Mixed-mode Fatigue Crack Growth Research Articles

An innovative approach to planar mixed-mode fatigue crack growth study

Determining fatigue crack growth parameters under mixed-mode loading is crucial for damage tolerance design, particularly in assessing a component's residual life with defects to prevent disasters. This study introduces a novel methodology for determining fatigue crack growth rate. A digital microscope is utilized to track the fatigue crack tip with respect to local coordinate systems established on the specimen surface. A grid is drawn and subdivided into units with proposed nomenclature. Compact Tension and Shear (CTS) specimens, extracted from AA-7085 plates, undergo fatigue loading in a servo-hydraulic universal testing machine. A fixture proposed by Richard et al. induces planar mixed-mode loading cases in the specimen. During experiments, the digital microscope tracks the crack tip using grid unit corners as local origins. The local coordinates of the crack tip are transformed into the crack tip coordinates with respect to the pre-crack tip. Crack evolution data are used to determine the fatigue crack growth rate by analyzing tangents of a three-parameter fitted curve. The equivalent SIF ranges are computed at different crack lengths in an XFEM script written in Ansys. The modified Paris parameters are found and experimentally observed crack deflection angles are compared with the Maximum Tangential stress, Strain energy density, and Richard’s criterion.

Initiation and growth of fatigue cracks in sheets with U-shaped notches in the first and mixed modes of fracture

Initiation and growth of fatigue cracks in sheets with U-shaped notches in the first and mixed modes of fracture

Mixed mode fatigue crack growth and fatigue threshold analysis in polyurethane adhesives at elevated temperatures

The paper investigates mixed-mode fatigue crack growth in ductile polyurethane adhesives, emphasizing mode decoupling to distinguish the impact of each loading mode component on crack propagation. It also explores the temperature sensitivity of fatigue crack growth rates for each loading mode. Individual scrutiny of the role of each loading mode in tests is accompanied by an analysis of fatigue fracture surfaces to clarify failure mechanisms. The findings indicate differential sensitivity to ambient temperature between the mode I and mode II components in a mixed mode fatigue test. Notably, the fatigue response of the mode I component exhibited higher sensitivity to temperature than the mode II component in mixed mode fatigue fracture of the tested polyurethanes. The polyurethane adhesives' composition, particularly the hard segment ratio, emerged as a pivotal factor influencing their sensitivity to fatigue loading at elevated temperatures. Temperature effects led to a significant reduction (63%) in the mode I component of mixed mode fatigue for one of the tested adhesives, while the other exhibited a noteworthy increase (154%). This trend which was attributed to the hard segment ratio of the adhesives was also persisted in the shear mode of the mixed mode fatigue results.

Modelling of Fatigue Delamination Growth and Prediction of Residual Tensile Strength of Thermoplastic Coupons.

Thermoplastic composites are continuously replacing thermosetting composites in lightweight structures. However, the accomplished work on the fatigue behavior of thermoplastics is quite limited. In the present work, we propose a numerical modeling approach for simulating fatigue delamination growth and predicting the residual tensile strength of quasi-isotropic TC 1225 LM PAEK thermoplastic coupons. The approach was supported and validated by tension and fatigue (non-interrupted and interrupted) tests. Fatigue delamination growth was simulated using a mixed-mode fatigue crack growth model, which was based on the cohesive zone modeling method. Quasi-static tension analyses on pristine and fatigued coupons were performed using a progressive damage model. These analyses were implemented using a set of Hashin-type strain-based failure criteria and a damage mechanics-based material property degradation module. Utilizing the fatigue model, we accurately foretold the expansion of delamination concerning the cycle count across all interfaces. The results agree well with C-scan images taken on fatigued coupons during interruptions of fatigue tests. An unequal and unsymmetric delamination growth was predicted due to the quasi-isotropic layup. Moreover, the combined models capture the decrease in the residual tensile strength of the coupons. During the quasi-static tension analysis of the fatigued coupons, we observed that the primary driving failure mechanisms were the rapid spread of existing delamination and the consequential severe matrix cracking.

