analysis of heterogeneous mismatched girth welds in clamped single-edge notched tension specimens

Flaw assessment procedures require a quantification of crack driving force, and such procedures are generally based on the assumption of weld homogeneity. However, welds generally have a heterogeneous microstructure, which will influence the crack driving force. This paper describes a stress-based methodology to assess complex heterogeneous welds using a J-based approach. Clamped single-edge notched tension specimens, representative of girth weld flaws, are analyzed and the influence of weld heterogeneity on crack driving force has been determined. The use of a modified limit load for heterogeneous welds is proposed, suitable for implementation in a ‘homogenized’ J-integral estimation scheme. It follows from an explicit modification of an existing solution for centre cracked tension specimens. The proposed solution provides a good estimate of crack driving force and any errors in the approximation may be accounted for by means of a small safety factor on load bearing capacity.

Numerical prediction of creep crack growth in different geometries using simplified multiaxial void growth model

This paper considers the prediction of creep crack growth (CCG) in different fracture mechanics geometries using finite element (FE) analysis based on a material independent simplified multiaxial failure strain model at the crack tip. The comparison is first made by modelling C(T) specimen tests under plane stress and plane strain conditions using creep properties of a C–Mn steel at 360°C. In addition, in order to examine CCG due to different geometries, a single edge notch specimen (SENT), centre cracked tension specimen (CCT) and three-point bending (3PB) specimen have been modelled and analysed. In all cases, it is found, depending on the geometry, that for this steel at low creep temperatures the applied load develops a high reference stress/yield stress (σref/σy) ratio, which helps reduce constraint at the crack tip. The predictions are analysed under plane stress/plane strain loading conditions identifying the effects of geometry on cracking rates and the implications for predicting long term test or component failure times exceeding where the applied σref/σy<<1.

Numerical investigation of fracture behavior of nanostructured Cu with bimodal grain size distribution

Nanostructured metals with bimodal grain size distribution, composed of coarse grain (CG) and nanograin (NG) regions, have proved to have high strength and good ductility. Here, numerical investigation, based on the mechanism-based strain gradient plasticity theory and the Johnson–Cook failure model, focuses on effects of (1) distribution characteristics of the CG regions and (2) the constitutive relation of the NG with different grain sizes on fracture behavior in a center-cracked tension specimen of bimodal nanostructured Cu. High strain rate simulations show that both of them directly influence load response and energy history, and importantly, they are closely related to the fracture pattern. This study shows that both CG region bridging and crack deflection toughen the bimodal nanostructured Cu significantly, while debonding enhances the overall ductility moderately. Simulations also show that with volume fraction of the CG regions increasing, both structural strength and ductility of the bimodal nanostructured Cu specimen can be improved.

Analysis of crack opening stresses for center- and edge-crack tension specimens

Accurate determination of crack opening stress is of central importance to fatigue crack growth analysis and life prediction based on the crack-closure model. This paper studies the crack opening behavior for center- and edge-crack tension specimens. It is found that the crack opening stress is affected by the crack tip element. By taking the crack tip element into account, a modified crack opening stress equation is given for the center-crack tension specimen. Crack surface displacement equations for an edge crack in a semi-infinite plate under remote uniform tension and partially distributed pressure are derived by using the weight function method. Based on these displacements, a crack opening stress equation for an edge crack in a semi-infinite plate under uniform tension has been developed. The study shows that the crack opening stress is geometry-dependent, and the weight function method provides an effective and reliable tool to deal with such geometry dependence.

Failures of High-Temperature Critical Components in Combined Cycle Power Plants

This article highlights briefly the reported failure of critical parts and equipment in gas turbine, heat recovery steam generator, and steam turbine, in addition to the requirements of lifetime predictions for the high-temperature components in the combined cycle power plant (CCPP). For assessing fracture strength of flawed structural components in high-temperature environments, the first and foremost thing observed is to ascertain the reason for cracking. Special considerations are to be given in case of stress corrosion cracking, environmentally assisted cracking or bulk creep damage. Sensitivity analysis has to be performed to identify the influencing material properties and crack sizes on the load-bearing capacity of the structural component. An elastic–plastic criterion is examined by considering the fracture data of center crack tension specimens on several materials.

Validation of a finite element model for fracture mechanics specimens

Single parameter formulations have shown to be insufficient to describe constraint effects infracture mechanics specimens. This has lead researchers to a two parameter approach like the J-Q theory.In order to investigate constraint effects, the authors have developed a generic finite element model. Priorto drawing conclusions this model must first be validated, which is the topic of this paper. This validationhas been done by comparing analytical expressions of the J-integral with those obtained from theperformed simulations. The compared geometries were center cracked tension (CCT) and double edgenotched tension (DENT) fracture mechanics specimens. The results showed good agreement with theanalytical expressions and, as such, the model can now be confidently applied to determine values of the Jintegral. This is a first step towards evaluating two parameter J-Q constraint.

Numerical Simulation of Crack Tip Behavior under Fatigue Loading

Fatigue damage is a localized phenomenon controlled by the near-tip crack behavior. This paper presents an application of a dislocation distribution technique to the simulation of crack tip behavior under fatigue loading. A centre-cracked tension specimen under uni-axial fatigue loading is used in the study. Crack opening and plastic deformation around the crack tip are simulated by distributions of dislocation dipoles in crack plane and four inclined planes ahead of the crack tip. Climb dislocation dipole is used to model the opening and closing of the crack while glide dislocation dipole is used to simulate the backward and forward slip in the inclined planes during loading and unloading of the fatigue cycle. Stress field around the crack tip is obtained by the superposition of the contributions of the applied external load and the distributed dislocation dipoles. Correct boundary conditions of the model are achieved by employing a quadratic programming technique to minimize a properly constructed non-negative object function. It is found that the simulated crack closure variations under the constant amplitude fatigue load agree well with the result of a previously developed modified strip yield model with an appropriate constraint factor.

Application of split Hopkinson tension bar technique to the study of dynamic fracture properties of materials

A novel approach is proposed in determining dynamic fracture toughness (DFT) of high strength steel, using the split Hopkinson tension bar (SHTB) apparatus, combined with a hybrid experimental-numerical method. The center-cracked tension specimen is connected between the bars with a specially designed fixture device. The fracture initiation time is measured by the strain gage method, and dynamic stress intensity factors (DSIF) are obtained with the aid of 3D finite element analysis (FEA). In this approach, the dimensions of the specimen are not restricted by the connection strength or the stress-state equilibrium conditions, and hence plane strain state can be attained conveniently at the crack tip. Through comparison between the obtained results and those in open publication, it is concluded that the experimental data are valid, and the method proposed here is reliable. The validity of the obtained DFT is checked with the ASTM criteria, and fracture surfaces are examined at the end of paper.