A study on the effect of different Paris constants in mixed mode (I/II) fatigue life prediction in Al 7075-T6 alloy

Mixed-mode (I/II) fatigue crack growth experiments in Al 7075-T6 alloy have been performed using a newly proposed single edge cracked circular (SECC) specimen. An equivalent stress intensify factor (ΔKeq) model based on the generalized MTS criterion (GMTS) has been tested for the first time for mixed-mode fatigue crack growth rate correlation and prediction of the fatigue life. Along with this proposed model, other widely used ΔKeq models have also been considered to study the effect of Paris constants on the fatigue life prediction. Three different mode mixity configurations (30°, 45°, and 60°) have been considered for experiments with multiple specimens to study the reproducibility aspect. With the help of detailed fatigue crack growth finite element simulations and experimental results, the performance of the various ΔKeq models has been tested in terms of correlation with the fatigue crack growth rate and prediction of the fatigue life. The results of the present investigation show that using the mixed-mode Paris constants along with Tanaka’s and Richard’s ΔKeq models accurately and consistently predicts the fatigue life compared to other Paris constants. The GMTS criterion has been shown to exhibit excellent performance in the prediction of crack growth path and thus signifies the importance of T- stress under mixed-mode fatigue loading. Additionally, the results of the present investigation establish the potential application of the SECC specimen for mixed-mode fatigue crack growth studies of metallic materials. Furthermore, fractographic studies also confirm the experimental observations in Al 7075-T6 alloy.

Scaled fatigue cracks under service loads

Scaled experimentation is a powerful engineering tool yet its application to fatigue is limited by significant changes in behaviour with scale. The recent discovery of new similitude rules however opens new possibilities that are explored in this work through numerical experimentation for industrially representative fatigue-crack growth scenarios. It is shown for the first time, how the geometric size effects present in mixed mode fatigue tests are eliminated by performing two appropriately designed scaled experiments. The first order finite similitude theory is applied to mixed mode (modes I and II) fatigue crack growth in three case studies, viz., compact tension shear (CTS) specimen, wing fuselage attachment lug, and a T-joint with an inclined semi elliptical crack. Both planar and non-planar crack growth feature, along with surface and through thickness cracks. Low and high cycle fatigue (up to circa 60,000 cycles) is examined for three different materials (Al-6061 T6 alloy, structural steel, and AISI 316 stainless steel) under a variety of load ratios. The new rules return near exact crack-path predictions whereas lifecycle predictions have errors ranging between 1 % and 9 %. Paris law constants C and m are predicted with up to 99.9 % accuracy supporting the theory that Paris law is a first order similitude rule. Geometric size effects afflicting industrial type scaled-fatigue studies employing a damage tolerant design approach are confirmed to be eliminated on combination of information from two appropriately designed scaled models.

A novel multiscale model for mixed-mode fatigue crack growth in laminated composites

A multiscale model is developed to predict mixed-mode fatigue crack growth (FCG) behavior in laminated composites by considering the micromechanical effects of fiber bridging. The proposed model consists of a micromechanical part dedicated to the fiber bridging mechanism near the crack tip, a macroscopic FCG model based on the maximum principal strain criterion, and an effective crack tip processing zone (i.e., an equivalent critical distance) connecting the two parts of the model. The core novelty of the presented model is to connect two scales (micro and meso) through a measurable physical quantity – called equivalent critical distance – accounting for various micromechanical as well as macroscopic phenomena occurring at both scales. The suggested model is validated against FCG test data available in the literature for laminated glass fiber composites under mode I, mode II, and mixed mode I/II conditions. It is found that the proposed framework is superior to its conventional (pure macroscopic) version, which eliminates fiber bridging effects, in the prediction of the cyclic mixed-mode crack propagation behavior in laminated composites. The multiscale nature of the proposed FCG model offers less complexity than fully micromechanical approaches while providing higher accuracy as compared to pure macroscopic models that ignore micromechanical phenomena occurring at the fiber scale.

A mixed-mode fatigue crack growth model for co-consolidated thermoplastic joints

In this work, a mixed-mode fatigue crack growth model for simulating interfacial fracture of co-consolidated thermoplastic joints was developed. The model is based on the cohesive zone modeling approach and was specifically designed to account for any I + II mode-mixity, requiring only pure mode I and II loading data as input. The fatigue crack growth rate is constantly updated using a function of the energy release rates and the computed mode-mixity ratio. A linear mode-mixity law is applied. Both force-controlled and displacement-controlled loads can be modeled in specimens ranging from coupon-scale sizes to larger structural elements. Implementation of the model was done for the low-melt polyaryletherketone (LM-PAEK) material by developing a user-defined subroutine in the LS-Dyna FE software. To feed the model, mode I and mode II fatigue tests were conducted using double-cantilever beam and end-notch flexure specimens, respectively, while to validate the model mixed-mode single lap shear (SLS) tests were conducted. The model reproduces accurately the mode I and II fatigue crack growth while it predicts also accurately the mixed-mode fatigue crack growth of the SLS specimens.

Study on two-dimensional mixed-mode fatigue crack growth employing ordinary state-based peridynamics

Mixed-mode fatigue crack propagation analysis is studied using ordinary state-based peridynamics. By introducing the concept of “remaining life”, the fatigue crack nucleation and propagation can be simulated in the PD framework. The PD fatigue modelling and the crack path prediction is carefully investigated. For the comparison purpose, the maximum circumferential stress criterion is introduced. The interaction integral and the peridynamic differential operator is employed to evaluate the fracture mechanics parameters. Two pre-cracked structures under mixed-mode loading conditions are provided with the validations from reference solutions.

The study of mixed mode fatigue crack growth mechanism of 25CrNiMo compact tensile specimens by experiment and finite element simulation

Fatigue cracking is the most common failure mode that endangers the safety and service life of parts. Initial manufacturing flaws are a critical factor affecting the growth of fatigue cracks. Currently, mixed-mode crack growth research frequently applies a simplistic two-dimensional finite element model, which cannot adequately represent the crack growth mechanism. An improved finite element method is proposed in this paper to overcome this drawback. Fatigue fracture propagation investigations on 25CrNiMo compact tensile specimens are conducted in this study, and the crack propagation rate is calculated using the Paris formula. Moreover, the special element modeling method and second-order Runge-Kutta integration method are utilized to perform finite element calculations on the 3D model. The results are highly consistent with the experimental test results. The propagation mechanism of cracks with varied initial inclination angles is explored depending on the finite element method. The relationship between the stress intensity measures KI, KII, and KIII is discovered to be competitive. The results have significant application value for the crack growth path prediction and crack life in parts with initial flaws.

Mixed mode (I/III) fracture studies using a new specimen setup

In the present work, mixed mode (I/III) fracture studies have been investigated using a new specimen and an out-of-plane loading fixture that can be used with the conventional uniaxial universal testing machines. The proposed specimen is a single edge cracked circular (SECC) specimen which can be employed on both metallic and non-metallic materials under static and fatigue loads. A large number of three-dimensional finite element analyses have been performed on the proposed specimen setup to demonstrate the efficacy of the proposed setup. Experimental fracture studies have also been performed under mixed mode (I/III) loading conditions. The present experimental results are in very good agreement with the available mixed mode (I/III) fracture criteria. Experimental results indicate that the pure mode III fracture toughness is nearly 1.46 times greater than that of the mode I. This has been found due to an increase in the inelastic region around the crack tip in pure mode III and is in accordance with the published results. Detailed analyses of the fractured surfaces have also been carried out. It has been demonstrated that the fractured surfaces become more rough as the mode III component increases. Preliminary results of mixed mode (I/III) fatigue crack growth studies on Al 7075-T6 using the metallic SECC specimen have also been presented. The results of the present study confirm that the proposed specimen setup can be used to study the mixed mode fracture behavior of linear elastic materials under static and fatigue loading.

Experimental and numerical investigation of mixed-mode fatigue crack growth in nickel-based superalloy at high temperature

Fatigue cracking is one of the most common damage modes of aeroengine hot-end components, usually subjected to mixed-mode cracking. In this study, mixed-mode fatigue crack growth experiments at 550 °C are carried out using compact tension shear specimens made of nickel-based superalloy GH4169. Adaptive finite element method was used to verify several models at high temperature. The accuracy of angle dependent models was higher at 550 °C, and the rate of da/dN increased and decreased twice with crack propagating, which is different from room temperature (20–25 °C). This research could provide a basis for lifespan prediction of aeroengine hot-end components.

Controlling mixed-mode fatigue crack growth using deep reinforcement learning

Mechanical discontinuity embedded in a material determines the bulk mechanical, physical, and chemical properties. Under external forces, mechanical discontinuity undergo spatiotemporal propagation; thereby altering various properties of the material. This paper is a proof-of-concept development and deployment of a reinforcement learning framework, based on deep deterministic policy gradient, to precisely control both the direction and rate of the fatigue crack growth. The ability to control mechanical discontinuity in essence determines the key material properties. The desired control is relatively hard to achieve considering the large, continuous state and action spaces along with the exponential relationship between crack growth and stress cycle. The reinforcement-learning scheme is capable of learning an optimal and computational tractable control strategy. In the proposed approach, the reinforcement learning framework is integrated into an OpenAI-Gym-based environment that implements the mechanistic equations governing the fatigue crack growth. The learning agent does not explicitly know about the underlying physics, nonetheless, the learning agent can infer the control strategy by continuously interacting the numerical environment. The paper formulates an adaptive reward function involving reward shaping that can be generalized to similar control problems to improve the training efficiency. The reinforcement learning framework can successfully control the fatigue crack growth in a material despite the complexity of the propagation/growth pathway determined by multiple goal points. The paper provides the mathematical/physical basis of the reward function and the effect of neural network size and architecture and the state and action space that boosts the training speed while preserving the stability of the RL agents for the desired control problem.

Fatigue crack growth determination under in-phase and out-of-phase mixed-mode loading conditions using an automated DIC evaluation tool

In this study Digital Image Correlation (DIC) is utilized for measuring complex fatigue crack paths under spatial mixed-mode loading conditions. Therefore, an existing automated script was extended by two criteria for measuring the crack length versus the number of load cycles. Experimental investigations were conducted under mode I conditions, to calibrate the new evaluation routine. Moreover, in-phase and out-of-phase mixed-mode experiments under superimposed tension-torsion loading were performed to validate the method. The results show that the newly presented procedure provides an accurate, automated evaluation tool for mixed-mode fatigue crack growth tests, independent of the crack orientation and possible branching.

A new simple specimen for mixed-mode (I/II) fracture and fatigue tests: Numerical and experimental studies

In the present investigation, a simple and efficient specimen geometry for conducting mixed mode (I/II) static fracture tests and fatigue crack growth studies has been proposed. No additional complicated fixtures are needed for loading the specimen and it can be used for both metallic and non-metallic materials. Large number of finite element analyses and mixed mode fracture experiments have been conducted. Present results of the experimental studies have been compared with widely used mixed mode (I/II) fracture criteria in terms of fracture toughness. The present experimental results are in very good agreement with the selected mixed mode (I/II) fracture criteria. Results of the present investigation clearly recommend the proposed specimen geometry as a useful mixed mode (I/II) specimen for fracture and fatigue studies.

Mixed-mode fatigue crack growth analysis of I-shaped steel girders with trapezoidal corrugated-webs

In bridge industry, the composite box-girder with corrugated steel webs and concrete flanges is quite a common practice over recent years. However, this innovation encounters fatigue-sensitive details not fully investigated, especially in the research area of mixed-mode fatigue crack growth. This study addresses the mixed-mode fatigue crack growth analysis of an I-shaped corrugated web girder associated with the represented web-to-flange detail. A linear elastic fracture mechanics (LEFM) based numerical framework was established to simulate the mixed-mode crack propagation. For comparison, a semi-analytical weight function framework was also introduced to predict the pure Mode-I crack propagation life of the same detail. Experimental results of a full-scale inclined corrugated web girder were employed to evaluate these two proposed frameworks. A parametric study was presented based on the proposed frameworks to investigate the effect of initial crack depth and crack shape on fatigue crack propagation life. By comparing the simulation results with test results, the applicability of the proposed LEFM-based numerical framework to the simulation of mixed-mode fatigue crack propagation behaviour in corrugated web girders was discussed.

Automated crack length measurement for mixed mode fatigue cracks using digital image correlation

It is well known that mode II leads to a kinking and mode III to a twisting of a fatigue crack. On the surfaces of an SEN specimen, an overlapping of these two crack loading modes occurs. Superimposed with mode I, this results in very complex fatigue crack paths and, in some cases, multiple crack branches. Thus, established methods for mode I crack growth measurement cannot be utilized. Therefore, the digital image correlation (DIC) technique is used to determine the crack length of mixed mode cracks on the surface of a specimen by means of the maximum principal strain. By Gehri et al. (2020) a concept is described to obtain the crack path by morphological thinning of the area on the surface, where the maximum principal strain exceeds a threshold value. In this paper, an extension of the provided MATLAB script is proposed that includes two criteria for measuring the crack length versus the number of load cycles (a-N-curve). For the first criterion, the crack opening is used to determine the current crack tip position and to obtain the crack length as a function of the number of load cycles. In the second criterion, a threshold value of the maximum principal strain is used for determining the number of cycles at the detected crack length. The new evaluation routine with both criteria is initially calibrated on mode I experiments using the direct current potential drop method. Moreover, mixed mode experiments under tension-torsion loading are conducted, to validate the method and compare the two proposed criteria. The experimental results in terms of the a-N-curves obtained with the marker load technique are in good agreement with the results using the presented method. Thus, the extended tool provides an evaluation routine to determine a-N-data for mixed mode fatigue crack growth tests independently from the crack orientation and possible branching.

Computational Simulation of 3D Fatigue Crack Growth under Mixed-Mode Loading

The purpose of this research was to present a simulation modelling of a crack propagation trajectory in linear elastic material subjected to mixed-mode loadings and investigate the effects of the existence of a hole and geometrical thickness on fatigue crack growth and fatigue life under constant amplitude loading. For various geometry thickness, mixed-mode (I/II) fatigue crack growth studies were carried out to utilize a single edge cracked plate with three holes and compact tension shear specimens with various loading angles. Smart Crack Growth Technology, a new feature in ANSYS, was used in ANSYS Mechanical APDL 19.2 to predict the cracks’ propagation trajectory and their consequent fatigue life associated with evaluating the stress intensity factors. The maximum circumferential stress criterion is implemented as a direction criterion under linear elastic fracture mechanics (LEFM). According to the hole position, the results demonstrate that the fatigue crack grows towards the hole due to the unbalanced stresses on the hole induced crack tip. The results of this simulation are verified in terms of crack growth paths, stress intensity factors, and fatigue life under mixed-mode load conditions, with several crack growth studies published in the literature showing consistent results.

Distinctive features of crack growth rate for assumed pure mode II conditions

The effect of an initial mode II loading on subsequent mixed-mode fatigue crack growth was investigated through experiments and computations for 34X and P2M steels, 7050 aluminum, and Ti-6Al-4V alloys in a compact tension shear (CTS) specimen. The experimental data on crack growth rate for all tested materials are represented in terms of elastic and plastic stress intensity factors (SIF) and total strain energy density (SED). To this end, the elastic–plastic fracture resistance parameters are calculated by finite element computation as a function of the position along the curvilinear crack path. Careful observation of both the crack path and the crack growth rate behavior revealed that the initial mode II loading has two contrasting effects on the subsequent mixed-mode crack growth, which depends on the elastic–plastic material properties. For each material, a comparison of the experimental results on the crack growth rate for pure mode 1 and mixed-mode fracture for specimens of the same geometry is presented. On this basis, a new dimensionless cyclic fracture resistance parameter in terms of elastic–plastic SIFs and total SED is proposed to establish the effect of mixed-mode loadings on the crack growth rate. Crack growth rate acceleration or retardation was observed because the initial mode II loading with respect to the crack growth rate under pure mode I was attributed to the plastic properties of the tested ductile steels, aluminum, and titanium alloys. This study shows that the mode I crack growth can be considered a predominant factor for evaluating the effect of an initial mode II loading in CTS specimens for subsequent mixed-mode cyclic fractures of different structural materials.

Fatigue crack growth of TiAl6V4 parts produced by SLM under biaxial mode I/mode II loading

Mode I and mixed-mode fatigue crack growth tests were performed using compact tension shear specimens made of Ti-6Al-4V by additive manufacturing for various loading angles. The accuracy of the methodology used to determine the equivalent stress intensity factor was studied, obtaining good results in a simpler method and particularly when the crack deflection angle was included in the algorithm. The crack growth speed did not suffer significant alterations due to similar values of crack deflection angle, mode I loading predomination and similar crack closure effect. Fractured surfaces presented irregular regions consequence of intergranular separation between β phase and agglomerations of α phase.